Fire: Fire safety and fire resistant design of steel structures for buildings according to Eurocode 3 9075146043, 9789075146042

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Steel Design 2

Fire

A.F. Hamerlinck

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Fire safety and fire resistant design of steel structures for buildings according to Eurocode 3

text dr.ir. A.F. Hamerlinck editing ir. C.H. van Eldik / Bouwen met Staal graphic design Karel Ley / Fig.84-Reclamestudio published by

Bouwen met Staal

ISBN (print) ISBN 978-90-75146-04-2 ISBN (PDF) ISBN 978-3-433-61156-2 The publication of this textbook has been made possible by: Bauforumstahl

www.bauforumstahl.de

Bouwen met Staal

www.bouwenmetstaal.nl

Infosteel

www.infosteel.be

Stahlbau Zentrum Schweiz

www.szs.ch

Tata Steel

www.tatasteelconstruction.com

World Steel Association

www.constructsteel.org

© Bouwen met Staal 2021 All rights reserved. No part of this publication may be reproduced, stored in an automated database and/or made public – in any form or by any means, electronic, mechanical, photocopying, recording or in any other way – without prior written permission from the publisher. The utmost care was taken in the preparation of this publication. Nevertheless, any errors and imperfections can not be ruled out. The publisher excludes – also for the benefit of all those who have participated in this publication – any liability for direct and indirect damage, caused by or in connection with the application of this publication.

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Colophon

the same author. The English translation has been prepared by dr.ir. A.F. Hamerlinck (Bouwen met Staal and Adviesbureau Hamerlinck), ing. K. Michielsen (Infosteel) and prof.ir. H.H. Snijder (Eindhoven University of Technology) and checked by dr. G. Couchman (The Steel Construction Institute). The text is based on the (English) EN version of the Eurocodes using default and/or recommended values. Where a country can make a national choice – or when non-contradictory complementary information may be used – this is indicated by the following symbol:

NA

. Separate annexes

contain the national choices for Belgium, Luxembourg, The Netherlands and Switzerland. These annexes – as well as any errata, corrections and additions to this textbook – can be downloaded free of charge from the websites of the (national) organisations. Fire is the second textbook in the Steel Design series. Previously published is Structual basics (Steel Design 1).

Illustrations All unnamed photographs and all drawings come from the archive of Bouwen met Staal. L = left, R = right. ABT 1.13, 1.26, p. 4-1

Moolenaar Fotografie 1.25

a/d amstel architecten 1.24, p. 3-1

Ossip Architectuurfotografie 3.26L

AVEQ 1.9

S. Pedneault 1.1

BAM Infra 3.14

Philippe Piraux 3.1

CTICM 3.10

Tom de Rooij Vakfotografie 1.11L

C.H. van Eldik 3.21

Tyco Fire Suppression & Building Products 1.4

Y. de Groot 1.15, p. 2-1

P. Varkevisser 1.5L

Bart van Hoek Architectuurfotografie 3.19

VolkerWessels 3.23

Fas Keuzenkamp 2.21

VVKH Architecten 1.5R

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This textbook was originally published in 2010 by Bouwen met Staal in Dutch as Brand by

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1-2

1.1 What is fire safety?

1-2



1.1.1 Goals of fire safety

1-2



1.1.2 Measures for fire safety

1-5

1.2 Development of a fire

1-7

1.3 Design of fire safe buildings

1-9



1.3.1 Construction concept

1-9



1.3.2 Monitoring concept

1-16



1.3.3 Extinguishing concept

1-17

1.4 Fire safety requirements

1-18



1.4.1 Building regulations

1-18



1.4.2 Structural fire safety

1-20



1.4.3 Equivalent fire safety

1-21

1.5 Fire as an accidental action

1-23

1.6 Behaviour of steel sections during fire

1-26

1.7 Literature

1-29

2

4

Fire safety

Calculation of the fire resistance

2-2

2.1 Terms and conditions

2-2



2.1.1 Standard fire curve

2-3



2.1.2 Effective yield strength of steel in the fire situation 2-3



2.1.3 Degree of utilization

2-3



2.1.4 Section factor

2-4



2.1.5 Critical steel temperature

2-7



2.1.6 Cross-section classification in the fire situation

2-8

2.2 Calculation of the thermal response

2-10



2.2.1 Net heat flux to the steel member

2-10



2.2.2 Heating of unprotected steel sections

2-10



2.2.3 Heating of unprotected galvanized steel sections 2-12



2.2.4 Heating of protected steel sections

2-13

2.3 Calculation of the mechanical response

2-17



2-17

2.3.1 Connections

2.4 Tension members

2-20

2.5 Beams not sensitive to lateral torsional buckling

2-21

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Content

2-26

2.7 Beams sensitive to lateral torsional buckling

2-31

2.8 Integrated beams, unprotected

2-33



2.8.1 Thermal behaviour

2-33



2.8.2 Simple calculation method

2-34



2.8.3 Advanced calculation method

2-35

2.9 Integrated beams, protected

2-43

2.10 Literature

2-46

3

Fire safety engineering

3-2

3.1 What is fire safety engineering?

3-3



3.1.1 Developments

3-4

3.2 Natural fires and local fires

3-5



3.2.1 LOCAFI

3-6



3.2.2 Example of a car park

3-8

3.3 Natural fires and compartment fires

3-10



3.3.1 Background

3-10



3.3.2 Method using zone models

3-10



3.3.3 Ozone

3-13

3.4 Natural fires and external steel structures

3-14

3.5 System behaviour of steel structures

3-16



3-18

3.5.1 MACS

3.6 Literature

3-21

4

4-1

Design tables

4.1 Reduction factor ky,θ derived from equation (4.22)

in EN 1993-1-2; see equation (2.2) in Fire 2 4-2

4.2 Reduction factors ky,θ and kE,θ according to table 3.1

of EN 1993-1-2

4-6

4.3 Reduction factor for the design load level in the fire situation ηfi for different occupancies and load factors 4-7 4.4 Steel temperature θa of an unprotected I-section

exposed to the standard fire curve for non-galvanized



and galvanized steel

4-9

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2.6 Columns

sections

4-14

4.6 Steel temperature θa of unprotected IPE and

HE sections after 30 minutes exposure to the



standard fire curve for both non-galvanized and



galvanized steel

4-17

4.7 Steel temperature θa,ext of an unprotected

I-section exposed to the external fire cuve

4-19

4.8 Critical steel temperature θa,cr for centrically loaded

compression members in grade S235 steel

4-20

4.9 Critical steel temperature θa,cr for centrically loaded

compression members in grade S275 steel

4-26

4.10 Critical steel temperature θa,cr for centrically loaded

compression members in grade S355 steel

4-32

4.11 Critical steel temperature θa,cr for centrically loaded

compression members in grade S420 steel

4-38

4.12 Critical steel temperature θa,cr for centrically loaded

compression members in grade S460 steel

4-44

4.13 Cross-section class of IPE, HEA, HEB and HEM

sections in bending and compression for grades



S235, S355, S420 and S460 steel

4-50

4.14 Cross-section class of readily available hollow sections

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in compression for grades S235, S275 and S355 steel 4-53

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4.5 Section factor A/V for IPE, HEA, HEB and HEM

Analysis and design of steel structures for buildings according to Eurocode 0, 1 and 3

Steel Design 1

H.H. Snijder H.M.G.M.  Steenbergen

Structural basics

Steel Design1

1 Structural safety 1.1 Probability of failure 1.2 Reliability principles 1.3 Design value of resistance 1.4 Design value of actions 1.5 Reliability 1.6 EN 1990 2 Actions and deformations 2.1 Structural requirements and relevant concepts 2.2 Structural safety 2.3 Permanent loads 2.4 Variable actions 2.5 Serviceability criteria 2.6 Actions according to EN 1991 2.7 Worked examples 3 Modelling 3.1 Schematisation 3.2 Cross-section properties

Structural basics This textbook covers the design and analysis of steel structures for buildings according to EN 1990 (Eurocode 0), EN 1991 (Eurocode 1) and EN 1993 (Eurocode 3). It is effective as a textbook for students and as a reference guide to the Eurocodes 0, 1 and 3 for practising structural engineers. The text is based on the (English) EN version of the Eurocodes using default and/or recommended values. Where a country can make a national choice – or when non-contradictory complementary information may be used – this is indicated by a symbol (black square). Separate annexes contain (for now) the national choices for Belgium, Luxembourg, The Netherlands and Switzerland. These annexes can be downloaded free of charge from the websites of the (national) organisations as well as any errata, corrections and additions to this textbook. H.H. Snijder and H.M.G.M. Steenbergen, Structural basics. Analysis and design of steel structures for buildings according to Eurocode 0, 1 and 3 (Steel Design 1), published by Bouwen met Staal, Zoetermeer 2019, ISBN 979-90-72830-98-2, format 23x25 cm, 272 p. Also available as e-book at Wiley / Ernst & Sohn with ISBN 978-34-33610-69-5.

