Fire Engineering of Structures: Analysis and Design 978-3-642-36153-1, 978-3-642-36154-8

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M.Y.H. Bangash Y.F. Al-Obaid F.N. Bangash

Fire Engineering of Structures Analysis and Design

Fire Engineering of Structures

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M.Y.H. Bangash • Y.F. Al-Obaid • F.N. Bangash

Fire Engineering of Structures Analysis and Design

M.Y.H. Bangash London, United Kingdom

Y.F. Al-Obaid Safat, Kuwait

F.N. Bangash ASZ Partners London, United Kingdom

ISBN 978-3-642-36153-1 ISBN 978-3-642-36154-8 (eBook) DOI 10.1007/978-3-642-36154-8 Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2013949739 © Springer-Verlag Berlin Heidelberg 2014 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

Preface

This book provides a general introduction to the topic of three-dimensional analysis and design of fire engineering structures and intended for a general readership. A major part of design for fire resistant involves the elements or components. The emphasis is placed on structure, which has a primary role in preventing serious damage or structural collapse. These elements or components are clearly established. Various design works are finally integrated. This comprehensive work includes: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

The intensify of fire and its depletion in the major analysis Fire loading is decided with its influence on the design Where experiment results are investigated and included in the analysis Finite element is the main analysis together with the solution procedures that have been presented in detail in this book The analysis and design are fully described using specific diagrams Results are fully established, wherever explanations are required; they are reported by tables Brief case studies are tested Diagrams and figures are self-explanatory A computer program has the possibility of diverting for specific problems The computer program has the ability of possible changing the analysis and design

London, UK Safat, Kuwait London, UK

M.Y.H. Bangash Y.F. AL-Obaid F.N. Bangash

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Symbols Used in Fire

(I) General used in literature on fire Greek symbols

Description

A A A αh αv B B β1 βn βpar Δ Δ ΔL Δ0 X χLT E εσ εcr εi εth εtr E Φ Ф Фf К γG γM γQ

Stress ratio Thermal diffusivity Ratio of hot wood strength to cold wood strength Horizontal openings ratio Vertical openings ratio Reliability index Measured charring rate Effective charring rate if corner rounding ignored Nominal charring rate Charring rate for parametric fire exposure Beam deflection Deflection Maximum permitted displacement Mid-span deflection of the reference specimen Buckling factor for columns Buckling factor for beams Strain Stress-related strain Creep strain Initial strain Thermal strain Transient strain Emissivity Configuration factor Strength reduction factor Strength reduction factor for fire design Elastic curvature Partial safety factor for dead load Partial safety factor for material Partial safety factor for live load

Units m2/s

mm/min mm/min mm/min mm/min mm mm mm mm

1/m

(continued) vii

viii

Symbols Used in Fire

Greek symbols

Description

Γ H Θ P ρi ρs Z Z Z Zf et E Ek Ef F F f* fa fb fb,t fc f 0c f 0 c;T ft ft,f fy fy,T F Fc Fcrit Fv F/V G G Gk H H hc hr ht H Hp Hr Hv ΔHc I jd K

Fictitious time factor Temperature ratio Plastic hinge rotation Density Density of insulation Density of steel Load factor Distance to neutral axis Elastic section modulus Elastic section modulus in fire conditions Fuel load energy density (per unit area of internal surfaces) Modulus of elasticity Characteristic earthquake load Total energy contained in fuel Factor in concrete-filled steel column equation Stress Calculated stress in member Allowable stress Characteristic bending strength Characteristic bending strength in fire conditions Crushing strength Characteristic compressive strength of concrete Compressive strength of concrete at elevated temperature Characteristic tensile strength Characteristic tensile strength in fire conditions Yield strength at 20  C Yield strength at elevated temperature Surface area of unit length of steel Crushing load of column Critical buckling load of column Ventilation factor (Av√Hv/At) Section factor Char parameter Dead load Characteristic dead load Slab thickness Height from mid-height of window to ceiling Convective heat transfer coefficient Radiative heat transfer coefficient Total heat transfer coefficient Height of radiating surface Heated perimeter of steel cross section Height of room Height of window opening Calorific value of fuel Moment of inertia Internal lever arm in reinforced concrete beam Growth parameter for t2 fire

Units

radians kg/m3 kg/m3 kg/m3 mm mm3 mm3 MJ/m2 GPa MJ MPa MPa MPa MPa MPa MPa MPa MPa MPa MPa MPa MPa m2 kN kN m0.5 m-1

mm m W/m2K W/m2K W/m2K m m m m MJ/kg mm4 mm (continued)

Symbols Used in Fire

ix

Greek symbols

Description

Units

K k20 ki ka kb kc kf kmean kc,T kE,T ky,T kd kp K l1,l2 L Lf Lu Lw Lv M mc md m M M M Mf Mn Mp My M*cold M*fire M*fire, red N Ncrit Nn Nf N* N*fire p P Q Qp Qfuel Qvent Q Qk

Thermal conductivity Factor to convert 5th percentile to 20th percentile Thermal conductivity of insulation Ratio of allowable strength to ultimate strength Compartment lining parameter Compartment lining parameter Strength reduction factor for heated wood Factor to convert allowable stress to mean failure stress Reduction factor for concrete strength Reduction factor for modulus of elasticity Reduction factor for yield strength Duration of load factor for wood strength Char factor for parametric fire Effective length factor for column Dimensions of floor plan Length of structural member Factored load for fire design Factored load for ultimate limit slate Load for working stress design Heat of gasification Moisture content Moisture content as % by weight Moisture content as % of dry weight Rate of burning Mass per unit length of steel cross section Mass of fuel Bending moment Flexural strength in fire conditions Nominal moment capacity Moment capacity of plastic hinge Bending moment at first yield Design bending moment in cold conditions Design bending moment in fire conditions Redistributed bending moment in fire conditions Axial load Critical buckling load Nominal axial load capacity Axial load capacity in fire conditions Design axial force Design axial force in fire conditions Perimeter of fire exposed cross section Axial force causing instability Rate of heat release Peak heat release rate Rate of heat release for fuel controlled fire Rate of heat release for ventilation controlled fire Live load Characteristic live load

W/mK W/m K min m2/MJ min m2.25/MJ

m mm

MJ/kg % % % kg/s kg kg kN m kN m kN m kN m kN m kN m kN m kN m kN kN kN kN kN kN m kN MW MW MW MW

(continued)

x

Symbols Used in Fire

Greek symbols

Description

Units

q00 r r r rload R Ra Rcold Rfire s S Sk t t tb th to tr ts tv T T T Tc Tf Ti Tlim Tm Tp T0 Ts Tw Ty U* U*fire V Vc Vf V V* V*fire V/F W W Wk w w wc

Heat flux Radius of gyration Radius of charred corner Distance from radiator to receiver Load ratio Load capacity Ratio of actual to allowable load at normal temperature Load capacity in cold conditions Load capacity in fire conditions Heated perimeter Plastic section modulus Characteristic snow load Time Thickness of steel plate Duration of burning Time Initial char time in parametric fire Time of fire resistance Time of fire severity Time delay Axial thrust Flange thickness Temperature Concrete temperature Fire temperature Initial temperature of wood Limiting temperature Maximum temperature Temperature of wood at start of charring Ambient temperature Steel temperature Surface temperature Tensile force at yield Load effect Load effect in fire conditions Volume of unit length of steel member Shear capacity in cold conditions Shear capacity in fire condition Shear force Design shear force Design shear force in fire conditions Effective thickness Width of compartment Width of radiating surface Characteristic wind load Ventilation factor Uniformly distributed load on beam Uniformly distributed load on beam, in cold conditions

kW/m2 mm mm m

mm mm3 h, min or s mm min h min min min min kN mm  C  C  C  C  C  C  C  C  C  C kN

m3 kN kN kN kN kN mm m m

kN/m kN/m (continued)

Symbols Used in Fire

xi

Greek symbols

Description

Units

wf x x y yb z z σ σ υp ξ

Uniformly distributed load on beam, in fire conditions Distance Height ratio Width ratio Distance from neutral axis to extreme bottom fiber Effective thickness of concrete member Thickness of zero strength layer Stefan–Boltzmann constant Stress Regression rate Reduction coefficient for charring of decks

kN/m

Mm Mm Mm kW/m2K4 MPa m/s

Alphabetic symbols A A af ah A Af Afi Afuel Ah Ai Al Ar As At Av B bf b bv bw B c ce ci cs cp cv C d d

Depth of heat affected zone below char layer Depth of rectangular stress block Depth of stress block, reduced by fire Thickness of wood protection to connections Cross section area Floor area of room Area of member, reduced by fire Exposed surface area of burning fuel Area of horizontal ceiling opening Cross sectional area of insulation Area of radiating surface Cross section area reduced by fire Cross sectional area of steel Total internal surface area of room Window area Breadth of beam Breadth of beam reduced by fire √Thermal inertia = √kρcp Vertical opening factor Breadth of web of T-beam Breadth of window opening Thickness of char layer Effective concrete cover to center of reinforcing Specific heat of insulation Specific heat of steel Specific heat Concrete cover to reinforcing Compressive force Depth of beam, effective depth of concrete beam Thickness of timber deck

Mm Mm Mm Mm mm2, m2 m2 mm2, m2 m2 m2 mm2 m2 mm2, m2 mm2 m2 m2 mm mm W s0.5/m2K mm m mm mm J/kg K J/kg K J/kg K mm kN mm mm (continued)

xii

d df di dϒ D D Db e ef b(TR) b(TR1) c C C C C1, C2, C3 Co cp Cw d D D D(i) D(T) D(TR; n 1) D(TR; n) Dmax dt e e E E Ec eF f F F Fdc fo Fv g Gi h h H he hG hv

Symbols Used in Fire

Diameter of circular column or width of square column Depth of beam reduced by fire Thickness of insulation Distance of line of thrust from top surface Depth of compartment Thickness of slab of burning wood Reinforcing bar diameter Eccentricity Fuel load energy density (per unit floor area) Stair width Width of partial flow from top floor n in main flow on stairs Specific heat of downstream gases Constant for arrangement and protection of stairs Concentration of contaminant at time, t Flow coefficient Trade-off coefficients Initial concentration of contaminant Specific heat capacity Dimensionless pressure coefficient Distance from door knob to edge of door (knob side) Constant for exposure hazard Density in persons per m2 Initial flow density Density through the door to staircase (no congestion on stairs) Density of group emanating from overcrowded area at level (n 1) Flow density on stairs without congestion Maximum flow density Delay time Compressive force Constant approximately 2.718 Total net energy at ambient moisture content Factor dependent upon height of floor above or below ground level Energy release rate into corridor Fire load density value Perpendicular projected area of an individual Rectangular radiating fac¸ade Total door opening force Force to overcome the door close Flow rate/unit stair width of 0.6 m Ventilation factor Gravitational constant Stress Distance from the neutral plane Distance above neutral density plane Height Effective thickness Floor height Effective vertical opening height

mm mm mm mm m m mm mm MJ/m2

(continued)

Symbols Used in Fire

IE IF IR K k10, k11, k12, k13 Kf Kv kw Kw l L L l(TR) Lx Muv + Muv+

xiii

Intensity of emitted radiation Radiant energy flux Intensity of received radiation Constant (1) Conversion factors used for fire zoning

Coefficient Coefficient Wetting down factor Coefficient Flow length Span of slab Limiting distance Travel distance on stairs between adjoining stories Protected limiting distance Absolute value of positive and negative plastic bending moment, respectively, at end of required period of standard fire exposure My Bending moment n Number of upper floors in building n Number of stories served by staircase N Number of exits required Flow rate of people per unit width down stairs N0 Bearing capacity for composite cross-section Npl Nst High-bearing capacity for steel Applied normal force Nx p Evacuation population per meter effective stair width p Number of persons in flow p Number of persons in the building P Absolute atmospheric pressure P Population a staircase can accommodate P Flame projection distance Po Outside air density Wind pressure Pw q Load on slab to be accounted for during fire Q Energy loss rate Q Volumetric airflow rate q(Dmax) Specific flow at maximum density q(i) Initial value of specific flow Q(I) Sum of capacities of all partial flows q(T; Dmax) Specific flow at maximum density through doorways Q(T;n 1) Flow capacity through door to staircase (each floor) q(T) Specific flow through the door to the staircase under free flow conditions on stairs q(TR; n) Specific flow on stairs (no congestion) q(TR; max) Maximum flow capacity of stairs q(TR; n 1) Value of specific flow on stairs (after merging process) q(TR; Dmax) Specific flow on stairs (maximum density) (continued)

xiv

Symbols Used in Fire

q(TR; max) Q(TR; n) Q(TR) q* Qi Qin Qout QT r R R R r(TR) Rpeak S t t00 (TR; STAU) t(F) t(F) t(TR; STAU) t(TR) t1 T2 td te tf T TF Ti Tl Tin To Tout ts ts

Stairs maximum flow capacity Initial flow capacity stairs Stairs initial flow capacity Load to be used in fire test Population of floor i Volumetric flow rate of air into fire compartment Volumetric flow rate of smoke out of fire compartment Total flow Floor number (1 to n) which gives the max value of te Standard rate of flow Radiation distance Gas constant of air Evacuation time for stairs (per floor) Maximum mass loss rate value reached during a fire Separation distance Time after doors closed in minutes Length of time required for flow to leave floor level (n 2) Travel time (last evacuee along corridor) Evacuation time of corridor (each floor) Length of time required for flow to leave the floor level (n 1) Travel time (person going from top floor to adjoining story) Travel time on stairs to descend one story Maximum fire compartment temperature Fire duration time Maximum permissible exit time from any one floor onto staircase Fire resistance rating (FRR) Absolute temperature of downstream mixture of air and smoke Absolute temperature of fire compartment Actual temperature Absolute temperature of air inside the shaft Absolute temperature of air into fire compartment Absolute temperature of outside air Absolute temperature of smoke leaving fire compartment Time for individual in unimpeded crowd to descend one story Time for person to traverse a story height of stairs at standard rate of flow v Flow velocity v Flow velocity down stairs of 0.3 m/s v Crowd walking velocity’(flow velocity) V Wind velocity Velocity of boundary between initial flow (stairs) and merged flow v00 changing its location v00 (T; STAU) Speed of congestion on corridor v0 (STAU) Speed of congestion on stairs Velocity of a flow through, doorway at maximum density v(T; Dmax) v(TR; n) Velocity of flow at density D(TR; n) v(TR; n 1) Velocity of flow emanating from congested area at floor level (n 1) v(TR; STAU) Flow velocity on stairs at maximum density (continued)

Symbols Used in Fire

v(TR; n 1) Vk Vo w W W Z σ cv σ c20 σ yv σ y20 ΔP ΔPϒ δ εi ε λ ρ ρ ρo ρl ρA ρn vc vc

xv

Velocity of flow on stairs at density D(TR; n 1) Critical air velocity to prevent smoke backflow Constant velocity Width of staircase Door width Corridor width Class of user of building Ultimate compressive strength Compression strength of concrete at ambient temperature Effective yield stress Yield stress at room temperature Pressure difference Total pressure difference Specific density Stress causing strain Emissivity Thermal conductivity Density of air entering the flow path Density of upstream air Air density outside the shaft Air density inside the shaft Configuration factor for rectangle A Total configuration factor Temperature of concrete Temperature

Abbreviations ACI AISI ASET ASHRAE ASTM BS BSI BTR CEB CEFICOSS CP CPA CTICM ECCS FFR FIP

American Concrete Institute American Iron and Steel Institute Available safe egress time American Society of Heating, Refrigerating and Air-Conditioning Engineers American Society for Testing and Materials British Standard British Standards Institute Building Technical Regulation (Taiwan) Comite´ Euro-International du Be´ton (European Concrete Committee) Computer engineering of the fire resistance for composite and steel structures Code of practice Construction and Planning Administration (Taiwan) Centre Technique Industriel de la Construction Me´tallique European Convention for Constructional Steelwork Fire-resistance rating Fe´de´ration Internationale de al Pre´contrainte (International Federation for prestressing) (continued)

xvi

GLC HMSO HVAC ISO MMI MOI MPV MRT NFD NFPA NIST RHR ROC RSET

Symbols Used in Fire

Greater London Council Her Majesty’s Stationary Office Heating, ventilating, and air-conditioning International Standards Organization Modified Mercalli Intensity Ministry of the Interior (Taiwan) Minimum proper value Mass rapid transportation Nominal fire duration National Fire Protection Association National Institute of Standards and Technology (Formerly National Bureau of Standards) Rate of heat release Republic of China Required safe egress time

Conversion table used in data in fire SI Mass 1g 1 kg Density 1 kg/m3 Force, Weight 1N 1 kN 1 MN 1 kN/M 1 kN/m2 Torque, Bending Moment 1 N-m 1kN-m Pressure, Stress 1 N/m2 = 1 Pa 1 kN/m2 = 1 kPa 1 MN/m2 = 1 MPa Viscosity (Dynamic) 1 N-s/m2 Viscosity (Kinematic) 1 m2/s Energy, Work 1 J = 1 N-m 1 MJ Power 1 W = 1 J/s 1 kW

American

Old metric

0.035274 oz 2.2046216 lbc

1g 1 kg

0.062428 lb/ft3

1 kg/m3

0.224809 lbf 0.112404 td 224.809 kips 0.06853 kips/ft 20.9 lbf/ft2

0.101972 kgf

0.73756 lbf-ft 0.73756 kip-ft

0.101972 kgf-m 101.972 kgf-m

0.000145038 psi 20.8855 psf 0.145038 ksi

0.101972 kgf-m

0.0208854 lbf-s/ft2

0.101972 kgf-s/m2

10.7639 ft2/s

1 m2/s

0.737562 lbf-ft 0.37251 hp-h

0.00027778 w-h 0.27778 kw-h

0.737562 lbf ft/s 1.34102 hp

1w 1 kw (continued)

Symbols Used in Fire

SI Temperature K = 273.15 +  C K = 273 15 + 5/9( F 32) K = 273.15 + 5/9( R.491.69)

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American

Old metric





F = ( C  1.8) + 32

C = ( F

32)/1.8

a

Hectare as a alternative for km2 is restricted to land and water areas 1 m3 = 219.9693 Imperial gallons c 1 kg 0.06822 slugs d 1 American ton = 2000 lb. 1 kN = 0.1003612 1Imperial ton = 2240 lb b

Abbreviations for units Btu  C cc cm  F Ft g gal hp h imp in. J K kg kgf kip km kN kPa ksi

British thermal unit Degree Celsius (centigrade) Cubic centimeters Centimeter Degree Fahrenheit Foot Gram Gallon Horsepower Hour British imperial Inch Joule Kelvin Kilogram Kilogram-force 1,000 pound force Kilometer Kilonewton Kilopascal Kips per square inch

kW lb lbf lbm MJ MPa m ml mm MN N oz Pa psf psi o R s slug Uo W yd

Kilowatt Pound Pound force Pound mass Megajoule Megapascal Meter Milliliter Millimeter Meganewton Newton Ounce Pascal Pounds per square foot Pounds per square inch Degree rankine Second 14.594 kg Heat transfer coefficient Watt Yard

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Acknowledgement

Professor M. Y. H. Bangash, a retired Professor of Structural Engineering, Consulting Engineer in Advanced Structural Analysis London, UK. Professor Yaqoob F. Al-Obaid is a professor of Impact, Structural Engineering and Biomedical Engineering at Faculty of Technological Studies, PAAET, Kuwait.

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Contents

1

Engineering Disaster Relief Caused by Fire . . . . . . . . . . . . . . . . . . . 1.1 Engineering Disaster Relief Caused by Fire . . . . . . . . . . . . . . . . 1.2 Disaster Caused by Fire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Buildings on Fire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Fire-Separation Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.1 Meaning of “Distance” . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.2 External Wall Collapse . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.3 Flying Brands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.4 Flame Contact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.5 Emissivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.6 Configuration Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.7 Emitted Heat Radiation . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.8 Received Heat Radiation . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Temperature-Time Relation . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1 1 4 7 11 17 19 20 22 22 22 27 28

2

Fire Analysis: Methods of Design Analysis . . . . . . . . . . . . . . . . . . . 2.1 Analytical Methods Materials . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Theoretical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Theoretical Work. Based on Advanced Analysis . . . . . . . . . . . 2.2.1 Loadings and Restraints . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 The Range of Fire Load Density . . . . . . . . . . . . . . . . . . 2.3 Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Concrete and Reinforcing Steel . . . . . . . . . . . . . . . . . . 2.3.3 Timber and Wood . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.4 Wood Mechanical Properties . . . . . . . . . . . . . . . . . . . . 2.3.5 Design Summary Based on BS 5268 . . . . . . . . . . . . . . . 2.4 Masonry/Brick/Block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Methods of Analysis and Design . . . . . . . . . . . . . . . . . . . . . . . 2.5.1 Empirical and Code Analytical Equations . . . . . . . . . . .

33 33 33 35 35 38 49 49 55 57 62 64 66 69 70

. . . . . . . . . . . . . . .

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Contents

2.5.2 2.5.3

2.6 2.7

2.8

2.9 2.10

2.11

2.12

2.13 2.14

Calculations of Fire Resistance of Steel Members . . . . . . Additional Methods of Protection for Hollow Columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Examples in Steel Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . Calculations of Fire Resistance of Concrete Members . . . . . . . . . 2.7.1 American Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7.2 Concrete Slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7.3 Simply-Supported Unrestrained Beams and One-Way Slab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7.4 Continuous Beams and Slabs . . . . . . . . . . . . . . . . . . . . . Calculations of Fire Resistance of Wood/Timber Members . . . . . 2.8.1 American Practice Based on ATSM E 119 . . . . . . . . . . . 2.8.2 The Load Carrying of Uncharred Timber . . . . . . . . . . . . 2.8.3 British Practice Based on BS 5628 . . . . . . . . . . . . . . . . . 2.8.4 The Section Exposed to Fire . . . . . . . . . . . . . . . . . . . . . . 2.8.5 Reduced Strength and Stiffness Methods . . . . . . . . . . . . . 2.8.6 Method (a) Effective Cross-Section Method . . . . . . . . . . 2.8.7 Method (b) Reduced Strength and Stiffness Method . . . . Deflection of Simple Beams in Reinforced and Prestressed Concrete Exposed to Fire: IStructE Method . . . . . . . . . . . . . . . . Limit State and Plastic Analysis . . . . . . . . . . . . . . . . . . . . . . . . 2.10.1 Basic Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.10.2 Plastic Analysis and Fire Temperature . . . . . . . . . . . . . 2.10.3 Beams and Temperatures: Tabulated Cases . . . . . . . . . . 2.10.4 Compression Members of Columns . . . . . . . . . . . . . . . 2.10.5 Portal Frames: Tabulated Cases . . . . . . . . . . . . . . . . . . Multi-bay: Multi-storey Framed Buildings Subject to Fire Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.11.1 Lateral Torsional Buckling Resistance (Based on EC3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.11.2 Calculation for Critical Temperature for Beam 406  178  67 kg/m UB . . . . . . . . . . . . . . . . . . . . . . 2.11.3 Normal Design of Column Prior to Fire Limit State (Based on EC3 Parts 1.1 and 1.2) . . . . . . . . . . . . . . . . . Finite Element Analysis of Buildings on Fire . . . . . . . . . . . . . . . 2.12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.12.2 Basic Heat Transfer Analysis . . . . . . . . . . . . . . . . . . . . 2.12.3 Heat Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Computer Subroutines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.13.1 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Case Study for Global Analysis Based on Finite Element Method: Canary Wharf Building . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.14.1 Introduction to the Analysis . . . . . . . . . . . . . . . . . . . . . 2.14.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

70 78 80 88 89 90 92 94 104 104 108 113 115 119 123 124 126 132 133 138 149 149 159 159 166 167 168 171 171 171 174 177 177 182 182 185

Contents

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4

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Dynamic and Temperature Analysis Adopted in Fire Analysis and Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Finite-Element Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Steps for Dynamic Non-linear Analysis . . . . . . . . . . . . . . . . . . . 3.3.1 Buckling State and Slip of Layers for Composite Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Strain Rate Effects on the Elastic: Viscoplastic Relationship for Earth Materials Under Impact and Explosion . . . . . . . 3.3.3 Finite Element of Concrete Modelling . . . . . . . . . . . . . . 3.3.4 Blunt Crack Band Propagation . . . . . . . . . . . . . . . . . . . . 3.3.5 Ottoson Failure Model . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Ice/Snow Impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Impact due to Missiles, Impactors and Explosions: Contact Problem Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 High Explosions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Spectrum Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8 Additional Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8.1 Range–Kutta Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8.2 Frequency-Domain Analysis . . . . . . . . . . . . . . . . . . . . . 3.8.3 Keierleber Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8.4 Additional Solution Procedures . . . . . . . . . . . . . . . . . . . 3.9 Solution Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.9.1 Time-Domain Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 3.10 Geometrically Non-linear Problems in Finite Element . . . . . . . . 3.10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.11 Finite Element Analysis of Explosion in Nuclear Facilities Using the Method of Explosive Factor . . . . . . . . . . . . . . . . . . . . . . . . . 3.11.1 Good Achievement of Explosive Burn . . . . . . . . . . . . . 3.12 Finite Element Mesh Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . Detailed Examples of Tests Results . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Tensile Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Tensile Tests at Room Temperature . . . . . . . . . . . . . . . 4.2.2 Tensile Steady State Tests: High Temperature . . . . . . . . 4.3 Characteristics of Investigated Steels . . . . . . . . . . . . . . . . . . . . 4.4 Proposal For Stress–Strain Relationships at Elevated Temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1 Analysis of Tensile Anisothermal Transient Tests . . . . . 4.4.2 Mathematical Model for Stress–Strain Relationship of Cold Formed Steels at Elevated Temperatures . . . . . . 4.4.3 Relative Vertical Displacement as a Function of Time and Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . .

191 191 191 200 205 207 210 212 215 216 219 221 224 226 226 229 229 230 232 232 233 233 236 238 238 239 239 239 239 239 240

. 242 . 242 . 242 . 244

xxiv

Contents

4.5 4.6

4.7 4.8

4.9 5

The Structure of a Premixed Flame . . . . . . . . . . . . . . . . . . . . . . Example Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6.1 Parametric Study with End Restrain and Imperfection Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Comparison of Test Results with Simple Calculation Rules . . . . Test on Tall Studs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8.1 Testing Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8.2 Test Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8.3 Experimental Results Versus Numerical Simulations . . . . 4.8.4 Experimental Results of Wall Element Test (VTT) . . . . . 4.8.5 Experimental Results of Floor-Wall Assembly Test (CTICM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Comparison of Fire Behaviour Between Elements and Assemblies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Fire-Resistant Composite Structures: Calculations and Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Calculations Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Stress–Strain Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Analytical Tools to Evaluate Building Spacing, Compartment Sizing and Exterior Walls in Tall Buildings . . . . . . . . . . . . . . . 5.3.1 Fire–Resistance Rating . . . . . . . . . . . . . . . . . . . . . . . . 5.3.2 Fire Behaviour of Composite Columns . . . . . . . . . . . . . 5.3.3 Practical Applications . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.4 Fire Design of Composite Concrete Slabs with Profiled Steel Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.5 Additional Means of Fire Protection for Composite Slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.6 Calculations of Minimum Slab Thickness . . . . . . . . . . . 5.3.7 Calculations for Additional Reinforcement . . . . . . . . . . 5.4 Fire Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.2 Assessing Fire Resistance . . . . . . . . . . . . . . . . . . . . . . 5.4.3 Fire Resistance Tests . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.4 Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.5 Test Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Fire Severity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5.1 Fire Severity and Fire Resistance . . . . . . . . . . . . . . . . . 5.5.2 Fire Severity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5.3 Standard Fire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 Equivalent Fire Severity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6.1 Real Fire Exposure . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6.2 Equal Area Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6.3 Maximum Temperature Concept . . . . . . . . . . . . . . . . .

250 254 257 258 259 259 263 267 268 271 273

. 279 . 279 . 281 . . . .

289 290 290 294

. 298 . . . . . . . . . . . . . . . . .

299 301 301 304 304 304 305 306 306 307 307 312 313 316 316 316 317

Contents

5.7

5.8

5.9

5.10

5.11

5.12

5.13

5.14

5.15

xxv

5.6.4 Minimum Load Capacity Concept . . . . . . . . . . . . . . . . . 5.6.5 Time-Equivalent Formulae . . . . . . . . . . . . . . . . . . . . . . . Design Fires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7.1 Hand Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7.2 Eurocode Parametric Fires . . . . . . . . . . . . . . . . . . . . . . . Concrete Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.8.1 Behaviour of Concrete Structure in Fire . . . . . . . . . . . . . 5.8.2 High-Strength Concrete . . . . . . . . . . . . . . . . . . . . . . . . . 5.8.3 Lightweight Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . 5.8.4 Fibre Reinforced Concrete . . . . . . . . . . . . . . . . . . . . . . . 5.8.5 Spalling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.8.6 Masonry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.8.7 Prestressed Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.8.8 External Reinforcing . . . . . . . . . . . . . . . . . . . . . . . . . . . Fire-Resistance Ratings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.9.1 Verification Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.9.2 Generic Ratings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.9.3 Protection Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.9.4 Joints Between Precast Concrete Panels . . . . . . . . . . . . . Concrete and Reinforcing Temperatures . . . . . . . . . . . . . . . . . . 5.10.1 Fire Exposure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.10.2 Calculation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 5.10.3 Thermal Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.10.4 Published Temperatures . . . . . . . . . . . . . . . . . . . . . . . . Mechanical Properties of Concrete at Elevated Temperatures . . . 5.11.1 Test Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.11.2 Components of Strain . . . . . . . . . . . . . . . . . . . . . . . . . 5.11.3 Thermal Strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.11.4 Creep Strain and Transient Strain . . . . . . . . . . . . . . . . . 5.11.5 Stress-Related Strain . . . . . . . . . . . . . . . . . . . . . . . . . . Timber Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.12.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.12.2 Description of Timber Construction . . . . . . . . . . . . . . . 5.12.3 Fire-Resistance Ratings . . . . . . . . . . . . . . . . . . . . . . . . Wood Temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.13.1 Temperatures Below the Char . . . . . . . . . . . . . . . . . . . 5.13.2 Thermal Properties of Wood . . . . . . . . . . . . . . . . . . . . . Mechanical Properties of Wood . . . . . . . . . . . . . . . . . . . . . . . . . 5.14.1 Mechanical Properties of Wood at Normal Temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.14.2 Mechanical Properties of Wood at Elevated Temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Design Concepts for Heavy Timber Exposed to Fire . . . . . . . . . . 5.15.1 Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

317 318 323 323 323 328 328 330 331 331 331 332 333 334 335 335 335 336 336 337 337 337 339 340 341 341 342 343 343 344 347 347 348 351 351 352 353 353 354 356 367 369

xxvi

5.15.2 Charring Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.15.3 Corner Rounding . . . . . . . . . . . . . . . . . . . . . . . . . . . . Material Properties in Fire . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.16.1 Testing Regimes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.16.2 Components of Strain . . . . . . . . . . . . . . . . . . . . . . . .

. . . . .

370 373 374 374 375

Fire Following Earthquakes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 A Historical Review in Brief . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.1 Institutions, Responsibilities and Roles . . . . . . . . . . . . . 6.1.2 Collaboration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.3 Community Participation . . . . . . . . . . . . . . . . . . . . . . . 6.1.4 Needs and Limitations . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.5 Analysis and Recommendations . . . . . . . . . . . . . . . . . . 6.2 South Asia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Extent and Types of Fires . . . . . . . . . . . . . . . . . . . . . . 6.2.2 Causes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.3 Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.4 Economic and Social Benefits . . . . . . . . . . . . . . . . . . 6.2.5 Prevention and Suppression . . . . . . . . . . . . . . . . . . . . 6.2.6 Institutions, Responsibilities and Roles . . . . . . . . . . . . 6.2.7 Collaboration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.8 Community Participation . . . . . . . . . . . . . . . . . . . . . . 6.2.9 Needs and Limitations . . . . . . . . . . . . . . . . . . . . . . . . 6.2.10 Analysis and Recommendations . . . . . . . . . . . . . . . . . 6.3 Southeast Asia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 Extent and Types of Fire . . . . . . . . . . . . . . . . . . . . . . . 6.3.2 Causes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.3 Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.4 Prevention . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.5 Suppression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.6 Community Participation . . . . . . . . . . . . . . . . . . . . . . . 6.3.7 Collaboration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.8 Needs and Limitations . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.9 Analysis and Recommendations . . . . . . . . . . . . . . . . . . 6.4 Australasia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.1 Extent and Types of Fire . . . . . . . . . . . . . . . . . . . . . . . 6.4.2 Causes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.3 Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.4 Prevention . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.5 Suppression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.6 Community Participation . . . . . . . . . . . . . . . . . . . . . . . 6.4.7 Needs and Limitations . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.8 Analysis and Recommendations . . . . . . . . . . . . . . . . . . 6.5 Southeast Europe/Caucasus . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.1 Extent and Types of Fires . . . . . . . . . . . . . . . . . . . . . . 6.5.2 Causes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

379 379 380 381 382 383 383 385 385 386 386 387 387 388 389 389 390 391 392 392 392 393 393 394 395 395 395 396 397 397 398 398 399 399 400 400 401 402 402 402

5.16

6

Contents

Contents

xxvii

6.5.3 6.5.4 6.5.5

6.6

6.7 6.8 6.9 6.10 6.11

6.12

6.13

Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Prevention and Suppression . . . . . . . . . . . . . . . . . . . . . Institutions, Roles and Responsibilities, and Community Participation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.6 Needs and Limitations . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.7 Analysis and Recommendations . . . . . . . . . . . . . . . . . . Baltic and Adjacent Countries . . . . . . . . . . . . . . . . . . . . . . . . . 6.6.1 Extent and Types of Fires . . . . . . . . . . . . . . . . . . . . . . 6.6.2 Causes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6.3 Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6.4 Prevention . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6.5 Suppression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6.6 Institutions, Responsibilities and Roles . . . . . . . . . . . . . 6.6.7 Collaboration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Seismograph and Seismicity . . . . . . . . . . . . . . . . . . . . . . . . . . Deterministic Assessment of the Fire Exposure of Exterior Walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Evaluation of Unit Exit Width in High-Rise Buildings . . . . . . . Modeling Pedestrian Movement . . . . . . . . . . . . . . . . . . . . . . . Permutations and Combinations . . . . . . . . . . . . . . . . . . . . . . . 6.11.1 Permutations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.11.2 Step-by-Step Solution Method . . . . . . . . . . . . . . . . . . 6.11.3 Fundamental Equilibrium Equations . . . . . . . . . . . . . . 6.11.4 Incident Command System . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.12.1 Needs and Limitations . . . . . . . . . . . . . . . . . . . . . . . . 6.12.2 Analysis and Recommendations . . . . . . . . . . . . . . . . . Northeast Asia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.13.1 Extent and Types of Fires . . . . . . . . . . . . . . . . . . . . . . 6.13.2 Causes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.13.3 Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.13.4 Prevention . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.13.5 Suppression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.13.6 Community Participation . . . . . . . . . . . . . . . . . . . . . . 6.13.7 Room-Fire Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.13.8 Room-Model Test Results . . . . . . . . . . . . . . . . . . . . .

. 402 . 403 . . . . . . . . . . . .

403 404 405 406 406 406 407 408 408 408 409 410

. . . . . . . . . . . . . . . . . . . .

411 413 423 427 427 427 428 428 430 436 437 438 438 439 439 440 441 450 454 456

Appendix: Computer Subroutines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533

Chapter 1

Engineering Disaster Relief Caused by Fire

1.1

Engineering Disaster Relief Caused by Fire

Figure 1.1 gives a pecularistic view of a building complex indicating a disaster meted out owing to fire. Figure 1.2 indicates a steel building destroyed by fire under aircraft impact in the 9/11, aircraft smashed caused by fire.

1.2

Disaster Caused by Fire

1. For each person proposed in any of the labor categories, complete one Labor Category Personnel Resume Summary to document how the proposed person meets each of the minimum requirements. This summary is required at the time of the interview. For example: If you propose John Smith, who is your subcontractor and you believe he meets the requirements of the Group Facilitator, you will complete the top section of the form by entering John Smith’s name and the subcontractor’s company name. You will then complete the right side of the Group Facilitator form documenting how the individual meets each of the requirements. Where there is a time requirement such as 3 months experience, you must provide the dates from and to showing an amount of time that equals or exceeds mandatory time requirement; in this case, 3 months. 2. Each form also includes examples of duties to perform. The proposed person must be able to fulfill those duties. 3. For each subject matter expert, the State will identify the particular area of expertise and the Master Contractor shall provide proof the individual has qualifications within that area of expertise.

M.Y.H. Bangash et al., Fire Engineering of Structures, DOI 10.1007/978-3-642-36154-8_1, © Springer-Verlag Berlin Heidelberg 2014

1

2

1

Engineering Disaster Relief Caused by Fire

Fig. 1.1 Disaster of a building complex

Fig. 1.2 Partial elevation of exterior bearing-wall frame showing exterior wall module construction were fractured by the impact

1.2 Disaster Caused by Fire

3

4. Additional information may be attached to each Labor Category Personnel Resume Summary that may assist a full and complete understanding of the individual being proposed.

Fire Management—Global Assessment

Photographic evidence suggests that from 27 to 32 columns along the south building face were destroyed over a five-story range. Partial collapse of floors in this zone appears to have occurred over a horizontal length of approximately 70 ft, while floors in other portions of the building appeared to remain intact. It is probable that the columns in the southeast corner of the core also experienced some damage because they would have been in the direct travel path of the fuselage and port engine. It is known that debris from the aircraft traveled completely through the structure. For example, a landing gear from the aircraft that impacted WTC 2 was found to have crashed through the roof of a building located six blocks to the north, and one of the jet engines was found at the corner of Murray and Church Streets. The extent to which debris scattered throughout the impact floors is also evidenced by photographs of the fireballs that occurred as the aircraft struck the building (Fig. 1.3). Figure 1.4 shows a portion of the fuselage of the aircraft, lying on the roof of WTC 5.

4

1

Engineering Disaster Relief Caused by Fire

Fig. 1.3 Conflagration and debris exiting the north wail of WTC 2, behind WTC 1

As described for WTC 1, this debris doubtless caused some level of damage to the structure across the floor plates, including interior framing; core columns at the southeast corner of the core; framing at the north, east, and west walls; and the floor plates themselves. Figure 1.3, showing the eastern side of the north face of the WTC 2 partially hidden behind WTC 1, suggests that damage to the exterior walls was not severe except at the zone of impact. The exact extent of this damage will likely never be known with certainty. It is evident that the structure retained sufficient integrity and strength to remain globally stable for a period of approximately 56 min. There are some important differences between the impact of the aircraft into WTC 2 and the impact into WTC 1. First, United Airlines Flight 175 was flying much faster, with an estimated speed of 590 mph, while American Airlines Flight 11 was flying at approximately 470 mph.

1.3

Buildings on Fire

Karachi: Two people sustained serious burn injuries as fire erupted at the Pakistan National Shipping Cooperation (PNSC) building adjacent to the Native Jetty Bridge on Sunday (Fig.1.5). The fire, which erupted at 11:00 am in the 11th storey of the PNSC building on Moulvi Tameezuddin Road in Karachi also spread to the 10th and 12th floors. More

1.3 Buildings on Fire

5

Fig. 1.4 A portion of the fuselage of the aircraft, lying on the roof of WTC 5

than 15 firemen of fire brigade reached on the spot and started extinguishing the fire. Windowpane of the building smashed with big bang when the fire again erupted. Meanwhile, Federal Ports and Shipping Minister Babar Khan arrived and rescue work.

6

1

Engineering Disaster Relief Caused by Fire

Fig. 1.5 PLNS building in Karachi under fire

Fig. 1.6 A Navy helicopter rescues the people trapped inside PNSC Building

Talking to media men on the occasion, he said, that three out six people on the roof building were safely rescued while the other would be rescued. The Minister went on to say that two people including Personnel of fire brigade and a citizen Nazar Shah received serious burn injuries while the fire inflicted great financial losses but caused no casualties. The injured were rushed to a nearby hospital for immediate medical treatment, Federal Ports and Shipping Minister maintained (Figs. 1.6, 1.7, 1.8, 1.9, 1.10, 1.11, 1.12, 1.13, 1.14, 1.15, 1.16, 1.17, 1.18, 1.19, 1.20, 1.21, 1.22, 1.23, and 1.24). A committee has been constituted to ascertain the reason behind fire eruption of fire in the building, he asserted. AF ¼ C1 Az

m2

(1.1)

1.4 Fire-Separation Method

7

Fig. 1.7 Modern settee (16) covered by unsupported PVC fabric, ignited by match on seat. (a) 2 min—PVC melted exposing filling; (b) 3½ min—flame spread to arm; (c) 30 min—flames finally out

Alternatively, using all three coefficients, the maximum permissible firecompartment area AFM can be derived as AFM ¼ C1 C2 C3 Az

1.4

m2

(1.2)

Fire-Separation Method

If they use the concept at all, most fire codes use only one or two radiation-flux values when considering the external walls of buildings. If it is satisfactory to assume that fire-compartment temperatures are proportional to time, then it should be equally satisfactory to assume that radiation-flux levels are proportional to time. On this premise, and using the standard time-temperature curve, a wider than usual range of design radiation values can be derived, which are in step with standard FRRs. The method allows building designers more flexibility in the choice of ordinary or fire windows, both in mirror-image and in non-mirrorimage situations (see discussion on distance in Sect. 1.4.1).

8

1

a

b

c

f

Engineering Disaster Relief Caused by Fire

d

g

e

h

Fig. 1.8 Curtain burning tests. (a) Cotton—22 s—flames burning up centre of fabric; (b) Cotton—36 s—curtain ablaze; (c) cotton/polyester—2 min 5 s—flames and black smoke; (d) cellulose diacetate—50 s—burning droplets; (e) acrylic—1 min 5 s—blazing and on floor; (f) acrylic/wool—1 min 10 s—blazing and on floor; (g) nylon with cotton lining—30 s—blazing; (h) woolen—2 min 20 s—burning slowly at top

1.4 Fire-Separation Method

9

Fig. 1.9 Acrylic carpet with fibre underlay ignited by wood crib. (a) 7 min—flame spreading along edge of underlay; (b) 9 min 50 s—carpet burning 30 cm from crib, and ignited by underlay at 60 cm; (c) 11 min 30 s—carpet burning along edge; (d) Final damage to carpet and underlay

Subdivided into five categories, the hazards likely to cause a neighbor’s property to ignite are external wall collapse, flying brands, flame contact, emitted heat radiation, and received heat radiation. In fire-engineering terms, an external wall is a special kind of wall that is different from ordinary internal walls, and may be different from fire walls and fire partitions. Within flame-contact range, the external wall needs to function like a fire wall and cope with fire from both sides. Beyond flame-contact range, but within radiation danger range, the external wall needs to cope with fire from inside and radiation on the outside. Once the distance between buildings is large enough, no measures need to be taken for the safety of the neighbor’s property.

10

1

a

b

c

d

Engineering Disaster Relief Caused by Fire

Fig. 1.10 Nylon carpet, with latex foam backing. (a) 7 min 10 s—carpet burning pile melted in front of flames; (b) 31 min 25 s—carpet burned to 60 cm mark, crib fire out; (c) 6 min 45 s—molten pile and backing burning vigorously; (d) 13 min 15 s—burning continuing away from crib

a

b

Fig. 1.11 Woollen carpet, with fibre underlay. (a) 11 min—crib collapsing, but carpet not burning; (b) Crib fire almost out, limited damage to carpet

1.4 Fire-Separation Method

11

Fig. 1.12 Plan view of mattress support used in fires involving beds

a

b

c

d

Fig. 1.13 Fire tests of beds with polyether mattress. (a) woolen blanket—46 min; (b) acrylic blanket—13½ min; (c) Polypropylene blanket—21 min; (d) cotton blanket—14 min

1.4.1

Meaning of “Distance”

Because the positions of owner and neighbor can be reversed in a fire, that is, either building can ignite, all wall criteria apply equally to both parties. In traditional fire codes, each building situation is regarded as being the mirror image of the other (see Fig. 1.25). Where the owner has no control over the neighbor’s construction,

12

1

a

b

c

d

Engineering Disaster Relief Caused by Fire

Fig. 1.14 Fire tests of beds with ‘new’ foam mattress with fire-retardant cover. (a) woolen blanket—untucked to show damage after extinguishing itself in 2½ min; (b) acrylic blanket— 14¾ min—burning vigorously; (c) woollen blanket—20 min—ignited in bed near pillow; (d) fireretardant acrylic blanket—46 min—ignited in bed near pillow

a

b

Fig. 1.15 Fire tests of beds with latex foam mattress with fire-retardant cover. (a) woolen blanket—44 min; (b) acrylic blanket—10½ min

mirror-imaging, or equal distancing, may not occur, but safety is not necessarily impaired (see Fig. 1.26). Furthermore, mirror imaging does not necessarily err on the side of safety for unequal limiting distances, as illustrated in Fig. 1.27.

1.4 Fire-Separation Method

a

13

b

Fig. 1.16 Fire tests of beds with interior-sprung mattress. (a) woolen blanket—45 min; (b) acrylic blanket—16 min

a

b

c

Fig. 1.17 Burning of plastics trays. (a) polypropylene tray—match applied to top edge; (b) ABS tray—2 min—match applied to bottom corner; (c) polystyrene tray—4 min—burning material dripping to floor

14

1

Engineering Disaster Relief Caused by Fire

a

b

Fig. 1.18 Burning of rigid foam desk panels. (a) polyurethane foam panel—6½ min; (b) ABS foam panel—17½ min

a

b

c

Fig. 1.19 Modern furniture in full-scale fire (1). (a) Furniture and wood crib; (b) sideboard charred, chair frame largely intact; (c) charred dining table and chairs

1.4 Fire-Separation Method

15

a

b

c

Fig. 1.20 Traditional furniture in full-scale fire (2). (a) test arrangement; (b) 21 min – left-hand chair burning, right-hand chair just ignited; (c) Final debris, upholstered chairs largely reduced to ash

a

b

Fig. 1.21 Polyether foam suite in full-scale fire (4). (a) Chair and settee frames after the fire; (b) Upholstered chair, dining table and chairs little damaged

The meaning of distance is important in fire-code applications and needs to be clearly understood. For the purpose of this discussion; the following definitions shall be used:

16

a

c

1

Engineering Disaster Relief Caused by Fire

b

d

Fig. 1.22 Traditional furniture in fully furnished room (6). (a) Test arrangement; (b) 49 min— state of settee and carpet at moment of increase in ventilation; (c) 58 min—rear corner of room burning vigorously; (d) Upholstered furniture destroyed, dining furniture and woolen carpet only partially affected

1. Radiation distance R shall be the distance between the flame front of a burning building and the face of any exposed building (owner’s or neighbor’s). 2. Separation distance S shall be the distance between the wall fate of the burning building and the wall face of any exposed building (owner’s or neighbor’s). 3. Limiting distance L shall be the distance between the face of a burning building and an adjacent building. L0 shall refer to the owner’s limiting distance and LN to the neighbor’s limiting distance (Note that limiting distance is not necessarily half of separation distance or radiation distance; refer to Fig. 1.25). 4. Protected limiting distance Lx shall be the value of the limiting distance specified by the writers of the fire code in which fire-resistance closures shall be mandatory. 5. Flame-projection distance P shall be either 2 m (6 ft) or less if calculated in an approved manner under full wind conditions, or zero if suitable fire windows are installed.

1.4 Fire-Separation Method

a

17

b

c

Fig. 1.23 Modern and semi-modern furniture in fully furnished room. (a) rear of settee re-ignited after increasing ventilation; (b) fire well established; (c) fire spread to bookcase and sideboard, and pile burned off acrylic/nylon carpet

Based on the foregoing definitions and as i1lustrated in Fig. 1.25, S¼RþP 1 L ¼ SðR þ PÞ 2

1.4.2

(1.3)

External Wall Collapse

In designing an owner’s building, the designer should ensure that the exterior walls remain standing for the duration of a fire because they act as heat barriers to prevent spread of fire to a neighbor’s building. In addition, ignition of the neighbor’s property by the owner’s wall can be controlled by ensuring that any external wall of the owner’s building within danger range (assumed as the height of the owner’s

18

1

Engineering Disaster Relief Caused by Fire

a

b

c

d

e

Fig. 1.24 Finite element mesh schemes. (a) Numerical modelling of the orthotropic steel decks; (b) FE mesh of the global model; (c) Dams without foundation; (d) Curved dams with foundation; (e) Dams subject to bomb explosion impact

wall) should also remain standing. If any parts of the external wall collapse too soon, projecting flame sizes may be increased and emitted radiation areas will certainly be increased. Both effects may cause ignition of the neighbor’s property, which otherwise might not occur.

1.4 Fire-Separation Method

19

a

Actual

Flame

Assumed

T1 IF

IR1

IR3 IE1

T1

IE2

IR3

IR2

Fire P

R Bdy LO

b

Actual

1

Assumed T1

IF

Fire

LN

IE5 IE1

IR1

IE4

IR4

P=O

Owners building

IR5

s

LO

LN

Neighbors building

Fig. 1.25 Diagrams illustrating separation distance S, flame-projection distance P, and limiting distance L. Radiation distance is R. (a) Ordinary windows, mirror-imaged; (b) Fire windows, mirror-imaged

1.4.3

Flying Brands

Combustible materials on or inside neighboring buildings can be ignited from a fire by, any of three forms of ignition, namely, spontaneous, pilot, and. Contact ignition. The most common combustible material found on the exterior, of buildings is wood, and its ignition behavior when preheated by radiation is representative of a large variety of combustible building materials. This is shown as IR1 in Figs. 1.25 and 1.26. Typical values of radiation intensities for pilot and spontaneous ignition of wood are 12.5 and 25 kW/m2, respectively. Where a neighboring building does not have any combustible material on the exterior and has fire windows installed, neither contact ignition nor pilot ignition will apply, and flying brands can be ignored. Where an adjacent building has ordinary glazing in its windows, which is liable to crack under radiant heat, broken openings may admit flying brands. These flying brands may cause, pilot ignition of combustibles inside the window, such as curtaining, wood paneling, or stored goods. This is indicated by IR3 in Figs. 1.25 and 1.26.

20

1

Engineering Disaster Relief Caused by Fire

Fig. 1.26 Diagrams illustrating differences between ordinary and fire windows at equal limiting distance when based on mirror imaging

1.4.4

Flame Contact

The danger range for flame contact depends on the dimensions of the projecting flame. In general it can be said ‘that under no wind conditions, flames will project a distance varying from half the window height for long windows, to 1½ times the window height for square windows. Ignition control between buildings depends on the selected design values of the f1ame-projection distance P and the specified protected limiting distance Lx. The values of P and Lx vary in different codes and

1.4 Fire-Separation Method

21

Neighbor L = I =0 m

1m

2m

3m

Owner L=

N

N

N

N

0m

0/0

0/1 N

0/2 N

0/3 N

N

1m

1/0

1/1

1/2 N

N

1/3 N

N

2m

2/0

2/1 N

2/2 N

2/3 N

N

3m

3/0

3/1

3/2

3/3

Fig. 1.27 Flame contact for P ¼ 2 m and Lx ¼ 1 m. Flame contact occurs in 1 case (2/0) out of 16. Two cases (O/l and 2/3) are unsafe from radiation hazard when owner and neighbor are reversed

are not always easy to determine from the codes themselves. For example, the British system seems to work from building face to building face, that is, P ¼ 0 m and Lx ¼ O m; the Canadian system seems to work from flame front to building face, using P ¼ 1.5 m and Lx ¼ 1.2 m; for New Zealand’s proposed new fire code, values of P ¼ 2 m and Lx ¼ 1.5 m have been recommended.

22

1

1.4.5

Engineering Disaster Relief Caused by Fire

Emissivity

The intensity of radiant heat energy given off by a heated object depends on its emissivity ε. The perfect emitter is a blackbody and has an emissivity of unity. A fire compartment, when heated, acts as a cavity radiator with holes in it, and thus approximates a blackbody with an emissivity of 1.00.

1.4.6

Configuration Factors

The intensity of radiant energy IR falling on a surface from an emitter can be found by using an appropriate configuration factor ρn which takes into account the geometrical relationship between emitter and receiver. For exterior facades, an enclosing rectangle, or rectangular radiating facade, F is assumed, having height H and width W, which in turn is divided into four equal rectangles A, B, C and D. The configuration factor pA for rectangle A is taken perpendicular to the central corner of rectangle A (and similarly for B, C, and D). This method of presentation takes advantage of the fact that configuration factors are additive. The value of pA can vary from 0 to 0.25 and the value of pA from 0 to 1.0. The total configuration factor pA for the whole rectangle is made up of the individual configuration factors for rectangles A, B, C, and D. Thus, ρn ¼ ρA þ ρB þ ρC þ ρD ¼ 4ρA

(1.4)

The following formula for a receiver parallel to the radiator is applicable: " # 1 x y y x 1 1 ΦA ¼ Tan þ Tan 360 ð1 þ x2 Þ 12 ð1 þ x2 Þ 12 ð1 þ x2 Þ 12 ð1 þ x2 Þ 12

(1.5)

where x ¼ HA/R ¼ H/2R;y ¼ WA/R ¼ W/2R HA ¼ height of quarter rectangle A, ¼ H/2 WA ¼ width of quarter rectangle A, ¼ W/2 R ¼ radiation distance between emitter and receiver tan1 ¼ degree mode Equations (1.4) and (1.5) do not depend on the use of water and, hence, can be applied in nonwater regions such as rural areas, small islands, and frozen climates.

1.4.7

Emitted Heat Radiation

Increasing the separation distance between buildings reduces the radiation hazard, and for a given separation distance, the intensity of received radiation IR on the nonburning building depends on the intensity of emitted radiation IE from the

1.4 Fire-Separation Method

23

Fig. 1.28 ISO temperature T2 and corresponding radiation IF versus time tm for a fire compartment

burning building. The maximum fire-compartment temperature T2 in degrees centigrade can be determined in a number of ways from a standard timetemperature formula such as BS 476 or ISO 834 as follows:

24

1

Engineering Disaster Relief Caused by Fire

Fig. 1.29 Various types of facades from which separation distances are calculated

T2 ¼ 345 log10 ð8tm þ 1Þ þ T1

o

C

(1.6)

The radiant energy flux IF present inside a fire compartment can be considered proportional to the difference in temperature of the fire compartment T2 and its surrounding T1 in kelvins. Thus IF ¼ εσðT2  T1 Þ kW=m2

(1.7)

IF can be considered as radiating in. all directions inside the fire compartment at once. Therefore it can be expected to be the same value as IE1 inside a compartment’s opening, as illustrated in Fig. 1.25. Thus IE1 ¼ IF. By using Eqs. (1.6) and (1.7), values of IE1 corresponding to standard FRR times can be determined, as shown in Fig. 1.28. Because of the emitted radiation just inside the opening IE1, the question arises as to what critical value of emitted radiation IEC should be used for outside a burning building. This depends on whether or not the glazing remains in position. Figure 1.25 shows the outside critical value from a burning building as IE2 for ordinary windows and IE4 for fire windows. When the glass remains in position, the radiation on the outside of the glass reduces to a value of between 10 and 50 % of the impressed radiant heat. Thus a radiation reduction factor k1 of 0.50 through wired glass would appear to be a reasonable design assumption. Provided the glass remains in position, that is, fire-resistant glazing, is used, this reduced radiation effect can be utilized in building-separation calculations. When ordinary glazing cracks, and falls out of an opening, flames begin projecting outside the building. The area of flame greater than the openings is ignored, and these radiating openings are assumed to be acting at a distance out from the building face (not at the face of the building wall) equal to the flameprojecting distance P. Radiation from projecting flames is usually neglected in fireseparation calculations. This is considered to be a conservative adjustment, which greatly simplifies the design procedure for radiation-distance calculations.

1.4 Fire-Separation Method

25

a

b

c

d

Fig. 1.30 Traditional settee (6) ignited by paper on seat. (a) 6½ min—flame went out but smouldering continued; (b) 95 min—smoke emission increasing rapidly; (c) 154 min—flaming again; (d) Final residue, following burning for more than 4 h

For ordinary glazing k1 ¼ 1.0, and thus, IEC ¼ IE2 ¼ IE1 ¼ IF, For fire-resistant glazing k1 ¼ 0.50, and thus, IEC ¼ IE4 ¼ 0.5IE1 ¼ 0.5IF. These values for IEC refer to the unit radiation from one opening. Most external walls have a number of openings, but the problem can be reduced to that of a single opening or radiator, termed the enclosing rectangle, which is considered as emitting radiation over its whole area at a reduced intensity IE3 (or IE5) (refer to Figs. 1.25 and 1.26). The enclosing rectangle should be calculated for a number of selected large and small cases, as shown on Fig. 1.29, and the worst case should apply. The reduction factor kv is taken as the ratio of the sum of the areas of all the vertical openings in the wall Av to the total area of the enclosing rectangle AE, which equals H x W. kv is also equal to the ratio between IE3 (or IE5) and IEC Thus, kv ¼

Av IE3 ¼ Ag IEC

or

IE5 IEC

(1.8)

26

1

a

b

c

d

Engineering Disaster Relief Caused by Fire

Fig. 1.31 Semi-modern settee (7) with one seat cushion, ignited by paper on floor. (a) Test arrangement; (b) 1½ min—small flame near arm; (c) 3 min—flames and debris on floor; (d) 20 min—residue

a

b

Fig. 1.32 Traditional fireside chair (9) covered by PVC-faced cotton. (a) 4 min—cigarette went out; (b) Smouldering within chair after ignition by paper on floor

1.4 Fire-Separation Method

27

a

b

c

d

Fig. 1.33 Traditional chair (12) ignited by cigarette on seat. (a) 23½ min—smouldering; (b) 102 min—arms and back smouldering vigorously; (c) 104 min—appearance of flame; (d) Residue after several hours

1.4.8

Received Heat Radiation

When a neighbor’s building receives heat radiation IR, there is not only the hazard to any combustible material on the outside of the building IR1 but there is also a hazard to the combustible contents in any room likely to receive radiation (Figs. 1.30, 1.31, 1.32, 1.33, 1.34, and 1.35).

1.4.8.1

Customs

There are a number of aspects to the Chinese culture and customs that affect the use of buildings. A number of fires in Taiwan can be attributed to some of these traditional customs (Fig. 1.36).

28

1

a

b

Engineering Disaster Relief Caused by Fire

c

Fig. 1.34 Modern chair (14) with acrylic cover ignited by match on seat. (a) 1¼ min—burning accelerating in back, exposing foam; (b) 3¼ min—back of chair burning vigorously; (c) 15½ min—wooden frame still burning

1.5

Temperature-Time Relation

A great deal of research, involving theory, experiment and data monitoring on site (705–954), has been carried out and is still continuing with regard to the timetemperature relation. In this section a few examples are given to show different practices. In general it is widely believed that the temperature course of fire may be divided into the following three periods: (a) the growth period (b) the fully developed period (c) the decay period.

1.5 Temperature-Time Relation

29

a

b

c

Fig. 1.35 Modern chair (15) covered by unsupported PVC fabric, ignited by match on seat. (a) 2¾ min—cushion fabric involved and flames spreading in back; (b) 9 min—back of chair fully involved; (c) 33½ min—burning arm collapsed and ignited adjacent panel furniture

To determine the temperature course, it is necessary to know at each moment during a fire the rate at which heat is produced and the rate at which heat is lost to exposed materials and surroundings. Several of the parameters that determine heat production and heat losses can be categorized as follows: (a) material properties (b) room dimensions (c) emissivity of flames (d) exposed materials (e) gases that burn outside the room (f) loss of unburnt particles through window (g) temperature difference in the room (h) temperature change with time during the fire, which in turn depends on: (i) (ii) (iii) (iv) (v)

amount surface area arrangement of combustible contents velocity and direction of wind outside temperatures

30

1

Engineering Disaster Relief Caused by Fire

Site plan

A

11 th floor plan

plan of the 2and floor

Fig. 1.36 Schematic diagram of Asia Union Building fire

1.5 Temperature-Time Relation

31

Fig. 1.37 Frequency spectra

Fig. 1.38 Acceleration-time relationship

Lig(t)

T'

T '=T active T ''=T quiet

T ''

t

TP

TP

Various unpredictables and variations in approaches exist for computing fire load densities. However, it is possible to indicate for any compartment a characteristic temperature-time curve whose effect will not be exceeded during the lifetime of the building. Such curves are useful for the fire-resistance design of buildings. A number of Japanese researchers have produced results (918); Figs. 1.37 and 1.38 summarize the results of the temperature-time curve for the resistance design.

Chapter 2

Fire Analysis: Methods of Design Analysis

2.1

Analytical Methods Materials

2.1.1

Theoretical Analysis

2.1.1.1

Introduction

Fire is the primary cause of loss of life and property throughout the world. During the past two decades fire has damaged hundreds of thousands of structures. Significant advances have been made in controlling or mitigating the effects of fire. Various methods have been developed (705–953) to protect buildings. New materials have been developed or invented. A considerable time is spent by various researchers (705–953) on the development of mathematical models to simulate the behaviour of structural members in fire. This is possible only if one uses numerical and computer techniques. A large number of computer programs that calculate the fire resistance of structural members now exist. The input data for these computer programs require, apart from loading and fire density, thermal and mechanical properties of various building materials at elevated temperatures. In addition, the expected severity of building fires and temperature-time relations have also been developed. Most of these properties have been codified. The closet measures related to building design are probably those for the confinement of afire. These measures include fire barriers capable of delaying or preventing spread of fire, dimensions and locations of buildings. All these measures are directly related to the detailed knowledge of the mechanics and severity of fire. It is, therefore, essential to outline some areas outside the domain of a structural engineer which he or she should be aware of. Some of these are described below: (a) (b) (c) (d)

Mechanics of fluids and building aerodynamics applicable to fire engineering. Conduction of heat in solids. Convection and radiation heat transfer. Thermochemistry.

M.Y.H. Bangash et al., Fire Engineering of Structures, DOI 10.1007/978-3-642-36154-8_2, © Springer-Verlag Berlin Heidelberg 2014

33

34

2 Fire Analysis: Methods of Design Analysis

Table 2.1 Factors for an Enclosure Factor k

Description Thermal conductivity of bounding material: 1.16 W/mK for a heavy material (ρ  1,600 kg/m3) 0.58 W/mK for a light material (ρ < 1,600 kg/m3). ρc Volumetric specific heat of bounding material: 2,150  103 J/m3 K for a heavy material (ρ  1,600 kg/m3) AT 1,075  1103 J/m3 K for a light material (ρ < 1,600 kg/m3) Total inner surface area bounding the enclosure including window area: 1,000 m2 AT H Window height: 1.8 m ϵ Emissivity for radiation transfer between hot gases and inner bounding surface of the enclosure: 0.7 Coefficient of heat transfer by convection between fire and inner bounding αc surface area: 23 W/m2
K αu Coefficient of heat transfer between outer bounding surface area and surroundings: 23 W/m2
K c Specific heat of combustion gases: 1,340 J/Nm3
 C G Volume of combustion gas produced by burning 1 kg of wood: 4.9 Nm3/kg q Heat released in the enclosure by burning 1 kg of wood: 10.77  106 J/kg Initial temperature: 20  C T0 V Volume of enclosurea: 1,000 m3 Δx Thickness of elementary layers of bounding material: 0.03 m Time increment: 0.0004167 h Δt D Thickness of bounding material: 0.15 m a It can be shown that the influence of the volume of the enclosure on the fire temperature is negligible. Courtesy: ASCE

(e) Chemical equilibrium and thermal decomposition. (f) Fire dynamics. (i) (ii) (iii) (iv) (v) (vi)

Flame height and fire plumes. Air entrainment into buoyant jet flames. Ceiling jet flows, vent flows and natural convention wall flows. Combustion conditions, and smoldering combustion. Flammability limits and flaming ignition of solids. Smoke production, smoke and heat venting.

The rate of burning R of the combustible materials in an enclosure is given by: R ¼ 360 Aw The duration time τ¼

pffiffiffiffiffiffi H

q c At Qc pffiffiffiffiffiffi ¼  330 F 330 Aw H

(2.1)

(2.2)

2.2 Theoretical Work. Based on Advanced Analysis

35

where qc ¼ the fire load=unit area Here qc ¼ 330 Fτ (g) (h) (i) (j) (k) (l)

(2.3)

Burning rates and calorimetry. Compartment fire modelling and fire models for enclosures. Stochastic models for fire growth. Explosion protection. Detection systems, automatic sprinkler systems. Foam system and foam agents.

Within the non-structural analysis, structural analysts must be aware of hazard calculations, risk analysis and probability methods. The main concern of the structural engineer is the properties of the various materials involved and the analytical tools available for the design of structural elements in fire. They are given later on in this text under various sections. No matter how many precautions are taken to improve the fire safety design of buildings, they will not be complete without sufficient availability of training professional education and practice. The main objective is to prepare sufficient manuals of awareness and to transfer knowledge of fire safety of buildings to the building design practitioners by way of courses and seminars at various institutions. Architects and engineers must place importance on fire safety provisions and allow funds for training facilities.

2.2 2.2.1

Theoretical Work. Based on Advanced Analysis Loadings and Restraints

The load bearing structures must be subjected to the characteristic dead loads GK and the characteristic imposed loads QK having the same values as normal design. The partial safety factors for dead and imposed loads according to BS8110 are 1.4 and 1.6 respectively. In case of fire they are 1.05 for dead load and 1.0 for composed load. In major analysis, it is essential to impose temperature load due to fire. Where dynamic analysis is performed, the fire load will be treated as an accidental overload. The American Society of Civil Engineers’ Standard ASCE7-93 is not explicit about such a load, as fire is not treated as a permanent load. The best combination is based on the total of the combined effects multiplied by a factor PF (Fig. 2.1):

36

2 Fire Analysis: Methods of Design Analysis 1400

Temperature,°C

1200 1000 800 600 400 Growth period

200 0

Fully developed Period

1

Decay Period

3

2

4

Time, hr

Fig. 2.1 Idealized temperature course of fire (reproduced from Report No. 5A, 1978)

PF ðL þ Lr þTÞ þ D

(2.4)

where PF ¼ 0.75 or 0.66 *T ¼ forces due to temperature changes etc. L ¼ live loads L r ¼ roof loads D ¼ dead loads. The opening factor F which has an effect on the temperature-time relation is given by (Fig. 2.2):

F¼

Aw

pffiffiffiffiffiffi H At

(2.5)

where AW ¼ area of the openings in compartments or enclosures H* ¼ height of the opening At ¼ area of the bounding surfaces (AT in British codes). K0 ¼ factor for fire resistance ¼ 1.5 for vertical structures ¼ 2.5 for fire-proof structures ¼ 1.25 for horizontal structures. This criterion is taken from ‘Building Standards and Rules’ SNi 11-A.585. Japan, in its State of the Art Report No. 5A (1978), recommends a fire load of 36 kg/m2, provided the duration of the fire does not exceed 45 min and the fire temperature does not exceed 150  C.

2.2 Theoretical Work. Based on Advanced Analysis

37

1400

Temperature,°C

1200 1000 a

800

b

600 400 200 0

1

2

3

4

Time, hr

Fig. 2.2 Temperature curves for fire resistance design (reproduced courtesy of the ASCE)

The Swedes, in their State of the Art Report 5B (1987), assume that tall buildings cannot be evacuated during a fire: they insist that the buildings should be provided with fire protection measures. They have established a relation between effective fire load q and resistance time τ for a structure in a fire compartment. The fire load qc initially is given by: qc ¼

1 X mv Hv ðMcal = m2 Þ Af

(2.6)

where Af ¼ floor area (m2) mv ¼ the total weight (kg) Hv ¼ effective heat value (Mcal/kg) for each individual material v qc is also given in terms of an equivalent amount of wood per unit area Af A modified formula exists for qc: qc ¼

1 X mv Hv At

(2.7)

in which At is the total area of the surfaces bounding the compartment (m2). The connection between the different fire load definitions is given by: qc ¼

At q ðMcal=m2 Þ and Af

qc ¼

At qðkg=m2 Þ 4:5 Af

(2.8)

A further development, leads to a more differentiated characterization of the fire load. The value of q is:

38

2 Fire Analysis: Methods of Design Analysis

q¼

1 X μv mv Hv At

(2.9)

in which μv denotes a dimensionless coefficient between 0 and 1, giving the real degree of combustible for each individual component v of the fire load. The coefficient μv depends on the duration of the fire and the temperature—time characteristics of the fire compartment.

2.2.2

The Range of Fire Load Density

It is concluded that for q the temperature—time relation is very important. It should be checked that the base case is not unsafe and that an appropriate fire growth rate has been chosen for the calculations. The traditional criteria can also be looked at in the following manner. Travel distance may be increased by a factor of 2 if a smoke control system is provided Fire resistance: the required fire resistance is increased by: (i) ½ h for every 10 m height to a maximum of 30 m. (ii) 1 h for basement 10 m deep and ½ h at the basement level with sprinkler systems. Compartment sizes: the floor area is increased by a factor of 2 where a sprinkler system is provided. The Russians define the fire resistance of the building as the ability of the structure to retain its operating functions in the period of fire for some definite time, after which the structure loses its carrying or protecting capacity. The heat of the fire, q which he calls warmth of the fire, is given as: q ¼ z βc QH n

(2.10)

where z ¼ factor for chemical burning βc ¼ coefficient of the speed of burning QH ¼ the lowest warmth of burning n ¼ weight speed of burning The fire load or the ‘heat load’ can be found by: Qr ¼ Qa f ðBi; FoÞ where Qr ¼ fire heating load during the period of time Qa ¼ maximum heat content of the structure f (Bi; Fo) ¼ function of the Bio and Fourie criteria

(2.11)

2.2 Theoretical Work. Based on Advanced Analysis

39

The fire resistance limit corresponding to these fire load equations is given by: where LF ¼ K0 τ

(2.12)

where LF ¼ required fire resistance limits in hours τ ¼ time of the fire in hours. between the available exits. The design can be considered acceptable if the available safe escape time (ASET) is: ASET  tdet þ Δtpre þ ðλflow Δtflow Þ

(2.13)

Where tdet ¼ detection time Δtpre ¼ pre-movement time Δtflow ¼ flow time λflow ¼ design factor applied to flow time ¼ 1 for offices and industrial premises ¼ 2 for large and complex public buildings such that ASET  tesc ¼ tdet þ Δtpre þ λflow

(2.14)

Where dynamic analysis using finite element technique for large buildings is required, the value of ASET must be considered in time-steps and overall time required for the resistance. A reference is made to Appendix. Where the occupants remain in tall and complex buildings for an extended period while fire fighting operations take place and where structural failure threatens the life of the occupants it is recommended that the adequacy of the structural fire resistance should be evaluated as follows: Lcrit  λstr L

(2.15)

where Lcrit ¼ fire load at structural failure L ¼ design fire load (80 % fractile) λst ¼ 1.0 for low-rise 30 m. However, if Δtflow is estimated at 2½ min with an inherent factor of 2, the ASET value will be 5 min. If the travel distance is increased and Δtflow is raised to 3 min, it will be necessary to increase ASET to 6 min such that ASET ASET ðbase designÞ  ðnew designÞ Δtflow Δtflow

(2.16)

40

2 Fire Analysis: Methods of Design Analysis

This increase in ASET may be achieved by a large smoke reservoir, smoke extract system or by controls on combustible materials that would reduce the expected rate of fire growth (Table 2.2). If ASET ðbase designÞ < 1:0 Δtflow

(2.17)

nature of the combustibles. In such circumstances, with a calorific value of 40 % of that of the total contents, the equivalent fire load density may be expressed as: qe ¼

qki Hw

(2.18)

Where qe ¼ equivalent fire load density of wood (kg/m2) qki ¼ measured fire load density (MJ/m2) Hw ¼ calorific value of dry wood (18 MJ/kg) Safety factors Safety factors have already been discussed under loads. If a fire may put a large number of people at risk, it may be appropriate to include additional safety factors within the design. In buildings where large numbers of people are unaware of exit routes (e.g. shopping centres), it will be appropriate to include additional safety factors to take account of uncertainties in the distribution of occupants The following expressions are adopted: qki ¼

P

mc Hc Af

(2.19)

Where qki ¼ fire load density of the compartment (MJ/m2) mc ¼ total weights of each combustible material in the compartment (kg) Hc ¼ calorific value of each combustible material (MJ/kg) Af ¼ total internal floor area of the compartment (m2). In the case that wet or damped materials are present, the effective calorific value Hc is modified by: Hc ¼ Hu ðl

0:01 MÞ

0:025 M

where Hc ¼ effective calorific value of the wet material (MJ/kg) Hu ¼ calorific value of the dry material (MJ/kg) M ¼ moisture content (in % by dry weight). Table 2.3 gives calorific values of typical materials.

(2.20)

0.452 0.46

0.465 0.473 0.486

0.3831

0.41 0.251

0.4459 0.444

0.234 0.234 0.2256 0.1344 0.3843

2,707 11,373

7,897 7,849

7,833 7,801 7,753

8,954

8,666 10,220

8,906 8,666

10,524 10,524 7,304 19,350 7,144

419 407 64 163 112.2

90 17

83 123

386

54 43 36

73 59

204 35

cρ, kJ/kg  C k, W/m  C

0.896 0.13

ρ kg/m

Metal

Aluminium pure Lead Iron Pure Wrought Iron 0.5% C Steel (C max ¼ 1.5 %): C ¼ 0.5 % 1.00 % 1.50 % Copper Pure Aluminium bronze 95 % Cu, 5 % Al Molybdenum Nickel: Pure (99.9 %) Ni-Cr 90 % Ni, 10 % Cr Silver: Purest Pure (99.9 %) Tin, pure Tungten Zinc, pure

3

Properties at 20  C

Table 2.2 Calorific values of typical materials

17.004 16.563 3.884 6.271 4.106

2.266 0.444

2.33 4.79

11.234

1.474 1.172 0.97

2.034 1.626

8.418 2.343

α,m /s  10

2

5

100  C

114

419 419 74

104

138

407

87

215 36.9

83 18.9

118

379

52 43 36

67 57

417 415 410 415 65.9 59 166 15 11 109

93 17.1

125

386

55 43 36

73 59

202 206 35.1 33.4

148  F 32  F 212  F

100  C 0  C

412 374 57 142 106

73 20.9

114

374

48 42 36

62 52

215 31.5

392  F

200  C

Thermal Conductivity k, W/m  C

36 126 93

133 100

59 24.6

109

363

42 36 33

48 45

249

752  F

400  C

362

64 22.8

111

369

45 40 35

55 48

228 29.8

572  F

300  C

800  C

1,000  C 1,200  C

112

106

353

35 33 31

40 36

76

102

31 29 28

36 33

99

29 28 28

35 33

92

31 29 29

36 33

1,112  F 1,472  F 1,832  F 2,192  F

600  C

2.2 Theoretical Work. Based on Advanced Analysis 41

42

2 Fire Analysis: Methods of Design Analysis

Table 2.3 Recommended values for characteristic fire load. Load densities in various occupancy types Substance Insulating material Asbestos Loosely packed Asbestos-cement boards Sheets Balsam wool, 2.2 lb/ft3 Cardboard, corrugated Celotex Corkboard, 10 lb/ft3 Cork, regranulated Ground Fiber, insulating board Glass wool, 1.5 lb/ft3

Temperature

k,

ρ,

C,

α,



W/m  C

kg/m 3

kJ/kg  C

m2/s  107

470–570

0.816

3.3–4

1.88

2–5.3

0.7

22.6

1,600 2,000

0.84

5.2

3,000

0.84

9.2 9.8 7.9

2,000

0.96

5.4

2,300

0.96

5.8

0.88 0.84

8.2–6.8 3.4

0.84

4

C

45 0 100 20 51 32 .... 32 30 32 32 20 23

0.149 0.154 0.161 0.74 0.166 0.04 0.064 0.048 0.043 0.045 0.043 0.048 0.038

Structural and heat-resistance materials Asphalt 20 – 25 Brick Building brick, common 20 Face Carborundum brick 600 1,400 Chrom brick 200 550 900 Diatomaceous earth, 200 moulded and fired 870 500 Fireclay brick, burnt 2,426  F 800 1,100

0.69 1.32 18.5 11.1 2.32 2.47 1.99 0.24 0.31 1.04 1.07 1.09

Insulating material Fireclay brick, burnt 2,426  F 500 800 Cement, Portland Mortar 23 Concrete, cinder 23 Stone 1–2–4 mix 20 Glass, window 20 Corosilicate 30 – 75 Plaster, gypsum 20 Metal lath 20 Wood lath 20

1.28 1.37 0.29 1.16 0.76 1.37 0.78(ave) 1.09 0.48 0.47 0.28

35

160 45–120 150 240 24

0.74–0.76

1,500

1,900–2,300 2,700 2,200 1,440

(continued)

2.2 Theoretical Work. Based on Advanced Analysis

43

Table 2.3 (continued) Temperature Substance Stone Granite Limestone Marble Sandstone



C

100–300 40

k,

C,

ρ, 

3

W/m C

kg/m

1.73–3.98 1.26–1.33 2.07–2.94 1.83

2,640 2,500 2,500–2,700 2,160–2,300

α,

kJ/kg C

m2/s  107

0.82 0.9 0.8 0.71

8–18 5.6–5.9 10–11.9 11.2–11.9



Wood (across the grain) 30 0.055 140 Balsa 8.8 lb/ft 3 Cypress 30 0.097 460 Fir 23 0.11 420 2.72 0.96 Maple or oak 30 0.166 540 2.4 1.28 Yellow pine 23 0.147 640 2.8 0.82 White pine 30 0.112 430 Source: J.P. Holman, Heat Transfer, McGraw Hill, New York (1,966). Reprinted by permission of McGraw Hill, Inc

(b) Statistical survey A statistical survey is needed for the characteristic fire load density of similar buildings in question. The following points are recommended: (a) a minimum of five buildings (b) buildings investigated should have comparable use and similar size and contents (c) the buildings should be located in the same country in regions of similar socio-economic conditions (c) Characteristic fire loads Recommended values for characteristic fire load densities in various occupancy types are determined from data collected in European countries. They are given in Table 2.3. For the deterministic study it is recommended that the 80 % fractile be taken as the characteristic value for design purposes. If only the average value is available, the 80 % fractile may be estimated by 1.5 qki. In the case of protected fire loads (combustible material stored within a container such as a steel filing cabinet), the effective fire load may be less and will depend upon the fire temperature and duration, container integrity. The other indication is to include a factored *T, i.e. 1.2*T in the above assessment of combined loads. The be combination will then be: 1:2 D þ 1:6 L þ 0:5 Lr þ 1:2 T

(2.21)

Where thermal properties of the structural materials are known, an approximate relationship has been by the Council of Tall Buildings as pffiffiffiffiffiffiffiffiffiffiffiffi L ¼ tf Aw AT (2.22)

44

2 Fire Analysis: Methods of Design Analysis

where L ¼ total weight of fireload in kilograms tf ¼ fire resistance in minutes Aw ¼ windowed area in square metres Aт ¼ surface area of the enclosed walls and ceiling of the compartment or room containing the fire in square metres. Generally the fire grading of buildings has been directly related to fire load per unit floor area. Fire loads for domestic, office and hospital buildings are considered as low, for shops and department stores as medium and for storage buildings as high. For modern buildings, based on recent surveys, an average of 25 kg/m2 (5.75 lbf/ft2) is used. The logical conclusion would be to keep full dead weight and reduced live load due to occupancy and its reduction in level and full load of the fire: ðPF L þ Lr þ FL Þ þ l:2 D

(2.23)

where FL ¼ fire load. The BSI (British Standards Institute) in their draft code 96/540837 indicate that the fire load is influenced by duration and severity of fire and the fire load density is related to a number of different types of occupancy. The effective fire load density is expressed in MJ/m2 of the floor area as discussed above in other cases. It is suggested that it can also be expressed in terms of equivalent: weight of wood as a function of floor area. Several methods may be used to establish the effective fire load in a room or a compartment: (a) direct measurement/assessment (b) statistical survey (c) use of characteristic fire load density. (a) Direct measurement/assessment Where the fire loading in the direct measurement is unlikely to change over the design life of the building, the fire load density may be estimated from a knowledge of the weight and calorific values of the contents. Where t ¼ time (min) T ¼ fire temperature ( C) ¼ Tf and T0 ¼ initial temperature ( C). In North America an analytical expression exists for temperature—time curves in the form of an exponential function: T0 ¼ a1 ð1 ea4t Þ þ a2 ð1 ea5t Þ þ a3 ð1 ea6t Þ (2.24) pffiffiffiffiffiffi If R ¼ KAW H  , then the value of K in imperial units is 330; 5.5 to 6 kg/(minm5/2) for ¼At and 9 to l0 kg/(min/2) for small area At has been adopted in Denmark, Japan, the USA, the UK and the former USSR. As an example if the window height H* is 1.8 m, AW ¼ total opening ¼ 356 m2 and At ¼ 6,337 m2 the temperature opening factor F will be 0.0754. T

2.2 Theoretical Work. Based on Advanced Analysis

45

The temperature curves for the fire resistance design can be described by: T ¼ 250 ð10FÞ0:1=F 0:3 e ð1

e

3t

Þ þ 4ð1

F2t

½3ð1

0:6t

Þ   600 0:5 e 12t ފ þ C F e

(2.25)

where T ¼ the fire temperature ( C) t ¼ time (h) F ¼ opening factor (m 1/2 ) C ¼ constant based on the properties of the bounding material in fire ¼0 for heavy materials with ρ  1,600 kg/m3 ¼1 for light materials with ρ < 1,600 kg/m3 ρ ¼ density t ¼ time 

0:08 þ1 F

(2.26)

If t>

0:08 0:08 þ 1 assume t ¼ þ1 F F

If > 0.15 take F ¼ 0.15 for design purposes. Figures 2.3, 2.4, 2.5, and 2.6 show some Temperature -time curves for design purposes. The temperature course of fire during the decay period is given by: 

 t T ¼ 600  1 þ Tτ γ

(2.27)

T ¼ 20 if T < 20o C The International Standards Organisation (ISO) give the following expression for their standard curves: T  T0 ¼ 345 log10 ð8t þ 1Þ

(2.28)

where a1 ¼ 532 for  C, 957 for  F; a2 ¼ 186 for  C, 334 for  F; a3 ¼ 820 for  C, 1,476 for  F; a4 ¼ 0.6; a5 ¼ 3; a6 ¼ 12. This heat transfer equation is integrable and is used in the finite element analysis. A number of countries have been involved in fire-temperature-time analysis and research. Harmathy is the first researcher to have collected data from some countries and presented a comparative study graph for the temperature - time relation. Figure 2.7 shows the graph by Harmathy with data from a few other countries added.