4 Analysis 4.1 Frames 4.2 Analysis methods 4.3 Braced frame 4.4 Unbraced frame 4.5 EN 1993-1-1, chapter 5 5 Analysis methods 5.1 Linear elastic analysis (LA) and materially nonlinear analysis (MNA) 5.2 Linear buckling (bifurcation or eigenvalue) analysis (LBA) 5.3 Geometrically nonlinear elastic analysis including imperfections (GNIA) 5.4 Geometrically and materially nonlinear analysis including imperfections (GMNIA) 6 Assessment by code checking 6.1 Standards (codes) and guidelines for steel structures 6.2 EN 1993: Eurocode 3 for steel structures 6.3 Assessment procedure 6.4 Modelling for analysis 6.5 Structural analysis 6.6 Force distribution and deformations 6.7 Design of cross-sections and members 6.8 Design of connections 7 Resistance of cross-sections 7.1 General principles 7.2 Section properties 7.3 Single internal forces 7.4 Combined internal forces 7.5 Elastic theory preliminary work | fire | 7.6 Plastic theory

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Structural basics

CONTENT

Steel Design 1

H.H. Snijder H.M.G.M.  Steenbergen

Structural basics

Fire safety and fire resistant design of steel structures for buildings according to Eurocode 3

Education and high quality textbooks are crucial to developing an interest in steel structures and their benefits

Steel Design 2

Fire

A.F. Hamerlinck

for clients, architects and designers. However, despite the need to inspire the industry’s next generation, many textbooks on steel structures are commissioned on a low

Steel Design 1

budget, resulting in material that lacks imagination and tends to feature, at best, moderate illustrations. These textbooks are usually intended for high school and university level students, as well as designers who are not Steel Design 2

yet specialised in steel and steel construction. Therefore, it is vital that lecturers have access to up-to-date books that offer clear and concise explanations, while inspiring readers about the possibilities of steel through beautiful graphics and images. Steel Design is a set of English textbooks translated from the original Dutch that are based on the EN version of Eurocode with differences in nationally defined parameters included in an annex. These textbooks are intended for high-school and university level students. The content is applicable to designers who are not specialised in steel and steel construction.

World Steel Association worldsteel has supported the development of study material related to steel in construction since 2018. This allows future architects and designers to take advantage of steel products and their features that support designs that meet the circular economy principles. A separate opt-in programme has been developed called 'constructsteel.org' and is able to be joined by steel producers and construction industry related organisations upon application. This programme focusses on the construction market sector exclusively to promote steel and steel products. Please see www.worldsteel.org and www.constructsteel.org for further details about the steel industry and specifically the construction market.

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Steel Design series

Analysis and design of steel structures for buildings according to Eurocode 0, 1 and 3

Fire safety

dr.ir. A.F. Hamerlinck

Bouwen met Staal and Adviesbureau Hamerlinck

fire safety

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Fire

The safety of buildings in case of fire is a subject, which is relatively unfamiliar to many structural engineers. This is strange because fire is one of the actions – along with e.g. self-weight, variable loads and wind – which structures have to withstand. By taking the fire load case into account early in the design phase, it is possible to assure sufficient fire safety of a structure at minimum cost. This chapter first describes the objectives of fire safety and the many measures, which a designer can take in order to meet the requirements concerning fire safety. Next, how a fire can develop is discussed – depending on the chosen fire safety concept – and which fire safety requirements the national building regulations ask for. The terms ‘main load bearing structure’ and ‘equivalent safety’ for fire conditions are also discussed. Finally, the fire load case as an accidental action, and the behaviour of steel sections at elevated temperatures, are briefly discussed.

1.1 What is fire safety? Fire is a chemical phenomenon, which usually involves a rapid chemical reaction (oxidation) of a combustible material (e.g. paper or oil) with oxygen. For this reaction to occur, a sufficiently high ignition temperature is required, caused for example by a cigarette, short circuit in an electrical device, or by arson. The largest threat of a fire to people and animals is not so much the flames themselves, but rather the smoke and hot gases. Fire safety concerns measures to prevent the ignition of a fire as much as possible, and limit the risks associated with, and effects of, a fire. This section discusses the objectives of fire safety in general, and provides an overview of the possibilities a designer has to assure the fire safety of a building.

1.1.1 Goals of fire safety Fire causes life-threatening situations for humans and animals (fig. 1.1). For this reason, the probability of occurrence and the possible consequences – casualties and damage – of a fire need to be limited by paying special attention to fire safety during the design, construction and use of the structure. Fire safety protection of buildings has two goals: – preventing fatal accidents (casualties); – reducing direct and indirect damage.

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Fire safety

The safety of humans and animals is in most countries controlled by the government through building regulations. The rules focus on preventing the formation of fire, limiting the number of victims, and preventing the fire spreading to neighbouring buildings. Insurance companies focus more on the limitation of material damage, such as loss of furniture, and interruption to the production process (i.e. the use of the building). Fire safety is an important aspect in the design of buildings and affects the architecture, the building structure and the services. The different design strategies to create a fire-safe building usually consist of a ‘package’ of measures. The use of the building and the organizational aspects – such as evacuation of non-self-reliant people – play an important role. The choice of the measures, which are taken – the fire safety concept – depends mainly on the layout and the use of the building. In public buildings, for example shops and libraries, the required fire safety is achieved through a combination of measures, such as smoke detection systems, smoke exhaust systems, and sprinklers. It is a misunderstanding to think that the fire resistance of a steel structure can only be achieved with protective measures such as fire-resistant coatings or coverings. Sophisticated computational methods are available which, for some cases, can demonstrate the acceptability of unprotected steel in a fire-safe building. Fire safety focuses in general on the following three topics: – safety of users; – smoke control and escape routes; – material damage.

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1.1 Fire causes life-threatening situations for humans and animals.

The measures necessary to save human lives during a fire do not depend on the structural material that is used. These measures are in fact intended to limit the development and spread of a fire, and to maintain the escape routes. For the assessment of fire safety, the number of people in a building, their mobility, and the required evacuation time are of great importance. The chosen measures often depend on the use: are there usually a lot of people in the building – such as in offices, hotels, shops, theatres and hospitals – or are there only a few people present in the building - such as in warehouses. In a hospital for example, the beds would need to be transported to a safe fire compartment on the same floor and then, when necessary, transported downwards in secured elevators.

Smoke control and escape routes The main cause of death during fires is smoke. Smoke contains toxic gases like carbon monoxide and forms an opaque ‘curtain’ which obstructs escaping (fig. 1.2). Required fire safety is therefore expressed as the time (in minutes) which a user needs to exit the building, and which the fire fighters needs to search the building. Sufficient escape routes are essential in order for all occupants to be able to safely exit a building. These routes should be free of obstructions, clearly marked and visible during a fire. It is preferable that these routes are well known by the users, for example because they are used as the main daily access, or as a traffic space.

Material damage The loss of the contents of a building, and interruption to its use, are the greatest material damages in case of a fire. The most effective strategy to limit fire damage is to take measures to prevent a major fire. Active fire safety measures – such as smoke detectors and automatic sprinklers, which limit the spread and the consequences of a fire – are therefore the most effective measures to protect property. An effective compartmentation and/or active measures to prevent the spread of a fire are crucial.

1.2 The main cause of death during a fire is smoke.

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Safety of users

Figure 1.3 gives an overview of the purpose of fire safety and of the main measures that a designer can take in order to reduce the risk of personal injuries and to reduce the damage. The different measures are explained briefly below.

Choice of material The load bearing structure, other building components, and the interior fittings should be made from non-combustible materials as far as is possible. This limits the risk of a fire starting and spreading. Also, the materials used should ensure minimum smoke production, to assure sufficient visibility during escaping and to prevent the danger of inhaling toxic smoke.

Management and maintenance Building managers play an important role in the prevention of fire. Provisions should be made for the safe storage of flammable substances. Equipment such as fire extinguishers and self-closing doors should be properly maintained. The most important how­ever is that the building occupants are sufficiently aware

prevent occurence of fire

of the fire safety issues, and can take appropriate actions in

limit the amount of ignition sources

case of a fire (evacuation according to a plan, and help for less

management and maintenance choice of material early fire detection

self-reliant people).

compartmentation limit smoke development

Escape routes

choice of material

Arranging escape routes – which allow people to quickly leave

sprinkler installation

the building – is the most effective way of preventing fatalities in

early fire detection

a fire. Secure escape routes with associated facilities are there­ fore demanded by all national building regulations.

Education and training Research into the behaviour of people during a fire shows they often react slowly to the first signs of danger. Also, it is often unclear who should take action. In public buildings, providing

prevent development and extension of fire fire safety = prevent (or limit the risk for) accidents and damage by fire in a building

limit the heat

limit fire extension

compartmentation sprinkler installation

ensure a timely warning

early fire detection

ensure proper escape

education and training

evacuate the persons present

less than 3 to 5 m. In shops and public buildings, where people in general are not so familiar with the building, the critical limit of visibility is much higher, at 15 to 20 m. prevent structural failure

1.3 Summary of the goals of fire safety and the measures, which can be taken.

choice of material

management and maintenance

but clear signage of escape routes and measures to prevent ronment, people can escape through smoke with a visibility of

ventilation

sprinkler installation

good information and training of personnel is very important, spreading of fire and smoke are equally so. In a familiar envi-

ventilation

limit the heat provide sufficient fire resistance

fire safety

heat detector and sprinkler installation

escape routes fire safe design structural design passive protection active protection (sprinkler)

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1.1.2 Measures for fire safety

A sprinkler installation (fig. 1.4) helps to extinguish a fire and prevent it spreading. Also smoke development is limited, which reduces the risk of personal accidents (casualties). Due to the relative low temperature at which the sprinklers activate, damage to the contents and structure of a building is limited (see also section 1.3.3).

Fire alarms Fire alarm systems – typically using heat and/or smoke detection – ensure that the people are alerted at an early stage of the fire so that the escape time is maximized. Although the reliability of fire alarm systems is good, in practice false alarms do regularly occur. Fire alarm systems make fast intervention of the fire fighters possible, which reduces the risk of flashover and limits damage.

Compartmentation The subdivision of a building into separate spaces – through smoke and fire walls – is an effective measure to reduce the impact of fire. For this reason, compartmentation plays an important role in all national building regulations.

Ventilation It is desirable to transport smoke and heat to the outside as quickly as possible, rather than keep­ ing it in the building. Indoor spread of smoke and heat not only endangers the people inside a building but can also hinder the fire fighters.

Passive protection A design solution using passive protection means that the load bearing structure is covered with an insulating material, or is ‘wrapped up’ to prevent failure of the structure during a fire (see section 1.3.1). Passive protection is commonly used for steel and timber load bearing structures, and is sometimes also used for concrete structures. For most buildings the use of passive protection is the least effective way of preventing fatalities and reducing economic damage. By the time the temperature in a compartment had become so high that the structure would fail, any persons present would already be dead. The contents of the building, by this time, would also be severely damaged.

Structural design Even without passive protection a steel structure can be designed to have significant fire resistance by using, amongst others, the following measures: – integration of the construction and the load bearing structure (see section 1.3.1); 1.4 Sprinklers extinguish or reduce the fire in size, and minimize material damage. By using sprinklers, the fire safety requirements are in certain cases reduced or even eliminated.

NA

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– correct sizing and detailing of the structural members and joints; – considering how different structural members can interact (e.g. to allow redistribution of forces to adjacent, cooler and therefore more resistant, structural members); – clever positioning of the structural members in relation to where a fire might occur (e.g. placing the steel structure outside the façade, in the open air).

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Sprinkler

By using the natural fire safety concept, it can sometimes be shown that a steel structure can remain unprotected (Fire fighters station, Berkel en Rodenrijs, The Netherlands).

Fire resistant design The temperature curve of a natural fire can be determined accurately with modern computational methods of ‘fire safety engineering’. As a result, the behaviour of a steel structure can be assessed more realistically than by traditional methods, which are based on the standard fire. The required thickness of the protection can therefore be determined more accurately. Sometimes it is also possible with the modern computational methods to show that a steel structure does not have to be protected at all to guarantee sufficient fire safety (fig. 1.5).

1.2 Development of a fire The development of a fire is divided into three phases, namely: the growing phase, the burning phase and the decay phase (fig. 1.6). The growing phase is of great importance because during this phase it is still possible for occupants to escape. With an early alert the fire can still be fought effectively. During the growing phase of a developing fire, the thermal effects are only local. Damage to the structure of the building itself is low and there is no risk of failure of the structure. Combustible materials decompose and there is smoke development. This means that people in the building are in danger. The most dangerous moment is the occurrence of flashover. This marks the transition from the growing to the burning phase: from a not entirely developed (local) to a fully developed fire. The temperature at flashover depends on the degree of combustibility of the materials in the fire area. For cellulosic products (such as paper and timber) this temperature is around 500 ˚C. In a fully developed fire, the temperature rises very rapidly to between 800 and 1000 ˚C. This could lead, after some time, to failure of the load bearing structure. Fighting of the fire in the fire area itself is by this stage impossible. The fire fighters can only protect surrounding spaces and buildings. The temperature during the burning and decay phases (post flashover) depends on many factors, of which the amount of combustible material and the ventilation conditions are the most important.

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1.5

growing phase

burning phase

decay phase

1200

1000

temperature (˚C)

standard fire 800

flashover

400

200

1.6 Development of a natural fire with the growing, burning and decay phase compared to the standard fire.

example natural fire

600

effect of active measures

start fire

0

time (minutes)

These factors differ for each situation. Therefore, the temperature development of the fire also varies from case to case. In figure 1.6 the possible temperature development over time for a real situation is sketched; this is called a natural or physical fire. The standard fire curve is also shown; this is the (assumed) standardized relationship between temperature and time. Based on either a natural fire or the standard fire, the behaviour of structures can be determined, both experimentally (through fire tests) and computationally. Traditionally, individual structural members such as beams and columns are assessed based on the standard fire curve, which was defined in the 1920s. The fire resistance is in this case the time (in minutes) that a member can resist this standard fire under the design level of loading. It is assumed that the standard fire starts at flashover and that in the earlier period (growing phase) all occupants can escape from the building. Modern design methods based on a natural fire – so called ‘fire safety engineering’ – offer the possibility of a more realistic approach. The structure is considered as a whole (or a part of one) in case of a fire. In reality, the temperature development over time in a natural fire determines to what extent the performance, which is expressed in minutes, corresponds to the fire resistance associated with a standard fire. The number of minutes resistance when subject to a standard fire provides only an indication of the real fire resistance. It is primarily a means of classification, and not much value in terms of identifying real minutes safety available for the fire fighters. Finally it should be noted that the (standard) fire resistance of a structural member should not be interpreted as a measure of the available escape time, or time for intervention of the fire fighters. The development of a real (natural) fire and the resulting structural behaviour can differ significantly from that suggested by considering a single structural member in a standard fire test. As a result, the actual fire resistance in minutes can be much longer, or indeed shorter, than that determined in a standard fire test.

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fully developed fire

not-fully developed fire

The fire safety of a building depends on how a fire develops, and on the effectiveness of the fire safety measures. The materials used, the building type, and the use of the building determine the quantity and nature of the combustible materials present, and hence the fire and smoke development. The construction measures (like fire resistant walls), the installations (like sprinklers) and the organizational measures (like trained staff for evacuation assistance) – which, all together, should be appropriate for the specific situation, taking into account building management and maintenance – determine the fire safety of the building. Ensuring fire safety therefore requires an integrated approach. The coherent package of measures is called a fire safety concept, which should be drafted in close consultation between owner, designer and fire fighters. The following fire safety concepts are available: – construction concept; – monitoring concept; – extinguishing concept. Building regulations are usually based on (passive) design requirements with respect to, for instance, flammability and smoke production of materials (so-called ‘reaction to fire’), compartmentation, and the fire resistance of (separating) structures. Achieving fire safety through technical installation measures to monitor and/or extinguish the fire is, in many countries, possible by using the so-called ‘equivalence principle’: the applicant must prove the equivalence of safety using the proposed technical installation measures compared to the safety achieved with passive measures. By using the monitoring and extinguishing concept – which make use of technical installations and are applied more and more – a high level of fire safety can be achieved. This can be possible even when the steel is only partially protected, or even unprotected. 1.7 Construction fire safety concept. Flashover may occur which leads to a very significant development of heat and smoke. Structural failure inside the compartment is accepted.

1.3.1 Construction concept The construction concept is most commonly used to assure fire safety, and is based on fire compartmentation in combination with fire protection of the load bearing structure. The basic assumption

consequence or accepted risk: – no structural failure outside fire compartment; – loss of content; – interruption of building use; – no guarantee to be able to repair the damaged building and resume use.

is that the fire is limited to one compartment, in which flashover may occur (fig. 1.7). This passive concept is especially suitable for buildings, which can easily be subdivided into compartments. Because fire compartments – which are assumed to define the limited area the fire can affect – are a fundamental aspect of this concept, it is acceptable for flashover to occur in the compartment before fire fighting has started. The required fire

temperature (˚C)

NA

flashover is accepted

resistance of the building parts (walls and floors) follows from the requirement that the fire may not extend outside the compartment. This means that the separating and (possibly) load time (minutes)

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1.3 Design of fire safe buildings

duration. When using combustible building materials, it should be ensured that the fire cannot spread via the separating structures. For partition walls, spreading of the fire through joints NA

should be prevented by appropriate detailing. With a carefully designed façade, fire spread to the upper floors (by a fire breaking out and coming back in at another floor level) does not occur. Sometimes it is more effective to use active fire protection measures – designed to prevent flash­ over – by using the monitoring and extinguishing concepts. The fire resistance requirements and provisions can then potentially be reduced, depending on the probability of a fire and the level of acceptable risk. The following solutions are available within the context of the construction concept: exposed steel structure

– designing members for fire (unprotected);



– placing the structure outside the building;

– filling with water (if possible);



– filling or covering with concrete;



– applying intumescent coating;

‘hidden’ steel structure

– structural integration (like integrated floor beams);



– fire protection to insulate structural members.