46

2 Fire Analysis: Methods of Design Analysis

Fig. 2.3 Comparison between temperature—time curves obtained by solving a heat balance and those described by an analytical expression for ventilation-controlled fires in enclosures bounded by dominantly light materials (ρ  1,600 kg/m3)

Fig. 2.4 Comparison between temperature—time curves obtained by solving a heat balance and those described by an analytical expression for ventilation-controlled fires in enclosures bounded by dominantly light materials (ρ  1,600 kg/m3)

The last step is to see how the fire loads qc can be graphically related to the temperature-time curve. For design purposes, it is important for the load to be algebraically added to other loads. Pettersson has presented four graphs for temperature-time — qc relations, for

2.2 Theoretical Work. Based on Advanced Analysis

47

1200 1100 Temperature rise (T-T0)ºC

1000 900 800 700 600 500 400 300 200 100 0

30 60 90 120 150 180 210 240 270 300 330 360 Time (t), min

Fig. 2.5 Standard time-temperature curve

Fig. 2.6 Standard fire temperature—time relations used in various countries for testing of building elements. (Reproduced courtesy of the ASCE)

F¼

Awpffiffiffiffi pffiffiffiffi pffiffiffiffi pffiffiffiffi pffiffiffiffi H ¼ 0:02 m; 0:04 m; 0:08 m; and 0:12 m AT

He has taken heat capacity ϓcp ¼ 400 kcal/m3C, thermal conductivity λ ¼ 0.7 kcal/m h. The value of qc is in Mcal/m2. Figures 2.7 and 2.8 show such relationships for four different openings.

48

2 Fire Analysis: Methods of Design Analysis

Fig. 2.7 Temperature—time—qc curves for F-values after Pettersson

2400

1400

2200 1200

2000 1800 1600 1400

800

1200 1000

600

800 400

600 400

200 2

Q = 5 kg/m

0

1

10 kg/m

2

2

2

2

20 kg/m

3

4

30 kg/m

5

6

40 kg/m

7

Fig. 2.8 Temperature-time qc curve for F ¼ 0.05, British and American practice

2

200

Temperature, ºF

Temperature, ºC

F=0.05 1000

2.3 Material Properties

49

pffiffiffiffi British practice allows the opening factor F ¼ 0:05 m for heavy bounding materials. Figure 2.7 shows a simplified temperature-time-fire load qc curve for pffiffiffiffi the opening factor F ¼ 0:05 m . This curve is in full agreement with American practice. The standard temperature-time curve adopted by BS 476: Part 8, 1972 is shown in Fig. 2.5 and is compared with other countries in Fig. 2.6.

2.3

Material Properties

Now that the fire-time relation has been thoroughly reviewed, it is necessary to look at various materials and how they react to the fire environment. The most common materials are steel, concrete, timber and brick. The properties of these materials must be known prior to design of building structures.

2.3.1

Steel

The material properties that affect the temperature rise and distribution in a structural steel section are (a) thermal conductivity (b) specific heat. The thermal conductivity K is given by the USDA Agricultural Handbook No. 72 1987 as K ¼ 0:022T þ 48 for 0  T  900o C ¼ 28:2 for T > 900 C

(2.29)

where T ¼ temperature in steel ( C). Specific heat is the characteristic that describes the amount of heat input required to raise a unit mass of material a unit of temperature. A constant of 600 J/(kg.K) of the specific heat of steel for the entire temperature range is a reasonable approximation. Where thermal conductivity and specific heat are involved, thermal diffusivity of the material cannot be ignored, since it is a measure of how the heat is dissipated through the material and is the ratio of the thermal conductivity to the volumetric specific heat of the material. The relationship for thermal diffusivity ‘a’ is given by a ¼ K=ρc

(2.30)

50

2 Fire Analysis: Methods of Design Analysis

where K ¼ thermal conductivity ρ ¼ density c ¼ specific heat. In British practice c ¼ cs ¼ 0.52 kJ/(kg. C) ρ ¼ ρs 7,850 kg/m3 K ¼ Ks ¼ 50 W/(m   C) 9 At 20 C; the elastic limit ðYoung’s modulusÞ is : E20 ¼ 206 kN=mm2 > = Elastic limit at 20 C stress : fy20 ¼ 250 N=mm2 Ultimate strength : ft20 ¼ 450 N= mm2

Grade 43A > ; ðBS 4360Þ

From these basic values, the properties at other temperatures are as given below. Temperature range Elastic properties fyT f y20

20–300  C To 1 3000

ET E20

1

To 3000

300–700  C T o  300 0:9  500 0:9 

700–900  C T o  700 0:1  200

T o  300 ð300  900 CÞ 611

Thus it is shown that the modulus of elasticity of steel decreases with increasing temperature. The strength of hot-rolled steel depends on yield and tensile strength. Figures 2.9 and 2.10 show these relations for British and American practices respectively. Lie and Stanzak (712, 726, 750) give the yield strength of steel with temperature as Fy ¼ Fy0 ð1  0:78θ  1:89θ4 Þ

(2.31)

where θ ¼ ðTF  68Þ=1800 TF ¼ temperature of steel ð FÞ: The European Convention for Constructional Steelwork (757, 957) utilizes the same concept: 0 < TC  600 C

(2.32)

Fy ¼ Fy0 ðð108  TC =1000Þ=ðTC  440ÞÞ 600 < TC  1000 C

(2.33)

Fy ¼ Fy0 ð1 þ TC =ð767 InðTC =1750ÞÞÞ

2.3 Material Properties

51

1.0 0.9 0.8 0.7

fyT/fy20 or

ET E20

Modulus of elasticity (E)

0.6 0.5 0.4 0.3 (fy) steel strength

0.2 0.1 100

200 300 400 500 600

700 800 900 1000

Fig. 2.9 Relationship between steel material properties and Temperature in  C (British Practice)

Modulus of elasticity MPa x 103

200

150

100

50

0

200

400

600

Temperature,°C

Fig. 2.10 Modulus of elasticity of steel at elevated temperatures (American Practice)

where Fy ¼ yield stress at elevated temperature Fy0 ¼ yield stress at room temperature Tc ¼ temperatures of steel ( C). Figure 2.11 shows strength versus temperature as used in fire resistance. The American Iron and Steel Institute (727, 926–929) gives the thermal expansion α (temperatures up to 650  C) as: α ¼ ð11 þ 0:0062T Þ  106 where T ¼ steel temperature ( C).

52

2 Fire Analysis: Methods of Design Analysis Temperature,°F 100

Strength, % of initial

80

32

400

800

1200 Structural steel (yield)

cold-drawn wire or stand (ultimate)

60

40

Highstrength alloy bars (ultimate)

20

0

200

400

600

Temperature,°C

Fig. 2.11 Strength of some steels at high temperature

The Eurocode ENV 1993-l-2 has an approach originally specified by ECCS which calculates the ratio of the required strength at elevated temperatures to that at ambient in order to ensure that the structural steel components do not collapse. Hence, for beams, the elastic design should be based on: famax;θcr ¼ fay;200 C0

    K Wel qsd;el θ Wpl qfi;d

(2.34)

where f amax,θcr / f ay,20  C is the stress ratio, ĸ, is a factor allowing for the nonuniform temperature distribution, geometric imperfections and strength variations, θ is a factor, greater than unity, allowing for redistribution between the elastic ambient moment distribution and the plastic distribution under fire, Wpl / Wel is the ratio between the plastic and elastic section moduli (known as the shape factor), and qfi,d/qsd,el is the ratio of the design load (action) in the fire to the elastic design load (action). In order to design a beam plastically, the relationship is given as:   famax;θcr qsd ¼K fay;20o Co qfi;d where qfi,d/qsd ratio of the fire action to the ultimate action.

(2.35)

2.3 Material Properties

53

The Eurocode now gives two methods for steelwork design: (a) load-carrying capacity (b) limiting temperature criterion. (a) Load-carrying capacity Sd;F  Rd;FðtÞ

(2.36)

where Sd,F is the design value of the internal force to be resisted and Rd,F(t) is, the design resistance at time t and should be calculated in accordance with ENV 1992-1-1 except for the use of temperature-modified mechanical properties of steel. For tension members (clause 4.2.2 1) Rd;FðtÞ ¼ kamax; θ Rd ;

(2.37)

where kamax,θ is the normalized strength reduction at a temperature of θa and Rd is the ambient design resistance. Note that if θa is less than 550  C at any cross-section, the member may be assumed to be able to carry the fire-induced loading. Where the temperature in a member is non-uniform, then θa should be taken as the maximum value in the cross-section. For beams (Class 1 and 2, clause 4.2.2.2), under uniform temperature, the rules for tension and bending are the same except that Rd is the design bending resistance. Under non-uniform temperature distribution, the temperature distribution Rd,F(t) is: Rd;FðtÞ ¼

Rd;FðθÞ k

(2.38)

where ĸ is a factor allowing for temperature gradient and varying end conditions (Pettersson and Witteveen, 1979/1980) and Rd,F(θ) is the design resistance calculated from the maximum temperature in the cross-section: K: ¼ 1:0 exposed on 4 sides

¼ 0:7 exposed on 3 sides

)

¼ 0 85 exposed on 4 sides ¼ 0:60 exposed on 3 sides

simple beams

)

hyperstatic beams

For compression members (Class 1 or 2 section classification; clause 4.2.2.3) Rd;FðtÞ ¼

kmax;θ Rd 1:2

(2.39)

where Rd is the ambient design strength calculated using the buckling curve c of ENV 1993-1-1, and the 1.2 factor is an empirical correction factor.

54

2 Fire Analysis: Methods of Design Analysis 800 100

700 600

80

200° C

20° C

60

400

400° C 300

stress ksi

500

40

600° C 200 20 100

0

0.02

0.04

0.06

0.08

0.10

0 0.12

Strain

Fig. 2.12 Stress–strain curves for a mild steel (ASTM A36) at various temperatures

θa here is less than 510  C; for members other than tension members θa < 350 C (b) Limiting Temperature Criterion For a member to perform adequately in a fire, ENV 1993-1-2 requires that θa  θac;r

(2.40)

where θa ¼ actual temperature θac,r ¼ critical temperature which depends on degree of loading μ(0). The following formulae are suggested using plastic theory and strength reduction due to temperature: 2

θa;cr ¼ 78:38 In4

1 0:9674ðμð0Þ Þ3:833

!1=2 3 5 þ 482 1

(2.41)

The parameter μ(0) is the degree of utilization and is given by μð0Þ ¼

Sd; F Rd;Fð0Þ

(2.42)

The ASTM stress–strain curve of mild steel under various temperatures is show in Fig. 2.12.

2.3 Material Properties 32 3.0

55 400

800

1200

1600

1.6

Thermal Conductivity, w/m ºC

2.5 1.2 2.0 NORMAL WEIGHT 0.8

1.5

1.0 0.4 LIGHTWEIGHT 0.5

0

200

400

600

800

0

Temperature,°C

Fig. 2.13 Thermal conductivity of normal weight and lightweight concrete as a function of temperature

2.3.2

Concrete and Reinforcing Steel

Thermal properties of concrete vary with the type and quantity of the aggregate in the concrete. Bangash (958) provides a comprehensive treatment of this subject. The thermal conductivity of concrete is invariant with respect to the direction of heat flow and is dependent on the degree of crystallinity of aggregate. The higher the crystallinity, the higher the thermal conductivity, which decreases with temperature. Figure 2.13 shows the relationship between thermal conductivity and temperature for normal and lightweight concretes. It is difficult to establish a constant value for specific heat—a value of 1,170 J/(kg  C) (0.28 Btu/(lb  F)) is commonly chosen. Figures 2.14 and 2.15 show specific heat values for different concretes. The modulus of elasticity and strength of concrete have a direct bearing on the fire-resistance design of building structures. Again Bangash (958) has dealt with this subject in greater detail. British Standard 8,110 gives the following expression prior to any fire effects being involved. sffiffiffiffiffiffiffi fcu E ¼ 5:5 kN=mm2 γm The compressive strength of concrete is defined in terms of Grades C, i.e. C2.5 C5, C7.5, C10, C12.5, C15, C20, C25, C30, C35, C40, C45, C50, C55, C60. The numerical Figs. 2.17–2.19 are the compressive strength of concrete in N/mm2 ¼ MPa.

56

2 Fire Analysis: Methods of Design Analysis

Fig. 2.14 Ranges of volumetric specific heats of normal weight and lightweight concrete

Fig. 2.15 Specific heat for different types of concrete

The ultimate strength of concrete is f cu / ϓm ¼ 0.67 f cu ( f 0 c cylindrical strength ¼ 0.78 f cu). The steel reinforcement has a characteristic strength f y of 250 and 460 N/mm2 for mild steel and high-yield steel respectively. The ultimate strength of the reinforcement is f y / ϓm ¼ 0.87 f y. Since modulus of elasticity Ec is reduced with temperature Fig. 2.16 shows the relationship between Ec for three different aggregates and temperature.

2.3 Material Properties

57 Temperature,°F

32

800

400

1200

Modulus of elasticity, % of initial (E0)

100 carbonate (E0=3.4x105KN/m5) 6 (E0=5.0x10 psi)

80

60

40

lightweight (E0=1.3x105KN/m5) (E0=2.8x106psi) silliceous (E0=2.6x105KN/m5) (E0=5.5x106psi)

20

0

200

400

800

Temperature,°C

Fig. 2.16 Modulus of elasticity of concrete

Figures 2.17, 2.18, and 2.19 summarize the compressive strength of concretes. Reference is made to Bangash (958) for an extensive treatment of this aspect of research. The tensile strength of concrete is dealt with in detail by Bangash (958). Figure 2.20 shows the tensile strength of concrete at various temperatures. Creep of concrete is determined by various factors, the most important being the fire temperature on concrete. For an extensive study on creep, reference is made to Bangash 855, 939, 940) shows creep information for two stress levels, 22.5 % and 45 % of the concrete strength, and several concrete temperatures for a period of 3 h. The creep plays a significant role when the temperature exceeds 400  C (752  F). The Eurocode ENV 1992 Design for concrete structures has been dealt with in detail elsewhere in this text. The work is not repeated in this section. However, a design example based on ENV 1992-l-2 with BS 8110 will be considered.

2.3.3

Timber and Wood

Of all the materials used for construction, timber is unique by virtue of being entirely natural. It has many problems and one of them is that there is no control over its quality, which affects its strength. To overcome this, the stress grading method of strength classification has been devised. The four machine specified in BS 4978 are MG5, MS5, M50, M75. In the structural design of timber this code (Part I) gives guidance to the limit state design and later on in Part IV fire resistance

58

2 Fire Analysis: Methods of Design Analysis Temperature,°F 400

32

1200

800

1600

Compressive strength, % of initail

100 Stressed to 0.4 Fc

80

60

Unstressed residual

Unstressed

40

20 0

200

400

600

800

Temperature,°C

Fig. 2.17 Compressive strength of carbonate aggregate concrete at high temperatures and after cooling

Fig. 2.18 Natural recovery of the compressive strength of a normal-weight concrete, heated at various temperatures

2.3 Material Properties

59 Temperature,°F

Compressive strength, % of initial

32 100

400

800

1200

1600

Stressed to 0.4 fc 80

60

Unstressed residual

Unstressed

40

20

° Avg. initial fc= 26.91 MN/m2 (3900 psi) 0

200

400

600

800

Temperature,°C

Fig. 2.19 Compressive strength of siliceous aggregate concrete at high and after cooling

Fig. 2.20 Effect of temperature on split-cylinder tensile strength aggregate concrete

of timber structures is dealt with. The Eurocode (BS DD-ENV-1995: Part 1.1) defines strength class as follows (Figs. 2.21 and 2.22): Softwood Hardwood Glulam

C14, C16, C18, C22, C24, C27, C30, C35, C40 D30, D35, D40, D50, D60, D70 GL2O, GL24, GL28, GL32, GL36

60

2 Fire Analysis: Methods of Design Analysis

Fig. 2.21 Influence of cement—aggregate ratio and load conditions concrete strength Temperature,°F

32

200

400

600

800

1000

1200

500

600 700

140

Stength, % of origional

120

100

80 60

Jura limestone Basalt Rhine sand Crushed clinker

40

20

0

100

200

300

400

Temperature,°C

Fig. 2.22 Influence of aggregate on compressive strength of concrete at elevated temperatures

Tables 2.4 and 2.5 give some strengths of various species. They are important since they show initial stress conditions prior to subjecting them to fire temperature. The American Institute of Timber Construction (AITC) produced classified Table 2.3 for softwood, hardwood and glulam. They are discussed later on in much greater detail. Similarly, the Canadian Institute of Timber Construction

2.3 Material Properties

61

Table 2.4 Comparison between calculated results for the fire resistance of timber elements Beams Calculation method BS 5268 No arrises Arrises Stillera ENV 1995-1-2 Effective section Reduced strength

Columns

Mfi,Rd

Mfi,Sd

Nfi,Rd

Nfi,Sd

(kNm)

(kNm)

Mfi,Rd/Mfi,Sd

(kNm)

(kNm)

Nfi,Rd/Nfi,Sd

5.35 4.92 0.98

4.30 4.30 2.87

1.24 1.14 0.34

34.30 30.40 43.30

30.00 30.00 30.00

1.14 1.01 1.44

1.50 2.02

3.87 3.87

0.39 0.52

32.80 42.40

27.00 27.00

1.21 1.57

Table 2.5 Charring rates from ENV 1995-1-2 Charring rate (β0) Timber type Coniferous timber Glued laminated (ρ  350 kg/m3) Solid (ρ  350 kg/m3) Hardwood (ρ  350 kg/m3) Glued laminated and solid Hardwood (ρ  350 kg/m3) Glued laminated and solid

(mm/min) 0.7 0.8 0.7 0.5

(CITC) has produced detailed manuals for timber. A number of other countries have given specifications for timber. They are beyond the scope of this book. As far as fire effects are concerned, their contributions will be taken into consideration in the analysis and design of timber in fire. When the timber is exposed to fire, a char layer is formed at the exposed surface of its member. The fire resistance of the member depends on the extent of wood charring and the load-carrying capacity of the remaining uncharred portions of the timber elements. The char layer has no strength. Since the rate of charring varies with wood to wood or timber to timber species, it is vital to know the strength and deformation properties for the timber concerned, as a function of temperature and time duration. It then becomes easy to calculate the fire resistance When the wood is converted to char and gas, thermal degradation (pyrolysis) results in reduction in the wood density. The American Society of Testing These values are for timber with minimum dimensions of 35 mm. Where timber density are lower than those in the above Table 2.3, the charring rates may be pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi increased by ð350=ρÞ where ρ is the density of the timber. Material (ASTM) has given some useful graphs for density of the wood as a function of temperature (Fig. 2.23b) and density versus the rate of charring (Fig. 2.24). These graphs are given in ASTME 119. The charring rates of lumber bonded with phenolic adhesives are consistent with that of solid wood. In fact, the

62

2 Fire Analysis: Methods of Design Analysis

b 150

Present of initial density

125 100 75 50 25

0

100

200

300

400

500

600

700

800

900

1000

1100

Temperature,°C

Fig. 2.23 (a) Effect of temperature and stress level on creep. (b) Density of wood as a function of temperature

fire-retardant treatments in some cases may slightly increase the time and reduce flame spread. The thermal properties of wood are functions of density, moisture content, grain orientation and temperature. The oven-dry density of wood is between 160 and 1,000 kg/m3 but most species are in the range 300–700 kg/m3 (USDA Agricultural Handbook No. 72, 1987). Both density and moisture content affect the thermal conductivity of wood. The thermal conductivity is thus related to temperature (see Fig. 2.25).

2.3.4

Wood Mechanical Properties

Figures 2.25 and 2.26 for the relevant code indicate the mechanical properties such as modulus of elasticity, tensile and compressive strength. Gerhards (701) indicates that Etimber with moisture content 0–12 % decreases slowly with timber temperatures up to

2.3 Material Properties

63

Fig. 2.24 Rate of charring of Douglas fir as a function of its density (dry condition) for various moisture contents when exposed to ASTM standard fire

Thermal conductivity, w/m ºC

0.250

0.200

0.150

0.100

0

100

200

300

400

500

600

700

800

900 1000 1100

Temperature,°C

Fig. 2.25 Thermal conductivity of wood as a function of temperature

180–200  C. This is strength classes and grades, design loads and design deflections and stresses are well documented in BS 5268. It is important to know the rate of charring Table 2.6 shows the charring rate for various species of timber and they are divided into three categories on the basis of their density. The amount of charring undergone is assumed to be rounded off at corners and for the purpose of analysis, it is taken as a sector of a circle with radius r, the depth of charring. The additional area lost during

64

2 Fire Analysis: Methods of Design Analysis

Percentage of orginal modulus of elasticity

120 100

80

40

20

0

50

100

150

200

250

300

Temperature,°C

Fig. 2.26 Modulus of elasticity of wood as a function of temperature Table 2.6 Notional rates of charring Rate of charring (mm) Timber per mina (1) All sections listed and all timber defined 0.66–0.70 in BS 5628 except (2) and (3) (2) Western red cedar 0.83 (3) Hardwood (oak, utile Keruing, green 0.50 back teak, Jarrah) a The rates are only for periods between 15 and 90 min and section e25 mm

Charring (mm) 30 min 20.00

60 min 40.00

25.00 15.00

50.00 20.00

rounding is equal to 0.215r2. The area loss can be ignored if the uncharred or residual section is at least 50 mm thick and the exposure to fire does not exceed 30 min.

2.3.5

Design Summary Based on BS 5268

(a) Flexurol members Bending zxx ¼

M approx: σ m;g;par K7 K8

(2.43)

zxx ¼

M final σ m;g;par K3 K7 K8

(2.44)

The risk of buckling has to be checked. A reference is made to Table 2.6 of the code. K3, K7, K8 are constants

2.3 Material Properties

65

Deflection δp ¼ permissible deflection

¼ 0:003 span with actual deflection δa ¼ δm þ δv δm ðUdlÞ ¼

5 WL3 19::2M þ 384 EI AE

δa ðconcentrated point loadsÞ ¼

1 WL3 19::2M þ 48 EI AE

ð2:45Þ (2.46)

(2.47)

Emin is used for isolated or load sharing members: Υ a ¼ applied shear stress ¼

3 Fv 2 A

Υ adm ¼ permissible shear stress @@@g K3 K8 ðcheck shear in notch; if anyÞ

(2.48)

(2.49)

Bearing σc;a;perp ¼ applied bearing stress ¼

Fv bearing area

σc;a;perp ¼ permissible bearing stress ¼ σc;a;perp K3 K8 where Fv ¼ vertical external shear force M ¼ bending moment σ m,a,perp ¼ applied bending stress parallel to grain σ c,g,perp ¼ grade bending stress parallel to grain Υadm ¼ permissible shear stress parallel to grain A ¼ area W ¼ load K3 ¼ modification for duration of loading K7 ¼ modification factor for depth K8 ¼ load sharing factor. (b) Compression members (i) Determine the effective length or height Le (ii) Calculate slenderness ratio λ

(2.50) (2.51)

66

2 Fire Analysis: Methods of Design Analysis

λ¼

Le < 180 i; radius of gyration

(2.52)

Le < 52 least dimension

(2.53)

Emin =ðσc;g;par x K3 Þ

(2.54)

λ¼ (iii) Calculate

(iv) Obtain K12 modification grade using Table 2.9 of the code and using λ and (iii). (v) Calculate permissible compressive stress: σc;g;par ¼ σc;g;par x K3 x K12 x K8

(2.55)

or K8 is where needed permissible load ¼ σc,adm,par  area > applied load If the column is eccentrically loaded, the following additional steps are necessary: (vi) Calculate Me ¼ eccentric moment load  e. (vii) Obtain σm,adm,par ¼ permissible bending stress from Table 2.3 of Choice. (viii) Obtain. σm;adm;par ¼ permissible bending stress parallel to grain ¼ σm;g;par K3 K7 (ix)

σm;a;par ¼ applied bending stress Mg < σm;adm;par ¼ Z

(2.56)

(2.57)

(x) Check interaction formula σ m;a;par σ m;adm;par f1  ½1:5σ c;a;par K12 ðLe =iÞ

2.4

2

=π 2 E

min g

þ

σ c;a;par  1: σ c;adm;par

(2.58)

Masonry/Brick/Block

Building brick materials do not undergo substantial physicochemical changes on heating. The density ρ of the brick ranges from 1,660 to 2,270 kg/m3, depending on the raw material used on moulding and firing technique The porosity of the brick is from 19 to 36 %. The modulus of elasticity, E, of the brick is between 10  103 and

67

a

b

0.015

1.75

0.010

1.25 k(wm-1k-1)

ΔL / L0

2.4 Masonry/Brick/Block

0.005

0

0

0.75

0.25 200

400

600

800

1000

0

200

Temperature, °C

c

400

600

800

1000

Temperature, °C

3500

Cp(Jkg-1k-1)

2500

1500

500 0

200

400

600

800

1000

Temperature, °C

Fig. 2.27 Specific heat and thermal conductivity curves for bricks

20  l03 MPa. Its compressive strength varies from 10 to 110 MPa. Purkiss (959) takes the compressive strength as 50 MPa. At room temperature, the coefficient of thermal expansion a of brick is about 5.5  106/(mmK). Harmathy developed an empirical equation for the specific heat cρ of the medium density brick as cρ ¼ 710:87 þ 0:512T 

8:676  102 T2

(2.59)

At room temperature, 298 K (298 Kelvin) cρ ¼ 710:87 þ 0:512ð298Þ 

8:676  102 ð298Þ2

¼ 765:75J=ðkg  KÞ

(2.60)

Figure 2.27a shows the dilatometric curve. Figure 2.27b shows the thermal conductivity versus fire temperature of the brick wall. Figure 2.27c shows specific heat versus fire temperature of a brick wall. BS5629 Code of practice for use of masonry (1989) covers materials and components, unreinforced, reinforced and prestressed masonry. The materials used in the construction of masonry walls are bricks, blocks, mortar and wall ties.

68

2 Fire Analysis: Methods of Design Analysis

Bricks are walling units not exceeding 337.5 mm in length, 225 mm in width and 112.5 mm in height. ‘Specification for Clay Bricks’ (BS 3921) has a standard format for a clay brick of 225  112.5  75 mm. This includes allowance for a 10 mm mortar joint. The worksize of the actual brick is 215  102.5  65 mm. Concrete bricks (BS 6073: Part 2: Precast Concrete Masonry Units) may have the following dimensions: Length (mm) 290 215 190 190

Thickness (mm) 90 103 90 90

Height (mm) 90 65 90 65

Add 10 mm to all dimensions for mortar joints

Masonry walls can also be of blocks which are walling units that exceed the sizes specified for bricks. They are solid, hollow, cellular and insulating blocks and are of the following dimensions: Length (mm) 390 440 590

Height (mm) 190 215 215

Thickness (mm) Varies from 60 to 250

For general purpose masonry construction a 1:1:6 cement:lime:sand mortar will be sufficient. For high-strength load-bearing masonry a 1:¼:3 cement:lime:sand mortar is more appropriate. For reinforced masonry a mix not weaker than 1:½:4. cement:lime:sand is normally adopted. The characteristic loads are given below: (a) design and imposed loads (b) dead, imposed and wind loads (c) accidental damage (this may be considered for a fire situation). Ultimate design load ¼0Υ f  characteristic load

¼0Υ f ðdead loadÞ þ0Υ f ðimposed loadÞ ¼ l:5Gk þ l:6Qk

ð2:61Þ

The characteristic compressive strengths of masonry, f k, give the values of f k for bricks and block in conjunction with the designated mortar mix. The ultimate compressive strength is equal to f k/Υ m where Υ m partial safety factor given by BS 5628: Part 1. Vertically loaded walls and brick columns can fail by crushing or, if they are slender, by lateral buckling. The slenderness ratio (SR) is needed if the walls fail by buckling to crushing during a fire. SRðwallÞ ¼

effective height ðhef Þ effective length ðlef Þ or effective thickness ðtef Þ effective thickness ðtef Þ

(2.62)

2.5 Methods of Analysis and Design Table 2.7 Capacity factor β (BS 5628 Part I, Table 2.8) 1978

69 Eccentricity of top wall ex ¼ wall ¼ ex

SR ¼

0 6 8 10 12 14 16 18 20 22 24 26 27

up to 0.05 t

0.1 t

0.2 t

0.3 t

1.00 1.00 1.00 0.97 0.93 0.89 0.83 0.77 0.70 0.62 0.53 0.45 0.40

0.88 0.88 0.88 0.88 0.87 0.83 0.77 0.70 0.64 0.56 0.47 0.38 0.33

0.66 0.66 0.66 0.66 0.66 0.66 0.64 0.57 0.51 0.43 0.34 – –

0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.37 0.30 – – –

For a masonry column the slenderness ratio is: SR ¼

hef 6> 27 tef

(2.63)

SR ðwallÞ 6> 20 iftef < 90mm in two storeys If the load occurring on walls is eccentric and the load capacity is reduced by buckling, then the capacity reduction factor β which is dependent on ex/tf ratio must be applied. Table 2.7 gives the reduction factor β. The vertical design strength of the wall ¼

β f fk γm

(2.64)

βbt fk γm

(2.65)

The vertical deign strength of the column ¼ All symbols have previously been defined except b and tf: b ¼ width of column tf ¼ actual thickness of wall or leaf and column.

2.5

Methods of Analysis and Design

A number of numerical and analytical techniques are available along with computer packages for the analysis of building structures, with particular reference to the fire environment. Practically every country has a fire code. Analytical, empirical and design equations are available to assess the fire protection of structural components

70

2 Fire Analysis: Methods of Design Analysis

in major materials such as steel, concrete, timber and masonry. In this text, the author has classified these equations in the following manner. 1. Empirical and code analytical equations. 2. Limit state and plastic analysis. 3. Finite element analysis, finite difference analysis and boundary element analysis

2.5.1

Empirical and Code Analytical Equations

All calculations of fire resistance involve the determination of the temperatures, deformations of the structural components and their strength during exposure to fire The temperature distribution analysis is generally done by finite element, boundary element and finite difference methods since it is time-dependent and the calculation procedure is always complex. In order to simplify these complex procedures, numerical methods such as finite element method and high-speed computers are very convenient

2.5.2

Calculations of Fire Resistance of Steel Members

The temperature rise in a steel structure or its elements can be estimated using quasisteady-state equations by Malhotra (777) equations are derived from one-dimensional heat transfer equations. (a) Unprotected steel members. The equation for temperature rise during a short time period Δt is given by: ΔTs ¼

α ðTt cs ðW=DÞ

Ts Þ Δt

(2.66)

where ΔTs ¼ temperature rise in steel ( F/ C) α ¼ heat transfer for coefficient from exposure to steel member (Btu/(ft2. s) or W/m) D ¼ heated perimeter (ft or m) cs ¼ specific heat for steel (Btu/(lb   F)) or J/(kg   C) W ¼ weight of steel (lbf/ft or kg/m) ¯¯ or K) Tf ¼ fire temperature (R ¯¯ or K) Ts ¼ steel temperature (R Δt ¼ time step (s)

2.5 Methods of Analysis and Design

71

where α ¼ αt þ αc

(2.67)

αr ¼ radiative portion of the heat transfer. (Malhotra considers: ¼

1 S Ps ¼ W=D ms ρs As

(2.68)

where S = area, ms = mass.) αc ¼ convective portion of heat transfer

¼ 9:8  104 to 1:2  103 Btu=ðft2  sÞ Δt
> > > < load on one side concentrated > > > > : load on other side

gypsum plaster Pp ¼ 800 kg =m3 p ¼ 20% R ¼ load ratio ¼

dead load 40 kN imposed load 70 kN dead load 40 kN imposed load 70 kN λp ¼ 0:2W=ðm  CÞ

Mfi mMfi  Mc Mb

236 0:89  236 ¼ 0:443  532:5 378 θlim ðEurocode 3Þ ¼ 633o C If ¼



tfi;d 40ðθlim  Ap=Vi ¼ 140=mÞ

1:3

¼ 9:06  104

88

2 Fire Analysis: Methods of Design Analysis

ρ0 p ¼ effective density

¼ ρp ð1 þ 0:03pÞ ¼ 1280 kg=m3

 0 !  ρp Ap 2 μ ¼ λp If Vi ρa   1280 ð9:06Þ  10  4 ð140Þ2 ¼ 0:20 7850 ¼ 0:579

μð0Þ ¼

Sd;f KSd;f ¼ Rd;F Rd;F

μð0Þ ¼ 0:7  0:556 ¼ 0:389 θa;cr ¼ 78:38 In ¼ 624 C

(

1 0:967ðμ0 Þ3833

!

 1 1=2

)

þ 482

For a 90-min fire duration, temperature ¼ 607  C and the spray thickness should be 21 mm. Check Fw ¼

ð1 þ 4μÞ1=2  1 ð1 þ 4  0:389Þ1=2  1 ¼ ¼ 0:76 2μ 2  0:389

dp ¼ thickness ðmÞ ¼ λp If Fw

  AP Vi

¼ 0:2  9:06  104  0:76ð140Þ ¼ 0:0193 m ¼ 19:3mm:

Adopt 21 mm as proposed.

2.7

Calculations of Fire Resistance of Concrete Members

Introduction. Various approximate formulae have been developed for reinforced and prestressed concrete elements. The situation is not the same as for steel. Concrete properties vary not only with time but with the location in the section and its non-uniform character. More complicated factors become apparent when

2.7 Calculations of Fire Resistance of Concrete Members

89

fire resistance calculations are performed. The reinforcement and concrete can resist different temperatures within the same section. An average rise in temperature of 250  F (121  C) on unexposed surface is regarded in American practice as failure. Hence in this case the thermal fire resistance is the time elapsed to reach a temperature rise of 250  F (121  C). In a composite slab or beam, the failure due to fire is defined when steel temperature reaches 1,100  F (532  C) for reinforcement and 800  F (6.4.2) for prestressing steel.

2.7.1

American Code

Reinforced Concrete Columns Based on Lie and Allen (950) and Lie et al. (950–953), the minimum dimensions of the column are as given below: tmin ðinÞ ¼ 3:2 f ðR þ 1Þ

rectangular shape



tmin ðinÞ ¼ 3 2 f ðR þ 0:75Þ normal weight siliceous aggregate:



tmin ðinÞ ¼ 4:0 f ðR þ 1Þ

þ

(2.82) (2.83)

normal weight (2.84) carbonate aggregate concrete:

tmin ðinÞ ¼ 3:0 f ðR þ 1Þ

* Design conditions columns (2) and (4), Table 2.13. Design conditions column (3), Table 2.13. For round columns the diameter must not be less than 1 2 times the value determined by Eqs. (2.18), (2.19), (2.20), and (2.21). + Overdesign factor is the ratio of the calculated load-carrying capacity of the column to the column strength required to carry the specified loads determined in conformance with ACI 318-89 ‘Building Code Requirements for Reinforced Concrete’. k ¼ the effective length factor obtained from ACT 318-89 ‘Building Code Requirements for Reinforced Concrete’ p ¼ the area of vertical reinforcement in the column as a percentage of the column area h ¼ unsupported length of the column (ft) Cmin ¼ minimum cover (in.) to vertical reinforcements +

For R  3h For R > 3h

Cmin ¼ R or 2 in:; whichever is less Cmin ¼ 1=2 ðR 3Þ þ 2

90

2 Fire Analysis: Methods of Design Analysis

Table 2.13 Factor f Where kh is more than 12 ft but not more than 24 ft (1) Overdesign factor 1.00 1.25 1.50

2.7.2

(2) Where kh is not more than 12 ft 1.0 0.9 0.8

(3) t is not more than 12 in. and p s not more than 3 % 1.2 1.1 1.0

(4) All other cases 1.0 0.9 0.8

Concrete Slabs

Harmathy (940) and Lie and Harmathy (951) give the semi empirical formula for a monolithic concrete slab (Fig. 2.34a), for which the failure temperature rise is 250  F (121  C) at the unexposed surface, as: R1 ¼ 0:205

ðρcÞ1:2 L1:85 k0:65

where R1 ¼ fire resistance of slab based on heat transmission criterion (h) L ¼ thickness of slab (ft) ρ ¼ density of concrete (lb/ft3) c ¼ specific heat of concrete (Btu/lb  F) k ¼ thermal conductivity of concrete (Btu/(ft h  F)) If k ¼ 1:0 Btu=ðft  h FÞ normal concrete ¼ 0:45 Btu=ðft  h FÞ lightweight concrete c ¼ 0:20 Btu=ðlb : FÞ both types of concrete

(2.85)

R2 ¼ 0:03ρ1:2 L1:85 normal concrete

(2.86)

then

R1 ¼ 0:05ρ1:2 L1:85

lightweight concrete:

(2.87)

For a double-layer slab (Fig. 2.34b), for a failure temperature rise of 250  F R2 ¼ 0:75

ðρcÞ1:1 L11:6 k0:5

where R2 ¼ thermal fire resistance of the slab (h) L1 ¼ thickness of one layer of the slab (ft) ρ ¼ density of the concrete (lb/ft3) c ¼ specific heat of the concrete (Btu/(ft. h.  F)) k ¼ thermal conductivity of the concrete (Btu/(ft. h.  F))

(2.88)

2.7 Calculations of Fire Resistance of Concrete Members

91

Fig. 2.34 Different slab shapes

Fig. 2.35 Moments for a simple beam of slab under loads and fire. M due to loads only; Mnθ due to fire

Where no data are available for k and c, Equation (2.88) can be used, then R2 ¼ sρ1:1 L11:6

(2.89)

where s ¼ 0:13 ¼ 0:216

for normal concrete for lightweight concrete:

For a hollow concrete slab in dry conditions, for a temperature rise of 250  F (121  C), the value of R is given by Harmathy (940) as

92

2 Fire Analysis: Methods of Design Analysis

2

R þ 4 b =b 1

1

2 1=2

ðR1 Þ

þ1

ðb1 =b2 = ðR2 Þ1=2

32 5

(2.90)

where R ¼ thermal fire resistance of the hollow slab (h) R1 ¼ thermal fire resistance of the monolithic slab (h) R2 ¼ thermal fire resistance of the double-layer slab (h) b1 ¼ thickness of a web (ft) b2 ¼ distance between the centrelines of two webs (ft). At the locations of web and cavity this slab may be considered as monolithic and double-layer respectively. Lie (946) and Abrams and Gustaferro (921) have carried out theoretical and experimental studies on composite slabs (layers of normal and lightweight concrete); with a failure temperature of 250  F (121  C) at the unexposed face, the value R is given as: R ¼ 0:057

 2l2

 R ¼ 0:063 l2

6 l

dl dl



4 d þ l 2



normal concrete

(2.91)

lightweight concrete

(2.92)

where R ¼ fire resistance of slab (h) l ¼ slab thickness (in.) l d e l in. d ¼ base slab thickness (in.) In some cases the top layer on the base slab is different from normal or light weight concrete. The top layer is converted to an equivalent thickness of concrete and is added to the base slab in order to calculate fire resistance R given above in Eqs. (2.91) and (2.92). Table 2.14 gives a multiplying factor for that top layer which has to be used to obtain equivalent thickness.

2.7.3

Simply-Supported Unrestrained Beams and One-Way Slab

Assuming the underside of the slab is exposed to fire, the bottom of this slab will expand more than the top, resulting in its deflection. As the temperature increases, the tensile strength of concrete and steel will decrease. At the elevated temperature, when the strength of steel reaches its limit, flexural collapse will occur. The nominal moment strength will be constant through the length:

2.7 Calculations of Fire Resistance of Concrete Members

93

Table 2.14 Multiplying factor for equivalent thickness Material of top layer Type X gypsum wallboard Cellular concrete (density 25–35 1b/ft3) Vermiculite and perlite concrete (density 35 lb/ft3 or less) Gypsum sand plaster Portland cement with sand aggregate Terazzo

where

Base slab of normal-weight Concrete 3

Base slab of lightweight concrete 2¼

2

1½

1¾ 1¼ 1 1

1½ 1 ¾ ¾

 M n ¼ As f y d

a 2

(2.93)

As ¼ area of reinforcing steel f y ¼ yield stress of reinforcing steel d ¼ distance from centroid of reinforcing steel to extreme compressive fibre a ¼ depth of equivalent rectangular compressive stress block at ultimate load, is 0 0 equal to As fy =0:85fc b where fc ¼ cylinder compressive strength of concrete and b is width of slab. The normal BM is: ωL2 BM ¼ M ¼ (2.94) 8 where ω ¼ uniformly distributed load per unit length L ¼ span length. After the material strength has reduced, the retained moment capacity Mnθ is  aθ  Mnθ ¼ As fyθ d (2.95) 2

where subscript θ defines the effects of temperature. A and d are not affected but aθ is reduced. Assuming the imposed and dead loads are constant and the concrete strength at the top is not reduced, Fig. 2.35 shows the two moments at 0 h and at 2 h. Flexural failure occurs when Mnθ ¼ M. The equations indicate that the fire resistance depends on the load intensity, strengthtemperature characteristics and fire duration. In general the cover to reinforcement is a protection and in some cases other materials are added. Table 2.15 shows the cover in American practice.

94

2 Fire Analysis: Methods of Design Analysis

Table 2.15 Minimum cover: American practice Fire resistance (h) Base slab concrete type Reinforced concrete (all types) Prestressed-concrete, normal-weight concrete (dominantly siliceous aggregate) Normal-weight concrete (dominantly carbonate aggregate) Lightweight concrete Courtesy: ASCE

2.7.4

½ ¾ 1 1½ 2 0.65 0.65 0.8 0.83 1.1 0.8 1.0 1.25 1.65 2.0

3 4 1.65 2.2 2.5 3.0

0.8

0.85 1.1

1.45 1.75 2.25 2.65

0.8

0.8

1.25 1.55 2.0

0.9

2.35

Continuous Beams and Slabs

A statical indeterminacy can create additional reactions of the indeterminate supports due to fire. There will be an increase in the negative moments. These are due to differential heating which causes lifting of the supports at the ends, Hence L 2

x1 ¼ Mnθ

ωL2 ¼ 2

Mnθ ω rffiffiffiffiffiffiffiffiffiffi þ 2Mnθ ωL ωL2 2

x0 ¼ 2x1

(2.96)

(2.97) (2.98)

If the spans are symmetrical, then x1 ¼ L=2 : Mx1 ¼

ωL2 8

Mnθ

(2.99)

but þ Mx1 ¼ Mnθ

(2.100)

ωL2 8

(2.101)

Mnθ ¼

þ Mnθ

Other beams/slabs with different loadings and restraints Other beams/slabs under loads can similarly be examined in this chapter, various structures under plastic analysis are examined later on under a separate section. Example 1.8 American practice. A two-span continuous reinforced is to be analyzed and designed for reinforcement to provide 3-h fire resistance. Use the following data and the ACI Code 318:

2.7 Calculations of Fire Resistance of Concrete Members

95

slab thickness 150 mm (6 in.) positive reinforcement #4 Grade 60 bars @ 150 mm (6 in.) spacing concrete grade 28 Mn/m2 (4,000 lb/in.2) compressive strength concrete aggregate siliceous concrete cover 19 mm (0.75 in.) each span 4.88 m (16 ft) concrete density 2,400 kg/m3 (150 lb/ft3) superimposed load 1,914 kN/m2 (40 lbf/ft2) Material properties of steel and concrete in fires are given in Table 2.16. Thus increasing the reactions at the interior supports. There will be a redistribution of moments. Hence the negative moments increase, while the positive moments decrease. The negative moments will cause yielding of the reinforcement. It is vital that compressive failure in the negative moment region is avoided, i.e. reinforcement 0 should be small enough so that, based on the ACI (9.24), As fy =bdfc is 16 mm2 fy ¼ 275 N=mm2 Class 1 (Table 3.1 Part 1.1): d  72ε ¼ 72  0:9235 ¼ 66:492 t C  10ε ¼ 9:235 T From steel Tables: d ¼ 41  66:492 t C ¼ 6:25  9:235 T This is acceptable, and so the class 1 section is satisfactory.

165

166

2 Fire Analysis: Methods of Design Analysis

2.11.1 Lateral Torsional Buckling Resistance (Based on EC3) Mb;Rd ¼ bending moment at the major axis at the fire limit state due to buckling, i.e. buckling resistance moment ¼

βw fb wpl;s Υ M1

Bw ¼ 1.0 for class 1 wpl;s ¼ 1350  103 mm3 ¼ βzp Υ M1 ¼ 51:05 fb ¼ bending strength based on Table 5.21 EC-3, K ¼ 1.0: 

K C1

0:5

¼ 0:729 ðTable: 5:22 of EC  3Þ

Determination of f b : iLT ¼ iz

minor axis radius of gyration 39:9 ¼ ¼ 45:341 buckling parameter 0:88

aLT ¼ minor axis radius of gyration x torsional index x ðsteel TablesÞ ¼ 39.9  30.5 ¼ 1216.95 βw0:5



K C1

0:5

L 3000 ¼ 48:28 ¼ ð1:0Þ0:5 ð0:729Þ0:5  iLT 45:341 L 3000 ¼ 2:465 ¼ aLT 1216:95

The code of fb ¼ 251:45 N=mm2 . Hence Mb;Rd ¼

1:0  251:45  1350  103 ¼ 323:3 kNm 1:05  106

2.11

Multi-bay: Multi-storey Framed Buildings Subject to Fire Loading

167

> Mmax ¼ 251 kNm: The beam is used for normal temperature design.

2.11.2 Calculation for Critical Temperature for Beam 406  178  67 kg/m UB Beam loading at fire limit state: ðΥ GA GK þ ψ i;1 QK;1 Þ  floor area ¼ 4.75  6  3 ¼ 85.5 kN Mmax ¼

ð85:5  6Þ 128:25 kNm 4

K(x, θ) method (non-iterative method approximation): normal slenderness temperature dependent slenderness λL;T ¼ iLT ¼ λL;T;θ ¼ load level ¼ nfi ¼ Kz;θ 

45:31 ¼ 0:53 85:5

K Υ M;1 Mfi ¼ ¼ Mmax KL Υ M;fi Mb;Rd 1:05 128:25 ¼ 1:0 323:3

K;θ ¼ 0:38 Using Eurocode EC-3 Table 3.1 θamax ¼ Ts ¼ 600 C Similar calculations have been carried out for other zones and members. Malhotra (777) carried out experiments and suggests that unprotected steel members between temperatures of 550–600  C

168

2 Fire Analysis: Methods of Design Analysis

Columns Axial load=storey w ¼ b1  b2 ðb1  b2ðΥ G GK þ Υ Q;1 QK;1 Þ ¼ 6  6 ðl:35  3:0 þ 1:50  3:5Þ ¼ 334:8 kN

maximum load on single column line acting axially ¼ No. storeys  334.8 kN ¼ 4  334.8 ¼ 1,339.2 kN

2.11.3 Normal Design of Column Prior to Fire Limit State (Based on EC3 Parts 1.1 and 1.2) MP from the plastic analysis of the frame for the column: Mpmax ¼ 124 kNm computed zp ¼

124  106 450 909:09 mm3 451 cm3 275 Zp ðY  YÞ ¼ 463 cm3 A ¼ 92:9 cm2 d d ¼ ¼ 23:3 t tw D c ¼ 8:94 ¼ T tf

Initial section: 254  254  73 kg/m UC Grade 43; class I section: column fy;20 ¼ 275 N=mm2 ε¼



235 ¼ 275 fy;20

0:5

¼ 0:924

i ¼ radius of gyration ¼ 6.46 cm (from steel tables)

2.11

Multi-bay: Multi-storey Framed Buildings Subject to Fire Loading

Nb;Rd ¼

χβA AFy Υ MI

λ ¼ normalized slenderness ¼ λ ðβA Þ0:5 λ1 λ1 ¼

 0:5 E fy

βA ¼ 1:0 ðclass 4:3 sectionÞ Υ MI ¼ 1:05 λ ¼ slenderness ¼ ¼ λ¼

L buckling length ¼ c radius of gyration

5000 ¼ 77:34 64:6

77:34 ð1:0Þ0:5 ¼ 0:892 93:9  0:924 2

@@@ ¼ 0:5 ð1 þ αðλ  0:2Þ þ λ Þ ¼ 1:067 α (buckling curve C, Eurocode) ¼ 0.49. Hence χ¼ Nb;Rd ¼

1 ϕ þ ðϕ2 λ2 Þ

0:5

¼ 0:605

0:605  1:0  9290  275 ¼ 1472 kN 1:05  103

which is greater than P ¼ 1,339.2 kN. Adopt column section 254  254  73 kg/m UC. Fire resistance wf;i ¼ b1  b2

169

170

2 Fire Analysis: Methods of Design Analysis

Fire limit state (approximation method): wfi ¼ b1  b2 ðΥ GA Gk þ ψ 1;1 Qk;1 ¼ 6  6(1  3.0 + 0.5  3.5) ¼ 171 kN Pmax ¼ on column ¼ 4  wfi ¼ 4  171 ¼ 684 kN buckling length lft ¼ 0:7L λθmax ¼ λft



ky;θ kE;θ

0:5

¼ 0:7λfi ¼ 0:7  0:892 ¼ 0:6244

ϕθ ¼ 0:5½ð1 þ 0:49 ð0:6244  0:2Þ þ ð0:6244Þ2 1 χ fi ¼ 0:5 f0:7989 þ ½ð0:7989Þ2  ð0:6244Þ2 g ¼ 0:771

adaptation factor ¼ 1 χ fi Akxθ fy;20 1:0   0:771 9290 kx;θ ð275Þ ¼ 792:9 kN ¼ 1:0 103

Nb;fi;t:Rd ¼

kx;θ ¼ 0:364

θ ¼ Ts ¼ 620 C If the entire frame is enveloped by fire, the temperatures on beam and column at failure will be 600 and 620  C. The maximum 620  C is adopted. Where the fire is on one floor, such as floor II, all other components have been reanalysed and the following table gives the developed temperatures and temperatures they can sustain at failure:

Beams

Columns

BN and NC EM and MF GL and LH 1K and KJ BE, NM and CF EG, ML and FH GI, LK and HJ JA, KO and JD

Ts ¼ θ (developed) 50  C 600  C 80  C 30  C 50  C 620  C 30  C 20  C

θa ¼ capacity at failure temp: ¼T (580  C) (600  C) (750  C) (850  C) (600  C) buckling (620  C) criteria (620  C) (620  C)

2.12

2.12

Finite Element Analysis of Buildings on Fire

171

Finite Element Analysis of Buildings on Fire

2.12.1 Introduction Structural solutions of building response to fire have been demonstrated in earlier sections. A comprehensive analysis of fire response of buildings is needed for the following reasons 1. Evaluation of the temperature distribution history of buildings in fire environments. This involves: (a) heat transfer analysis of both linear and non-linear planar and axisymmetric heat conduction problems (b) type of analysis such as steady-state or transient with initial and boundary conditions using one-, two-, and three-dimensional elements. 2. Thermal properties and dimensional changes due to the intensity of fire. Types of changes characterizing degradation and the influence of both convective and radiative mechanisms. 3. Partial and complete damage of the overall building structure predicted by the finite element package, involving correlation and corroborative results. A number of finite element packages can offer such options. The best package should indicate the following major evaluations: (a) material behaviour and dimensional changes caused by temperature differentials; (b) non-linear direct stiffness evaluation coupled with time-step integration should form the basis of the program; (c) correct formulation of fire environment; (d) efficiency in producing complex results using a combination of a variety of elements where possible; (e) it should be interactive.

2.12.2 Basic Heat Transfer Analysis The governing equation for heat conduction is the heat balance equilibrium equation   00 @T T 00 fvg fLgT þ fLgT fqg ¼ q ρc @t where ρ ¼ density c ¼ specific heat T ¼ temperature (¼ T(x, y, z, t))

(2.181)

172

2 Fire Analysis: Methods of Design Analysis

t ¼ time T 00 ¼ transpose of the matrix ρc

@T ¼e @t

(2.182)

@T ¼ T_ @t

(2.183)

9 8 @ > > > > > > > @x > > > > = < @ > ¼ vector operator ¼ r fLg ¼ > > @y > > > > > > > > > ; : @ > @z

(2.184)

00

fLgT ¼ rT or ½½LŠT fqg ¼ r  fqg

8 9 > = < vx > fvg vy ¼ velocity vector for mass transport of heat > ; : > vz

(2.185)

fqg ¼ heat flux vector

q ¼ heat generation rate per unit volume The heat flux vector to the thermal gradients can be determined using Fourier’s Law: fqg ¼ -½K t rT 2

Kxx ½K t ¼ conductivity matrix ¼ 4 0 0

0 Kyy 0

3 0 0 5 Kzz t

(2.186)

Kxx ; Kyy ; Kzz ; ¼ conductivity in the element x; y and z directions; respectively: Combining Eqs. (2.182)and (2.186) and writing in a more familiar form:   @T @T @T @T þ vx þ vy þ vz pc @t @x @y @z       @ @T @ @T @ @T ¼qþ Kx Ky Kz þ þ @x @x @y @y @z @z

(2.187)

2.12

Finite Element Analysis of Buildings on Fire

173

Boundary conditions (a) Specified temperatures acting on surface 1 (S1): T  ¼ T1

(2.188)

(b) Specified heat flows acting on surface 2 (S2): fqgT fng ¼ -q

(2.189)

where fng ¼ unit outward normal vector q ¼ specified heat flow (c) Specified convection surfaces acting on surface 3 (S3) q ¼

hf ðTB

(2.190)

TÞ

where s hf ¼ film coefficient at temperature TB þT for the element 2 TB ¼ bulk temperature Ts ¼ temperature at the surface of the model

Equation (2.190) for q* can now be written as 00

fngT ½KŠt rT ¼ q ¼ hf ðTB

TÞ

(2.191)

Integrating Eq. (2.191)over the volume of the element and combining with the finite element formulation: ð 



@T þ fυgT f LgT ρcδT @t

vol

¼

ð

s2



δTq dðS2 Þ þ

ð

s3



δT hf ðTB

 þ fLg ðδTÞð½ DŠfLgTÞ dðvolÞ T

TÞd ðS3 Þ þ

ð

vol

vol ¼ volume of the element δT ¼ an allowable virtual temperature (¼ δT (x, y, z, t))

δTqd ðvolÞ

(2.192)

174

2 Fire Analysis: Methods of Design Analysis

2.12.3 Heat Flow In a fire situation, temperature T varies in both space and time. In the finite element formulation given in the Appendix, the following equations assume a major role. The temperature T is written as: 00

T ¼ fNgT fTe g

(2.193)

where T ¼ Tðx; y; z; tÞ ¼ temperature fNg ¼ fNðx; y; zÞg ¼ element shape functions fTe g ¼ fTe ðtÞg ¼ nodal temperature vector T 00 ¼ transpose: The time variation is written as: δT T_ ¼ ¼ fNgT fT_ e g δt

(2.194)

δT has the same form as T:

00

δT ¼ fδTe gT fNg

(2.195)

The combination {L}T is written as:

@@@T ¼ f LgT ½ BŠ fTe g 00

where [B] ¼ {L}{N}T

The variational Eq. (2.196) can now be written as:

(2.196)

2.12

Finite Element Analysis of Buildings on Fire T 00

ð

175

00

ρcfδTe g fNgfNgT ðT_ e ÞdðvolÞ vol ð 00 00 þ ρcfδTe gT fNgfυgT ½BŠfT_ e gdðvolÞ ðvol 00 00 þ fδTe gT ½BŠT ½DŠ½BŠfTe gdðvolÞ ðvol 00 ¼ fδTe gT fNgq dðS2 Þ s ð2 00 00 þ fδTe gT fNg hf ðTB fNgT fTe gÞ dðS3 Þ S ð3 00 þ fδTe gT fNgqdðvolÞ

(2.197)

vol

The quantities outside the matrix symbols, c and q in particular, do vary over the element. fTe g, fT_ e g and fδTe g are nodal quantities which do not vary and they are taken outside the integral. Equation (2.197) is to be multiplied by an arbitrary term 00 fδTe g and may be dropped where fδTe g, fδTe gT appears out of the rest. Equation (2.194) is reduced to: ρ

ð

vol

ð 00 00 cfNgfNgT dðvolÞfT_ e g þ ρ cfNg fυgT ½BŠ dðvolÞfTe g vol ð 00 ½BŠT ½DŠ½BŠ dðvolÞfTe g þ vol ð ð ¼ fNgq dðS2 Þ þ TB hf fNgdðS3 Þ S2 S3 ð ð 00 hf fNgfNgT fTe gdðS3 Þ þ qfNgdðvolÞ

(2.198)

vol

S3

Equation (2.198) now assumes the following form, involving element specific heat, total conductivity and heat flow matrices: ½Cte ŠfT_ e g þ ð½Ketm Š þ ½Ketb Š þ ½Ketc ŠÞ þ fTe g ¼ fQe g þ fQCe g þ fQge g where ½Cte Š ¼ ρ

ð

00

cfNgfNgT dðvolÞ vol

(2.199)

176

2 Fire Analysis: Methods of Design Analysis

element specific heat (thermal damping) matrix evaluated from enthalpy curve

Ketm ¼ ρ

ð

ð vol

00

cf N gfvgT ½ BŠ dðvolÞ 00

¼ρ ½ BŠT ½ DŠ½ BŠ dðvolÞ vol ð tc 00 hf fNgfNgT dðS3 Þ Ke ¼



tb

Ke

S3



 Qfe ¼



 Qce ¼



 Qge ¼

ð

fNgq dðS2 Þ

ð

TB hf f N gd ðS3 Þ

ð

qf N g dðvolÞ

S2

S2

vol

g

g

¼ total element conductivity matrix

¼ total element heat flow vector

Based on the Stefan-Boltzmann Law, the radiation heat flux from the surface, i.e. heat transfer rate, Q, between two surfaces ‘i’ and ‘j’ due to radiation is given as: Qi ¼ σεi Fij Ai ðTi4

Tj4 Þ

(2.200)

where Qi ¼ heat transfer rate from surface i σ ¼ Stefan—Boltzmann constant εi ¼ effective emissivity Fij ¼ view factor from surface to surface j Ai ¼ area of surface i Ti, Tj ¼ absolute temperature at surface i and surface j, respectively. If the surface considered is small compared with the surrounding environment at uniform temperature Tj , the effective or resultant emissivity εi ¼ εs , the surface emissivity. The effective value of εi is calculated when radiation is between two infinitely long parallel planes as εi ¼

1 1 εi

þ ε1g

1

(2.201)

where εg ¼ gas or flame emissivity. The total heat flux at a boundary ¼ q þ Qi

convection and radiation:

(2.202)

2.13

Computer Subroutines

177

The shape functions and other parameters are given for elements in the Appendix. The heat flow equilibrium equation in matrix form given above can be solved by time integration. The critical time increment Δtcr is taken to be: Δtcr ¼

2 λmax

(2.203)

When λmax is the maximum eigenvalue and is given by :    1X K λmax  maxi ctij = Kiitb þ j f ij 2

(2.204)

The upper limit to the critical time increment is: Δtcr ¼



mini ctii =



Kiitb

 1X K þ j f ij 2

(2.205)

where ctii ¼ specific heat matrix given above Kiitb ¼ element conductivity matrix Kf ij ¼ stiffness matrix All these parameters are fully discussed in the preamble of this section on fire.

2.13

Computer Subroutines

Some important subroutines given in the Appendix are reproduced from TASEF-2, a two-dimensional FE program on temperature analysis of structures exposed to fire, linked with the program ISOPAR, the description of this 3D finite element analysis program (Appendix).

2.13.1 Applications (a) Concrete beams and columns. The program ISOPAR has been tested on beams and columns. Heat is transferred from three faces. The temperature rise and isotherms are examined. Figures 2.60 and 2.61 show a more rapid rise in beams than in slabs. The I-beam has a much higher temperature rise than do rectangular beams or square beams. The higher temperature exists in the central part of the I-beam. Figure 2.62a, b show isotherms for various RC columns. The finite element results shown indicate that inside of these columns the temperature rise is more rapid than that in beams of the same cross-section.

178

2 Fire Analysis: Methods of Design Analysis 4T36 250

750

T10-300 1000

Temperture, Ts(°C)

18T-40 (3 rows) 800 500

Beam exposure 1 hr 1 1/2 hr 2 hr 4 hr

600

400

200

0

20

40

60

80

100

120 130140150 160

Distance from face (mm)

Fig. 2.60 Temperature versus distance for T-beams Fig. 2.61 Temperature versus distance for reinforced concrete beams and slabs

(b) Steel and composite beams and columns. Figure 2.63a, b show isotherms for steel and composite sections. In the case of composite columns with embedded steel profiles, and due to reduction in strength and stiffness in the outer part of concrete portions with temperatures above 300  C, the stresses in steel are enhanced or augmented and early collapse occurs before the steel reaches

2.13

Computer Subroutines

179

Fig. 2.62 Isotherms for various reinforced concrete columns

temperatures up to 500  C, a critical temperature. The failure theory of concrete is chosen to be the Ottoson failure criterion in the three-dimensional finite element analysis. (c) Full-scale prototype building under fire using three-dimensional finite element analysis Two types of buildings have been examined; the description of each of them is given prior to the analysis. The following points are kept in mind when a building is on fire. (a) A finite element method in connection with a time-step integration is used to calculate the temperature distribution in any component of a building. (b) Knowing the temperature distribution, it is possible to determine the relations between loads and deflections of the building system. (c) The procedure takes into account the geometric effects, thermal material laws and material non-linearity. (d) Any frame composed of interconnected columns and beams is divided into discrete elements. In order to decide what type of element is used, it is necessary to take into account the heat balance between adjacent mesh elements. (e) At ambient temperature the fire resistance of composite concrete slabs with profiled steel sheets can, in the absence of a suitable flooring system, be simulated into the finite element program. Such composite slabs transmit tensile stresses due to positive bending moments. The temperature of the steel sheets will increase in fire, and material properties will decrease. At a certain temperature, dependent on load level and frame static system, the steel may no longer be able to transmit tensile force and, as a result, the slab fails for no load-bearing capacity. These facts include the failure associated with the insulation, if any (Fig. 2.64). (f) All research work indicates that static continuity of beams or columns has an explicitly favourable, increasing effect on the fire-resistance time of these

180

2 Fire Analysis: Methods of Design Analysis

a 1 hour

4 hours

1 hour

500 300 200

2 hour

600

100

800

400

200 200

100

400

200 400 700

600 700 800

600

400X400 4 hours

1000

800

300X300 6 hours

Z

600 100

400 200

Y

Y

100 200 400 600

800 1000

500X500

Z

100

211' 179' 120' 10.5cm

0' 225' 228' 230' 2.8cm

N=17 500KN

reversed bucking

on

N/edmN =1.0

500

flango web concrete core

40

50

elongation

80

time n fire action in min

Fig. 2.63 (continued)

cti

HE 200 B fy=348 MPa 300.300 f0= 28 MPa 4 0 12 fy= 470 MPa Nat / NP1 =0.52

fle

ISO Curve

de

horizontal column deformation history

temperature in °C

10.0m

6.0m

1000

120

defonnation in m

00

10

800

2.13

Computer Subroutines

181

Fig. 2.63 (a) Steel and composite beams and columns. (b) Isotherms for steel and composite sections (three-dimensional finite-element analysis)

182

2 Fire Analysis: Methods of Design Analysis

Fig. 2.64 Typical finite element mesh for the pyramid

structural elements. The global behaviour of real structures during fires, although fires remain localized through the use of building compartments, is important, since there is a probability of not inducing global collapse at an early stage of the fire. All structural components are assumed interconnected. (g) It is assumed no wind and snow loads occur simultaneously during fire. Generally, the global safety factor recommended must not exceed 1.9 for 100 min of fire, after which global equilibrium failure occurs due to structural mechanisms. The service loads, in that case, are to be increased by 1.9. (h) The same conditions are considered in composite construction for the local fire simulations.

2.14

Case Study for Global Analysis Based on Finite Element Method: Canary Wharf Building

2.14.1 Introduction to the Analysis The Canary Wharf tower shown in Fig. 2.65 is located in the East London docklands area. Figures 2.66 and 2.67 show particular features of this tower. The tower consists of a three-level substructure. Plant floor level is on the 2nd floor. The tower is a square of 58.5 m sides in plan, with its reentrant corners rising to 235.8 m above ground level. There is a total of 49 floors, 45 of which are allocated for offices. The total height at the tip is 245.8 m above ground level. The remaining floors are allocated for penthouses, mechanical plant and cooling towers. Figure 2.68 shows

2.14

Case Study for Global Analysis Based on Finite Element Method: Canary. . .

Fig. 2.65 Canary Wharf building Fig. 2.66 Diagrammatic elevation of tower

183

184

2 Fire Analysis: Methods of Design Analysis

Fig. 2.67 Typical low-rise floor framing plan

Fig. 2.68 Floor- to-floor height and structural details

floor-to-floor height and structural details. Typical floor height is 4.11 m, including an allowance of 140 mm for an access floor. Two setbacks all around are considered, one on the 45th floor of about 4 m and the other of 3.5 m at penthouse level. The perimeter framing consists of closely spaced columns and deep girders of the dimensions shown in Fig. 2.69. The wind-resisting system is located on the perimeter of the floors. In each tube, identical tree-like framing units exist. A floor system identical to that shown in Fig. 2.69. is used for all office floors. The interior framing of the service core takes only gravity loads. The lower portion of the substructure consists of concrete floors, columns, encased steel columns and walls. The building is assumed to have a fire somewhere in the uppermost levels.

2.14

Case Study for Global Analysis Based on Finite Element Method: Canary. . .

185

Fig. 2.69 Closely placed steel columns

2.14.2 Data structural steel: Grade 50 for perimeter tube, others Grade 43 maximum column plate: 150 mm composite deck: 60 mm acting with 465 mm deep floor beams at 3 m on centre spanning from the core to the perimeter tube office floor area: 32.51  29 m with spans 14.23 and 12.17 m total gravity load on foundation: 2,664  103 kN Figure 2.70 shows the finite element mesh scheme of the entire building. The steel sections are three-noded isoparametric elements; each node has a two-degrees of freedom system. All concrete elements are represented by four-noded brick elements. A reference is made to the Appendix for steel and concrete failure criteria. Based on tables given earlier, the fire resistance time is taken to be 35 min. The following data for the elements are taken into consideration: Steel—350 000 elements Concrete—290 000 elements Others—15 000 elements According to the temperature rise (500–600  C), this column when fully loaded will collapse after About 85 min

186

2 Fire Analysis: Methods of Design Analysis

Fig. 2.70 Finite element mesh scheme for the Canary Wharf building (with-out canopy)

D or Pi ¼ 2ða þ bÞ ¼ 2ð205:2 þ 209:2Þ ¼ 828:8 mm ¼ 0:8288 m di 0:025 ¼ 0:17 ¼ ki 0:15 Δt ¼

D or Pi 0:8288 ¼ ¼ 109 As 76  104

25000 ¼ 229 Sec 109

As ¼ 76  104 m2

Δt ¼ 4 min as time interval ΔTs ¼

Pi Tf  Ts cs ρs ki   Δtð60Þ As c s ρ s c s ρs þ c i ρ i d i P i di ZAs

¼ 2

6 4

109  4  60ðTf  Ts Þ 520  7850 3

  7 0:15 1095 0:025 520  7850 þ 1200  300  0:025  2 520  7850

¼ 0:064ðTf  Ts Þð0:8Þð6Þ ¼ 0:0307ðTf  Ts Þ ΔTs ¼ 0:0307ð330  20Þ ¼ 9:5 C 10 C Hence Ts ¼ 20 þ 10 ¼ 30 C Check pi ¼ 109 ignoring thermal capacity of the insulation As

8 di ¼ 0:025m > > < ki ¼ 0:15 W=mðm  CÞ insulation properties > ci ¼ 1200 J=ðkg  CÞ > : ρi ¼ 25000 Δtu D orPs =Az Tf ¼ initial furnace temperature ¼ 330 C for 1 min based on ISO standard Tf ¼ 345 logð8t þ 1Þ þ T0 T0 or Ts ¼ ambient or initial temperature 20  C at zero time. European practice Column size 254  254  60 kg/m D 1:636 ¼ 77:17 m Ps or ¼ As 21:2  101 25000 ¼ 324 s Δtu 77:17 Adopt Δt ¼ 300 s ð5 minÞ αð300Þð77:17Þ ðTf  Ts Þ ¼ 0:00596 or ðTf  Ts Þ ΔTs ¼ 520  7850 Ts ¼ temperature rise ð CÞ Tf ¼ 345 log10 ð0:133  t þ 1Þ þ T036:80 ¼ 113:20 Δt t ¼ 5 min Tf ¼ 34 logð0:133  5 þ 1Þ þ 20 α ¼ αc þ αy h  þ2734 i  Tf þ273 4 x 0:5 W=m2 o C αy ¼ 5:77  Ts100 100 ðTf Ts Þ

(continued)

A column 203  203 60 kg/m is protected on all four sides by 25 mm insulation of vermiculite slabs. Using the following data and the relevant Eurocodes, calculate the time for protection such that for the furnace temperature Tf of 950  C, the temperature rise Ts on the assembly is no more than 340  C, which is the temperature for column collapse. As ¼ 76 cm2 depth of section ¼ 209:2 mm ( breadth of section ¼ 205:2 Cs ¼ 250 J=ðkg  CÞ steel properties ρs ¼ 7850 kg=m3 :

Table 2.29 Initial temperature distribution for columns—a typical example 2.14 Case Study for Global Analysis Based on Finite Element Method: Canary. . . 187

.. . 49.75 .. . 69.36 .. . 109.14 .. . 174.1

.. . 219.48 .. . 259.59 .. . 317.36 .. . 358.94

.. . 38.0 .. . 44.83 .. . 57.70 .. . 81.38

224.71

.. . 312.69

.. . 402.61

.. . 529.73

.. . 680.46

.. . 894.21

15.00

.. . 25.00

.. . 35.00

.. . 55.00

.. . 75.00

.. . 100.0

On the lines suggested in Example (above), the following table can be utilized Time (min) Tf Ts ð CÞ ΔTs ð CÞ Tr ð CÞ 0 330 310 10 .. .. .. .. . . . . 60 950 632 25

.. . 134.08

33.6

31.17

Ts ð CÞ 20 30 .. . 340

.. . 398.59

164.36

126.74

.. . 318.52

32.92

23.55

16.80

163.54

76.40

10.00

ΔTs ( C)

29.92

Tf – Ts ( C)

113.20

(W/(m2. C))

α ¼ αc + αr

Tf ( C)

t (min) 0.00 5.00

Table 2.29 (continued)

.. . 814.14

.. . 495.62

.. . 321.52

.. . 212.38

.. . 143.02

Ts ( C) 20 .. . 36.80 .. . 60.35 .. . 93.27

188 2 Fire Analysis: Methods of Design Analysis

2.14

Case Study for Global Analysis Based on Finite Element Method: Canary. . .

Fig. 2.71 Fire damage at particular floor levels for a portion of the building

Fig. 2.72 Fire scenario (typical example)

di ¼ 0:17 ki Ts at 60 min ¼ 360 C:

189

190

2 Fire Analysis: Methods of Design Analysis

Hence the protection time is around 60 min. The program ISOPAR covers material criteria give in Appendix and in the above mentioned paragraphs. Pseudo-fire is assumed to occur on the 25th floor and on the 45th floor simultaneously. The time assumed prior to the arrival of the fire fighters in 35 min. The black band on the finite element scheme is the area of the transfer floor shown in Fig. 2.70 and the details assumed are given in Fig. 2.66. The temperature developed in the concrete of the flooring system is 360  C (see Table 2.29) and a great deal of the yielding has occurred in the steel complex. The floor system has collapsed but no serious damage has occurred to the tubing system. Some additional floor shown by hatched zones in most areas on the 25th and 45th floor. Floors 24 and 23 have reached 55  C to 65  C in all areas. The pyramid is not affected but the temperature in most areas is 45  C. This example was computed in 75 min on a Cray 3. A typical floor and frame damage is shown in Fig. 2.71. The computer program FIRES-T3 (Fire Response of Structures—Thermal, Threedimensional)* in association with ISOPAR, which conducts the fire scenario at the floor level is demonstrated by Fig. 2.71. The fire scenario is illustrated in Fig. 2.72. The procedure is to excite fire at a specific floor and then produce a scenario and damage at floors above and below. The procedure is continued from the bottom floor/ basement to the canopy in successive stages by artificial generation of fire. A 1-h limit is established prior to the arrival of the fire ambulances. A typical damage zone of the floor and verticals is shown by blue lines and brown colors. In the elevations, the green color represents floor levels which show temperatures from 80 to 120  C and are still robust. No damage of serious consequence occurs. It appears that the structure has been designed for much worse conditions. Concrete elements in the floor receive cracking, as shown by blue lines along the walls. Again no bursting of reinforcements occurs elsewhere. Overall, conditions of the building for 1-h continuous fire affect very little. If the fire is extended for 4 h, the floor segments fall where the red rectangles are shown. The corresponding temperature rise to 550  C. Yellow zones indicate total damage in areas at 550  C but the steel has yielded and is not collapsed. The limiting time of 4 h is sufficient. The overall performance of this build-up is very satisfactory.

Chapter 3

Dynamic and Temperature Analysis Adopted in Fire Analysis and Design

3.1

Introduction

Numerical techniques has on finite element have been influenced in Chap. 2. Various solutions procedures are suggested with finite element analysis. Examples are used to justify this method of analysis.