­Design for fire For structures that only marginally fail to meet the 30 minutes fire resistance requirement, it is often still possible to meet the requirement by making the structure (a little bit) stronger than required for room temperature design. This designing for fire can be done in several ways. Examples are: • Using (slightly) heavier sections. This makes the steel structure a bit more massive, which leads to a slower heating of the members and to a higher strength (structural engineers call this ‘over-designing'). For instance, by choosing a cold-formed square hollow section 200x200x10 mm instead of 200x200x8 mm on the one hand the section factor decreases from Am /V = 125 m–1 to

Am /V = 100 m–1 and as a result the steel temperature after 30 minutes decreases from 800 ˚C to

770 °C (see Fire 4 (Design tables), table 4.1), leading to a 22% less reduction in strength (from ky,θ = 0,121 to ky,θ = 0,148). On the other hand the plastic section modulus increases with 21%

(from Wpl = 421·103 mm3 to Wpl = 508·103 mm3), so the overall result is 48% increase in plactic moment resistance. • Using higher grade steel. This leads to sufficient increase in load bearing capacity even af-

ter the strength of the steel has decreased due to the fire (since there is a larger difference between the stress levels in fire and at room temperature). • Designing the beams and columns to be continuous beams or restrained columns, during a fire. Often a plastic moment distribution occurs in continuous beams during a fire, where the temperatures at the supports are a bit lower than in the spans. The buckling length of columns under fire conditions is often smaller than for ambient temperatures. During a fire, a difference in behaviour of the steel structure inside the compartment, which is exposed to the fire (high temperatures), and in other compartments (ambient temperatures), occurs. 10

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bearing function of the building elements should be maintained throughout the expected fire

section factor

designing for fire. When choosing bigger (heavier) sections, it is preferable to use more compact H sections: these heat up less rapidly than I sections due to the thicker flanges (fig. 1.8), see also

Am V

=

perimeter exposed to fire cross-section area

equal cross-section area different perimeter

section 1.6. Choosing a hollow section with thicker walls is also effective. The computational analyses for these solutions are relatively simple.

Placing the structure outside the building A steel structure placed outside the building (external) heats up more slowly due to cooling by outdoor air. Moreover, during a fire in the building the heat transfer by radiation to the steel structure is only from one side. The load bearing capacity of the external structure therefore

Am V

Am

= large

V

= small

reduces much more slowly than an internal structure during standard fire exposure. Based on the ‘principle of equivalence’ (see section 1.4.3), in many cases an external steel structure can be left unprotected or fewer fire resistance measures will be necessary (fig. 1.9). Under circumstances,

1.8 Thicker sections heat up more slowly than thinner sections with the same cross-section area.

an alternative to fire engineering with respect to the heat transfer to the external steel structure is to take an external fire into account in the analysis which limits the maximum temperature to 680 ˚C. The structure has to be designed to resist this maximum temperature.

Filling with water A steel structure comprising hollow sections can be filled with water (fig. 1.10). During a fire, the water heats up until a maximum temperature of 100 ˚C (boiling point) is reached. The transport of the heated water can be achieved in two ways, namely by: – natural flow; – forced flow. 1.9 External steel structure protected by intumescent coating.

1.10 Circular hollow section filled with water. The heat in the fire exposed steel transfers to the water and is removed by natural or forced flow.

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Good cooperation between the fire engineer and the structural engineer is necessary when

25,2 m

return pipeline

hollow core slab prefab concrete double T beams

steel tubular columns filled with water

steel tubular columns and beams filled with water

supply pipeline

1.11 Fire station in Breda (The Netherlands): circular hollow sections filled with water. A water pump takes away the heated water (forced flow).

With natural flow the physical principle that hot water is lighter than cold water is relied upon, leading to an upward flow of the hot water. A pump may be used to achieve forced flow (fig. 1.11). Whichever flow method is used the temperature of the steel structure can be designed to remain below 200 ˚C; a temperature at which the steel retains its full strength. This makes all durations of fire resistance achievable as long as the water flows, requiring a reliable water supply. Previous experience is desirable before going down the route of a water-filled steel structure. Using water filled columns is particularly interesting for buildings with more than four storeys.

Filling or covering with concrete The heat capacity of a steel member increases strongly when hollow sections are filled with

1.12 Steel sections filled with, or encased in, concrete. The mass of the concrete delays the heating of the steel. Some of the force can be transferred from the steel into the concrete at elevated temperatures.

concrete, or when rolled sections are encased in concrete (fig. 1.12). The heating of the steel is delayed. In addition, loads can be partly transferred from the steel section to the cooler concrete cross-section. Filling of hollow sections is a conventional way of increasing their fire resistance while maintaining the architectural expression of the steel. Partial or total encasement of I and H sections is also common in several European countries. Concrete filled hollow section columns usually have a minimum fire resistance of 30 minutes, even when the concrete is unreinforced and the column is relatively slender. When the steel section and the concrete work together structurally, this is known as steel-concrete composite construction (fig. 1.13). A fire resistance of 120 minutes is achievable. For (the fire resistance of) steel-concrete composite structures, see reference [5]. NA

The free computer program Potfire[3] can be used for the analysis of both reinforced and unreinforced concrete filled hollow section columns. A3C[1] is another free program for the design of steel and composite columns (partially or totally encased with concrete).

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12,6 m

surface: blasted and treated

intumescent coating

finished in desired colour

Applying intumescent coating Intumescent coating is a form of contour encasement that is effectively applied by means of a special paint, spayed of brushed on to blasted surfaces, which are also subject to a primer

1.14 Intumescent coating. During a fire, the coating foams into an insulating layer.

(fig. 1.14). Its behaviour is based on a chemical change of the coating at elevated temperatures. The initially thin coating foams into an insulation layer with a thickness of approximately twenty to fifty times the original (room temperature) thickness. It is possible to apply a coloured finish (top layer) to the coating. In some cases – such as external applications or in humid areas – a top layer is required both to protect the intumescent coating and to prevent corrosion of the steel. Intumescent (fire resistant) coatings make fire resistances up to 120 minutes possible for steel structures. Hollow sections require special attention if an economic coating system is to be achieved. The fire resistance depends strongly on the steel sections used and on the thickness of the coating. It is recommended to choose open sections with relatively thick flanges, or hollow sections with relatively thick walls, and to let a structural engineer determine the critical steel temperature and specify this temperature in the project documentation. To achieve a fire resistance of 60 minutes, a layer thickness of about 0,5 to 1 mm is usually sufficient for compact sections. A significantly thicker layer is required to achieve a fire resistance of 90 or 120 minutes. An intumescent coating generally looks less attractive than normal paint, although the aesthetic possibilities of intumescent coatings have improved significantly over the past years (fig. 1.15). 1.15 Intumescent coating allows the steel structure to be visually exposed (Kennedy-tower, Eindhoven, The Netherlands).

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1.13 Example of a steel-concrete composite column where the steel section is covered with reinforced concrete.

With off-site application any damage that occurs during transportation will need to be repaired, and there will need to be on-site treatment of the joints. Also, attention to the thickness of the coating must be paid, because it affects drying time in the fabrication shop. Most intumescent coatings are suitable for use in a non-aggressive internal environment. Some are suitable for outdoor applications. Approved test reports based on a standardized testing method[11] play a very important role in the approval by regulatory authorities and the fire department. Also, quality assurance during the application of the coating, including controlling the application conditions and checking the applied layer thickness, is important. Specific guidance on NA

quality assurance is available, see [2].

Structural integration The designer can choose to integrate steel columns partially or totally within the depth of a façade or separating wall (fig. 1.16). This is also true for bracing members and other means of providing stability. The floor structure can also be designed such that the steel floor beams are 1.16 Integrated steel in floor and wall structures.

located within the depth of the floor.

integrated beam with a hollow core slab

integrated beam with a deep composite slab

column in a (metal stud) wall

column in a masonry wall

1.17 Integration of a steel column in a timber framed façade (covered with gypsum board on the inner side). Without additional measures, the fire resistance of the column is at least 30 minutes.

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The coating can be applied either off-site, in the fabrication shop, or on the construction site.

low for integrated steel structures. Choosing such a solution does, however, have other design consequences. Also, the steel structure itself is not exposed so its aesthetic benefits can not be used (fig. 1.17). An integrated steel structure always has a fire resistance of 30 minutes and sometimes even 60 minutes. A fire resistance of 120 minutes can be achieved with limited additional measures. The fire resistance of integrated beams can be calculated relatively easy, see Fire 2 (Calculation of fire resistance), section 2.8.

Heat-insulating protection Over-designing, i.e. using bigger members than needed at

1.18 Heat-insulating protection: board encasement around a section and sprayed mortar as a contour encasement.

room temperature, is not a suitable option for a fire resistance of 60 minutes or more. The steel temperature after 60 minutes of fire is more than 900 ˚C, which leads to a strength reduction of 5% or less. However the heating of the steel structure can be slowed down significantly by application of heat-insulating protection in the form of a hollow encasement by suitable boards fixed around the section, or by sprayed mortar as a contour encasement (fig. 1.18, 1.19 and 1.20; see also fig. 1.15). When insulation by boards or sprayed mortar is applied it is often not necessary to consult the structural engineer. The thickness of the protection can be determined based on information provided by the manufacturer, derived from tests[10]. This is based on safe values for the critical steel temperature. However, such a solution does not normally result in the most economical solution, so it is useful to consult a structural engineer. The manufacturer(s) can

1.19 Protection of the bottom flange of an integrated beam with mineral wool boards. With a minimum plate thickness often a fire resistance of 120 minutes can be achieved.

then determine the most economic thickness of the material, based on information from the engineer. If information about the critical steel temperatures is already included in the contract documentation, the contractor can choose the most suitable solution. With heat-insulating protection a fire resistance of 120 minutes can be achieved. The fire resistance of a protected steel section can be calculated relatively easily, see Fire 2, section 2.5 (with example 2.3), 2.2.4 and 2.9.

1.20 Application of a heat-insulating sprayed cementitious mortar layer. Any level of fire resistance can be achieved with this method.

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The costs of additional fire resistance measures are relatively

The monitoring concept is based on automatic fire detection, which automatically sends an alarm signal to the fire department (fig. 1.21), followed by fire fighting. For this concept to be appropriate there must be a fire department – preferably an on-site team or a professional offsite fire brigade – that is adequately equipped and ready 24 hours per day. A monitoring concept offers the possibility of reducing the fire resistance requirement for structural elements, and can be the best option if the normal use of the building requires minimum partitioning. It is a

particularly appropriate in a low-rise building with a small fire load, where a fire usually develNA

ops slowly, so sufficiently fast and effective action by the fire fighters is assured. • Fire detection. Automatic fire alarms are activated by smoke, heat or flames. They work mechanically or electrically. Smoke detection is preferred because this is in general the most effective. When a fire alarm is activated an alarm is generated automatically. To be truly effective, the fire alarm should have a direct connection with the nearest team of fire fighters. Alarms with sound effects – like sirens – are also effective as protection against arson. A sprinkler system is used for controlling or extinguishing the fire but also functions as an automatic alarm. However activation is somewhat slower than an independent alarm because of the method of activation (heat detection by the sprinkler heads and the subsequent water flow causing the switch of the alarm). • Fire fighting. The effectiveness of the fire fighting depends to a large extent on the arrival time of the fire fighters, and on the accessibility of the location of the fire. The use of hand extinguishers is the most obvious, provided that the fire is discovered quickly enough and the people present are familiar with the equipment. Professional fire fighting is done by off-site (municipal) or in-house fire fighters. The advantages of an in-house team of fire fighters are familiarity with the situation, and the short distance to travel to the fire. It is important for all fire fighters that access roads are

1.21 Monitoring fire safety concept. Flashover may be avoided through automatic detection and the intervention of the fire fighters. Heat and smoke development are limited. Requirements for compartmentation and/or fire resistance of the structure can be reduced.

suitable for the vehicles which are used, and there is a sufficient supply of water.

temperature (˚C)

b NA

consequence or accepted risk: – no flashover; – no structural failure in fire compartment; – no structural damage; – minimum damage to content; – no interruption of use; – full refurbishment of the building is possible.

flashover not accepted

effective intervention by fire department automatic detection and fire alarm to fire department

time (minutes)

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1.3.2 Monitoring concept

The extinguishing concept is based on an automatic extinction with water (via sprinklers), or other extinguishing agents, in combination with an automatic alarm to the fire department (fig. 1.22). The extinguishing concept – together with limited or no fire resistance requirements for the structure – is the best choice if the use of the building only allows limited compartmentation. It is most suitable for buildings with an average or high fire load, where there is a chance of rapid fire development. Building owners are often concerned about the damage that can be caused by an extinguishing installation due to the large amounts of water, which could end up on stored goods or production facilities. That is a misconception. Usually a single sprinkler head, or a few localised heads, are enough to extinguish or control a fire and the amount of water used is a lot less than would be used by fire fighters extinguishing the fire. Both the owner and the fire department are alarmed through an automatic alarm. Automatic fire

NA

a

alarm systems and automatic extinguishing systems should be maintained by specialists, once or twice per year.

Sprinklers A sprinkler system ensures that a fire is extinguished at an early stage of development, thereby limiting fire damage. Sprinkler heads are activated when a temperature of 70 ˚C to 140 ˚C is exceeded (depending on the occupancy and the corresponding sprinkler head selected for that situation). The fire temperatures stay relatively low and the steel temperature usually does not exceed 300 ˚C. Failure of the structure will not occur at these temperatures, so the building can be repaired quickly and at relatively low cost. It is often possible to decrease the fire resistance requirement of the structure by 30 or 60 minutes, or even drop it completely, if a sprinkler installation is used. However, fixed rules do not exist in all countries. It is recommended to

NA b

discuss the possibilities with the municipality and the fire brigade at an early stage in the design process. With sprinklers there may therefore be opportunities to use unprotected steel elements,

temperature (˚C)

and to save (significantly) on the costs of the fire resistance measures. consequence or accepted risk: – no flashover; – no structural failure in fire compartment; – no structural damage; – minimum damage to content; – no interruption of use; – full refurbishment of the building is possible.

flashover not accepted

1.22 Extinguishing fire safety concept. Flashover is prevented by automatic extinguishing. Fire protection of the structure is normally unnecessary or can be reduced,

start automatic extinguishing and immediate alarm brandweer

time (minutes)

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1.3.3 Extinguishing concept

damage expectation is much lower compared to other buildings where no sprinklers are a

used. NA

Most sprinkler systems are designed for efficient watering of the building’s contents. This results in an even distribution of the sprinkler heads. With these sprinkler systems, the limitation of the heating of the steel elements gives rise to an indirect favourable effect. Other less common automatic extinguishing systems are specifically designed to cool steel elements. In these specific installations, the position and orientation of the sprinkler heads are determined by the geometry of the steel elements.

1.4 Fire safety requirements This section discusses, in a general way, the safety requirements which are applicable to structures in the case of fire. More specific information on the (prescribed and/or performance based) requirements can vary between European member states. The following topics are discussed below: – background and requirements in building regulations; – structural fire safety; – principle of equivalent fire safety.

1.4.1 Building regulations On a European level, the certification of products is regulated by means of the CPR (Construction Products Regulation), which defines products with harmonised standards and for which CE marking is mandatory. The ‘essential requirement’ fire safety is part of this CE marking. In this framework, the European classification system (reaction to fire classes as well as fire resistance classes of e.g. fire protection) and testing system is of general importance. However, the pre­scription of the requirements and the (fire) safety level are not defined at a European level, but rather by the individual member states. National building regulations usually incorporate requirements concerning fire safety, consisting of requirements for escape routes, the use of materials, which can contribute to fire propagation and produce smoke, compartmentation, and the fire resistance of structures. b NA

Fire resistance is the ability of a structure to fulfil its required functions (load bearing function and/or fire separating function) under a specified load level, for a specified fire exposure and for a specified period of time. Fire resistance therefore has two separate aspects; ‘fire resistance in terms of the load bearing function’ and ‘fire resistance in terms of the fire separating function’. The latter is often less relevant for steel load bearing structures. The term ‘fire resistance in terms of the load bearing function’ is therefore shortened to simply ‘fire resistance’ in this chapter.

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Also, a discount on the fire insurance premium is possible if sprinklers are used and the fire

gas temperature Θg (˚C)

1000 800 Θg = 20 + 345 log10(8t + 1) 600 400 200

0

20

40

60

80

100

120

time t (minutes)

The definition of fire resistance in EN 1991-1-2 is ‘the ability of a structure or a member to sustain specified actions during the relevant fire, according to defined criteria’. The actions to be taken into account during fire are specified in the Eurocode, together with the National Annex of the country in which the building is erected. The same holds for the relevant fire, for which in most cases the ‘standard fire curve’ is applied. However, EN 1991-1-2 also enables the use of other fire curves, whose specific application is defined in the National Annex of each country.

NA

The standard fire curve describes the assumed development of temperature over time and is defined in EN 1991-1-2 (fig. 1.23). Requirements for the ‘fire resistance in terms of the fire separating function’ are important for structures where fire compartmentation is particularly relevant (floors, fire walls and façades). It is the time (in minutes) during which a structure can fulfil its fire separating function when exposed to the standard fire. The most important criteria for a fire separating function are indicated with the letters R, E, I and W. – criterion R: load bearing function (no structural failure); – criterion E: prevent the passage of flames and hot gases and prevent the occurrence of flames on the unexposed side; – criterion I: thermal insulation expressed as surface temperature on the unexposed side (temperature increase not larger than 180 ˚C locally or 140 ˚°C on average); – criterion W: thermal insulation in terms of heat radiation (radiation at 1 m from the unexposed side not larger than 15 kW/m2). Which criteria are relevant often depends on the type of fire separating structure: – floor or inner wall: REI; – façade assessed from inside to outside (fire inside that spreads to the outside): REW; – façade assessed from outside to inside (fire outside that spreads to the inside) for an external fire curve with a maximum temperature increase of 660 ˚C: REI; – glazed inner walls (depending on the situation and country): REW or REI; – smoke separations: RE.

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1.23 Standard fire curve.