3.2

Finite-Element Equations

A three-dimensional finite-element analysis is developed in which a provision has been made for time-dependent plasticity and rupturing in steel and cracking in materials such as concrete, etc. The influence of studs, lugs and connectors is included. Concrete steel liners and studs are represented by solid isoparametric elements, shell elements and line elements with or without bond linkages. To begin with, a displacement finite element is adopted. The displacement field within each element is defined in Fig. 3.1 as fxg ¼ ½NŠfxge ¼

n  X



(3.1)

ð½Bi Šfxi gÞ ¼ ½DŠfσg

(3.2)

i¼1

Ni ½IŠfxgi

The strains and stresses can then be expressed as, fEg ¼

Xn

i¼1

In order to maintain equilibrium with the element, a system of external nodal forces {F}C is applied which will reduce the virtual work (dW) to zero. In the general equilibrium equation, both Eqs. (3.1) and (3.2) are included. The final equation becomes M.Y.H. Bangash et al., Fire Engineering of Structures, DOI 10.1007/978-3-642-36154-8_3, © Springer-Verlag Berlin Heidelberg 2014

191

192

3 Dynamic and Temperature Analysis Adopted in Fire Analysis and Design z zc h hc =constant 8 z

h = +1

6

z

x

5 z

7

y h

z

h

6

4

3

1

z = +1

2 8 - noded solid element with line element

(i)

z x

19 3

13

10

7

z

1

11

12 9

z

h 16 15

z

14

2

y

17

18

20

8

line element

5

6

y

4 2

1

x

3

(ii)

6 5

7

z

4

x

z 1

22

y

h 8

32 global 21 co-ordinate

2

29

28

z 20

27

h

18

16

15

2

14

panel element (iii)

3

5 10 11 12

8

9 zy x 1

h

7 z

line element 5

5

3

2

panel element

Fig. 3.1 (continued)

3 4

7

4

2

8 6

1

1

19

10 9

11 12

26

25

23 24

17

13

3

30

31

4

3.2 Finite-Element Equations

193 8

7

Z 6

5

Y

a(i) GLOBAL CO-ORDINATE

1

18

19

3

4

X

2

17 line element

20 16

14 13

constant

12

11

15

Z

ISS

Y X constant

10

9 8

5

6

7

X

Z

4

2

1

Y

3

a(ii) 29

30

28

27

31 32

20 23

22

26

21 16 17

9 11

13

25 24 18 8

15

14

10

12

line element 19

6

constant

solid element constant

7

5

a(iii)

1

2

3

4

b

Fig. 3.1 (a) Isoparametric elements. (i) Parent element, three dimensional isoparametric derived element; (ii) solid element (20-noded); (iii) 32-noded solid element. (b) Line elements within the body of the solid isoparametric elements (ISS ¼ isoparametric solid element)

T

ðfdδge Þ fFge ¼ ðfdδge Þ

T

ð

vol

½BŠT fσgdV

(3.3)

In terms of the local coordinate (ξ,n,ζ) system, Eq. (3.3) is written as fFge ¼

ð

vol

½BŠT ½DŠfεgdξ; dn; dζ det½JŠfxge

(3.4)

194

3 Dynamic and Temperature Analysis Adopted in Fire Analysis and Design

The force–displacement relationship for each element is given by fFge ¼ ½KŠe fuge þ fFb ge þ fFs ge þ fFσ ge i þ fFε ge c

(3.5)

where the element stiffness matrix is. ½Kc Š ¼

ð

vol

½BŠT ½DŠ½BŠdV

(3.5a)

The nodal force due to the body force is ð

fFb Þe ¼

vol

½NŠT fGgdV

(3.5b)

The nodal force due to the surface force is ð

e

fFs g ¼

½NŠT fpgds

s

(3.5c)

The nodal force due to the initial stress is e

fPσ g i ¼

ð

vol

½BŠT fσ0 gdV

(3.5d)

The nodal force due to the initial strain is ð

e

fPε g i ¼

vol

½BŠT ½DŠfε0 gdV

(3.5e)

Equations (3.4) and (3.5) represent the relationships of the nodal loads to the stiffness and displacement of the structure. These equations now require modification to include the influence of the liner and its studs. The material compliance matrices [D] are given in Tables 3.1 and 3.2. The numerical values are given for various materials or their combinations in Tables 3.3, 3.4, 3.5 and 3.6. These values of the constitutive matrices are recommended in the absence of specific information. If the stiffness matrix [Kc] for typical elements is known from Eqs. (3.4) and (3.5) as: ½Kc Š ¼

ð

vol

½BŠT ½DŠ½BŠdvol

(3.6)

The composite stiffness matrix [KTOT], which includes the influence of liner and stud or any other material(s) in association, can be written as ½KTOT Š ¼ ½Kc Š þ ½Kℓ Š þ ½Ks Š

(3.7)

3.2 Finite-Element Equations

195

Table 3.1 Material compliance matrices [D] with constant Poisson’s ratio (a) [D] for steel components (isotropic) Constant Young’s modulus and Poisson’s ratio 0 1 v v v 0 B v 1 v v 0 B B B v v 1 v 0 E ½DŠ ¼ ð1þvÞð1 2vÞ B 1 2v B 0 0 0 B v B @ 0 0 0 0 0 0 0 0 (b) [D] for concrete: variable E and constant v

0 0 0 0 1 2v 2

0 0 0 0 0

0

1 2v 2

1 C C C C C C C C A

where [Kℓ] and [Ks] are the liner and stud or connector matrices. If the initial and total load vectors on the liner/stud assembly and others are [FT] and {RT], respectively, then Eq. (3.4) is rewritten as fFge þ fFT g

fRT g ¼ ½KTOT Šfxg

(3.8)

The displacement {x}* is different from {x} in Eq. (3.4), since it now includes values for both unknown displacements and restrained linear boundaries. Hence {x}* is defined in matrix form as

fxg x;y;z

9 8 xunx > > > > > > > xuny > > > > >  =  < xun xunz ¼ ¼ xb > > xbx > > > > > > x > > > ; : by > xbz

(3.9)

where xun and xb are displacement values in unrestrained or unknown conditions and restrained conditions. Similarly, the values for {FT) and {RT} can also be written as fFT g ¼



Fun Fb



fRT g ¼



Run



Rb

x;y;z

x;y;z

ð3:10Þ

The quantities for the liner corresponding to unknown displacements can be written as ½Kl Šfxun gx;y;z ¼ fFun gx;y;z

(3.11)

196

3 Dynamic and Temperature Analysis Adopted in Fire Analysis and Design

Table 3.2 (D) with variable Young’s modulus and Poisson’s ratio for concrete and other materials 0

0 3

E1 ðE Þ E00 B D11 ¼ B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B @

Ecr

0 2

Þ D12 ¼ vE1 E2 ðE E00

0 2

D22 ¼ E2 E3 ðEE00Þ

þEcr

þEcr

0 2

Þ D13 ¼ vE1 E3 ðE E00

þEcr

D14 ¼0

D15 ¼0

D61 ¼0

þEcr

D62 ¼0


E¼1 v12 v21 v13 v31

E1 v21 ¼ E2 v12

D24 ¼0

D25 ¼0

D63 ¼0

v23 v32 v12 v23 v31

D64 ¼0 D65 ¼0

v21 v13 v32

D55 ¼ G23

E3 v13 ¼ E1 v31 D66 ¼ G13 The values of G12, G23 and G13 are calculated in terms of the modulus of elasticity and Poisson’s ratio as follows 2 3 h i E1 E2 E1 5 1 1 4 E1  G12 ¼ 2 2ð1þv12 Þ þ 2ð1þv21 Þ ¼ 2 2ð1þv12 Þ þ 2

G23 ¼ G13 ¼

h

E2 1 2 2ð1þv23 Þ

h

E3 1 2 2ð1þv31 Þ

þ þ

E3 2ð1þv32 Þ

E1 2ð1þv13 Þ

i i

¼ ¼

2

E1 E2 þv12

1 4 E1 2 2ð1þv23 Þ

þ 

E1

1 4 E3 2 2ð1þv31 Þ

þ 

E3

2

For isotropic cases: E1 ¼ E2 ¼ E3 ¼ E

2

2

E2 E3 þv23

E3 E1 þv31

3

5 3

5

D26 ¼0

1 D14 ¼0 D15 ¼0 D16 ¼0 C C C D24 ¼0 D25 ¼0 D26 ¼0 C C C C D34 ¼0 D35 ¼0 D36 ¼0 C C C D44 D45 ¼0 D46 ¼0 C C C D54 ¼0 D55 D56 ¼0 A

D44 ¼ G12

E2 v32 ¼ E3 v23

1

C C C C E3 ðE0 Þ3 Ecr C D ¼0 D ¼0 D ¼0 D33 ¼ 34 35 36 C E00 C D44 ¼G12 D45 ¼0 D46 ¼0 C C D55 ¼G23 D56 ¼0 C C D66 ¼G31 C 0C 2 ½DŠ¼Ecr ¼v E1 E2 E3 E C E0 ¼ðE1 þE2 þE3 Þ=3 C C C C 3 C E00 ¼ðE0 Þ 2E1 E2 E3 v2 E0 v2 ðE1 E2 þE1 E3 þE2 E3 Þ C C C C G12 ¼E12 =2ð1þvÞ C C C C E12 ¼ðE1 þE2 Þ=2 C C C C G23 ¼E23 =2ð1þvÞ C C C C C E23 ¼ðE2 þE3 Þ=2 C C C C G31 ¼E31 =2ð1þvÞ C C A E31 ¼ðE3 þE1 Þ=2Þ 0 2

Þ D23 ¼ vE2 E3 ðE E00

ð1 v23 v32 Þ ðv12 þv12 v32 Þ ðv13 þv12 v23 Þ E1 D12 ¼ E2 D13 ¼ E3


B D11 ¼ E E E B B B D21 ¼ ðv21 þv23 v31 Þ E1 D22 ¼ ð1 v13 v31 Þ E2 D23 ¼ ðv23 þv13 v21 Þ E3 B


E E E B B B D ¼ ðv31 þv21 v32 Þ E D ¼ ðv32 þv12 v31 Þ E D ¼ ð1 v12 v21 Þ E 1 32 2 33 3 B 31


E E E B B D42 ¼0 D43 ¼0 D41 ¼0 B B @ D51 ¼0 D52 ¼0 D53 ¼0 0

D16 ¼0

v12 ¼ v13 ¼ v23 ¼ v21 ¼v31 ¼v32 ¼ v

D66

3.2 Finite-Element Equations

197

Table 3.3 Material properties of concrete, bovine, steel and composites (1) Concrete σ1 ¼ σ2 v13 ¼ v23 ¼ 0.2 for any value of σ3 up to 500 bar σ1 < σ2 v13 ¼ v23 σ1 ¼ 0 v13 ¼ 0.2 to 0.4 for any value of σ2 ¼ 0.4 for up to σ3 ¼ 500 bar for 80 C temperature, the above values are increased by 35–50 % Ec (kN/mm2) v

24 0.15–0.18

30 0.17–0.20

35 0.20–0.25

40 0.25–0.30

alternatively v ¼ 0:2 þ 0:6ðσ2 = σcu Þ4 þ 0:4ðσ1 =σcu Þ4 where σ1, σ2 and σ3 are the pressures/stresses along the three principle axes and σcu is an ultimate compressive stress of concrete. (2) Bovine material E1 ¼ 11 to 18 GPa; E2 ¼ 11 to 19 GPa; E3 ¼ 17 to 20 GPa G12 ¼ 3:6 to 7:22 GPa; G13 ¼ 3:28 to 8:65GPa; G23 ¼ 8:285 to 8:58 GPa v12 ¼ 0:285 to 0:58; v13 ¼ 0:119 to 0:31; v23 ¼ 0:142 to 0:31 v21 ¼ 0:305 to 0:58; v31 ¼ 0:315 to 0:46; v32 ¼ 0:283 to 0:46 (3) Steel E ¼ 200 GN=m2 ; v ¼ 0:3 to 0:33 (4) Composite Hot-pressed silicone nitride ðHPSNÞ versus tungsten carbide # # E ¼ 32O GPa E ¼ 32O GPa v ¼ 0:26 v ¼ 0:24 Carbon fibre (reinforced epoxy with 60 % fibres by volume) Tensile strength (σtu) Compressive strength Tensile Modulus (Et ) Compressive modulus (E’c) Failure strain in tension (εtu)% Failure strain in compression (εtu)%

Longitudinal 1,750 1,300 138 138 1.34 0.85

Mpa Mpa Gpa GPa

Transverse 60 0 9.1 9.1 0.8 2.9

Mpa Gpa GPa

The shear force t acting on studs or any other type is evaluated as fτg ¼ ½Kgs Š fxun gx;y;z

(3.12)

E ¼ 200 GN=m2 v ¼ 0:3 to 0:33

Steel indenter #

G12 ¼ 4:0 GN=m2 v12 ¼ 0:06

E2 ¼ 7:93 GN=m2

G12 ¼ G23 ¼ G13 ¼ 3:52 GN=m2 v12 ¼ 0:30 Polyurethane foam E ¼ 0:0431 GN=m2 ; G ¼ 0:017 GN=m2 ; v ¼ 0:267

E1 ¼ 120:7 GN=m2 ;

(4) Graphite/epoxy (Web stiffened foam sandwich panels with orthotropic facing and a number of 4 equally embedded stiffeners in a polyurethane (PU) core)

E (GN/m2) v

(3) Aluminium and FRPs

G11 ¼ 19 GN=m2 ; v11 ¼ 0:31

(2) Laminate: thornel 300/5,208 with fibres oriented (0,+60, 60) E2 ¼ 11:6 GN=m2 E1 ¼ 50 GN=m2 ;

(1) Plexiglass E ¼ 3:435 GN=m2 v ¼ 0:394

versus

Table 3.4 Material properties of additional composites

Aluminium 70 0.3

BFRPa 78.7 0.32

GFRPb 7.0 0.30

CFRPc 70 0.30

CFRPd 180 0.28

198 3 Dynamic and Temperature Analysis Adopted in Fire Analysis and Design

b

Quasi-isotropic Random mat d Unidirectional

a,c

p at plastic level

Ep2 ¼ 0:04 GN=m2 ;

E2 ¼ 21:4 GN=m2 ; v ¼ 0:208

(7) Other Materials Type CSM/polyester WR/Polyester Glass fibre/polyester UD Glass/polyester UD Kevlar/epoxide UD carbon/epoxide GY70/epoxy (celion with graphite fibre) MODMORE II/epoxy HMS/E (with graphite fibres) T300/E (thornel 300/epoxy with graphite fibres) GL/E (glass/epoxy) Carbon fibre (60 % volume) reinforced epoxy compound

(6) Layers of woven roving and chopped strand mat E ¼ 14:5 GN=m2 ; σyt ¼ 215 N=mm2 ; v ¼ 0:21

σyt ¼ 1:1 GN=m

2

Gp ¼ 0:008 GN=m ;

2

Ep1 ¼ 2:41 GN=m ;

2

E1 ¼ 219:8 GN=m2 ;

(5) Boron/epoxy composites

E2 (GN/m2) 8 15 25 10 8 10 7 9.6 12 14.9

E1 (GN/m2) 8 15 25 40 76 148 102 76.8 54.86 30.3

0.305 0.3 0.32

Longitudinal 140 140 1.8 1.3 0.3 E 1 (GN/m2) E c (GN/m2) ð tu(GN/m2) ð cu (GN/m2) V

v12 0.32 0.15 0.17 0.3 0.34 0.31 0.318 3.83 3.83 3.84

G (GN/m2) 3 4 4 4 3 4 4.14

Transverse 9.00 9.00 0.06 0.27 0.02

3.2 Finite-Element Equations 199

200

3 Dynamic and Temperature Analysis Adopted in Fire Analysis and Design

Table 3.5 Material properties for brick and stone masonry and soil/rock (1) Brick masonry Brick strength (MN/m2)

92 46 46 (2) Stone Masonry Stone Sandstone Limestone Whinstone Granite

fb ¼ 20–70 N/mm2 fb > 70N/mm2 Mortar Mortar mean cube strength (MN/m2) 1:¼:3 19.30 1:¼:3 13.70 1:1:6 3.94 Strength, fb (MN/m2) 112 31 167 130.6

Mortar Strength (MN/m2) 0.78 2.78 2.78 2.78

E ¼ 300fb 2,000 E ¼ 100 fb þ 12,750 Wall thickness Wall strength (mm) (MN/m2) 102.5 18.40 102.5 13.65 102.5 10.48

1:2:9 mix

Failure stress (MN/m2) 2.78 4.88 9.86 12.32

(3) Soil/rock

Fine sand Silty clay Silty sand Plastic clay Silt stone Limestone Aalluvial clay Clay (embankment fill) Saturate soil Jointed rock Sandstone

E  102 (MN/m2) 57.456 48.84 47.88 3.56 8.4 114.0 3.0 20.0 200.0 150.0 253.0

v 0.35 0.4 0.35 0.4 0.3 0.25 0.2 0.2 0.3 0.25 0.11

Density, p (Kg m2)

2,622 2,671 1,517

For high plasticity, the frictional angle ϕ0 c ¼ 18 For low plasticity, the frictional angle ϕ0 c ¼ 25 For rocks, ϕ0 c ranges between 20 and 30 For adhesion coefficient c is around 1 kN/m2

3.3

Steps for Dynamic Non-linear Analysis

The solutions of Eqs. (3.6), (3.7), (3.8), (3.9), (3.10), (3.11), and (3.12) require a special treatment such as under any increment of dynamic loading, stresses, strains and plasticity are obtained in steel, concrete and composites such as the liner and its anchorages and other similar materials. An additional effort is needed to evaluate the rupture of the steel or other material when cracks develop, especially in concrete beneath the liner or its anchorages. The dynamic coupled equations are needed to solve the impact/explosion problems and to assess the response history of the structure, using the time increment ðt. If [M] is

3.3 Steps for Dynamic Non-linear Analysis

201

Table 3.6 Material properties of timber Basic stresses and moduli Strength group Bending Tension (N/mm2 ) (N/mm2 ) Parallel to grain 37.5 22.5 S1 30 18 S2 S3 24 14.4 S4 18.7 11.2 15 9 S5 Dry grade stresses and moduli Grade/species Bending Tension (N/mm2) (N/mm2) Parallel to grain SS/Douglas fir 6.2 3.7 GS/Douglas fir 4.4 2.6 SS/Redwood Whitewood 7.5 4.5 GS/Corsican pine 3.3 3.2 GS/European pine 4.1 2.5

Compression to grain (N/mm2) parallel 24.4 20 17.9 13.5 13.3

Perpendicular 7.5 6 4.8 3.7 3

Compression to grain (N/mm2)

Emin (N/mm2) 13,800 11,900 10,400 9,200 7,800 Emin (N/mm2)

parrallel 6.6 3.6

perpendicular 2.4 2.1

7,000 6,000

7.9 6.8 3.2

2.1 1.8 1.4

7,000 5,000 4,500

Plywood: all stresses and moduli are multiplied by the following factors Tension Compression to grain (N/mm2) Grade/glued Bending (N/mm2) Laminated (N/mm2) Parallel to grain Parallel Perpendicular LA/4 1.85 1.85 1.15 1.33 LB/10 1.43 1.43 1.04 1.33 LB/20 or more 1.48 1.48 LC/10 0.98 0.98 0.92 1.33 1.11 LC/20 or more 1.11 permissible stresses 8 N/mm2 12 mm ply 5 N/mm2 thickness

Emin (N/mm2) 1 0.9 0.8

8,700 7,400

the mass and [C] and [K] are the damping and stiffness matrices, the equation of motion may be written in incremental form as ½MŠf€ x ðtÞg þ ½Cin Šf€ xðtÞg þ ½Kin ŠfδðtÞg ¼ fRðtÞg þ fF1 ðtÞg

(3.13)

where F1(t) is the time dependent load including impact/explosion load. If the load increment of F1(t) is ðPn(t), where n is the nth load increment, then Pn ðtÞ ¼ Pn 1 ðtÞ þ δPn ðtÞ

(3.13a)

and hence {R(t)} ¼ {ðPn(t)}, which is the residual time-dependent load vector.

202

3 Dynamic and Temperature Analysis Adopted in Fire Analysis and Design

The solution of Eq. (3.13) in terms of t + ðt for δt increment becomes _ þ^ xðt þ δtÞg þ ½Cin Šfxðt ½MŠf€ otÞg þ ½Kin ŠfδRðt þ δtÞg þ fδPðt þ δtÞg

(3.14)

where ‘in’ denotes initial effects by iteration using the stress approach; ðP(t + ðt) represents the non-linearity during the time increment δt and is determined by fσg ¼ ½DŠfεg

fε0 g þ fσo g

(3.15)

The constitutive law is used with the initial stress and constant stiffness approaches throughout the non-linear and the dynamic iteration. For the iteration: fxðt þ δtÞgi ¼ ½KinŠ 1 fRTOT ðt þ δ tÞgi

(3.16)

The strains are determined using fεðt þ δ tÞgi ¼ ½BŠfxðt þ δ tÞgi

(3.17)

where [B] is the strain displacement. The stresses are computed as fσðt þ δ tÞgi ¼ ½DŠfε ðt þ δtÞgi þ fσ0 ðt þ δ tÞgi

1

(3.18)

where {σ0(t + δt)} is the total initial stress at the end of each iteration. All calculations for stresses and strains are performed at the Gauss points of all elements. The initial stress vector is given by f fεðt þ δtÞgi

fσ0 ðt þ δtÞgi

½DŠfεðt þ δ tÞgi

(3.19)

Using the principle of virtual work, the change of equilibrium and nodal loads { δP(t + δt)}i is calculated as F1 ðt þ δtÞ ¼ fδPðt þ δtÞgiTQT þ1 ð þ1 ð þ1 ð 1

1

(3.20)

00

½BŠT fδσ 0 ðt þ δtÞgi dξdd ζ

1

σ0 ðtÞ ¼ fσ0 ðt þ δtgi ¼ 0 where dἑ, dɳ and dζ are the local co-ordinates and T00 is the transpose. The integration is performed numerically at the Gauss points. The effect load vector F1(t) is given by

3.3 Steps for Dynamic Non-linear Analysis

− σ − σi

isotropic hardening

C1

Stress

B′ B1

σ FTR δ −

SH = E s = 0

Es

A1

V-1

δ− σ

− σ1

C′

i

− σy − σi 1

203

(− σ i– − σ i –1)

− σv

from two similar (− σ i –1) σ y– −

Δ s A' b' c' and A' b1 c1

− σi-1

− σi

(− σ i –1) σ y– − FTR = − − ( σ – σ –1) i

Es

yield surface

i

− σ2

`e `e i −1

`e i

Strain

Fig. 3.2 Transitional factor and plastic point

F1 ðt þ δtÞ ¼ f δPðt þ δtÞgiTQT   ¼ δCðtÞin fxðt þ δtÞgi

 fxðtÞg   δKðtÞin fxðt þ δtÞgi ¼ ½δCðt þ δtފi fxðt þ δtÞgi ¼ ½δKðt þ δtފi fxðt þ δtÞgi

fxðtÞgi



(3.21)

The Von Mises criterion is used with the transitional factor f *TR to form the basis of the plastic state, such as shown in Fig. 3.2,  fTR ¼

σ y ðtÞ σðt þ δtÞi

σ y 1 ðtÞ σðt þ δtÞi

(3.22) 1

The elasto-plastic stress increment will be fδσi g ¼ ½DŠep fσðt þ δtÞgi 1 ð1

f  TR Þfδεg

(3.23)

If σ(t + δt)i < σy(t), it is an elastic limit and the process is repeated. The equivalent stress is calculated from the current stress state where stresses are drifted; they are corrected from the equivalent stress–strain curve. The values of [D]ep and [D]p are derived using plastic stress/strain increments. In the elasto-plastic stage, the time-dependent yield function is f (t). It is assumed that the strain or stress increment is normal to the plastic potential Q(σ,K). The plastic increment, for example, is given by δεðt þ δtÞp ¼ @Q=@σ ¼ λb where λ ¼ proportionality constant > 0 b  @Q=@σðt þ δtÞ

(3.24)

204

3 Dynamic and Temperature Analysis Adopted in Fire Analysis and Design

When f (t) ¼ Q δεðt þ δtÞp ¼ λa a ¼ @f =@σðt þ δtÞ therefore; df ¼ ½@f =@σðt þ δtŠ dσðt þ δtÞ þ ð@f =dKÞdK

(3.25)

If A is the hardening plastic parameter, then 1 A ¼ ð@f =dKÞdK λ An expression can easily be derived for the proportionality constant λ 00

λ¼

aT D δ ε ðt þ δtÞ ½A þ aT DbŠ

(3.26)

hence δε(t + δt)p ¼ bλ The value of the elasto-plastic matrix [D]ep is given by 00

½DŠep ¼ D

DbaT Db ½A þ aT 00 Db

(3.27)

The value of the plastic matrix [D]p is given by ½DŠp ¼



00

DbaT D A þ aT 00 Db



(3.28)

where [D] is the compliance matrix for the elastic case. The elasto-plastic stress increment is given by  fδσi gt ¼ ½DŠep fσi gt Y 1

 f tr fδεgt

(3.29)

For the sake of brevity, {ðo: 0 i} oˆo: 0 (t + ðٍt) for the ith point or increment and other symbols are as given above. The total value becomes 

fo: 0 i gTOT ¼ fo: 0i gYt þ ððo: 0 i Þt If {o: 0 i}t, < o: 0 yt it is an elastic point and {o: 0 i }t ¼ {o: 0 i}t. The process is repeated. Looking at the plastic point in the previous iteration, it is necessary to check for unloading when o0  o0 y, the unloading will bring about the total stress {o0 i}t {o0 i-1}t + {ðo: 0 i}t and set {o0 y}t ¼ {o0 i-1}t. Then loading at this point gives

3.3 Steps for Dynamic Non-linear Analysis

ððo: 0 i g ¼ ½DŠep fo0 i 1 gt fðἑ Þt

205

(3.31)

The total stress is then written as fo: 0 i gTOT ¼ fo0 i 1 gt fðo: 0 i g

(3.32)

Stresses are calculated using the elasto-plastic material matrix, which does not drift from the yield surfaces, as shown in Fig. 3.2. Stresses are corrected from the equivalent stress—strain curve by fo0 corr g ¼ fo0 i 1 gt þ K fðἑp Þt

(3.33)

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi nqffiffiffiffiffiffiffiffiffi o δ εpij δ εpij ¼ equivalent plastic strain increment. K is the where fðἑp gt ¼ t

strain-hardening parameter, such that ffðἑp gt ¼ ʎ. The equivalent stress is calculated from the current stress state, as shown below foi geq ¼ f fo0 i Þgt

(3.34)

the value of o0 corr =o0 is a factor

(3.35)

Therefore the correct stress state on the yield surface is given by foi g ¼ factor xfoi g

(3.36)

 . A reference is made to Fig. 3.2 for evaluating this factor as fTR

3.3.1

Buckling State and Slip of Layers for Composite Sections

Within the above stages, there can be a possibility of plastic buckling of the liner or any embedded anchors or layers. The buckling matrix is developed so that at appropriate stages the layer/liner/anchor system is checked against buckling. The plastic buckling matrix is given below 

 K i þ λc K i G F T ¼ 0

(3.37)

λc ¼ 1 þ Eps

(3.37a)

where Ki is the elasto-pla`stic stiffness matrix as a function of the current state of plastic deformation using the above steps and KG is the geometric stiffness matrix.

206

3 Dynamic and Temperature Analysis Adopted in Fire Analysis and Design

Table 3.8 T” transformation matrices [Twε] ¼

[Twσ] ¼

l21 l22 l23 2l1l2 2l2l3 2l1l3 l21 l22 l23 l1l2 l2l3 l1l3

m21 m22 m23 2m1m2 2m2m3 2m1m3 m21 m22 m23 m1m2 m2m3 m1m3

n21 n22 n23 2n1n2 2n2n3 2n1n3 n21 n22 n23 n1n2 n2n3 n1n3

l1m1 l2m2 l3m3 (l1m2 + (l2m3 + (l1m3 + 2l1m1 2l2m2 2l3m3 (l1m2 + (l2m3 + (l1m3 +

l2m1) l3m2) m1l3)

l2m1) l3m2) l3m1)

m1n1 m2n2 m3n3 (m1n2 + (m2n3 + (m1n3 + 2m1n1 2m2n2 2m3n3 (m1n2 + (m2n3 + (m1n3 +

m2n1) m2n3) m3n1)

n1m2) n2m3) m3n1)

l1n1 l2n2 l3n3 (l1n2 + (l2n3 + (l1n3 + 2l1n1 2l2n2 2l3n3 (l1n2 + (l2n3 + (l1n3 +

l2n1) l3n2) n1l3)

l2n1) l3n2) n1l3)

where EPS represents accuracy parameters. Where composite layers, liner and studs are involved, the incremental slips from the nodal displacements are assessed in the following manner: fΔSi gx;y;z ¼ ½T 0 Š fdði g

(3.38)

where Si is a slip at node i and T00 is the transformation matrix given in Table 3.8. The total slip at iteration is given without subscripts as fSiÞ ¼ fSi

1g

þ fSig

(3.39)

The strains are computed as fεi gt ¼ fE i 1 gt þ fðE i gt

(3.40)

The incremental stress {o0 B} between the studs and concrete or between any composite materials for the ith node can then be computed as fðo0 Bi gt ¼ ½Ks Šfo0 Bi 1 gtfðSi gt

(3.41)

fo0 Bi gTOT ¼ fo0 Bi 1 gt þ fðo0 Bi gt

(3.42)

The total stresses are

If [Si] > Smax the bond between the stud and the concrete or any composite materials is broken and the pull-out occurs, i.e. {o0 Bi} ¼ 0 and Smax has a value which is maximum. If [Si] < Smax the ‘value [Si] is calculated. The procedure is linked with the general finite element work discussed already in the non-linear dynamic cases for impact and explosion.

3.3 Steps for Dynamic Non-linear Analysis

3.3.2

207

Strain Rate Effects on the Elastic: Viscoplastic Relationship for Earth Materials Under Impact and Explosion

It is assumed that for each dynamic loading increment, the strain rate Ɛij can be expressed as the sum of the elastic and visco-plastic components: fdεij gt ¼ fdεij geþ fdεij gvp

(3.43)

Where the subscripts e and VP denote the elastic and viscoplastic respectively. The elastic strains are related to the stress rate o0 ij by fdεij ge ¼

1 1 XðdJ1 =dtÞδij þ XdSij =dt 9K 2G

(3.44)

where J1 ¼ deviatoric stress: first invariant Sij ¼ {ðij ⅓ J1 ðij}t ðij ¼ Knonecker delta K ¼ elastic bulk modulus G ¼ elastic shear modulus The shear modulus is expressed in terms of the invariant J0 2, where 1 J 02 ¼ Sij Sij 2 K¼ G¼

Ki  1 1 K1

Gi h 1 1 G1

(3.44a)

K1 e

G1 e

K 2 J1

0

G2 _J2

(3.44b)

i

(3.44c)

where Ki, K1, Gi, G1, K2 and G2 are material constants. The values of J0 2 and Ss are given below 0

J2 ¼

 1 2 Sx þ S2y þ S2z þ τ2xy þ τ2yz þ τ2zx is the second stress invariant 2 S x ¼ o0 x

o0 m

Sy ¼ o0 y

o0 m Sz ¼ o0 z

o0 m

(3.44d) (3.44e)

The linear values of K and G are K¼

E 3ð1

2vÞ

;G ¼

E 2ð1 þ vÞ

(3.44f)

208

3 Dynamic and Temperature Analysis Adopted in Fire Analysis and Design

Table 3.9 Bulk modulus model for earth materials      0 8 9 K þ 43 G K 23 G K 23 G 0 δσ     > > x B > > 4 2 > > K þ G K G 0 > > B δσ y > 3 3  >  > > < =B 4 G 0 K þ δσ z B 3 B B δτxy > > G 12 > > > >B > B δτyz > > > > > @ sym : ; δτzx t

0 0 0 0 G23

or in short {δσ} ¼ [D]{δϵ} where [D] is the required material matrix G12 ¼ G23 ¼ G13 ¼ G ¼ Ge

α loge

1 8 9 0 δ2x > > C > > 0 C> > δ2y > > > > > C> < = 0 C δ2 z C C 0 C> > δxy > > > δyz > > C> > > > 0 A> : ; δzx t G13

J2 for J2 > J2e J2e

G ¼ Ge for J2  J2e

Tables 3.1 and 3.2 are used for variable properties of E and v The components of the viscoplastic strain rate are calculated using the abovementioned plastic flow rule for rate-sensitive material.  fέIJ gVP ¼ ϓ f ðσ D =BÞ δσ D =δσ Dij Št

(3.45)

where ϓ ¼ viscosity parameter f (σD/B) ¼ f (σs β/B) σs ¼ static yield stress B ¼ material parameter β¼f ðe 1 Þvp ¼

1

( " #) ðd2KK ÞVp þ ð2e 1 Þ2vp 1   γ 3ð@δs =@J1 Þ2 þ 1 @δs =@J 0 2 2

(3.45a)

2

1=2 1 deij and is the square root of the second invariant of the 2 vp viscoplastic strain rate (3.45b)



Using this bulk modulus approach for soils, the time-dependent stress—strain relation is given in Table 3.9. With reference to rocks, the failure strength of the rock is defined in exactly the same way as described earlier; the values for E and v will vary. Nevertheless, the various alternative failure models given in Table 3.10 for rocks are related in terms of strain rates by
¼ σ dyn ¼ 1 þ c log ε_ M σs ε_ s

(3.46)

3.3 Steps for Dynamic Non-linear Analysis

209

Table 3.10 Numerical models for rocks (1) Sandstone τ ¼ 1538 þ σ tan φ (1) Where τ and o0 ¼ shear and compressive stresses, respectively φ ¼ 29 150 (2) Rupture of sandstone:  Mohr failure envelope τmax =σ cu ¼ 0:1 þ 0:76 σ m =σ cu Þ0:85 (2)

where o0 cu is the uni-axial compressive stress at rupture under pure shear o0 1 ¼ o0 3 (3) Realistic rock including friction αðσ 1 þ σ 2 þ σ 3 Þ þ ðσ 1 σ 2 Þ2 þ ðσ 2 σ 39 Þ2 þ ðσ 3 σ 1 Þ2 ¼ K  (3) where α ¼ Öð6 tan φÞ= Öð9 þ 12 tan φÞ > > > > = K  ¼ Öð6cÞ=Öð9 þ 12 tan φÞ can be obtained from Mohr envelope > φ ¼ angle of friction > > > ; c ¼ cohesion A generalized Mohr coulomb criterion is written as p σσtu (4) τ2 ¼ ½ ðn þ 1Þ 1Š σ @@@ tu where o0 ,τ ¼ normal stress and shear stress on the fractured plane σtu ¼ uni-axial tensile strength n ¼ brittleness σcu ¼ uni-axial compressive strength Equation (4) can be expressed in terms of o0 m, mean stress, and o0 s, the maximum shear stress, by h

σ s ¼ τ0 Ö 1

σs ¼ σtu ðσm = σtu Þ

where σm ¼ (σ₁ + σ₂ )/2; σs ¼ (σ₁ - σ₂ )/2 σ₁, σ₂ ¼ principle stresses (σ₁ > σ₂)

for σtu > σm0 > σm

σm

ðτ0 = 2 σ tu Þ

2

i

for σm0 < σm

ð5Þ

σm0 ¼ σtu τ20 =2σtu p τ0 ¼ ½ ðn þ 1Þ 1Š σtu ð6Þ The stress state is assessed for σm and σs from the failure surface as R ¼ σs =σsðcriticalÞ  1 (7) representing the failure condition. If σs ¼ σs(critical) equation of σs is satisfied.

where σdyn ¼ dynamic stress σs ¼ static stress ε ¼ strain rate (dynamic) εs ¼ strain rate (static) c ¼ constant The range of strain rate is ε ¼ 10 failure criterion can then be written as

5

s

1

up to 5  10

5

s 1. The dynamic

 σ 2cu X12 4τ20 X32 σ f ¼ τ 0 X3 þ σ for σ < 0 compression 4σ cu X1 τX3

(3.47)

210

3 Dynamic and Temperature Analysis Adopted in Fire Analysis and Design

σ 2f

¼

τ20 X32

τ2 X2 σ 2tu X22 þσ 0 3 σ tu X2



σ 2 for σ > 0 tension

(3.48)

 Aε1=3 3
1
2 Mþ M 40 25 3
7
2 Mþ M X2 ¼ 100 1000 1
1
2 þ M : X3 ¼ M 40 100

where X1 ¼

ð3:49Þ

τ0 octahedral shear stress under static loads In the case where the soil/rock is orthotropic, the values of G₁₂, G₂₃ and G₁₃ are given as indicated in Table 3.2. In the case of brick material, Khoo and Hendry relationships given below are used in the above failure models and strain rate simulations. The non-linear principle stress relationship (bi-axial) is given by σ1 =σcu ¼ 1 þ 2:91ðσ2 =σc Þ0:805

(3.50)

Where σ₁ ¼ major principle stress σ₂ ¼ minor principle stress σcu ¼ uni-axial compressive strength The brick-failure envelope with the mortar tri-axial strength curve is given by the polynomials σt =σtu ¼ 0:9968 σ3 =σcu ¼

2:0264ðσ=σcu Þ þ 1:2781ðσ=σcu Þ2 0:1620 þ 0:1126 ðσ1 =σcu Þ2

0:2487ðσ =σcu Þ2

0:0018 ðσ1 =σcu Þ3

(3.51) (3.52)

where σ/σcu ¼ ratio of compressive strength σt /σtu ¼ ratio of tensile strength σt ¼ ασ₃ where α ¼ 0.15 and 0.40 for mortars of 1:¼:3 and 1:1:6, respectively.

3.3.3

Finite Element of Concrete Modelling

A number of modelling methods are available for simulation into the finite element method on impact and explosion work, methods such as the endochronic, Ottoson

3.3 Steps for Dynamic Non-linear Analysis

211

Table 3.11 Cracks using endochronic theory Uncracked matrix 8 9 9 18 0 δσx þ δσpx > δσx > D11 D12 D13 0 0 0 > > > > > > > > > > δσy > > > B 0 0 0 C D21 D23 δσy þ δσpy > > > > > > > > C> B < < = = C B δσ 0 0 0 D z 33 δσz þ δσpz C B ¼ 0 p C B δγ D 0 0 β > > δτ þ δτxy > 44 > > > C> B > xy > > xy > > > @ p > δγyz > 0 A> β0 D55 > > > > > > > > : : δτyz þ δτyz ; ; p δγzx t βD66 δτzx þ δτzx t where D11 ¼ D22 ¼ D33 ¼ K þ 34 G β ¼ aggregate inter locking  ½ to ¾ D12 ¼ D13 ¼ D23 ¼ K 23 G E1 E2 D44 ¼ G12 ¼ 12 ½2ð1þv 12 Þ þ 2ð1þv21 ފ E2 ½2ð1þv23 Þ 1 E3 2 ½2ð1þv31 Þ

D55 ¼ G23 ¼ 12 D66 ¼ G13 ¼

3

E þ 2ð1þv 32 ފ 1

E þ 2ð1þv 13 ފ

and Blunt crack have been widely used. They are covered this section. The bulk modulus model of Table 3.9 is reviewed to include cracking with and without aggregate interlocking. On the basis of the endochronic concept, which is widely reported, the following equation applies

δσx;y;z



t

P 

 þ δ σ x;y;z ¼ ½D T Š 2x;y;z t

(3.53)

where the superscript p denotes stresses in the plastic case. Table 3.11 gives details of uncracked and cracked cases for Eq. (3.52). When cracks in three directions are open the concrete loses its stiffness, then 

DT ¼ ½0Š

( 3.54)

Stresses {oi}t are checked against the cracking criteria. For example, if there is crack normal to the X-direction, the concrete can no longer resist any tensile stress in that direction, then δσ x ¼ 0 Then D11 δεx þ D12 δεy þ D13 δεz ¼ δεp x δ εx ¼



δ σ xp D11

D12  δε D11 y

D13  δε D11 y

In a similar manner, examples for shear terms can be written as

(3.55)

212

3 Dynamic and Temperature Analysis Adopted in Fire Analysis and Design

average cracking direction θ n+1 θn Δα 2 r2 A 2 α2

θn

θGn

θGn θGn θn + 1

α1 r1 A1 Δα1 w= A = A Δα r cos α

θA = 1 3 (0n - 1 + 0 n + 0n +1) direction of crack

definition of symbols used in crack propagation

n

θE = Σ (0G – 0A1) crack error 1

aggregate

mortar

n

δt

t

crack plan

8n d

crack plane

d

8t δn < (1/2) - (d + d')

Qc nt

Qc nn

crack morphology

Fig. 3.3 Blunt crack propagation. r ¼ centroidal distance from the last cracked elements in the front element, α ¼ angle measured from the established crack to the line between the centroids, Gf ¼ energy release rate ¼ δE(Pia)/ δa ¼ ΔE(Pia)/δa, a ¼ cracked area, P ¼ loads  δτxy þ δτp xy ¼ βD44 ϓxy

 δτyz þ δτp yz ¼ βD55 ϓyz

 δτzx þ δτp zx ¼ βD66 ϓzx

3.3.4

(3.56)

Blunt Crack Band Propagation

The smeared crack concept, rather than the isolated sharp inter-element crack concept described above, is gaining ground. Here the element topology does change. The smeared crack band of a blunt front is that in which one can easily select cracks in any direction without paying a penalty, even if the crack direction is not truly known.

3.3 Steps for Dynamic Non-linear Analysis

213

Bazant et a1 and Bangash introduced the equivalent strength and energy variation which are utilized for crack propagation once it is initiated within the element The equivalent strength criterion is used for crack propagation by specifying an equivalent stress within the surrounding elements of an existing crack at which cracking should be propagated. The expression for the equivalent strength o0 eq is given (see Fig. 3.3) as

 σeq ¼ C EGf =W 1

σ0 2v 20 σσ 1

1 2

(3.57)

where C ¼ a constant dependent on the choice of elements E ¼ elastic modulus v ¼ Poisson’s ratio W ¼ A/ٍδa ¼ A/rcosα A ¼ area of the element at the front. The values of E and v are given in Tables 3.3, 3.4, 3.5 and 3.6 The band length is specified as a + Δa/2 In the initial state prior to cracking, the strain energy U0 is based on the principal stresses σ₂0 where σ₁0 is the largest tensile stress. After cracking, σ₁₁ becomes 0 and σ₂₁ ¼ 0, which is used for the current value of U₁. The change of strain energy δU ¼ U U₁ is equated to the crack length (Δa  Gf), where U is the total strain energy in a cracked body and δU is the energy released by the structure into the element which cracks. The crack direction within an arbitrary grid is given by 1 θA ¼ ðθn 3

1

þ θn þ θnþ1 Þ

(3.58)

where θA is the average crack direction, θn 1 and θn, are the cracking angles of the next to last cracked element, and θn 1 is the impending cracking angle of the element adjacent to the crack front. Since in the arbitrary grid the cracking direction is specified by the accumulated error of the cracked direction, the accumulated cracking error θE is given by θE ¼

n X i

ðθGi

θAi Þ

(3.59)

where n is the number of cracked elements and θG is the actual average crack propagation angle within each element. A better formulation by Gamborov and Karakoc, reported by Bangash, is given of the tangent shear modulus GCR whenever cracking is initiated: GCR ¼

σ cnt rða3 þa14 ½rŠ3 Þ k 2CR nn

(3.60)

214

3 Dynamic and Temperature Analysis Adopted in Fire Analysis and Design

or GCR ¼

 σ0 k 1 2CR nn



2ðP=Da Þ 2CR nn

1 2



where k¼

a3 þ 4a4 ½ΥŠ3

3a3 a44

ð1 þ a4 Υ4 Þ

(3.61)

2

and a3, a4 ¼ coefficients as a function of the standard cylindrical strength f ´c τo ¼ crack shear strength (ranging from 0.25 to 0.7f ´c) Da ¼ maximum aggregate size (up to 4 mm) Pc ¼ large percentage of crack asperities ϒ ¼ δt/δn δt ,δn ¼ crack displacements along the normal and tangential directions (Figs. 3.3 and 3.4) Curves have been plotted showing a decrease in the value of GCR when a crack opening linearly increases at increasing shear. The constitutive law in which a confinement stress within the rough crack model is given by σ cnn ¼

a1 a 2 

δt σ cnt q þ δ2t

(3.62)

δ2n

where o0 cnn ¼ interface normal stress o0 cnt ¼ interface shear stress a1,a2 ¼ constant (a1a2 ¼ 0.62) q ¼ a function of the crack opening; taken to be 0.25 For different types of crack dilatancy δn/o0 cnt (Fig. 3.3) the tangent shear modulus GCR is plotted against the ratio r of the crack displacement. The value of o0 cnt is given by o0

c nt

 ¼ τo 1

p

2p=Da εCR nn



r

a3 þ a4 ½rŠ3 1 þ a4 r 4

CR r ¼ γ CR ni =εmn

(3.63)

where p is the crack spacing and CR is cracked concrete, c εCR nn ¼ δn=p ¼ strain against σ nn

(3.64)

The σ CR nn values have been computed using points common to the curves of crack opening and constant confinement stress.

3.3 Steps for Dynamic Non-linear Analysis

215

rough crack model Daschnar σcnn f'cc = 0.80

14

0.60

12 σcnt (N/mm2)

0.40 0.30

10 0.20

8

δn = 0.01 mm 0.10 0.25 0.50 0.75 0.05 0.08 0.10 1.00 0.03 1.50

0.15

6 4 2 0 0.0

0.5

1.0

2.0

1.5

δt (mm)

σcnt σcnn (N/mm2)

Gc=11100N/mm2 (N/mm2)

12x103

6 t0 = 0.25 f'c σcnt

4

8

GCR (N/mm2)

σcnt 2 =13.8 N/mm σn

6.9 4

2

3.45 0 0.0 0.5

σcnn 0

1.0

1.5

y =δt /δn

3

δn (mm)

δn = 0.5 mm

6x10

1.0 0.5

GCR (N/mm2)

/3/ test 1/0.2/0.4

4

Da=30mm 19

2 0.0 0.0

0.5

1.0

1.5

8

0

2.0

0.0

δn (mm)

0.5

1.0

1.5

2.0

y =δv /δn

Fig. 3.4 Crack displacement versus tangent shear modulus

3.3.5

Ottoson Failure Model

The Ottoson four-parameter model has a smooth but convex surface with curved meridians determined by the constants a and b The analytical failure surface is defined by f ðI1 ; J2 ; JÞ ¼ a

J2 ðf 0 c Þ2

þλ

ÖJ2 I1 þb 0 f 0c fc

1¼0

where I1 ¼ o0 x þ o0 y þ o0 z ¼ the first invariant of the stress tensor

(3.65) (3.65a)

216

3 Dynamic and Temperature Analysis Adopted in Fire Analysis and Design

J2 ¼ the second invariant of the stress deviator tensor  1 ¼ S2 x þ S2 y þ S2 z þ τ2 xy þ τ2 yz þ τ2 zx 2

 p  J ¼ cos 3θ ¼ 1:5 3 J3 =ÖJ2

(3.65c)

J3 ¼ the third invariant of the stress deviator tensor ¼ Sx Sy Sz þ 2τxy τyz τzx

Sx τ2 yz

Sy τ2 xz

(3.65b)

Sz τ2 xy

(3.65d)

Sx ¼ σx I1/3 Sy ¼ σy I1/3 Sz ¼ σz I1/3 λ ¼ λ(cos3θ) > 0 a and b are constant λ ¼ K₁ cos(⅓ cos 1 (K2 cos3θ)) for cos3θ > 0 λ ¼ K₁ cos(π/3 ⅓ cos-1( K₂ cos3θ)) for cos3θ  0 K₁, K₂, a and b are material parameters (0  K2  1) f ´c ¼ uni-axial compressive cylinder strength for concrete 0.87o0 cu o0 t ¼ uni-axial tensile strength for concrete Table 3.12 lists some of the relevant parameters. The knowledge of the mechanical properties of concrete and the reinforcement (conventional and pre-stressing steel) at high strain rates is essential for rational application of materials in those constructions where impact and explosion loadings can be expected. The usual magnitude of the strain rate (dƐ/dt ¼ ἑ ) for all concrete structures is of the order of 5  105/s in the range of the ultimate load. For reinforcement, the range is between 105/s and 102/s. Table 3.13 gives relevant data. Figure 3.5 gives experimental stress - strain relationships for reinforcement for various strain rates. The theoretical expression in Eq. (3.46) was used.

3.4

Ice/Snow Impact

When floating ice sheets move under the influence of strong winds and currents, a sea going vehicle or a semi-submersible will be subject to an impact given by F1 ðtÞ ¼ F10 ðtÞ þ F0I ðtÞ

(3.66)

where F10(t) and Fi(t) are constant and fluctuating values of the ice impact force, respectively. The value of F10(t) is given by The following three failure states were represented: (1) Uni-axial compressive strength, f c (θ ¼ 60 ): Uni-axial tensile strength, o0 t (θ ¼ 0 ) ¼ Kf ´c.

3.4 Ice/Snow Impact

217

Table 3.12 Ottoson’s failure model for concrete O1 (O1 , O2 , O3) B

P

θ

Pc

Pt = tensile meridian Pc = compressive meridian

A

Pt

O3

O2

p/fc 13 12 11 10 9 8 7 6 5 4 3 2 1 -18 -16 -14 -12 -10

-8

-6

-4

-2

0

Comparison for the four-parameter model Four material parameters (k ¼ σt/σc) k A 0.08 1.8076 0.10 1.2759 0.12 0.9218

b 4.0962 3.1962 2.5969

K1 14.4863 11.7365 9.9110

Values of the function (k ¼ σt/σc) k λt 0.08 14.4925 0.1 11.7109 0.12 9.8720

λc 7.7834 6.5315 3.6979

λcλt 0.7378 0.5577 0.5772

p/f'c

failure criterion

7

compressive meridian

6 5 4 3

tensile meridian

2 1

-8 -7 -6 -5 -4 -3 -2 -1

1

S1(uni-axial compressive strength) ε/f'c

S3(uni-axial tensile strength) S2(bi-axial compressive strength)

Determination of material parameters (S1, S2, S3, S4 ¼ failure stresses)

K2 0.9914 0.9801 0.9647

218

3 Dynamic and Temperature Analysis Adopted in Fire Analysis and Design

Table 3.13 Strain rate for concrete and reinforcement. The relationship between the fracture strain Ɛf and the strain rate ἑ is given by 1

εf ¼ αε3 ð1Þ for plain concrete α ¼ 206; for reinforced concrete α ¼ 220 Another expression given by DELFT for plain concrete is 1

εf ¼ 100 þ 109ε3 (2) In equation (1), for say ἑ/s ¼ 35, the value of εf for reinforced concrete will be 740  10 6. For ἑ/s ¼ 30, the value of Ɛf for plain concrete will be 650  10 6. For fibre-reinforced concrete, the influence of the strain rate upon the tensile strength for concrete is given by σt ¼ α þ βloge ε (3) α ¼ 0 for no fibres, i.e. plain concrete o0 t ¼ 1.7 + 0.0364 loge ἑ for 3 % fibres o0 t ¼ 1.87 + 0.0424 loge ἑ For low, intermediate and high strain rate, DELFT gives an expression: o0 t ¼ α þ βN (4) where N is the number of fibres/reinforcements

α β

Low 3.32 1.85  10

3

Intermediate 4.87 2.85  10 3

High 3.49 6.3  10

3

For the fracture energy, Gf as stated in the endochronic theory will be modified as follows: Gf ¼ α þ βN Low Intermediate High α 12.72 22.90 29.200 β 0.12 0.18 0.211

(2) Bi-axial compressive strength, o0 1 ¼ o0 2 ¼ 1.16o0 c; o0 3 ¼ (θ ¼ 0 ) (test results of Kupfer) (3) The tri-axial state (є/f´c, ρ/f´c) ¼ ( 5, 4) on the compressive meridian (θ ¼ 60 ) F10 ðtÞ ¼ S1 S2 S3 f ðεÞTW  hσc ðor fc Þ

(3.67)

where S1 ¼ contact factor around the member during crushing S2 ¼ shape factor Sf of the impactor S3 ¼ temperature factor which is (1–0.012T)/(1–0.012Ts) (T: 0.5 C > T > 20 C)(Ts ¼ 10 C standard temperature) 0 o c ¼ compressive strength of ice measured at a strain rate of 5  10 4/s which is ἑ0 W ¼ transverse width of the member h ¼ ice sheet thickness 1

f ðεÞ ¼ ðε=ε0 Þγ ; ϕ ¼ a1 þ a2 ðh=WÞ2

(3.67a)

3.5 Impact due to Missiles, Impactors and Explosions: Contact Problem Solutions

219

Fig. 3.5 Stress—strain relationships for various strain rates

_ ε¼ x=4W

(3.67b)

where x˙ ¼ ice flow velocity ϒ ¼ empirical coefficient dependent on strain rate a1,a2 ¼ factors dependent on the ice thickness/diameter ratio of a member Depending on the type of impact (direct or angular) and the stiffeness of members and ice floes, the global equation of motion, (3.13), will be influenced by roll, pitch and yaw motions (θr,φp,Ψy) and surge, sway and heave motions (θs,φs,Ψh) respectively. Generally, the values of θr,φp,Ψy, θs,φs, and Ψh range as shown below: θr ¼ 0.012 to 0.04  10 3radians; θs ¼ 075 to 6 m φp ¼ 0.012 to 004  103 radians; φs ¼ 1.5 to 3m Ψy ¼ 0.012 to 0.04 radians; Ψh  θs

3.5

Impact due to Missiles, Impactors and Explosions: Contact Problem Solutions

Contact problems have been solved using Hallquist contact method. In addition, at the time of impact constraints are imposed on global equations such as (3.13), (3.13a), (3.14), (3.15), (3.16), (3.17), (3.18), (3.19), (3.20), and (3.21). Hallquist et al. developed a useful concept of master and slave nodes sliding on each other. As shown in Fig. 3.6, slave nodes are constrained to slide on master segments after

220

3 Dynamic and Temperature Analysis Adopted in Fire Analysis and Design

Fig. 3.6 Hallquist contact method (modified by Bangash)

impact occurs and must remain on a master segment until a tensile interface force develops. The Zone in which a slave segment exists is called a slave zone. A separation between the slave and the master line is known as void. The following basic principles apply at the interface: 1. Update the location of each slave node by finding its closest master node or the one on which it lies. 2. For each master segment, find out the first slave zone that overlaps. 3. Show the existence of the tensile interface force. Constraints are imposed on global equations by a transformation of the nodal displacement components of the slave nodes along the contact interface. Such a transformation of the displacement components of the slave nodes will eliminate their normal degrees of freedom and distribute their normal force components to the nearby master nodes. This is done using explicit time integration as described later under solution procedures. Thereafter impact and release conditions are imposed. The slave and master nodes are shown in Fig. 3.6. Hallquist et al. gave a useful demonstration of the identification of the ‘contact point’, which is the point on the master segment to the slave node ns and which finally becomes non-trivial. As shown in Fig. 3.6, when the master segment t is given the parametric representation and ˙t is the position vector drawn to the slave node ns, the contact point co-ordinate must satisfy the following equations: @ ðξ ;c ÞX½t @ξ c @ ðξ ;c ÞX½t @ c

ðξc ;c ފ ¼ 0 ðξc ;c ފ ¼ 0

(3.68)

where ξc, ηc are the co-ordinates on the master surface segment Si. Where penetration through the master segment Si occurs, the slave node ns (containing its contact point) can be identified using the interforce vector fs added, then:

3.6 High Explosions

221

fs ¼

lki ni

if l < 0

(3.69)

to the degrees-of-freedom corresponding to ns, and f i m ¼ Ni ðξc; ηc Þ f s

if l < 0

(3.70)

 where l ¼  ni
t’ r ðξc; ηc Þ < 0

(3.70a)

A unit normal  ni ¼  ni ðξc; ηc Þ;

t’i ¼  ni

ki ¼ fsi Ki A2i =Vi

n X j¼1

Nj ðF1 Þj ðtÞ

(3.70b)

(3.70c)

where (F1)j(t) ¼ impact at the jth node ki ¼ stiffness factor for mass segment Si Ki, Vi, Ai ¼ bulk modulus, volume and face area, respectively f si ¼ scale factor normally defaulted to 0.10 Ni ¼ ¼(1 + ξξi) (1 + ηηI) for a 4-node linear surface Bangash extended this useful analysis for others such as 8-noded and 12-noded elements. On the basis of this theory and owing to the non-availability of the original computer source, a new sub-program CONTACT was written in association with the program ISOPAR. CONTACT is in three-dimensions; the values of Ni for 8- and 12-noded elements are given in Table 3.14.

3.6

High Explosions

The pressure P is generally defined as a function of relative volume and internal energy. Assuming F1(t) is the final surface load, the pressure P must replace F1(t) in relevant equations by taking into consideration the surface volume on which it acts. All equations defining relevant detonation pressures P must first be evaluated. They are then first applied as stated, in Eqs. (3.13), (3.13a), (3.14), (3.15), (3.16), (3.17), (3.18), (3.19), (3.20), and (3.21). The cause of explosions can be nuclear (air burst or underground). The pressures, which are time-dependent, can then act as surface loads on the body of the element concerned or at nodal points of the element as concentrated loads derived on the basis of shape functions. It is essential to choose a proper time-aspect ratio as it will affect the type of solution procedure adopted. The interaction between the loads and the structure can be considered and the method shown ‘in Sect. 3.5 must be included.

Ni(ξ,n)

1 2

9 32 9 32

¼ (1 – n)(2ξ + n) ξ (1 – n) ¼ (1 – n)(2ξ – n) ½ (1 – n2) ¼ (1 + n)(2ξ + n) ξ (1 + n) ¼ (1 + n)(2ξ – n) ½ (1 – n2)

@Ni @ξ

Derivatives

10 9 ]

9 32 9 32

(1 – n) [2ξ – ξ2 (3ξ2 2ξ – 1)

Eight-noded membrane element

(1 – ξ) (1 – n) [ξ2 + n2 – (1 – ξ) (1 – ξ2) (1 – n)

Twelve-noded membrane element

Eight-noded membrane element 1 ¼(1 – ξ) (1 – n)( ξ n – 1) 2 ½(1 – ξ2) (1 – n) 3 ¼(1 + ξ) (1 – n)(ξ n – 1) 4 ½(1 – n2) (1 + ξ) 5 ¼(1 + ξ) (1 + n)(ξ + n – 1) 6 ½(1 – ξ2) (1 + n)2 7 ¼(1 – ξ) (1 + n)( ξ + n – 1) 8 ½(1 – n2) (1 ξ)

Nodei

Shape functions

Table 3.14 Ni for 8- and 12-noded elements

n2 + 10 9 ]

9 32

(1 – ξ) [2n 3n2 2 9 32 (1 – ξ) (1 – ξ )

¼(1 – ξ) (2n + ξ) ½(1 – ξ2) ¼(1 + ξ) (2n ξ) n(1 + ξ) ¼(1 + ξ) (2n + ξ) ½(1 – ξ2) ¼(1 – ξ) (2n ξ) n(1 – ξ)

@Ni @ξ

ξ2 +

10 9 ]

222 3 Dynamic and Temperature Analysis Adopted in Fire Analysis and Design

3 4 5 6 7 8 9 10 11 12

9 32 9 32 9 32 9 32 9 32 9 32 9 32 9 32 9 32 9 32

9 32 9 32 9 32 9 32 9 32 9 32 9 32 9 32

(1 – n) (1 2ξ –3ξ2) (1 – n) [2ξ + 3ξ2 + n2 – 10 9 ] (1 – n2) (1 – n) (1 – n2) (1 + n) (1 + n) [2ξ – 3ξ + n2 – 10 9 ] (1 + n) (1 – 2ξ – 3ξ2) (1 + n) (3ξ2 – 3ξ – 1) (1 + n) [2ξ – 3ξ – n2 + 10 9 ] 2 9 32 (1 + n) (1 – n ) 2 9 32 (1 – n) (1 – n )

Twelve-noded membrane element

(1 – n) (1 ξ2) (1 + ξ) (1 + ξ) (1 – n) [ξ2 + n2 – 10 9 ] (1 + ξ) (1 n2) (1 – n) (1 + ξ) (1 n2) (1 + n) (1 + ξ) (1 + n2) [ξ2 + n2 – 10 9 ] (1 + n) (1 ξ2) (1 + ξ) (1 + n) (1 ξ2) (1 – ξ) (1 – ξ) (1 + n2) [ξ2 + n2 – 10 9 ] 2 (1 – ξ) (1 n ) (1 + n) (1 – ξ) (1 n2) (1 – n) 9 32 9 32 9 32 9 32 9 32 9 32 9 32 9 32 9 32

(1 – ξ2) (1 + ξ) (1 – ξ) [2n – 3n2 ξ2 – (1 + ξ) (3n2 2n – 1) (1 + ξ) (1 2n – 3n2) (1 + ξ) [2n + 3n2 + ξ2 (1 – ξ2) (1 + ξ) (1 – ξ2) (1 – ξ) (1 – ξ) [2n + 3n2 + ξ2 (1 – ξ) (1 2n – 3n2) (1 – ξ) (3n2 2n – 1) 9 32

10 9 ]

10 9 ]

10 9 ]

3.6 High Explosions 223

224

3.7

3 Dynamic and Temperature Analysis Adopted in Fire Analysis and Design

Spectrum Analysis

Spectrum analysis is an extension of the mode frequency analysis, with both base and force excitation options. The response spectrum Table 3.14 is generally used and includes displacements, velocities and accelerations. The force excitation is, in general, used for explosions and missile aircraft impact. The masses are assumed to be close to the reaction points on the finite element mesh rather than the master degrees of freedom. The base and forced excitations are given below. For the base excitation for wave Υ ¼ f ΨgTR00 ½ MŠ fbg

(3.71)

Υ ¼ fΨgTR00 fF1 ðtÞg

(3.72)

For the impact excitation

where {Ψ}R ¼ the slave degree of freedom vector-mode M ¼ mass {b} ¼ unit vector of the excitation direction {F1(t)} ¼ an input force vector due to impact and explosion The values of {Ψ}R are normalized and the reduced displacement is calculated from the eigenvector by using a mode coefficient {M}. fxg i ¼ ½ M i Š fΨgi

(3.73)

where {x} reduced displacement vector and [M] ¼ mode coefficient and where (a) for velocity spectra : ½Mi Š ¼ ½Xsi Šfγi g=ωi

(3.74)

where x˙si ¼ spectral velocity for the ith mode; (b) for force spectra 

Mi Š ¼ ½Fsi Šfγg=ω2t

(3.75)

where Fsi ¼ spectral force for the ith mode; (c) caused by explosion P or impact F1(t) 

xsi Šfγi g=ω2i Mi Š ¼ ½€

where x¨si ¼ spectral acceleration for the ith mode; (d)

(3.76)

3.7 Spectrum Analysis

225



Mi Š ¼ ½xsi Šfγi g=ω2i

(3.77)

{x}i may be expanded to compute all the displacements, as in  1 fxΥ 0 gi ¼ Kγ0 γ0 Kγ0 γ fxi gR

(3.78)

where {xϒ0 }i ¼ slave degree of freedom vector of mode i [Kϒ 0 ϒ 0 ],[Kϒ 0 ϒ ] ¼ sub-matrix parts γγ0 ¼ retained and removed degrees of freedom The impact/explosion load is then equal to h   1 i Kγ0 γ Kγγ0 Kγ0 γ fxγ g ½Kγ㠊    ¼ fFγ g Kγγ0 Š ½Kγγ0 1 Fγ0 xg ¼ fF1 ðtÞg or ½KŠf€


¼ ½Kγ㠊 where ½KŠ fF
1 ðtÞg ¼ fFγ g



(3.79)

  1 Kγγ0 Kγ0 γ0 Kγ0 γ

(3.80)

 1  Kγγ0 Kγ0 γ0 Fγ 0

(3.81)

xg ¼ fxγ g f€

(3.82)

and [K] and {F¯1(t)} are generally known as the substructure stiffness matrix and the impact load vector, respectively. frequency ω assumes the form eiωt , then € x ¼ iωxs ; € xs ¼

ω2 xs ; fxg ¼ iωfxg and fxg ¼

ω2 fxg

(3.95)

Equation (3.94) can thus be written as 

½KŠ þ iω½CŠ

 ω2 ½MŠ fxg ¼ fJF gKn xs

(3.96)

For a given value of ω, a set of algebraic equations is solved using any numerical scheme. The displacement of a mass can be written as  fxg ¼ ½KŠ þ iω½CŠ

ω2 ½MŠ



1

fJF gKn xn

(3.97)

From displacements, accelerations, velocities, strains and stresses can be computed. The amplification function (AF) for each frequency x1/xs may be derived. Repeated solutions of Eq. (3.95) are necessary for a proper definition of this function. If the fast Fourier transform is used then AF must be tabulated at each frequency interval.

226

3 Dynamic and Temperature Analysis Adopted in Fire Analysis and Design

Table 3.15 The Runge-qc ¼ 330Fτ Kutta–Method  ð1Þ  xnþ1 ¼ xn þ 8tt þ 2f ð2Þ þ 2f ð3Þ þ f ð4Þ (a) 6 f ð1Þ ðxnÞ ðzÞ ðxnþ8t=2 ð1Þ Where f ¼ f ; f ¼ f f f ð3Þ ¼f ðxnþ8t=2 f ð2Þ f ð4Þ ¼ f ðxnÞ þ 8t f ð3Þ some computations are needed to calculate f (1) to f (4) f ¼ kx (b)

3.8

Additional Methods

3.8.1

Range–Kutta Method

It is an accurate method of time integration and is explicit in nature. Table 3.15 summarises this method. This method of higher order is a robust algorithm used to solve non-linear equations but may have problems which have discontinuously as the load increases strain localization which will be difficult to produce in numerical simulations. Non-linear equations have bi-furcation. The fault problem has bifurcation. The non-linear equation of stochastic elastoplasty is more suitable for finding the most unstable solution compared with the non-linear equation of deterministic elastoplasty in the coefficients change continuously.

3.8.1.1

Linear Implicit with θ Method Operators 8 9 9 8 < x€i = < x€iþ1 = x_iþ1 ¼ ½AŠ x_ i þ fLgðriþθ Þ ; : ; : xi xiþ1

where

riþθ

2

Fiþθ ; ¼ m

γβ ð1 þ γβÞ ½AŠ ¼ 4 Δt 2 Δt2 6 ð2 þ γβÞ

8 9 < β = Δt β fLg ¼ : Δt22 ; 6 β

1 Δt ðϕβÞ

1 2 ð2 þ ϕβÞ Δt 6 ð6 þ ϕβÞ

1 Δt2 ð 1 2Δt ð 1 6 ð6

3 ω2 Δt2 βÞ ω2 Δt2 βÞ 5 ω2 Δt2 βÞ

3.8 Additional Methods

227

β¼ γ¼

6 6θ þ 6ξωθ2 Δt þ ω2 θ3 Δt2

12ξωθΔt þ 6ξωθ2 Δt 6

6 þ 60

3ω2 θ2 Δt2 þ ω2 θ2 Δt2 ¼

3.8.1.2

ω2 Δt2 θ

2ξωΔ

Quadratic Implicit with θ Method Operators 9 9 8 8 x€i > x€iþ1 > > > > > > > = = < < x_i x_ i 1 ¼ ½AŠ þ fLgðriþθ Þ x > x > > > > > ; ; : iþ1 > : i > xiþ1 xi

where

riþθ ¼

2

γβ 6 1 ½AŠ ¼ 6 4 Δt ð8 þ 5γβ 12 Δt2 24 ð10 þ 3γβÞ β¼ γ¼ ρ¼

Fiþθ ; m

9 8 β > > > = < 0 > fLg ¼ 5Δt β > > > 122 > ; : Δt 8 β

ρβ 0 Δt ð 1 þ 5 ρβÞ 12 Δt2 24 ð 1 þ 3 ρβÞ

1 Δt ðϕβÞ

1 12 ð12 Δt 8 ð8

0 þ 5ϕβÞ þ ϕβÞ

1 Δr2

3 ð ω2 Δt2 βÞ 7 0 7 5 2 2 5 ð ω Δt βÞ 12Δt 1 2 2 ω Δt βÞ 8 ð8

24 12ðθ þ θ2 Þ þ 4ξωΔtð3θ2 þ 2θ3 Þ þ ω2 Δt2 ð2θ3 þ θ4 Þ 12ð1

12ðθ

θ2 Þ

8ξωΔtð3θ θ3 Þ 12

θ2 Þ þ 4ξωΔtð3θ2 Φ¼

24

ω2 Δt2 ð6θ2

θ4 Þ

2θ3 Þ þ ω2 Δt2 ð2θ3

θ4 Þ

2ξωΔt ω2 Δt2 θ

228

3 Dynamic and Temperature Analysis Adopted in Fire Analysis and Design

3.8.1.3

where

Cubic Implicit with θ Method Operators 9 9 8 8 x€i > x€iþ1 > > > > > > > > > > > > > = = < x_ i 1 > < x_i > x_ i 1 ¼ ½AŠ xi 2 þ fLgðriþθ Þ > > > > > > > > > > > > > x_ i > > x_ iþ1 > ; ; : : xi xiþ1

riþθ ¼

Fiþθ ; m

fLg ¼

8 > >
> =

3Δt > 8 β > > > ; : 19Δt 2 180 β

f€ xtþδt g ¼ ð6=θτ2 Þðfxtþτ g fxt gÞ ð6=τθÞfx_ t g þ ð1

ð3=θÞÞf€xt g

(3.87)

xt g þ f€ xtþδt g fx_ tþδt g ¼ fx_ t g þ ðτ=2θÞf€

(3.88)

xtþδt g fxtþδt g ¼ fxt gÞ þ ðτ=θÞfx_ t g þ ðτ2 =6θ2 Þð2f€xt g þ f€

(3.89)

 fFtþδt g ¼ fFt g þ δFi t!tþτ

(3.90)

Calculation by Quadratic Integration When the velocity varies linearly and the acceleration is constant across the time interval, appropriate substitutions are made into Eq. (3.13), giving ½f1 ½MŠþf2 ½Ct Šþ½K@@@t ŠŠ fxt g ¼ fF1 ðtÞg þ ff3 ð½Ct Š; ½ MŠ; xt1 ; xt2 ; . . . :Þg (3.91) where f 1, f 2 are functions of time. This results in an implicit time integration procedure. The only unknown is {xt} at each time point and this is calculated in the same way as in static analysis. Equation (3.91) is then written as 

   2 δt0 δt1 2 0 ½CŠ þ ½K t Š fxt g ¼ fF1 ðtÞg þ ½MŠ ½MŠ þ fxt 1 g δt0 δt0 δt0 δt1 δt0 δt0     2 δt0 δt0 fxt 1 g fxt 2 g ð3:92Þ fx2 2 g þ ½Ct Š δt0 δt0 δt0 δt0 δt0 δt1

where δt0 ¼ t0 t1 and t0 ¼ time of current iteration δt1 ¼ t1 t2 and t1 ¼ time of previous iteration

3.8 Additional Methods

229

δt2 ¼ t2 t3 and t2 ¼ time before previous iteration δt2 ¼ δt0 + δt1 ¼ t0 t2 and t3 ¼ time before t2

Calculation by Cubic Integration Equation (3.91) becomes cubic and hence is written as ða1 ½MŠ þ a2 ½Ct Š þ ½Kt 0 Š Þ fxt g ¼ fFt ðtÞg þ f½MŠða3 xt 1 g a4 fxt 2 g þ a5 fxt 3 g þ½CŠ ða6 fxt 1 g þ ða7 fxt 2 g þ a8 fxt 3 gÞ

(3.93)

where a1 to a8 are functions of the time increments; these functions are derived by inverting a 4  4 matrix. For clear-cut solutions, the size of the time step between adjacent iterations should not be more than a factor of 10 in non-linear cases and should not be reduced by more than a factor of 2 where plasticity exists.

3.8.2

Frequency-Domain Analysis

The original equation of motion is reproduced as _ þ ½KŠfxg ¼ fJF gfFg xg þ ½Cgfxg ½MŠf€

(3.94)

where {JF} is a vector with all components zero except the last one, which is 1. The terms [K] and [C] shall be frequency dependent. The value of {F} ¼ [KN]{xs} can be taken for solutions of rigid rock problems. If the excitation with

3.8.3

Keierleber Method

Keierleber C.W. developed a method of implicit method with θ operators. The author developed linear implicit, quadratic implicit and cubic implicit all with θ operators. They are based on time integration approval. Figure 3.7 Plate 1 give a summary of them.

230

3 Dynamic and Temperature Analysis Adopted in Fire Analysis and Design

Fig. 3.7 Plate 1 Keierleber method

3.8.4

Additional Solution Procedures

The following additional solution procedures are recommended. They are included in the programs isopar and Bang-2.

3.8.4.1

Newton–Raphson Method

This concept benefits from the Taylor expression. Similar to the direct method given in Fig. 3.8 and tabulated below. The Newton–Raphson Method is as stated earlier can be viewed at for comparison: A reference is made to Plate 3 (Fig. 3.9)

Direct Iteration Method (Fig. 3.8) Newton–Raphson Method ψðuÞ ¼ Ku þ F ¼ 0 3:98 ψ½unþ1 Š ¼ ½KŠnþ1 funþ1 g ff g Where k ¼ k (u)   1 dψ U1 ¼ ½K0 Š :f where K0 ¼ K ðu0 Þ ¼ ψ ½un Š ¼ fΔun g ¼ 0 3:99 du For nth iteration, one can write 3:101 1 3:100 Un ¼ ½Kn 1 Š :F With funþ1 g ¼ fun g þ fΔun g 3:102 The process is terminated when the error In the above derivatives represents, the e ¼ un un 1 becomes sufficiently small TANGENTIAL MATRIX usually expressed in terms of NORM The improved value un+1 can be obtained as fΔun g ¼

½Kn Š 1 T00 ψn ¼ ½Kn Š 1 T00 ½Fn þ FŠ Where T’’ represent transpose 3:103

3.8 Additional Methods

231

Fig. 3.8 Plate 2 Direct Iteration Method

F = KU

F

R

KT2

ΔF

KT1

KO

Fig. 3.9 Plate 4 Modified Newton–Raphson Method

U

F

F = KU

R

K0 K0 K0

K0

ΔF

K0

K0

3.8.4.2

U

Modified Newton–Raphson Method (Fig. 3.9)

Since there is a difficulty of having to solve a completely new system of equations at each iteration, an approximation can be introduced. This can be done to ½KŠn T00 ¼ ½K0 ŠT00

(3.104)

and a simple solution known as “resolution” of the same system of equations is repeatedly used.

3.8.4.3

Incremental Method

This method is elaborately explained in the text. It is realized that the solution for {u} is known when the load term is zero. Once the starting point is known it will be

232

3 Dynamic and Temperature Analysis Adopted in Fire Analysis and Design

useful to study the behavior of u as F is incremented. For small increment of F, convergence is highly likely for the loading process, the intermediate computed results would be useful information. Thus the method begins with fFgfug þ fΔF0 g ¼ 0

(3.105)

Differentiation is now needed. Assuming it is an exact differentiation, then d f Fg d fug d fug : þ fF0 g ¼ ½KŠT00 þ fF0 g ¼ 0 d fug d fλ g d fλ g

(3.106)

in simplified form dU ¼ dλ

½KT00 fugŠ

1

fF0 g

(3.107)

Here one can identify the tangentical matric. To simply equation such as the above one, Euler’s Method is used which states: fUmþ1 g fUm g ¼

½KT00 ŠfUm g

1

fF0 g fΔλm g ¼

½KT00 Š 1 fΔFm g

(3.108)

where Λmþ1 ¼ λm þ Δλm

(3.109)

Fmþ1 ¼ Fm þ ΔFm

(3.110)

or

Improved integration schemes available in the text can be used.

3.9

Solution Procedures

Three types of solution procedure are available for impact and explosion analysis, namely, time-domain, frequency-domain and modal analysis.

3.9.1

Time-Domain Analysis

The following steps are adopted using a direct implicit integration procedure. Initialization

3.10

Geometrically Non-linear Problems in Finite Element

233

(1) The effective stiffness matrix is  ½K0  Š ¼ 6=τ2 ½MŠ þ ð3=τÞ½C0 Š ¼ ½K0 Š

(3.111)

(2) Triangularize [K0*]

For each time step, calculate the displacement {xt+τ} • Constant part of the effective load vector fR tþτ g ¼fRt g þ θ ðfRtþδt g fRt gÞ þ fFt g þ ½MŠx ð6=τ2 Þfxt g þ ð6=τÞfx_ t g xt gÞ þ ½C0 Šðð3=τÞfxt g þ 2fx_ t g þ ðτ=2Þfxt gÞ þ 2f€ ð3:112Þ • Initialization, i ¼ 0, {δFit!t+τ} ¼ 0 • Iteration (a) (b) (c) (d) (e)

i3!0 i þ 1 Effective load vector {R*t+τ TOT} ¼ {R*t+τ} + {δF i 1˜t!τ} Displacement {xi t +τ}[K*0 ]{xit } ¼ R*I t!I + τ TOT Velocity {x˙it} + (3/τ)({xit + τ} {xt}) 2{x˙t} (τ/2){x¨t}) Change of initial load vector caused by non-linear behaviour of the material n o

   i δ F ¼ ½δC0!t Š x_ i tþτ fx_ t gðtÞ δCi t!tþτ x_ i tþτ  ½δKo!t Š ¼ t!tþτ  i    i  x tþτ δK t!tþδt xi tþτ fxt g ð3:113Þ

In fact, {δF it!t +τ } is calculated using the initial-stress method: (f) Iteration convergence

 k δFi t!tþτ



 δF
i 1 t!τþτ k=k δFi t!tþτ k < to1 ¼ 0:01

(3.114)

or, analogously, on stresses. Calculation of velocity and acceleration Calculate the new acceleration {x¨t+δt}, velocity (x˙t+δt} displacement {xt+δt} and initial load {Ft+δt}:

3.10

Geometrically Non-linear Problems in Finite Element

3.10.1 Introduction Geometrically non-linear problems are assumed to be those associated with large displacement and large strains. In presence of large displacement the structure

234

3 Dynamic and Temperature Analysis Adopted in Fire Analysis and Design

subjected to static or dynamic loads alter shape and hence change distributions. Large displacements normally affect stress—strain relationship. Equilibrium equations are written for deformed geometry. In dynamic condition or under dynamic loading, the deformed geometry can be included in the dynamic non-linear equilibrium equations. The linear analysis forms the basis and there is no need to revise these equations. During deformation the coordinates are displaced which are known as MOVING COORDINATES and they cause solution problems. In plate 5 Fig. 3.10, the stiffness matrix of AB changes to AC position and [K] is not constant. The matrices [K]{Δu} ¼ {ΔR} are the loads applied to the distorted nodes of the distorted elements and effectively are the arrayed of unbalanced forces. The main idea is that for a typical solution. Procedures described in Sect. 3.8, the iterative solution will always be looking for or seeking the configuration which conforms to or with {ΔR} ¼ 0. One way is to account for rigid body displacement where a distortion of the local axis x’ is introduced and for example the distortion member angle Ф can be written for element AB as nodes 1 and 2. ;

¼ tan

1

YL XL

(3.111)

If an element is distorted, it can also be expressed in the local coordinate system various parameters are written as: p δ2 ¼ L L0 ¼ x2 2 þ y2 2 L0 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ¼ ðx0 ¼ F4 F1 Þ2 þ ðY 0 þ θ5 θ2 Þ L0

(3.112)

and θ₁ and θ₂ are evaluated as: θ 1 ¼ M3 θ 2 ¼ M6

ðθ ðθ

θ0 Þ ¼ M 3



θ0 Þ ¼ M 6



tan

1

tan

1









YL XL YL XL

θ0



(3.113)

θ0



(3.114)

forces F₆(1,2) applied at nodes 1 and 2 by the distorted element are written in local coordinates: fF6ð1;2Þ g ¼ ½KŠfδg

3.10

Geometrically Non-linear Problems in Finite Element

a

235

X P B

c

b Y

X

L L0

Y

2

YL

1

Y

M6 L0

F4

XL X

2 F5 Y O 1

F1 X0 X

Fig. 3.10 Plate 5 Geometrically Non-linear Problems

8 9 o> > > > > > > o> > > > = < > θ1 where δ ¼ θ2 > > > > > > > o> > > > ; : > θ2

(3.115)

Several computer packages exist to solve geometrically distorted structures. Mostly based on the following criteria: 1. 2. 3. 4. 5. 6. 7. 8. 9.