– houses and apartments (residential); – hospitals, hotels and prisons (with individual rooms where people sleep, but non-residential); – office, education, sport, retail and public function; – industrial. Building regulations give specific performance requirements in terms of required fire resistance. a

NA

1.4.2 Structural fire safety Structural fire safety concerns the following two objectives: – enabling people to escape from a building early and safely following the outbreak of a fire (require­ ments to keep escape routes intact); – limiting the damage to a building, and particularly preventing progressive collapse (requirements for the main load bearing structure). Building regulations in European countries usually refer to EN 1990 and EN 1991-1-2 for determining the actions to be taken into account during a fire.

Escape routes The first objective means in practice that the escape routes from a compartment, which is on fire, should remain intact for a specific time (should not collapse), should stay accessible (free from other collapsed components), and should stay free from heat and smoke. For this reason, a fire resistance b NA

of 30 or 60 minutes is required in most European countries for all structural members the failure of which would result in an unusable escape route in another compartment. An example is the floor of a compartment above the burning compartment, where an escape route is located. Structures which carry such floors or stairs should also meet this requirement.

Main load bearing structure The second objective means that the main load bearing structure of a building – when there is a fire in a specific fire compartment – should be able to resist the loading for a certain amount of time to prevent progressive collapse of the structures in other fire compartments (where there is no fire). In single-storey buildings with only one fire compartment the fire resistance requirements for the main load bearing structure – if any – are usually less onerous than those for multi-storey buildings. This is due to the lower consequences of failure. Failure of the structure of the fire compartment may – under some circumstances – be acceptable as long as the other fire compartments (where there is no fire) stay intact. In most European countries the required fire resistance of the main load bearing structure depends c

NA

on the occupancy and the height of the building. Besides the explicit requirements for the fire resistance of the main load bearing structures – due to progressive collapse – there are often implicit fire resistance requirements for structural elements in relation to safe escape routes and the prevention of fire spread to other compartments or buildings. These requirements in general are restricted to 30 or 60 minutes.

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Building regulations usually distinguish between different types of occupancy, such as:

1.4.3 Equivalent fire safety In some cases there are no specific requirements for a situation that may occur in practice; in such cases some European countries allow requirements to be defined based on equivalent fire safety. This is the case if the realistic temperature development of the fire differs substantially from

NA

the temperature development of the standard fire curve. The standard fire curve only provides a reasonable approximation of real conditions for relatively small spaces (cellular offices), and for combustion of a large amount of material. In these situations, the applicant for the building permit should show that the design or calculation approach provides an equal safety level. The local authority will decide whether the approach is justified. Early consultation with the fire department and building authorities is advised in these cases. The acceptance may be different depending on the country or municipality. As an illustration, the following examples of equivalent fire safety are briefly discussed below: – open car park; – single-storey building with limited fire load density; – steel structure outside the building; – large atria and open spaces.

Open car park For above ground car parks of which at least one third of the façade surface is open, a large exhaust of heat occurs during a fire as a result of natural ventilation, see Fire 3 (Fire safety engineering), section 3.2.2. Therefore, high temperatures – which are a threat to the load bearing structure – do not easily occur. The temperature development during a fire in an open car park differs to a large extent from the standard fire curve because of both the natural ventilation and the limited fire load, and the rate of heat release of a number of burning cars. An open car-park building can therefore often be built with unprotected steel based on the ‘principle of equivalent safety’ (fig. 1.24). fire safety

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1.24 Open car-park building with unprotected steel.

a

There are often no specified requirements for the fire resistance of the structure for some specific NA

occupancies and uses, for example storage of metals. If the single-storey building is also built with a low amount of combustible materials, there is no danger of failure of the structure because of the low fire load density. The total fire load density in such cases is not larger than 200 MJ/m2 or approximately 10 kg wood per m2, which corresponds with a (standard) fire of 10 minutes. A steel structure without any protection has a fire resistance of approximately 15 to 20 minutes and for that reason will not fail during such a short fire.

External steel structure (outside the building) External structures that are located outside the building façade also need to fulfil certain fire resistance requirements, especially if they are part of the main load bearing structure. If the structure does not have direct contact with the flames from a fire on the inside of the building, the heat to which the structure is exposed is much lower than during a standard fire, see Fire 3, section 3.4. This – in combination with cooling of the steel in the open air – leads to a steel temperature, which is usually much lower than the critical steel temperature (fig. 1.25). For these cases unprotected steel can be used. A calculation method for the heating and mechanical resistance is provided in annex B of EN 1991-1-2 and EN 1993-1-2. In some countries there are requirements for external load-bearing structures with regard to possible fires external to the building (e.g. burning parked lorries or waste containers close to the building, or even the radiation caused by a fire in an adjacent building).

1.25 For this office building, in The Hague (The Netherlands), it could be shown that flames do not spread outside the building, impinging on the structure. The steel structure on the outside of the building is therefore only heated by radiation and this leads to a steel temperature which is lower than the critical steel temperature.

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Single-storey building with limited fire load density

NA b

In large open spaces – for example atria (fig. 1.26), train station halls and exhibition buildings – the standard fire is also not applicable. The point of flashover (after which the whole space is on fire) is usually not reached. A fire can develop and spread in specific situations but usually does not form a threat to the structure, which is often located high above the ground floor. Due to the large volume of the space, and often in combination with limited fire load density, the steel temperature remains limited. Smoke and heat exhaust by ventilation is then a more effective way to increase the fire safety. A calculation method of the heating during a local fire scenario is provided in annex C of EN 1991-1-2 and EN 1993-1-2. See also Fire 3, section 3.2.1.

1.5 Fire as an accidental action National building regulations contain requirements for structures subject to fire. Separate Eurocodes for different building materials contain computational assessment procedures that can be used to show that the load bearing structure as designed satisfies these requirements. The Eurocode for steel structures is EN 1993-1-2 and the one for composite steel-concrete structures is EN 1994-1-2. The fire resistance of a structure or building part can alternatively be determined from tests. EN 13501-2 provides an experimental assessment procedure. The actions that a structure should be able to resist during a fire are provided in EN 1990 and in EN 1991-1-2. Fire is an accidental load case which should be taken into account in the accidental design situation.

1.26 Unprotected steel can often be used in large open spaces, like in the atrium of the University of the Arts in Arnhem, The Netherlands. The temperature is limited because smoke and heat exhaust via the roof.

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Large atria and open spaces

time (minutes) 30 60 90 120

Component approach

0

The fire resistance of a structure is traditionally

deflection (mm)

system

related to the behaviour of separate structural

50

components – such as floors, beams and columns

4,2

– instead of to the behaviour of the structure as 100

a whole. In other words a component approach

4,2

component

is applied, rather than a system approach (fig. 6,0 m

4,5

150

1.27). With the computational assessment methods

0

200

400

600 800 temperature (˚C)

1000

1200

given in the Eurocodes it is possible, in principle, to analyse the behaviour of the whole structure during fire and for example take the

beneficial effect of redistribution of forces, or of the presence of an alternative load path, into

1.27 Example of the difference between component and system behaviour during a standard fire test. The individual beam failed after 25 minutes at a temperature of 800 ˚C. The same beam in a steel frame with composite steelconcrete slabs did not fail even after 120 minutes and with a temperature of 1050 ˚C because of membrane action.

account. Such an approach offers designers possibilities to better describe the behaviour of a structure during a fire, compared to the component approach. Although a system approach often leads to favourable results compared to a component approach, sometimes the results are less favourable. One example of a system approach is the MACS+-method and corresponding software, in which the beneficial membrane effect of composite steel-concrete slabs is taken into account, see Fire 3, section 3.5.1. Applying this method may lead to a safe design with approximately 50% of the secondary steel beams left unprotected[4]. NA

According to EN 1991-1-2, cl. 2.4.1, in case of application of the standard fire curve (see fig. 1.23), the component approach is sufficient and it is not necessary to consider the changing boundary conditions at support ends and the effects of axial or in-plain thermal expansions.

Thermal loading The thermal actions (heating) on a structure depend on the temperature development of the fire. Usually the standard fire curve is applied (see fig. 1.23). The standard fire curve however represents a schematized fire – according to an internationally accepted standard – to which structures are assessed and classified. It should be noted that the real situation during a fire can differ significantly from the standard fire (see section 1.2 and fig. 1.6). Buildings sometimes have a relatively low fire load density, especially in large spaces. This means that the fire risk is limited and that the temperatures in the compartment are lower than for a standard fire during 60 or 90 minutes. When the temperatures in a compartment and the temperature of the steel structure are determined using a computational model, a more realistic estimation of the fire resistance of the structure can be made. This approach is known as the natural (or physical) fire safety concept. EN 1991-1-2, cl. 3.3 allows the use of a natural fire in the analysis. This advanced procedure is especially interesting for steel structues, see Fire 3, section 3.3. Extensive research has been carried out into the factors that contribute to the behaviour of a

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real fire depends on the: – amount and distribution of the combustible material; – rate of heat release of this material; – ventilation (non-fire resistant openings like windows and doors); – geometry of the fire compartment; – thermal properties of the surrounding walls, floor and ceiling. The temperature development over time is different for real fires compared to the standard fire. The heating rate during a fire actually depends on the combustible material, the amount of oxygen available, and the heat exchange through walls and openings. To determine the temperature development in both the fire compartment and the steel structure, the rate of heat release, the fire load density, the ventilation conditions and the thermal properties of the building parts of the enclosure of the compartment, therefore all need to be known. Natural fire models are now internationally accepted. The effects of real fires are analysed based on the credible worst case scenario which could occur in practice. This leads to a larger design freedom compared to using the standard fire approach, while the required safety level is still maintained. Steel structures can sometimes remain unprotected, for example in large open spaces with limited fire load density, in car parks with open façades, stadia, arrival and departure halls of airports and stations, and (high) atria. The use of physical models to describe the behaviour of the fire and the effect on the building and users, is called ‘fire safety engineering’, see Fire 3 (Fire safety engineering).