Establish initially local coordinates using global displacements Compute element distortions in local coordinates Establish [K] the stiffness matrix; {F₆} ¼ [K] {δ} in local coordinates Transfer [K] and {F₆} to global coordinates The transfer technique is followed for all the distorted elements under new distributed loads. Repeat for all. Assemble Global structural matrices [K] ¼ ∑[K] and [R]₆ ¼ ∑ {F₆} Compute the {ΔR}, the unbalanced forces for the vector of the applied loads and {R} Solve for the displacement increment {Δu} from the structural equations [K] {Δu} ¼ {ΔR} Add increments {Δu} to global displacements {δ} accumulated in previous iterations.

236

3 Dynamic and Temperature Analysis Adopted in Fire Analysis and Design

10. Update estimate of the equilibrium configuration. 11. Apply convergence criteria given in the text 12. When it doesn’t converge to step 1.

3.11

Finite Element Analysis of Explosion in Nuclear Facilities Using the Method of Explosive Factor

In order to simulate detonation controlling of the release of chemical energy is needed. A factor is needed to multiply the equations of high explosives given in books. The finite element method would require at the initial stage a lighting time t1l for each element. Assuming the detonation velocity is Ud, the value of t18 will be computed as: Distance from the center line Of the detonation point to the center of the element divided by Ud The Explosive factor fexp between two points 1 and 2 will be f exp ¼ ff 1;exp ; f 2;exp g Such that Fexp ¼ @@@for t > t1

(3.117)

For t  t1e ¼ 0

(3.118)

For f2;exp ¼

1 v 1 Vcj

(3.119)

Where c ¼ detonation velocity Ae max ¼ maximum are on which detonation or burn occurs t ¼ current time Vcj ¼ Chapman–Jouguet relative volume V ¼ current volume The value of fe exp has several steps towards unity and according to Milkins M.L, spread the burn front over several elements. After reaching unity, fexp is held constant and if exceeds 1, it is reset to 1. According to the author, the high explosive material can behave as an elastic perfectly plastic solids prior to detonation. Hence it will be necessary to update the stress tensor to an elastic stress *Sijn+1 such that 

sij nþ1 ¼ sn ij þ sip Ωpj þ sjp Ωpi þ 2G ε’ij dt

(3.120)

3.11

Finite Element Analysis of Explosion in Nuclear Facilities Using the. . .

237

Where G is the shear modulus, and έ’ij is the deviotoric strain rate. The von Mises yield condition is give by: σ2y

ϕ ¼ J2

(3.121)

3

Where the second stress variant, J2, defined in terms of the deviatoric stress components as 1 J2 ¼ Sij Sij 2

(3.122)

and the yield stress σy, If yielding has occurred i.e., ф > 0 the deviatoric trial stress is scaled to obtain the final deviatoric stress at time n + 1: For detailed investigation in this field a reference is made to the following publication by the author: “Manual of Numerical Methods in Concrete, Thomas Telford, London, 2001” The value of Sijn+1 can be written as: σy Snþ1 ¼ pffiffiffiffiffiffiffi  Snþ1 ij 3J2 ij

If ф  0 , then

Snþ1 ¼Snþ1 ij ij

(3.123)

(3.124)

Before detonation pressure is given by the expression p

nþ1

¼K



1

V nþ1

1



(3.125)

where K is the bulk modulus. Once the explosive material detonates: ¼0 Snþ1 ij

(3.126)

And the material behaves like gas. For the practical application a reference is made to the author’s book on Explosion Resistance Buildings—Springer Verlag 2006.

238

3 Dynamic and Temperature Analysis Adopted in Fire Analysis and Design

3.11.1 Good Achievement of Explosive Burn It will be necessary to look into the following points in order to achieve good explosive burn: 1. Where the input occurs the F.E. mesh must be kept constant. 2. The characteristic element dimension must be found by checking all explosive elements for the largest diagonal. 3. The detonations points, if possible, must be within or at the boundary of the explosion. 4. Check always the computed lighting time for the explosive material. The lighting time in Program. LS DYNA is kept at a negative number. This is true in Program BANG F-Fire. In order to the line of detonation must have sufficient number of detonation points in order to visualize the line fire.

3.12

Finite Element Mesh Schemes

Several finite element Analysis packages are available together their mesh generating schemes. Although the subject is beyond the scope of this calc., however the following packages are mentioned for the reader in depth studies: ANSYS ABACUS BYNA 3D ASAS LUSAS L S DYANA

IDBAS OAYES WASTRAN MARC F. BANG F. ISOPAR

Various mesh generation schemes are available as front ended to various computer packages such as mentioned above.

Chapter 4

Detailed Examples of Tests Results

4.1

Introduction

In this Chapter, detailed examples of the results obtained from the testing activity in this project are reported. For all other detailed experimental results, they are already given in references-Bibliography Section.

4.2 4.2.1

Tensile Tests Tensile Tests at Room Temperature

For each investigated steel three tensile tests at room temperature were carried out. An example of the test results for steel grade S350 Large is shown in Fig. 4.1.

4.2.2

Tensile Steady State Tests: High Temperature

For each investigated steel steady state tensile tests at three different temperature levels, were carried out. In particular the selected temperature values were T 400  C, T 600  C and T 800  C. The majority of above tests were performed under load control condition. As a consequence, the curves are not available in electronic format at the moment that the specimen failure occurs, because before failure arrival the extensometer was taken off. Only the last tests performed on AWS steel were performed under strain control condition. In particular for the Small C1 steel at high temperature level T ¼ 800  C it was not possib1e to apply the extensometer due to too soft behaviour of this temperature, so only the tensile strength was evaluated. Figure 4.2 the trend of strain rate versus temperature is shown in order to give an idea about the method used to define the strain per cent value at collapse: the M.Y.H. Bangash et al., Fire Engineering of Structures, DOI 10.1007/978-3-642-36154-8_4, © Springer-Verlag Berlin Heidelberg 2014

239

240

4 Detailed Examples of Tests Results

Fig. 4.1 Large C3 steel grade S350—Stress—Strain curve

Fig. 4.2 Example of the evaluation of the collapse temperature

discontinuity detectable in the graph highlights the temperature value at which the specimen collapsed and therefore the strain per cent value at failure moment. The strain rate has been evaluated using following formula: :

ε¼

4.3

εtf tf

εt0 t0

(4.1)

Characteristics of Investigated Steels

In this research programme, two steel grades, S350 and S280, supplied by different partners were experimentally investigated. The following Table 4.1 gives details of the investigated materials. It has been noted that the steels of grade S350 were provided by steel manufacturers of west Europe and they were made according to corresponding European standard. Nevertheless, the steel of grade S280 investigated in this project was purchased by plasterboard manufacturer and used only for non load bearing

4.3 Characteristics of Investigated Steels Table 4.1 Investigated materials

Steel grade S280 S350 S350 S350

241 Label Small C1 Medium C2 C3 AWS

Section size (mm) 100  50  0.6 l50  57  1.2 250  80  2.5 150  1.2

Supplier Lafarge Corus Rautaruukki Rautaruukki

Fig. 4.3 Tensile anisothermal transient tests results—Steel grade S350 Medium C2

Fig. 4.4 Tensile anisothermal transient tests results—Steel grade S350 Large C3

partition walls. Therefore its origin and quality are not known. In this case its application should be strictly limited to lightweight steel members in non load bearing partition walls if they are made of the same type of steel. The results are presented in Figs. 4.3 and 4.4.

242

4 Detailed Examples of Tests Results

As expected, for all investigated steel grades, the behaviour that the collapse temperature decreases as redefine due to temperature effects as all the applied stress increases is generally confirmed.

4.4

Proposal For Stress–Strain Relationships at Elevated Temperatures

On the basis of the experimental activity carried out on the selected steels, numerical investigations were made in parallel in order to obtain a mathematical model representing the stress—strain relationships for cold formed steels at elevated temperatures. In order to achieve this goal the following steps were followed: • • • •

analysis and post processing of the tensile anisothermal transient tests, selection of the mathematical model, derive of suitable parameters to be used in the mathematical model, comparison between the experimental results and the mathematical model. These steps will be described in detail in following paragraphs.

4.4.1

Analysis of Tensile Anisothermal Transient Tests

The strain versus temperature curves obtained by means of tensile anisothermal transient tests, from which the “parasite strain” was subtracted, were analysed in order to get stress–strain curves in conditions as close as possible to real building heating conditions in event of fire. The results of this type of analysis are shown in Figs 4.5, 4.6, and 4.7. These results together with the ones from tensile isothermal tests at high temperature values, constituted a basic database to develop the mathematical model describing the stress–strain relationship for cold formed steels at elevated temperatures.

4.4.2

Mathematical Model for Stress–Strain Relationship of Cold Formed Steels at Elevated Temperatures

The mathematical model hereby proposed to define the stress–strain relationships for cold formed steels at elevated temperatures is based on Part 1.2 of Eurocode 3. The stress–strain relationship proposed in Part 1.2 of Eurocode 3 is reported in detail in Table 4.2. In particular, as it can be found in Fig. 4.8 where the shape of the corresponding curve for a defined temperature values θ is represented, the stress–strain curve is divided into four different regions depending on the strain range.

4.4 Proposal For Stress–Strain Relationships at Elevated Temperatures

243

400 T = 200°C

Stress (MPa)

300 T = 300°C T = 400°C

200

T = 500°C

100

0 0.00

T = 600°C

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Strain

Fig. 4.5 Stress—Strain curve derived from anisothermal transient tests—Steel grade S280 Small C1

400 T = 200°C

Stress (MPa)

300 T = 300°C T = 400°C

200

T = 500°C T = 600°C

100

T = 700°C T = 800°C

0 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 Strain

Fig. 4.6 Stress—Strain curve derived from anisothermal transient tests—Steel grade S350 Medium C2

400 T = 200°C T = 300°C

Stress (MPa)

300

T = 400°C

200

T = 500°C T = 600°C

100

T = 700°C T = 800°C

0 0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

Fig. 4.7 Stress—Strain curve derived from anisothermal transient tests—Steel grade S350 Large C3

244

4 Detailed Examples of Tests Results

Table 4.2 Stress—strain relationship recommended in Eurocode 3 Part 1, 2 Strain range ε  εpθ εpθ < ε < εyθ

Stress σ εEaθ fp,θ c + (b/a)[a2-(εy,θ-ε)2]0,5

Tangent modulus Eaθ bðεy;θ εÞ



a a2

εyθ  ε  εtθ εt,θ < ε < εyθ ε ¼ εu,θ Parameters Functions

fy,θ fy,θ[1-(ε-εt,θ)/(εu,θ-εt,θ)] 0.00 εp,θ ¼ fp,θ/Ea,θ εy,θ ¼ 0.02 εt,θ ¼ 0.15 εu,θ ¼ a2 ¼ (εy,θ-εp,θ)(εy,θ-εp,θ + c/Ea,θ) b2 ¼ c(εy,θ-εp,θ)Ea,θ + c2 2 ðfy;θ fp;θ Þ c¼ ε ε E 2 f f ð y;θ p;θ Þ a;θ ð y;θ p;θ Þ

0 – – 0.20

2 0:5

ðεy;θ εÞ



Fig. 4.8 Stress—strain relationship recommended in Eurocode 3 Part 1, 2

The mechanical properties such as, yield strength, proportional limit and Young modulus, at different temperature levels can be evaluated by means of appropriate reduction factors recommended by the Eurocode 3 Part 1.2 and reported in Table 4.3.

4.4.3

Relative Vertical Displacement as a Function of Time and Loading

The maximum relative deflections as function of loading and time are presented in the Figs. 4.4 and 4.5. One can conclude from these Figures that—again—for an imposed load of 3 kN/m2, the floor is about to fail. For an imposed load of 5 kN/m2 the failure criterion is just breached. In other words: the choice of 700  C seems to be a fair estimate for the reference steel temperature θref, at least under fuel bed controlled conditions (Figs. 4.9, 4.10, and 4.11).

4.4 Proposal For Stress–Strain Relationships at Elevated Temperatures

245

Table 4.3 : Reduction factors recommended in part 1.2 of Eurocode 3 Steel Temperature θa( C) 20 200 300 400 500 600 700 800 900 1,000 1,100 1,200

Reduction factor for effective yield strength kyθ ¼ fyθ/fy 1.000 1.000 1.000 1.000 0.780 0.470 0.230 0.110 0.060 0.040 0.020 0.000

Reduction factor for proportional limit kyθ ¼ fpθ/fy 1.000 0.807 0.613 0.420 0.360 0.180 0.075 0.050 0.0375 0.025 0.0125 0.000

Reduction factor for the slope of the linear elastic range kEθ ¼ Eaθ/fy 1.000 0.900 0.800 0.700 0.600 0.310 0.130 0.090 0.0675 0.045 0.0225 0.000

Fig. 4.9 Maximum relative vertical displacement as function of the loading

The above calculation results apply to basic case “b”, i.e. a medium size fire compartment. With a view to investigate the effect of increasing compartment size, a similar analysis has been carried out for basic case “a” (large fire compartment). As in the previous analysis, two values of the fire load density have been chosen, i.e. 300 and 700 MJ/m2 and two values of the imposed load: 3 and 5 kN/m2. The analysis is limited to fuel bed controlled fire conditions. The procedure explained in Section 4.2 has been followed, taking θref 700  C. All cases exhibit a similar behaviour, which will be explained hereafter by reference to the situation characterised by a fire load density of 300 MJ/m2 and an imposed load of 3.0 kN/m2.

246

4 Detailed Examples of Tests Results

Fig. 4.10 Maximum relative vertical displacements of the primary beam as function of time (basic case b with fire load density of 300 MJ/m2 and fuel bed controlled conditions)

The compartment analysed is illustrated in Fig. 4.6a. In this figure, also the position is indicated of some nodes of the secondary beams for which critical deformations occur. Figure 4.12a shows the deflected shape of the fire compartment at peak beam temperature (at ~ 3,720 s). Note that the maximum deflections occur in the end bay and are of the order of 500 mm. These deflections are total deflections and need to have secondary beam deflections subtracted to check relative deflection. Deflections in the middle bays are only of the order of 350 mm. Figure 4.12b shows the deflected

4.4 Proposal For Stress–Strain Relationships at Elevated Temperatures

247

Fig. 4.11 Position of nodes for relative vertical displacements of main secondary beams for case a300.3

Fig. 4.12 Vertical displacements of slab. (a) at peak temperature; (b) at end of analysis

shape at the end of the analysis. Note that the deflections in the end bay have now decreased to around 150 mm but deflections in second bay have increased to around 500 mm, even though the entire structure is cooling down together. This must be due to the recovery of the strength of the main secondary and primary beams and locked in plastic strain in those beams, which occurs on heating. Relative deflections of the main secondary beams are shown in Fig. 4.13. For illustration, the deflection curves for a situation characterised by an fire load density of 300 and an imposed load of 5 kN/m2 are also presented. For the other case, the maximum relative deflection criterion of 450 mm (span/20) is about to be reached at 3,600 s for the secondary beam in the end bay between columns (node 50604—Fig. 4.11) and at ~ 5,400 s,

248

4 Detailed Examples of Tests Results

a

b

-100

reinforcement in x& y direction x direction only y direction only

deflection (mm)

A142 X phi6-200 A142 y phi6-200

0 A251X&y phi8-200

A142X&y phi6-200

A251 X phi8-200 A251 y phi8-200

-200 -300

reinforcement in x& y direction x direction only y direction only

-400 -500 -600

time (min)

time (min)

Fig. 4.13 Relative deflection for various amounts of reinforcement. (a) Ø6-200; (b) Ø8-200

on cooling, for the secondary beam in the second bay between columns (node 50613—Fig. 4.11). The situation for case a appears to be more critical: here the deformation criterion is breached. The results show that replacing 6 mm diameter bars by 16 mm bars diameter gives only a 17 % decrease of the maximum deflection. However, the steepest part of the bar increases from 0.142 mm (¼Ø6-200) to 0.25l mm (¼Ø8-200) equivalent thickness. In this range, the maximum deflection decreases 7 %. The cases Ø6-200 and Ø8-200, simulations have been carried out with the reinforcement applied in direction. The results of these simulations are shown in Fig. 4.13. The relative deflection of the secondary beam at y ¼ 6 m in the first bay is representative for the total of the floor. Since this particular beam spans in x-direction, it is hardly surprising that the reinforcement in x-direction appears to be the most effective. If reinforcement in y-direction is omitted, it would hardly influence the deflection. Generally, it is impossible to omit the reinforcement in one direction. However, the results of the stimulation show that if there is any improvement to be realised by adding reinforcement, it is needed to add Ø8-200 reinforcement in x-direction, and leave the y-direction at Ø6-200. 4.4.3.1

Structural Grid Spacing

There is a lot of scope to consider different structural grid spacing. Two cases were chosen for analyses, grid spacing was based upon CARDINGTON building. Concrete slab is 130 mm crack over secondary beams at 3 m spacing. Column spacing across 21 m direction are 6 m-9 m-6 m respectively and across 45 m direction are 5  9 m bays. The grid spacing to be considered in the present analysis has a concrete slab of 130 mm thick over secondary at 3 m spacing. Column spacing across 21 m direction are 6 m-9 m-6 m respectively and cross 48 m direction are 4  12 m bays. Steel frame and floor slabs have been designed on the basis of room temperature and

4.4 Proposal For Stress–Strain Relationships at Elevated Temperatures

249

Fig. 4.14 Alternative structural grid spacing

Table 4.4 Review of the parametric study into the effect of the structural grid spacing

Imposed load Fire load density 700 MJ/m2 300 MJ/m2

3 kN/m2

5 kN/m2

G-1 G-3

G-2 G-4

design considerations. Refer to Fig. 4.14 for the alternative plan and selected steel profiles. In addition to the above, also the mechanical loading (imposed mechanical load: 3.0 and 5.0 kN/m2) and the fire load (300 and 700 MJ/m2) have been decided to be varied in the calculations. For a review of the considered situations, refer to Table 4.4. For all calculations, basic case “b” applied (medium size fire compartment). As in earlier analyses, the opening factors were chosen such, that the maximum temperature in the lower flange of the primary beam was 700  C. It may be concluded that in all four cases the criterion with regard to the relative deformation (in this case: (δ/L)ref  600 mm) is not breached. Note that in the original design, breaching of the deformation criteria depends very much on the design values for the fire load density and the imposed load. See the discussion on the effect of the mechanical loading. Reason for this different result is that—by choosing practical steel profiles for the alternative grid spacing—a relatively low utilisation factor for the secondary beams is achieved when compared to the original design. The thermal response is hardly affected.

250

4 Detailed Examples of Tests Results

a

PREMIXED FLAME

b PREMIXED FLAME

POROUS DISC AIR MIXING CHAMBER

GAS FUEL

AIR

Fig. 4.15 (a) Premixed flame a Bunsen burner with full aeration (b) Flat premixed flame stabilized on a porous disc [e.g. Botha and Spalding (1954)]

The analysis shows, that an unintended side effect of the room temperature design, may significantly influence the outcome of the structural fire safety design.

4.5

The Structure of a Premixed Flame

A premixed flame can be studied experimentally by stabilizing it on a gas burner. The simplest is the Bunsen burner operating with full aeration (Fig. 4.15a): the characteristic blue cone is a premixed flame which, although fixed in space, is propagating against the gas flow. However, the porous disc burner is more suitable for experimental work as it produces a stationary flat flame, ideal for measurement (Fig. 4.15b). By use of suitable probes, temperature and concentration profiles through the flame can be obtained (e.g. Fristrom and Westenberg 1965). These temperature through the flame. The leading edge is located at x ¼ 0. Three distinct zones may be identified, as follows: I. a pre-heat zone in which the temperature of the unburnt gases rises to some arbitrary value Ti (see below); II. the reaction zone in which most of the combustion takes place; and III. the post-flame region, characterized by high temperature and radical recombination, leading to local equilibrium. Cooling will subsequently occur. Of these, zone (ii) is the visible part of the ‘flame’ and is about 1 mm thick for common hydrocarbon fuels at ambient pressure, but less for highly reactive species such as hydrogen and ethylene. The thickness of the preheat zone ((j) above) can be estimated from an analysis of the temperature profile (Fig. 4.16). If it is assumed that no oxidation occurs at

4.5 The Structure of a Premixed Flame

251

Fig. 4.16 Temperature and concentration profiles through a plane combustion wave (reproduced by permission of Academic Press from Lewis and von Elbe 1961)

temperatures below T1 (a convenient, but fictitious ‘ignition temperature’), the following quasi-steady state equation may be written to describe conduction of heat ahead of the leading edge of the flame (which lies at x ¼ 0) :  2  d T k dx2

ρu Su c p



dT dx



¼0

(4.2)

where ρu is the density of the unburnt gas at the initial temperature T0 and Su is the rate at which unburnt gas flows into the flame . Integration between the limits x ¼ 1 to x ¼ 0 (i.e. from T0 to Ti) gives:   dT k dx

ρu Su cp ðTi

T0 Þ

(4.3)

Setting dT/dx equal to (Ti T0)/η0 as shown in Fig. 4.17, where η0 is taken to be a first-order approximation to the thickness of the pre-heat zone, gives: 0¼

k ρu Su c p

(4.4a)

(Lewis and von Elbe 1961). The derived value of the zone thickness depends on how the leading edge of the pre-heat zone is defined. Gaydon and Wolfhard (1979) identify it as the point at which (T—T0) ¼ 0.01  (T—T0); Eq. (4.3) must be integrated twice to give:

252

4 Detailed Examples of Tests Results

Fig. 4.17 Analysis of the temperature profile in the pre-heat zone of the combustion wave (reproduced by permission of Academic Press from Lewis and von Elbe 1961)

0 0

¼

4:6k ρu Su c p

(4.4b)

• In ANSYS, the load is applied as a surface load as shown in Fig. 4.18 and is applied by increment up to the failure. The load application direction (parallel to Z axis) is constant during calculations. For specimens under centric load, an eccentricity of 5 mm is used in numerical simulations. In ABAQUS, the load is applied as a prescribed displacement. • Initial imperfection obtained from eigenvalue buckling analysis is used in numerical simulations. It consists of sinusoidal waves in the web with maximum amplitude of 1 mm. • At room temperature the mechanical properties of steel stud are those given by part 1.1 of Eurocode 3. • The connection with plasterboard is represented by a boundary condition restraining the lateral displacement of steel stud at position of screws reported in Fig. 4.19. These restrained displacement conditions are located at the centre of both flanges for studs maintained by plasterboards on two sides and only at the centre of one flange (corresponding to supported side) for studs fixed with one plasterboard only. • In accordance with tests, the behaviour of steel studs is simulated with two different end conditions, namely: Fixed at both ends (restraining UX, UY, UZ, ROTX, ROTY and ROTZ), or Fixed at one end (restraining all degrees of freedom) and hinged at the other end (restraining UX, UY, ROTY and ROTZ).

4.5 The Structure of a Premixed Flame

253

Fig. 4.18 Applied load conditions (pressure on free end surface parallel to Z axis)

Fig. 4.19 Position of screws along the steel stud

• Moreover, in ANSYS both ends of steel stud are modelled using a stiffer material (corresponding to blue colour element) with the value of modulus of elasticity taken as 210  105 MPa. As an example, Fig. 4.15 shows the boundary conditions which have been adopted in the numerical simulations of some tests, when the steel stud is assumed as hinged at one end and fixed at the other end.

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4 Detailed Examples of Tests Results

Fig. 4.20 Example of boundary conditions adopted for steel suds

In ABAQUS, each end of the C-section is connected to the load/support point by a series of rigid links (Fig. 4.20).

4.6

Example Analysis

Detailed example of the numerical analysis has been carried out, the numerical results obtained with the computer code ANSYS for the specimen with medium section: tests number 3 and 7 are given below. Tests were performed with the studs connected to plasterboard on two sides. The steel studs were omitted to an eccentric axial load. The ordinary temperature steel studs are designed as hinged at one end and fixed at the other end. Assuming the same support conditions, the calculated failure load is 48.5 KN. When the steel stud is assumed as fixed at both ends, the calculated failure load becomes 52 KN which is comparable to the experimental loads, namely 54.9 KN for test number 3 and 57,9 KN for test number 7. The evolution of the lateral displacement calculated at several points along the steel stud of test number level of sections N1, N2 and N3) are shown in Figs. 4.21 and 4.22. These displacements compared to the measured ones. Figures 4.23 and 4.24 give similar results for test number 7. The results would be noted that in the case of hinged support conditions at both ends, the stud displacements are somewhat sub-estimated in comparison to experimental displacements. Moreover, when

4.6 Example Analysis

255

Fig. 4.21 Lateral displacement of specimen of test n 3 assuming the steel stud as fixed at one end

Fig. 4.22 Lateral displacement (mm) of specimen of test n 3 assuming the steel stud as fixed at both ends

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4 Detailed Examples of Tests Results

Fig. 4.23 Lateral displacement of specimen of test n 7 assuming the steel stud as fixed at one end

Fig. 4.24 Lateral displacement of specimen of test n 7 assuming the steel stud as fixed at both ends

the specimen is assumed as fixed at both ends, calculations results agree very well with test results. Example Fig. 4.25 shows the deformed shape of the specimen at the last load step when the steel is assumed fixed at one end. Figure 4.26 gives similar results when the steel stud is fixed at both ends. A photograph of specimen the test number 7 is given in Fig. 4.27.

4.6 Example Analysis

257

Fig. 4.25 Deformed shape of the specimen assumed as fixed at one end

Fig. 4.26 View of specimen after test number 7

4.6.1

Parametric Study with End Restrain and Imperfection Conditions

One special parametric study was carried out with the computer code ABAQUS to investigate the influence of different end restrain and imperfection condition on tall stud resistance at room temperature. One example is given here in which numerical modelling was compared to one of the tests performed by CORUS with medium section. Figure 4.27 shows Numerical failure mode governed by distortional buckling of flange but also by torsional-flexural buckling. Table 4.5 shows comparison of numerical simulation with various tests.

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4 Detailed Examples of Tests Results

Fig. 4.27 Numerical failure mode governed torsional flexural bukling of flange but also by torsional flexural buckling

Table 4.5 Comparison of numerical simulation with tests. The characteristic resistance according 1–3 of Eurocode 3 [1] is 44.5 kN with end boundary conditions similar to FEA_2

Test result (Test number 19—Chap. 3 with idealised end conditions) Test result (Test number 19—Chap. 3 with studs in channel tracks fixed by screws) FE simulation without global imperfection about strong axis (FEA_1) FE simulation without global imperfection about strong axis (FEA_2) FE simulation with global imperfection about strong axis (FEA_3)

4.7

Compression resistance 50.9 kN 496 kN 539 kN 47.8 kN 41.0 kN

Comparison of Test Results with Simple Calculation Rules

Design of cold formed steel sections is carried out of Eurocode 3 [1]. The general procedure to calculate the resistance, according to Eurocode, of a cold formed lipped C-section steel strut which is restrained by plasterboard on both sides about its minor axis in axial compression and combined axial compression and bending moment at the ultimate limit state is as follows: 1) Choose basic yield strength and ultimate tensile strength from depending on type of steel 2) Check that sections conform with thickness limitations for code 3) Calculate net area of section by deducting area of holes 4) Calculate dimensions of section by allowing for the effect of rounded corners 5) Check geometrical proportions to check for validity of design calculations

4.8 Test on Tall Studs

259

6) Choose modelling strategy for individual elements of section under pure compression and pure bending. 7) Calculate effective area of section taking into account the effects of local buckling on each element 8) Calculate resistance of cross-section under relevant sectional forces a. Axial compression b. Bending moment c. Calculate buckling resistance of member under axial compression including checks on: d. Flexural buckling e. Torsional buckling and torsional flexural buckling 9) Calculate combined resistance of section under combined axial compression and bending moment noting that bending moment is equal to eccentricity applied axial load. It should be noted that perforated sections, such as the AWS and TC150 section, are not within the scope of either code. In these cases, designers must refer to the relevant manufacturer to obtain design information on the section concerned. Therefore, comparisons have only been made for lipped C sections. The results of the stub column tests can be compared with the calculated value of effective area of the cross-section (step 7). The results of the test and calculated values to the Eurocode are given in Table 4.6. The comparisons of the test results for the double stud tests with the calculated values from the design codes are given in Tables 4.7 and 4.8. The AWS section results are also included for completeness. In terms of performance, the AWS section is closest to the medium lipped C section having flange widths and thicknesses closest to this Section (Figs. 4.28 and 4.29).

4.8 4.8.1

Test on Tall Studs Testing Methodology

Fire tests on all studs fully engulfed in fire were performed at CTICM. Altogether six tests were performed. The specimens were 3,500 mm tall steel studs of three different types of lightweight steel sections designated as Medium, Large and AWS. The basic characteristics of the steel section are given in Table 4.1. In the fire tests, all specimens were subjected to an axial load, which were applied before the test and eccentricity kept constant until failure. Some specimens were tested with eccentric load. At room temperature, the specimens were considered as hinged at one end and restrained against rotation at the other end above the strong axis. All rotations about weak axis at both ends of studs are assumed to be restrained. The boundary condition in AWS section stud test is presented in Fig. 4.30.

√

74.1 kN

Small (100  50  0.6) Medium (150  57  1.2) Large (250  80  2.5) 280 Mpa 350 MPa 350 MPa 59.6 kN 195.5 kN 8.6 kN 7.5 kN 54.9 kN 214.3 kN – – – Key: 8.6 kN ¼ Test Result (values in normal bold type) 7.5 kN ¼ EN 1993-l-3 Design Value (underlined values in bold Italics)

Eccentric (0.25 h)

Testing conditions Loading Centric √

AWS (150  1.2) 350 MPa –

Size and grade of sections

Table 4.6 Comparison with design rules for stub column test results

√

Section type No perf. Perf. √

260 4 Detailed Examples of Tests Results

44.5 kN 48.6 kN

√

√

Centric

Small (100  50  0.6) Medium (150  57  1.2) Large (250  80  2.5) 280 Mpa 350 MPa 350 MPa 50.8 kN 177.0 kN 4.1 kN 3.6 kN 28.3 kN 194.3 kN – – – – – – Key: 4.1 kN ¼ Test Result (values in normal bold type) 3.6 kN ¼ EN 1993-l-3 Design Value (underlined values in bold Italics)

AWS (150  1.2) 350 MPa –

Loading

√

Eccentric (0.25 h)

Testing conditions

Size and grade of sections

Table 4.7 Comparison with design rules for tall stud test results

√

No perf.

√ √

Perf.

Section Type

4.8 Test on Tall Studs 261

262

4 Detailed Examples of Tests Results

Table 4.8 Comparison with design rules for boundary condition test results Size and grade of sections

Testing conditions

Medium (150  57  1.2) 350 MPa 34.6 kN

En1993-1-3 31.0 kN

Loading Eccentric (0.25 h) √

49.6 kN

32.2 kN

√

54.9 kN

32.2 kN

√

1.0 0.8 Load level

Fig. 4.28 Failure load level (NTest.fi/NTest.ref) as a function of the temperature for different steel sections (Load level 1.0 corresponds to reference load Ntest.ref)

Section type Boundary conditions Studs simply inserted in channel tracks Studs in channel tracks fixed by screws One end fixed/one end pinned

0.6 0.4 0.2 0.0

0

200

400

600

TEMPERATURE ( C)

º

C 150

800

1000

1200

*No failure at load level 0.07 C 100

AWS

C 250

TC 150

Fig. 4.29 Strain (ΔL/L) as a function of temperature for different steel sections and load levels

During all the tests, the furnace temperature was continuously recorded. In order to determine the temperature field in the steel studs, thermocouples were installed on the steel studs (both flanges at web) at four different levels N1, N2, N3 and N4 along the specimen length. The positions of the thermocouples are shown in Fig. 4.31 for the C-sections and in Fig. 4.32 for the AWS section. Lateral and longitudinal displacements of the specimens were recorded during the tests. The location, the displacement measurements for the AWS section is presented in Fig. 4.33.

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263

Fig. 4.30 Boundary condition of AWS section stud test

Fig. 4.31 Location of the temperature measurement points in the C-sections

605

775

N1

A

N2

B 775

N3 C

775

Thermocouple N4

570

The test program is presented in Table 4.9.

4.8.2

Test Results

The failure time measured during the tests, which are reported in Table 5.3, corresponds to the condition when each specimen (steel stud) could not carry the applied load any more. As an example, temperatures measured at different levels in the test on the AWS section are presented in Figs. 4.34, 4.35, 4.36, and 4.37, lateral displacements

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4 Detailed Examples of Tests Results

Fig. 4.32 Location of the temperature measurement points AWS section

605

N1

775

E

A

N2

D

B 775 C

N3 775

Thermocouple N4

570

Fig. 4.33 Location of the displacement measurement points in AWS section

D7 875 D4

D1 D8

D9 D1, D2, D3

875

D7 D2 D10

D9

D10

D5 875 D3 875

D4, D5, D6

D6

Table 4.9 Summary of fire tests on tall studs Loading condition Test 03-S-373 03-S-357 03-S-369 03-S-316 03-S-348 03-S-379

Stud Medium Medium Medium Large Large AWS

Length (mm) 3,500 3,500 3,500 3,500 3,500 3,500

Load (kN) 15 25 15 60 60 18

Ecc.(mm) 37.5 0 0 0 0 0

Maximum temp ( C) 257.0 245.0 500.0 565.0 540.0 529.0

Test tin (min) 18.0 23.0 28.5 57.0 51.0 35.0

measured along strong axis and along weak axis of AWS section in Figs. 4.38 and 4.39 and vertical displacement in Fig. 4.40. The actual applied load during the test is presented in Fig. 4.41. Some specimens after the tests are shown in Figs. 4.42, 4.43, 4.44, 4.45, and 4.46 in order to give an idea about the failure mode of these studs.

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265

Fig. 4.34 Temperatures measured on section N1 versus time in the test on AWS section

Fig. 4.35 Temperatures measured on section N2 versus time in the test on AWS section

The temperature evolution in the numerical model was applied at four different levels on the stud. The temperatures were taken as the mean value from different levels recorded in the test. The mean value of the temperature was calculated from the five tests A–E, at the layers N1, N2, N3 and N4, see Fig. 4.38. The temperature curve used in the numerical simulations was also extended to a time beyond the failure time for the test. This has to be the most important one because the

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4 Detailed Examples of Tests Results

Fig. 4.36 Temperatures measured on section N3 versus time in the test on AWS section

Fig. 4.37 Temperatures measured on section N4 versus time in the test on AWS Section

temperature record from the test stops when failure of the steel stud occurs, after 29 min. From that point the temperature evolution was extended linearly to 29 min. The temperature variation across the section in the numerical simulation was neglected.

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267

Fig. 4.38 Temperature evolution at different levels used in the numerical simulation Laterral displacement - strong axis Displacement (mm) 40 20 0

Test - D1

–20

Test - D2 Test - D3

–40

D1

–60

D2

–80

D3

–100 –120

0

10

20 30 Time (min)

40

50

Fig. 4.39 Lateral displacement along strong axis versus time for numerical model FEA_1 compared to test results

4.8.3

Experimental Results Versus Numerical Simulations

The result from the numerical simulations shows a good agreement with the test particularly the numerical model CTICM test FEA_l. The failure temperature recorded in the test is compared with the two simulations with different end boundary conditions in Table 4.10. The displacements recorded in the numerical simulations are compared to the test and one example is shown in Fig. 4.39. In some cases it can be difficult to

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4 Detailed Examples of Tests Results

Fig. 4.40 The Wall Structure

compare the results because the displacements very small displacements. But it seems to correspond well with the test if the difference in the failure time is taken into account.

4.8.4

Experimental Results of Wall Element Test (VTT)

The wall element is composed of six studs with a cross section of C150  54  15  1.2. These studs are inserted respectively at bottom and top sides in two lightweight steel tracks (see Fig. 4.40). The two layers of plasterboards are used at

4.8 Test on Tall Studs

269

Fig. 4.41 Test set up of wall element

Fig. 4.42 Some representative experimental results

both exposed side and unexposed side of the wall. For exposed side, the directly exposed layer is a fire board of 15 mm thick and the second layer is a standard board of 13 mm thick. The wall has a total height of 2,800 mm and its width is 3,000 min. It was supported simply at bottom with a roller and fully restrained at top. The load was applied at the bottom through two jacks (see Fig. 4.41) without any eccentricity.

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4 Detailed Examples of Tests Results

Fig. 4.43 Some representative experimental results. (a) Measured furnace temperatures versus EN1364-1 fire curve; (b) Measured temperatures in steel studs and plasterboards at mid-height; (c) Measured temperatures in steel stud at the top; (d) Measured temperatures in steel studs at the bottom

The total applied load corresponds to a value of 33  4 ¼ 132 kN (considering only four loaded studs) and remained constant during the test. The wall was exposed to standard fire and the test lasted for about 87 min. The typical experimental results from the test are shown in Figs. 4.42, 4.43, and 4.44. The behaviour of the wall can be summarised as follows: • the temperature increased slowly and remained at relative low level (about 100  C) until 45 min of fire; • from 45 min of fire, the temperature rise was more rapid and it increased quite linearly until the collapse of the wall; • at collapse instant, the maximum temperature was about 450  C; • The deflection of the wall remained quite small until 45 min of fire and its value doesn’t exceed 3 mm. At this moment, the axial contraction seems to be only the effect of thermal elongation; • from 45 min of fire, the temperature rise led to a higher increase of lateral deflection and the axial contraction changed the sign due to the loss of stud stiffness at higher temperatures meanwhile the inclination changed also the sign due to more important thermal bowling; • after reaching a maximum level of about 12 mm towards the exposed side at 65 min of fire, the lateral deflection of the wall stayed then at this level until its collapse which occurred on the contrary in the opposite side (unexposed side);

4.8 Test on Tall Studs

271

Fig. 4.44 Typical experimental results of wall element test. (a) Applied load per stud versus time; (b) Lateral displacement versus time; (c) Axial displacement versus time; (d) Lateral displacement versus time

• the failure mode towards unexposed side was exactly the same as that already observed with maintained individual studs which may be caused by an additional eccentricity due to the shift of both hot section gravity centre and redistributed load centre.

4.8.5

Experimental Results of Floor-Wall Assembly Test (CTICM)

In order to be consistent with floor and wall elements, the assembly is composed of a floor element supported at one side by a wall element (see Fig. 4.45). The wall element is made of six studs with a cross section of C150  54  15  1.2 inserted respectively at bottom and top sides in two lightweight steel tracks. These studs were insulated by two layers of plasterboards at exposed side and only one layer for unexposed side. For exposed side, the directly exposed layer is a fire board of 15 mm thick and the second layer is a standard board of 13 mm thick. The wall element of the assembly has a total height of 2,800 mm and a width of 3,000 mm. It was placed at bottom on a steel frame. The top of the wall is linked to floor element with the detail shown in Fig. 4.46.

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4 Detailed Examples of Tests Results

Fig. 4.45 Support and load condition of floor-wall assembly

Fig. 4.46 Typical experimental results of UK floor-wall assembly test

The floor element of the assembly has total length of 5,500 mm, same as the floor test. It is simply placed at one side on a roll and linked to wall element on other side. The span of the floor considered from the central line of studs to the roll is 5,240 mm which is also the same used in floor test.

4.9 Comparison of Fire Behaviour Between Elements and Assemblies

273

Table 4.10 Summary of failure temperatures from test and numerical simulations CTICM test FEA_1 FEA_2

Maximum failure temperature ( C) 529 501 479

Numerical modelling/(CTICM test) 0.95 0.91

Concerning the load condition, the wall element was loaded on the top of every studs through three jacks without any eccentricity. The total applied load corresponds to a value of 25  6 ¼ 150 kN (considering all six loaded studs) and the loads remained constant during the test. The floor was loaded with steel blocks to simulate uniformed distributed load. The total weight of all steel blocks is 5,802 kg leading to uniformly distributed load of 369 kg/m2. In this case, the applied load on joist is 221 kg/m2. The whole assembly was exposed to standard fire according to part 1 of EN1.363. The test lasted for 78 min. The typical experimental results from the test are shown in Fig. 4.47. The behaviour of the assembly can be summarised as follows: • the temperature increased slowly and remained at relative low level (about 100  C) in floor steel joists until 60 min of fire; • the fall of first layer of bottom plasterboards in floor took place near 50 min of fire and it seems to occur firstly near simple support and about 20 min after at other location; • after the fall of first layer of bottom plasterboards in floor, the temperature rise began to be slightly more important and it increased then more and more rapid until the collapse of the assembly • In parallel, the temperature of wall element increased slowly to about l00  C after 50 min of fire and then more rapidly to about 400  C at collapse; • The collapse of the assembly was caused by loss of load carrying capacity of floor after 76 min of fire. At this instant, the maximum temperature of steel joints is about 300  C; • The maximum lateral displacement of wall before collapse is about 10 mm towards the fire and at the moment of collapse, these displacements changed the sign which was apparently caused by the increase of floor deflection turning the wall away from the fire.

4.9

Comparison of Fire Behaviour Between Elements and Assemblies

As it has been explained previously, the floor and wall elements were tested separately at VTT and their assemblies were tested at CTICM. Therefore, it is very useful to compare the fire behaviour between individual elements and their assemblies. In addition, this comparison can be made with two different systems,

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4 Detailed Examples of Tests Results

Fig. 4.47 Some representative experimental results. (a) Furnace temperatures according to EN 1363-1versus time; (b) Measured temperatures in steel joists and plasterboards of floor at midspan; (c) Measured temperatures in steel joists of floor near simple support; (d) Measured temperatures in steel joists of floor near joint; (e) Measured temperatures in steel studs of wall at mid-height; (f) Measured temperatures in steel studs of wall at top; (g) Measured temperatures in steel track at floor-wall joint; (h) Lateral displacement of wall versus time

4.9 Comparison of Fire Behaviour Between Elements and Assemblies

275

that is Finnish and UK systems since they have been both investigated in our fire tests. Concerning the Finnish system, VTT carried out tests on individual floor element in 2000 and on wall element within this project. In the fire test performed at CTICM on the assembly of floor and wall element, the failure occurred at about 56 min of fire with floor joists. The comparison here is then focused on the behaviour of this element under two different types of structural systems. However, the fire resistance is significantly different (58 min in CTICM test and 84 min in VTT test). If more attention is paid to the heating regime recorded during these tests, one can observe that this difference of fire resistance is induced by a very different behaviour of plasterboards. In CTICM test, the fall of the first layer of exposed plasterboards happened at only 35 min of fire. At mean time, in VTT test, it happened only after 70 min of fire. Nevertheless, the measured floor deflections in both tests are not only very small but also very close to each other until 45 min of fire. Another phenomenon to mention is the temperature rise of double joists in CTlCM test, which is much quicker from 45 min of fire compared to single joist. However, in VTT test, no difference of heating between single and double joists is observed until 70 min of fire. Apparently, this important temperature rise would increase considerably deflection of the floor element leading to its premature collapse by an earlier fall of the second layer of plasterboard. As a consequence, the behaviour of plasterboard is the determinant parameter for the different fire rating between assembly test and individual floor element. The different behaviour of plasterboards between VTT and CTICM tests could be explained by a different heating regime of two edge steel joists of the floor element. It has been observed during CTICM test that failure occurred at one edge instead of a uniform collapse (see Figs. 4.48 and 4.49). In reality, this failure mode was due to the fact that the lower flange of one edge steel joist was much more heated than that of other edge joist. In this case, its bowing effect will be amplified compared to other edge steel joist resulting in more important deflection which appears to be the dominant parameter for good maintaining behaviour of plasterboards. In addition, the failure started firstly at the side of more heated edge joist due to its heating regime. It has to be mentioned here that this heating regime could be very different from reality in which steel joists would be homogeneously insulated by plasterboards and the boundary effect should be eliminated by appropriate constructional arrangement. The fire tests with UK system on floor element, wall element and floor-wall assembly were all carried out within actual project. As it is with Finnish system, VTT and CTICM performed respectively individual element tests and assembly test. In addition two fire tests were carried out by CTICM with floor-wall assemblies. In the first assembly test, the collapse of the specimen was caused by the failure of floor element and in the second one, failure occurred at floor-wall joint by squash of steel joists as well as stiffeners under applied load of jacks. So the comparison between the first UK system assembly test and individual element tests seems to be more interesting and meaningful as well.

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4 Detailed Examples of Tests Results

Fig. 4.48 Comparison of test results with Finnish construction system. (a) Comparison of temperatures in plasterboards near simple support; (b) Comparison of temperatures in plasterboards at mid-span; (c) Comparison of temperatures in single steel joist at mid-span; (d) Comparison of temperatures in double steel joists at mid-span; (e) Comparison of deflection comparison of floor element; (f) Comparison of lateral displacements of wall element

A brief comparison table, in which the similarities and differences of both VTT individual element and CTICM assembly tests are listed, is given below (Table 4.11). Comparing the temperature rise between individual element tests and this assembly test, one can find (Fig. 4.50) that the fall of first layer of bottom plasterboards in VTT floor test occurred everywhere (mid-span and near support) between 45 and 50 min. However in CTICM assembly test, this fall occurred at about the same time near the simple support but at mid-span and near floor-wall joint between 65 and 70 min of fire so much later. This difference may explain why

4.9 Comparison of Fire Behaviour Between Elements and Assemblies

277

Fig. 4.49 Failure mode of assembly test with Finnish construction system. (a) Deformed floor after collapse (view above); (b) Deformed floor after collapse (view below); (c) Temperatures measured in left edge steel joist; (d) Temperatures measured in right edgesteel joist

Table 4.11 Comparison of testing conditions for UK construction system Parameters Span of floor joist Height of wall stud Boundary conditions

Floor

Wall

Applied load

VTT test 5,240 mm 2,800 mm Simple supported

Fully restrained at top and hinged at bottom 2.5 kN/m per joist of floor and 33 kN on each stud of wall

CTICM test 5,240 mm 2,800 mm One side simply supported and other side assembled to wall studs Bottom inserted in tracks and top side assembled with floor joists 2.68 kN/m per joist of floor and 32 kN on each stud of wall

the failure of VTT floor test happened earlier than that of the floor in CTICM assembly test since the temperature rise is quicker if the fall of plasterboard happens earlier which in turn increases the floor deflection creating therefore more cracking in plasterboard as well as higher temperature rise of steel joists. As far as the heating of wall studs is concerned, it does not vary much between wall element test and assembly test.

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4 Detailed Examples of Tests Results

Fig. 4.50 Comparison of test results with UK construction system. (a) Comparison of temperatures in steel joist near simple support; (b) Comparison of temperatures in steel joist at mid-span; (c) Comparison of temperatures in steel studs on top side; (d) Comparison of temperatures in steel studs at mid-height; (e) Comparison of temperatures in steel studs on topside; (f) Comparison of lateral displacements of wall element

In this assembly test with UK system, the mechanical collapse occurred once again on floor joists. But contrary to Finnish system, in assembly test with UK system, the floor resisted longer than that in individual floor element test (77 min rather than 69 min) because of a less heating regime as explained earlier even the steel joists in assembly test are slightly more loaded.

Chapter 5

Fire-Resistant Composite Structures: Calculations and Applications

Composite steel-concrete structures ideally combine advantages of both their components: reduced overall dimensions easy prefabrication and connections, and reduced thermal diffusivity for steel; easy shaping and reduced section factor F/V concrete, Fig. 5.1 shows some typical plan sections of structures that have been investigated.

5.1

Calculations Principles

Analytical models for determining thermal material properties for concrete and steel are described in this chapter. These models lead into the application of the computer program STABA-F which was developed to support the experimental investigations on the load bearing and deformation behavior of uniaxial structures during fire. Heat transfer from a fire to a structural element depends on the material and nature of the absorbing surface of the member; the color of the flames; the geometry, material, and the material properties of the test furnace/Extensive investigations into the heating of structural columns and beams in the test furnace at the Technical University of Braunschweig, Germany, showed that there were sufficient correspondence between measured and calculated respondence assumed the coefficient of convection heat transfer to be α ¼ 25 W/m2. K and the resultant emissivity ε ¼ 0.3–0.7 for concrete and 0.5–0.9 for steel. Heat conduction is described by the well-known equation from Fourier, which is valid for homogeneous and isotropic materials in the application of this equation to composite structures, the following simplifications are necessary: Water vaporizes as soon as it reaches the boiling point. Movement of stem is taken together with other effects.

M.Y.H. Bangash et al., Fire Engineering of Structures, DOI 10.1007/978-3-642-36154-8_5, © Springer-Verlag Berlin Heidelberg 2014

279

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5 Fire-Resistant Composite Structures: Calculations and Applications

Fig. 5.1 Typical cross section of composite structures

Typical Cross-Section Colums

Beam And TBeam

Fig. 5.2 Design values, thermal material properties for concrete with siliceous aggregates

Consumption of energy for vaporizing water is accounted for by using suitable values for or the specific heat capacity of concrete up to 200  C (390  F). Concrete is considered a homogeneous material, while the heterogeneous structures, as well as capillary pores and internal cracks, are grouped together. A finite-element method in connection with a time-step integration is used to calculate the temperature distribution in a section. The time steps chosen have to be quite small (Δt ¼ 2.5–5 min) because the characteristic values of the thermal conductivity λ, specific density δ, and specific heat capacity cp are very much dependent on temperature. Figures 5.2 and 5.3 shows the temperature dependence of the thermal material properties for concrete and steel. To determine the temperature distribution, a rectangular network is preferred with a maximum width of less than 20 mm (1 in.). In the area of the structural steel, it is advantageous to reduce the width of the network to the thickness of the structural steel profile. The elements of the cross-sectional discretization have corresponding thermal materials of steel or concrete.

5.2 Stress–Strain Relationships

281

Fig. 5.3 Design values, thermal material properties of steel

Fig. 5.4 Design values, thermal strains of concrete with siliceous aggregates and steel

Due to temperature effects, the thermal strains for the cross-section elements are derived by using the specific temperature dependent thermal structural concrete and steel as shown in Fig. 5.4.

5.2

Stress–Strain Relationships

In an actual fire, material is normally subjected to a transient process with varying temperatures and stresses. To get material data of direct relevance, transient creep tests were carried out. During the tests, the specimen was subjected to a certain constant load and a constant heating rate. Form these tests, uniaxial between the

282

5 Fire-Resistant Composite Structures: Calculations and Applications

populations of distinct flow parameters.) m can be assessed by an iteration The value the delay time t is given by the following equation: dt

v0 x½tðFÞ

tðTRފ

vðTR; nÞ vðTRÞ; n 1Þ vðTR; nÞ vðTR; n 1Þ vn

(5.1)

where T(F) ¼ travel time of last evacuee along corridor t(TR) ¼ travel time of person going from the top floor of the stairs to the adjoining story 00 v ¼ velocity by which the boundary between the Initial flow on the stairs with the parameters D(TR; n) and q(TR;n) and the merged flow with the parameters D(TR; n 1) and q(TR n 1) changes its location. v(TR; n) ¼ velocity of flow at density D(TR; n) v(TR; n 1) ¼ velocity of flow on stairs at density D(TR; n 1). If the value of the specific flow on the stairs exceeds the maximum during the merging of the partial flows at story n 1, congestion occurs on the stairs as well as at the entry to the staircase. In this case qðTR; n

1Þ ¼ 1Þ ¼

QðT; n

1Þ þ QðTR; nÞ > qðTR; maxÞ bðTRÞ

(5.2)

where q(TR; n 1) ¼ value of specific flow on stairs after merging process Q(T; n 1) ¼ flow capacity through door to staircase on each floor Q(TR; n) ¼ initial flow capacity on stairs. b(TR) ¼ stair width q(TR; max) ¼ maximum flow capacity on stairs The percentage of contribution of each partial flow to the main flow can be obtained as follows: bðTÞ pðTÞ ¼ (5.3) bðTÞ þ bðTRÞ pðTRÞ ¼ where b(T) ¼ door width to staircase b(TR) ¼ stair width

bðTRÞ bðTÞ þ bðTRÞ

(5.4)

To determine the new width of the partial flows on the stairs, the main width of the flow b(TR) is multiplied by the following fractions: bðT1 Þ ¼ pðTÞbðTRÞ

(5.5)

5.2 Stress–Strain Relationships

283

bðTR1 Þ ¼ pðTRÞbðTRÞ

(5.6)

Due to the congestion on the stairs, the evacuees from the other floors cannot enter the staircase immediately. A backup occurs at the floor exit and the partial flow on the corridor extends backward at a speed of: v}ðT; STAUÞ ¼

qðT; D maxÞbðT1Þ bðTÞ

qðTÞ D max

(5.7)

DðTÞ

where v"(T; STAU) ¼ speed of congestion on corridor qðT; DmaxÞ ¼ specific flow at maximum density through doorways b(T1) ¼ width of partial flow from each floor in main flow on stairs. b(T) ¼ door width to staircase, or width of flow from each floor under free-flow conditions q(T) ¼ specific flow through door to staircase under free-flow conditions on stairs Dmax ¼ maximum flow density. D(T) ¼ density through door to staircase without congestions on stairs After the last person of the flow on the corridor reaches the queue at the entry to the staircase, the congestion diminishes at the following speed: vðT; STAUÞ ¼

vðT; Dmax ÞbðT1 Þ bðTRÞ

(5.8)

where v(T; Dmax) is the velocity of a flow through a doorway at the maximum density, The flow movement on the corridor ends at the instant t(F;STAU) indicated as F; STAU in Fig. 5.5; t(F;STAU) is the egress time from a story. From the beginning of the merging process of the partial flows until the end of queuing at the exit door to the stairway, congestion also occurs on the stairs. Due to this, the flow on the stairs extends backward at a rate of: v0 ðTR; STAUÞ ¼

qðTR; Dmax ÞbðTR1 Þ=bðTRÞ Dmax

qðTR; nÞ

DðTR; n

1Þ (5.9)

where v0 (TR; STAU) ¼ speed of congestion on stairs qðTR; DmaxÞ ¼ specific flow on stairs at maximum density b(TR1) ¼ width of partial flow from top floor n in main flow on stairs b(TR) ¼ stair width, or width-of flow on stairs under free-flow conditions q(TR, n) ¼ specific flow on stairs without congestion Dmax ¼ maximum density

284

5 Fire-Resistant Composite Structures: Calculations and Applications

Fig. 5.5 Flow motion process calculated using f ¼ 0.14 m2 (1.5 ft2). Delay time due to congestion is Δr ¼ 0.43 min, repeated on each floor level. t(Ges) ¼ 15.34 min

D(TR; n) ¼ flow density on stairs without congestion, or density of partial flow from top floor. Here two different situations may arise: 1. t(F) + t(TR) > t(F; STAU). For example, if the last person from the floor under the top story enters the staircase before the last person froth the top floor reaches the line on the stairs, then the partial flow from the top floor can use the total stair width after t(F; STAU) (Fig. 5.5). In this case, the speed of congestion on the stairs changes as follows: v}ðTR; STAUÞ ¼

qðTR; Dmax Þ qðTR; nÞ Dmax

DðTR; nÞ

(5.10)

After the last person from top floor reaches the line on the stairs, the congestion diminishes at the speed vðTR; Dmax Þ, which corresponds to the flow velocity on the stairs at the maximum density. 2. If t(F) + t(TR) > t(F; STAU), then the last person from the top floor reaches the line on the stairs before the last person from the story below enters the staircase. In this case the congestion on the stairs diminishes at the following speed until t(F; STAU):

5.2 Stress–Strain Relationships

285

vðTR; STAUÞ ¼

vðTR; Dmax ÞbðTR1 Þ bðTRÞ

(5.11)

where v(TR; STAU) ¼ flow velocity on stairs at maximum density b(TR1) ¼ width of partial flow from top floor in main flow b(TR) ¼ stair width, or width of flow from top floor under uncongested-flow conditions After the end of congestion at the entry to the staircase, the partial flow from the top floor can use the total width of the stair again. The movement process at floor (n 1) is complete at the point indicated as TR; STAU in Fig.5.5. The flow moving down the stairs from floor (n 1) consists of two different groups of people. The movement parameters of the part ahead are q (TR; n) and v(TR; n), which are the initial flow parameters. This group is followed by the evacuees emanating from the overcrowded area at the level (n 1) and moving by the specific flow q(TR; Dmax), but at a lower density than the maximums. During the merging process of both groups, the boundary between them changes its location at a speed of v00 , which can be determined by the following equation: v} ¼

qðTR; Dmax Þ DðTR; n 1Þ

qðTR; nÞ DðTR; nÞ

(5.12)

where q(TR;.Dmax) ¼ specific flow on stairs at maximum density q(TR; n) ¼ specific flow on stairs at beginning of flow movement D(TR; n 1) ¼ density of group of people emanating from overcrowded area at level (n 1) D(TR; n) ¼ initial flow density on stairs Simultaneously, on. the corridor of story (n 2), and on the stairs between floors (n 1) and (n 2), the flow motion forms in a manner similar to the flow movement the upper flows. There the velocity of the flow extending backward on the stairs will be different according to whether it reaches the boundary mentioned before or after t(F; STAU). [t(F; STAU) is the egress time from a floor.] If the end of the line arrives at the boundary before t(F; STAU), then the rate of congestion is determined by Eq. (5.9). Otherwise the rate of congestion is predicted by the following equation: 00

v ðTR; STAUÞ ¼

qðTR; Dmax ÞbðTR1 Þ bðTRÞ

qðTR; Dmax Þ Dmax DðTR; n 1Þ

(5.13)

286

5 Fire-Resistant Composite Structures: Calculations and Applications

It should be noted that, in this case, the values of the specific flows for both groups, the incoming flow as well as the uptaking flow, are the same. After the last evacuee from floor (n 2) enters the staircase, the length of the congested flow on the stairs remains constant until the last person from story (n 1) reaches the waiting population on the stairs. Then the congestion diminishes at the rate v(TR; Dmax), which is the flow velocity at the maximum density. The flow movement at story (n 2) ends at the point t(TR; STAU), indicated as B in Fig. 5.5. If the last person from floor (n 1) had reached the adjoining story without any delay, due to congestion, he or she would arrive there after the time t1. The delay time due to congestion on escape routes dt, repeated at each floor level, is predicted by dt ¼ t 00 ðTR; STAUÞ

(5.14)

t1

where t00 (TR; STAU) is the length of time required for the flow to leave the floor level (n 2). In case of congestion on escape routes, the total evacuation time of a multi-story building is determined by the following equation: tðGesÞ ¼ tðTR; STAUÞ þ

ðn 1ÞlðTRÞ þ ðn vðTR; n 1Þ

2Þ dt

(5.15)

where t(TR; STAU) ¼ length of time required for flow to leave floor level (n 1) l(TR) ¼ travel distance on stairs between adjoining stories v(TR; n 1) ¼ velocity of flow emanating from congested area at floor level (n 1) dt ¼ delay time due to congestion n ¼ number of upper floors in building The total evacuation time t(Ges) is influenced in a nonlinear fashion by the projected area factor (or the density increase). Figure 5.6 illustrates the change in evacuation time in three high rise administration buildings, plotted against the projected area factor f and the number of persons per floor P(G). Within the range of experimental data from real evacuation tests and by using the average value of f ¼ 0.12–0.14 m2 (1.29–1.51 ft2) per person, the predictions of the presented egress odd are likely to provide an adequate basis for the assessment of flow movement on escape routes. Improvement of the model is certainly possible, but it would require additional specific data in terms of flow density. Figure 5.7 shows the diagram of an office occupancy floor of one of the highrise administration buildings where a real evacuation test was conducted. This building consists of a ground floor, one mezzanine, 21 upper floors, and two tower stories. The height between two floors was measured as 3.60 m (11.8 ft). The building is arranged around a triangular core with a staircase at each corner

5.2 Stress–Strain Relationships

287

Fig. 5.6 Graphic representation of total evacuation time- t(Ges). In three high-rise office buildings in terms of projected area factor f and the number of persons per floor P(G). When determining the total evacuation time in terms of the number of persons per floor P(G), the projected area factor is assumed to stay constant at f ¼ 0.12 m2 (1.29 ft2)

of the core layout. Each staircase is approached by a protected lobby with a length of 0.90 m (2.6 ft). The continuous corridor leading to a staircase has a width of b(F) ¼ 1.87 m (6.13 ft). The greatest travel distance along the corridor measures l(F) ¼ 29.40 m (96.4 ft). The doorway opening between the corridor and the protected lobby, as well as the exit door to the staircase has a width of b(T) ¼ 0.82 m (2.68 ft). Due to the triangular form of the ground plan, the staircases are also arranged around a triangular pillar, with three flights between two floors. The width of the stair is b(TR) ¼ 1.25 m (4.1 ft). During the evacuation test, 567 persons were evacuated via the observed staircase. The average number of persons per floor was p(G) ¼ 26 (approximately 20 m2 (215 ft2) per person. Although the building was apparently under occupied, the flow downstairs was delayed for the first 3–4 min because of the door with fairly inappropriate dimensions swinging into the protected lobby. In this case the model predicts the flow from the floors through the protected lobby into a staircase and downstairs to the final exit. Furthermore, it presumes that the evacuation has already been initiated, and at the time 0, indicated as point A in Fig. 5.5, the fire person of the partial flow on each floor passes through the doorway into the protected lobby.

288

5 Fire-Resistant Composite Structures: Calculations and Applications

12.50 m (41 ft)

5

25.40 m (83.34 ft) 1

2

7 6

43.70 m (134.4 ft) 7 5

7 5

26

.87

m

(88

.15

ft)

6

Fig. 5.7 Office occupancy floor of high rise administration building

By changing the number of persons per floor per staircase, or changing the corridor width leading to the staircase or the width of the floor exits, the egress model predicts the results listed in Table 5.1 (Kendik 1985a). Given the data corresponding to the real evacuation test (Table 5.1, column I), the model predicts the total evacuation time to be 10.29 min, which is fairly close to the measured time of 10.47 min. The floor egress time from an upper floor (except the top and ground floors) as estimated to be 0.79 min under congested— flow conditions. The length of the congestion would be 0.71 m (2.3 ft) at the floor exit and 1.11 m (3.6 ft) on the stairs. By increasing the number of persons per floor per staircase from 26 to 40, the total evacuation time increases significantly (15.34 min from Table 5.1, column II). By decreasing the corridor width from 1.87 to 1.25 m (6.13–4.1 ft), the total evacuation time of 40 persons per floor per staircase is predicted to be 14.50 min, which is less than the time estimated in the previous example, since due to higher

5.3 Analytical Tools to Evaluate Building Spacing, Compartment Sizing and. . .

289

Table 5.1 Results predicted by egress model Number of persons Corridor length, m Corridor width, m Door width, m Flow density on corridor Flow velocity on corridor, m/min Special flow density on corridor, m/min Egress time from top floor, min Initial flow density on stairs Speed of congestion at floor exit of any upper floor, m/min Maximum length of congestion at floor exit, m Egress time from any upper floor, min Speed of congestion on stairs, m/min Maximum length of congestion on stairs, m Total evacuation time via this staircase, min Real evacuation time, min (Seeger 1978)

I 26 29.4 1.87 0.82 0.07 44.43 2.94 0.69 0.10 −1.75 0.71 0.79 −2.11 1.11 10.29 10.47

II 40 29.4 1.87 0.82 0.1 39.00 3.97 0.80 0.16 −6.76 2.48 1.10 −4.31 2.57 15.34

III 40 29.5 1.87 0.82 0.15 32.73 4.99 0.93 0.12 −3.17 1.87 1.18 −2.90 2.23 14.50

IV 40 29.4 1.87 0.82 0.15 32.73 4.99 0.93 0.12 −0.63 0.41 1.00 −3.48 2.59 14.55

density in the corridor, less persons can enter the staircase in the same time period. Hence the initial stair density and the speed of congestion decrease. Widening the floor exit from 0.82 to 1.25 m (2.7–10.8 ft) which corresponds to the stair width does not change the evacuation pattern significantly, in this case the floor egress time decreases, which leads to a greater congestion on the stairs (Table 5.1, column IV). For the building the total length of the corridor on each floor is approximately 1.10 m (3.6 ft). Decreasing the corridor width would not threaten the flow movement. (The predictions show that the total evacuation time slightly decreases.) Less corridor width would mean approximately 70 m2 additional space on each story and approximately 1,540 m2 (16,575 ft2) more rental area for this entire building (corresponding to the equivalent area of one floor).

5.3

Analytical Tools to Evaluate Building Spacing, Compartment Sizing and Exterior Walls in Tall Buildings

A primary way to reduce fire loss in neighboring buildings is to provide adequate fire barriers if the buildings are close together, or to provide adequate separation with sized and controlled openings where the buildings are spaced apart (Barnett 1988). Once the buildings are far enough apart, no measures are required to protect neighboring property. Conversely, the only ways to, reduce fire loss within an owner’s building are to install sprinklers or to reduce the areas at risk, that is, to reduce the fire-compartment size. However, few, if any, fire codes state how fire compartment sizes are to be determined—they merely prescribe maximum sizes.

290

5 Fire-Resistant Composite Structures: Calculations and Applications

Two fire-engineering design methods are discussed in this chapter. They have considerable flexibility and determine fire separation in conjunction with the firecompartment size. Both use the common factor of fire resistance rating (FRR), which, with suitable factors, can be linked to a nominal fire duration (NFD). Both design methods encourage the use of smaller fire compartments, which in turn will reduce the cost of property lost by fire. Both separation distance and compartment size can be related to fire duration, which in turn can be linked to FRR. Hereafter, the fire duration is referred to as the nominal fire duration, or NFD.

5.3.1

Fire–Resistance Rating

FRR is determined in a fire test laboratory by subjecting a loaded or unloaded construction to a fire environment controlled to a standard time temperature, as in BS 476, ISO 834 (1975), or ASTM E-119. For the fire design of a particular building, four types of FRR need to be considered. First, there are what may be termed collapse and noncollapse FRRs.

5.3.2

Fire Behaviour of Composite Columns

As an example of composite members, the behavior of different types of columns during fire tests is discussed in this section. In concrete sections, temperature propagates at approximately 1/20 the rate in steel sections (Figs. 5.8 and 5.9). This accounts for the long fire resistance times of composite columns with embedded steel profiles, as seen in Fig. 5.10. Due to the reduction of strength and stiffness in the outer parts of the concrete section with temperatures above 300  C (570  F), the stresses in the steel are augmented and, therefore, collapse occurs before the steel is heated up to 500  C (930  F), which is normally the critical temperature. It is preferable to have a high bearing capacity Nst for the steel, compared with that of concrete. This means that columns with a high ratio of Nst/Npl are less affected by fire attack (Npl being the bearing capacity of the composite cross section). Only a minimum number of longitudinal bars and stirrups are necessary to avoid loosening of the concrete cover by spalling and provide bond between concrete and steel. The fire resistance of concrete-filled tubes is primarily due to the fire resistance of the reinforced concrete core. The temperatures develop somewhat slower compared with concrete columns because of the greater water content of enclosed concrete. Due to restraining of the greater thermal elongation of steel, which heats up more quickly than concrete the tube takes more of the column force at the beginning of the fire action. Because of this reduction in load, decompression of the concrete may occur after 15 min of fire exposure under ISO conditions, yielding of the tube takes place and the total load is taken by the reinforced concrete core. Local buckling of the tube may

5.3 Analytical Tools to Evaluate Building Spacing, Compartment Sizing and. . .

291

Fig. 5.8 System of bar element without intermediate supports

N =3792.0kN curvature in 1/m

4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5

–0.1

5.0

column length in SR

moment in kNm

column length in m

5.0

0

0.1

deflection m

4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5

–100

0

100

bending moments kNm

Fig. 5.9 Ultimate limit state of composite columns consisting of a rolled shape HE 240 B embedded in concrete and 0.5 % reinforcement after 30-min fire exposure. Determined ultimate load is 3,792.0 kN

Fig. 5.10 Experimental data of 4.20 m (13.7 ft) long composite column with embedded HEB profile, Tested with one end fixed and the other pin-joined

occur but it only seems to affect the deflections slightly and does not affect the stability of the composite column. This can be seen in Fig. 5.11. With increasing temperatures, the column stiffness decreases and, finally, the column fails due to the loss of stiffness, which causes a stability failure with remarkable deflections. It is preferable for the tube to have a low bearing capacity compared to that of the reinforced concrete core. The fire resistance increases when the ratio Nst/Npl decreases, unlike for columns with embedded steel sections.

292

5 Fire-Resistant Composite Structures: Calculations and Applications

Fig. 5.11 Experimental data of 4.20 m (13.7 ft) long composite columns with concrete filled quadratic tubes 6.3 and 12.5 mm (0.25 and 0.5 in.) thick, tested with one end fixed and the other pin jointed

Figure 5.12 shows the various stresses of the tube, the concrete, and its reinforcement during fire action. A minimum amount of longitudinal reinforcement is necessary to control the crack width during the temporary decompression of the concrete. Otherwise a single widely opened crack can occur, which causes a plastic hinge when the tube initially yields at one side only. In this case the deflection of the column becomes so large that it immediately leads to rapid failure. Openings in the tubes are important to avoid excessively steam pressure inside the tube. To attain a fire resistance of 60 min or more, load reductions are unavoidable. Therefore N/Nadm ratios smaller than 1.0 have to be chosen. This is the reason why in Canada, for example, the bearing capacity is determined for the tube only, without taking into account any capacity of the concrete. In both cases the admissible load of the composite column depends on the required fire-resistance time. The temperature in the steel is not a suitable 5 criterion for the ultimate limit state. By using a special high-temperature-resistant concrete with steel-fiber reinforcement, load reduction may be avoided as some tests have proven. Braced columns in frames are generally centrically loaded, or are assumed to be, for simplification of a stability check. During an isolated fire in only one story, end rotations are significantly restrained due to the fact that the stiffness of the hot column decreases, whereas the stiffness of the connected elements beneath and above the referred column remains unchanged. Only the ceiling is heated, whereas

5.3 Analytical Tools to Evaluate Building Spacing, Compartment Sizing and. . .

0 minutes 150 fire action

60 minutes Steel tube concrete reinforcement QR 260.7,1

293

15 minutes

90 minutes

Fy = 240 MPa Fc = 30 MPa Fy = 420 MPa

Fig. 5.12 Calculated stress distribution for reinforced tube section after different times of fire action. Stresses are related to corresponding strengths to allow for better comparison

the floor is protected by cool air, ashes or other materials. Tests on columns were carried out by controlling end rotations in a manner that imposed equivalent or restraining actions on them Typical results are shown in Fig. 5.13. At the beginning a fire test approximately 30 min a nearly constant rate of dilatation of heated ceiling causes imposed bending moments, which are released when a specimen’s steel tube yields. After 30 min the rate of displacement decreases due to increasing deflections of the ceiling. Therefore, and because of the continuous loss of column stiffness, the restraint decreases. It disappears completely when a certain flexural deformation of the columns is attained. Then the increasing deflection is hindered by the connected beams or similar elements. Differences between stiff connections joining flanges and webs of the beams and soft connections joining only the webs were observed only at the beginning of the fire action time. The measured re-resistance time corresponds well with that obtained when the columns with fixed ends, and without displacements were tested (Euler mode no. 4). For edge columns of a multi bay frame, node rotations due to beam deformation have to be considered. The tests revealed that the fire-resistance time for this case corresponds very well with that of the columns tested with one end fixed and the other pin-jointed. At present research on composite columns is continuing.

294

5 Fire-Resistant Composite Structures: Calculations and Applications

Fig. 5.13 Restraining moments due to floor dilatation in 4.20 m (13.7 ft) long columns, tested with fixed ends

5.3.3

Practical Applications

Although research on the structural behavior of composite elements under fire conditions is not yet finished, some results of this work have already been applied in practice. Investigations are mainly concerned with the load-bearing behavior of composite slabs with profiled steel sheets, composite beams, different types of composite columns, and—as a special aspect—the connections between composite beams and composite columns These types of construction, which are illustrated in Figs. 5.14 and 5.15 do not yet have regulated fire protection in most of the European countries and fire assessment still has to be done for each individual building. Because of this complex process, some details of practical application are discussed below especially connections, which need no further cladding or additional fire protection. The application of composite structures for certain fire-resistance requirements is facilitated by recently developed tables in which the load-bearing capacity of these strutura1 element is given for specific times of standard fire exposure. The classification of elements for various fire-requirements does not cover all possible types of construction in practice. As an example of composite construction, two buildings which were constructed in 1984 with a composite construction method are presented, in the following discussion. Example 1. The first example is a four-story laboratory building in Stuttgart, Germany. Regulations required that all structures have a fire resistance of at least 90 min (ISO standard temperature-timed curve). A number of different types of composite structures were constructed to demonstrate their use advantages, especially for structural fire requirements. For instance, there are: 1. Composite concrete slabs with profiled steel sheets 2. Composite beams-with concrete in fill in connection with reinforced concrete slabs or composite concrete slabs with-profiled steel sheets. 3. Different kinds of composite columns such as concrete-filled and reinforced hollow sections, hollow sections filled with refractory concrete and steel fibers, steel I

5.3 Analytical Tools to Evaluate Building Spacing, Compartment Sizing and. . . Fig. 5.14 Composite slab with profiled steel sheet

295

reinforcement providing contraction cracking steel sheet

Fig. 5.15 Typical sections of composite columns and composite beams

sections embedded in concrete, steel I sections with concrete infill, extruded steel sections welded together and filled with concrete, and water-filled hollow sections. The connections between columns and beams are of special interest. As the building has a central steel core, the connections should only transfer shear forces. Except for the water-filled hollow sections, which are part of the central core, all columns stand outside the building. As a result, only the beams without slabs are in connection with the columns. Two principal types of connections are applied in this building example. The first has a vertically installed connecting plate, as shown in Fig. 5.16, which transfers shear forces from the earns to the columns. The plates are fixed to the webs of the beams by screws. If this type of connection is used to join a beam to a concrete-filled hollow section, the plate should pass through the column. It is not sufficient to fix the plate only to the hollow section because the steel sheet of the column buckles as a result of heating. The second principal type of connection that was built uses a steel cleat, which forms a support for the beam, as shown in Fig. 5.15. To connect composite beams and columns, this steel cleat can be welded directly to I-section columns that are in filled with concrete or totally embedded in concrete. The fire resistance of this connection depends on the solidity of the steel cleat and the sizes of the welding seams If this column-beam connection is used in combination with concrete-filled hollow sections, the steel cleat should be anchored to the concrete core of the column, by studs. The reason for this is the effect of local buckling on the steel sheet of the column. Future plans will demonstrate a real fire in the top story of a building, which simulates the fire load of furnishings by substituting them with wooden describes. After the fire, the damaged building will be repaired. One of the aims of this

296

5 Fire-Resistant Composite Structures: Calculations and Applications

Fig. 5.16 Connection through composite column and composite beam (plate stuck through section column)

Fig. 5.17 Connection between composite column and composite beam (cleat as a support for beam)

demonstration is to show the repair ability of fire-damaged composite structures (Fig. 5.17). Example 2. The second building example erected utilizing the composite construction method is a seven-story laboratory and office building in Berlin. A circularshaped testing shed with a diameter of about 60 m (180 ft) is surrounded by the laboratory section. The fire-resistance requirements are different in the two parts of the building. Because of the low fire load, there are no requirements in the testing shed so that the load-bearing steel structure can remain unprotected. The laboratory requires a fire resistance oِ f 90 min (ISO standard temperature-time curve). The columns in the laboratories are concrete-filled circular hollow sections with diameters ranging from about 250 to 500 mm (10–20 in.). The columns are reinforced in their upper stories, where the loads are less. The columns have an internal I-beam section embedded in concrete and wrapped by hollow sections in their lower stories where loads are large. These types of sections have a high fire resistance because the steel profiles are isolated by the surrounding concrete and, therefore they maintain their load-bearing capacity for a long period of fire exposure. The beam used in this seven-story building are I-beam sections which are in filled with concrete in connection with prefabricated concrete slabs. In case of fire, the reinforcement takes over the tensile stresses from the heated lower flange. There are holes in the webs of the steel profiles and in the concrete for the installation of supply lines running transverse to the axis of the beams. In case of fire, the areas of

5.3 Analytical Tools to Evaluate Building Spacing, Compartment Sizing and. . .

297

Fig. 5.18 Composite beams concreted between flanges, with holes for supply lines

Fig. 5.19 Connection between composite column and composite beam (beam hung up to welded section)

the beams below these holes are heated from all sides. To take over the tension force, there are T sections welded to the webs of the I sections, as shown in Fig. 5.18. The connections between beams and columns are pinned joints. The beams are hung to welded sections which pass through the columns and are protected from heating by a concrete floor above, as shown in Fig. 5.19. Under ambient temperature, high-strength screws transfer the shear forces from the beams to the columns. There is a clear space between the end of the beams and the columns so that the connections are actually hinged. In case of fire, the beams expand and the construction turns into a continuous girder, providing the advantages of a strong beam with respect to load-bearing conditions during fire. The sections which pass through the columns take over tension forces and the compression forces are passed directly from beam to column. These, few examples show that it is frequently not advisable to use standardized constructions or tables for the design of structures with specific fire requirements. On the contrary, there is a need for individual solutions to each condition. It has been proven that the design of structure can optimize load-bearing behavior under ambient temperatures and under fire conditions.

298

5.3.4

5 Fire-Resistant Composite Structures: Calculations and Applications

Fire Design of Composite Concrete Slabs with Profiled Steel Sheet

A composite assembly composed steel-reinforced concrete-slab and a profiled steel sheet is the type of composite system most frequently found in buildings today. The fire resistance of such slabs is significant, even if no additional fire-safety precautions are taken. If necessary, the fire resistance can be increased to almost any desired level by simple and reliable means. Until recently, however, structural fire-engineering design of composite slab could only be based on fire-resistance tests. This procedure is time-consuming and expensive, and sometimes gives rise to anomalies due to variations in test results. Consequently there has been a strong need for a practical design method by which the fire resistance of composite slabs can be determined analytically. This should lead to more uniform levels of safety. Furthermore, this method should be simple and systematic, thus stimulating the use of composite slabs. Such a design method was derived for normal-weight concrete and is discussed in this section. It was established by the Technical Committee 3 of the European Convention for Constructional Steelwork (ECCS) and is available now (ECCS-TC3, 1988). Criteria for Fire Resistance. Fire resistance is determined under standard fire conditions, which are characterized by the so-called standard gas-temperaturetime curve. This curve is shown in Fig. 5.20. Composite steel-concrete slabs have both a load-bearing and a separating function, and the following criteria for fire resistance shall therefore be taken into account, as defined in ISO 834: Load-bearing capacity. Resistance to collapse or excessive deflection under structural loading Insulation. Limitation of temperature increase on unexposed side of slab Integrity. Ability of slab to resist penetration of flames or hot gases through formation of cracks and openings. The time taken to fail, any of these three criteria is taken as the fire rating of the slab, even though failure under other criteria may not occur until much later. It is common practice to determine the fire resistance by means of standard fireresistance tests. During such tests the test specimen is exposed to a standard fire on its underside while loaded to produce the normal maximum working stresses in its floor construction. Similar assumptions are adopted when using analytical approach. For proper verification of the performance criteria in an analytical approach however, some additional assumptions are necessary. Since the following discussion uses such an analytical approach rather than actual experiments, such as were discussed earlier in this chapter, the load-bearing criterion is used here. The criterion of load-bearing capacity requires that a slab shall not, during a fire, cease to perform the load-bearing function for which it was constructed. During tests, collapse of a slab is avoided by limiting its deflection. This prevents damage to the furnace and other apparatus.

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299

Fig. 5.20 Standard fire curve

To fulfill the insulation criterion, the temperature rise of the unexposed side of a test specimen should not exceed 180  C (350  F) at any point and the average should not exceed 140  C (280  F). This criterion is applied in most national standards (ISO 834). Because of the profiled shape of the slab, care must be taken when checking that the insulation criterion is satisfied. Theoretically the temperature at the unexposed side will vary as a function of the location at which the temperature is measured. Tests show, however, that in practical cases, the temperature differences are small. In theory it is also possible that passage of heat through joints may result in a nonuniform temperature distribution at an unexposed side. However, composite steel-concrete slabs are normally manufactured in situ, and this complication does not arise. Therefore a uniform temperature distribution at the unexposed side is assumed in this discussion. A temperature increase of 140  C (280  F) at this same side is taken as the limiting insulation criterion. Integrity is a measure of the ability of the construction to resist the passage of flames and hot gases through cracks. For composite steel-concrete floors, the integrity criterion is not difficult to fulfill. The main reason is that, as mentioned, the floor slab is cast in situ. This means that joints are adequately sealed. Any cracks which may occur, in the concrete during fire exposure are unimportant because the steel sheet will prevent penetration by the flames and hot gases. Therefore it is assumed that if the insulation criterion is fulfilled. Then the integrity criterion is fulfilled.

5.3.5

Additional Means of Fire Protection for Composite Slabs

The following means to provide additional fire protection for composite slabs can be utilized and are discussed in this section: additional reinforcement, thermal barriers, and suspended ceilings.

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5 Fire-Resistant Composite Structures: Calculations and Applications

1. Additional Reinforcement In a composite slab a minor percentage of steel reinforcement is normally included to control shrinkage and creep of the concrete. This reinforcement may be placed directly on the steel sheet. When no coating or suspended ceiling is used, the steel sheet is directly exposed to fire. As a result, the temperature increase in the steel sheet and in the reinforcement can be expected to be approximately the same. Consequently the beneficial effect of the shrinkage reinforcement on the fire resistance of the slab may only be marginal. However, additional reinforcement placed in the center of the ribs may significantly contribute to its fire resistance. The same advantage is true of continuous slabs for the top reinforcement over intermediate supports. Figure 5.21 illustrates the various possibilities. 2. Thermal Barriers A thermal barrier may be necessary when extremely high fire-resistance ratings are required or when deflections have to be severely limited under fire exposure. Spray-applied coatings (for example, coatings based on mineral fibers or vermiculite) are directly applied to the surface of the steel sheet. In order to achieve good adhesion, the steel surface should be properly cleaned to remove dirt and grease. Fire-resistive slab material can also be used (for example, vermiculite, gypsum, fiber). These are directly adhered or mechanically fixed, to the ribs of the steel sheet. As with sprayed coatings, a thorough cleaning is necessary to ensure good adhesion. Special attention n should be paid to the type of adhesive used and to ensure adequate connections of boards during fire conditions. Such construction details must be verified by experimental evidence. Only a relatively small thickness of insulation is necessary to achieve a considerable fire resistance. Nevertheless the application of fire-protective coatings will involve considerable extra cost. 3. Suspended Ceilings A suspended ceiling specifically designed to function as a heat shield for the structural components above it can contribute to the fire resistance of the floor assembly. In the cavity above the fire-protective ceiling a time-temperature curve which is less severe than the standard fire curve can be assumed. This is subject to the condition that there is only a limited amount of combustible material in the (unventilated) cavity. The extent to which the standard fire curve is thus reduced will depend on the insulating qualities of the ceiling and on-the floor above it. The behavior of a suspended ceiling during a fire is critical, but unfortunately it may vary because it depends on good detailing, workmanship, and maintenance. These design aspects have to be verified experimentally. Fire-resistance tests are therefore essential.

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Fig. 5.21 Reinforcement in composite concrete slab with profiled steel sheet

Thus additional steel reinforcement is a simple, reliable, and economical means for increasing the fire resistance of composite concrete-steel slabs Moreover, the assessment of additional reinforcement is open to theoretical analysis. The reliability of the two other means of fire protection, therma1 barriers, and suspended ceilings, is much more difficult to determine because they are highly dependent on factors such as detailing and workmanship. Experimental verifications is necessary if these options are to be used.

5.3.6

Calculations of Minimum Slab Thickness

The insulation criterion of fire resistance is fulfilled if the average temperature increase at the unexposed side of the slab exceeds 140  C (280  F), as discussed earlier. This requires sufficient slab thickness, which depends on the period of fire resistance required. As is seen from the equation for he, the effective thickness corresponds to an arithmetic average of the thickness, which accounts for the profiled shape of a slab. The calculation rule applies to stanc.ard fire exposure and normal-weight concrete.

5.3.7

Calculations for Additional Reinforcement

Failure Conditions. The load-bearing capacity may be analyzed on the basis of elementary-plastic theory (limit-state) design. For various static systems, the failure conditions can then be easily formulated. þ Muσ is the absolute value of In Table 5.2 the following notation is used: Muσ the positive and the negative plastic bending moment, respectively, at the end of the required period of standard fire exposure, q is the load on the slab to be accounted for during fire, and L is the span of the slab. To evaluate the failure conditions, it is necessary to quantify the plastic moments þ Muθ and Muθ . Typical stress distributions over the cross section are represented in Figs. 5.22 and 5.23, respectively. Some assumptions are made for simplicity and these are discussed in the following.

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5 Fire-Resistant Composite Structures: Calculations and Applications

Table 5.2 Failure conditions for slabs Statical system No negative reinforcement

Failure condition

Negative and positive reinforcement

2 Mþ uϑ þ
0:5 : Muϑ  q: L =8 or þ 2 q  8Muϑ þ 4 Muϑ =L Mþ  q : L2 =8 or uϑ þ Muϑ
þ  q  8 : Muϑ þ Muϑ L2

No negative reinforcement

þ Muϑ  q : L2 =8 or 2 q  8 : Mþ uϑ = L

Muϑ  q: L2 =8 or 2 q  8 : Mþ uϑ =L

General. The tensile strengths of concrete and the steel sheet do not contribute to the load-bearing capacity at elevated temperatures and thus may be ignored. Positive Plastic Moment. The ultimate strength of concrete in the compression zone is not influenced by temperature and the room temperature values may be used. The effective yield stress of the additional reinforcement is affected by temperature. Negative Plastic Moment. In performing calculations, the profiled concrete slab may be replaced by a slab with a uniform thickness equal to the effective thickness he. The ultimate strength of concrete in the compression zone (exposed side) is affected by temperature. The effective yield stress of the reinforcement (unexposed side) is not influenced by temperature, and room temperature values may be used. The load q on a slab during a fire follows from 0.85q*, where q is the load to be used in the fire test and is chosen in accordance with ISO 834. Due to the assumptions noted, a reduced value is used because the calculation rule gives a conservative result (compared with the amount of fire resistance measured in a fireresistance test). The value of the reduction factor (0.85) is based on comparative calculations (Pettersson and Witteveen 1978/1980). On the basis of the foregoing assumptions (and using the temperature distribution and mechanical properties of steel and concrete which are discussed here after), at elevated temperatures, the evaluation of the failure conditions can proceed in a manner similar to the case of conventional reinforced concrete slabs under ambient temperature conditions. First, however, additional design considerations should be discussed.

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Fig. 5.22 Positive plastic moment Mþ uϑ. Notes: The factor 0.8 is introduced to correct the assumed full plastic stress distribution in the concrete compression zone. In the ultimate state, a nonuniform stress distribution will occur due to the limited capacity of the concrete to accept deformation

Fig. 5.23 Negative plastic moment Muθ. Note: The factor 0.8 is introduced to correct the assumed full-plastic stress distribution in the concrete compression zone. In the ultimate state a nonuniform stress distribution will occur due to the limited capacity of the concrete to accept deformation

For concrete Thermal conductivity Density Specific heat Thermal inertia Conversion factor Window height Window width Window area Ventilation factor Equivalent fire severity Law formula Net calorific value of wood Equivalent fire severity

k ¼ 1.0 W/mK ρ ¼ 2,200 kg/m3 cp ¼ 880 J/kg K pffiffiffiffiffiffiffiffiffi  kρcp ¼ 1391 Ws 5 =m2 K ðmediumÞ 2.25 kc ¼ 0.07 min.m /MJ Hv ¼ 2.0 m B ¼ 3.0 m Av ¼ Hv B ¼ 2.0  3.0 ¼ 6.0 m2 w ¼ Af /(Av At Hv  5)0.5 ¼24/(6  108  20.5) 5 ¼ 0.793 m 0.25 te ¼ ef kc w ¼ 800  0.7  0.793 ¼ 44.4 min ΔHc ¼ 16 MJ/kg te ¼ ef Af/[ΔHc (Av (At Av))0.5] ¼ 800  24/[16  (6(108 6))0.5] ¼ 48.6 min

304

5.4

5 Fire-Resistant Composite Structures: Calculations and Applications

Fire Resistance

This section describes fire resistance, the standard fire resistance test and the ways in which it is used for achieving fire-resistance ratings of building elements. This chapter also describes methods for calculating the fire resistance of structural members and discusses the importance of fire resistance of components and assemblies in real buildings.

5.4.1

Overview

Fire resistance is a measure of the ability of a building element to resist a fire. Fire resistance is most often quantified as the time for which the element can meet certain criteria during exposure to a standard fire-resistance test. Structural fire resistance can also be quantified using the temperature or load capacity of a structural element exposed to a fire. It is important to recognize that individual materials do not possess fire resistance. Fire resistance is a property assigned to building elements which are constructed from a single material or a mixture of materials. Some building elements may be simple elements such as a single steel column or a concrete floor slab. Other building elements may be complex assemblies of several layers of different materials such as a composite floor and suspended ceiling system. A fire-resistance rating is the fire resistance assigned to a building element on the basis of a test or some other approval system. Some countries use the terms fire rating, fire-endurance rating or fire-resistance level. These terms are usually interchangeable. Fire resistance ratings are most often assigned in whole numbers of hours or parts of hours, in order to allow easy comparison with the fire-resistance requirements specified in building codes. For example, a wall that has been shown by test to have a fire resistance of 75 min will usually be assigned a fire resistance rating of 1 h.

5.4.2

Assessing Fire Resistance

Building elements need to be assigned fire-resistance ratings for comparison with the Fire severity specified by codes. The most common method of assessing fire resistance is to carry out a full scale fire resistance test. It is becoming increasingly possible to assess fire resistance by calculation In lieu of full scale tests, as permitted explicitly by codes such as the Uniform Building Code. The results of assessment of fire resistance obtained from tests, calculations or expert opinions are

5.4 Fire Resistance

305

listed in various documents maintained by testing authorities, code authorities or manufacturers. These listing of fire resistance rating are in three main categories; generic rating, which apply to typical materials, proprietary ratings, which are linked to particular manufacturers and approved calculation methods. Generic and proprietary rating is obtained directly or indirectly from full scale fire resistance tests. This chapter describes all these methods of assessing and listing fire resistance. Fire resistance of any building element depends on many factors, including the severity of the fire test, the material, the geometry and support conditions of the element, restraint from surrounding structure and the applied loads at the time of the fire. Many building codes and manufacturers documents simply list fire resistance of 1, 2 or 4 h with little or no reference to these factor which are discussed in this book.

5.4.3

Fire Resistance Tests

Almost all countries have building codes that specify fire resistance rating for building elements. Fire resistance ratings are most often specified in hours or minutes, with typical values ranging from half an hour to 2, 3 or 4 h. The timetemperature curves followed in the tests have been described in previous section. Fire-resistance test are not intended to simulate real fires. Their purpose is to allow a standard method of comparison between the fire performance of structural assemblies. Many countries require that fire resistance be based on the results of full scaled fire resistance tests. The required sizes for full scale tests are given below. Full scale tests are expensive, but for many years it has been considered essential to test elements of building construction at a large scale because cheaper small scale tests are not able to assess the effects of potential problems caused by connections, shrinkage, deflections, and gaps between panels of lining materials. Full scale testing is the most common methods of obtaining fire resistance rating, but fire resistance tests are very expensive, so are only undertaken when considered necessary. The high expense of full scale fire resistance testing is encouraging manufacturers to share test results within trade organizations, and is hastening the developing of new calculation methods to predict fire resistance by calculation rather than by a test. All calculations should be based on the results of full scale test to avoid the potential problems described above. Fire resistance test are carried out on representative specimens of building elements. For example, if a representative sample of flooring system has been exposed to the standard fire for at least 2 h while meeting the specified failure criteria, a similar assembly can be assigned a 2 h fire resistance rating for use in real

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5 Fire-Resistant Composite Structures: Calculations and Applications

building. The implication is that the built assembly will behave at least as well a real building. The implication is that the built assembly will behave at least as well in a real fire as the tested assembly did in the full scale fire test. Obvious difficulties are that there are many differences between the tested and built assemblies. The tested assemblies nearly always have different sizes.and shapes, and different loads or boundary conditions than in real buildings, and the test fire may be very different from a real fire. These problems are addressed later in this book.

5.4.4

Standards

For fire resistance testing, many countries use the International Standard ISO 834 (International Standards Organisation 1975) or have national standards based on ISO 834 (for example AS 1530 Part 4. Most European countries have standards similar to ISO 834. The standard used in the United States and some other countries is ASTM E119, first published in 1918. The Canadian standard (ULC 1989) is based on ASTM E 119. The relevant British Standards are BS 476 Parts 20–23.

5.4.5

Test Equipment

A typical fire-test franc consists of a large steel box lined with fire bricks or a ceramic fibre blanket. The furnace will have a number of burners, most often fuelled by gas but sometimes by fuel oil. There must be an exhaust chimney, several thermocouples for measuring gas temperatures and usually a small observation window. National and international standards for fire-resistance testing do not specify the construction of the furnace in detail, which sometimes causes problems when making comparisons, between tests from different furnaces. The standards are more concerned with the fire temperatures to be followed during the test and the failure criteria. As stated in this chapter, most national standards are based on either the ASTM E119 test or the ISO 834 test, which have some minor but important differences. Fortunately, despite minor differences, fire-resistance test methods are very similar around the world, so that international comparisons are always possible. It is exceedingly difficult for any country to make a major change to standard test procedures because of the cost of re-testing and re-classifying the large number of assemblies which have been tested in the past. In a typical test, a wall or floor assembly is constructed in a frame remote from the furnace, then brought to the furnace in its frame, and used to close off the furnace opening before the test begins. The burners are ignited at the start of the test and controlled to produce the time-temperature curve specified by the testing standard. Temperatures, deformations and applied loads are monitored during the

5.5 Fire Severity

307

test. The essential temperature measurements are those in the furnace itself and on the unexposed face of the specimen. In some tests, temperatures are measured at other locations within the test specimen or inside the furnace for research and development purposes. The most common apparatus for full-scale fire-resistance testing is the vertical wall furnace. The minimum size specified by most testing standards is 3.0  3.0 m2 (ISO 834 or ASTM El19). Some furnaces are 4.0 m tall.

5.5

Fire Severity

This section gives an overview of basic methods for designing structures for fire safety. It describes methods or quantifying the severity of post-flashover fires, for comparison with the provided fire resistance. This chapter describes the standard fire used for fire-resistance testing and approvals, and the concept of equivalent fire severity which is used for comparing real fires with the standard time temperature curve.

5.5.1

Fire Severity and Fire Resistance

5.5.1.1

Verification

The fundamental step in designing structures for fire safety is to verify that the fire resistance of the structure (or each part of the structure) is greater than the severity of the fire to which the structure is exposed. This verification requires that the following design equation be satisfied: fire resistance  fire severity

(5.16)

where fire resistance is a measure of the ability of the structure to resist collapse, fire spread or other failure during exposure to a fire of specified severity, fire severity is a measure of the destructive impact of a fire, or a measure of the forces of temperatures which could cause collapse or other failure as a result of the fire. There are several different definitions of fire severity and fire resistance, leading to different ways of comparing them using different units. These comparisons can be confusing if not made correctly, so it is important for designer to understand the alternatives clearly. As shown in Table 5.3, there are three methods for comparing fire severity with fire resistance. The verification may be in the time domain, the temperature domain or the strength domain, as discussed below.

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Table 5.3 There are three methods for comparing fire severity with fire resistance Domain Time

Units Minutes or hours

Fire resistance Time to failure

Temperature



Temperature to cause failure

Strength

kN or kNm

5.5.1.2

Time Domain

C

Load capacity at elevated temperature

 Fire severity  Fire duration as calculated or specified by code  Maximum temperature reached during the fire  Applied load during the fire

By far the most common procedure is for fire severity and fire resistance to be compared in the time domain such that: tfail  ts

(5.17)

where tfail is the time to failure of the element, and ts is the fire duration, as specified by a code or calculated, both times having units of minutes or hours. The time to failure of a building element is usually a fire-resistance rating, which may be obtained from a published listing of ratings or by calculation, as described in Chap. 4. The fire duration, or fire severity, is usually a time of standard fire exposure specified by a building code, or the equivalent time of standard fire exposure calculated for a real fire in the building, as described later this chapter.

5.5.1.3

Temperature Domain

It is sometimes necessary to verify design in the temperature domain by ensuring at the maximum temperature ( C) in a part of the structure is no greater than the temperature ( C) which would cause failure. Failure in this context could be thermal failure of a separating element or structural collapse of load-bearing member. Verification in the temperature domain requires that: Tfail  Tmax

(5.18)

where Tfail is the temperature which would cause failure of the element, and Tmax is the maximum temperature reached in the element during the fire, or the temperature at a certain time specified by the code. The temperature reached in the element can be calculated by a thermal analysis of the structural assembly exposed to the design fire. For a separating element, the failure temperature is the temperature on the unexposed face which would allow fire to spread into the next compartment. For a structural element, the temperature which would cause collapse can be calculated from knowledge of the loads on the

5.5 Fire Severity

309

element, the load capacity at normal temperatures, and the effect of elevated temperatures on the structural materials. The temperature domain is the most likely to be used for an element which serves an insulating or containing function. The temperature domain is less suitable for structural elements because it does not adequately consider internal thermal gradients or structural behavior.

5.5.1.4

Strength Domain

Verification in the strength domain is a comparison of the applied load at the time of the fire with the load capacity of structural members throughout the fire, such that Rf  Uf

(5.19)

where Rf is the minimum load capacity reached during the fire, or the load capacity at a certain time specified by the code, and Uf is the app lied load at the time of the fire. These values may be expressed in Units of force and resistance for the whole building, or as internal member actions such as axial force or bending moment in individual members of the structure. The load capacity during the fire can be calculated from a thermal analysis and a structural analysis at elevated temperatures, as described later in this chapter. The load capacity must be obtained by calculation because almost no structural test results are available for full burnout fires. The loads at the time of the fire can be calculated using load combinations from national loadings codes. No safety factors are shown in Eqs. (5.17), (5.18), and (5.19). This is because the required level of safety is obtained by using conservative values for the individual terms.

Example The comparison of fire severity with fire resistance described above can be rather confusing, so the three different domains of verification are illustrated with a simple example. Figure 5.24a shows the temperature of a steel beam during fire exposure. Calculations show that the beam will fail when the steel temperature reaches Tfail at time tfail. The building code requires that the beam should have a fire resistance of tcode or in other words the required fire severity is tcode. Verification in the time domain requires checking that the beam does not fail prematurely, so that the time to failure tfail is greater than the fire severity specified by the code tcode (check 1 in Fig. 5.24a). Verification in the temperature domain requires checking that the steel temperature which would cause failure Tfail is greater than Tcode which is the temperature reached in the beam at time tcode

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5 Fire-Resistant Composite Structures: Calculations and Applications

a

(steel tempereture)

Fig. 5.24 Behaviour of a steel beam in fire: (a) temperature increase, (b) loss of strength

T rail T code

2

failure of steel beams

1

code fire resistance time

load capacity

b

R colde

R code U1

failure of steel beams

3

code fire resistance

T code

T rail

time

(check 2 in Fig. 5.24a). These two checks will give identical results because they are both based on the same process. Figure 5.24b shows the load capacity of the same steel beam during the fire. The imposed load at the time of the fire is Uf. The load capacity before the fire is Rcold and the graph shows how this decreases during the fire. At the time tcode the load capacity of the beam has reduced to Rcode. Verification in the strength domain simply requires checking that the reduced load capacity is greater than the applied load (check 3 in Fig. 5.24b). All three of these verification checks give identical results. Figure 5.25 illustrates a range of different design situations. The left-hand column shows three fire exposure models which represent three different ways in which a design fire can be specified. Fire exposure H1 represents exposure to a standard test fire for a specified period of time, tcode as prescribed by a building code. This is the most common specification of fire exposure. Traditional prescriptive codes specify the required fire resistance directly, leaving little opportunity for fire engineers to calculate a specific fire severity for any particular building. Prescriptive codes usually require fire

5.5 Fire Severity Structural Response Modal

311 S1 Elements

S2 Sub-assemblies

S3 Structures

------------------------Fire Exposure Modal H

Test or Calculation

Calculation Occasional test

Difference in schematization becomes too large

Test or Calculation

Calculation Occasional test

Calculation unpractical

Calculation occasional

Calculation

Calculation occasional and for research

1

H 2

H 3

Fig. 5.25 Fire models and structural response models (Reprinted from CIB (1986) with permission from Elsevier Science)

resistance to be somewhere between half an hour and 4 h, in half hour or 1 h steps, with little or no reference to the severity of the expected fire. Fire exposure H2 represents a modified duration of exposure to the standard test fire. The equivalent time, te is the time of exposure to the standard test fire considered to be equivalent to a complete burnout of a real fire in the same room. Methods of calculating equivalent fire severity are described later in this chapter. Many performance-based codes allow the use of time equivalent formulae as an improvement on simple prescriptive fire-resistance requirements. Fire exposure H3 represents a realistic fire which would occur if there was a complete burnout of the room, with no intervention or fire suppression. The other columns of Fig. 5.25 show that assessment of fire resistance may consider a single element, a sub-assembly or a whole structure. The words in the lower boxes show that test results are only likely to be used for single elements exposed to H1 or H2 fires, with calculations becoming necessary in most other cases. Verification that a member or structure has sufficient fire resistance will be by comparison of times, temperatures, or strength as described above. With reference to Fig. 5.25, verification to fire exposures H1 and H2 is likely to be in the time

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Table 5.4 Design combinations for verifying fire resistance Combination 1 2 3

Fire exposure model Prescriptive code (H1) Time-equivalent formula (H2) Predicted real fire

Assessment of fire resistance Listed rating or calculation Listed rating or calculation Calculation

Verification domain Time Time Temperature strength

domain, where an assigned fire resistance (in hours) is compared with the required fire resistance (also in hours). Verification using exposure to a complete burnout (H3) is more likely to be a comparison of temperatures for insulating elements or a comparison of strength for structural elements.

5.5.1.5

Design Combination

The above options illustrate that several alternative methods can be used for verifying fire resistance requirements. Because of the large number of possible combinations, it is essential for designers to specify clearly which combination of exposure and resistance is being used. Both the design and the assessment of the design can become very confusing if the selected combination is not clearly stated and used accordingly. Table 5.4 shows a list of the most common combination to help designer select a combination of a particular design. In very general terms, both the accuracy of the prediction and the amount of calculation effort increase downwards in the Table 5.4.

5.5.2

Fire Severity

Fire severity is a measure of the destructive potential of a fire. Fire severity is most often defined in terms of a period of exposure to the standard test fire, but this is not appropriate for real fires which have very different characteristics. The fire severity used for design depends on the legislative environment and on the design philosophy. In a prescriptive code environment, the design fire severity is usually prescribed with little or no room for discussion. In a performance-based code environment, the design fire severity is usually complete burnout fire or the equivalent time of a complete burnout fire. In some cases the design fire may be a shorter time which, only allows for escape, rescue or fire-fighting. The equivalent time of a complete burnout is the time of exposure to the standard test fire that would result in an equivalent impact on the element, as described later in this chapter. Damage to a structure is largely dependent on the amount of heat absorbed by the structural elements. Heat transfer from post-flashover fires is mainly radiative which is proportional to the fourth power of the absolute temperature. Hence the severity of a fire is largely dependent on the temperatures reached and the duration

5.5 Fire Severity

313

of the high temperatures. Some damage such as phase changes or melting are temperature dependent rather than heat-dependent, the maximum temperature as well as the duration of the fire is also important.

5.5.3

Standard Fire

Most countries around the world rely on full-size fire-resistance tests to assess the fire Performance of building materials and structural elements. The time–temperature curve used in fire-resistance tests is called the ‘standard fire’. Full-size tests are preferred to small-scale tests because they allow the method of construction to be assessed, including the effects of thermal expansion and deformation under load. Babrauskas and Williamson (1978c, d) and Cooper and Steckler (1996) describe the origin of the standard fire-resistance test. The most widely used test specifications are ASTM E 119 and ISO 834 (ISO 1975). Other national standards include British Standard BS 476 Parts 20–23, Canadian Standard CAN/ULC-S101-M89 and Australian Standard AS 1530 Part 4. Most national standards are based on either the ASTM E l19 test or the ISO 834 test, which are compared below. This chapter concentrates on the fire temperatures in test furnaces. Other aspects of fire-resistance furnaces are described in more detail in Chap. 6.

5.5.3.1

Time-Temperature Curves

The standard time–temperature curves from ASTM E119 and ISO 834 are compared in Fig. 5.26. They are seen to be rather similar. All other international fire resistance test standards specify similar time—temperature curves. In the ISO 834 specification (ISO 1975) the temperature T ( C) is defined by T ¼ 345 1og10 ð8t þ lÞ þ T0

(5.20)

where t is the time (minutes) and T0 is the ambient temperature ( C). The ASTM E119 curve is defined by a number of discrete points, which are shown in Table 5.5, along with the corresponding ISO 834 temperatures. Several equations approximating the ASTM E119 curve are given by Lie (1995), the simplest of which give the temperature TðCÞ as T ¼ 750½1

e

p 3:79553 th

Š þ 170:41

p

t h þ T0

(5.21)

where th is the time (hours). Figure 5.26 also shows two alternative design fires from the Eurocode. The upper curve is the hydrocarbon fire curve, intended for use where a structural

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5 Fire-Resistant Composite Structures: Calculations and Applications

Fig. 5.26 Standard time— temperature curves

Table 5.5 ASTM E 119 and ISO 834 time—temperature curves Time (minutes) 0 5 10 30 60 120 240 480

ASTM E119 temperature ( C) 20 538 704 843 927 1,010 1,093 1,260

ISO 834 temperature ( C) 20 576 678 842 945 1,049 1,153 1,257

member is engulfed in flames from a large pool fire. The temperature T ( C) in the hydrocarbon fire curve is given by T ¼ 1080ð1

0:325e

0:167t

0:675e

2:5t

Þ þ T0

(5.22)

The lower curve is intended for the design of structural members located outside a burning compartment. Unless they are engulfed in flames, exterior structural members will be exposed to lower temperatures than members inside a compartment. The temperature T ( C) for external members is given by T ¼ 660ð1

0:687e

0:32t

0:313e

3:8t

Þ þ T0

(5.23)

where for Eqs. (5.22) and (5.23), t is the time (minutes) and T0 is the ambient temperature ( C).

5.5 Fire Severity

5.5.3.2

315

Furnace Parameters

Fire severity in a test environment depends on a number of characteristics of the testing furnace. Even if two furnaces are operated according to the same timetemperature curve, they may not impact the test specimen with the same severity of fire exposure, depending on various parameters. Temperatures are not always uniform throughout the furnace. Even if the average temperature follows the specified curve precisely, this may be an average of lower and higher temperatures which could have a severe local impact on the test specimen. It is clear from Fig. 5.26 that the ASTM E119 and ISO 834 curves are similar. The tests can be considered to give roughly equivalent thermal exposure, but there are some significant differences. Heating of furnaces is controlled to ensure that the temperatures measured by thermocouples follow the prescribed curve given by Eq. (5.20) or Table 5.3. The ASTM E 119 specification requires furnace temperatures to be measured with thermocouples located in heavy steel pipes with capped ends, which heat up more slowly than the exposed thin wire thermocouples specified in the ISO 834 test, so even for the same temperature curve, the furnace gas temperatures will be higher in the furnace with capped thermocouples than in a furnace with bare wire thermocouples. Babrauskas and Williamson (1978b) have shown that the temperature difference is most significant during the first 5 min of the test. For the same method of measuring temperature, and the same time—temperature curve, there can be significant differences between the heating conditions in various furnaces, depending on the size of the furnace, the type of fuel and the furnace lining material. Fire-resistance furnaces can be fuelled with either oil or gas. Some gas-fired furnaces have pre-mixed burners, others diffusion burners. These differences in fuel and fuel mixing can affect the luminosity of the flames, which affects the emissivity, hence the heat transfer to the furnace walls and to the test specimen. The most common wall lining materials are fire bricks or ceramic fibre blankets which have very different thermal properties, hence different rates of heat transfer to the test specimen. Temperatures will increase less rapidly in furnaces lined with bricks. The differences between furnaces has been a particular problem in Europe, where harmonization of testing standards between many countries is in progress. As a solution it is being proposed that furnace conditions should be controlled by replacing the usual small thermocouples with a ‘plate thermometer’ which is designed to measure the exposure of the test sample rather than the temperature of the furnace gases. Most European countries- are supporting the adoption of a European standard for the plate thermometer, which is expected to greatly reduce the differences in severity of exposure between furnaces in different countries.

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5 Fire-Resistant Composite Structures: Calculations and Applications

Fig. 5.27 Equivalent fire severity on equal area basis

5.6 5.6.1

Equivalent Fire Severity Real Fire Exposure

The concept of equivalent fire severity is used to relate the severity of an expected real fire to the standard test fire: This is important when designer want to use published fire-resistance rating from standard tests with estimates of real fire exposure. This section describes methods of comparing real fires, to the standard test fire.

5.6.2

Equal Area Concept

Early attempts at time equivalence compared the area under time-temperature curves. Figure 5.27 illustrates the concept, first proposed by Ingberg (1928a), by which two fires are considered to have equivalent severity if the areas under each curve are equal, above a certain reference temperature. This has little theoretical significance because the units of area are not meaningful. Even though Ingberg was aware of its technical inadequacy he used the equal area concept as a crude but useful method of comparing fires. After carrying out furnace tests, he developed a relationship between fire load in a room and the required fire resistance of the surrounding elements. This approach, subsequently used by US code writers to specify fire-resistance ratings, has been useful, but ignores the effects of ventilation and fuel geometry on fire severity. The equal area concept is used for correcting the results of standard fireresistance tests if the standard curve is not exactly followed within the tolerances specified in the standard.

5.6 Equivalent Fire Severity

317

The impact of a fire on a surrounding structure is a function of a heat transfer into the structure. A problem with the equal area concept is that it can give a very poor comparison of heat transfer for fires with different shaped time-temperature curves. Heat transfer from a fire to the surface of a structure is mostly by radiation the balance by convection. Because radiative heat transfer is proportional to the fourth power of the absolute temperature, heat transfer to the surface in a short hot fire may be much greater than in a long cool fire, even if both have equal areas under the time-temperature curves. Babrauskas and Williamson (1978a, b) also point out that there could be a critical difference between a short hot fire and a longer cool fire if the maximum temperature in the former is sufficient to cause melting or some other critical phase change in a material which would be much less affected in the cooler fire.

5.6.3

Maximum Temperature Concept

A more realistic concept, developed Law (1971), Pettersson et al. (1976) and others, is to define the equivalent fire severity as the time of exposure to the standard fire that would result in the same maximum temperature in a protected steel member as would occur in a complete burnout of the fire compartment. This concept is shown in Fig. 5.28 which compares the temperatures in a protected steel beam exposed to the standard fire with those when the same beam is exposed to a particular real fire. In principle, this concept is applicable to insulating elements if the temperature on the unexposed face is used instead of the steel temperature, and is also applicable to materials which have a limiting temperature, such as the 300  C temperature at which charring of wood generally begins. The maximum temperature concept is widely used, but it can give misleading results if the maximum temperatures used in the derivation of a time-equivalent formula are much greater or lower than those which would cause failure in a particular building.

5.6.4

Minimum Load Capacity Concept

In a similar concept based on load capacity, the equivalent fire severity is the time of exposure to the standard fire that would result in the same load bearing capacity as the minimum which would occur in a complete burnout of the firecell. This concept is shown in Fig. 5.29 where the load bearing capacity of a structural member exposed to the standard fire decreases continuously, but the strength of the same member exposed to a real fire increases after the fire enters the decay period and the steel temperatures decrease. This approach is the most realistic time equivalent concept for the design of load bearing members. The minimum load concept is difficult to implement for a-material which does not have a clearly defined minimum load capacity, for example with wood members where charring can continue after the fire temperatures start to decrease.

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5 Fire-Resistant Composite Structures: Calculations and Applications

Fig. 5.28 Equivalent fire severity on temperature basis

Fig. 5.29 Equivalent fire severity on load capacity basis

5.6.5

Time-Equivalent Formulae

A number of time-equivalent formulae have been developed by fitting empirical curves to the results of many calculations of the type shown conceptually in Fig. 5.28. The resulting formulae are based on maximum temperature of protected steel members exposed to realistic fires. The most widely used time equivalent formula is that published by the CIB W14 group (CIB 1986), derived by Pettersson (1973) based on the ventilation parameters of the compartment and the fuel load. The equivalent time of exposure to an ISO 834 test te (min) is given by t e ¼ ke w ef

(5.24)

where ef is the fuel load (MJ/m2 of floor area), kc is a parameter to account for different compartment linings, and w is the ventilation factor (m 0.25) given by:

5.6 Equivalent Fire Severity

319

Af w ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Av At Hv

(5.25)

where Af is the floor area of the compartment (m2), Av is the total area of an opening in the walls (m2), At is the total area of the internal bounding surfaces of the compartment (m2), and Hv is the height of the window (m).

5.6.5.1

Law Formula

A similar formula was developed by Margaret Law on the basis of tests in smallscale compartments (Thomas and Heselden 1972) and larger-scale compartments. The formula is given by: te

Af e f pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ΔHc Av ðAt Av Þ

(5.26)

where ΔHc is the calorific value of the fuel (MJ/kg). The CIB formula and the Law formula are only valid for compartments with vertical openings in the walls. They cannot be used for rooms with openings in the roof. The Law formula gives similar results to the CIB formula, generally with slightly larger time equivalent values.

5.6.5.2

Eurocode Formula

These formulae were later modified and incorporated into the Eurocode, referred to often as the Eurocode Formula giving te (minutes) as te ¼ kb w ef

(5.27)

where kb replaces kc and the ventilation factor w is altered to allow for horizontal roof openings. The ventilation factor is given by #  0:3 " 6:0 90ð0:4 αv Þ4 w¼ 0:62 þ > 0:5 Hr 1 þ bv ah

(5.28)

where Hr is the compartment ceiling height (m) αv ¼ Av =Af 0:05  αv  0:25

(5.29)

αh ¼ Ah =Af αb  0:20

(5.30)

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5 Fire-Resistant Composite Structures: Calculations and Applications

Table 5.6 Values of kc or kb in the time equivalent formulae b ¼ √kρc p High

Medium

Formula Term Units >2,500 720–2500 min m2.25/MJ 0.05 0.07 CIBWI4 kc Eurocode kc min m2.25/MJ 0.04 0.055 min m2.25/MJ 0.05 0.07 Large compartments kc k thermal conductivity (W/mK), ρ density (kg/m3), cp, sped: heat (J/kg K)

bv ¼ 12:5 ð1 þ 10 αv

αv 2 Þ

Low b2 then the b value depends on the thickness of the heavier material and the time of the heating period of the fire. The limiting thickness Slim,1 of the fire-exposed material is calculated from Slim;1

sffiffiffiffiffiffiffi tk ¼ ρcp

(5.36)

where t is the time of the heating period of the fire(s) and the thermal properties are for material 1. If s₁ > Slim,₁ then b ¼ b₁, and if s₁ < Slim,₁ then b ¼ (s₁/Slim,₁) b₁ + (1 s₁/Slim,₁) b₂.

5.7.2.3

Duration of Burning Period

The equation for the duration of the burning period td (hours) in the Eurocode simplifies to td ¼

0:00013et 0:00013E pffiffiffiffiffiffi ¼ Fv Av Hv

(5.37)

where et is the fuel load (MJ/m2 total surface area), and E is the total energy content of the fuel (MJ). Assuming a value for heat of combustion of ΔHc ¼ 15.5 MJ/kg, the duration of the burning period given by Eq. (5.37) is only 67 % of the theoretical duration. The reason for this is not stated in the Eurocode, but it is probably intended to allow for some burning to take place during the decay period of the fire. If the heat release rate is constant during the burning period with a linear decay rate, the implied curve of heat release rate versus time is shown in Fig. 5.36 where the duration of the decay period is equal to the duration of the burning period.

Decay Rate The Eurocode uses a reference decay rate (dT/dt) ref equal to 625 per hour for fires with a burning period less than half an hour, decreasing to 250 per hour for fires with a burning period greater than 2 h, based on the ISO 834 testing standard (ISO 1975). This decay rate is shown in Fig. 5.32. In the Eurocode, the reference temperature is modified using fictitious time from Eq. (5.33). This fictitious time, derived for use during the burning period, has not

5.7 Design Fires

327

Fig. 5.32 Heat release rate implied by Eurocode parametric fire

been justified for use in the decay period, and has been shown to give unsatisfactory results, with extremely fast decay rates for large openings in well-insulated compartments and extremely slow decay rates for small openings in poorly insulated compartments (Fig. 5.33). Feasey and Buchanan (2000) have shown that it is more accurate to modify the reference decay rate for ventilation factor and thermal insulation in a different way, with the resulting design decay rate given by dT ¼ dt



dT dt



ref

qffiffiffiffiffiffi Fv 0:04

qffiffiffiffiffiffiffi

(5.38)

b 1900

This is equivalent to using a second fictitious time, similar to that in the growth period, but using square root rather than squared terms to give a much better fit to test results and computer simulations.

5.7.2.4

Time-Temperature Curves

Figure 5.34 shows the modified Eurocode time-temperatures equation plotted for a range of ventilation factors, fuel loads, and materials. The temperatures in the burning period have been calculated from Eqs. (5.34) and (5.37). The rate of temperature decay is from Eq. (5.38), not from the Eurocode. In each part of Fig. 5.34, curves have been drawn for three fire loads and for two types of construction, showing the significant dependence of fire are 400, 800 and 1,200 MJ/m2 floor area, for a room 5  5 m in plan and 3 m high. The materials are normal weight concrete(b ¼ 1,900 W s0.5m2K) and gypsum plaster board (b ¼ 410 W s0.5m2K). A typical commercial office building with a mixture of

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5 Fire-Resistant Composite Structures: Calculations and Applications

Fig. 5.33 Rate of temperature decay in Eurocode parametric fires

these material on the walls and ceiling would give curves between these two, similar to a building made from lightweight concrete. The Eurocode suggestion of limiting the lower value of thermal inertia to b ¼ 1,000 Ws0.5m2K has not been followed, in order to give closer results to the European test fires.

5.8

Concrete Structures

This section describes simple methods of designing reinforced concrete structure to resist fires, including information on thermal and mechanical properties of concrete and structural design methods. Prestressed concrete and composite steel-concrete structures are also covered briefly.

5.8.1

Behaviour of Concrete Structure in Fire

Concrete structures have a reputation for good behavior in fires. A very large number of reinforced concrete buildings which have experience severe fires have been repaired and put back into use (Fig. 5.35). Concrete is non-combustible and has a low thermal conductivity. The cement paste in concrete undergoes an endothermic reaction when heated, which assists in reducing the temperature rise in fire-exposed concrete structures. Concrete tends to remain in place during a fire, with the cover concrete protecting the reinforcing steel, with the cooler inner core continuing to carry load (Fig. 5.36).

5.8 Concrete Structures

329

Fig. 5.34 Parametric time—temperature curves (fuel load is 400, 800 and1,200 MJ/m2 floor area)

Fig. 5.35 Non-structural fire damage to a typical reinforced concrete office building

Calculation of the behaviour of concrete structures in fire depends on many factors, the most important being the applied loads on the structure, the elevated temperatures in the concrete and reinforcing and the mechanical properties of the steel and concrete at those temperatures. When a reinforced concrete structure is exposed to a fire, the temperatures of both steel and concrete increase, leading to increased deformation and possible failure, depending on the applied loads and the support conditions. Most types of concrete behave similarly in fires. This chapter

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5 Fire-Resistant Composite Structures: Calculations and Applications

Fig. 5.36 (a) A multi-storey office building engulfed in flames. The reinforced concrete structure did not collapse in the fire [Sao Paolo, Brazil, 1972]. (b) Severe spalling of a reinforced concrete wall in the fire

refers to the slightly different performance of concrete made with different types of aggregate, lightweight concrete and high-strength concrete. Catastrophic failures of reinforced concrete structures in fire are rare, but some occasionally occur (Fig. 5.37). Observations have shown that when concrete buildings fail in real fires, it is seldom because of the loss of strength of the materials, but nearly always because of the inability of other parts of the structure to absorb the large imposed thermal deformations in the horizontal direction which can cause shear or buckling failures of columns or walls (A. van Acker personal communication).

5.8.2

High-Strength Concrete

There has been considerable interest recently in high-strength concrete as a high performance construction material. High-strength concrete contains additives such as silica fume and water-reducing admixtures which result in compressive strength in the range 50–120 MPa. An extensive survey of high-strength concrete properties at elevated temperatures by Phan (1996) shows that they tend to have a higher rate of strength loss than normal concrete at temperatures upto 400, and explosive spalling is a problem in some cases. Fire tests on high-strength columns are reported by Aldea et al (1997) and Kodur (1997). In some studies, the compressive strength at elevated temperatures is found to be higher when the concrete is heated at stress, rather than loaded after heating. Design recommendations are give by Tomasson (1998) who recommends the simplified method of Eurocode 2 (EC2 1993), ignoring the strength contribution of concrete which is hotter than 500. For columns he suggests changing the limiting temperature to 400.

5.8 Concrete Structures

331

Fig. 5.37 Major structural damage to a multi-storey reinforced concrete department store [Athens, 1980]. Reproduced from Papaioannou (1986) by permission of John Wiley and Sons, Ltd

5.8.3

Lightweight Concrete

Lightweight concrete is usually made with normal cement and some form of lightweight aggregate such as pumice or expanded clay or shale. Other possible materials include perlite and vermiculite. Lightweight concrete has been shown to have excellent fire resistance, due to its low thermal conductivity compared with normal weight concrete. Many listings of generic fire-resistance ratings have separate tables for lightweight concrete. Many lightweight aggregates have been manufactured at high temperatures, so they remain very stable during fire exposure.

5.8.4

Fibre Reinforced Concrete

Steel-fibre reinforced concrete uses small steel fibres added to the concrete mix, to improve concrete toughness and strength. The fibres are typically 0.5 mm diameter, and 25–40 mm long with crimped or hooked ends to improve the bond. Thermal and mechanical properties of steel-fiber reinforced concrete at elevated temperatures are given by Lie and Kodur (1996). They show that the presence of steel fibres increases the ultimate strain and improves the ductility of the concrete.

5.8.5

Spalling

The design recommendations in this book for calculating thermal gradients and structural behaviour in concrete members, are based on tile assumption that all the concrete-remains intact for the duration of the fire. This assumption is not valid if

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5 Fire-Resistant Composite Structures: Calculations and Applications

the cover concrete spalls off a member during a fire, exposing some or all of the main reinforcing steel to the fire. Experiments and real fire experience have shown that most normal concrete members can withstand severe fires without serious spalling, but minor spalling often occurs. Note that ‘cover concrete’ refers to the concrete outside the main reinforcing cage, protecting the reinforcing steel from moisture, corrosion and fire. The ‘cover’ is the distance from the surface of the concrete to the reinforcing steel. For durability considerations, the cover is usually measured from the concrete surface to the closest face of the main bars, but for fire engineering the cover is usually measured from the concrete surface to the centre of the main bars. Care must be taken to avoid confusing these two definitions. The phenomenon of spalling is not well understood because it is a function of several different factors, often leading to unpredictable behaviour. In some cases spalling is related to the type of aggregate or to thermal stresses near corners, but it is more often linked to the behaviour of the cement paste. It is generally agreed that spalling most often occurs when water vapour is driven, off from the cement paste during heating, with high pore pressures creating effective tensile stresses in excess of the tensile strength of the concrete. Experiments have shown that increased susceptibility to spalling results from high moisture content concrete, rapid rates of heating, slender members, and high concrete stresses at the time of the fire (Fig. 5.38). Malhotra (1984) and Phan (1996) review studies of spalling. Highstrength concrete tends to be more susceptible to spalling than normal concrete since it has smaller free pore volume (higher paste density), so that the pores become filled with high-pressure water vapour more quickly than in normal weight concrete and the low porosity results in slower diffusion of the water vapour through the concrete. Even though serious spalling of concrete is unlikely, the probability of occurrence requires consideration for critical structures or those containing high-strength concrete. The addition of an additional reinforcing cage to prevent spalling is impractical and expensive. The best economical method of preventing spalling is the addition of fine polypropylene fibres to the concrete mix (0.15–0.3 %). These fibres reduce the likelihood of spalling because the polypropylene melts during fire exposure, increasing the porosity by leaving cavities through which the water vapor can escape, as described by Kodur (1997). Steel fibres added to concrete mix will reduce the probability of spalling by increasing the fracture toughness of the concrete, but this is much more expensive than adding polypropylene fibres.

5.8.6

Masonry

Concrete masonry consists of hollow concrete blocks mortared together, most often used in walls. In many areas, especially seismic regions, reinforcing bars are placed in the hollow cores which are then filled with concrete to create solid reinforced concrete masonry which has essentially the same fire behavior as reinforced

5.8 Concrete Structures

333

Fig. 5.38 Local spalling at the corner of a concrete beam

concrete. Concrete masonry blocks are often manufactured from lightweight concrete, giving enhanced fire-resistant properties. Fire resistance rating of many different types of concrete masonry are given by Allen (1970). Unfilled unreinforced masonry has less thermal mass and potential lines of integrity failure at the mortar joints, but has demonstrated excellent fire resistance, provided that the foundations and supporting structure can keep the wall in place during the anticipate fire. Hollow-core block walls can be considered to have the equivalent thickness of a solid wall of the same volume of concrete, and to have the same generic fire-resistance rating (NBCC 1995). All joints between blocks and shrinkage control joints must be able to provide the same fire rating as the rest of the wall. Some construction details are given in the Uniform Building Code (UBC 1997). Some method for fire design of masonry are given in Eurocode 6 (EC6 1995). Brick masonry also behaves well in fires. Ceramic bricks are made by firing clay at high temperatures, producing bricks which remain stable when exposed to fires. Brick masonry can be reinforced if it is made from hollow bricks, but most brick masonry consists of solid bricks joined only with lime or cement mortar. Thermal bowing of very tall unreinforced cantilever masonry walls can lead to collapse during a severe fire on one side of the wall.

5.8.7

Prestressed Concrete

The term prestressed concrete refers to concrete structures which are stressed prior to the application of any external loads. There are two main types of prestressing; pre-tensioned and post-tensioned. For pre-tensioned prestressed concrete, the steel tendons are stressed in tension against a reaction frame or the mould before the

334

5 Fire-Resistant Composite Structures: Calculations and Applications

concrete is cast, so that the prestressing force is resisted by bond stresses between the concrete and the tendon after the tendons are cut. Post-tensioned prestressed concrete is cast with ducts for the steel tendons which are stressed with hydraulic jacks after the concrete has cured. The prestressing force is resisted by permanent anchorage points at the ends of the tendons. Pre-tensioned prestressed concrete is most often used for precast components for flooring, including flat panel’s, hollow-core panels, double-tee floor units or concrete planks for supporting non-prestressed components. Post-tensioning is used within large components such as beams or slabs, or for connecting several precast concrete elements together. Prestressing tendons are made of high-strength steel, often manufactured by pulling steel wires through a die, or otherwise cold-working the steel. Cold-worked steel suffers permanent loss of strength when subjected to elevated temperatures. Most of this chapter refers to reinforced concrete. The same principles apply to prestressed concrete which is often more vulnerable in fires because prestressing steels are much more sensitive to elevated temperatures than mild steel reinforcing bars, because prestressed concrete is often manufactured in slender components with thin cover concrete and because some failure modes such as debonding, shear and spalling are more critical in prestressed concrete (Gustaferro and Martin 1988). Recent full-scale fire tests have shown that bond failures of pre-tensioned tendons have caused premature failures much before the calculated fire-resistance time. A series of tests on double-tee and hollow-core slabs, simply supported without axial restraint over a span of 6 m, showed that the ends of the tendons were pulled into the concrete due to loss of bond near the ends of the specimens. In these tests, collapse resulted from shear failure in the web after the compressive stresses had been reduced near the ends of the slabs. Similar results for hollow-core slabs have been observed elsewhere.

5.8.8

External Reinforcing

Various forms of external reinforcing are used in special structures. The most common is steel decking used as permanent formwork in composite constructions. Design of composite steel decking construction exposed to fires is described later in this chapter. The use of fibre-epoxy coatings is new technology being used to improve the strength of existing reinforced concrete structures. The fibre-epoxy coatings consist of mats of glass, carbon or teflon fibres surrounded by epoxy resin. These fibreepoxy coatings can be wrapped around columns to improve the confinement to the concrete or can be glued to the surface of beams to increase the flexural strength External fibre-epoxy coatings have zero fire resistance because the epoxy will melt and burn away at low temperatures. However, the residual reinforced concrete structure will usually have sufficient strength to carry the applied loads, and the coating can be re-applied after a fire.

5.9 Fire-Resistance Ratings

5.9 5.9.1

335

Fire-Resistance Ratings Verification Methods

The emphasis of this section is on using scientific knowledge to estimate the fire performance of concrete members and structures. The design process for fire resistance requires verification that the provided fire resistance exceeds the design fire severity. Verification may be in the time domain, the temperature domain or the strength domain. For reinforced concrete structures, fire resistance is most often verified in the time domain, by comparing generic fire resistance ratings with codespecified levels of fire resistance. For more detailed assessment of important structures, the load bearing capacity is compared with the expected loads on the structure at the time of the fire, in the strength domain. Calculations comparing critical temperatures (in the temperature domain) are not usually used for concrete structures.

5.9.2

Generic Ratings

In contrast to steel structures, there are very few proprietary rating used for concrete structures, and generic ratings are most often used. Generic rating, or ‘tabulated ratings’ are those which assign fire resistance to materials with no reference to individual manufacturers or detailed specifications. Many national codes and some trade organizations list generic ratings for concrete constructions, usually giving minimum sizes and minimum concrete cover to reinforcing steel. It is assumed in all these tables that the concrete has sufficient reinforcing to resist the loads at normal temperatures. Some generic ratings distinguish between normal weight and lightweight concrete, and others further differentiate normal weight concrete into siliceous aggregate and calcareous (limestone) aggregate concretes. Table 5.7 shows typical values of generic fire resistance ratings for reinforced concrete members, from BS 8110. The Table 5.7 gives minimum width (or thickness) and minimum cover to the reinforcing, steel for several different types of reinforced concrete members. The cover is measured to the surface of the reinforcing bar. Similar tables are available for prestressed concrete. This type of information is usually very conservative, it applies only to standard fire exposure, and it makes no allowance for the shape of the fire exposed member or the level of load. There is no guidance for situations where the cover is different from that shown in the Table 5.7. The minimum thicknesses of floor slabs and walls are mostly based on the insulation criterion of preventing a temperature increase of 140  C on the unexposed surface. More comprehensive generic ratings are given in the Eurocodes, those for load-bearing walls and columns including the level of applied load, and those for beams giving several optional combinations of beam width and concrete cover.

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5 Fire-Resistant Composite Structures: Calculations and Applications

Table 5.7 Minimum width (mm), and minimum cover (mm) for generic fireresistance ratings of reinforced concrete members

0.5 h 1.0 h 1.5 h 2h 3h 4h

Width Cover Width Cover Width Cover Width Cover Width Cover Width Cover

Beams 80 20 120 30 150 40 200 50 240 70 280 80

Columns 150 20 200 25 250 30 300 35 400 35 450 35

Slabs 75 15 95 20 110 25 125 35 150 45 170 55

Walls 75 15 75 15 100 25 100 25 150 25 180 25

Because concrete structures usually have good fire performance, many will meet the generic approvals with no increase in cover from normal temperature design, so that detailed calculations may not be necessary for fire-resistance ratings up to about 1.5 h. Calculations are most likely to be useful for members which are thin or slender, members with little concrete cover to the reinforcing, and members which are very highly stressed under gravity loads.

5.9.3

Protection Systems

It is possible to enhance the fire performance of a concrete member by the application of protective layers such as gypsum board or trowelled on plaster, but this is not often clone because it is cheaper to simply increase the member size or move the reinforcing bars further from the surface to increase the cover. Some generic listings include extra plaster protection or overlays of various forms of lightweight concrete.

5.9.4

Joints Between Precast Concrete Panels

It is often necessary to provide fire resistance to gaps between precast concrete panels. Gustaferro and Martin (l988) report tests on various types of protection for such gaps. Compressed ceramic fibre blanket can give excellent fire resistance. An additional water-proofing sealant can be used to seal the joint for weatherproofing and visual appearance.

5.10

5.10

Concrete and Reinforcing Temperatures

337

Concrete and Reinforcing Temperatures

5.10.1 Fire Exposure In any specific design of concrete structures exposed to fires, it is essential to know the temperatures of the concrete and the reinforcing steel. The fire exposure may be the standard time—temperature curve or a more realistic fire curve, depending on the design philosophy. Many design charts are available giving thermal gradients in beams, columns and slabs exposed to the standard fire, but no for realistic design fires. It is best to use computer-based thermal calculations to provide accurate temperature gradients in concrete members exposed to realistic fires.

5.10.2 Calculation Methods When making thermal calculations in reinforced or prestressed concrete members, it is usual to assume that the heat transfer is a function of the thermal properties of the concrete alone, and the temperature of the reinforcing is the same as the temperature of the surrounding concrete. Steel has a much higher thermal conductivity than concrete, but most reinforcing steel is parallel to the fire-exposed surfaces, so does not have a significant influence on heat transfer perpendicular to the surfaces. Some authorities have suggested that the much higher specific heat of steel than concrete, and possible moisture condensation, may result in the reinforcing steel being cooler than the surrounding concrete, but this concept is not used in design. Unlike steel members, the only accurate way to calculate temperatures is to use a two-dimensional finite-element computer program which gives the temperature distribution with time over the cross section. The advantage of such a program is that any combination of materials, shapes and voids can be included, for exposure to any desired fire. Most programs do not consider the mass transport of water or water vapor in fire-exposed concrete, although this has been studied by Ahmed and Hurst (1995). For simple members of normal-weight concrete, empirical hand calculation methods are available, derived from computer-based thermal analysis. The simple lumped-mass approach used for steel members is not appropriate for concrete. Wickstrom’s method of calculating the temperatures in a normal weight concrete slab in the standard fire is based on the fire-exposed surface temperature Tw being: Tw ¼ ηw Tf nw ¼ 1

0:0616th

(5.39) 0:88

where Tf is the fire temperature and th is the time (hours).

(5.40)

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5 Fire-Resistant Composite Structures: Calculations and Applications

Fig. 5.39 Temperatures in concrete slabs exposed to the standard fire (Reproduced from Wade (1991b) by permission of Building Research Association of New Zealand)

At any depth x (m) into the slab, at time th the concrete temperature Tc is a factor ηx of the surface temperature Tw with ηx given by: ηx ¼ 0:18 Inðth =x2 Þ

0:81

(5.41)

Hence the concrete temperature Tc is given by Tc ¼ ηx ηw Tf

(5.42)

This formula generally gives similar results to those shown in Fig. 5.39. The method can be used for corners of beams where there is heat conduction in two directions, using ηy calculated in the same way as ηx so that the concrete temperature Tc is now given by h Tc ¼ ηw ðηx þ ηy

i 2 η x η y Þ þ η x η y Tf

(5.43)

This approximate equation gives temperatures roughly similar to those for 160 mm wide beams, but does not make any allowance for the different rates of temperature increase in wider or narrower beams. Wickstrom (1986) shows how these equations can be modified for other types of concrete, and also gives approximate methods of calculating temperatures in concrete members exposed to realistic fires with a decay period. Empirical calculations in the decay period are less accurate because the maximum concrete temperatures occur a considerable time after the fire temperature passes its peak value (as shown in Fig. 5.40). A finiteelement calculation method is recommended for thermal analysis of concrete structures exposed to real fires.

Concrete and Reinforcing Temperatures

Fig. 5.40 Temperature-time curves inside concrete slabs exposed to design fires (Reproduced from Wade (1994) by permission of Society of Fire Protection Engineers)

339

700

opening factor = 0.08 fire load = 600 MJ/m2 (floor)

600 10 mm 20 mm 30 mm 40 mm 50 mm 60 mm 80 mm 100 mm 120 mm 150 mm Peak Temp

500 Temperature °C

5.10

400

300 200

100

0

0

60

120

180

240

Time (min)

5.10.3 Thermal Properties In order to calculate temperatures within structural assemblies it is necessary to know the thermal properties of the materials. These are discussed briefly below. The density of concrete depends on the aggregate and the mix design. Typical ‘dense’ concrete has a density of about 2,300 kg/m3. There are many ‘lightweight’ concretes which use porous aggregates or air entrainment to reduce the density to half or two-thirds of this value. When heated to 100  C the density of most concretes will be reduced by up to 100 kg/m3 due to the evaporation of free water, which has a minor effect on thermal response. Other than moisture changes, the density of concrete does not change much at elevated temperature, except for limestone (calcareous) aggregate concrete which decompose above 800  C with a corresponding decrease in density. The thermal conductivity of concrete is temperature dependent, and varies in a broad range, depending on the type of aggregate. Values from EC2 (1993) are shown in Fig. 5.41. Approximate values for design purposes are 1.6 W/mK for siliceous concrete 1.3 W/mK for calcareous (limestone) aggregate concrete, and 0.8 W/mK for lightweight concrete. Data for other types of concrete are given by Schneider (1988). The specific heat of concrete also varies in a broad range, depending on the moisture content, with design values from EC2 (1993) shown in Fig. 5.42. The peak between 100 and 200  C allows for water being driven off during the heating process. Approximate design values are 1,000 J/kgK for siliceous and calcareous aggregate concrete, and 840 J/kgK for lightweight concrete.

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5 Fire-Resistant Composite Structures: Calculations and Applications

Fig. 5.41 Thermal conductivity of concrete (Reproduced from (EC2 1993) by permission of CEN)

5.10.4 Published Temperatures There is good published information available on temperatures within concrete members exposed to the standard fire. Most of these data have been derived from the work of Abrams and Gustaferro (1968). The availability of this information makes it much easier to design for standard fire exposure than for realistic fire temperatures, especially for the simple hand calculated design methods.

5.10.4.1

Slabs and Beams

Typical temperatures in concrete slabs exposed to the standard fire are shown in Fig. 5.43. Note that the distance from the fire-exposed surface is to the centre of the reinforcing steel, not the cover to the surface of the steel which is usually specified to control durability. For exposure to typical real fires, very little published information is available on thermal gradients. Figure 5.44 shows typical peak temperatures reached at various depths in a concrete slab, calculated by Wade (1994) using the design fires proposed by Lie (1995) for a range of opening factors (ventilation factors) and a fuel load of 600 MJ/m2 floor area. Figure 5.45 shows the progression of temperature versus time at various depths within the slab, for one of those real fires. It can be seen that temperatures within the slab continue to increase well beyond the time of 35 min when the fire reached its peak temperature. The greater the cover, the greater delay in reaching the peak temperature. Typical internal temperature contours at the corner of concrete beams exposed to the standard fire.

5.11

Mechanical Properties of Concrete at Elevated Temperatures

341

Fig. 5.42 Specific heat of concrete (Reproduced from EC2 (1993) by permission of CEN)

Fig. 5.43 Temperature in concrete slabs exposed to the standard fire-reproduce from Wade (1991b)

5.11

Mechanical Properties of Concrete at Elevated Temperatures

5.11.1 Test Methods The same test methods as described earlier for steel are applicable to concrete. Properties of concrete at elevated temperatures are described by Schneider (1986), Bazant and Kaplan (1996) and Harmathy (1993).

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5 Fire-Resistant Composite Structures: Calculations and Applications

Fig. 5.44 Peak temperatures in concrete slabs exposed to design fires (Reproduced from Wade (1994) by permission of Society of Fire Protection Engineers)

Fig. 5.45 Temperature-time curves inside concrete slabs exposed to design fires, reproduce from Wade (1994)

700

opening factor = 0.08 fire load = 600 MJ/m2 (floor)

600 10 mm 20 mm 30 mm 40 mm 50 mm 60 mm 80 mm 100 mm 120 mm 150 mm Peak Temp

Temperature °C

500 400 300 200 100 0 0

60

120

180

240

Time (min)

5.11.2 Components of Strain The deformation of concrete at elevated temperatures is slightly more complicated than that of steel, because of an additional component of strain called transient strain. The deformation of concrete is usually described by assuming that the total stain ɛ consists of four components, being ε ¼ εth ðTÞ þ εσ ðσ; T Þ þ εcr ðσ; T; tÞ þ εtr ðσ; T Þ

(5.44)

5.11

Mechanical Properties of Concrete at Elevated Temperatures

343

where ɛth (T) is the thermal strain being a function only of temperature T, ɛσ (σ,T) is the stress related strain, being a function of both the applied stress σ and the temperature, ɛcr (σ,T,t) is the creep strain, being also a function of time, t and ɛtr (σ,T) is the transient strain, being a function of both the applied stress and the temperature. These components of strain are described in slightly different ways by different researchers (Schneider 1988) (Fig. 5.46). Some details are given below. A slightly different strain model is given by Schneider et al. (1994). For simple structures such as simply-supported beams, only the stress-related strain needs to be considered, allowing the reduced strength at elevated temperatures to be calculated without reference to the deformations. For more complex structural systems, especially where members are restrained by other parts of the structure, the thermal strain, creep strain and the transient strain must also be considered, using a computer model for the structural analysis.

5.11.3 Thermal Strain Approximate expressions for thermal elongation ΔL/L of concrete are given by ΔL=L ¼ 18  l0 6 Tc for siliceous aggregate concrete

ΔL=L ¼ 12  l0 6 Tc for calcareous aggregate concrete ΔL=L ¼ 8  l0 6 Tc for lightweight concrete

ð5:45Þ

where Tc is the concrete temperature. These values are from EC2 (1993) which gives more precise expressions for detailed calculations. It is difficult to separate thermal strain and shrinkage in tests, so the above expression also include effects of shrinkage.

5.11.4 Creep Strain and Transient Strain Creep strain and transient strain are closely linked. If a concrete specimen is heated under load all of the strain components described above combine to produce deformations as shown in Fig. 5.47 (Schneider 1988). Khoury et al. (1985) have measured creep strains during testing under constant temperature and stress producing results such as those shown in Fig. 5.47. They also describe transient thermal strain, which occurs during the first time heating of concrete under load to 600  C, but not on subsequent heating. During all these processes there are complex changes in the moisture content and chemical composition of the cement paste, interacting with the aggregate which remains relatively inert (Schneider 1988).

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5 Fire-Resistant Composite Structures: Calculations and Applications

Fig. 5.46 Total deformation in different concretes during heating (Reproduced from Schneider (1988) with permission from Elsevier Science)

Concrete Structures 1.60 Heating rate 2 °C/minutes a=0 f a=

1.4

fc (20 ºC)

Total delormation (%)

1.2 1.0

Quartzite concrete

0.8

cLightweight concrete

a = 0.10 a=0

0.6 0.4

a = 0.30

0.2 0 a = 0.15 –0.2

a = 0.45 s = 0.70 a = 0.30

–0.4

s = 0.60

–0.6 0

200

400

600

800

1000

Temperature ( ºC)

5.11.5 Stress-Related Strain The stress-related strain includes the elastic and plastic components of strain resulting from applied stresses. Typical stress-strain relationships for normal concrete at elevated temperatures are shown in Fig. 5.48. It can be seen that the ultimate compressive strength drops, and the strain at peak stress increases with increasing temperature. Similar curves and corresponding equations are given by EC2 (1993). The reduction in ultimate compressive strength with temperature for typical structural concrete is shown in Fig. 5.49 (Schneider 1988), derived from several studies.

5.11.5.1

Confined Concrete

It is well established that confinement of concrete by reinforcing such as hoops or ties gives a significant increase in ductility at normal temperatures. This is used to good effect in the seismic design of concrete structures. No specific studies of such confined concrete under elevated temperature are known of, although Schneider (1988) reports studies showing that the ratio of biaxial compressive strength to uniaxial strength increases at elevated temperatures. It follows that confined concrete members designed for seismic attack probably have enhanced fire resistance as well. Franssen and Bruls (1997) describe how the flexural performance of a fire-

5.11

Mechanical Properties of Concrete at Elevated Temperatures

345

Fig. 5.47 Creep in concrete 1 day after loading at 10 % of the initial strength (Reproduced from Khoury and Sullivan (1988) with permission from Elsevier Science)

Fig. 5.48 Stress–strain relationships for concrete at elevated temperatures (Reproduced from EC2 (1993) by permission of CEN)

exposed prestressed concrete tee-beam can be enhanced with confining reinforcing around the tendons.

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5 Fire-Resistant Composite Structures: Calculations and Applications

Fig. 5.49 Reduction in compressive strength with temperature (Reproduced from Schneider (1988) with permission from Elsevier Science)

5.11.5.2

Design Values

Typical stress-strain curves for concrete at elevated temperatures have been shown above in Fig. 5.48. The tensile strength of concrete is usually assumed to be zero at elevated temperatures. In similarity with steel properties, the reduction of ultimate strength with temperature is variable and a simple expression is necessary for design purposes. Figure 5.50 shows the lines used in BS 8110 (also SAA (1994), SNZ (1995) for normal weight concrete). More detailed expressions are given in EC2 (1993). The line for normal weight concrete in Fig. 5.50 is given by kc;T ¼ 1:0 kc;T ¼ ð910

TÞ=560

for T < 350 C for T > 350 C

(5.46)

The line for lightweight concrete in Fig. 9.15 is given by kc;T ¼ 1:0

kc;T ¼ ð1000

for T < 500 C TÞ=500

for T > 500 C

(5.47)

5.12

Timber Structures

347

Fig. 5.50 Design values for reduction of compressive strength with temperature

5.11.5.3

Modulus of Elasticity

The modulus of elasticity of concrete also drops with increasing temperature. Figure 5.51 shows the line used in BS 8110. More detailed expressions are given in EC2 (1993). Lightweight and high-strength concretes behave similarly to normal weight concrete. The line in Fig. 5.51 is given by kE;T ¼ 1:0

kE;T ¼ ð700

for T < 150o C TÞ=550

for T > 150o C

ð5:48Þ

A problem occurs with the use of Figs. 5.50 and 5.51 at high temperatures, because the compressive strength and the modulus of elasticity can be seen to reach zero at different temperatures. Because this is physically impossible, Inwood (1999) has proposed a minor alteration shown by the dotted line in Fig. 5.51, in order to increase the temperature at which the modulus of elasticity reaches zero.

5.12

Timber Structures

5.12.1 Overview This section describes the fire behaviour of timber construction, and gives design methods for heavy timber structural members exposed to fire. Fire behavior of connections in timber structures is also discussed.

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5 Fire-Resistant Composite Structures: Calculations and Applications

Fig. 5.51 Design values for reduction of modulus of elasticity with temperature

5.12.2 Description of Timber Construction Timber structures tend to fall into two distinct categories: ‘heavy timber’ structures and ‘light timber frame’ construction (‘light wood frames’ in North America). Heavy timber structures are those where the principal structural elements are beams, columns, decks, or truss members made from glue-laminated timber or large-dimension sawn timber. Many innovative structures using heavy timber structural members are described by Goِ tz et al. (1989). Light timber frame construction uses smaller sizes of wood framing, as studs in walls, and as joists in floors. Walls and floors are covered with panels of lining materials to provide resistance to impact, sound transmission and fire spread.

5.12.2.1

Heavy Timber Construction

‘Heavy timber construction’ describes all uses of large-dimension timber framing in buildings. Many historic commercial and industrial building consist of external load-bearing masonry walls, with internal timber columns and beams supporting thick timber floor decking. The term ‘heavy timber construction’ or ‘mill construction’ has a specific meaning in North American fire codes where it applies to beams and columns with a minimum nominal dimension of 150 mm and decks with a minimum nominal thickness of 50 mm. In this book, the term ‘heavy timber’ generally refers to timber members whose smallest dimension is no less than 80 mm.

5.12

Timber Structures

5.12.2.2

349

Glulam

‘Glue laminated timber’ (glulam) describes timber members which are manufactured from several laminations glued together. The length of individual laminations is often the full length of the member, joined end-to-end with fingerjoints. Glulam members can be manufactured in any size or shape, the major limitation being transportation. The individual laminations must be thin in curved members (10–25 mm thickness, depending on the radius of the curve) and are thicker in straight members (usually 35–45 mm thickness). The most common adhesives for glulam are based on resorcinol, melamine urea, or casein. Many fire tests have shown that glulam members exposed to fires behave in the same way as solid sawn-timber members of the same cross section, with the possible exception of those manufactured with casein adhesives. Epoxy-based adhesives do not behave well in fires. In some countries, especially in North America, the laminations at the top and bottom edges of glulam members are made from specially selected high-strength wood, in order to increase the flexural strength and stiffness. This practice must be allowed for in fire design when the outer laminations may be burned away, placing more reliance on the inner laminations which are of lower strength.

5.12.2.3

Behaviour of Timber Structures in Fire

Heavy timber construction has become recognized as having very good fireresistance. There are many well-documented examples of structures surviving severe fire exposure without collapse, and many of these have been repaired for re-use (Figs. 5.52. and 5.53). When large timber members are exposed to a severe fire, the surface of the wood initially ignites and burns rapidly. The burned wood becomes a layer of char which insulates the solid wood below. The initial burning rate decreases to a slower steady rate which continues throughout the fire exposure. The charring rate will increase if the residual cross section becomes very small. The layer of char shrinks, making it thinner than the original wood, causing fissures which facilitate the passage of combustible gases to the surface. The char layer does not usually burn because there is insufficient oxygen in the flames at the surface of the char layer for oxidation of the char to occur. When the wood below the char layer is heated above 100  C, the moisture in the wood evaporates. Some of this moisture travels out to the burning face, but some travels into the wood, resulting in an increase in moisture content in the heated wood a few centimeters below the char front (White and Schaffer 1980).

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5 Fire-Resistant Composite Structures: Calculations and Applications

Fig. 5.52 (a) Severe fire damage to an industrial building with curved glulam portal frames. (b) One of the beams being repaired for re-use by sandblasting (Both figures are reproduced from TRADA (1976) by permission of New Zealand Timber Industry Federation)

Fig. 5.53 Curved glulam roof beams after repair following a severe fire (Reproduced by permission of McIntosh Timber Laminates Ltd)

5.12.2.4

Fire-Retardant Treatments

A number of fire-retardant chemicals are available for treating wood to reduce its combustibility. The main purpose of such chemical treatments is to reduce the rate of flame spread over the surface of the wood, to improve fire safety in rooms lined with wood or wood-based panel products. Pressure impregnation of chemicals is considered more effective than surface painting. The pressure impregnation process is similar to that used for applying chemicals to resist decay, but the retentions of salts required for fire retardancy are much higher. Impregnation by fire-retardant chemicals can have some negative effects including loss of wood strength and

5.13

Wood Temperatures

351

corrosion of fasteners, exacerbated by the hydroscopic nature of many of the chemicals. Fire-retardant chemicals do not significantly improve the fire-resistance of timber members, because even though treated wood will not support combustion, it will continue to char if exposed to the temperatures of a fully-developed fire. Some proprietary intumescent paints have been advertised with properties which can increase the fire-resistance of timber members, but insufficient test results have been published to recommend such products for general use. A discussion is given by White (1984). Recently developed fibre-glass reinforced coatings are described by del Senno et al (1998).

5.12.3 Fire-Resistance Ratings The fire-resistance of timber structures can be assessed using the same general principles as for other materials.

5.12.3.1

Verification Methods

The design process for fire-resistance requires verification that the provided fireresistance exceeds the design fire severity. Using the terminology from previous chapters, verification may be in the time domain, the temperature domain or the strength domain. The temperature domain is not used for timber structures because there is no critical temperature for fire-exposed timber. In most countries, fire design of heavy timber structures is by calculation using the methods outlined in this chapter. The results of these calculations are verified in the time domain by comparing the time of structural collapse with a specified fire-resistance time, or in the strength domain by comparing the residual strength with the applied loads after a certain period of fire exposure. Some countries have generic fire-resistance ratings for heavy timber construction. For example, some US codes allow heavy timber construction to be used in certain classes of buildings, with no calculations required. There are very few proprietary ratings for heavy timber, in contrast to light timber construction where there are many proprietary ratings based directly on test results.

5.13

Wood Temperatures

When heavy timber members are exposed to severe fires, the outer layer of wood burns and is converted to a layer of char. The temperature of the outer surface of the char layer is close to the fire temperature, with a steep thermal gradient through the char. The boundary between the char layer and the remaining wood is quiet distinct, corresponding to a temperature of about 300  C. The commonly accepted charring

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5 Fire-Resistant Composite Structures: Calculations and Applications

Fig. 5.54 Char layer and pyrolysis zone in a timber beam

Timber Structures

Char layer Char base Pyrohysis zone Pyrohysis zone base Normal wood

temperature in North America is 288  C (550  F), but the precise temperature is not important because of the steepness of the temperature gradient. Below the char layer there is a layer of heated wood about 35 mm thick. The part of this layer above 200  C is known as the pyrolysis zone, because this is undergoing thermal decomposition into gaseous pyrolysis products, accompanied by loss of weight and discoloration. Moisture evaporates in the wood above 100  C. The inner core of the member remains at its initial temperature for a considerable time. These layers are shown in Fig. 5.54. Structural design of heavy timber members is based on the rate of charring of the wood surface, so it is not necessary for designers to calculate temperatures within the fire-exposed wood.

5.13.1 Temperatures Below the Char Temperatures in the wood below the char layer have been measured in many tests. For wood thick enough to be considered as a semi-infinite solid, Eurocode 5 gives the temperature T ( C) below the char layer as T ¼ Ti þ ðTp

Ti Þ ð1

x=aÞ2

(5.49)

where Ti is the initial temperature of the wood ( C), Tp is the temperature at which charring starts (300  C), x is the distance below the char layer (mm), and a is the thickness of the heat-affected layer (40 mm). Janssens and White (1994) show that a better fit to experimental data is obtained with a ¼ 35 mm.

5.14

Mechanical Properties of Wood

353

Fig. 5.55 Variation of thermal conductivity of wood with temperature

5.13.2 Thermal Properties of Wood The temperatures inside fire-exposed timber members can be calculated using finite element numerical methods. The thermal properties are not well defined, and vary considerably with temperature as moisture is driven off at 100  C and as wood turns to char over 300  C. The values given below are typical average values from recent literature. The density of wood varies significantly between species. It also varies between trees of the same species and within individual trees. The density drops to about 90 % of its original value when the temperature exceeds 100  C, and to about 20 % of its original value when the wood is converted to char above 300  C. The thermal conductivity varies greatly between different authors. Figure 5.55 shows the variation of thermal conductivity with temperature as proposed by Knudson and Schneiwind (1975) which is about the average of other published values. Konig and Walleij (1999) found that they had to increase the thermal conductivity to much higher values at temperatures over 500  C in order to give good predictions of measured behaviour. Figure 5.56 shows the variation of specific heat with temperature as proposed by Kooِ nig and Walleij (1999). The large spike at 100  C represents the heat required to evaporate the moisture in the wood.

5.14

Mechanical Properties of Wood

Wood has several significant differences from other common materials such as steel and concrete. For example: • wood strength is very variable, both within boards and between boards; • mechanical properties are different in diff rent directions (parallel and perpendicular to the grain); • strength and ductility are very different in tension and compression;

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5 Fire-Resistant Composite Structures: Calculations and Applications

Fig. 5.56 Variation of specific heat of wood with temperature

• failure stresses depend on the size of the test specimens; and • the strength reduces under long duration loads. Figure 5.57 shows different ways in which wood can be loaded, each producing a different failure mode. This chapter reviews wood behavior at normal temperature before describing properties at elevated temperatures.