Mechanical loading Fire is specified as a load case in an accidental design situation. The probability of occurrence is relatively small but the consequences can be severe. According to EN 1990, cl. 6.4.3, the actions under fire conditions need to be accounted for as a load combination. EN 1990, cl. A1.3.2 states NA

that for the partial load factors γG and γQ a value of 1,0 may be used. In an analysis considering the standard fire, EN 1991-1-2, cl. 4.1(4) states that the accidental load (generated by ‘indirect’ mechanical effects during the fire exposure) Aind, d = 0. This means that there are no additional mechanical actions on the structure due to the fire itself, whereas in a real situation these actions may be substantial. The mechanical actions in the accidental load combination fire are:

(1.1)

Where: G permanent action; Q variable action; ψ combination value of a variable action with which the characteristic (extreme) value of the variable action needs to be multiplied.

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real fire, and to the corresponding behaviour of a steel structure. The temperature reached in a

Every country specifies in its National Annex whether the frequent combination value ψ1 has to be used in the accidental load combination fire (according to EN 1990, cl. 4.3.1), or the quasipermanent combination value ψ2. For wind loads ψ1 = 0,2 and ψ2 = 0. The combination values for variable actions depend on the occupancy of the building (category), see EN 1990, table A1.1: ψ1 = 0,5; ψ2 = 0,3

floors of residential buildings, hotels and offices (category A and B);

ψ1 = 0,7; ψ2 = 0,6

floors of meeting rooms and stores (category C and D);

ψ1 = 0,9; ψ2 = 0,8

floors for storage (category E);

ψ1 = 0; ψ2 = 0

roofs.

So, under fire conditions a roof structure is analysed for permanent action only (ψ1 = ψ2 = 0), unless the wind has to be taken into account (countries in which ψ1 is mandatory) or the snow action on the roof (e.g. the Alpine and Scandinavian countries). See Fire 4 (Design tables), table 4.3 for the reduction factor for the design load level in the fire situation as a function of the occupancy and the national choice whether ψ1 or ψ2 has to be applied.

1.6 Behaviour of steel sections during fire The temperature of a steel structure rises when exposed to fire. This causes a decrease in both the strength and stiffness of the steel. These decreases can be observed in the relationship between temperature and the effective yield strength (fig. 1.28), and in the relationship between temperature and the Young’s modulus (fig. 1.29). The decreases in strength and stiffness of concrete and cold formed reinforcing steel are also shown for comparison. The full strength of the

1,2

1,2

1,0

1,0 structural steel

0,8 f ky,θ = y,θ fy

0,6

0,8 normal weight concrete kE,θ =

0,4

Ea,θ Ea

0,6 0,4

cold-formed reinforcing steel 0,2

0,2

200

0

400

600

800

1000

1200

temperature (˚C)

1.28 Decrease of strength of structural steel, reinforcing steel and normal weight concrete with temperature.

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normal weight concrete

200

400

600

800

1000

1200

temperature (˚C)

1.29 Decrease of stiffness of structural steel, reinforcing steel and normal weight concrete with temperature.

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increases. By 600 ˚C half the strength of the steel has already been lost. A structure fails during a fire when the (decreased) effective yield strength becomes lower than the stress level in the structure due to the mechanical actions. The temperature at which this occurs is called the critical steel temperature. To satisfy the fire safety requirements the steel temperature must not exceed the critical steel temperature, which depends on: – the degree of utilisation μ0 (a measure for the stress level in the steel); – the section factor Am/V (a measure for the heating rate of the steel).

Degree of utilisation The degree of utilisation μ0 (at time t = 0) depends on the design of the structure at ambient temperature, and is the ratio between the effect of the mechanical actions during fire Efi,d according to equation (1.1) and the design value of the resistance at ambient temperature (at time t = 0) Rfi,d,0:

(1.2)

In simple cases, the degree of utilisation has a direct relationship with the critical steel temperature. If a section is heated uniformly, the relationship between the degree of utilisation and the critical steel temperature corresponds with the relationship between the decreasing effective yield strength and the steel temperature (see fig. 1.28). Correction factors take into account the effect of non-uniform heating for beams loaded in bending. A correction factor κ1 allows for the way the section is heated (three or four sided), and a correction factor κ2 allows for possible thermal protection of the intermediate supports of a continuous beam. If global flexural buckling or lateral torsional buckling are of importance, whether the resistance of the heated structure – taking into account the decreased strength and stiffness – is larger than the applied loading from the accidental fire load case should be determined. A critical steel temperature can also be derived for this situation. This should be done using an iterative procedure because the Young’s modulus affects global buckling and lateral torsional buckling, and decreases more rapid with temperature than the effective yield strength.

Section factor The mass per unit length of an unprotected steel structure has a big influence on the heating rate. If the mass is larger, more energy is required to heat the section. The exposed surface area is also of importance: a heavy section heats up more slowly than a slender section. The thickness and thermal properties of the protection also affect the heating rate of a protected section. The protection slows down the heat transfer to the section, which results in lower temperatures in the section. The geometrical factor which affects the heating rate is called the section factor. • For unprotected sections, the section factor is Am /V and this factor is determined by dividing the surface area exposed to fire Am by the volume V of the section. Per unit of length, this is equal to the contour of the section divided by the cross-sectional area (see fig. 1.8). A high

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steel is retained up to a temperature of 400 ˚C, but it then decreases rapidly as the temperature

Am/V = 251 m–1

HEM 300

Am/V = 39 m–1

1000

temperature (˚C)

800

standard fire

600

400

200

1.30 Influence of the section factor Am/V on the heating rate and the fire resistance for four sided fire exposure.

0

15

30

45

60

time (minutes)

section factor means heating of the section will be rapid (fig. 1.30). A heavy section (for example HEM 300) has a low section factor (Am/V = 39 m–1) and a slender section (for example IPE 120)

has a high section factor (Am/V = 251 m–1). The section factor for hollow sections is 1/t, where t is the wall thickness in meters. The section factor is a section property that can be found in books of section tables. For unprotected I- and H-sections there is a ‘shadow effect’. Heat radiation from the fire source to the web and inner faces of the flanges is limited due to the shielding effect of the flanges. When determining steel temperatures the factor should be used to take this effect into account. • For protected sections, the section factor is Ap/V and this factor is determined by dividing the surface area of the inner side of the protection Ap by the volume V of the section. Per unit length, this is equal to the contour of the inside of the protection divided by the cross-sectional area of the steel section.

Fire resistance Enough options are available to ensure that all fire resistance requirements can be satisfied for a steel structure. Section 1.3.1 provides an overview of the possibilities to protect a steel structure against fire. The principle of determining the fire resistance of unprotected and protected steel beams loaded in bending (without lateral torsional buckling) is shown in figure 1.31. The left part of this figure shows the calculated steel temperature as function of the fire duration. The right part shows the relationship between the corrected degree of utilisation (the product of the degree of utilisation and the correction factors κ1 and κ2 – see above and Fire 2 (Calculation of the fire resistance) – and the critical steel temperature. This is in fact a mirrored version of the graph showing the decrease in strength of structural steel with temperature (see fig. 1.28). The

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IPE 120

800

temperature (˚C)

800 15 mm coating Ap / V = 100 m–1

600

600

400

400

200

200 steel temperature

0

20

40

60

80

100

time (minutes)

120

0,0

0,2

0,4

0,6

0,8

1,0

critical steel temperature (˚C)

1000

standard fire

0

1.31 Graphical representation of the determination of the fire resistance of protected steel beams in bending.

corrected degree of utilisation (–)

critical steel temperature is determined with the corrected degree of utilisation (on the right), which is set equal to the steel temperature (on the left). The fire resistance can then be read off from the figure. These graphs summarize the analysis method for determining the fire resistance according to EN 1993-1-2.

1.7 Literature 1. A3C: free program for the design of steel and composite columns (partially or totally encased with concrete). Free to download at: sections.arcelormittal.com. 2. CEPE, EAIPC and EAPFP, European industry best practice guide on the application of intumescent coating to constructional steel, 2015. To be downloaded free of charge from: www.brandveiligmetstaal.nl/pag/210/brandwerende_verf.html 3. Potfire: free computer program for the analysis of both reinforced and unreinforced concrete filled hollow section columns. Free to download at: www.cticm.com (search for ‘potfire’). 4. Research Fund for Coal & Steel, Macs+. Membrane action of composite structures in case of fire, 2012. To be downloaded free of charge from: research.bauforumstahl.de 5. J.W.B. Stark and R.J. Stark, Composite structures. Analysis and design of composite steel and concrete structures for buildings according to Eurocode 4 (Steel Design 4), Zoetermeer 2022. 6. EN 1990 (Eurocode. Basis of structural design), 2002 (incl. A1, 2005 and AC, 2010). 7. EN 1991-1-2 (Eurocode 1. Actions on structures. Part 1-2. General rules. Actions on structures exposed to fire), 2002 (incl. AC, 2013).