5.14.1 Mechanical Properties of Wood at Normal Temperatures 5.14.1.1

Tension and Compression Behavior

Figure 5.57 shows typical stress–strain relationships for small clear specimens of wood with no defects. Considering behaviour parallel to the grain, the straight line in tension indicates linear elastic behaviour to brittle failure at a tensile stress f t. Wood is brittle in tension because there is no load sharing within the wood material, so that a crack can lead to sudden failure as soon as it reaches a certain critical size. In compression the stress-strain relationship is linear in the elastic region, with the same modulus of elasticity as in tension. The line then curves, indicating yielding (or crushing), it reaches a peak and eventually drops as the wood is crushed further. With larger strains the specimen will continue to deform in a ductile manner. Compression yielding is accompanied by visible wrinkles on the surface of the wood. The compression curves in Fig. 5.58 indicate crushing of wood in short columns. Long slender columns have lower load capacity because they will fail by bucking at loads well below the crushing strength. In clear wood, the tension strength ft is usually much greater than the compression strength fc. In commercial quality timber, the relative strengths are often

5.14

Mechanical Properties of Wood Perpendicular to grain

Parallel to grain

355

Bending

Flexural tension Failure

Split Tension

Split Tension Compression

Compression

Shear failure

Fig. 5.57 Loading of wood in different directions

reversed because growth characteristics such as knots have a severe effect on tensile strength but only a small effect on compressive strength. The dotted line in Fig. 5.58 shows the stress-strain relationship for wood loaded perpendicular to the grain direction. The slope indicates a lower modulus of elasticity than for loading parallel to grain. The wood is ductile in compression, with the load slowly increasing as strains increase. In tension perpendicular to the grain, the strength is very low and unpredictable, with splitting causing brittle fractures. This weakness can lead to structural failure if it is not properly allowed for in design.

5.14.1.2

Bending Behavior

Bending behaviour is a combination of tension and compression behavior. Commercial quality timber beams tend to fail suddenly due to poor tensile strength at knots in the tension zone. Some ductility is available in timber beams when the material is stronger in tension than in compression, and this ductility can increase during fire exposure because of softening of the wood in the compression zone.

5.14.1.3

Design Values

Structural design calculations requite values of the design strength of the wood material. For limit states design (LRFD) the design stress, or ‘characteristic stress’, is the fifth percentile failure stress under short-duration loading, for a typical population of timber boards. Because the strength of timber is much more variable than that of steel or concrete, characteristic stresses are usually obtained from in-grade tests of large numbers of representative samples of full size timber members, selected from typical production. This allows the effects of size, grade, defects, and variability to be determined directly. To accommodate a very large number of species and grades, most codes specify characteristic values of strength

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5 Fire-Resistant Composite Structures: Calculations and Applications

Fig. 5.58 Stress-strain relationships for clear wood

Compression

Stress fc

Elasto-plastic approximation

Parallel to grain

Perpendicular to grain

Brittle fracture Tension

fc

and stiffness for a number of defined strength classes. The fifth percentile value for design in normal temperature conditions may be modified to the 20th percentile strength value for fire design. Failure stresses in timber depend on many factors, including the size of the test specimen. Large timber members tend to fail at lower stresses than similar small members, because a large member has a larger number of potential defects, hence a greater probability of a large knot, than a small member. Size effects are recognized in some codes. The design strength of timber also depends on the duration of the applied load, so that most timber design codes include a duration-of-load factor. In limit states design (LRFD) codes, the duration-of-load factor is usually 1.0 for short-duration loads. decreasing to 0.8 or 0.6 for medium- and long-duration loads. In working stress design codes, allowable stresses are for long-duration loading, derived from test results of small clear specimens of wood. In this case the duration-of-load factor is usually 1.0 for long-duration loads, increasing to 1.25 or 1.6 for medium- and short-duration loads. The duration-of-load factor for fire design should be appropriate value for short-duration loads, because the duration of the load during the fire is likely to be less than 1 h.

5.14.2 Mechanical Properties of Wood at Elevated Temperatures 5.14.2.1

Sources

The most comprehensive review on the effect of moisture content and temperature on the mechanical properties of wood is by Gerhards (1982) who reported the results of many previous studies. Some of this information is summarized by Buchanan (1998) and the Wood Handbook (1987). Wood properties are affected by steam at 100  C, wood begins to pyrolyse at about 200  C and turns into char by

5.14

Mechanical Properties of Wood

357

300  C. The range of interest for fire engineering is therefore from room temperature to 300  C.

5.14.2.2

Effect of Moisture Content

The strength of wood at elevated temperatures is not well understood. When testing timber at elevated temperatures, the moisture content is sensitive to the test method and the size of the test specimen. Some test specimens are maintained at constant moisture content throughout the test with a climate-controlled testing facility or an oil bath. In other tests the specimen is at certain moisture content before the test and allowed to dry out when heated, either before or during the test, in which case some moisture may migrate into the interior of the specimen and the moisture gradients will depend on the size of the specimen. If wood is heated to a temperature above 100  C in dry air, all moisture will evaporate after some time, depending on the permeability of the particular species.

5.14.2.3

Plasticity

The, strength of a structural timber member is reduced in fire, because the wood converted, to char has no strength and the temperature and moisture gradients below the char layer reduce the strength and increase the plasticity of that wood. The increase in wood plasticity is very important, especially for tension and bending members which would have brittle failures at room temperatures. When a timber beam is tested in bending at normal temperatures, it usually fails suddenly, with fracture at a weak point on the tension edge when a small crack reaches a critical size. If heated wood were to lose strength with no increase in plasticity, cracks would occur in the heated tension zone of the beam, leading to premature failure in fire. The excellent performance of large timber beams in fire results from plastic behaviour in the heated wood, allowing redistribution of stresses into the cooler wood further from the char layer.

5.14.2.4

Steam Softening

It is well known from the furniture and boat building industries that hot moist wood can be bent into curved shapes using steam bending. Steam bending occurs because wood becomes plastic in compression under certain combinations of temperature and moisture content. There is very little literature on this subject, other than Stevens and Turner (1970) and the Wood Handbook (1987) which states the following: ‘Wood at 20–25 % moisture content needs to be heated without losing moisture; at lower moisture content, heat and moisture must be added. As a consequence, the recommended plasticizing processes are steaming or boiling for about 1/2 h per

358

5 Fire-Resistant Composite Structures: Calculations and Applications

inch of thickness for wood at 20–25 % moisture content and steaming or boiling for about 1 h per inch of thickness for wood at lower moisture content values.’ Because most of the deformation must take in compression, it is often necessary to apply a net compressive force on the member, using a steel strap to reinforce the tension side of the cross section during the bending process. When wood is heated in a fire, the conditions which produce softening of the wood may occur for only a short period of time. If the moisture content subsequently decreases, the wood will harden, even if temperatures continue to increase. The effect of wood softening will be very different for large and small members. In a large member, conditions to produce softening may occur in a thin layer which progresses into the wood at about the same velocity as the rate of charring, having little effect on the overall strength or stiffness of the member. Small members may experience these conditions over a large proportion of the cross section, in which case the member may deform plastically in compression or bending, leading to premature failure. These conditions may only occur for a short time period, so if the assembly can resist the applied loads during this short period, with the help of other load paths or cladding materials, the wood may regain strength after it dries and be able to survive a much longer time of fire exposure.

5.14.2.5

Parallel to the Grain Properties

Modulus of Elasticity. Figure 5.59 shows the modulus of elasticity of wood at elevated temperatures from the Wood Handbook (1987). This is similar to Fig. 5.59 which combines results from Nyman (1980) an and Ostman (1985) with those from Schaffer (1973) and Preusser (1968). Other results shown by Gerhards (1982) fit into the same envelope. The effect of temperature on modulus of elasticity parallel to the grain is roughly linear up to 200  C. There is increased scatter over 200  C where Preusser shows a much more sudden drop than that measured by Schaffer or Ostman. Figure 5.60 also shows recent results derived by Konig and Walleij (2000) from tests of 145  45 mm timber studs in insulated wall assemblies, exposed to the ISO 834 standard furnace fire while loaded in bending. Similar results were obtained by Young (2000) who used even lower values of modulus of elasticity to model the results of full-scale fire-resistance tests of timber stud walls. Tensile Stregth. Ostman (1985) tested samples of spruce (1 mm by 10 mm cross section) at a range of temperatures and moisture contents, obtaining the stress-strain relationship redrawn in Fig. 5.60 for temperatures of 25  C and 90  C at low and high moisture content. It can be seen that the failure stress at 90  C and 29.5 % moisture content is about 60 % of that of dry cool wood. All the lines are curved, indicating a small amount of plastic behaviour before failure. The only reported ‘in-grade testing’ at elevated temperatures is by Lau and Barrett (1997) who tension tested a large number of 90  35 mm boards, 25 min after heating the surfaces to temperatures up to 250  C. They show that the tension behaviour remains brittle, and failure is governed by the weakest link in the test

5.14

Mechanical Properties of Wood

359

Fig. 5.59 Modulus of elasticity of wood parallel to the grain versus temperature

specimen, generally a knot. Lau used a damage accumulation model to predict the tensile strength under constant temperature, finding that the strength reduction over 150  C depends on the duration of loading. A comparison with other test data is shown in Fig. 5.60 where the results of Ostman (1985) lie between those of Schaffer (1973) and Knudson and Schneiwind (1975). Nyman (1980) has similar results to Ostman. The upper curves are for dry specimens, Knudson and Schneiwind’s test specimens were at 12 % moisture content before rapid (30 s) heating at the time of testing, and Lau and Barrett’s specimens were at 7–11 % moisture content before heating. Figure 5.62 also shows the relationship derived by Konig and Walleij (2000). Compressive Strength. The effect of temperature on compressive strength parallel to the grain is shown in Fig. 5.63, which is the envelope of all the results quoted by Gerhards (1982). All of these results are for dry wood except the marked shaded region which shows results for tests with moisture content between 12 % and the fibre saturation point. There are very few reported compression test results for moist wood over 60  C where plastic behaviour is expected. As discussed earlier in this chapter, plastic behaviour of wood in compression becomes very important in some timber structures exposed to fire. Figure 5.63 also shows the relationship derived by Koِ nig and Walleij (2000) which follow the earlier results for moist wood to 100  C, followed by a straight line to zero-strength at 300  C. The question as to whether the strength of initially moist wood increases again after the moisture is driven off at temperatures over 100  C requires further research, because this information is required for finite-element modelling of timber structures exposed to fires. Bending Strength. Bending behaviour in wood can be best described from an understanding of the tension and compression behaviour. The effect of elevated

360

5 Fire-Resistant Composite Structures: Calculations and Applications

Fig. 5.60 Modulus of elasticity of wood parallel to the grain versus temperature (Adapted from (Gerhards 1982) with permission of Society of Wood Science and Technology)

temperatures on bending behaviour is, in theory, predictable. from the information presented in Figs. 5.58, 5.59, 5.60, 5.61, 5.62, and 5.63. Dry wood will lose strength and stiffness at the rate given in those figures. The situation is much more complicated for moist wood, because if conditions become suitable. for plastic behaviour, large strains will occur in the compression zone resulting in a relocation of the neutral axis, leading to large deformations. There are limited test results available. The shaded areas on Fig. 5.64 show the results collected by Gerhards (1982) which include only one test series for temperatures over 80  C. The upper dashed line shows the results obtained by Glos and Henrici (1991) for bending strength of 70  150 mm beams at temperatures of 100  C and 150  C. The moisture content at the time of the tests was in the range 7–10 % for the 100  C beams and 3–6 % for the 150  C beams. The lower dashed line shows the previous German design values obtained from tests by Kollman and Schulz (1944). The wood used in the earlier tests may have been more moist which would explain the different slope. The German design values given by Kordina and Meyer-Ottens (1995) have been changed to reflect the results of Glos and Henrici. Koِ nig (1995) performed fire-resistance tests on single joists with the narrow edge unprotected and the wide sides protected by rock wool insulation. The joists were tested in bending with the fire-exposed side in tension or compression. Extreme plastic behaviour was observed, with a very large shift in the neutral axis location, especially for those members with the fire-exposed edge in compression. Fire tests of unprotected timber joist floors by Woeste and Schaffer (1979) and tests of studs by Nore´n (1988) showed a reduction of variability and an increase in load sharing during fire, resulting from increased ductility. Tests of glulam beams by Bolonius Olesen and Hansen (1992) showed continued softening of the wood during the cooling period, even after charring had stopped.

5.14

Mechanical Properties of Wood

361

Fig. 5.61 Stress–strain relationship for wood in tension parallel to the grain

Fig. 5.62 Tensile strength parallel to the grain versus temperature (Adapted from Gerhards (1982) with permission of Society of Wood Science and Technology)

5.14.2.6

Perpendicular to the Grain Properties

Modulus of Elasticity. For modulus of elasticity perpendicular to the grain, Gerhards (1982) reports eight studies which all lie in the wide rang shown in Fig. 5.65, for temperatures up to 100  C. The dependence on temperature tends to

362

5 Fire-Resistant Composite Structures: Calculations and Applications

Fig. 5.63 Compression strength parallel to the grain versus temperature (Adapted from Lan and Barrett (1977) by permission of IAFSS)

Fig. 5.64 Bending strength of wood versus temperature (Adapted from Gerhards (1982) with permission of Society of Wood Science and Technology

be greater for moisture content above 20 %, but there is a lot of overlap between the studies. Much of the data show negligible stiffness for moist wood as the temperature approaches 100  C, indicating plastic behaviour as reported for parallel to the grain behaviour. Tensile Strength. The effect of temperature on tensile strength perpendicular to the grain is shown in Fig. 5.66, where all the data are from Gerhards (1982). It can be seen that there is a wide range of results with much overlap for the different moisture contents, but a trend of a greater strength reduction as the moisture content increases. There are no results of tests over 100  C. Tensile strength perpendicular to the grain is an indication of resistance to splitting, which is a very unpredictable wood property, even in the best of conditions.

5.14

Mechanical Properties of Wood

363

Fig. 5.65 Modulus of elasticity perpendicular to grain versus temperature (Adapted from Gerhards (1982) with permission of Society of Wood Science and Technology)

Compressive Strength. Figure 5.67 shows the effect of temperature on strength in compression perpendicular to the grain. This shows data from five studies reported by Gerhards (1982) which all overlap with much scatter and even less dependence on moisture content than for tension. The measured strength in these tests was the proportional limit which is very difficult to define when the stress-strain relationship may be curved from very low loads as shown in Fig. 5.68. The proportional limit is not an important strength property, because some local compression yielding is expected in situations such as highly loaded studs bearing on bottom plates in light frame construction. The ultimate crushing strength is more useful, but also difficult to measure because it requires very large strains, and there may be no maximum value, also shown in Fig. 5.68.

5.14.2.7

Shear

Shear in beams Fig. 5.68a shows a beam with applied loads. The elemental volume near the left-hand support is enlarged in Fig. 5.68b. In a momogeneous isotropic material, the stresses shown in Fig. 5.68b would usually produce a diagonal tension failure along the dotted diagonal line A-A. However, in wood, which has a welldefined longitudinal grain structure, a shear failure will usually result in a horizontal split along the grain as shown by the line B-B and the split in Fig. 5.68c. Standard tests are available to measure the shear strength and shear modulus (shear stiffness) of wood. Shear failures rarely occur in timber beams, and shear only becomes critical if there are pre-existing splits at the ends of the beam or if very high shear stresses are developed near connections. Gerhards (1982) only reports two studies on shear strength of wood at elevated temperatures. Figure 5.69, reproduced from Gerhards, shows shear strength dropping rapidly to 150  C in wet wood. The data points are from Ohsawa and Yoneda (1978) and Sano (1961). For shear modulus (or modulus of rigidity)

364

5 Fire-Resistant Composite Structures: Calculations and Applications

Fig. 5.66 Effect of temperature on tensile strength perpendicular to the grain (Adapted from Gerhards (1982) with permission of Society of Wood Science and Technology)

Fig. 5.67 Effect of temperature on compression strength of wood perpendicular to the grain (Adapted from Gerhards (1982) with permission of Society of Wood Science and Technology)

Gerhards (1982) only reports one study, by Okuyama et al. (1977) who observed the shear modulus dropping to 20–50 % of the 20  C values at 80  C.

5.14.2.8

Derived Results

Reduction Factors. The temperature and moisture gradients in heated wood (below the char layer in a glulam beam) affect the strength and stiffness of the member. An approximate estimate of the reduced strength and stillness can be made by combining the predicted temperatures of the wood beneath the char with the effects of temperature on strength. Figure 5.70b shows the temperature profile from

5.14

Mechanical Properties of Wood

365

Fig. 5.68 Shear stresses and shear failure in timber beam

Fig. 5.69 Effect of temperature on shear strength of wood

Janssens and White (1994). Figure 5.70a shows the assumed effect of temperature on mechanical properties, estimated from the test results summarized earlier. The modulus of elasticity is assumed to drop linearly to 50 % of its normal temperature value at 300  C. The tension strength follows the same relationship to 200  C, then drops to zero at 300  C. These properties are assumed to be the same for wet and dry wood. For compression strength, dry wood drops linearly to zero at 300  C. Wet wood is assumed to drop to 50 % of its normal temperature value at 100  C and remain at that value until it reaches a temperature of 160  C, after which it follows the relationship for dry wood. Figure 5.70c shows the resulting drop in strength of the wood below the char layer. All three properties are significantly reduced in the 25 mm of wood below the char, the greatest reduction being in the compression strength, with a plateau at 15 mm depth which corresponds with wood temperatures at or above 100  C. Stress-Strain Relationship. Figure 5.71 shows stress-strain relationships derived by Konig and Walleij (2000) from computer modelling of bending tests carried out

366

5 Fire-Resistant Composite Structures: Calculations and Applications

Fig. 5.70 (a) Effect of temperature on mechanical properties of wood; (b) Temperature profile below the char layer; (c) Reduction in strength of wood below the char layer

by Konig (1995). These relationships are consistent with the lines shown on Figs. 5.59, 5.61 and 5.62. They are similar to relationships derived by Thomas et al. (1995) who investigated the structural performance of light timber frame walls and floors exposed to fire using finite-element models for thermal and structural analysis. These derived properties were used in a finite-element model to predict the results of fire-resistance tests of timber stud walls. The moisture content was not

5.15

Design Concepts for Heavy Timber Exposed to Fire

367

Timber structures Compression 20°C

Stress

4

60°C 100°C 200°C Strain

200°C

100°C

Tension

60°C 20°C

l

Fig. 5.71 Derived stress–strain relationships for wood at elevated temperatures

monitored during Konig’s tests, but the wood studs had a typical initial moisture content of about 12 %. The relationships in Fig. 5.71 are idealized in a simple way to allow prediction of overall behaviour. It can be seen that in the tension region, linear elastic behaviour has been assumed until failure. There may be some plasticity in tension as shown in Ostman’s results (64) but that will be of little significance in bending and compression members where compression yielding dominates the behaviour. In the compression region, idealized elasto-plastic behaviour has been assumed, which has been shown by Buchanan (1990) to give good results when modelling flexural behavior. The derived curves shown in Fig. 5.71 include the creep that takes place in the duration of typical fire-resistance testing. The different moduli of elasticity in tension and compression at elevated temperatures are a result of greater creep in compression than in tension. Similar results are reported by Young (2000) who included an increase in compressive strength as the heated wood dried out over 100  C.

5.15

Design Concepts for Heavy Timber Exposed to Fire

Large timber members exposed to fire have excellent fire-resistance (Figs. 5.72 and 5.73). The fire-resistance is easily calculated because of the predictable rate of charring on surfaces exposed to the standard fire. Figure 5.74 shows the common cases of three- and four-sided fire exposure of a rectangular member. The original cross

368

5 Fire-Resistant Composite Structures: Calculations and Applications

Fig. 5.72 Fire-resistance test of glulam beams; the beams span a 4 m long furnace with loads applied using concrete blocks

section b x d is reduced to the residual cross section bf  df as a result of chaffing. The depth to the char front is shown as the dimension c (mm) which is equal on all exposed surfaces, given by c ¼ βt

(5.50)

where β is the rate of charring (mm/min), and t is the time of fire exposure (minutes). The dimensions of the residual cross section are given by bf ¼ b

df ¼ d df ¼ d

2c c ðthree 2c ðfour

sided exposureÞ sided exposureÞ

ð5:51Þ

The boundary between the char layer and the remaining wood is quite distinct, corresponding to a temperature of about 300  C. There is a layer of heated wood about 35 mm thick below the char layer, and the inner core remains at room temperatures. The residual cross section is capable of supporting loads, providing a level of fire-resistance which depends on the load ratio. Failure occurs when the residual cross section is stressed beyond it ultimate strength. Structural design of timber members is based on the strength and stiffness of the residual member considering the depth of char, the temperature and moisture profile of the wood below the char line, and the mechanical properties of wood at elevated temperatures. This is a simple concept, but national codes give many different methods of making the calculations. The main methods are described below.

5.15

Design Concepts for Heavy Timber Exposed to Fire

369

Fig. 5.73 Residual cross section of a large glulam beam after a fire test (Reproduced by permission of American Institute of Timber Construction)

Fig. 5.74 Design concepts for large timber members

5.15.1 Verification As with other materials, verification of the strength during fire exposure requires that U  fire  Rfire

(5.52)

370

5 Fire-Resistant Composite Structures: Calculations and Applications

where U *fire is the design force resulting from the applied load at the time of the fire, and Rfire is the load capacity during the fire situation. Design forces are obtained from the applied loads by conventional structural analysis. Calculations of the load-bearing capacity are described below, based on the mechanical properties of wood at elevated temperatures. The design force U *fire may be axial force N *fire, bending moment M *fire or shear force V *fire occurring singly or in combination, with the load capacity calculated accordingly as axial force Nf, bending moment Mf or shear force Vf in the same combination. Calculation of the load capacity is described below.

5.15.1.1

Simply Supported Beams

Design concepts are discussed here with reference to beams because they are the most commonly used heavy timber members. For a member submitted to a bending moment, the design is verified by satisfying the design equation M fire  Mf

(5.53)

where M *fire is the bending moment at the time of the fire, and Mf is the design flexural capacity under fire conditions, given by Mf ¼ Z f ff

(5.54)

where ff is the design strength of wood in fire conditions (MPa), and Zf is the elastic section modulus (mm3) reduced for fire exposure. The value of the design strength of wood in fire conditions ff is handled differently in different codes, but it should always be the strength under shortduration loads because the duration of the fire exposure is short. For a rectangular section with no corner rounding, the elastic section modulus is Zf ¼ bf df 2 =6

(5.55)

Note that that Eq. (5.53) does not include a partial safety factor for mechanical properties ƴM (or a strength reduction factor ϕ) because both have a value of 1.0 in fire conditions.

5.15.2 Charring Rate Investigations in many fire-resistance tests have shown that the rate of charring of timber is predictable in the standard test fire, depending on the density and moisture content of the wood. Many national codes specify a constant charring rate in the range 0.60–0.75 mm per minute for softwoods and about 0.5 mm per minute for

5.15

Design Concepts for Heavy Timber Exposed to Fire

Fig. 5.75 Charring rate as affected by density and moisture content (Lie 1972)

371

0.9 5% 10 % 15 % 20 %

0.8 0.7 0.6

Moisture content (by weight

0.5 0.4 0.3 0.2 0.1 0 300

400

500

600

Density ( kg/m )3

hardwoods. Glulam and solid wood are usually considered to char at the same rate. The charring rate may reduce after prolonged fire exposure due to the increasing thickness of the insulating layer of char, but this is not usually recognized in design codes. The effect of density and moisture content on the charring rate is shown in Fig. 5.75. The Australian code gives the following equation for charring rate β (mm/min) as a function of wood density, which gives similar values to those shown in Fig. 5.75 for moisture content between 10 and 15 %: β ¼ 0:4 þ ð280 =ρÞ2

(5.56)

where ρ is the wood density (kg/m3) More recent charring studies have been carried by a number of people including Schaffer (1977), Mikkola (1990), Hadvig (1981) and White and Nordheim (1992), as summarized by White (1995). Konig and Walleij (1999) experimentally studied the charring rates of glulam in the standard fire and in parametric fires, and investigated the effect of protective materials before and after they fell off the surface of the wood. The New Zealand code specifies a charring rate of β ¼ 0.65 mm per minute, derived from Collier (1992) who carried out charring tests on radiata pine glulam beams, and used the equations of White and Nordheim (1992) to relate charring rate to density for typical radiata pine which has a density of 550 kg/m3 at 12 % moisture

372

5 Fire-Resistant Composite Structures: Calculations and Applications

Table 5.8 Charring rates for design Material Glue-laminated softwood timber Solid or glue-laminated hardwood timber Softwood panel products (plywood, particle board) minimum thickness 20 mm

Minimum density (mg/m3) 290 450 450

Char rate β (mm/min) 0.64 0.50 0.9

β1 (mm/min) 0.70 0.55

content, as described by Buchanan (1994b). Correlations with density must be made with care, because wood density varies considerably both within and between trees and sites, and there are several different definitions of wood density depending on how the moisture is included in the calculation. Charring of small size wood members has been studied by Lau et al. (1999). Table 5.8 shows recommended charring rates based on Eurocode 5. The measured charring rate β is intended to be used with the actual cross section with rounded corners, and a 10 % larger notional charring rate β1 is to be used if there is no allowance made for corner rounding in the calculations. It is more accurate to use the values of β and modify the section properties for corner rounding, but the effect of rounding becomes very small and can be ignored for large members. Many other national codes have β values similar to those in Table 5.8. In North America, recommendations for the charring rate are given by AFPA (1999), based on the non-linear model of White (1988). The proposed charring rate β is the average charring rate (mm/min) over the period to time t (minutes), given by β ¼ 2:58βn =t0:187

(5.57)

where βn the nominal chairing rate obtained from the char depth measured after 1 h of fire exposure (βn ¼ 0.635 mm per minute), and t is the time (minutes). The resulting char layer thickness c (mm) at time t (minutes) is given by c ¼ βt ¼ 2:58 βn t0:813

(5.58)

Equation (5.57) includes a 20 % increase in charring rate over measured rates to allow for rounding at the corners and the reduction of strength of the heated layer below the char front. It has been converted from imperial units in the original publication, based on βn ¼ 1.5 in. per hour. The curve in Fig. 5.76 shows the resulting depth of char during 4 h of standard fire exposure, compared with the straight line which is the depth of char for a uniform charring rate of 0.762 mm per minute (1.2  0.635). It can be seen that there is little difference up to 1 h where the curve crosses the line, but the AFPA non-linear equation gives less depth of char than the uniform charring rate for exposure times over 2 h. All the charring rates given above are for timber exposed to the standard fireresistance test. Charring rates in more realistic fires are given below in the description of the Eurocode design method for parametric fires.

5.15

Design Concepts for Heavy Timber Exposed to Fire

373

Fig. 5.76 Depth of char from North American recommendations

5.15.3 Corner Rounding All fire tests of large rectangular timber sections show some rounding of the corners, because the corners are subjected to heat transfer from two surfaces. Data of the shape of a typical charred cross section has been taken from BS 5268. Most design codes use the simple relationship whereby the radius of the rounding is equal to the depth of the charred layer. This is supported by several studies, including Hadvig (1981). Majamaa (1991) proposed a radius equal to 80 % of the char depth. The Eurocode gives a radius approximately equal to the char depth in the early stages of the fire, but less after 30 min. If corner rounding is taken into account, the section properties will be affected slightly, depending on the size of the member. For a beam exposed to fire on three sides, the section modulus Zf,r of the reduced cross section is given approximately by Zf ¼ bf df 2 =6

0:215 r2 df

(5.59)

where bf is the residual width of the beam, df is the residual depth of the beam, and r is the radius of the charred corner. with the internal forces at that cross section. If equilibrium is not achieved, another total strain, profile must be used in the next trial Repetitive calculations such as these can be used to construct moment—curvature relationships for each member, leading to calculations of individual members and whole structures exposed to fires.

374

5 Fire-Resistant Composite Structures: Calculations and Applications

Fig. 5.77 Testing regimes for- determining mechanical properties of materials at elevated temperatures (Reprinted from Anderberg (1988) with permission from Elsevier Science)

5.16

Material Properties in Fire

Material properties at normal temperatures have been briefly described with reference to Fig. 5.77. The strength and modulus of elasticity of all materials change with elevated temperature. Methods of deriving material properties at elevated temperature are discussed below. Details for specific materials are given in the following chapters.

5.16.1 Testing Regimes When structural elements are exposed to fire, they experience temperature gradients and stress gradients, both of which vary with time. Mechanical properties of materials for fire design purposes must be determined and published in a way that is consistent with the anticipated fire exposure. Constant temperature tests of materials can be carried out in four possible regimes.

5.16

Material Properties in Fire

375

1. The most common test procedure to determine stress-strain relationships is to use a testing machine to impose a constant rate of increase of strain (by controlling the rate of travel of the machine loading head) measuring the load, from which the stress can be derived. 2. A similar regime is to control the rate of increase of load (or stress) and measure the deformation (hence the strain). 3. A creep test is one in which the load is kept constant and the deformations over time are measured. 4. A relaxation test is one in which a constant initial deformation is imposed and the reduction in load over time is measured. When the effects of changing temperatures are added, there are two more possible testing regimes. 5. In a transient creep test, the specimen is subjected to an initial load, then the temperature is increased at a constant rate while the load is maintained at a constant level and deformations are measured. 6. The final test regime is similar except that the applied load is varied throughout the test in order to maintain a constant level of strain as the temperature is increased at a constant rate. These six regimes are illustrated in Fig. 5.77 derived from Anderberg (1988) and Schneider (1988). The most common of these are regimes (1) and (5). The results of regime (1) tests depend on the rate of loading, because of the influence of creep. The results of regime (5) tests depend on-the rate of temperature increase. All these regimes present some difficulties because the effect of creep influences all of the test results, and a difficulty with transient tests on large specimens is that the rate of temperature increase may not be uniform over the cross section. Figure 5.77 does not consider the effect of changing moisture content which can be another important variable, especially for timber structures, making testing for material properties even more difficult. For most materials, stress-strain relationships at certain elevated temperatures can be obtained directly from steady-state tests at certain elevated temperatures. (Regime (1)), or they can be derived from the results of transient tests. Anderberg (1988) compares stress-strain relationships obtained in both ways and points out that there are differences due to the effect of creep. For most materials, yield strength and modulus of elasticity both decrease with increasing temperature.

5.16.2 Components of Strain Analysis of a structure exposed to fire requires consideration of the deformation of the structure under the applied loads. The deformation of materials at elevated temperature is usually described by assuming that the change in strain Δɛ consists of four components, being Δε ¼ ε

εi ¼ εσ ðσ; T Þ þ εth ðTÞ þ εcr ðσ; T; tÞ þ εtr ðσ; T Þ

(5.60)

376

5 Fire-Resistant Composite Structures: Calculations and Applications

where ɛ is the total strain at time t, ɛi is the initial strain at time t ¼ 0, ɛσ (σ,T) is the Mechanical, or stress-related strain, being a function of both the applied stress σ and the temperature, ɛth(T) is the thermal strain being a function only of temperature, T, ɛcr (σ,T,t) is the creep strain, being additionally a function of time and ɛtr (σ,T) is the transient strain which only applies to concrete.

5.16.2.1

Stress-Related Strain

The stress-related strain (or mechanical strain) refers to the strain which results in stresses in the structural members. These stresses are based on the stress-strain relationships, used for the structural design of all materials. For the fire design of individual structural members such as simply supported beams which are free to expand on heating, the stress-related strain is the only component of strain that needs to be considered. If the reduction of strength, with temperature is known, member strength can easily be calculated at elevated temperatures using simple formulae such as those given in this chapter. The stress-related strains in fire exposed structures may be well above yield levels, resulting in extensive plastification, especially in steel buildings with redundancy or restraint to thermal expansion. Computer modelling of fire exposed’ structures requires knowledge of stress-strain relationships not only in loading, but also in unloading, as members deform and as structural members cool in real fires.

5.16.2.2

Thermal Strain

Thermal strain is the well-known thermal expansion that occurs when most materials are heated, with expansion being related to the increase in temperature. Thermal strain is not important for fire design of simply supported members, but must be considered for frames and complex structural systems, especially where members are restrained by other parts of the structure and the thermal strains can induce large internal forces.

5.16.2.3

Creep Strain

Creep is the term which describes long-term deformation of materials under constant load. Under most conditions, creep is only a problem for members with very high permanent loads. If the load is removed there will be slow recovery of some of the creep deformations, as shown in Fig. 5.78a. Creep becomes more important at elevated temperatures because creep can accelerate as load capacity reduces, leading to secondary and tertiary creep as shown in Fig. 5.78b. ‘Relaxation’ is the complementary term which describes the reduction of stress in materials subjected to constant deformation over a long period of time.

5.16

Material Properties in Fire

377

Fig. 5.78 Creep in structural materials: (a) creep under normal conditions, (b) creep at elevated temperatures

Creep is relatively insignificant in structural steel at normal temperatures. However, it becomes very significant at temperatures over 400 or 500  C and is highly dependent on stress level. At higher temperatures the creep deformations in steel can accelerate rapidly, leading to plastic behaviour and ‘runaway’ failure. Creep in wood is complicated by changes in moisture content such that creep deformations tend to be larger in environments where the moisture content of the wood fluctuates over time, hence creep can become a major concern in fire-exposed wood which is at temperatures around 100  C. Creep strain is not usually included explicitly in fire engineering calculations because of the added complexity and the lack of sufficient input data.. This applies to both hand and computer methods. Any structural analysis computer program for elevated temperature is already very complex without having to explicitly include the effects of time-dependent behavior. The effects of creep are usually allowed for implicitly by using stress-strain relationships which include an allowance for the amount of creep that might usually be expected in a fire-exposed member.

378

5.16.2.4

5 Fire-Resistant Composite Structures: Calculations and Applications

Transient Strain

Transient strain is caused of cement paste when it is heated for the first time under load. Transient strain is often included in analytical models for predicting the behaviour of reinforced concrete structures exposed to fire.

5.16.2.5

Effect of Strain Components

Equation (5.60) can be simplified, ignoring the last two terms to give εtotal ¼ εmechanical þ εthermal

(5.61)

Chapter 6

Fire Following Earthquakes

6.1

A Historical Review in Brief

While fire following an earthquake has long existed as a major source of loss potential, the problem has generally gone unrecognized or untreated by most groups, including many, who should be specifically concerned with the problem. Fire protection and structural engineers are examples of groups in which recognition of the problem has generally faded since the 1906 San Francisco and 1923 Tokyo earthquakes and fires. Recognition of the loss potential has remained within the insurance industry, but very little has been done to treat the problem. An exception to the foregoing is Japan, where the problem receives considerable attention. Aside from Japan, however, this lack of attention is surprising, especially given that the two earthquakes noted have been the sources of the two single greatest (nonmilitary) urban fires of the twentieth century. (The major difference between San Francisco and Tokyo at the time of those earthquakes and the cities of today is the many hundreds of high-rise buildings which were not present in the earlier events.) Recently attention has been called to the general problem of fire following earthquakes in the United States, although the particular problems of fire following earthquakes in high-rise buildings have not been specifically addressed (Scawthorn 1987). That the problem of fire following an earthquake in high-rise buildings has largely been overlooked is not too surprising when one considers the relatively small number of earthquakes that have actually caused major damage to high-rise buildings. These would include San Francisco 1906, Tokyo 1923, Alaska 1964, Caracas 1967, Tangshan 1976, Bucharest 1977, and Chile and Mexico 1985—only eight in all, and only six in relatively modern times. (This list neglects several other earthquakes affecting urban areas with only a handful of high-rise buildings, such as Managua 1972 and Guatemala 1976.) Today, however, we are faced with large and rapidly increasing numbers and densities of high-rise buildings in seismic zones (Council on Tall Buildings, Group CL 1980) in the United States, Japan, and elsewhere, to the point where it is only a matter of time until a major urban area such as San Francisco, Tokyo, or Los Angeles M.Y.H. Bangash et al., Fire Engineering of Structures, DOI 10.1007/978-3-642-36154-8_6, © Springer-Verlag Berlin Heidelberg 2014

379

380

6 Fire Following Earthquakes

is strongly shaken with potentially catastrophic results. In a modest attempt to partially avert such a disaster, and fill the gap concerning the problems of fires following earthquakes in high-rise buildings, the following discussion will focus a general model of fire following earthquake, and then examine ignition, fire spread, and fire prevention specific to the postearthquake high-rise environment. fire management policy has been delayed due to ongoing changes in state forestry management, earlier problems with adoption of the new forest code, uncertainty regarding the allocation of authority, shortage of financing, and technical problems.

6.1.1

Institutions, Responsibilities and Roles

Forest protection is generally an important component of the national policy of all countries, providing ecological sustainability and preserving ‘green’ potential. But in the Northeast Asian region, legislation and the ability to implement it differ from country to country. Major achievements have been made in several countries of the region with regard to their institutional framework. In China, Japan, the Republic of Korea and Russia, national and local versions of Agenda 21 have been formulated, directly relating to their national forests. In addition, environmental plans or strategies have been developed, such as Japan’s Basic Environment Plan, the Republic of Korea’s Green Vision 21, the Democratic People’s Republic of Korea’s National Strategy for Conservation and Sustainable Use of Natural Resources, and Russia’s Concept on Forestry Development. Progress has been achieved in virtually all areas of environmental protection in all countries, but expenses have increased and thus the extent of progress differs. Recent initiatives, such as the creation of the Presidential Commission on Sustainable Development in the Republic of Korea, which involves people from the business sector, academia and NGOs, seem to provide the potential for an effective multi stake holder voice in policy implementation. China’s Forest Action Plan for its Agenda 21 of 1995 laid the foundation for a comprehensive range of sustainably managed forest ecosystems together with a fully developed forest industry by 2010. In Japan, the nationwide Forest Plan (1996) was developed, together with policy directions and guidelines for forest management. The 4th Forest Development Plan of the Republic of Korea (1998) created the basis for sustainable forest management by improving forest resources, fostering competitive industries and maintaining a healthy forest environment. Russia has well-defined laws on forest protection, but law enforcement is quite weak. There were not many supporters of the recently prepared forest code, which will radically change the property and management system in Russian forestry and is now set to begin implementation from January 2007. The Russian Far East is a part of the all-Russia forest fire management system, with two lead departments: the Federal Forestry Agency and the Aerial Forest Protection Service. Both departments have

6.1 A Historical Review in Brief

381

subdivisions in the various regions of the country. The Ministry of Emergency Situations becomes involved in extreme circumstances. The importance of forestry research and education is widely recognized through Northeast Asia as a prerequisite for effective management of natural resources. Research, education and information systems vary across the region, depending mainly on the availability of funding, other resources and facilities. But, without exception, countries invest less in forestry research than in related sectors such as agriculture. Understanding the need for partnerships in managing forest-fire events, the countries in the region have ratified, accessed to or accepted most multilateral environmental agreements and conventions adopted prior to or after the 1992 UNCED. Despite this, there is still no international forest fire cooperation programme in the region. Further, the control of fires is a national issue that must be addressed in a coordinated manner on the basis of the resources and expertise of individual nations. Technical assistance may have a key role to play here, together with the development of partnerships. There are fewer federal (central) resources available and many issues have been devolved to local governments, NGOs and partners. New models for partnership, cooperation and, in some cases, trilateral agreements by the private sector, NGOs and national and local governments may be expected in the near future.

6.1.2

Collaboration

Unacceptable losses of resources and transboundary pollution have had a positive impact on collaboration between nations, especially between neighbouring countries such as China and Russia. A number of Northeast Asian countries have participated actively in the international dialogue on forests. This includes discussions in the Intergovernmental Panel on Forests, the Intergovernmental Forum on Forests, and subsequently in the United Nations Forum on Forests. A number of countries from the region have sponsored or hosted initiatives and meetings, directly contributing to this international dialogue. A variety of other regional forestry agreements, institutions and ad hoc meetings promote international cooperation on forestry within the region. FAO, the International Network for Bamboo and Rattan (INBAR), the International Plant Genetic Resources Institute (IPGRI), ITTO, IUCN, UNDP, the World Bank and the World Wide Fund for Nature (WWF), among others, have a range of forestry programmes or involvement in forestry. A wide variety of forestry-related NGOs also operate in the region, implementing bilateral and multilateral development projects, and they play important roles in facilitating dialogue and exchange. Japan is one of the main donor countries, both in the region and on a global scale, contributing substantially to forestry projects in the Asia and the Pacific region, while the Global Environment Facility is supporting

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Forest Fire Management in Biologically Valuable Forests of the Amur-Sikhote-Aline Ecoregion. This Russian Far East project involves all components of civil society in its implementation. In 2004 the Regional Northeast Asia Wildland Fire Network was established under the UN-ISDR GWFN. This regional network is coordinated by the Korean Forest Research Institute and facilitated by the Pacific Forest Forum. It is currently providing a platform for fire information dissemination and exchange, which could, through increased cooperation, lead to effective work on fire management.

6.1.3

Community Participation

The region is undergoing a positive change with regard to society’s perception of the problem of fires. However, people are still not fully aware of the consequences of forest fires. The countries of the region have recognized the immense pressures on forests in densely populated areas, and also that authoritarian styles of centralized forest management are neither appropriate nor effective in meeting the broader forest management objectives of today. Forest departments have increasingly found their management objectives unattainable, or seriously compromised, unless they empower communities and stakeholders to participate in decision-making. Many villages in China and some other countries have developed community regulations and agreements and have successfully strengthened forest fire management at the local level. But this is not widespread, nor has technology transfer gone far. The main measures for managing fires are to raise public awareness through publicity and educational activities, legislate for fire management, build firefighting teams, develop an enabling framework for society’s involvement in fire prevention and reinforce the development of infrastructure and fire preparedness in key danger zones. Local people may have extensive knowledge on fire management that is well adapted to the local environment and thus may be in a position to manage or prevent fires without outside assistance. However, in the case of very large fires, communities often cannot manage the situation because of inadequate training, experience and professional expertise. In the Russian Far- East, USAID established the Forest Resources and Technology (FOREST) Project, devoted to forest fire prevention through changing people’s behaviour in the forest. The project has been working in Khabarovsk, Krasnoyarsk and Primorski territories and Sakhalin and Irkutsk regions. It introduced an integrated approach to forest fire prevention awareness activities among local citizens. The approach involved three interdependent components: development of educational campaigns and general awareness for targeted groups; development of the Fire Prevention Awareness Program for Preschool and School Age Children; and strengthening of foresters’ skills in communication/community participation.

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Although changes in people’s behaviour and attitudes usually take place gradually over decades, checks showed that, in 1 year, about 90 % of the people had become familiar with and remembered some elements of the campaigns and 18 % declared that they had changed at least one aspect of their behaviour in the forest. As the FOREST Project shows, regular fire prevention awareness activities among citizens cannot be implemented without laws, stable finance and established institutions. Moreover, financing systems and institutional structures must also be in place.

6.1.4

Needs and Limitations

Major constraints on forest fire management face Northeast Asian countries: • limited institutional and technological capacities; • organizational and Financial problems in implementing international cooperation; • the challenge of full implementation of Agenda 21 measures and actions at national and regional levels; • lack of public awareness of fire issues; • lack of technical cooperation, training capacity, educational programmes and the ability to combine the efforts of all components of civil society; • absence of a clear legal, institutional and financial base, including new measures for taxation; • absence of measures to increase the responsibility of civil society for the condition of forests; • the need to enhance the capacity of government institutions, research entities, business and NGOs with regard to planning and implementation of sustainable development programmes; • the need to develop institutional mechanisms that integrate both the developed and developing countries in the region; • shortage of modern fire control equipment, insufficient use of satellite data and information technologies.

6.1.5

Analysis and Recommendations

Comparing the periods 1988–1992 and 1998–2004, an increase can be observed in: scale and frequency of forest fires, area burned, economic damage (albeit with great differences among countries), costs of fire suppression, efforts to regroup forces and attract voluntary firefighters, and-awareness among the general public and national/local politicians of the necessity for fire management. In summary, the goals of sustainable forest fire management are most likely to be achieved through:

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• adopting enabling approaches, forming partnerships and activating participatory mechanisms; • building capacity of partners; • monitoring and evaluating progress, and learning from each other’s successful practices through networking and the use of modern information technologies; • developing international cooperation to facilitate active participation at all levels of government and by all relevant partners in decision-making, policy formulation, implementation, evaluation and resource allocation. Vegetation fires and their negative impact continue to be a major issue in Northeast Asia: fires cause deforestation and influence the quality of life, land, air and water. Unacceptable resource losses and the spread of transboundary pollutants need immediate attention by the nations of the region and their international partners. Integrated programmes and strategies must be developed to address the wildfire problem at its roots, while at the same time creating an enabling environment in which appropriate tools are developed to enable policy-makers to deal with wildfire proactively. The traditional approach of dealing with fires exclusively through fire exclusion schemes must be replaced by an intersectoral and interdisciplinary approach. Fire management experts from Northeast Asia have a good picture of how to improve methods and incorporate modern technologies of forest fire prevention and suppression. There is also a clear perception of the need to take into account postfire ecological consequences and their role in global processes. Fire impact on forest ecosystems is now perceived as many-sided, useful as well as harmful, and a necessary element in fire management. Large forest fires are still the main threat, since they have been increasing proportionally over the last 30–40 years. However, there is still no regional database on forest fires. Due to different approaches, information is not always compatible among countries. Efforts are underway to further such compatibility, but political will and government support are needed to realize this concept. Institutional capacities are among the weakest points in forest fire management in the region and need to be improved. Emergency preparedness and response programmes must he coupled with better land-use policies and practices. Fire prevention should become a priority in the forest protection system, while the application of prescribed fires and preventive controlled burnings as a measure of fuel management should be increased. The quality of training for fire risk assessment (fire danger index) must be improved, and there is a need to unify approaches to regional zoning according to forest fire risk. Advanced technologies for forecast and detection of fires should he introduced, and other information technologies as well. There is a need for development and provision of free access to a global early-warning system for fire occurrence and fire risk. The establishment of fire management networks can be a very effective tool to support local communities in fire preparedness.

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The interrelationship of fires with climate change and the global carbon cycle, the expected long-term socio-economic consequences and the change in forest resources should be studied. International cooperation in suppressing forest fires should include not only information exchange, but also the transfer of fire suppression resources such as airplanes, ground forces and equipment from country to country. The main problems facing the use of aerial means are the operational and maintenance costs, but comparing suppression costs with the possible ecological and economic damage, a balanced solution must be found. There is a need to improve capabilities in local, national, regional and global early warning and risk assessment and in the detection, monitoring and regular assessment of fires.

6.2

South Asia

This region includes Bhutan, India, Nepal and Sri Lanka. It stretches from the mountain forests of the Himalayas in the north, to tropical evergreen forests in south India and Sri Lanka. The range of landforms and climates in South Asia has resulted in a high diversity of ecosystems and forest types, and consequently diverse fire regimes and vulnerabilities (details are provided in FAO Fire Management Working Paper FM/14/E).

6.2.1

Extent and Types of Fires

The latest and only data on forest fires in South Asia that are compatible with other regions are provided by the FRA 2005 country profiles. In 1990 the average area in South Asia affected annually by fire was 1.43 million ha, excluding the Kingdom of Bhutan, where no data were reported before 1992. In 2000 the approximate annual fire-affected area was 4.11 million ha, of which 90 % was in India. However, no information is available on fires in other wooded lands. Moist deciduous forest is the most vulnerable to fire in India. Nearly 15 % of this ecosystem is frequently disturbed by fire and 60 % is occasionally affected. Nine percent of the wet/semi-evergreen forests burn frequently and an additional 40 % burn occasionally. In the northeastern region of India, recurrent fires annually affect up to 50 % of the forests. The coniferous forests in the Himalayan region, notably Pinus roxburghii stands, are also very fire prone. Many wildfires occur during the winter drought. The 2005/ 2006 winter was a typical example: numerous fires burned in the high-altitude forests and shrublands of Bhutan, Nepal and Sikkim (India). In neighbouring Tibet, a major wildfire burned for almost 2 weeks at the foot of Mount Qomolangrna (Mount Everest) and destroyed valuable bushland in the county of Tingri.

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Causes

In all countries in the region, fire is used by the rural population as a common tool to clear agricultural land. It is also used to facilitate the gathering of NWFPs and in hunting and herding. Uncontrolled fires are common in regions with a long, intense dry season. All of these fires have the potential to cause major damage. Over 90 % of fires are due to human causes. There are very few cases of fires ignited by lightning. Bhutan’s climate conditions during winter (freezing temperatures, lack of rainfall and high wind velocities) strongly favour fires. Moreover, at the end of the dry winter season the fields are prepared, and these fires often escape and cause damage. In Nepal, analysis revealed that 58 % of the fires were deliberate, followed by those caused by negligence (22 %) and accident (20 %). With human populations moving into WUIs, an increasing number of fires were human- induced, caused, for example, by discarded cigarette butts and by the collectors of NWFPS and fuelwood. Fires were started deliberately by livestock owners, shepherds and herders, who ignited grasslands to promote a new flush of growth for their animals. These fires often spread to forests—and this was a key threat in the Terai area. India gave an example of a case study area (the Nilgiri Biosphere Reserve in Coimbatore) in which successful fire management had been practised for a long time, but where it suddenly started to fail. The reasons were a reduction in the means and funds for fire prevention and control, continuous encroachment by herders and NWFP collectors, and a decreasing sense of responsibility for fire control among local people.

6.2.3

Effects

The consequences of uncontrolled fires in South Asia are serious degradation of forests, ecological changes and deterioration of social and economic conditions. According to reports from the region, the main environmental damages to forests included destruction of biodiversity, extinction of plants and animals, soil degradation with erosion and loss of fertility, loss of wildlife habitats and depletion of wildlife, degradation of watersheds and halting or slowing of natural regeneration. Microclimates were affected, with changes in soil moisture balance and increased evaporation. Important carbon sinks were lost or degraded, leading to an increase of carbon in the atmosphere. Smoke haze polluted the atmosphere and endangered people’s health. Economic and social losses due to fire included losses of valuable timber resources, NWFPs, fuel wood and fodder. Loss of employment was seen, as well as destruction of property and loss of lives. According to the FRA 2005 country profile of India, 3.7 million ha of forest were affected annually by fire, creating damage of US$107 million equivalent. In

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Bhutan from 1981–1985, 232 fires were reported, affecting an area of 29,516 ha and causing damage of US$19.2 million equivalent. In Nepal the average annual loss of saw logs and fuelwood in Bara district in 2004, at market price, was some US$370,000. Sri Lanka lost 26 ha due to forest fires in 2000. In the years from 1994 to 1998, 641 fires were reported, burning an area of 1,648 ha and causing estimated damage of US$75,000 equivalent.

6.2.4

Economic and Social Benefits

In Nepal firewood collectors evidently prefer dola daura (round fuelwood of saplings killed by fire and dried) to freshly cut wood because it burns slowly and produces higher heat yield. Farmers welcome the first post-monsoon flash floods from burned forest to their lands because they carry organic matter, available phosphorus, potash and nitrogen. Fires boost the formation of fresh, palatable shoots as cattle fodder. The collection of minor NWFPs, such as seeds of sal (Shorea robusta), niguro (edible ferns), mushroom and kurilo (Asparagus racemosus), is facilitated by fire because they are more easily seen, and the forest is more accessible.

6.2.5

Prevention and Suppression

Among the South Asian countries, only India and Sri Lanka have information on forest fire prevention. Bhutan and Nepal seem to have no preventive methods at all, due to lack of capacity, including human resources. Preventive measures in India and Sri Lanka consist mainly of traditional practices such as fire lines and tracks, prescribed burning and hiring fire spotters during the fire season. Villagers in the vicinity of forest areas often have permission to gather dead wood free of charge in order to reduce the fuel load. They are also expected, even if not legally required, to assist the forest authorities in fire suppression. In Sri Lanka forest management plans do not include activities to prevent forest fires. They consist mainly of training programmes for local officers and villagers in firefighting, and few projects have been launched to develop community involvement. The Indian Ministry provides financial assistance to state governments within the Modern Forest Fire Control Methods plan. Financial support is used to buy hand tools, fire-resistant clothing, firefighting tools and radios, build fire watchtowers and pay spotters. The funds are also applied to the creation of fire lines, as well as for research, training and awareness-raising. This plan has been implemented in more than 70 % of the forested area.

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The Joint Forest Management (JFM) Programme, a UNDP project (1985–1990) and a project in Western Ghats in 1994 served to raise awareness among communities and increase their participation in fire prevention and forest conservation. The programmes were quite successful: fire outbreaks decreased by up to 90 % in some regions.

6.2.6

Institutions, Responsibilities and Roles

In most South Asian countries, the destruction caused by forest fires is well known and acknowledged by governmental authorities. Most politicians are aware of the necessity to practice fire prevention and to have a functioning fire control system. But this awareness and acceptance are often forgotten as soon as the monsoon season starts. Nevertheless, most countries have a forest law, which contains at least a clause prohibiting the setting of fire under certain conditions. This is often the only legal provision for fire control and prevention and its enforcement is often difficult. The Social Forestry Division of the Bhutan Government recently took the first steps to prevent and fight fires through awareness campaigns and building capacity for prevention and control. Activities of the Nepalese Government towards fire prevention are confined to television and radio broadcasts, since the Nepalese Department of Fire has neither the capacity nor the capability to prevent forest fires. However, the involvement of volunteer firefighters is increasing and is promoted by the Firefighters volunteer Association of Nepal (http://www.fan.org.np/). In Sri Lanka the Forest Department is in charge of all forest fire prevention and suppression activities, which are carried out by provincial district officers. Government support is provided through programmes promoting community involvement, for which fire management plans have been created. A new forest policy was introduced in 1995, but was not implemented until 1999. In 1988 India had a quite visionary National Forest Policy, which focused on the protection of forests against fire and called for improved and modern management practices to deal with forest fires. The Ministry of Environment and Forests developed a National Master Plan for Forest Fire Control, which introduced a fire management plan focusing on education, research and development. The Indian Government also set up guidelines for national forest fire prevention and control. The main features are: identification of vulnerable areas on maps, creation of a data bank on forest fires, fire danger and forecasting systems, provision for a crisis management groups involvement of JFM committees and efficient enforcement of legal provisions. In the future, India intends to create a National Institute of Forest Fire Management, equipped with the latest firefighting technology using satellites. It will carry out research, training and technology transfer on a long-term basis to obtain sound information in order to improve fire management planning in forests.

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In South Asia the local people and the administrative authorities are aware of the damage caused by forest fires, but the environmental and socio-economic consequences of these fires are usually underestimated. The governmental environmental/forest institutions of all countries play a key role in any activity related to forest fires. The local forest authorities are responsible for suppression, as well as for detection. Responsibilities are only shared in areas where local people are actively participating in fire management programmes, such as in India, or where the forest is community property and managed by the community, as in Nepal. In general, there seems to be a lack of feeling of responsibility on both sides— government and local populations. Tackling the difficult issue of fire is postponed by national parliaments as soon as the season changes and the danger recedes. Since law enforcement is rarely practised, nobody feels guilty and therefore nobody feels responsible.

6.2.7

Collaboration

Most international cooperation is implemented through organizations such as the Center for International Forestry Research (CIFOR), FAO, ITTO, IUCN, UNDP, UNEP, the World Bank and WWF. Some regional institutions and programmes support collaboration and assist in the dialogue between partners, For example the Asian Development Bank, South Asian Association for Regional Cooperation, South Asia Co-operative Environment Programme and FAQ’s Asia-Pacific Forestry Commission. Organizations that have launched programmes explicitly concerning forest fires are few. The Asia Forest Partnership is addressing the problem of forest fires and in the future is planning to assign some projects to forest fire prevention. Furthermore, the Asia-Pacific Regional Workshop on Scientific Dimensions of Forest Fires, held in India in 2000 and initiated by the Committee for Science and Technology in Developing Countries, was organized to discuss how science and technology can he used to improve fire prevention, management and mitigation. Specific cooperation agreements among the South Asian countries pertaining to forest fire management, as proposed by the GWFN, is not yet in place

6.2.8

Community Participation

Community involvement in forest fire management in South Asia is receiving increasing attention. In India community involvement is actively promoted through the creation of JFM committees, which have been founded throughout an area of over 10 million

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ha. They are now an essential component of the Modern Forest Fire Control Plan and have been given responsibility to protect forests from fire. As a result, forest fires were reduced significantly. Moreover, the forestry authorities accepted the control plan willingly and dialogue with the villagers improved, with the result that people were much more willing to cooperate in fire prevention and control. Other attempts of the Indian Government to apply a fire management system have been more negative, since they replaced traditional, community-based fire management systems, for example in the Mizoram region. The governmental management systems deprive people of responsibilities and tasks, so they no longer feel in charge of fire prevention. In Nepal there is increasing interest in community involvement and participatory approaches. In Sri Lanka community involvement in forest fire management has been voluntary, but few programmes have been developed to attract villagers interest. A new management plan was created containing a “participatory management working circle”. The government intends to launch another participatory forestry management programme to enhance fire prevention and communication between communities and the forest authority.

6.2.9

Needs and Limitations

Most countries of the South Asian region lack a national focus and the technical resources required to sustain a systematic forest fire management programme. Facing such a situation, it is clear that the needs and limitations are considerable. They include: • establishment of a fire division within the Forestry Departments, which would be in charge of all fire issues; • provision of a legal and financial base for fire management; • enforcement of existing or revised laws; • absence of a specific forest fire management plan, or of fire management provisions within the forest management plan; • launching of forest fire management programmes; • introduction of community-based fire management; • improvement of the present limited institutional and technological capacities; • capacity-building within the forestry department as well as among local populations; • provision of basic tools and materials for fire prevention and fighting; • education of the population, including awareness-raising campaigns; • lack of cooperation among South Asian countries, especially for knowledge and data exchanges; • improvement of cooperation with international organizations, NGOs, etc.

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Additional research is needed on fire outbreaks, suppression and fire ecology for better forest fire management. Modern technologies, such as remote sensing and satellite imagery, should be used for fire detection. India has already undertaken some initiatives in the use of these technologies.

6.2.10 Analysis and Recommendations Many of the South Asian countries have a long way to go to achieve sound forest fire management, as in the case of Bhutan, Nepal and Sri Lanka. India, on the other hand, seems to be realizing some improvements. The destruction caused by forest fires is recognized to a limited extent by the people and by decision-makers in all countries, and some knowledge exists on how to address the problem of fires. The question is how countries decide to tackle these issues and what support and incentives may be available from outside. The following recommendations aim to establish a sound, basic forest fire management system: • In most South Asian countries, governments should first be more aware of and committed to fire prevention and fire suppression. As long as governments refuse to take into account the negative effects of fires, it is very unlikely that changes will he accomplished. • The definition of responsibilities and the creation of internal structures in charge of fire-related matters within Forestry Departments are still lacking in several South Asian countries. These bodies should be responsible for, inter alia, developing fire management concepts, building up capacities at all levels and initiating awareness-raising campaigns. • A legal framework is essential to fire prevention and control, since it can remove incentives that encourage people to start harmful fires. • Development of fire management plans and programmes is an important parallel step. • Awareness-raising and the creation of a sense of responsibility among rural people can be pursued by campaigns using the media, meetings and the enrolment of villagers in forestry programmes. • Community-based approaches should be given priority in forest fire management by empowering local people and institutions and engaging them actively in management issues, including giving them user rights. • Fire management capacities should he built at local and national levels. • Basic tools must he provided for preventing and combating fires. • National science bodies should be involved in data collection on forest fires and in collaboration with forest departments to support fire prevention suppression, and mitigation. • Stronger collaboration among South Asian countries is advisable for the purpose of information exchange. • Cooperation with international organizations and NGOs should be intensified.

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Once the basic needs for a working fire management system are met, other technologies, such as remote sensing and satellite imageries for fire detection, should be introduced to improve the efficiency of fire management.

6.3

Southeast Asia

The regional paper for Southeast Asia reviewed the countries of insular and continental Southeast Asia—members of ASEAN. Through the ASEAN Agreement on Transboundary Haze Pollution, member states are forming a network that will serve as the UN-ISDR Regional South East Asia Wildland Fire Network (details are given in FAO Fire Management Working Paper FM/10/E).

6.3.1

Extent and Types of Fire

There has been almost no data on fire occurrence for the region since 1997/1998. Thailand offered the only source of fire-related data for this study, including fire numbers and extent. Data for the post 1997/1998 period were difficult to obtain, other than the limited data reported for FRA 2005 for six countries, or extracted from publications. Most available statistics dealt only with area burned and frequently there were no data at all relating to numbers of fires or causes. In the past two decades, severe Fire events in the region have been notable for the level of intraregional and global concern, but between these occurrences, there was little data collated to enable monitoring or evaluation at national or regional levels. Despite the level of inputs, including donor projects, almost no data were routinely collected and thus there were no time series against which routine performance and progress might be measured, other than the series of spikes at irregular intervals at the upper end of the spectrum.

6.3.2

Causes

Past analysis of the underlying causes of wildfires—by groups such as Project Firefight South East Asia and CIFOR—is still relevant and valid. Some reasons for fire use included: • • • • •

land—use change/conflict; increasing land-use pressure; inconsistent land-tenure policies; perverse economic incentives; direct economic incentives.

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The most direct reason for fire use in the region was the search for subsistence and income, i.e. using fire as part of an agricultural cycle for either food or plantation crops. The Integrated Forest Fire Management (IFFM) Project of the German Agency for Technical Cooperation (GTZ) drew together the elements of fire management and coherently structured them into a tropical fire management framework. IFFM included a clear basis for the underpinning information required (e.g. cause, impact, behavior) to create an understanding of fire at management levels and to define the linkage between understanding the causes of fire and achieving effective fire prevention. Prevention campaigns were often aimed at sections of the community that did not cause a significant number of fires, e.g. school-aged children, while those that use and cause the most fires, the farming and plantation management communities, were ignored.

6.3.3

Effects

Forest and other land fires in 1997/1998 caused significant ecological and human impacts that focused world attention on the underlying nature of fire problems and their causes within the region. International attention had been directed to this region following severe drought and fire in 1982/1983, 1991 and 1994. As might be expected, with the increasing ability to remotely monitor fire occurrence and extent, albeit very coarsely, the 1997/1998 episode drew far more global attention than prior events, and future events will attract at least similar levels of scrutiny, driven heavily by neighbours that cause little fire but are impacted by the outputs from it. Since 2000, there has been no new reported country-level information on specific social, economic and environmental impacts. Smoke haze episodes generated by wildfires and land-use fires have occurred repeatedly, such as in August 2000 and August 2005. The fires in peat soils were burning in deep strata and thus it was not possible to suppress them by conventional techniques. Numerous slash-and-burn agricultural or land-clearing fires burned out of control as well, because of very dry weather conditions.

6.3.4

Prevention

The use of satellites for detection of active fires peaked following the 1997/1998 fires, following recognition of the technology’s limitations, ‘Hotspot’ identification using NOAA’s AVHRR is increasingly recognized as offering no practical value for strategic and tactical suppression purposes. The use of fire location maps generated by AVHRR is limited owing to coarse resolution, cloudiness, time delays in information relay to field sites, and accuracy. Given the general development

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status of fire management capabilities and systems in Southeast Asia, the application of spaceborne information other than for monitoring purposes is difficult to justify at this stage. The availability of fire-related weather information has improved in the period 2000–2004. The ASEAN Specialized Meteorological Center and the Southeast Asian Fire Danger Rating System now provide relevant fire danger and meteorological information via their websites. These tools are valuable to the fire manager, although difficulty in accessing and interpreting the information remains in some rural and semi-rural locations. Viet Nam is operating a National Fire Danger Rating system. Fire-related weather data are collected in the field, analysed centrally and distributed as a fire danger warning across the country. The fire danger rating is made available in rural areas via various media, including facsimile, radio and roadside signboards. An ASEAN-burning policy was ratified in 1999. It is apparent that the prohibition on burning is proving ineffective in reducing fire in the region. It is now more widely recognized that fire has a deeper role in society and in livelihood creation than a policy can prohibit. Some potential modification of this policy is now beginning to affect national fire considerations, including recently developed guidelines for prescribed burning aimed at small landholders, farmers and shifting cultivators.

6.3.5

Suppression

Fire suppression resources are available but are insufficient in most countries. Thailand, for example, has a nationally organized fire suppression capability, but it recognized in 2000 that it could offer coverage of only 20–30 % of forested lands. No other national coverage estimates are presently available. Indonesia has begun a programme to develop fire brigades with trained and equipped staff in localities considered highly fire-prone. The equipment and resources available in the region comprise a range of locally developed and imported technologies. Fire suppression field crews, equipped with standardized levels of manual and mechanized equipment, are being developed. Crew sizes vary from 3 to 15 people and have designated leaders and specialists capable of operating and repairing firefighting equipment. These suppression crews are the backbone of firefighting operations, and their continued development and increasing numbers across the region will mark significant changes in fire suppression in the future, provided they are supported by effective management systems. Vehicles fitted with water tanks and pumps of varying capacities continue to be used. Their utility is limited by road access. Heavy equipment (bulldozers and excavators) is utilized more widely by plantation owners, particularly in peat soil fires. The use of aircraft for fire suppression is just beginning in the region. One of the most successful aircraft uses in recent times is of light and medium helicopters for remote and rapid access to fires, with self-contained and well-equipped field

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crews, and for their support. Fixed-wing aircraft have not yet been widely engaged for rapid fire detection or work such as infrared scanning.

6.3.6

Community Participation

Significant evolution in understanding of CBFiM has taken place in the region since 2000. The first international workshop on this topic took place in 2001 in Bangkok, Thailand, and was jointly managed by the Regional Community Forestry Training Centre for Asia and the Pacific (RECOFTC) and Project FireFight South East Asia (operated by WWF and IUCN). The workshop was followed by an international conference in Balikpapari, Indonesia. Concurrently, several higher order reports and collations of case studies on CBFiM have been published, placing CBFiM firmly in a field of study and understanding that is now increasingly appreciated as a more socially adaptive and capable management method. For further information, see the regional paper. Continued attention to CBFiM as a practical and suitable form of fire management in the region will increasingly enhance the overall fire management outcomes.

6.3.7

Collaboration

A significant policy development over the period 2000–2004 was the ASEAN Agreement on Transboundary Haze Pollution, which was signed by all ASEAN member countries in June 2002 and entered into force on 25 November 2003. This was the culmination of concerted and intensive regional efforts over several years to address trans boundary haze pollution since the 1994 and 1997/1998 severe haze episodes. The agreement is the first legally binding ASEAN regional environmental accord, although not all ASEAN member countries have yet ratified it, and until this occurs, questions about its potential effectiveness will remain.

6.3.8

Needs and Limitations

First, while international action and input are seen as necessary to assist the region in guiding fire management along a path that will achieve a level of self-sufficiency, the ultimate goal is to achieve a state in which effective and practicable fire management can be sustained within the region, indeed within individual countries, without significant external input. In essence, the solution is for individual countries to develop their own or collective fire management solutions matched to their specific cultural, physical and financial constraints, rather than adopting fire management

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solutions developed for different circumstances. To achieve this, however, the region needs support and assistance from the wider global fire management community. Second, there is apparently an increasing willingness for governments to cooperate on regional action on fire management issues. This willingness needs to be harnessed through the development of appropriate fire management capabilities at national, provincial and local levels. Third, the routine collection and collation of fire information at local, provincial and national levels is essential to sound fire management decisions, policies and plans. Each country needs to direct efforts towards the collection of fire-related data such as the number of fires, area burned, vegetation types within which they occurred and, if possible, measures of impact. This will assist in identifying fire management needs and suitable programmes of management appropriately targeted and scaled to the circumstances. Fourth, fire in the region is an annual event, not something that occurs without warning or understanding. The management of fire is a balance between livelihood creation and health and environmental concerns. The adverse livelihood, economic, health and environment impacts are all appreciated. For example, the heightened international awareness and pressure that result from haze events must be directed into longer-term management efforts, not simply immediate suppression and restoration. The majority of fire management efforts must he directed to long-term prevention.

6.3.9

Analysis and Recommendations

The management and impact of fire within the Southeast Asian region is a matter that requires a combined multinational and regional approach. The ASEAN Agreement on Trans boundary Haze Pollution was one of the events of greatest significance in the region. Although this agreement has been accepted in principle and serves as a model for other regions to follow, not all member countries have yet ratified it or given it their full endorsement. Until all member countries have ratified the agreement, it will not become legally binding and its effectiveness will remain open to question. The August 2005 fires, although brief in nature, could serve as a trigger to ensure that this agreement is fully adopted and implemented. CBFiM has emerged as a new and increasingly adaptive mechanism for working with and managing fire. The region has embraced the early development of CBFiM through donor projects, international workshops and the hosting of international conferences. The future of CBFiM and the benefits it can bring to communities will only be ensured if regional and international efforts for its development continue. Although the underlying motivations for the use of fire are Increasingly understood, whenever adverse fire weather conditions persist, it is almost a foregone conclusion that a severe air pollution/haze event will ensue, induced by fire- associated smoke. The lack of baseline annual fire data will continue to hamper well-structured fire management efforts in the region.

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Without identifying action to sever the linkages between fire causes and fire prevention actions, and more particularly, to identify who sets fires and why, the effective targeting of sound fire management practices, particularly fire prevention, will remain a difficult task. There is a strong need for fundamental analyses of fire situations on an ongoing basis—and not only when disaster strikes. If it is to be effective, fire management must be a daily, weekly and monthly programme of systematic management in any region of the globe. The attention to and effort in fire management in this region must achieve such time regimes if it is to have any effect in the long term. Fire is an inescapable part of the environment in this region. As is the case elsewhere on the globe, a box of matches remains the simplest and least expensive tool available to fire users. Put simply, fire will remain a crucial part of the ASEAN environment for the foreseeable future.

6.4

Australasia

The regional paper for Australasia covered Australia and New Zealand (details are provided in FAO Fire Management Working Paper FM/13/E).

6.4.1

Extent and Types of Fire

In the period from 2000 to 2005, the 2003 fire season in Australia was one of the most dramatic since European settlement in terms of its impact on people and homes, although the most extensive area was burned in 2001 (Table 6.1). Very large areas of southeastern Australia experienced fires under severe weather conditions, following a long and harsh drought. The damage to assets and the nature of the fire season led to a number of inquiries and reviews of fire management for Australian states and the nation as a whole. In northern Australia, tropical savannah and grasslands are ‘easy’ to burn. Many living on the land, and relying on it for their livelihood, do not fear fire—they use it. In southern Australia, where settlement is denser, the landscape is highly fragmented and there are high-value fire-vulnerable assets. In addition, coastal communities are overwhelmingly urbanized and the majority of civil society and those that influence it see fire as ‘bad’. The area subject to yearly fires has declined significantly since European settlement, due to changed land-use patterns, fire suppression and the cessation of burning by aboriginal populations. These changes are leading to altered forest structures, emerging forest health problems such as dieback, and an increase in landscape—scale, high-intensity fires. Prescribed burning in southeastern Australia has been under pressure from public opinion, and the area undergoing such burning has been shrinking.

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Table 6.1 Approximate fire-affected areas across Australia 1997–2003 % of total land area % of fire affected area consisting Calendar year Area (million ha) fire affected of tropical savannah 1997 48.3 6.3 86 1998 26.3 3.4 92 1999 60.0 7.8 86 2000 71.5 9.3 65 2001 80.1 10.4 84 2002 63.8 8.3 63 2003 31.6 4.1 85 Source: Western Australian Department of Land Information, cited in Ellis, Kanowski and Whelan (2004)

In New Zealand the average number of fires per season and the average area burned per fire, while indicative rather than definitive, suggest that the fire management system is working well. An average fire size of 2.4 ha is small for an annual average of 2,669 fires. While small fires can be significant in losses for plantations or natural ecosystems, particularly small-scale or localized habitats, the figures reflect effective arrangements for preventing, preparing for and responding to fires.

6.4.2

Causes

In addition to lightning, people cause the overwhelming number of fires in Australia. Human-caused ignitions are generally unintentional, although there has been an increase in arson. This recent increase is not reflected in the number of people convicted of offences following the 2002/2003 fire season, where, out of a national total of over 10,000 fires identified as deliberately lit or as potentially arson, there were 43 convictions. In New Zealand, also, fires are mainly caused by people. Lightning fires occur, but represent a very small percentage of ignitions.

6.4.3

Effects

In Australia, generally, all fires are assumed by the public and the media to be bad. Research, experience and history generally demonstrate that this is not the case, but, except in the north, this overriding impression is widely held. As a result, questions are not asked about which fires, or parts of fires, were detrimental and which were beneficial. There is generally very little information available on the economic impact of unwanted fires. Historically, the recording of losses has been limited nor are the details of the type of loss considered. Possible types of loss might include: reduced productivity, impact on tourism, infrastructure damage, loss of sales and loss of employment.

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It is possible to extract indications of firefighting costs from annual reports and other sources. These are not necessarily clear or simple to calculate. In the recent past, the strong impression has been of increasing budgets for fire agencies and perhaps decreasing budgets for the management of land, including fire prevention. There have been no assessments of ecological or environmental impacts. This information is essential to explain changes in land management practice and to support the evolution of policy, a need emphasized by persistent media descriptions of large and damaging fires as “environmental disasters”. Development controls require the assessment of significant environmental impacts, for which there are sophisticated and highly regulated schemes and systems. Major wildfire events, on the other hand, attract no such assessment or evaluation of their environmental impact or the chances for recovery. Consequently, there is no information to support or prioritize efforts for restoration of landscapes and ecosystems, despite the availability of the skills and technical capacity to undertake restoration. As in many countries, the costs of combating fires and the value of losses are not comprehensively measured in New Zealand.

6.4.4

Prevention

The three elements of prevention are prevention of ignition, of the movement of fires across landscapes and of damage. The measures and management needed to address these elements are most easily applied to preventing ignition and damage. Ignition-reduction strategies are quite well developed in Australia and are evolving as civil society evolves. The places where people choose to live are changing, shifting the rural/urban interface into natural areas, including protected areas and rural lands. At this interface, education about fire and systems to reduce fire damage (engineering and managing human behaviour) are applied in all Australian states. The prevention of fires moving across the landscape involves managing or reducing fuels, and there have been increasing efforts in this area as well. The difference between the tropical and non-tropical areas of Australia highlights the variation across the nation with respect to fire. In tropical areas, there is no real fire prevention focus at all. The emphasis is more on education as to when the community should use fire, rather than on not using fire at all; the issue is timing, not prohibition. There are also differences in land use, in some cases historically based, which influence the role fire plays. Some landscapes have a strong prevention culture and there are no random fires. In other Landscapes, rural landowners use fire in a very unstructured way, “throwing around matches” as they move across their properties.

6.4.5

Suppression

There is a high level of fire suppression taking place. The majority of fires are contained and controlled, with the uncontained 5 % of fires responsible for 95 % of

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the damage suffered. Fires are put out mainly by ground firefighting techniques, but the use of aerial firefighting resources is increasing. Air support to fire suppression operations was significant during the 2002/2003 fire season. States and territories incurred a total cost of over $A 110 million. On the busiest day, over 100 aircraft were used. Helicopters and fixed-wing aircraft have consistently gained extensive public exposure, especially through the media, but the costs of aircraft are considerable and weigh heavily in overall fire management costs. The International Wildland Fire Summit was held following the 3rd International Wildland Fire Conference in Sydney, Australia, in October 2003. One of its outcomes was an international agreement for the exchange of fire management personnel among Australia, New Zealand and the United States that is a model for other international agreements on cooperation in fire management.

6.4.6

Community Participation

Fire management in Australia has largely shifted from the community to government agencies. There is little input expected from communities and few significant opportunities for them to have substantial involvement in decision-making. The volunteer bush fire movement, which does not strictly meet the accepted definition of CBFiM, is, however, still heavily relied on for fire suppression.

6.4.7

Needs and Limitations

In vegetation-fire risk assessment in Australia—also called bushfire and wildfire— identified three categories of actors and stakeholders to consider: 1. those that create the risk—these are the formal planning and land development systems and the informal attitudes and actions of people at risk; 2. those dealing with the results of the activities that create the risk—the key groups are the fire and emergency services, insurers and groups that work with them, such as forest and land managers. In an informal way, the media and the behaviour of volunteers, individuals and groups are all part of dealing with the risk; 3. those that create the future risk—these are factors such as urban expansion, governance, changes in lifestyle or values, possibly emergency management trends and climate change. Except for the last, these influences arise both from institutions and from individual choices and behaviour. One aspect that is clear from Handmer’s discussion is that these three groups of actors and stakeholders operate separately from each other: “Those creating the risk

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historically have no direct interaction with those dealing with the results, the fires. Worse perhaps is the absence of any useful engagement with those creating the future risk—the risk that fire and emergency services, insurers and society, will be dealing within the future.” This may well be a characteristic that is experienced more widely even outside Australia in the future. In New Zealand there may be another future change. There is a trend towards an increase in biomass and the quantity of available fuels. Native forest, tussock land, wetland and scrubland areas that had been converted to pasture are becoming uneconomical or non-viable. They are reverting to scrubland or being converted to plantations, which contribute to a dynamic export industry. There have also been attempts to stabilize and vegetate steep landscapes hosting introduced exotic animals, in particular deer. Thus some parts of the New Zealand landscape are moving from less complex systems with low fuel loads to increasingly complex systems with higher loads. Fuels are also physically more continuous, meaning that fires have a greater chance to spread across the landscape once they start. Fires will become more difficult to control, may occur in more remote areas and are likely to be much larger in size when fire weather conditions are severe. Severe conditions in New Zealand may recur every 15–25 years. The expansion of the plantation estate also suggests that losses will be higher.

6.4.8

Analysis and Recommendations

In Australia, fire management has largely shifted away from the community to government agencies. The country needs to develop an agreed, consistent data collection process on all aspects of fires. The lack of such data will hinder research, operational planning and evidence-based funding of bushfire response capability. The legal framework may also require review because of the declining use of prescribed fire (because of inadequate recognition of the role and benefits of deliberate fire use), and failure to support individuals and agencies engaged in applying fire to landscapes. In New Zealand, changes in the composition and complexity of the vegetation in rural areas, and the implications of these changes for fuel loads in particular, will require adjustments to the way fire management is practised. The National Rural Fire Authority has recognized this and has started to identify changing needs and altered circumstances. The first important step in both Australia and New Zealand is the development of research projects: to support and enhance fire danger rating; increase the understanding of fuel characteristics and dynamics; predict fire behaviour; and create a decision-support tool or system to assist rural fire managers in their planning and decision-making. In parallel, the management of resources, people and information is evolving to meet the expected needs of fire prevention, suppression and incident management.

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Australia has noted the historic absence of interaction and engagement between those creating the risk of fire and those dealing with the results. It is an increasing threat in Australia, and one that is likely to be experienced elsewhere in the future.

6.5

Southeast Europe/Caucasus

This region comprises the Balkans and includes Greece and Turkey, which are also part of the Mediterranean region (details are given in FAO Fire Management Working Paper FM/11/E).

6.5.1

Extent and Types of Fires

The number of forest fires per year in the Balkan region varied greatly from 1988 to 2004. Over this period, the smallest number of forest fires was recorded in 1991 (2,765) and the largest in 2000 (16,922). With the exception of 2000, the trend in forest fire occurrence increased steadily. Over this period, the total burned forest area was 1,250,892 ha, and the annual average area burned amounted to 156,361 ha. The countries most threatened were Bulgaria, Croatia, Greece, The former Yugoslav Republic of Macedonia and Turkey.

6.5.2

Causes

The changing land uses and rural exodus in some parts of the region are resulting in increased wildfire hazards and vulnerability of ecosystems. Conversely, urban encroachment into wildlands means increased vulnerability of human populations to fire, particularly at WUIs. During the last 15 years, wars and economic and political disorders have had a significant role in forest fire occurrence, behaviour and suppression. On average, 58.8 % of total forest fires have a human origin, 3.3 % a natural one and 37.9 % arise from unknown causes (Table 6.2). The human causes are often arson and negligence (including the negligence of tourists). Even those fires of ‘unknown’ origin are often caused by people.

6.5.3

Effects

There are no international standards to define economic and ecological damages caused by fire, but according to available evidence, there is no significant social impact of forest fires in the region. The economic and environmental damages are much more important.

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Table 6.2 Causes of forest fires in the Balkan region Causes (%) Country Human Natural Unknown Albania 63.7 0.8 35.5 Bulgaria 30.4 1.7 67.9 Croatia 75.3 0.8 23.9 Greece 55.5 3.0 41.5 Serbia and Montenegro (Serbia)a 66.0 3.0 31.0 Slovenia 45.9 8.3 45.8 The former Yugoslav Republic of Macedonia 72.5 2.0 25.5 Turkey 60.9 6.7 32.4 Average 58.8 3.3 37.9 a Now Serbia, but the statistics for Serbia and Montenegro refer to the Serbian Republic of the commonwealth (State Union) before the independence of Montenegro in 2006

The environmental damages include soil erosion, which is observed in all countries with large burned areas. The mass outbreaks of bark beetles (Ips spp.) are a very significant problem in the pine forests of The former Yugoslav Republic of Macedonia. The effect of forest degradation on tourism in the region is significant, especially in Albania, Croatia, Greece, The former Yugoslav Republic of Macedonia and Turkey.

6.5.4

Prevention and Suppression

Legal regulations regarding fire prevention exist in each country in the region. Other measures, such as awareness-raising and education, have also been used in most countries. Their quantity and quality depend on the economic situation and organizational potential of each country and they are usually carried out by the Ministries of Interior or Forestry, voluntary protection unions or some NGOs. Human intervention is the most important means of extinguishing fires, given that the number of naturally extinguished forest fires is very low (no more than 3 %)—usually when the cause of forest fire is lightning accompanied by rainfall. Regional exercises in the suppression of forest fires have been held in the interests of increased efficiency.

6.5.5

Institutions, Roles and Responsibilities, and Community Participation

Institutional roles and responsibilities for wildfire management are different in each country in the region, but there are also similarities. In several countries, the forest services at federal or regional levels are responsible. In others, all fires are the

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responsibility of a fire department. Serious fires may require the assistance of other bodies through an interagency agreement. Turkey reported that, since 1997, there have been substantial improvements in handling forest fires through the Fire Command Center, which is responsible for all fire management issues. A more comprehensive national database on forest fires is being created. The Pact on Stability for South Europe developed an initiative to form the Regional Disaster Management Center in Croatia. It covers Albania, Bosnia and Herzegovina, Greece, Italy, Montenegro, Serbia, Slovenia and The former Yugoslav Republic of Macedonia. The aim of the centre, which is in the organizational phase, is to facilitate cooperation in planning, preparation, prevention and reaction, and in reducing disaster consequences, including forest fire suppression in the area of southeastern Europe. Turkey reported that local people are required by law to respond to a fire situation if and when requested. The positive response of local people and communities in combating fires has increased considerably in recent years—mostly as a result of public awareness campaigns and a change in attitudes towards forest resources. Croatia has signed agreements on multilateral assistance with a number of countries. Bulgaria has received targeted support to improve forest fire management capabilities from Germany, Switzerland, the United States, FAO, UNDP and the World Bank. In 2006 a European Union Twinning Project is supporting the country in harmonizing legislative, reporting and preventive measures with European Union standards. GFMC has supported the Bulgarian-Swiss Forestry Programme in developing a national fire management strategy and the European Union in implementing the Twinning Project. The former Yugoslav Republic of Macedonia has international agreements with Bulgaria and Greece. Turkey reported that the Fire Command Center participates in interregional cooperation—firefighting assistance was provided to Georgia and Syria in 2005. Universities have a role in fire ecology and management research in the former Yugoslav Republic of Macedonia and Turkey.

6.5.6

Needs and Limitations

In April 2005, the former Yugoslav Republic of Macedonia hosted the International Technical and Scientific Consultation “Forest Fire Management in the Balkan Region” under the auspices of the Regional Balkan [now Southeast Europe/Caucasus] Wildland Fire Network of GWFN. The following gaps in fire management were noted during the consultation: • consistent information and statistics on fires, their causes and their effects; • applied research in social sciences and humanities, including financing of research; • integration of social, economic, environmental considerations and institutions in developing tangible policies and practices related to fire;

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• integration of fire as a component of land, resource and forest management; • community-based approaches to fire management; • training in the appropriate use of fire (prescribed burning for fuel reduction and nature conservation); • training in the safe and efficient use of resources for fire suppression (and appropriate equipment); • compatible approaches, e.g. global implementation of the Incident Command System and the international Wildland Fire Agreements template. The consultation was followed by the “Eastern European, Near East and Central Asian States Exercise on Wildland Fire Information and Resources Exchange— EASTEX FIRE, 2004”, a regional forest fire exercise organized by the host country, Bulgaria, the UN-ISDR regional network and GFMC. Fire and forest services from Albania, Bosnia and Herzegovina, Bulgaria, Greece, Romania, Serbia and Montenegro. The former Yugoslav Republic of Macedonia and Turkey participated in the exercise (http://www.fire.uni-freiburg.de/GlobalNetworks/SEEurope/SEEurope_4.html).

6.5.7

Analysis and Recommendations

The consultation recommended the following plan of action to governments, international organizations and NGOs for cooperation on vegetation fire research and management in the Southeast European/Caucasus region: • • • • • • • •

secure financing of a regional fire research programme; strengthen fire research cooperation between neighbouring countries; develop standardization of terminology and procedures; develop standardized data collection, including further development of global fire data collection; encourage increased involvement of the science community in fire-related, interdisciplinary research programmes; support the establishment of national or regional fire research centres; establish a regional fire weather network; approach the Erasmus/Socrates programme of the European Union about developing a dedicated programme for fire information exchange.

It is evident that the majority of countries in the region are ready to establish and strengthen a regional dialogue on cooperation, exchange of information, research and fire management as a contribution to forest and environmental protection, stability and peace. In May 2006, the Regional Southeast Europe/Caucasus (formerly Balkan) Wildland Fire Network presented a proposal for “Development of a Strategy for International Cooperation in Wildland Fire Management in Southeast Europe” to the 33rd Session of the FAO European Forestry Commission (Zvolen, Slovakia, 25 May 2006). The proposal aimed to enhance international cooperation in the region, including the development of standards and bilateral and multilateral agreements.

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Baltic and Adjacent Countries

The working paper for this region covered Austria, Belgium, the Czech Republic, Denmark, Estonia, Finland, Germany, Latvia, Lithuania, Luxembourg, the Netherlands, Poland, the Russian Federation (Karelia), Slovakia, Sweden, Switzerland and the United Kingdom (details are provided in FAO Fire Management Working Paper FM/7/E). The Central European countries, the Alps and non-Mediterranean southeastern Europe belong to the temperate vegetation zone, where mesic and more fertile forests are generally dominated by broadleaved trees. The most fire-prone forest ecosystems in this area are often dominated by pine (predominantly Pinus sylvestris L.) in dry and dryish site types, primarily plantations. The Nordic countries largely belong to the boreal and hemi-boreal vegetation zones. In this region, also, the most fire-prone ecosystems are pine-dominated forests (predominantly P. sylvestris) in dry and dryish site types. In the United Kingdom, especially in Scotland, t he most fire-prone ecosystems are the heathlands, dominated by Calluna vulgaris. Fires have always had social, economic and environmental effects that have generally been regarded as negative—especially in fire-prone ecosystems. But in Europe, especially in boreal ecosystems, fire has been reintroduced to forest ecosystems after a long period of no-burn policies. It is now used as a restoration and management tool for forest regeneration and biodiversity management.

6.6.1

Extent and Types of Fires

In the southern part of the region, most fires occur in the spring, from February to April. Towards the north, where spring starts later, the highest fire frequency is in May and June. Another peak in the number of fires and area burned occurs in most countries in August. In this region, the number of fires and the area burned annually vary mostly with the weather conditions. In general, the average size of a fire in the region is very small, often below 1 ha and not above 5 ha. Exceptions can be found in some countries, such as Poland, where a clear increase in the number of fires and area burned has been observed.

6.6.2

Causes

Arson is an important and increasing cause of forest fires; in Poland it is the reported cause in 44 % of fires. The reason seems to be the high unemployment rate, which has led to fires being deliberately set to produce at least temporary jobs

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in firefighting and forestry. Arson has also been reported as a rather common cause of fires in Lithuania (16 %) and Estonia (13 %). In both the southern part of the region and the Baltic countries, burning of grass in the context of agriculture is often carried out in the spring and is a common factor in the spread of fires. This seems to be a particular problem in many eastern countries of the region The practice has ceased in Fennoscandia. Changes in land tenure and ownership have led to omission of the necessary precautionary measures, especially in the Baltic countries, where a high number of new, small-scale forest owners have emerged. In addition, migration from the country and abandonment of rural lands have resulted in increased fuel loads and changes in vegetation composition and succession, leading to a higher fire hazard. Abandoned agricultural land has significantly increased in many countries of the region since the transition towards a market economy began. This has resulted in an enormous increase in the number of fires observed on such land. In Poland, for example, the number of fires increased from approximately 5,000 in 1994 to 53,000 in 2003. The extent of burned area in Poland has also increased—from about 13,000 ha in 1995 to 95,000 ha in 2003. Regionally, large plantations of exotic species, particularly those of coniferous trees such as Pinus contorta, have led to an increased fire risk. Preventive actions to reduce fire risk, such as changing tree species composition from coniferous to deciduous species, are being carried out in some countries, for example Poland. Uncontrolled fire use, especially in agriculture, and, infrequently, prescribed burning in forestry have been a cause of fires escaping into wildlands and occasionally into forests. But the rise of fire for prescribed burning depends on the level of local public awareness and knowledge of the principles of fire ecology and management. In some countries, for example in Estonia, the attitude of the public and the national authorities is opposed to prescribed burning, This opposition, together with an effective fire suppression policy, has led to fuel accumulation, especially in conservation areas, and thus to an increased fire risk. The use of prescribed fire in nature conservation and landscape management is increasing, including the use of fire in forestry and forest certification. The European Fire in Nature Conservation Network, an initiative of GFMC and the FAO/ UNECE/ILO Team of Specialists on Forest Fire, reflects the broad variety of prescribed burning objectives and the increasing number of projects throughout the region (http://www.fire.uni-freiburg.de/programmes/natcon/natcon.htm).

6.6.3

Effects

The economic costs of fire vary greatly within the region and among countries. However, the economic losses are generally quite low compared with other regions in which fires are more common and have more drastic consequences. Ecological damage is rare, but avalanches occasionally occur after fires, especially in the Alps. Health effects of fire are also rare, as the average size of fires in the region is small.

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However, the impact of smoke pollution from wildfires and land-use fires burning in neighbouring Russia has severely affected the Baltic region, notably in 2001 and 2006.1

6.6.4

Prevention

Financial support for fire management varies within the region, and lack of resources causes difficulties in fire management, especially in the Baltic countries. Aerial control may not be available due to competing demands.

6.6.5

Suppression

Training in wildland and forest fire management and suppression and even in the use of prescribed burning is inadequate in most countries of the region, especially concerning the ability to respond to large and lengthy forest fires. Decision-support systems need further development for these situations, as well as for specialized training in fire management. Bilateral and multilateral agreements on cooperation in fire management are also needed. The ICS, as an international standard for all incident management, should be introduced into interested countries.

6.6.6

Institutions, Responsibilities and Roles

Increasingly, fire management is no longer the responsibility of forestry staff, but of national fire and rescue services (F&RS). More often than not, these F&RS lack training in fire management and specifically in aspects of fire behaviour, including techniques in backfiring. Responsibilities shared between the authorities and organizations, as in Germany, can occasionally cause problems as well. There appears to be no community involvement in fire management. Some regional bilateral and multilateral fire emergency exercises have been carried out, e.g. among Baltic countries, but more need to be arranged. Exchange visits and programmes should be promoted regionally. Specific attention should be paid to developing online information systems through Web sites. During the last five-year period, fire research in the region has increased and northern countries have begun participating in European Union-funded fire research 1

Results for 2002 are available at http://www.fire.uni-freiburg.de/iffn/country/rus/IFFN%2ORussia% 202002%20Fire%/20Report.pdf, and for 2006 at http://www.fire.uni-freiburg.dc/rncdia/2006/GFMCBulletin-0l-2006.doc and http://www.fire.uni-freiburg.de/rnedia/2006/05/news_20060518_uk.htm

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projects. Regional cooperation in the field of fire research has been initiated between the Baltic and Nordic countries. Finland, Germany, Poland and the United Kingdom are participating in the research programme Fire Paradox (http://www. fircparadox.org/). The emphasis is on the use of prescribed burning and fire suppression.

6.6.7

Collaboration

In May 2004, a Regional Baltic Wildland Fire Meeting was held in Helsinki, Finland, followed by a side meeting to promote Baltic cooperation in fire research. At the meeting, trends in fire management in the Baltic region were studied and the Helsinki Declaration on Cooperation in Wildland Fire Management in the Baltic Region was issued. It included proposals to harmonize and strengthen efforts by UN-ISDR, WFAG and United Nations agencies and programmes to reduce the negative impacts of fires on the environment, but also to support and promote the knowledge and techniques to utilize the beneficial role of fire in ecosystem management, including the application of prescribed burning for the benefit of ecosystem stability and sustainability, with special emphasis on biodiversity. The primary interest is of course in active faults, along which crustal displacements can be expected to occur. Many of these faults are in rather welldefined tectonically active regions of the Earth, such as the mid-oceanic ridges and young mountain ranges. However, sudden fault displacements can also occur away from regions of clear present tectonic activity. Whether on land or beneath the oceans, fault displacements can be classified into three types. The plane of the fault cuts the horizontal surface of the ground along a line whose direction from the north is called the strike of the fault. The fault plane itself is usually not vertical but dips at an angle down into the Earth. When the rock on that side of the fault hanging over the fracture slips down wards, below the other side, we have a normal fault. The dip of a normal fault may vary from 0 to 90 . When, however, the hanging wall of the fault moves upwards in relation to the bottom or footwall, the fault is called a reverse fault. A special type of reverse fault is a thrust fault in which the dip of the fault is small. The faulting in mid-oceanic ridge earthquakes is predominantly normal, whereas mountainous zones are the sites of mainly thrust-type earthquakes. Both normal and reverse faults produce vertical displacements—seen at the surface as fault scarps—called dip-slip faults. By contrast, faulting that causes only horizontal displacements along the strike of the fault is called transcurrent or strike-slip. It is useful in this type to have a simple term that tells the direction of slip. For example, the arrows on the strike-slip fault show a motion that is called left-lateral faulting. It is easy to determine if the horizontal faulting is left-lateral or right-lateral. Imagine that one is standing on one side of the fault and looking across it. If the offset of the other side is from right to left, the faulting is left-lateral,

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whereas if it is from left to right, the faulting is right-lateral. Of course, sometimes faulting can be a mixture of dip-slip and strike-slip motion. In an earthquake, serious damage can arise not only from the ground shaking but also from the fault displacement itself, although this particular earthquake hazard is very limited in area. It can usually be avoided by the simple expedient of obtaining geological advice on the location of active faults before construction is undertaken. These concepts are clearly indicated in the world conferences on Earthquake Engineering, mostly held in California Institute of Technology, California.

6.7

Seismograph and Seismicity

Seismicity is a description of the relationship of time, space, strength and frequency of earthquake occurrence within a certain region and its understanding is the foundation of earthquake study. Since there is still no practical way to control earthquakes, one can only try to understand and follow their nature wisely to prepare for possible strong earthquakes through prediction, earthquake engineering and society or governmental efforts of disaster reduction. At the central zone, the impact corresponding to the air plane fuselage and engines is the worst zone. Away from the central zone, outer wing structures create also an impact zone. (e) Existing Loads on WTC-1 Apart from Those due to Aircraft Impact The upper 55 stories of the building’s exterior-wall frame were explicitly modeled using beam and column elements. This encompassed the entire structure above the zone of impact and about 20 stories below. The lower 55 stories of the exterior were modeled as a “boundary condition” consisting of a perimeter super-beam that was 52 in. deep (1,321) and about 50 in. (5,270) wide, supported on a series of springs. A base spring was provided at each column location to represent the axial stiffness of the columns from the 55th floor down to grade. The outrigger trusses at the top of the building were explicitly modeled, using truss-type elements. The interior core columns were modeled as spring elements. An initial analysis of the building was conducted to stimulate the pre-impact condition. In addition to the weight of the floor itself (approximately 54 psf (259 kN/m2) at the building sides), a uniform floor loading of 12 psf (0.76 kN/m2) for partitions and an additional 20 psf was conservatively assumed to represent furnishings and contents. At the impact area, all columns are damaged. The assumption is valid in the impact analysis. (f ) Fireball and Temperature Fireballs erupted and jet fuel across the impact floors and down interior shaft ways igniting fire. The term fireball is used to describe deflagration or ignition of fuel vapour cloud. As a result, give raged shroud out the upper floors of the Towers. Program BANG-FR is invoked to get necessary quantities in terms of pressures of loads and are algebraically added to those pressures produced from aircraft-impact

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specifically floors receiving hot fuel and floors should be analysed using the above analysis. In this analysis for the jet-oil-Tower structure interaction, based on FEMA Report—3,000 gal escaped with 4,000 gal remained on the impacted floor. The total peak rate of fire energy per Tower is assumed as 3–5 trillion Btu/h (1–1.56 GW), with a ceiling gas temperature 1,100  C (2,000  F). growth of fire balls with final full size of 200 ft (60.96 m) occur after 2 s. (g) Concentrated Loads BANG-FR for fire analysis is initially concentrated on 80th floor level. The columns above the damage area are predicted to act as tension members, transferring around 10 % of the load carried by the damaged columns upward to outrigger trusses and this load is assumed back on core columns.

6.8

Deterministic Assessment of the Fire Exposure of Exterior Walls

An alternative method to describe fire-exposure level for exterior walls involves relating these to the source or compartment fire causing the exposure. Conventionally the fire resistance of exterior walls, or any enclosing element for that matter, is determined by utilizing an exposure based on a standard fire-endurance test. The accepted standard fire severity of the “typical” compartment fire is represented by the time-temperature relationship given in ASTM E-119 (1988) or in ISO 834 (1975). These methods are almost universally accepted—for both design and building-regulation purposes for those structural elements and fire-rated enclosures directly exposed to a fully developed post flash over room fire. This standard fire, however, defined as it is in terms of time-temperature, cannot be translated into any specific room fire, nor can the time-temperature curve be used directly as a scalar for the fare severity generated by any specific room fire. This definition does not pose any intractable problems if all that is desired is the acceptability of a given structural element or enclosure exposed to the “standard” fire, because the specimen in question can be tested. However, one can easily visualize a typical room fire in a building, after the fire has developed to the post flash over condition, the window openings in the exterior walls would be venting flames out the top and feeding combustion air to the fire through the bottom of the window. These venting flames would expose the exterior face of the wall above the windows to both radiant and convective thermal flux. In addition, the venting flames and window openings would be “radiators” exposing any nearby buildings to heat. Furthermore, if the adjacent building is quite close to the building on fire, the venting flames could wash over its surface, subjecting it to convective thermal flux. While the fire may be exposing the assemblies in the room to something akin to a standard fire, the venting flames and window radiators are exposing the external assemblies to something significantly less than the standard fire.

412

6 Fire Following Earthquakes

This scenario is pertinent to the design of exterior walls and to the sitting of buildings on a lot. If two buildings are close enough to each other that one could expose the other to enough thermal flux as to cause significant damage to its exterior wall, there is an even greater danger of fire transfer to the combustible con If the evacuation time on the corridor of each floor t(F)exceeds the evacuation time on the stairs per floor t(TR), then the partial flows from each floor encounter the rest of the evacuees entering the staircase on the landing of the story below. Even though this event causes an increase in density on the stairs, the capacity of the main flow remains below the maximum value Qmax (Fig. 6.1). This indicates that the stair width is still appropriate to take up the merged flow. In other words, if tF > tTR and qðTR; n

1Þ ¼ QT; n

1 þ QðTRÞbðTR; maxÞ

(6.1)

where q(TR; n 1) ¼ value of specific flow on stairs after merging process Q(T; n 1) ¼ flow capacity through door to staircase on each floor Q(TR) ¼ initial flow capacity on stairs q(TR; max) ¼ (maximum flow capacity on stairs) Then the total evacuation time is given by tGes ¼ tF þ ntTR þ mdt

(6.2)

where the last term relates the delay time of the last person from the top floor. The factor m is the number of patterns of higher density, which is reduced during the course of the evacuation process. (These are the areas between the dashed lines Fig. 6.2). The dashed lines are representing the boundaries beings, trying to reach people moving ahead, or searching for contact or information. The formation of a congested flow (queuing) is an analogous process. If Q(i) > Q(i + 1), lines begin at the boundary between the passages of distinct flow capacities. At the beginning of congestion, the flow consists of two parts, namely, a group of persons with the maximum flow concentration (Dmax ¼ 0.92), which has already arrived at the critical section of the escape route, and the rest of the evacuees approaching with a higher velocity and a density less than Dmax. In this case the rate of congestion is given by the following equation: v00 ðSTAU Þ ¼ Q

Dmax bði þ 1Þ=bðiÞ

qðiÞDmax

where q(Dmax) ¼ specific flow at maximum density b(i + 1) ¼ width of congested flow b(i) ¼ initial width of flow q(i) ¼ initial value of specific flow D(i) ¼ initial flow density

DðiÞ

(6.3)

After the last person moving at the higher velocity has reached the end of the line, the congestion diminishes at the following rate:

6.9 Evaluation of Unit Exit Width in High-Rise Buildings A

32 OG

413

B

V TR.V

V TR.V

Z A

31 OG

F TR

V TR.V

A

30 OG

V TR.V

A

B

A

0

V TR.V

V TR.V

F TR

B

V TR.V V TR.V

28 OG

V TR.V

F TR

V TR.V V TR.V

29 OG

Y

B

F

VTR.V V TR.V

V TR.V

B

TR

1

2

3

MIN

Fig. 6.1 Partial flows move down the stairs without interaction. Due to brief delay in protected lobby on each floor level, a merger of partial flows does not occur

vðSTAUÞnDmaxb ði þ 1ÞbðiÞ

(6.4)

where V(Dmax) is the flow velocity at the maximum density. This calculation method, of which the basic considerations have been summarized, has been applied by Predtechenskii and Milinski mainly to the evacuation of auditoriums and halls. Section 6.9 deals with the calibration of the method and its application to high-rise buildings (Fig. 6.3).

6.9

Evaluation of Unit Exit Width in High-Rise Buildings

For the prediction of flow movement in multistory buildings, an egress model was developed based on the work presented in Sect. 6.8 (Kendik 1982). This has been calibrated against the data from the evacuation tests carried out by the Forschungsstelle fu¨r Brandschutztechnik at the University of Karlsruhe, Germany, in three high-rise administration buildings (Seeger et al. 1978).

414

6 Fire Following Earthquakes A

23 OG

N

B

V TR.N V TR.N

V TR.N

22 OG A

TR

F

B

F

V22/1/

V TR.N

21 OG

V TR.N

TR

A

B

V22/1/

V TR.N

V TR.N TR

20 OG A

F

V21/1/

V21/1/

B

V21/1/

V TR.N

V TR.N

19 OG

A

TR

F

V20/1/

V20/1/

V20/1/

V20/1/

B

V TR.N

18 OG

A

V TR.N

TR

V20/2/

F

V20/2/

0

V20/2/

V20/2/

V20/2/

B

1 MIN

Fig. 6.2 Flow movement is delayed due to periodical increase in density on each floor level t(Ges) ¼ 6.67 min Begin of the 1. flow

j

j

V

=1

4. 3

1

D

=1

6.

37

20

A1strem. 1 =6.60m

D

Dj=2.70

C

=1

V =3 2 9.3

7

2

V

10

n

0.1

5

Dj= 2.70

Dj=0.25

Fig. 6.3 Merging process of flow

t2=1.80

1.00

t2=1.21

0

End of the 2 flow

2.00

6.9 Evaluation of Unit Exit Width in High-Rise Buildings

415

The egress model presented here addresses the time sequence (within the available safe egress time) from when people start to evacuate floors until they finally reach the exterior or an approved refuge area in a high-rise building. Hence it does not consider the time prior to their awareness of the fire nor their decisionmaking processes. However, it can cope with the problem of potential congestion on stairs and through exits (including the interdependencies of adjacent egress-way elements, which appears to be a major problem), especially in cases of high population densities. The method differs from other egress models mainly in its flexibility in predicting variations, of the physical flow parameters during the course of movement. In this it neither assigns fixed values to the flow density or velocity nor assumes fixed flow rates. Hence it provides a performance-oriented predictive tool for the evaluation of a building’s means of egress in terms of pedestrian movement. The model presumes that during the evacuation of a multistory building, the occupants build up a partial flow on the corridor of each floor, which is defined between the first and the last persons of the flow. If the following simplifications are introduced into the general model, the flow movement via staircases shows some regularities. 1. The length of the partial flow on each floor is assumed to be equivalent to the greatest travel distance along the corridor. 2. The number of persons as well as the escape route configurations are identical on each story. 3. Each partial flow attempts to evacuate simultaneously and enters the staircase at the same instant. These simplifications result in the following regularities 1. If the evacuation time on the corridor of each floor t(F) is less than the evacuation time on the stairs per floor t(TR), then the partial flows from each floor can leave the building without interaction. In this case, the total evacuation time is given by the following equation: tðGesÞ ¼ tðFÞ þ ntðTRÞ

(6.5)

where t(F) ¼ evacuation time on corridor of each floor n ¼ Number of floors t(TR) ¼ evacuation time on stairs per floor three restrictions, namely, horizontal passages, doors, and stairs. Hence the main condition for free flow is the equivalence of flow capacities on successive parts of the escape route: Qi ¼ Qi þ 1 or from Eqs. 6.3 and 6.6,

(6.6)

416

6 Fire Following Earthquakes 12 1

Q [m2. min–2]

10

1 2

8 6 3

4

4

2 0

0

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

D [m2. m–2]

Fig. 6.4 Specific flow versus flow density for different kinds of escape routes under normal environmental condition. 1—doorways; 2—horizontal routes; 3—stairs (upward); 4—stairs (downward) (After Kendik 1984) bi;1 Boundary

bi+1

bi+2

bi;3

Fig. 6.5 Merging for flows

qibi ¼ qi þ 1bi þ 1

(6.7)

Figures 6.4 and 6.5 illustrates a scheme for the merging of three partial flows coming from different directions. In this case the condition of the free flow can be described as follows:

6.9 Evaluation of Unit Exit Width in High-Rise Buildings

Qi ;

1 þ qi;

2 þ Qi ;

417

3 ¼ Qi þ 1

or qi þ 1 ¼ QðIÞb ði þ 1Þ

(6.8)

where Q(I) is the sum of the capacities of all partial flows. If the value of the specific flow q(i + 1) exceeds the maximum, that is, qi + 1 > q, the flow density increases spontaneously to its maximum value (Dmax ¼ 0 .92), which leads to a line at the boundary to the main route i + 1. Due to this congestion, not all persons may attempt to participate in the merging process simultaneously. It is presumed that the contribution of the partial flows to the main flow is proportional to their capacity Q. The percentage of the contribution of each flow to the main flow can be obtained from the ratio between the width of each partial flow and the sum of the widths of all partial flows, pð1Þ ¼ bð1; iÞBðiÞ

pð2Þ ¼ bð2; iÞBðiÞ

pðnÞ ¼ bðn; iÞBðiÞ

(6.9)

where B(i) is the sum of the widths of all partial flows. If during the merging process of the partial flows the specific flow q(i + 1) does not exceed the maximum value, that is, q(i + 1) no congestion occurs on escape routes. Observations of crowd movement under normal environmental conditions show that during the merging of two flows with distinct density and velocity the movement parameters of the incoming flow will be changed by adjusting its density and speed to the parameters of the up taking flow. According to this context, a boundary will be formed between the flows with the parameters D(i), q(i), D(i + 1), and q(i + 1), and its location changes at the following speed If vðiÞ < vði þ 1Þ then v00 ¼ qðiÞ

qð i þ 1Þ DðiÞ

Dði þ 1Þ

(6.10)

If vðiÞ > vði þ 1Þ, then v00 ¼ qði þ 1Þ

qðiÞ Dði þ 1Þ

DðiÞ

(6.11)

One may consider this phenomenon to be also appropriate for emergency evacuations, for example, where groups of persons initially have different flow densities and velocity, but a common purpose such as leaving the building and the minimum evacuation, time via the staircase is

418

6 Fire Following Earthquakes

t ¼ 10hG þ 15h G n

(6.12)

The maximum required stair width is given by bmax ¼

0:08P nhG

(6.13)

Mu¨ller suggested limiting the building height rather than widening the staircase. Flow Models Based on Empirical Studies of Crowd Movement During the last decade Paul’s developed the “effective width” model. This model is based on his extensive empirical studies of crowd movement on stairs as well as on data about the mean egress flow as a function of stair width. In this context he conducted several evacuation drills in high-rise office buildings and observed normal crowd movement in large public assembly buildings. The model describes the following phenomena (Pauls 1980a,b, 1982, 1984). 1. The usable portion of a stair width, or the effective width of a stair, begins approximately at a distance of 150 mm (0.5 ft) from a boundary wall or 88 mm (0.29 ft) from the centerline of a graspable handrail (edge effect). 2. The relation between mean evacuation flow and stair width is a linear function and not a step function, as assumed in traditional models based on lanes of movement and units of exit width. The evacuation flow is directly ‘proportional to the effective width of a stair. 3. The mean evacuation flow is influenced in a nonlinear fashion by the total population per effective width of a stair. Pauls provides the following equation for the evacuation flow in persons per meter of effective stair width: f ¼ 0:206p0:27

(6.14)

where p is the evacuation population per meter of effective stair width. The total evacuation time is given by: t ¼ 0:68 þ 0:081 p0:73

(6.15)

This calculation method has recently been accepted as an appendix to the National Fire Protection Association’s Life Safety Code (1982, 5th edition). The calculation method of Predtechenskii and Milinski is a deterministic flow model which predicts the movement of an egress population on a horizontal or a sloping escape route, instantaneously, in terms of its density and velocity. In general, the mean concentration, or the density of flow, is often defined as the number of persons per unit area, and sometimes the reciprocal has been used. These definitions are based on the implicit assumption that the physical dimensions

6.9 Evaluation of Unit Exit Width in High-Rise Buildings

419

of the human frame are identical for all people, or the differences might be negligible. The following equation relates the ratio between the sum of the persons’ perpendicular projected areas and the available floor area for the flow, and it estimates the flow density homogeneously over the area of an escape route: D ¼ Pfbl

(6.16)

where p ¼ number of persons in flow f ¼ perpendicular projected area of a person b ¼ flow width, identical to width of escape route l ¼ flow length D is dimensionless The egress population passing a definite cross section on an escape route of width b is referred to as flow capacity, Q ¼ Dvb

m2 per min :

(6.17)

where v is the flow velocity. Predtechenskıˆi and Milinski define the flow velocity on horizontal escape routes, through doors, and on the stairs in terms of the flow density, given in Eq. 6.16: v ¼ f ðDÞ

(6.18)

Being a steady-state expression, Eq. 6.16 implies that the flow density remains constant provided neither the escape route configurations nor the flow outlines change. Theoretically the density distribution of an infinitive flow may change during the lateral displacement of the crowd, that is, the density increase escalates in the direction of flow as persons running into part of the flow with increased density are moving faster. Inversely the density diminution in the course of flow leads to decomposition of the flow into separate parts of distinct densities. Hence a correction factor, which is proportional to the density increase, should be, added to Eq. 6.18, v ¼ f ðDÞ




 dD c ;c>0 dx

(6.19)

However, a sensitivity analysis of this model, which changed the projected area factor, did not produce the expected variation in evacuation time. The model predicted higher evacuation times for the tested building as the value of the projected area factor (inherently, the flow density) was decreased.

420

6 Fire Following Earthquakes

10

Spot measurement Case average

0.5

Fruin(1971)

S=108 –2 29d

P&M

0 0

1

2

3

4

5

Fig. 6.6 Relation between speed and density on stairs

On the other hand, observations of crowd movement with limited flow lengths, as in the case of egress from buildings, do not corroborate the previous considerations. This might indicate that Eq. 6.17 provides sufficient proximity for the determination of flow density on escape routes in buildings. However, further research is needed on this subject. Another important flow parameter is the flow capacity per meter of escape route width, which is defined as the specific flow, q ¼ Dv m per min

(6.20)

The specific flow is function of density. It increases over an interval, and after passing an absolute maximum, q max it decreases again. The value of q max is different for distinct kinds of escape routes. Figure 6.6 illustrates the variation of the specific flow in terms of density. The efficiency of an evacuation depends on the continuity of flow between space and, during ambulation, systematically occupies and relinquishes additional space. The extra space is utilized, first for the activity of moving, and second as a buffer against physical contact with other parts of the environment and against interactive contact with other people (Templer 1975). The space required for pedestrian movement depends on the physical dimensions of the human frame, standing at rest, which is described in this discussion as the perpendicular projected area of a person (or the projected area factor). Moreover, it also depends on the volumetric requirements of the body during locommotion (Templer 1975). The human ecology addresses these zones in the concept of individualraum (individual space), defined as the stretch between an individual and a specific event,

6.9 Evaluation of Unit Exit Width in High-Rise Buildings

421

Table 6.3 Pedestrian waiting spaces: level of service standards Level of service category A B C D E F

Average area per person 2

Interperson spacing

m 2

0.6–0.9 0.6 –

2–3 2 –

Circulation through queue Unrestricted Slightly restricted Restricted but possible by disturbing others Severely restricted Not possible Not possible

Table 6.4 Projected area per person Projected area per person Person Children Teenagers Adults in Summer clothes Spring clothes Winter clothes Adults in clothes and carrying A briefcase A suitcase Two suitcases Source: After Knotig (1980)

m2 0.04–0.06 0.06–0.09

ft2 0.4–0.6 0.6–1.0

0.1 0.11 0.125

1.1 1.2 1.35

0.18 0.24 0.39

1.9 2.6 4.2

and the concept attributes to every environmental relation both an “informatory aspect” as well as a “material-energetic aspect” (Kno¨tig 1980). Fruin recommends, for the design of some types of spaces, a body ellipse 450 by 610 mm (18 by 24 in.), equivalent to an area of 0.21 m2 (2.3 ft2). This figure has been used to develop the capacity of New York City subway cars but, as discussed later, it would be too high for building-evacuation purposes. Fruin also states that the human body can be crowded into an area of about 0.14 m2 (1.5 ft2) for the average man and 0.09 m2 (1 ft2) for the average woman, representing the limit of body dimensions. His recommendation for the dimensions of the average man is fairly similar to the author’s investigations. Based on the analysis of body dimensions and observation of waiting lines, Fruin proposed standards for these types of spaces, as summarized in Table 6.3. Table 6.4 shows the values for the perpendicular projected areas of different age groups given by Kno¨tig (1980). In Table 6.5 the mean values for the perpendicular projected areas of persons by means of anthropometric measurements of a randomly selected Austrian group of people of different ages are represented (Kendik 1984).

422

6 Fire Following Earthquakes

Table 6.5 Anthropometric measurements of an Austrian group of people, in square meters 5 years 10–15 years

>30 years

15–30 years

All Women Men All Women A(Du); x 0.705 1.300 1.290 1.291 1.683 Standard deviation 0.171 0.175 0.203 0.208 0.115 F(N); x 0.0696 0.1092 0.1126 0.1113 0.1383 Standard deviation 0.0078 0.0202 0.0174 0.0187 0.0172 F(M); x – 0.1453 0.1326 0.1386 0.1809 Standard deviation – 0.0178 0.0191 0.0186 0.0213 F(S); x – 0.1262 0.1221 0.1238 0.1508 Standard deviation – 0.0198 0.0170 0.0180 0.0163 A(Du); x DuBois- area, mean value f(N); x Mean projected area per person, standing and without coats f(M); x Mean projected area per person, standing and wearing coats f(S); x Mean projected area per person, walking Source: After Pauls (1984)

Men 1.894 0.379 0.1484 0.0171 0.1892 0.0296 0.1645 0.0191

All 1.825 0.334 0.1458 0.0172 0.1862 0.0272 0.1600 0.0193

All 1.872 0.252 0.1740 0.0315 – – 0.1918 0.0356

There, by using an artificial sun which provided parallel rays of light, and a mirror arrangement set up with an angle of 45 , the body frames of test persons were projected to the floor, drawn, and measured. Thus approximately 600 drawings of different test persons in standing position, with and without coats and taking a step have been evaluated. The results from this Austrian statistical analysis do not comply with the Russian data given in Table 6.4. This might indicate that the projected area per person (projected area factor) f varies in terms of population. The spatial requirements of pedestrians also change in terms of velocity. Researchers such Templer 1975; Pauls (1980a), and Seeger and John (1978) conducted speed surveys outside or inside buildings on horizontal walkways as well as on stairs. Predtechenskii and Milinski measured the flow density and velocity in different types of buildings nearly 3,600 times under normal environmental conditions. Their observations indicated that the flow velocity shows wide variations, especially in the range of lower densities. Hence they assumed the values of the flow velocity and capacity above the mean walking speeds and capacities under normal environmental conditions to be analogous to the pedestrian parameters in case of emergency. Therefore three movement levels have been defined: 1. Normal flow conditions 2. Comfortable flow conditions 3. Emergency flow conditions The mean values of velocity under comfortable flow conditions have been estimated from the lower range of the measured walking speeds, and for emergency flow conditions, from the upper range of the measured values. Figure 6.6 compares the evacuee speed down the stairs in terms of the density given by Pauls (1980b), Predetechenskii and Milinski (1978).

6.10

6.10

Modeling Pedestrian Movement

423

Modeling Pedestrian Movement

The current models evolving from people movement may be classified as follows (Kendik 1985a): 1. Flow models based on the carrying capacity of independent egress-way components, or the unit exit-width concept 2. Flow models based on empirical studies of crowd movement 3. Computer simulation models 4. Network optimization models. The more important of these models are discussed in this section. Flow Models Based on the Carrying Capacity of Independent Egress-Way Components Unit Exit-Width Concept The historical development of carrying-capacity investigations has already been broadly reviewed in several publications by Stahl and Archea (1977) and Pauls (1980a, 1984). An early NFPA document recommended as a guideline, for stair design an average flow rate of 45 persons per minute per 0.56-m (22-in.) width unit (Stahl and Archea 1977). In 1935, in a publication of the U.S. National Bureau of Standards [now National Institute of Standards and Technology (NIST)], test results about measurements of flow rates through doors, corridors, and on stairs under non-emergency conditions were presented. For different types of occupancies the measured maximum flow rates varied between 23 and 60 persons per minute per unit stair width, and 21 and 58 persons per minute per unit door or ramp width (National Bureau of Standards 1935). To date, the NFPA Life Safety Code 101 (NFPA 1982) utilizes the unit exit-width concept together with travel distances and occupant-load criteria. However, for some reason, the time component is absent in the present code. In the United Kingdom, the first national egress guidance for places of public entertainment was produced in 1934 (Home Office 1935). The recommendations were “based not only on experience gained in the UK, but on a study of disasters which have happened abroad and of the steps taken by the authorities of foreign countries” (Read, to be published). In this document, the following formulas were provided for the determination of the total width of exits required from each portion of a building, reflecting the concept of the unit exit width: A¼

zð floor area; ft2 Þ EBCD

where A ¼ number of units of exit width required B ¼ constant, referring to type of construction of building C ¼ constant for arrangement and protection of stairs D ¼ constant for exposure hazard

(6.21)

424

6 Fire Following Earthquakes

E ¼ factor dependent on height of floor above or below ground level. Z ¼ class of building use (closely seated audience, for example) Then N¼

A þ1 4

(6.22)

where N is the number of exits required. In this document it was also stated that about 40 persons per minute per unit exit width down the stairs or through exits is an appropriate figure in connection with these formulas. Forty persons per minute per unit exit width is also recommended in Post-War Building Studies No 29. The width of staircases in the current GLC Code of Practice (Greater London Council 1974) as well as in BS 5588 Part 3 (BSI 1983) is computed by this method (Tidey 1983). Calculation of the total population that a staircase can accommodate is based on the following assumptions: 1. Rate of flow through an exit is 40 persons per unit width per minute 2. Each story of the building is evacuated onto the stairs in not more than 2.5 min. This average clearance time was proposed after an evacuation experience during a fire in the Empire Palace Theatre in Edinburgh in 1911 (HMS 1952). 3. There is the same number of people on each story. 4. Evacuation occurs simultaneously and uniformly from each floor 5. In moving at a rate of 40 persons per unit width per minute, a staircase can accommodate 1 person per unit width on alternate stair treads and 1 person per each 0.3 m2 (3 ft2) of landing space. 6. The story height is 3 m (10 ft) 7. The exits from the floors onto the stairs are the same width as the stairs. 8. People leaving the upper floors are not obstructed at the ground floor exit by persons leaving the ground floor. Then P ¼ staircase capacity x number of upper stories þ ðte

te Þrw

(6.23)

where P ¼ total population that a staircase can accommodate. te ¼ maximum permissible exit time from any one floor onto staircase, taken as 2.5 min ts ¼ time taken for a person to traverse a story height of stairs at standard rate of flow, predicted as 0.4 min. r ¼ standard rate of flow, taken as .40 persons ‘per unit width per minute w ¼ width of staircase, units The staircase capacity is predicted after point 5 of the preceding assumptions. This method of calculation predicts that with an increasing number of stories, the building has fewer persons per floor.

6.10

Modeling Pedestrian Movement

425

In 1955, K. Togawa in Japan was apparently the first researcher who attempted to model mathematically the people movement through doorways and on passage ways, ramps, and stairs (Pauls 1984; Stahl and Archea 1977, and Kobayashi 1981). He provided the following equation: v ¼ VoD

0:8

(6.24)

where v ¼ crowd walking velocity or flow velocity Vo ¼ constant velocity ¼ 1.3 m/s, which is apparently the velocity under free-flow conditions D ¼ density in persons per square meter. Hence the flow rate N is given by N ¼ VoD0:2

(6.25)

(Note: N here is the same as the specific flow q referred to later.) The maximum population M which can be evacuated to a staircase, assuming a permitted evacuation time of 2.5 min, is given approximately by M ¼ 200b þ ð18b þ 14b2 Þðn

1Þ

(6.26)

where b ¼ staircase width, m n ¼ number of stories served by staircase. This equation predicts a higher number of persons than the method presented in Post-War Building Studies No, 29. The minimum evacuation time Te for a multistory building is given by Te ¼

Pn

i¼v

N 0 br

Q 1

þ rts

(6.27)

where r ¼ floor number (1 to n), which gives the maximum value of Te Qi ¼ population of floor i b ¼ width of staircase between floors r 1 and r N1 ¼ flow rate of people per unit width down the stair Te ¼ time for a member of an unimpeded crowd to descend one story If the population Q and the staircase width b are the same for each floor, then Te is the larger of T1 and Tn where: T1 ¼ nQN 0 b þ ts

(6.28)

426

6 Fire Following Earthquakes

Tn ¼ QN 0 b þ nts

(6.29)

T1 corresponds to congestion on all floors and Tn to no congestion. Melinek and Booth suggested as typical values on N’ and ts 1.1 persons per second per minute and 16 s. Compared with evacuation tests in multistory buildings, the method predicted in most cases evacuation times that were too low. A further application of the unit width concept has been the mathematical model of Muller (1966, 1968, 1969). Assuming a flow rate of 30 persons per minute per 0.6-m (2.0-ft) stair width, Muller provided the following equations for the assessment of total evacuation time in multistory building: t ¼ t1 þ Pbfo=0:6

(6.30)

t ¼ 3hGv þ Pbfo=0:6

(6.31)

where t1 ¼ travel time on stairs to descend one story hG ¼ floor height P ¼ number of persons in building b ¼ stair width v ¼ flow velocity down the stairs, ¼ 0.3 m/s(1.0 ft/s) fo ¼ flow rate per unit stair width of 0.6 m (2.0 ft) Muller presumed that the flow velocity would decrease to 0.2 m/s (0.7 ft/s) due to interaction of flows from each upper floor, which would cause an increase in density on the stairs. Hence the travel time between two upper stories is given by t2 ¼ 3hG0:2 ¼ 15hG

(6.32)

evaluating the initial number of devices, displacements, velocities and accelerations for various heights and floor areas of the buildings. This procedure as cut down the time and effort of making decisions regarding devices and building final displacement, velocity and acceleration. The exact analysis for a particular building will be carried out both with and without such devices. The extent of control within specified limitations will be known. The limitations on the following will be adhered to: (a) (b) (c) (d)

Response acceleration Response relative displacement (using linear, non-linear and damage analyses) Response material stress Physical positioning of devices in a specific layout in three dimensions

The variables concerning (d) shall require the knowledge of total building floor area, standard area per floor, floor height and final building height. Once the total number of devices “S” is known from the graph, the next step is to initially spread these devices across the building structure when the above requirements are met. Various methods are available and their boundary conditions must be such that the

6.11

Permutations and Combinations

427

requisite number must easily be accommodated after the analytical decisions are made. In this text the selected method is based on permutation and/or combination. The permutation is for single-type device and combination is for two or more types of devices placed in sequence or in others to reduce drift, acceleration and velocity commensurate with the codified methods and clauses noted in design practices. This method cuts down the time and cost involved in arriving at the optimum choice finally placed before a specific computer program to assess and meet the targets given by designers and clients. It is therefore necessary to remind the reader about the method.

6.11

Permutations and Combinations

6.11.1 Permutations A permutation for the devices of identical shape, make and performance shall be the “rearrangement number” or “order” in specific area of a floor from an ordered list “S” required for a building within specific seismic zone. The rearrangement of devices in permutation will finally determine the optimum positions, when put to a specific analysis-cum-computer program, such that the targets are met. For example, the number of permutations for devices {1, 2}, namely {1, 2} and {2, 1}, shall be 2! ¼ 2  1 ¼ 2 two places two permutations in two positions; 3! ¼ 3  2  1 ¼ 6 three places and six permutations in three positions for the devices to be placed at the floor level. In order to further explain, the 3! would be in the following six set-up and in six orders as

6.11.2 Step-by-Step Solution Method The most general solution method for dynamic analysis is an incremental method in which the equilibrium equations are solved at times Δt, 2Δt, 3Δt, etc. There are a large number of different incremental solution methods described in this chapter. In general, they involve a solution of the complete set of equilibrium equations at each time increment. In the case of non-linear analysis, it may be necessary to reform the stiffness matrix for the complete structural system for each time step. Also, iteration may be required within each time increment to satisfy equilibrium. As a result of the large computational requirements it can take a significant amount of time to solve structural systems with just a few hundred degrees of freedom. In addition, artificial or numerical damping must be added to most incremental solution methods in order to obtain stable solutions. For this reason, engineers must be very careful in the interpretation of the results. For some non-linear structures, subjected to seismic motions, incremental solution methods are necessary.

428

6 Fire Following Earthquakes

For very large structural systems, a combination of mode superposition and incremental methods has been found to be efficient for systems with a small number of non-linear members as stated by Wilson of University of California. The response of real structures, when subjected to large dynamic loads, often involves significant non-linear behaviour. In general, non-linear behaviour includes the effects of large displacements and/or non-linear material properties. The more complicated problem associated with large displacements, which cause large strains in all members of the structures, requires a tremendous amount of computational effort and computer time to obtain a solution. However, certain types of large strains, such as those in rubber base isolators and gap elements, can be treated as a lumped non-linear element by the fast non-linear analysis (FNA) method.

6.11.3 Fundamental Equilibrium Equations The global dynamic equilibrium equations, at time t, of an elastic structure with non-linear or energy-dissipating elements are of the following form: € MU

ðtÞ þ Cin ðtÞ þ KnðtÞ þ RðtÞ ¼ RðtÞn ¼ RðtÞ

(6.33)

All elements in the equation have already Pbeen defined. In addition R(t) is the external applied load where RðtÞ ¼ FðtÞ ¼ nj f jgðtÞj. R(t)N is the global mode force vector due to the sum of the forces in the non-linear elements and is

6.11.4 Incident Command System This annex is a condensed and modified version of Paper 3, The Incident Management System written by Murray Dudfield, National Rural Fire Authority New Zealand, and Buck Latapie, United States Forest Service and adopted during the Wildland Fire Summit in Sydney, Australia in 2003. The full text of the original paper can be viewed at: http://www.fire.uni-freiburg.de/iffn/iffn_29/IWFS-3Paper-3.pdf The complexity of incident management, coupled with the growing need for multi-agency involvement at incidents has increased the need for a standard interagency incident management system not only within a country/state but increasing internationally. It is becoming increasingly important to base any international agreements on a common incident management system. The Incident Command System (ICS) may need to be adapted to suit a particular country’s existing political, administrative or cultural systems, customs and values. Where the primary purpose is to enhance emergency management within a country,

6.11

Permutations and Combinations

429

such adaptations are not only beneficial, but may be essential to have the ICS system adopted. Given that ICS is a proven model in many countries and given that training materials for ICS are freely available, there is considerable benefit to be gained by a country adopting this system. The ICS framework provides an effective forum for interagency emergency management issues to be addressed. By establishing a unified command of the respective agency/jurisdictional representatives together at a single interagency incident command location, the following advantages will be achieved: • One set of objectives is developed for the entire incident. • A collective approach is made to developing strategies to achieve incident objectives. • Information flow and co-ordination is improved between all jurisdictions and agencies involved in the incident. • All agencies with responsibility for the incident have an understanding of each other’s priorities and restrictions. • No agency’s authority or legal requirement will be compromised or neglected. • Each agency is fully aware of the plan, actions, and constraints of other agencies. • The combined effects of all agencies are optimised as they perform their respective assignments under a single Incident Action Plan. • Duplication of effort is reduced or eliminated thus reducing costs and the chance of frustration and/or conflict. The ICS structure is based on the following principles: Common terminology: ICS terminology is standard and consistent among all of the agencies involved. Modular organization: The ICS structure can be scaled up to multiple layers that are implemented to meet the complexity and extent of the incident. Integrated communications: Integrated communications requires a common communications plan, standard operating procedures, clear text, common frequencies, and common terminology. Consolidated Incident Action Plans: Incident Action Plans describe response goals, operational objectives, and support activities. Manageable span of control: A manageable span of control is defined as the number of individuals or functions one person can manage effectively. In ICS, the span of control for any person falls within a range of 3–7 resources, with five being the optimum. Designated incident facilities: It is important that there are designated incident facilities with clearly defined functions to assist in the effective management of an incident. Comprehensive resource management: Comprehensive resource management is a means of organising the total resource across all organisations deployed at an incident, including maximizing personnel safety. The ICS organisation incident structure is built around four major components:

430

6 Fire Following Earthquakes

1. CONTROL—the management of the incident 2. PLANNING—the collection and analysis of incident information and planning of response activities 3. OPERATIONS—the direction of resources in combating the incident 4. LOGISTICS—the provision of facilities, services and materials required to combat the incident. These four major structural components are the foundation upon which the ICS organization is built. They apply during a routine emergency, when preparing for a major event, or when managing a response to a major disaster. The ICS structure can be expanded or contracted to manage any type and size of incident.

6.12

Conclusions

Safety, effectiveness and efficiency are achievable where a seamless integration of agencies is possible at an emergency for a local level incident as well an international deployment to assist a country in need. A globally implemented ICS will improve firefighter safety, efficiency and effectiveness in management response. ICS provides the model for command, control and co-ordination of an emergency response. It provides a means of co-ordinating the efforts of agencies as they work towards the common goal of stabilising an incident and protecting life, property, and the environment. It will also reduce the risk of agency overlap and potential confusion at an emergency through poor understanding and inadequate co-ordination. It is critical that a common global incident management system is adopted that will enable any assistance to quickly function in an effective manner. ICS is that tool which can enable that goal to be achieved.

Glossary

Biomass

2

The following terms have been selected from the updated FAO terminology2 (1) The amount of living matter in a given habitat, expressed either as the weight of organisms per unit area or as the volume of organisms per unit volume of habitat. (2) Organic matter that can be converted to fuel and is therefore regarded as a potential

For additional fire terms please refer to the revised FAO Wildland Fire Management Terminology: http://www.fire.uni-freiburg.de/literature/glossary.htm. Terms marked with have been added to this glossary from other sources.

6.12

Conclusions

Community-based fire management (CBFiM)

Fire danger

Fire danger rating

Fire exclusion

Fire hazard

431

energy source. Note: Organisms include plant biomass (phytomass) and animal biomass (zoomass). (3) In fire science the term biomass is often used synonymously with the term “fuel” and includes both living and dead phytomass (necromass) the zoomass is usually excluded. Fire management approach based on the strategy to include local communities in the proper application of land-use fires (managed beneficial fires for controlling weeds, reducing the impact of pests and diseases, generating income from non-timber forest products, creating forage and hunting, etc.), wildfire prevention, and in preparedness and suppression of wildfires. CBFiM approaches can play a significant role in fire management, especially in most parts of the world where human-based ignitions are the primary source of wildfires that affect livelihood, health and security of people. The activities and knowledge communities generally practice are primarily those associated with prevention. They include planning and supervision of activities, joint action for prescribed fire and fire monitoring and response, applying sanctions, and providing support to individuals to enhance their fire management tasks. Communities can be an important, perhaps pivotal, component in large-scale fire suppression, but should not be expected to shoulder the entire burden. A general term used to express an assessment of both fixed and variable factors of the fire environment that determine the ease of ignition, rate of spread, difficulty of control, and fire impact often expressed as an index. A component of a fire management system that integrates the effects of selected fire danger factors into one or more qualitative or numerical indices of current protection needs. Planned (systematic) protection of an ecosystem from any wildfire, including any prescribed fire, by all means of fire prevention and suppression in order to obtain management objectives. (1) A fuel complex, defined by volume, type, condition, arrangement, and location, that determines the degree both of ease of ignition and

432

Fire management

Fire management plan

Fire pre-suppression

Fire prevention

6 Fire Following Earthquakes

of fire suppression difficulty; (2) a measure of that part of the fire danger contributed by the fuels available for burning. Note: Is worked out from their relative amount, type, and condition, particularly their moisture contents. All activities required for the protection of burnable forest and other vegetation values from fire and the use of fire to meet land management goals and objectives. It involves the strategic integration of such factors as knowledge of fire regimes, probable fire effects, values-at-risk, level of forest protection required, cost of fire-related activities, and prescribed fire technology into multiple-use planning, decision making, and day-to-day activities to accomplish stated resource management objectives. Successful fire management depends on effective fire prevention, detection, and pre-suppression, having an adequate fire suppression capability, and consideration of fire ecology relationships. (1) A statement, for a specific area, of fire policy and prescribed action; (2) The systematic, technological, and administrative management process of determining the organization, facilities, resources, and procedures required to protect people, property, and forest areas from fire and to use fire to accomplish forest management and other land use objectives (cf. fire prevention plan or fire campaign, pre-suppression planning, pre-attack plan, fire suppression plan, end-of-season appraisal). Activities undertaken in advance of fire occurrence to help ensure more effective fire suppression includes overall planning, recruitment and training of fire personnel, procurement and maintenance of firefighting equipment and supplies, fuel treatment, and creating, maintaining, and improving a system of fuelbreaks, roads, water sources, and control lines. All measures in fire management, fuel management, forest management, forest utilization and concerning the land users and the general public, including law enforcement, that may result

6.12

Conclusions

Fire protection

Fire regime

Fire regime types Fire-dependent ecosystems

Fire-sensitive ecosystems

433

in the prevention of outbreak of fires or the reduction of fire severity and spread. All actions taken to limit the adverse environmental, social, political, cultural and economical effects of fire. The patterns of fire occurrence, size, and severity— and sometimes, vegetation and fire effects as well— in a given area or ecosystem. It integrates various fire characteristics. A natural fire regime is the total pattern of fires over time that is characteristic of a natural region or ecosystem. The classification of fire regimes includes variations in ignition, fire intensity and behaviour, typical fire size, fire return intervals, and ecological effects. Fire is essential in maintaining predominant ecosystem composition, structure, function and extent. If fire is removed, or if a fire regime is altered beyond its historical range of variability, the ecosystem changes to something else; dependent species and their habitats decline or disappear. Vegetation is fire-prone and highly flammable. Ecosystem structure and plant architecture facilitate fire spread. Also known as fire-maintained ecosystems. Boundaries between fire-dependent and fire-independent ecosystems are largely determined by the relative continuity of burnable fuels or probability of fire-enabling climatic conditions. Ecosystem structure and composition tend to inhibit ignition and fire spread. The majority of species generally lack adaptations to respond positively to fire. Fire can influence ecosystem structure, relative abundance of species, and/or limit ecosystem extent, or may occur naturally very infrequently or during extreme climatic events. Fire may create habitats for key species by creating gaps, regeneration niches, or by initiating or affecting succession. If fires are too frequent or too large, they can be damaging and cause ecosystem shifts to more fire-prone vegetation. Some fire-sensitive ecosystems are also known as fire-influenced, particularly those adjacent to fire dependent ecosystems.

434

Fire-independent ecosystems

Fire season

Fire suppression

Fire weather

Fuel

Fuel management

Fuel reduction

Incident Command System

Prescribed burning

6 Fire Following Earthquakes

Fires characteristically would not occur because of a lack of fuel and/or ignition sources. Fire regimes can be altered by a change in fuels (e.g., invasive species) or ecologically- inappropriate humancaused ignitions. (1) Period(s) of the year during which fires are likely to occur and affect resources sufficiently to warrant organized fire management activities; (2) a legally enacted time during which burning activities are regulated by state or local authority. All activities concerned with controlling and extinguishing a fire following its detection (syn. fire control, fire fighting). Weather conditions which influence fire ignition, behaviour, and suppression. Weather parameters are dry-bulb temperature, relative humidity, wind speed and direction, precipitation, atmospheric stability, winds aloft. All combustible organic material in forests and other vegetation types, including agricultural bio-mass such as grass, branches and wood, infrastructure in urban interface areas which create heat during the combustion process. Act or practice of controlling flammability and reducing resistance to control of fuels through mechanical, chemical, biological, or manual means, or by fire, in support of land management objectives. Manipulation, including combustion, or removal of fuels to reduce the likelihood of ignition, the potential fire intensity, and/or to lessen potential damage and resistance to control. A standardized on-scene emergency management concept specifically designed to allow its user(s) to adopt an integrated organizational structure equal to the complexity and demands of single or multiple incidents, without being hindered by jurisdictional boundaries. Controlled application of fire to vegetation in either their natural or modified state, under specified environmental conditions which allow the fire to be confined to a predetermined area and at the same time to produce the intensity of heat and rate of spread required to attain planned resource

6.12

Conclusions

Prescribed fire

Prescribed natural fire

Prescription

Rehabilitation

Residential/wildland interface Restoration

Risk

Smoke management

435

management objectives (cf. prescribed fire). Note: This term has replaced the earlier term “controlled burning”. A management-ignited fire or a wildfire that burns within prescription, i.e. the fire is confined to a predetermined area and produces the fire behaviour and fire characteristics required to attain planned fire treatment and/or resource management objectives. The act or procedure of setting a prescribed fire is called prescribed burning (cf. prescribed burning). A wildfire burning within prescription may result from a human-caused fire or a natural fire (cf. prescribed natural fire, wildfire). Naturally ignited fires, such as those started by lightning, which are further used to burn under specific management prescriptions without initial fire suppression and which are managed to achieve resource benefits under close supervision (cf. prescribed fire, wildfire). Written statement defining the objectives to be attained as well as the conditions of temperature, humidity, wind direction and speed, fuel moisture, and soil moisture, under which a fire will be allowed to burn. A prescription is generally expressed as acceptable ranges of the prescription elements, and the limit of the geographic area to be covered. The activities necessary to repair damage or disturbance caused by wildfire or the wildfire suppression activity (cf. restoration). The transition zone between residential areas and wildlands or vegetated fuels (cf. urban/wildland interface). Restoration of biophysical capacity of ecosystems to previous (desired) conditions. Restoration includes rehabilitation measures after fire, or prescribed burning where certain fire effects are desired (cf. rehabilitation, reclamation burning). (1) The probability of fire initiation due to the presence and activity of a causative agent. (2) A causative agent. The application of knowledge of fire behaviour and meteorological processes to minimize air quality degradation during prescribed fires.

436

Urban/wildland interface

Wildfire

6 Fire Following Earthquakes

The transition zone (1) between cities and wildland (cf. urban, wildland, wildland fire), (2) where structures and other human development meets undeveloped wildland or vegetative fuels (syn. residential/wildland interface, wildland/urban interface, rural urban interface). (1) Any unplanned and uncontrolled fire which regardless of ignition source may require suppression response, or other action according to agency policy. (2) Any free burning fire unaffected by fire suppression measures which meets management objectives (cf. wildland, wildland fire, prescribed natural fire, prescribed fire and its buffer zones).

However, the project did not leave any institutional structures that could he regarded as substantial or sustainable,

6.12.1 Needs and Limitations The main limitations to fire management in the region are institutional weaknesses and economic constraints (which, in some countries, are a consequence of economic transition) and a lack of awareness, adequate policies and commitment and involvement by civil society. These limitations translate into the following needs: • institution-building, especially improved capacities of government institutions, research entities, businesses and NGOs with regard to the planning and implementation of sustainable development programmes; • improved technological capacity, including the provision of modern fireextinguishing equipment, use of satellite information and information technologies; • improved public awareness and increased sense of responsibility of civil society in issues related to fires; • training and educational programmes; • a clear legal and institutional basis for forest protection; • increased and continuing funds for fire management; • implementation of international cooperation, including compliance with Agenda 21 of the United Nations Conference on Environment and Development (UNCED) and the conventions related to fire issues in Central Asia—notably the CBD, UNCCD, UNFCCC and Ramsar Convention on Endangered Species; • links to and interaction with the Europe and North Asia Forest Law Enforcement and Governance process, related to the increase in intentionally set fires in conjunction with illegal logging or to obtain salvage logging permits.

6.12

Conclusions

437

6.12.2 Analysis and Recommendations Over the past decade, many countries of Central Asia have witnessed a growing number and size of wildfires in forest and non-forest ecosystems, usually caused by people, but also by lightning in sparsely populated areas. These fires have caused considerable ecological and economic damage and some have had transnational impacts, for example through smoke pollution, loss of biodiversity or forest degradation at the landscape level. The depletion of terrestrial carbon by fires burning under extreme conditions in some vegetation types, especially in temperate, hemiboreal and boreal peatlands, is an important factor in disturbance of the global carbon cycle. The increasing vulnerability of human populations living in or around forest environments has been noted throughout the region. Projected trends in the impact of climate change on vegetation cover and fire regimes, as well as observed demographic and socio-economic trends, suggest that fire may continue to play a major role in the destruction of vegetation cover in Central Asia, resulting in the accelerated formation of steppe conditions, among other effects. Based on this analysis, the following recommendations are made. Given the significance of Eurasia/Central Asia’s boreal forest in the functioning of the Earth’s climate, and the continuing and predicted loss of forest cover and terrestrial carbon storage potential, the increasing destruction of these forests should be addressed vigorously at national and international levels. Forest and fire management are the responsibility and in the interests of all countries. However, currently and for the near future, some countries of Central Asia do not seem to be in a position to ensure sustainable forest fire management practices. Weak institutional capacities in fire management and law enforcement are limiting the ability to halt forest destruction by illegal logging and/or wildfires and these must be addressed. The international community has a vital interest in preserving the multifunctional role of forests and other vegetation—including wetlands—through efficient fire management in Central Asia. International conventions, other international negotiations and recent international ministerial meetings have confirmed the interest of the international community in cooperating in sustainable forest management, which includes fire management. Such international cooperation and targeted projects and programmes must rely on accurate and meaningful fire data and information in assessing the current fire situation and trends. Fire statistics from individual countries are often incomplete and are not comparable owing to different methodologies and lack of coverage. Satellite remote sensing is not yet used systematically to assess the extent and impact of fire, and there is no agreed system in place for economic and environmental fire damage assessment. International cooperation will be important in developing internationally or regionally accepted standards and protocols, and in sharing knowledge, expertise and resources in joint projects and programmes in fire management. Most fire-prone forests and other vegetation in Central Asia are located in countries in which

438

6 Fire Following Earthquakes

Russian is the official or prevailing language. Thus investments in training materials, guidelines, terminologies, etc. could be easily shared. The Regional Central Asia Wildland Fire Network, together with its neighbouring networks (the Baltic area and Northeast Asia) may offer a suitable vehicle for developing cooperative efforts and synergies. The recommendations of governments represented at the regional forest congress, Forest Policy: Problems and Solutions, held in Bishkek, Kyrgyzstan, in November 2004, revealed a positive atmosphere for enhancing cooperative efforts in the region. Existing joint activities in fire management research should be continued and strengthened.

6.13

Northeast Asia

The Northeast Asia Wildland Fire Network, includes China, the Democratic People’s Republic of Korea, Japan, the Republic of Korea and the Far East area of the Russian Federation. This part of the world is highly diverse in socioeconomic, environmental management systems and their trends, and each country faces different driving forces of development, as well as different, but always major, challenges (details are provided in FAO Fire Management Working Paper FM/6/E). In considering the Russian Federation, it should be appreciated that while much is typical of Northeast Asia, other, western parts of Russia are more typical of Europe. The Russian Far East has closer economic and trade connections with Northeast Asian countries than with most western parts of Russia.

6.13.1 Extent and Types of Fires A comparison of national statistics for the Northeast Asian countries shows an average of about 1 million ha of forests burned each year during the period 1990–2004. The occurrence of forest fires varies with climate variability and the accumulation of combustible materials between years. However, the trend in areas affected by vegetation fires and estimates of the damage show an increase in recent decades. The average annual number of forest fires in Japan is about 3,000, of which about 150 were larger than 1 ha. During the last 20 years, the largest area affected by forest fires was about 1,000 ha. The average annual number of forest fires in China during 1990–2004 was 5,337, covering an average of 135,050 ha. The latest peak of fires was in 2004 with 13,401 fires, covering 345,585 ha of forests. In Russia in recent years, with the advent of international satellite coverage and in collaboration with Russian fire scientists, more realistic burned-area estimates

6.13

Northeast Asia

439

have been made than in the past. For example, during the 2002 fire season, satellite imagery revealed that about 12 million ha of forest and non-forest land (wildland) had been affected by fire in Russia, while official sources reported only 1.2 million ha of forest land and 500,000 ha of non-forest land burned in the protected areas of 690 million ha. During the early summer of 2003, remote sensing data indicated that the total area affected by fire in Russia exceeded 22 million ha. Based on recent remote sensing data, it appears that the annual burned area in Russia can vary from 2 to 15 million ha per year. In addition, agricultural prescribed burning (e.g. pasture management) in Russia is estimated to affect 30 million ha annually. Estimates for the Far East are about 1 million ha per year. There are two reasons for the official under-recording: insufficient monitoring of fires in the extensive territories of northern Russia, Siberia and the Far East, and an attempt by local authorities to hide their inefficiency in combating fires. This inefficiency is often not technical, however, but rather related to lack of funds.

6.13.2 Causes In Northeast Asian states, human activities in the forest are expanding because of demographic and socio-economic changes in the developing countries of the region, and for mainly cultural/aesthetic reasons in the developed ones. The origins of fires are invariably linked with human activities such as commerce (wood production), cultural-aesthetic spheres (hunting with a camera, tourism, etc.) and arson. Fires are intensified by current non-burn policies in fire-adapted ecologies, and are caused by accidental burning; land conversion (agriculture, pasture lands, industry and construction, forestry practice and plantations); harvesters of non-wood products; cattle herders; tourists; road and rail workers; traditional uses of fire such as hunting; and infrastructure development. Vegetation fires overwhelmingly originate from human actions: 95 % in China, 71 % in the 1990s in Japan, and 79 % in the Republic of Korea. The present harsh economic realities force the North Korean population to clear forests in order to collect wood for heating and cooking. According to government statistics in Russia, the share of human-caused forest fires in the Far East during the last two decades was 60–80 % (84 % in 2004).

6.13.3 Effects Uncontrolled vegetation fires were the principal causes of deforestation and forest degradation in the Northeast Asia region. There have also been estimates that timber losses in the region, due to forest fires alone, are on the order of US$0.5–1 billion per year.

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6 Fire Following Earthquakes

The temperate and boreal forests of the Northeast Asia region may account for more than 2 % of both global biomass burning and carbon emissions. Furthermore, there is growing concern that fires on permafrost sites in the region will lead to the degradation or disappearance of forests on these sites, due to the long restoration process. Increased numbers of fires in the boreal forests of Russia are a major threat to the global carbon budget. The scale of the negative impact of fire on nature and society during the last decades (environmental damage, economic losses, resources spent on fire suppression) seems to be increasing. The impact on human health is also estimated to be growing. The outbreak of large-scale forest fires in October 2004 in two areas of the Russian Far East caused atmospheric pollution, felt also in neighbouring countries. During the period 1959–1998, China’s losses in firefighting were about 100 human lives and 500 injured. Significant human losses were also recorded in 1998 and 2003 in neighbouring Russia. In the Republic of Korea, huge property losses of US$83 million were recorded in April 2000, with associated severe effects on forests. It is doubtful that existing methods of data collection provide a true picture of the economic losses to society caused by vegetation fires. There is great variation in the estimation of annual regional forest fire damage. For example, the Russian methodology of post-fire assessment is not able to give a detailed figure. During the spring, summer and autumn of 1998, fires ravaged 2.2 million ha of forests in the Russian Far East. At the time the damage was estimated at US$200 million. However, a recalculation of lost resources using world market prices amounts to US$4.2 billion and provides a more accurate picture.

6.13.4 Prevention Northeast Asian countries employ a wide range of preventive and fire awareness measures. Advanced fire management systems, including the use of remote sensing for detecting and monitoring fires, are in place in China, Japan, the Republic of Korea and Russia. The Republic of Korea is introducing a new ground-based system equipped with automatic cameras for detecting forest fires, capable of covering 93 % of total forest area (6.4 million ha). No other country in the region has a similar system. The creation of green fire belts and mineralized strips of soil in China and Russia, air patrolling, fire watchtowers, satellite monitoring and radio communication are all common fire prevention methods in the countries of the region, except in the Democratic People’s Republic of Korea. In Japan, the Republic of Korea, the forest region of Daxinganling (China) and the Territory (Russia), a lightning detection and monitoring system has been established to identify and locate fires ignited by lightning.

6.13

Northeast Asia

441

In Northeast Asian countries, fire is used for clearing land to plant crops, develop pastures or establish forest plantations. It is appreciated that fire, when properly prescribed and skillfully managed, can be less destructive to site quality than mechanical clearing methods, since soil disturbance is minimized and there is no soil compaction by heavy equipment. Prescribed fires are used to prevent forest fires of high intensity and to improve conditions for the growth of forest trees. Most countries in the region have adopted a policy of fire prevention through Awareness—raising programmes and training for local populations.

6.13.5 Suppression Fire suppression practice is advancing in the region, despite often insufficient financing and technical support. There are few differences in the fire suppression techniques of the Northeast Asian countries, but management systems and the level of equipment use are quite varied. For example, in Japan, which is a densely populated country where it is possible to reach forest sites in a relatively short time, fires are eliminated by the urban fire and rescue services, but in the Republic of Korea, firefighters use helicopters to reach fire spots in any part of the country within half an hour. Russia is currently changing its policy of total suppression of all forest fires, taking into account experience from other parts of the world. The application of a new forest symbol F and the product F1.2.A1 is known as the ‘exchange area’. By symmetry F1:2  A1 ¼ F2:1  A2

(6.34)

Values of the integrated configuration factor are available in the literature in the form of charts and tables. From Fig. 6.7, values of F1.2 can be deduced for radiation exchange between two parallel rectangular plates. Figure 6.8 can be applied to plates at right angles to each other. As with the configuration factor Ø, F’s are additive and can be manipulated to obtain an integrated configuration factor for more complex situations such as that shown in Fig. 6.9. Their application to fire problems is discussed in detail by Steward (1974a). It is important to remember that radiative heat transfer is a two-way process. Not only will the receiver radiate but also the emitting surface will receive radiation from its surroundings, including an increasing contribution from the receiver as its temperature rises. This can best be illustrated by an example. Consider a vertical steel plate, 1 m square, which is heated internally by means of electrical heating elements at a rate corresponding to 50 kW (Fig. 6.10a). The final temperature of the plate (Tp) can be calculated from the steady-state heat balance, Eq. (6.35). 50 000 ¼ 2εσ TP4


TO4 þ 2h Tp

To




(6.35)

442

6 Fire Following Earthquakes

Fig. 6.7 View factor for total radiation exchange between two identical, parallel, directly opposed flat plates (Hamilton and Morgan 1952)

1.0 0.8

Ratio Y/D

x y

0.6

A2

0.4

D

A1

10 5 3 2 1.5 1.0 0.8 0.6 0.4

0.2

0.3

F1-2

0.2

0.1 0.08 0.06

0.1

0.04

0.02

0.01 0.1

1.0

10

20

Ratio X/D

where T0 is the ambient temperature, 25  C. The factor of two appears because the plate is losing heat from both surfaces: it is assumed that the plate is sufficiently thin for heat losses from the edges to be ignored. Equation (6.35) can be reduced to: 2εσTp 4 þ 2hTp

50 000 þ 50h ¼ 0

(6.36)

as 2 ε σ TP4 50,000. Equation (6.36) may be solved for Tp with 2 ¼ 0.85 and h ¼ 12 W/m2.K, using the Newton – Raphson method (Margenau and Murphy 1956) to give Tp ¼ 793 K (520  C). If a second steel plate, 1 m square but with no internal heater, is suspended vertically 0.15 m from the first (Fig. 6.10b) then, ignoring reflected radiation, the following two steady state equations can be written: For plate 1: 50 000 þ A2 F2;1 ε2 σT2 4 þ ð1 ¼ 2A1 hðT1

A2 F2;1 ÞεTo 4

To Þ þ 2A1 εσT1 4

(6.37)

And for plate 2: A1 F1;2 ε2 σT1 4 þ ð1 ¼ 2A2 hðT2

A1 F1;2 ÞεσTo 4 To Þ þ 2A2 εσT2 4

(6.38)

Of the two terms expressing radiative heat gain on the left-hand sides of Eqs. (6.37) and (6.38), the first contains ε2 which is equivalent to the product: (emissivity of emitter)  (absorptivity of receiver). The second refers to radiation from the surroundings at ambient temperature and can be ignored. From Fig. 6.7, A1 F1,2 ¼ A2 F2,1  0.75. The above equations then become:

6.13

Northeast Asia

443

Fig. 6.8 View factor for total radiation exchange between two perpendicular flat plates with a common edge (Hamilton and Morgan 1952)

0.50 y = 0.1 Dimension ratio, y = 0.1

0.2

0.40

0.3

View Factor f12

0.4

0.30

0.6 0.8 1.0

0.20 1.5 2.0 3.0

0.10

4.0 6.0 Scale changes here

8.0

0 0

1.0

2.0

3.0

Asymptotes

4.0

6

8

10

Dimension ratio, Z

z

A2 X

y

A1

A1 = Area on which heattransler equation is based y = y/z z = z/x

Fig. 6.9 View factors for surfaces A and B can be calculated from Fig. 6.8 (see text)

9:639 T1 4 þ 2:4x 109 T1

3:072T2 4

5:715x1012 ¼ 0

(6.39)

2:4  109 T2 þ 7:152  1011 ¼ 0

(6.40)

and 3:072 T1 4

9:639 T2 4

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6 Fire Following Earthquakes

Fig. 6.10 (a) Heat losses from a vertical, internally heated flat plate (Eqs. (6.35) and (6.36)); (b) Heat losses and radiation exchange between two vertical, flat plates, one of which is internally heated (Eqs. 6.37, 6.38, 6.39, and 6.40)

These give T1 ¼ 804 K (531  C) and T2 ¼ 526 K (253  C), thus illustrating the results of cross-radiation in confined situations. This general effect is even more significant at temperatures associated with burning, and is extremely important in fire growth and spread, particularly in spaces such as ducts, ceiling voids and even gaps between items of furniture.

6.13.5.1

Radiation from Hot Gases and Non-luminous Flames

Only gases whose molecules have a dipole moment can interact with electromagnetic radiation in the ‘thermal’ region of the spectrum (0.4–100 μm). Thus, homonuclear diatomic molecules such as N2, O2 and H2 are completely transparent in this range, while heteronuclear molecules such as HCI, CO, H2O and CO2 absorb (and emit) in certain discrete wavelength bands (Fig. 6.11). Such species do not exhibit the continuous absorption which is characteristic of ‘black’, and ‘grey’ bodies and absorption (and emission) occur throughout the volume of the gas and consequently the radiative properties depend on its depth or ‘pathlength’. Consider a monochromatic beam of radiation of wavelength λ passing through a layer of gas (Fig. 6.11). The reduction in intensity as the beam passes through a thin layer dx is proportional to the intensity Iλx, the thickness of the layer (dx) and the concentration of absorbing species within that layer (C), i.e. dIλ ¼ kλC Iλx dx

(6.41)

where kλ, the constant of proportionality, is known as the monochromatic absorption coefficient. Integrating from x ¼ 0 to x ¼ L gives: IλL ¼ Iλo exp

kλ CL

(6.42)

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Fig. 6.11 Absorption spectra of (a) water vapour, 0.8–10 μm, at atmospheric pressure and 127  C: thickness of layer 104 cm; (b) carbon dioxide, 1.6–20 μm, at atmospheric pressure: curve 1, thickness 5 cm; curves 2 and 3, thickness 6.3 cm. Adapted from Kreith (1976)

445

a 100 80 60 40 20 0

1

15

2

3

4

5

6 7 8

9 10

b 100 80 60 40 20 0

6.13.5.2

2

3

4

5

6

7

8

9 10 12 14 16 18

Limits of Flammability and Premixed Flames

In premixed burning, gaseous fuel and oxidizer are intimately mixed prior to ignition. Ignition requires that sufficient energy is supplied in a suitable form, such as a electric spark, to initiate the combustion process which will then propagate through the mixture as a flame (or ‘deflagration’). The rate of combustion is typically high, determined by the chemical kinetics of oxidation rather than by the relatively slow mixing of fuel and oxidizer which determines the structure and behavior of diffusion flames. However, before remixed flames are discussed further, it is appropriate to examine flammability limits of some detail and identify the conditions under which mixtures of gaseous fuel and air, or any other oxidizing atmosphere, will burn.

6.13.5.3

Limits of Flammability

Measurement of Flammability Limits Although it is common practice to refer to gases and vapours such as methane, propane and acetone, as ‘flammable’, their mixtures with air will only burn if the fuel concentration lies within well-defined limits, known as the lower and upper flammability (or ‘explosive’) limits. For methane, these are 5 % and 15 % respectively. The most extensive review of the flammability of gases, and vapours is that of Zabetakis (1965) which, despite its age, remains the standard reference. It is based largely on a collection of data obtained with an apparatus developed at the US Bureau of Mines (Fig. 6.12). Although there are certain disadvantages in this method, these data are considered to be the most reliable that are available.

446 Fig. 6.12 The essential features of the US Bureau of Mines apparatus for determining limits of flammability of gases and vapours. The circulation pump is necessary to ensure rapid and complete mixing of the gases within the flame tube

6 Fire Following Earthquakes

FLAME TUBE

CIRCULATION PUMP

SPARK GAP

COVER PLATE

Fig. 6.13 Variation of observed flammability limits for methane/air mixtures. o,upward propagation; x, downward propagation

Alternative methods do exist, (e.g. Sorenson et al. 1975; Hirst et al. (1981/1982) but none has been used extensively enough to provide a challenge to the Bureau of Mines apparatus. In this method the experimental criterion used to determine whether or not a given mixture is flammable, is its ability to propagate flame. The apparatus, which is shown schematically in Fig. 6.13, consists of a vertical tube 1.5 m long and 0.05 m internal diameter, into which premixed gas/air mixtures of known compositions can be introduced. An ignition source, which may be a spark or a small flame, is introduced to the lower end of the tube which is first opened by the removal of a cover plate. The mixture is deemed flammable if flame propagates upward by at least 75 cm. The limits are established experimentally by a process of ‘bracketing’ and defined as L ¼ 1=2ðLw þ Lr Þ

(6.43)

U ¼ 1=2ðUw þ Ur Þ

(6.44)

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where Lw and, Ur are the greatest and least concentrations of fuel in air that are non-flammable, and, Lr and, Uw are the least and greatest concentrations of fuel in air that are flammable (Zabetakis 1965). The limits are normally expressed in terms of volume percentage at 25  C although they are functions of temperature and pressure. Flammability limit data are given (Table 6.6). of low power electrical equipment which are intrinsically safe and may be used in locations where there is a risk of a flammable atmosphere being formed. This can be achieved by designing the equipment and circuits in such a way that even the worst fault condition cannot ignite a stoichiometric mixture of the specified gas in air. Limits of ignitability which vary with the strength of the ignition source can be distinguished from limits of flammability (Fig. 6.14). The latter must be determined using an ignition source which is sufficiently large to ignite near-limit mixtures. However, as the limits vary significantly with temperature (Fig. 6.15), flame may propagate in a mixture which is technically ‘non-flammable’ under ambient conditions if the ignition source is large enough to cause a local rise in temperature. Thus the criterion for flammability in the US Bureau of Mines apparatus is propagation of flame at least half-way up the flame tube. At this point it is assumed that the flame will be propagating into a mixture which has not been affected by the ignition source. Various criticisms can be made of the US Bureau of Mines apparatus, relating mainly to procedure. In its original form, it is unsatisfactory for examining the effects that small quantities of chemical extinguishants (e.g. the halons) have on the limits, as the method used to prepare the mixture is cumbersome. Furthermore, -air mixtures tend to ‘slump’ from the tube when the cover plate is removed. This will affect the local concentration of vapour at the lower end of the tube where the ignition source is located. The need to make accurate measurements of the flammability limits of mixtures containing chemical extinguishants has led to the examination of a new method which relies not on flame propagation as the criterion of flammability, but on pressure rise inside a spherical steel vessel, 6 l in volume (Fig. 6.16). This is a very sensitive indicator as outside the limit the pressure rise is effectively zero, provided that the energy dissipated by the ignition source is not excessive. In general, data obtained with this apparatus agree quite well with flame tube results for the limit, although the upper limit values are less satisfactory. However, the lower flammability limit obtained for hydrogen in air using the pressure criterion (~8 %) is much higher than that based on observations of flame propagation (~4 %). This behavior is likely to be unique, arising from the high molecular diffusivity of hydrogen combined with buoyancy effect to produce finger-like flamelets capable of propagating vertically, but consuming little fuel (Lewis and von Elbe 1961; Hertzberg 1982). Further study is required to establish whether or not the new method is more relevant and reliable means of measuring the limits.

Hydrogen Carbon monoxide Methane Ethane Propane n-Butane n-Pentane n-Hexane n-Heptane n-Octane n-Nonane n-Decane Ethene Propene Butene-1 Acetylene Methanol Ethanol n-propanol Acetone Methyl ethyl ketone Diethyl ketone Benzene

% vol 4.00 12.50 5.00 3.00 2.10 1.80 1.40 1.20 1.05 0.95 0.85 0.75 2.70 2.40 1.70 2.50 6.70 3.30 2.20 2.60 1.90 1.60 1.30

g/m 3.6 157 36 41 42 48 46 47 47 49 49 48 35 46 44 29 103 70 60 70 62 63 47

3

kJ/m 435 1,591 1,906 1,952 1,951 2,200 2,090 2,124 2,116 2,199 2,194 2,145 1,654 2,110 1,998 1,410 2,141 1,948 1,874 2,035 1,974 2,121 1,910

3

Lower flammability limit (L)

Table 6.6 Flammability data for gases and vapours

0.55 0.50 0.49 0.52 0.52 0.55 0.48

L 0.13 0.42 0.53 0.53 0.52 0.58 0.55 0.56 0.56 0.58 0.58 0.56 0.41 0.54 0.50

% vol 75.0 74.0 15.0 12.4 9.5 8.4 7.8 7.4 6.7 – – 5.6 36.0 11.0 9.7 (100.0) 36.0 19.0 14.0 13.0 10.0 – 7.9

g/m 67 932 126 190 210 240 270 310 320 0 0 380 700 210 270 0 810 480 420 390 350 0 300

3

Upper flammability limit (U) U 2.5 2.5 1.6 2.2 2.4 2.7 3.1 3.4 3.6 0 0 4.2 5.5 2.5 2.9 0 2.9 2.9 3.2 2.6 2.7 0 2.9

m/s 3.2 0.43 0.37 0.44 0.42 0.42 0.42 0.42 0.42 0 0 0.4 >0.69 0.48 0.48 1.7 0.52 0 0.38 0.5 0 0 0.45

Su (m J) 0.01 0 0.26 0.24 0.25 0.26 0.22 0.23 0.24 0 0 0 0.12 0.28 0 0.02 0.14 0 0 1.1 0 0 0.22

Minimum ignition energy (mm) 0.5 0 2 1.8 1.8 1.8 1.8 1.8 1.8 0 0 0 1.2 0 0 0 1.5 0 0 0 0 0 1.8

Minimum quenching distance

448 6 Fire Following Earthquakes

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Fig. 6.14 Ignitability curve and limits of flammability for methane/air mixtures at atmospheric pressure and 26  C (Zabetakis et al. 1965)

Fig. 6.15 Effect of temperature on the limits of flammability of a flammable vapour/air mixture at constant initial pressure (Zabetakis et al. 1965)

A number of bilateral agreements in forest fire management are in place between China and Mongolia, China and Russia, the Islamic Republic of Iran and Russia, Russia and Finland, and Russia and Mongolia. A number of regional conferences and consultations held since 2000 have brought some countries of the region together. One important activity was a meeting of the prime ministers of the six member countries of SCO: China, Kazakhstan, Kyrgyzstan, Russia, Tajikistan and Uzbekistan. The first SCO summit, held in September 2001, concluded that member countries needed to work together in a variety of fields, including forest fire prevention.

450

6 Fire Following Earthquakes Ball-bearing

Electrode ring Electrode

Electrode

Fig. 6.16 The essential features of the spherical pressure vessel used to determine limits of flammability of gases and vapours Hirst et al. (1981/1982). The equator ring also carries the gas inlet port and the outlet port to a vacuum line. Pressure rise can be detected by means of a pressure transducer or a low pressure relief valve (as shown)

Numerous scientific initiatives have been undertaken in recent years to clarify the role and importance of natural and anthropogenic fires in forests and other vegetation. The main research issues addressed in Central Asia/Eurasia included: • • • •

recent changes in fire regimes due to anthropogenic and climatic influences; carbon pools and carbon fluxes affected by changing fire regimes; improvement of monitoring tools; the role of fire on permafrost ecosystems.

Several interdisciplinary research campaigns were initiated from 1993 to 2000 (Goldammer et al. 2004). The most recent initiatives include establishment of the Northern Eurasian Regional Information Network, the Siberian/Far Eastern Regional Network, the Western Russian/Fennoscandian Regional Network of GOFC-GOLD, the Siberia II project and the Northern Eurasian Earth Science Partnership Initiative (NEESPI). The Siberia II project contributed to improving assessment of emissions of radioactive trace gases from fires in the Russian Federation. NEESPI is an active, strategically evolving programme of internationally supported earth systems science research. It focuses on issues in northern Eurasia regarding regional and global scientific and decision-making communities. By establishing a large-scale, multidisciplinary programme of funded research, NEESPI aims to develop an enhanced understanding of the interactions between the ecosystem, the atmosphere and human dynamics in northern Eurasia. It is expected that forest-fire research will continue to play an increasing role in the overall NEESPI programme.

6.13.6 Community Participation In the Russian Federation, increasing attention to fire prevention indicates the overall involvement of the general public in reducing human-caused wildfires.

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In Kazakhstan, Civil Defence, Department of Home Affairs, Emergency Office and the Rayon Home Affairs Department stipulate the participation of human resources and equipment for fire management not only from enterprises and agencies, but also from family farms adjacent to forests. In Pakistan, a community—based forest firefighting system is being established with the assistance of the United Nations Development Programme (UNDP), which is providing firefighting training and equipment to communities living in the forest. From 1997 to 2000, the Integrated Fire Management Project—supported by Germany—was operational in Mongolia in the Khan Khentii Strictly Protected Area of the earthquake source mechanism and of the interior construction of the Earth. Although the Earth’s materials show rheological properties under static forces from plate tectonic movement, they show elastic properties under the dynamic action of seismic waves from earthquakes; the weak viscosity under dynamic forces can be considered in terms of energy-absorbing damping added to the elastic properties. Nowadays, for the great majority of earthquakes, the location is determined from the time taken by P seismic waves (and sometimes S-waves) to travel from the focus to a seismograph. Many hundreds of modern seismographs are operated worldwide continuously and reliably for this and other purposes. In some seismic areas, special local networks of seismographic stations have been installed to locate the foci of even very small earthquakes. Today, almost everyone is familiar with the concept of digital signals rather than continuous recordings, the latter provided by the continually varying electric currents that drove the old-style pen-and-ink (or even magnetic tape) recording seismographs. New technology allows modern seismographs to record the continuous ground motions as a finely spaced series of separate numbers; such discrete numerical sampling is defined by the binary number or “bits”. This form makes the recordings, unlike analog seismograms, immediately accessible for computer processing. In the 1970s, seismologists began to take full advantage of this emerging digital technology; now it is commonplace. The first global project of any size to convert globally distributed seismographs began in the 1970s. The digital samples had 14 bits. This number provided the dynamic range of frequencies that spanned what is called a broad band seismographic system—that is, from periods of a fraction of a second to the periods of free vibrations of the Earth (approximately 1 h)—and even out to the tidal deformations of the Earth (days). The intensity of shaking is observed to vary greatly with the direction around a fault rupture. The physical reason is that the seismic source is a moving energy emitter—like the whistle on a moving train. The energy increases as the source approaches and decreases as it moves away. A simple comparison of seismograms from the 1992 Landers, California, earthquake has been plotted. The shaking is represented as ground acceleration, velocity and displacement.

452

6.13.6.1

6 Fire Following Earthquakes

Magnitude of the Earthquake

The first known seismic instrument, the Houfeng seismometer, made in the year AD 132 in the Late Han dynasty by the ancient Chinese scientist Heng Zhang, successfully recorded an earthquake in AD 138. The modern type of seismograph started in the eighteenth century and includes three subsystems: sensor, amplifier and recorder. For the special requirements of the seismologist, the seismograph records usually the displacement of the ground motion due to an earthquake. The most popular way to study seismicity is empirically or statistically. A seismic belt is defined first to have a similar past earthquake distribution and geological and tectonic background, with dimensions somewhat similar to the ones already familiar. Although earthquake-recording instruments, called seismographs, are now more sophisticated, the basic principle employed is the same. A mass on a freely movable support can be used to detect both vertical and horizontal shaking of the ground. The vertical motion can be recorded by attaching the mass to a spring hanging from an anchored instrument frame; the bobbing of the frame (as with a kitchen scale) will produce relative motion. When the supporting frame is shaken by earthquake waves, the inertia of the mass causes it to lag behind the motion of the frame, and this relative motion can be recorded as a wiggly line by pen and ink on paper wrapped around a rotating drum (alternatively the motion is recorded photographically or electromagnetically on magnetic tape or as discrete digital samples for direct computer input). For measurements of the sideways motion of the ground, the mass is usually attached to a horizontal pendulum, which swings like a door on its hinges. Earthquake records are called seismograms. A seismograph appears to be no more than a complicated series of wavy lines, but from these lines a seismologist can determine the hypocentre location, magnitude and source properties of an earthquake. Although experience is essential in interpreting seismograms, the first step in understanding the lines is to remember the following principles. First, earthquake waves consist predominantly of three types—P-waves and S-waves, which travel through the Earth, and a third type, surface waves, which travel around the Earth. If you look closely enough, you will find that almost always each kind of wave is present on a seismogram, particularly if it is recorded by a sensitive seismograph at a considerable distance from the earthquake source. Each wave type affects the pendulums in a predetermined way. Second, the arrival of a seismic wave produces certain telltale changes on the seismogram trace: The trace is written more slowly or rapidly than just before; there is an increase in amplitude; and the wave rhythm (frequency) changes. Third, from past experience with similar patterns, the reader of the seismogram can identify the pattern of arrivals of the various phases. A common time standard must be used to compare the arrival times of seismic waves between earthquake observatories around the world. Traditionally, seismograms are marked in terms of Universal Time (UT) or Greenwich Mean Time (GMT), not local time. The time of occurrence of an earthquake in UT can easily be converted to local time, but be sure to make allowance for Daylight Saving Time when this is in effect.

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6.13.6.2

453

Seismic Waves

Human understanding of earthquakes, and of other physical sciences, comes first from macroseismic phenomena, but ultimately from instrumental observation. It is the instrumental data for seismic waves that provide quantitative tents of the exposed building through its windows. Good fire-protection practice calls for building setbacks on a lot and limiting window areas or other transparent openings in exterior facing walls. Such practices minimize the potential for fire spread from building to building. The exterior wall above a venting window will be subjected to some level of thermal flux, and this situation is immutable. As long as room fires develop to the post flashover condition and ordinary glazing is used for windows of exterior walls, fire exposure to these walls must be considered. For fire escaping from a window, a quantitative technique is desired which assesses the level of fire severity incident on an exterior surface above a venting window. A drawback to developing such a technique is that the venting flame exposure occurs when a “real” room burns in the post flashover mode. The standard interior exposure, however, comes from a standard fire identified only by a time-temperature relationship. Two problems arise: first, the standard fire is not associated with a standard room and, second, the standard time-temperature does not provide a proper scalar for transposing exposed components of a real venting flame to similar components of a standard fire. One step toward determining a more equitable exposure would be to determine the total incident thermal flux inflicted on a test assembly in a standard fireendurance test. This would create a time—thermal-flux relationship equivalent to the standard time temperature relationship and would partly alleviate the second problem noted. This, at least, would overcome the inconsistency that the convective energy component of incident flux is a linear function of the gas and flame temperature while the radiant energy component of incident flux is a function of the fourth power of the radiator temperature. Thus the radiant flux and the convective flux, in consistent units of energy per unit area per unit time, could be calculated and summed to obtain the total incident flux. It is generally accepted that the proportionate level of the radiant and convective components in the total incident flux is not defined in the standard fire, and this mix of components varies from standard furnace to standard furnace. Furthermore, the impact inflicted on an exposed assembly by these components is materialistic specific the effect of the incident radiant flux on an exposed assembly is a function of the emissivity of the surface of that assembly, while the effect of the incident convective flux on an exposed assembly is a function of the convective transfer coefficient of the surface of the assembly.

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6 Fire Following Earthquakes

The fact that no “standard” room is currently defined when assessing exposure poses another problem. Even a cursory study of the progress of a fully developed fire in a room will reveal a myriad of parameters which affect the burning process and the generation of thermal energy on a time dependent base. The geometry of the room, the geometry, number, and location of ventilating openings, and the mass distribution, specific surface, and composition of the fuel are only some major variables that affect the time release of thermal energy. Similar parameters affect the venting flame plume, which is a major source of exterior fire exposure.

6.13.7 Room-Fire Model In spite of all the deficiencies mentioned, it is desirable to quantify the severity of exposure on an exterior wall above a venting window. One way to examine this is to consider a post flashover room fire model which includes a reasonable number of significant parameters affecting fire development. The model selected for this discussion was developed by Margaret Law at Ove Arup & Partners, resulting from a study (1977) performed for the American iron and Steel Institute (AISI). That study produced a design guide, which is useful for organizing calculations of specified assessments. A spread-sheet program is used on a microcomputer to perform the calculations. The program’s required input is the geometry and location of the ventilation openings; the depth, width, and height of the fire room; and the specific density and specific surface of the fuel in the room. With this information, the program calculates the ratio of burning, the height, width, and thickness of the venting flame and an estimate of the fire duration. The program then calculates the geometry factor and the temperature of the venting flame. From this, the emissivity and the average incident radiant flux from the venting flame are calculated. Likewise, the convective transfer coefficient and the average incident convective flux from the venting flame are also calculated. Adding these two components of incident flux results in the total average incident flux on the exterior wall area above the venting window. Calculations can be made using this, technique for a range of room geometries, window geometries, and fuel conditions. In this study, the rooms tested varied from 3.05 by 3.05 m (10 by 10 ft) to 24.38 by 24.38 m (80 by 80 ft). The room height was set at 2.44 m (8.0 ft), but in specific rooms the height as varied up to 8.53 m (28.0 ft). The windows varied from 0.91 m wide by 0.91 m high (0 by 3.0 ft) to full wall width by full room height. The windows were placed in one wall defined by the room width and also in one perpendicular wall defined by the room depth. A total of 82 separate combinations of room and window geometries were calculated for a fuel density of 48.8 kg/m2 (10 lb/ft2) and for a fuel density of 97.6 Kg/m2 (20 l lb/ft2). The specific surface of the fuel was taken so that, for the fuel surfacecontrolled fire, the entire fuel load is consumed in 20 min.

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Fig. 6.17 Incident flux equivalent to standard ASTM E-119 time-temperature

The total average incident flux on the exterior wall area above the venting window can be compared to the total incident flux imposed on a test assembly when exposed to the standard fire The graph in Fig. 6.17 is taken from a thesis research project from Ohio State University. Oberg measured and recorded the incident radiant flux and the total incident flux imposed on a 3.05-lb, 3.05-m (10- by 10-ft) concrete-block wall assembly exposed to the standard ASTM E-119 fireendurance test. The measurements were taken at the center of the exposed face of concrete block and at the center of each of the four quarter sections of the specimen. The measurements were taken at intervals throughout the exposure test period. The average of the results of four separate tests is shown in Fig 6.17. Inspection of Fig 6.17 shows that the total incident flux follows the general characteristics of the standard time-temperature curve. It can also be noted that the incident convective flux is essentially constant after the early portion of the test. The equivalent severity of the fire exposure incident on a wall above a venting window is determined by comparing the area under the ASTM E-119 time-flux curve obtained by Oberg to the area under the time-flux curve calculated from the computer model. In both cases the area below a thermal flux of 1.25 W/cm2 (66 Btu/ ft2 min) is excluded. This flux is the threshold flux for pilot ignition of ordinary combustible materials. The assumption is that flux levels below this would have no significant damaging effect on the wall assembly. Figure 6.18 illustrates this relationship for one typical room-fire situation. The area under the ASTM E-119 time-flux curve is calculated for the actual fire duration by dividing the total fuel by the rate of burning or by the duration, based on a specific fuel density first suggested by Ingberg, whichever is less (1928). The fire duration based on Ingberg is 60 min for a 48.8-kg/m2 (10-lb/ft2) fuel density and 120 min for a 97.6-kg/m2 (20-lb/ft2) fuel density. The area under the maximum calculated flux curve is indicated in Fig. 6.18 by the crosshatched area B. This area is then reconstructed under the ASTM E-119

456

6 Fire Following Earthquakes 700

13

incldent flux (Btu\sq ft/min)

12

ASTM E-119 equivalent time-flux curve

600

11 10

500

9 8

400 Equlvalent fire exposure - 18 min

7

300

6 5 C

200

4 Maximum calculated flux

3

B

100 66

18

Threshold pilot lgnition flux

Fire duration

2 1.25 1

0 0

10

20

30

45

incldent flux (w\sq cm)

Fig. 6.18 Calculated incident flux versus equivalent ASTM E-119 time-flux

50

60

0

Time (min)

time-flux curve to equal the crosshatched area C. The time required under the ASTM curve to obtain an equal area, is the equivalent fire exposure.

6.13.8 Room-Model Test Results Tables 6.7, 6.8, 6.9, 6.10, 6.11, 6.12, 6.13, 6.14, 6.15, 6.16, 6.17, 6.18, and 6.19 show the results of room-fire calculations. Table 6.7 gives the fire duration, the average total incident flux on the wall above the venting window and the equivalent fire exposure on that wall for 82 distinct room fires for a specific fuel load of 48.8 kg/m2 (10 lb/ft2). Table 6.8 shows comparable data for a fuel load of 97.6 kg/m2 (20 lb/ft2). Tables 6.9 and 6.10 contain the same information as Table 6.7 [room-fire results for a fuel density of 48.8 kg/m2 (10 lb/ft2)], while Tables 6.11 and 6.12 contain the same information as Table 6.8 [room-fire results for a fuel density of 97.6 kg/m2 (20 lb/ft2)]. In Tables 6.9 and 6.11 the room-fire cases are listed by fire duration, in Tables 6.10 and 6.12 they are listed by equivalent fire exposure. In Table 6.9 there are four room cases (15, 16, 17, and 73) which had fire durations of 20 min. These four cases were provided with sufficient ventilation air so that the surface area of the fuel controlled the mass burning rate. In all the other cases shown in Tables 6.9 and 6.12 [at both 48.8- and 97.6 kg/m2 (10- and 20-lb/ft2) fuel density], the mass burning rate was controlled by the ventilation air available. Those cases where the mass-burning rate was so slow that it resulted in unusually long fire durations [those in excess of 480 min for the 48.8-kg/m2 (10-lb/ft2) fuel density and 960 ‘min for the 97.6-kg/m2 (20-lb/ft2) fuel density] were unrealistic

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Table 6.7 Effect of room geometry and window size and location on the exposure of exterior walls above venting window openings from 10-lb/ft2 fuel-load compartment fires Room size, ft Room case 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

D 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 40.0 40.0 40.0 40.0 40.0 40.0 40.0

W 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 10.0 10.0 10.0 10.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 40.0 40.0 40.0 40.0 40.0 40.0 20.0 20.0 20.0 20.0 20.0 40.0 40.0

Window size, ft H 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0

w1 3.0 3.0 5.0 10.0 3.0 5.0 10.0 10.0 3.0 3.0 5.0 10.0 10.0 3.0 5.0 10.0 10.0 3.0 10.0 3.0 10.0 3.0 10.0 20.0 20.0 3.0 10.0 10.0 3.0 3.0 10.0 20.0 40.0 40.0 3.0 10.0 20.0 3.0 20.0 3.0 10.0

h1 3.0 5.0 5.0 5.0 3.0 5.0 5.0 8.0 3.0 5.0 5.0 5.0 8.0 3.0 5.0 5.0 8.0 3.0 8.0 3.0 8.0 3.0 5.0 5.0 8.0 3.0 5.0 8.0 3.0 8.0 5.0 5.0 5.0 8.0 3.0 5.0 5.0 3.0 8.0 3.0 5.0

w2

h2

3.0 5.0 10.0 10.0

3.0 5.0 5.0 8.0

3.0 5.0 10.0 10.0

3.0 5.0 5.0 8.0

3.0 10.0

3.0 8.0

10.0 10.0

5.0 8.0

3.0 20.0

3.0 8.0

Fire duration, min 60 39 34 31 29 22 23 25 76 43 32 27 25 32 20 20 20 153 50 63 37 211 53 45 43 73 32 31 297 75 54 41 36 34 595 108 81 211 49 841 127

Incident flux, Btu/ ft2 min 103 88 80 59 82 72 61 36 108 104 97 85 70 97 82 73 65 104 42 80 48 104 86 71 48 89 74 70 109 122 103 92 79 58 104 85 75 83 61 104 98

Equivalent exposure, min 12 8 6 0 6 4 0 0 13 10 8 6 3 8 5 4 0 12 0 8 0 12 8 4 0 10 5 4 13 15 11 8 6 0 12 9 6 8 0 12 11

458

6 Fire Following Earthquakes

Table 6.8 Effect of room geometry and window size and location on the exposure of exterior walls above venting window openings from 10-lb/ft2 fuel-load compartment fires Room size, ft Room case 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82

D 40.0 40.0 40.0 40.0 40.0 40.0 40.0 40.0 40.0 40.0 40.0 40.0 40.0 40.0 40.0 80.0 80.0 80.0 80.0 80.0 80.0 80.0 80.0 80.0 80.0 80.0 80.0 80.0 80.0 80.0 10.0 10.0 80.0 80.0 80.0 20.0 20.0 20.0 80.0 80.0 80.0

W 40.0 40.0 40.0 40.0 40.0 40.0 40.0 40.0 80.0 80.0 80.0 80.0 80.0 80.0 80.0 40.0 40.0 40.0 40.0 40.0 40.0 40.0 80.0 80.0 80.0 80.0 80.0 80.0 80.0 80.0 80.0 80.0 10.0 10.0 10.0 80.0 80.0 80.0 20.0 20.0 20.0

Window size, ft H 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0

w1 20.0 40.0 40.0 3.0 10.0 20.0 20.0 40.0 3.0 3.0 80.0 3.0 20.0 40.0 80.0 3.0 5.0 10.0 20.0 40.0 3.0 40.0 3.0 10.0 80.0 3.0 20.0 40.0 80.0 80.0 3.0 80.0 3.0 10.0 10.0 3.0 3.0 80.0 3.0 10.0 20.0

h1 5.0 5.0

w2

h2

3.0 5.0 5.0 8.0 5.0 3.0 8.0 8.0 3.0 5.0 5.0 5.0 3.0 5.0 10.0 20.0 40.0 3.0 8.0 3.0 5.0 8.0 3.0 5.0 5.0 5.0 8.0 3.0 8.0 3.0 8.0 8.0 3.0 8.0 8.0 3.0 8.0 8.0

3.0 10.0 20.0 20.0 40.0

3.0 5.0 5.0 8.0 5.0

3.0 20.0 20.0 40.0

3.0 5.0 5.0 5.0

3.0 40.0

3.0 8.0

3.0 20.0 40.0 40.0 80.0

3.0 5.0 5.0 5.0 8.0

10.0

8.0

20.0

8.0

Fire duration, min 81 63 56 297 58 45 40 48 1,190 273 43 421 42 42 36 2,380 664 335 183 94 841 60 3,365 469 71 1,190 93 63 62 46 149 20 1,190 143 86 421 98 26 1,683 156 74

Incident flux, Btu/ ft2 min 92 82 66 91 90 80 77 77 109 127 76 104 101 92 81 104 91 91 89 72 83 71 104 100 81 91 97 88 83 75 137 52 101 56 64 119 148 68 106 78 67

Equivalent exposure, min 10 8 0 10 10 6 6 6 13 16 5 12 10 8 6 12 10 10 10 5 8 5 12 12 8 10 11 9 8 5 18 0 12 0 0 15 19 3 13 7 2

6.13

Northeast Asia

459

Table 6.9 Effect of room geometry and window size and location on the exposure of exterior walls above venting window openings from 20-lb/ft2 fuel-load compartment fires Room size, ft Room case 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541

D 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 40.0 40.0 40.0 40.0 40.0 40.0 40.0

W 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 10.0 10.0 10.0 10.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 40.0 40.0 40.0 40.0 40.0 40.0 20.0 20.0 20.0 20.0 20.0 40.0 40.0

Window size, ft H 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0

w1 3.0 3.0 5.0 10.0 3.0 5.0 10.0 10.0 3.0 3.0 3.0 10.0 10.0 3.0 5.0 10.0 10.0 3.0 10.0 3.0 10.0 3.0 10.0 20.0 20.0 3.0 10.0 10.0 3.0 3.0 10.0 20.0 40.0 40.0 3.0 10.0 20.0 3.0 20.0 3.0 10.0

h1 3.0 5.0 5.0 5.0 3.0 5.0 5.0 8.0 3.0 3.0 5.0 5.0 8.0 3.0 5.0 5.0 8.0 3.0 8.0 3.0 8.0 3.0 5.0 5.0 8.0 3.0 5.0 8.0 3.0 8.0 5.0 5.0 5.0 8.0 3.0 5.0 5.0 3.0 8.0 3.0 5.0

w2

h2

3.0 5.0 10.0 10.0

3.0 5.0 5.0 8.0

3.0 5.0 10.0 10.0

3.0 5.0 5.0 8.0

3.0 10.0

3.0 8.0

3.0 10.0 10.0

3.0 5.0 8.0

3.0 20.0

3.0 8.0

Fire duration, min 119 78 67 61 57 43 45 51 153 85 66 54 50 63 38 36 37 307 100 126 74 422 106 91 86 157 64 61 595 150 108 81 71 69 1,190 216 162 423 98 1,683 254

Incident flux, Btu/ ft2 min 103 88 80 59 82 72 61 36 108 104 97 85 70 97 83 73 67 104 42 80 48 104 86 71 48 89 74 70 109 122 103 92 79 58 104 85 75 83 61 104 98

Equivalent exposure, min 18 10 8 0 6 4 0 0 18 14 10 8 4 10 6 4 2 18 0 10 0 18 12 4 0 14 6 4 20 22 16 12 6 0 18 12 8 10 0 18 16

460

6 Fire Following Earthquakes

Table 6.10 Effect of room geometry and window size and location on the exposure of exterior walls above venting window openings from 20-lb/ft2 fuel-load compartment fires Room size, ft Room case 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582

D 40.0 40.0 40.0 40.0 40.0 40.0 40.0 40.0 40.0 40.0 40.0 40.0 40.0 40.0 40.0 80.0 80.0 80.0 80.0 80.0 80.0 80.0 80.0 80.0 80.0 80.0 80.0 80.0 80.0 80.0 10.0 10.0 80.0 80.0 80.0 20.0 20.0 20.0 80.0 80.0 80.0

W 40.0 40.0 40.0 40.0 40.0 40.0 40.0 40.0 80.0 80.0 80.0 80.0 80.0 80.0 80.0 40.0 40.0 40.0 40.0 40.0 40.0 40.0 80.0 80.0 80.0 80.0 80.0 80.0 80.0 80.0 80.0 80.0 10.0 10.0 10.0 80.0 80.0 80.0 20.0 20.0 20.0

Window size, ft H 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0

w1 20.0 40.0 40.0 3.0 10.0 20.0 20.0 40.0 3.0 3.0 80.0 3.0 20.0 40.0 80.0 3.0 5.0 10.0 20.0 40.0 3.0 40.0 3.0 10.0 80.0 3.0 20.0 40.0 80.0 80.0 3.0 80.0 3.0 10.0 10.0 3.0 3.0 80.0 3.0 10.0 20.0

h1 5.0 5.0 8.0 3.0 5.0 5.0 8.0 5.0 3.0 8.0 8.0 3.0 5.0 5.0 5.0 3.0 5.0 5.0 5.0 8.0 3.0 8.0 3.0 5.0 8.0 3.0 5.0 5.0 5.0 8.0 3.0 8.0 3.0 8.0 8.0 3.0 8.0 8.0 3.0 8.0 8.0

w2

h2

3.0 10.0 20.0 20.0 20.0

3.0 5.0 5.0 8.0 5.0

3.0 20.0 20.0 40.0

3.0 5.0 5.0 5.0

3.0 40.0

3.0 8.0

3.0 20.0 20.0 40.0 40.0

3.0 5.0 5.0 5.0 8.0

10.0

8.0

20.0

8.0

Fire duration, min 163 127 112 595 115 90 79 96 2,380 547 85 841 85 84 72 4,759 1,327 669 365 188 1,683 120 6,730 939 141 2,380 186 125 125 92 297 31 2,380 286 171 841 195 52 3,365 312 149

Incident flux, Btu/ ft2 min 92 82 66 91 90 80 77 77 109 127 76 104 101 92 81 104 91 91 89 72 83 71 104 100 81 91 97 88 83 75 137 62 101 56 64 119 148 68 106 78 67

Equivalent exposure, min 14 10 0 14 14 8 6 8 20 24 6 18 14 12 8 18 14 14 14 6 10 6 18 16 10 14 16 12 10 6 26 0 16 0 0 22 30 2 18 8 2

6.13

Northeast Asia

461

Table 6.11 Effect of room geometry and window size and location on the exposure of exterior walls above venting window openings from 10-lb/ft2 fuel-load compartment fires (sorted on fire duration) Room size, ft Room case 16 73 15 17 6 7 13 8 79 12 5 4 28 14 11 27 3 34 56 33 21 2 48 32 55 54 10 52 25 24 47 71 49 39 19 23 31 44 46 1 63

D 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 20.0 10.0 10.0 10.0 20.0 10.0 10.0 20.0 10.0 20.0 40.0 20.0 20.0 10.0 40.0 20.0 40.0 40.0 10.0 40.0 20.0 20.0 40.0 80.0 40.0 40.0 20.0 20.0 20.0 40.0 40.0 10.0 80.0

W 20.0 80.0 20.0 20.0 10.0 10.0 20.0 10.0 80.0 20.0 10.0 10.0 20.0 20.0 20.0 20.0 10.0 40.0 80.0 40.0 10.0 10.0 40.0 40.0 80.0 80.0 20.0 80.0 20.0 20.0 40.0 80.0 40.0 20.0 10.0 20.0 40.0 40.0 40.0 10.0 40.0

Window size, ft H 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0

w1 10.0 80.0 5.0 10.0 5.0 10.0 10.0 10.0 80.0 10.0 3.0 10.0 10.0 3.0 5.0 10.0 5.0 40.0 80.0 40.0 10.0 3.0 20.0 20.0 40.0 20.0 3.0 80.0 20.0 20.0 20.0 80.0 40.0 20.0 10.0 10.0 10.0 40.0 10.0 3.0 40.0

h1 5.0 8.0 5.0 8.0 5.0 5.0 8.0 8.0 8.0 5.0 3.0 5.0 8.0 3.0 5.0 5.0 5.0 8.0 5.0 5.0 8.0 5.0 8.0 5.0 5.0 5.0 5.0 8.0 8.0 5.0 5.0 8.0 5.0 8.0 8.0 5.0 5.0 8.0 5.0 3.0 8.0

w2 10.0

h2 5.0

5.0 10.0 5.0 10.0

5.0 8.0 5.0 5.0

10.0

8.0

3.0

3.0

10.0 3.0

8.0 3.0

10.0

5.0

40.0

5.0

10.0

8.0

20.0

8.0

20.0 20.0

5.0 5.0

20.0 80.0 20.0 20.0

5.0 8.0 5.0 8.0

10.0

5.0

40.0

8.0

Fire duration, min 20 20 20 20 22 23 25 25 26 27 29 31 31 32 32 32 34 34 36 36 37 39 40 41 42 42 43 43 43 45 45 46 48 49 50 53 54 56 58 60 60

Incident flux, Btu/ ft2 min 73 52 82 65 72 61 70 36 68 85 82 59 70 97 97 74 80 58 81 79 48 88 77 92 92 101 104 76 48 71 80 75 77 61 42 86 103 66 90 103 71

Equivalent exposure, min 4 0 5 0 4 0 3 0 3 6 6 0 4 8 8 5 6 0 6 6 0 8 6 8 8 10 10 5 0 4 6 5 6 0 0 8 11 0 10 12 5

462

6 Fire Following Earthquakes

Table 6.12 Effect of room geometry and window size and location on the exposure of exterior walls above venting window openings from 10-lb/ft2 fuel-load compartment fires (sorted on fire duration) Room size, ft Room case 70 20 43 69 66 82 30 9 26 37 42 76 68 61 78 36 41 75 72 18 81 60 38 22 51 45 29 59 77 53 65 35 58 40 62 50 74 67 80 57 64

D 80.0 20.0 40.0 80.0 80.0 80.0 20.0 10.0 20.0 40.0 40.0 80.0 80.0 80.0 20.0 40.0 40.0 80.0 10.0 20.0 80.0 80.0 40.0 20.0 40.0 40.0 20.0 80.0 20.0 40.0 80.0 40.0 80.0 40.0 80.0 40.0 80.0 80.0 80.0 80.0 80.0

W 80.0 10.0 40.0 80.0 80.0 20.0 40.0 20.0 20.0 20.0 40.0 10.0 80.0 40.0 80.0 20.0 40.0 10.0 80.0 10.0 20.0 40.0 20.0 20.0 80.0 40.0 40.0 40.0 80.0 80.0 80.0 20.0 40.0 40.0 40.0 80.0 10.0 80.0 20.0 40.0 80.0

Window size, ft H 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0

w1 80.0 3.0 40.0 40.0 80.0 20.0 3.0 3.0 3.0 20.0 20.0 10.0 20.0 40.0 3.0 10.0 10.0 10.0 3.0 3.0 10.0 20.0 3.0 3.0 3.0 3.0 3.0 10.0 3.0 3.0 10.0 3.0 5.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0

h1 5.0 3.0 5.0 5.0 8.0 8.0 8.0 3.0 3.0 5.0 5.0 8.0 5.0 8.0 8.0 5.0 5.0 8.0 3.0 3.0 8.0 5.0 3.0 3.0 8.0 3.0 3.0 5.0 3.0 3.0 5.0 3.0 5.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0

w2 40.0 3.0

h2 5.0 3.0

40.0

5.0

20.0

8.0

3.0

3.0

10.0 20.0

8.0 5.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

Fire duration, min 62 63 63 63 71 74 75 76 78 81 81 86 93 94 98 108 127 143 149 153 156 183 211 211 273 297 297 335 421 421 469 595 664 841 841 1,190 1,190 1,190 1,683 2,380 3,365

Incident flux, Btu/ ft2 min 83 80 82 88 81 67 122 108 89 75 92 64 97 72 148 85 98 56 137 104 78 89 83 104 127 91 109 91 119 104 100 104 91 104 83 109 101 91 106 104 104

Equivalent exposure, min 8 8 8 9 8 2 15 13 10 6 10 0 11 5 19 9 11 0 18 12 7 10 8 12 16 10 13 10 15 12 12 12 10 12 8 13 12 10 13 12 12

6.13

Northeast Asia

463

Table 6.13 Effect of room geometry and window size and location on the exposure of exterior walls above venting window openings from 10-lb/ft2 fuel-load compartment fires (sorted on fire duration) Room size, ft Room case 16 73 15 17 6 7 13 8 79 12 5 4 28 14 11 27 3 34 56 33 21 2 48 32 55 54 10 52 25 24 47 71 49 39 19 23 31 44 46 1 63

D 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 20.0 10.0 10.0 10.0 20.0 10.0 10.0 20.0 10.0 20.0 40.0 20.0 20.0 10.0 40.0 20.0 40.0 40.0 10.0 40.0 20.0 20.0 40.0 80.0 40.0 40.0 20.0 20.0 20.0 40.0 40.0 10.0 80.0

W 20.0 80.0 20.0 20.0 10.0 10.0 20.0 10.0 80.0 20.0 10.0 10.0 20.0 20.0 20.0 20.0 10.0 40.0 80.0 40.0 10.0 10.0 40.0 40.0 80.0 80.0 20.0 80.0 20.0 20.0 40.0 80.0 40.0 20.0 10.0 20.0 40.0 40.0 40.0 10.0 40.0

Window size, ft H 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0

w1 10.0 80.0 5.0 10.0 5.0 10.0 10.0 10.0 80.0 10.0 3.0 10.0 10.0 3.0 5.0 10.0 5.0 40.0 80.0 40.0 10.0 3.0 20.0 20.0 40.0 20.0 3.0 80.0 20.0 20.0 20.0 80.0 40.0 20.0 10.0 10.0 10.0 40.0 10.0 3.0 40.0

h1 5.0 8.0 5.0 8.0 5.0 5.0 8.0 8.0 8.0 5.0 3.0 5.0 8.0 3.0 5.0 5.0 5.0 8.0 5.0 5.0 8.0 5.0 8.0 5.0 5.0 5.0 5.0 8.0 8.0 5.0 5.0 8.0 5.0 8.0 8.0 5.0 5.0 8.0 5.0 3.0 8.0

w2 10.0

h2 5.0

5.0 10.0 5.0 10.0

5.0 8.0 5.0 5.0

10.0

8.0

3.0

3.0

10.0 3.0

8.0 3.0

10.0

5.0

40.0

5.0

10.0

8.0

20.0

8.0

20.0 20.0

5.0 5.0

20.0 80.0 20.0 20.0

5.0 8.0 5.0 8.0

10.0

5.0

40.0

8.0

Fire duration, min 20 20 20 20 22 23 25 25 26 27 29 31 31 32 32 32 34 34 36 36 37 39 40 41 42 42 43 43 43 45 45 46 48 49 50 53 54 56 58 60 60

Incident flux, Btu/ ft2 min 73 52 82 65 72 61 70 36 68 85 82 59 70 97 97 74 80 58 81 79 48 88 77 92 92 101 104 76 48 71 80 75 77 61 42 86 103 66 90 103 71

Equivalent exposure, min 4 0 5 0 4 0 3 0 3 6 6 0 4 8 8 5 6 0 6 6 0 8 6 8 8 10 10 5 0 4 6 5 6 0 0 8 11 0 10 12 5

464

6 Fire Following Earthquakes

Table 6.14 Effect of room geometry and window size and location on the exposure of exterior walls above venting window openings from 10-lb/ft2 fuel-load compartment fires (sorted on fire duration) Room size, ft Room case 70 20 43 69 66 82 30 9 26 37 42 76 68 61 78 36 41 75 72 18 81 60 38 22 51 45 29 59 77 53 65 35 58 40 62 50 74 67 80 57 64

D 80.0 20.0 40.0 80.0 80.0 80.0 20.0 10.0 20.0 40.0 40.0 80.0 80.0 80.0 20.0 40.0 40.0 80.0 10.0 20.0 80.0 80.0 40.0 20.0 40.0 40.0 20.0 80.0 20.0 40.0 80.0 40.0 80.0 40.0 80.0 40.0 80.0 80.0 80.0 80.0 80.0

W 80.0 10.0 40.0 80.0 80.0 20.0 40.0 20.0 20.0 20.0 40.0 10.0 80.0 40.0 80.0 20.0 40.0 10.0 80.0 10.0 20.0 40.0 20.0 20.0 80.0 40.0 40.0 40.0 80.0 80.0 80.0 20.0 40.0 40.0 40.0 80.0 10.0 80.0 20.0 40.0 80.0

Window size, ft H 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0

w1 80.0 3.0 40.0 40.0 80.0 20.0 3.0 3.0 3.0 20.0 20.0 10.0 20.0 40.0 3.0 10.0 10.0 10.0 3.0 3.0 10.0 20.0 3.0 3.0 3.0 3.0 3.0 10.0 3.0 3.0 10.0 3.0 5.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0

h1 5.0 3.0 5.0 5.0 8.0 8.0 8.0 3.0 3.0 5.0 5.0 8.0 5.0 8.0 8.0 5.0 5.0 8.0 3.0 3.0 8.0 5.0 3.0 3.0 8.0 3.0 3.0 5.0 3.0 3.0 5.0 3.0 5.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0

w2 40.0 3.0

h2 5.0 3.0

40.0

5.0

20.0

8.0

3.0

3.0

10.0 20.0

8.0 5.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

Fire duration, min 62 63 63 63 71 74 75 76 78 81 81 86 93 94 98 108 127 143 149 153 156 183 211 211 273 297 297 335 421 421 469 595 664 841 841 1,190 1,190 1,190 1,683 2,380 3,365

Incident flux, Btu/ ft2 min 83 80 82 88 81 67 122 108 89 75 92 64 97 72 148 85 98 56 137 104 78 89 83 104 127 91 109 91 119 104 100 104 91 104 83 109 101 91 106 104 104

Equivalent exposure, min 8 8 8 9 8 2 15 13 10 6 10 0 11 5 19 9 11 0 18 12 7 10 8 12 16 10 13 10 15 12 12 12 10 12 8 13 12 10 13 12 12

6.13

Northeast Asia

465

Table 6.15 Effect of room geometry and window size and location on the exposure of exterior walls above venting window openings from 10-lb/ft2 fuel-load compartment fires (sorted on equivalent exposure) Room size, ft Room case 21 73 44 4 25 8 7 76 19 17 75 34 39 82 13 79 6 16 28 24 63 71 52 27 61 15 12 56 49 33 48 37 5 3 47 81 20 66 70 23 43

D 20.0 10.0 40.0 10.0 20.0 10.0 10.0 80.0 20.0 10.0 80.0 20.0 40.0 80.0 10.0 20.0 10.0 10.0 20.0 20.0 80.0 80.0 40.0 20.0 80.0 10.0 10.0 40.0 40.0 20.0 40.0 40.0 10.0 10.0 40.0 80.0 20.0 80.0 80.0 20.0 40.0

W 10.0 80.0 40.0 10.0 20.0 10.0 10.0 10.0 10.0 20.0 10.0 40.0 20.0 20.0 20.0 80.0 10.0 20.0 20.0 20.0 40.0 80.0 80.0 20.0 40.0 20.0 20.0 80.0 40.0 40.0 40.0 20.0 10.0 10.0 40.0 20.0 10.0 80.0 80.0 20.0 40.0

Window size, ft H 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0

w1 10.0 80.0 40.0 10.0 20.0 10.0 10.0 10.0 10.0 10.0 10.0 40.0 20.0 20.0 10.0 80.0 5.0 10.0 10.0 20.0 40.0 80.0 80.0 10.0 40.0 5.0 10.0 80.0 40.0 40.0 20.0 20.0 3.0 5.0 20.0 10.0 3.0 80.0 80.0 10.0 40.0

h1 8.0 8.0 8.0 5.0 8.0 8.0 5.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 5.0 5.0 8.0 5.0 8.0 8.0 8.0 5.0 8.0 5.0 5.0 5.0 5.0 5.0 8.0 5.0 3.0 5.0 5.0 8.0 3.0 8.0 5.0 5.0 5.0

w2

h2

10.0 10.0 10.0

8.0 5.0 8.0

10.0

8.0

20.0 20.0

8.0 8.0

5.0 10.0 10.0

5.0 5.0 8.0

40.0 80.0

8.0 8.0

10.0

5.0

5.0

5.0

40.0 20.0

5.0 5.0

20.0

8.0

3.0

3.0

20.0

5.0

3.0

3.0

40.0

5.0

Fire duration, min 37 20 56 31 43 25 23 86 50 20 143 34 49 74 25 26 22 20 31 45 60 46 43 32 94 20 27 36 48 36 40 81 29 34 45 165 63 71 62 53 63

Incident flux, Btu/ ft2 min 48 52 55 59 48 36 61 64 42 65 56 58 61 67 70 68 72 73 70 71 71 75 76 74 72 82 85 81 77 79 77 75 82 80 80 78 80 81 83 86 82

Equivalent exposure, min 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 3 4 4 4 4 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 7 8 8 8 8 8

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6 Fire Following Earthquakes

Table 6.16 Effect of room geometry and window size and location on the exposure of exterior walls above venting window openings from 10-lb/ft2 fuel-load compartment fires (sorted on equivalent exposure) Room size, ft Room case 2 55 14 62 32 38 11 36 69 26 42 59 10 60 46 67 58 54 45 31 41 68 64 65 40 57 22 18 1 35 74 53 50 29 80 9 30 77 51 72 78

D 10.0 40.0 10.0 80.0 20.0 40.0 10.0 40.0 80.0 20.0 40.0 80.0 10.0 80.0 40.0 80.0 80.0 40.0 40.0 20.0 40.0 80.0 80.0 80.0 40.0 80.0 20.0 20.0 10.0 40.0 80.0 40.0 40.0 20.0 80.0 10.0 20.0 20.0 40.0 10.0 20.0

W 10.0 80.0 20.0 40.0 40.0 20.0 20.0 20.0 80.0 20.0 40.0 40.0 20.0 40.0 40.0 80.0 40.0 80.0 40.0 40.0 40.0 80.0 80.0 80.0 40.0 40.0 20.0 10.0 10.0 20.0 10.0 80.0 80.0 40.0 20.0 20.0 40.0 80.0 80.0 80.0 80.0

Window size, ft H 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0

w1 3.0 40.0 3.0 3.0 20.0 3.0 5.0 10.0 40.0 3.0 20.0 10.0 3.0 20.0 10.0 3.0 5.0 20.0 3.0 10.0 10.0 20.0 3.0 10.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0

h1 5.0 5.0 3.0 3.0 5.0 3.0 5.0 5.0 5.0 3.0 5.0 5.0 5.0 5.0 5.0 3.0 5.0 5.0 3.0 5.0 5.0 5.0 3.0 5.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 8.0 3.0 8.0 3.0 8.0

w2

h2

20.0 3.0 3.0

5.0 3.0 3.0

3.0

3.0

40.0 3.0

5.0 3.0

10.0 3.0

5.0 3.0

20.0 3.0

5.0 3.0

20.0

5.0

3.0

3.0

Fire duration, min 39 42 32 841 41 211 32 108 63 78 81 335 43 183 58 1,190 664 42 297 54 127 93 3,365 469 841 2,380 211 153 60 595 1,190 421 1,190 297 1,683 76 75 421 273 149 98

Incident flux, Btu/ ft2 min 88 92 97 83 92 83 97 85 88 89 92 91 104 89 90 91 91 101 91 103 98 97 104 100 104 104 104 104 103 104 101 104 109 109 106 108 122 119 127 137 148

Equivalent exposure, min 8 8 8 8 8 8 8 9 9 10 10 10 10 10 10 10 10 10 10 11 11 11 12 12 12 12 12 12 12 12 12 12 13 13 13 13 15 15 16 18 19

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Table 6.17 Effect of room geometry and window size and location on the exposure of exterior walls above venting window openings from 20-lb/ft2 fuel-load compartment fires (sorted on fire duration) Room size, ft Room case 573 516 517 515 506 507 513 508 579 512 505 504 528 514 527 511 503 534 533 556 521 502 548 532 555 510 554 552 525 547 524 571 549 539 519 523 531 544 546 501 563

D 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 20.0 10.0 10.0 10.0 20.0 10.0 20.0 10.0 10.0 20.0 20.0 40.0 20.0 10.0 40.0 20.0 40.0 10.0 40.0 40.0 20.0 40.0 20.0 80.0 40.0 40.0 20.0 20.0 20.0 40.0 40.0 10.0 80.0

W 80.0 20.0 20.0 20.0 10.0 10.0 20.0 10.0 80.0 20.0 10.0 10.0 20.0 20.0 20.0 20.0 10.0 40.0 40.0 80.0 10.0 10.0 40.0 40.0 80.0 20.0 80.0 80.0 20.0 40.0 20.0 80.0 40.0 20.0 10.0 20.0 40.0 40.0 40.0 10.0 40.0

Window size, ft H 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0

w1 80.0 10.0 10.0 5.0 5.0 10.0 10.0 10.0 80.0 10.0 3.0 10.0 10.0 3.0 10.0 5.0 5.0 40.0 40.0 80.0 10.0 3.0 20.0 20.0 40.0 3.0 20.0 80.0 20.0 20.0 20.0 80.0 40.0 20.0 10.0 10.0 10.0 40.0 10.0 3.0 40.0

h1 8.0 5.0 8.0 5.0 5.0 5.0 8.0 8.0 8.0 5.0 3.0 5.0 8.0 3.0 5.0 5.0 5.0 8.0 5.0 5.0 8.0 5.0 8.0 5.0 5.0 5.0 5.0 8.0 8.0 5.0 5.0 8.0 5.0 8.0 8.0 5.0 5.0 8.0 5.0 3.0 8.0

w2

h2

10.0 10.0 5.0 5.0 10.0

5.0 8.0 5.0 5.0 5.0

10.0

8.0

3.0

3.0

10.0 3.0 10.0

8.0 3.0 5.0

40.0 10.0

5.0 8.0

20.0

8.0

20.0

5.0

20.0

5.0

20.0

5.0

80.0 20.0 20.0

8.0 5.0 8.0

10.0

5.0

40.0

8.0

Fire duration, min 31 36 37 38 43 45 50 51 52 54 57 61 61 63 64 66 67 69 71 72 74 78 79 81 84 85 85 85 86 90 91 92 96 98 100 106 108 112 115 119 120

Incident flux, Btu/ ft2 min 62 73 67 83 72 61 70 36 68 85 82 59 70 97 74 97 80 58 79 81 48 88 77 92 92 104 101 76 48 80 71 75 77 61 42 86 103 66 90 103 71

Equivalent exposure, min 0 4 2 6 4 0 4 0 2 8 6 0 4 10 6 10 8 0 6 8 0 10 6 12 12 14 14 6 0 8 44 6 8 0 0 12 16 0 14 18 6

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6 Fire Following Earthquakes

Table 6.18 Effect of room geometry and window size and location on the exposure of exterior walls above venting window openings from 20-lb/ft2 fuel-load compartment fires (sorted on fire duration) Room size, ft Room case 570 569 520 543 566 582 530 509 526 537 542 576 568 561 578 536 541 575 572 518 581 560 522 538 551 545 529 559 577 553 565 535 558 540 562 550 574 567 580 557 564

D 80.0 80.0 20.0 40.0 80.0 80.0 20.0 10.0 20.0 40.0 40.0 80.0 80.0 80.0 20.0 40.0 40.0 80.0 10.0 20.0 80.0 80.0 20.0 40.0 40.0 40.0 80.0 10.0 20.0 40.0 80.0 40.0 80.0 40.0 80.0 40.0 80.0 80.0 80.0 80.0 80.0

W 80.0 80.0 10.0 40.0 80.0 20.0 40.0 20.0 20.0 20.0 40.0 10.0 80.0 40.0 80.0 20.0 40.0 10.0 80.0 10.0 20.0 40.0 20.0 20.0 80.0 40.0 40.0 40.0 80.0 80.0 80.0 20.0 40.0 40.0 40.0 80.0 10.0 80.0 20.0 40.0 80.0

Window size, ft H 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0

w1 80.0 40.0 3.0 40.0 80.0 20.0 3.0 3.0 3.0 20.0 20.0 10.0 20.0 40.0 3.0 10.0 10.0 10.0 3.0 3.0 10.0 20.0 3.0 3.0 3.0 3.0 3.0 10.0 3.0 3.0 10.0 3.0 5.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0

h1 5.0 5.0 3.0 5.0 8.0 8.0 8.0 3.0 3.0 5.0 5.0 8.0 5.0 8.0 8.0 5.0 5.0 8.0 3.0 3.0 8.0 5.0 3.0 3.0 8.0 3.0 3.0 5.0 3.0 3.0 5.0 3.0 5.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0

w2 40.0 40.0 3.0

h2 5.0 5.0 3.0

20.0

8.0

3.0

3.0

10.0 20.0

8.0 5.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

Fire duration, min 125 125 126 127 141 149 150 153 157 162 163 171 186 188 195 216 254 286 297 306 312 365 422 423 547 595 595 669 841 841 939 1,190 1,327 1,683 1,683 2,380 2,380 2,380 3,365 4,759 6,730

Incident flux, Btu/ ft2 min 83 88 80 82 81 67 122 108 89 75 92 64 97 72 148 85 98 56 137 104 78 89 104 83 127 91 109 91 119 104 100 104 91 104 83 109 101 91 106 104 104

Equivalent exposure, min 10 12 10 10 10 2 22 18 14 8 14 0 16 6 30 12 16 0 26 18 8 14 18 10 24 14 20 14 22 18 16 18 14 18 10 20 16 14 18 18 18

6.13

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Table 6.19 Effect of room geometry and window size and location on the exposure of exterior walls above venting window openings from 20-lb/ft2 fuel-load compartment fires (sorted on equivalent exposure) Room size, ft Room case 521 573 544 504 525 508 507 576 519 534 575 539 582 517 579 516 506 513 528 524 563 571 552 527 561 533 548 505 515 556 512 537 549 503 547 581 520 566 570 543 562 502

D 20.0 10.0 40.0 10.0 20.0 10.0 10.0 80.0 20.0 20.0 80.0 40.0 80.0 10.0 20.0 10.0 10.0 10.0 20.0 20.0 80.0 80.0 40.0 20.0 80.0 20.0 40.0 10.0 10.0 40.0 10.0 40.0 40.0 10.0 40.0 80.0 20.0 80.0 80.0 40.0 80.0 10.0

W 10.0 80.0 40.0 10.0 20.0 10.0 10.0 10.0 10.0 40.0 10.0 20.0 20.0 20.0 80.0 20.0 10.0 20.0 20.0 20.0 40.0 80.0 80.0 20.0 40.0 40.0 40.0 10.0 20.0 80.0 20.0 20.0 40.0 10.0 40.0 20.0 10.0 80.0 80.0 40.0 40.0 10.0

Window size, ft H 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0

w1 10.0 80.0 40.0 10.0 20.0 10.0 10.0 10.0 10.0 40.0 10.0 20.0 20.0 10.0 80.0 10.0 5.0 10.0 10.0 20.0 40.0 80.0 80.0 10.0 40.0 40.0 20.0 3.0 5.0 80.0 10.0 20.0 40.0 5.0 20.0 10.0 3.0 80.0 80.0 40.0 3.0 3.0

h1 8.0 8.0 8.0 5.0 8.0 8.0 5.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 5.0 5.0 8.0 8.0 5.0 8.0 8.0 8.0 5.0 8.0 5.0 8.0 3.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 8.0 3.0 8.0 5.0 5.0 3.0 5.0

w2 10.0

h2 8.0

10.0 10.0 10.0

8.0 5.0 8.0

20.0 20.0 10.0

8.0 8.0 8.0

10.0 5.0

5.0 5.0

10.0

8.0

40.0 80.0

8.0 8.0

10.0

5.0

20.0 3.0 5.0 40.0

8.0 3.0 5.0 5.0

20.0

5.0

20.0

5.0

3.0

3.0

40.0

5.0

3.0

3.0

Incident Fire duration, flux, Btu/ ft2 min min 74 48 31 62 112 66 61 59 86 48 51 36 45 61 171 64 100 42 69 58 286 56 98 61 149 67 37 67 52 68 36 73 43 72 50 70 61 70 91 71 120 71 92 75 85 76 64 74 188 72 71 79 79 77 57 82 38 83 72 81 54 85 162 75 96 77 67 80 90 80 312 78 126 80 141 81 125 83 127 82 1,683 83 78 88

Equivalent exposure, min 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 4 4 4 4 4 6 6 6 6 6 6 6 6 6 8 8 8 8 8 8 8 10 10 10 10 10 10 (continued)

470

6 Fire Following Earthquakes

Table 6.19 (continued) Room size, ft Room case 538 514 511 536 523 532 555 569 526 542 559 510 560 546 567 558 554 545 531 541 568 574 565 540 557 522 509 580 535 501 553 564 518 529 550 530 577 551 572 578

D 40.0 10.0 10.0 40.0 20.0 20.0 40.0 80.0 20.0 40.0 80.0 10.0 80.0 40.0 80.0 80.0 40.0 40.0 20.0 40.0 80.0 80.0 80.0 40.0 80.0 20.0 10.0 80.0 40.0 10.0 40.0 80.0 20.0 20.0 40.0 20.0 20.0 40.0 10.0 20.0

W 20.0 20.0 20.0 20.0 20.0 40.0 80.0 80.0 20.0 40.0 40.0 20.0 40.0 40.0 80.0 40.0 80.0 40.0 40.0 40.0 80.0 10.0 80.0 40.0 40.0 20.0 20.0 20.0 20.0 10.0 80.0 80.0 10.0 40.0 80.0 40.0 80.0 80.0 80.0 80.0

Window size, ft H 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0

w1 3.0 3.0 5.0 10.0 10.0 20.0 40.0 40.0 3.0 20.0 10.0 3.0 20.0 10.0 3.0 5.0 20.0 3.0 10.0 10.0 20.0 3.0 10.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0

h1 3.0 3.0 5.0 5.0 5.0 5.0 5.0 5.0 3.0 5.0 5.0 5.0 5.0 5.0 3.0 5.0 5.0 3.0 5.0 5.0 5.0 3.0 5.0 8.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 8.0 3.0 8.0 3.0 8.0

w2 3.0 3.0

h2 3.0 3.0

20.0 40.0 3.0

5.0 5.0 3.0

10.0 3.0

5.0 3.0

20.0 3.0

5.0 3.0

20.0

5.0

3.0

3.0

Fire duration, min 423 63 66 216 106 81 84 125 157 163 669 85 365 115 2,380 1,327 85 595 108 254 186 2,380 939 1,683 4,759 422 153 3,365 1,190 119 841 6,730 306 595 2,380 150 841 547 297 195

Incident flux, Btu/ ft2 min 83 97 97 85 86 92 92 88 89 92 91 104 89 90 91 91 101 91 103 98 97 101 100 104 104 104 108 106 104 103 104 104 104 109 109 122 119 127 137 148

Equivalent exposure, min 10 10 10 12 12 12 12 12 14 14 14 14 14 14 14 14 14 14 16 16 16 16 16 18 18 18 18 18 18 18 18 18 18 20 20 22 22 24 26 30

6.13

Northeast Asia

471

and perhaps should be excluded. They are included in the results, however, because they are within the range of room and window geometries being examined. Table 6.10 shows that the most severe exterior fire exposure was 19 min, and it occurred from the equivalent of a 1-h standard fire. All of the more severe cases occurred in rooms ventilated by a single narrow window. This was to be expected since an almost unventilated fire would result in a large proportion of released volatiles in the room, and these would be starved for combustion air. Consequently the volatiles would burn after venting out the window, where combustion air is available. Table 6.12 shows that the most severe cases of exterior fire exposure was 30 min for what is defined as a 2-h standard room fire. Comparing Tables 6.10 and 6.12 shows essentially the same order of room cases for the more severe exposures. However, doubling the fuel density does not result in twice the equivalent exposure. The fact that some measurable exterior fire exposure can be expected when a room fire vents out the windows strongly suggests that some minimum level of fire resistance be required of all exterior walls.

Appendix: Computer Subroutines

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476

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TITLE BLOCK

MAIN PROGRAM Part 1. Basic analysis

Part 2. Calculation of missile impact data

SUBROUTINE.

Interpolation procedure for evaluating the coefficient for moment of inertia calculation

SUBROUTINE.

Evaluation of stiffness coefficient

SUBROUTINE.

National Defence Research Committee formulae

SUBROUTINE.

Bechtel formulae

SUBROUTINE.

ACE formulae

SUBROUTINE.

CKW-BRL formulae

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480

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482

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496

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498

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502

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503

504

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506

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507

508

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509

510

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512

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514

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515

516

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517

518

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519

520

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521

522

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523

524

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525

526

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527

528

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529

530

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531

532

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References

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Fire Ecology1 Bond, W.J., van Wilgen, B.W.: Fire and Plants. Population and Community Biology Series, vol. 14, p. 263. Chapman and Hall, London (1996) Bond, W.J., Woodward, F.T., Midgley, G.F.: The global distribution of ecosystems in a world without fire. New Phytol. 165(2), 525–537 (2005). doi:10.1111/j.1469-8137.2004.01 252.x Booysen, P. de V., Tainton N.M. (eds.): Ecological Effects of Fire in South African Ecosystems. Ecological Studies48, Springer, Berlin, 426 p (1984) Brooks, M.L., D’Antonio, C.M., Richardson, D.M., Grace, J.B., Keeley, J.E., Ditomaso, J.M., Hobbs, R.J., Pellant, M., Pyke, D.: Effects of invasive alien plants on fire regimes. Bioscience 54, 677–688 (2004) Gill, A.M., Groves, R.H., Noble, I.R. (eds.): Fire and the Australian Biota. Australian Academy of Science, Canberra (1981). 582p Goldammer, J.G. (ed.): Fire in the Tropical Biota. Ecosystem Processes and Global Challenges. Ecological Studies 84. Springer Verlag, Berlin (1990). 497 p Goldammer, J.G. (ed.): Tropical Forests in transition. Ecology of Natural and Anthropogenic Disturbance Processes. Birkhauser-Verlag, Basel (1992). 270 p Goldammer, J.G., Furyaev, V.V. (eds.): Fire in Ecosystems of Boreal Eurasia. Kluwer Academic Publishers, The Hague (1996). 528 p Goldammer, J.G., Jenkins, M.J. (eds.): Fire and Ecosystem Dynamics. Mediterranean and Northern Perspectives. SPB Academic Publishers, The Hague (1990). 199 p Johnson, E.A., Miyanishi, K. (eds.): Forest Fires. Behaviour and Ecological Effects. Academic Press, San Diego, CA (2001). 594 p Kozlowski, T.T., Ahlgren, C.E. (eds.): Fire and Ecosystems. Academic Press, New York, NY (1974). 542 p Trabaud, L. (ed.): The Role of Fire in Ecological Systems. SPB Academic Publishers, The Hague (1987). 157 p van Wilgen, B., Andreae, M.O., Goldammer, J.G., Lindesay, J. (eds.): Fire in Southern African Savannas. Ecological and Atmospheric Perspectives. The University of Witwatersrand Press, Johannesburg (1997). 256 p Wein, R.W., MacLean, D.A. (eds.): The Role of Fire in Northern Circumpolar Ecosystems. John Wiley & Sons, New York, NY (1983). 322 p

1

Note: The following bibliography does not intend to provide an all-embracing list of sources. It rather aims to facilitate the search or literature on wildland fire ecology, history, management and related fields such as atmospheric chemistry, climatology, and remote sensing. The list includes major monographs, sourcebooks, and several peer-reviewed journal publications with references to a broad secondary literature, and well as internet portals facilitating a literature search.

560

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Whelan, R.J.: The Ecology of Fire. Cambridge Studies in Ecology. Cambridge University Press, Cambridge (1995). 346 pp Wright, H.A., Bailey, A.W.: Fire Ecology. United States and Southern Canada. John Wiley & Sons, New York, NY (1982). 501 p

Fire History Pyne, S.J.: Fire in America. Princeton University Press Press, Princeton, NJ (1982). 654 p Pyne, S.J.: Burning bush. A fire history of Australia. Henry Holt and Company, New York, NY (1991). 520 p Pyne, S.J.: World Fire. Henry Holt, New York, NY (1995). 379 p Pyne, S.J.: Vestal Fire. An Environmental History, Told Through Fire, of Europe and Europe’s Encounter with the World. University of Washington Press, Washington, DC (1997). 680 p

Atmospheric Chemistry, Climatology, Remote Sensing Ahern, F., Goldammer, J.G., Justice, C. (eds.): Global and Regional Vegetation Fire Monitoring From Space: Planning a Coordinated International Effort. SPB Academic Publisher, The Hague (2001). 302 p Clark, J.S., Cachier, H., Goldammer, J.G., Stocks, S.J. (eds.): Sediment Records of Biomass Burning and Global Change. Springer-Verlag, Berlin (1997). 489 p Crutzen, P.J., Goldammer, J.G.: Fire in the Environment: The Ecological, Atmospheric, and Climatic Importance of Vegetation Fires. Dahlem Workshop Reports. Environmental Sciences Research Report, vol. 13. John Wiley & Sons, Chichester (1993). 400 p Innes, J., Beniston, M., Verstraete, M.M. (eds.): Biomass Burning and its Interrelationships with the Climate System. Kluwer Academic Publishers, The Hague (2000)

Fire Management Brown, A.A., Davis, K.P.: Forest Fire. Control and use. McGraw Hill, New York (1973). 686 p Chandler, C. et al.: Fire in Forestry, Vol. I and II. John Wiley & Sons, New York, (1983) 450 + 298 p. Heikkila, T.V., Gronqvist, R., Jurve´lius, M.: Handbook on Forest Fire Control. A Guide For Trainers, vol. 21. Forestry Training Programme (FTP) Publication, Helsinki (1993). 239 p Pyne, S.J., Andrews, P.J., Laven, R.D.: Introduction to Wildland Fire, 2nd edn. John Wiley & Sons, New York, NY (1996). 769 pp Teie, C.W.: Fire Officer’s Handbook on Wildland Firefighting. CA Deer Valley Press, 601 p. (2003) Teie, C.W.: Fire Manager’s Handbook on Veld and Forest Fires—Strategy, Tactics and Safety. South African Edition (edited by Christiaan F. Pool). Southern African Institute of Forestry, 488 p. (2003)

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International Fire Management Guidelines: Food and Agriculture Organization of the United Nations (FAO): Guidelines on Fire Management in Temperate and Boreal Forests. Forest Protection Working Papers, Working Paper FPI1/E. Forest Resources Development Service, Forest Resources Division. FAO, Rome (2002) Goh, K.T., Schwela, D.H., Goldammer, J.G., Simpson O.: Health Guidelines for Vegetation Fire Events. Background Papers. Published on behalf of UNEP, WHO, and WMO. Institute of Environmental Epidemiology, Ministry of the Environment, Singapore. Namic Printers, Singapore, 498 p (1999) Goldammer, J.G., de Ronde C. (eds.): Wildland Fire Management Handbook for Sub-Sahara Africa. Global Fire Management Center and Oneworldbooks, Freiburg—Cape Town (2004) International Tropical Timber Organization (ITTO): ITTO Guidelines on Fire Management in Tropical Forests. ITTO Policy Development Series No.6. ITTO, Yokohama, 40 p (1997) Schwela, D.H., Goldammer J.G., Morawska L.H., Simpson O.: Health Guidelines for Vegetation Fire Events. Guideline document. Published on behalf of UNEP, WHO, and WMO. Institute of Environmental Epidemiology, Ministry of the Environment, Singapore. Double Six Press, Singapore, 291 p. (1999) Schwela, D.H., Morawska L.H., Abu Bakar bin Jafar.: Health Guidelines for Vegetation Fire Events. Teachers’ Guide. Published on behalf of UNEP, WHO, and WMO. Institute of Environmental Epidemiology, Ministry of the Environment, Singapore. Double Six Press, Singapore, 114 p (1999)

An Introduction to Fire Dynamics Law, M.: A relationship between fire grading and building design and contents. Fire Research Note No. 877 (1971) Law, M.: Heat radiation from fires, and building separation. Fire Research Technical Paper No. 5. HMSO, London (1963) Law, M., O’Brien, T.: Fire Safety of Bare External Structural Steel. Constructional Steel Research and Development Organisation, London (1981) Lawson, D.I.: Fire and the atomic bomb. Fire Research Bulletin No. 1. HMSO, London (1954) Lawson, D.I., Simms, D.L.: The ignition of wood by radiation. Br. J. Appl. Phys. 3, 288–292 (1952) Le Chatelier, H., Boudouard, O.: Limits of flammability of gaseous mixtures. Bulletin de la Socie´te` Chimique (Paris) 19, 485 (1898) Lee, B.T.: Quarter scale modeling of room fire tests of interior finish. NBSIR 81-2453. National Bureau of Standards (1982) Lees, F.P.: Loss Prevention in the Process Industries, vols. 1 and 2. Butterworths, London (1980) Lewis, B.: Selected Combustion Problems, p. 177. AGARD (Butterworths) (1954) Lewis, B., von Elbe, G.: Combustion, Flames and Explosions of Gases, 2nd edn. Academic, New York (1961) Lie, T.T.: Fires and Buildings. Applied Science, London (1972) Lie, T.T.: Characteristic temperature curves, for various fire seventies. Fire Technol. 10, 315–326 (1974) Linnett, J.W., Simpson, C.J.S.M.: Limits of inflammability. In: Sixth Symposium (International) on Combustion, pp. 20–27. Reinhold, New York (1957) Lovachev, L.A., Babkin, V.S., Bunev, V.A., V’yun, A.V., Krivuhn, V.N., Baratov, A.N.: Flammability limits: an invited review. Combust. Flame 20, 259–289 (1973) Lyons, J.W.: The Chemistry and Uses of Fire Retardants. John Wiley, New York (1970)

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Mackinven, R., Hensel, J.G., Glassman, I.: Influence of laboratory parameters on flame spread over liquid surfaces. Combust. Sci. Technol. 1, 293–306 (1970) Madorsky, S.L.: Thermal Degradation of Organic Polymers. Inter Science, John Wiley, New York (1964) Magee, R.S., McAlevy, R.F.: The mechanism of flame spread. J. Fire Flamm. 2, 271–297 (1971) Malhotra, H.L.: Design of Fire-Resisting Structures. Surrey University Press (1982) Malhotra, H.L.: Movement of smoke on escape routes. Instrumentation and effect of smoke on visibility. Fire Research Note Nos. 651, 652, and 653 (1967) Marchant, E.W.: Effect of wind on smoke movement and smoke control systems. Fire Saf. J. 7, 55–63 (1984) Marchant, E.W.: Some aspects of human behavior and escape route design. In: 5th International Fire Protection Seminar, Karlsruhe, September 1976 Margenau, H., Murphy, G.M.: The Mathematics of Chemistry and Physics. Van Nostrand, Princeton, NJ (1956) Markstein, G.H.: Radiative energy transfer from turbulent diffusion flames. Combust. Flame 27, 51–63 (1976) Markstein, G.H., de Ris, J.N.: Flame spread along fuel edges. J. Fire Flamm. 6, 140–154 (1975) Markstein, G.H., de Ris, J.: Upward fire spread over textiles. In: 14th Symposium (International) on Combustion, pp. 1085–1097. The Combustion Institute, Pittsburgh (1972) Markstejn, G.H.: Radiative energy transfer from gaseous diffusion flames. In: 15th Symposium (International) on Combustion, pp. 1285–1294. The Combustion Institute, Pittsburgh (1975) Markstejn, G.H.: Radiative properties of plastics fires. In: 17th Symposium (International) on Combustion, pp. 1053–1062. The Combustion Institute, Pittsburgh (1979) Martin, S.B., Wiersma, S.J.: An experimental study of flashover criteria for compartment fires. Final Report, Products Research Committee PRC No. P-77-3-1, Stanford Research Institute, International Project No. PYC 6496 Martin, S.: Diffusion-controlled ignition of cellulosic materials by intense radiant energy. In: 10th Symposium (International) on Combustion, pp. 877–896. The Combustion Institute, Pittsburgh (1965) Maulen, A.W.: Horizontal projections in the prevention of spread of tire from storey to storey. Report TR52/75/397. Commonwealth Experimental Building Station, Australia (1971) McCaffrey, B.J.: Purely buoyant diffusion flames: some experimental results. NBSIR 79-1910. National Bureau of Standards (1979) McCaffrey, B.J., Quintiere, J.G., Harkleroad, M.F.: Estimating room temperatures and the likelihood of flashover using fire test data correlations. Fire Technol. 17, 98–119; 18, 122 (1981) McCarter, R.J.: Smoldering of flexible polyurethane foam. J. Consumer Prod. Flamm. 3, 128–140 (1976) McCarter, R.J.: Smoldering combustion of cotton and rayon. J. Consumer Prod. Flamm. 4, 346–357 (1977) McCarter, R.J.: Smoldering combustion of wood fibers: cause and prevention. J. Fire Flamm. 9, 119–126 (1978) McGuire, J.H.: Heat Transfer by Radiation. Fire Research Special Report No. 2. HMSO, London (1953) MeAlevy, R.F., Magee, R.S.: The mechanism of flame spreading over the surface of igniting condensed phase materials. In: 12th Symposium (International) on Combustion, pp. 215–227 (1969) Meidl, J.: Explosive and Toxic Hazardous Materials. Glencoe Press, Fire Science Series (1970) Meyer, E.: A theory of flame propagation limits due to heat loss. Combust. Flame 1, 438–452 (1957) Ministry of Aviation: Report of the Working Party on Aviation Kerosene and Wide-Cut Gasoline. HMSO (1962) Mitchell, N.D.: Quarterly Journal of the National Fire Protection Association, vol. 45, p. 165 (1951)

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