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1000

design), 2005 (incl. AC, 2009). 9. EN 1994-1-2 (Eurocode 4. Design of composite steel and concrete structures. Part 1-2. General rules. Structural fire design), 2005 (incl. AC, 2008 and A1, 2014). 10. EN 13381-4 (Test methods for determining the contribution to the fire resistance of structural members. Part 4. Applied passive protection to steel members), 2013. 11. EN 13381-8 (Test methods for determining the contribution to the fire resistance of structural members. Part 8. Applied reactive protection to steel members), 2013. 12. EN 13501-2 (Fire classification of construction products and building elements. Part 2. Classification using data from fire resistance tests, excluding ventilation services), 2016.

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8. EN 1993-1-2 (Eurocode 3. Design of steel structures. Part 1-2. General rules. Structural fire

Calculation of the fire resistance

dr.ir. A.F. Hamerlinck

Bouwen met Staal and Adviesbureau Hamerlinck

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Fire

Fire safety is an important aspect of building design. The objectives of fire safety and an overview of the many measures a designer can take to meet the fire safety requirements are explained in Fire 1 (Fire safety). In there also the accidental action fire to structures as well as the behaviour of steel in the fire situation are described. This chapter deals with the calculation of the fire resistance of a steel structure with regard to failure, shortened to ‘fire resistance’. This is the time (expressed in minutes) that a structural member resists the fire, usually the standard fire. For the calculation of composite steel and concrete structures exposed to fire, reference is made to Composite structures 2 (Composite beams) and Composite structures 3 (Composite slabs). First of all, the most important concepts that play a role in the calculation of the fire resistance of steel structures are discussed. Then the simple calculation model is discussed for connections and for tension members, steel beams that are not sensitive to lateral torsional buckling, steel columns and steel beams that are sensitive to lateral torsional buckling. Finally, the advanced calculation model is used for the calculation of integrated beams, both unprotected and protected.

2.1 Terms and conditions EN 1993-1-2 provides a simple calculation model to calculate the fire resistance of steel structures. This model can be used to verify whether a construction meets the requirements of the national building regulations with regard to the resistance during fire exposure. This assessment must be carried out in the ‘accidental’ case of fire according to EN 1990 (see Fire 1 (Fire safety), section 1.5). The following terms and conditions play an important role in the calculation of the fire resistance of a steel structure: – standard fire curve; – effective yield strength of steel in case of fire fy,θ; – degree of utilization µ0; – section factor A/V; – critical steel temperature θa,cr – cross-sectional classification in the fire situation; – behaviour of fire protection materials.

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Calculation of the fire resistance

The standard fire curve is the standardised development of the gas temperature in the fire compartment as a function of the time according to EN 1991-1-2, cl. 3.2.1 (fig. 2.1): (2.1)

Where: Θg gas temperature in the fire compartment (˚C); t

time (min).

2.1.2

2.1 The standard fire curve describes the assumed development of temperature as a function of time.

Effective yield strength of steel in the fire situation

At temperatures beyond 400 ˚C, the strength of the steel decreases (fig. 2.2). EN 1993-1-2, table 3.1 shows for a number of discrete points (every 100 °C) the reduction factors ky,θ as a ratio between the (effective) yield strength fy,θ at an elevated temperature θa and the yield strength fy at 20 °C. These points may be linearly interpolated. Table 3.1 also shows the reduction factors kE,θ for the modulus of elasticity Ea,θ during fire exposure. Note that the modulus of elasticity already decreases beyond 100 ˚C. See also table 4.2 in Fire 4 (Design tables). The reduction factor ky,θ for the reduction of the yield strength, can also be expressed in an equation, being derived from equation (4.22) for the critical steel temperature in EN 1993-1-2:



(2.2)

Where: fy,θ (effective) yield strength at elevated steel temperature θa; fy yield strength at normal temperature (20 ˚C);

2.2 Reduction factor ky,θ for the effective yield strength and kE,θ for the modulus of elasticity of steel at elevated temperature according to EN 1993-1-2.

θa steel temperature (˚C). Equation (2.2) is elaborated in tabular form in table 4.1 of Fire 4.

2.1.3 Degree of utilization The degree of utilization µ0 (at time t = 0) is the ratio between the load present in the accidental load case fire Efi,d and the load bearing capacity, expressed as the calculated value of the resistance of a steel element at normal temperature Rfi,d,0. It is evident that this load bearing capacity is at least equal to the load at normal temperature Ed, in accordance with the load combinations according to EN 1990.

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2.1.1 Standard fire curve

level in the fire situation ηfi = Efi,d /Ed. The reduction factor ηfi is therefore an upper limit approach to the degree of utilization of µ0. Take as an example a floor beam in an office building with combination factor ψ2 = 0,3, loaded by a permanent load Gk and a variable load Qk. If the beam has been designed on strength and meets the requirements at normal temperature (unity check of Ed /Rfi,d,0 less than or equal to 1,0), then Ed = Rfi,d,0 and therefore also μ0 = ηfi. This yields to the equation: (2.3) The partial load factors are used according to EN 1990: γG = 1,2 for the permanent and γQ = 1,5 NA

for the variable action (dependant on the National Annex). Depending on the loads, for offices the reduction factor for the the design load level in the fire situation varies usually between ηfi = 0,48 (Gk = Qk) and ηfi = 0,59 (Gk = 2Qk). Equation (2.3) is shown graphically in figure 2.3 for different occupancies (different values of ψ2). See also table 4.3 in Fire 4. For countries in which the combination factor ψ1 for frequent actions is mandatory instead of the combination factor ψ2 for quasi-permanent actions, the equation has to be slightly modified. For centrically loaded columns in braced frames with n storeys, the upper limit for the degree of utilization in offices (with ψ2 = 0,3 for fire and ψ0 = 0,5 for normal load combinations (in which two storeys are fully loaded and n – 2 stories with combination factor ψ0)) is set at:

(2.4)

For two storeys, the equations (2.3) and (2.4) are the same. For three or more storeys, the degree of utilization for columns is higher than that for beams. This is because the fundamental combination of actions for columns at normal temperature consists of two storeys fully loaded with a variable 2.3 Relationship between the reduction factor for the design load level in a fire situation ηfi and the ratio between the permanent and the variable load Gk/Qk for different values of the combination factor ψ2.

load, which is reduced on the other storeys by the combination factor ψ0. The effect of the factor ψ therefore decreases with an increasing number of storeys and is less for columns than for beams. In practice, the degree of utilization is usually in the order of 0,5. This value is smaller than follows from equation (2.3) or equation (2.4). This is because there is often extra loadbearing capacity available, for example in the case of beams because the deflection criterion is decisive, or in the case of columns because for practical reasons the same profile is used at several storeys. In the event of a fire, a reduced buckling length of the columns can often be applied (see section 2.6).

2.1.4 Section factor The section factor takes into account the influence of the geometry of the steel section on the heating. The section factor is defined as the heated area A (in m2 per metre of length) divided by the volume of the steel section V (in m3 per metre of length), using m–1 as the unit. In practical terms, the section factor is therefore equal to the heat-exposed circumference (in m) divided by the area of the steel cross-section (in m2).

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The degree of utilization µ0 is always less than or equal to the reduction factor for the the design load

Am is the heated circumference of the profile and V is the area of the steel cross-section (fig. 2.4). • In the case of protected sections, the section factor is referred to as Ap/V (index p for ‘protected’), where Ap is the inner circumference of the protection and V is the area of the steel cross-section (fig. 2.5a). For protection that is not placed directly against the section – e.g. by means of spacers or a framework – no larger circumference is used and the smallest circumference around the heated section of the profile applies (fig. 2.5b). In the case of a protected steel girder below a concrete floor, the circumference of the steel section must be reduced by the width of the top flange. The concrete floor protects the upper flange against heating (fig. 2.5c and d). 

2.5 Section factor Ap/V for protected sections.

2.4 Section factor Am/V (without ‘shadow effect’) for unprotected sections.

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• For unprotected sections, the section factor is referred to as Am/V (index m for member), where

contour encasement

hollow encasement

section

four-sided heating

three-sided heating

four-sided heating

three-sided heating

four-sided heating

three-sided heating

IPE 240

166

138

236

205

184

153

IPE 270

159

132

227

197

176

147

IPE 300

151

125

216

188

167

139

IPE 330

141

118

200

175

157

131

IPE 360

131

110

186

163

146

122

IPE 400

124

104

174

152

137

116

IPE 450

117

99

162

143

130

110

IPE 500

109

93

151

134

121

104

IPE 550

102

88

140

124

113

97

IPE 600

95

82

129

115

105

91

HEA 140

156

116

253

208

174

129

HEA 160

145

108

234

192

161

120

HEA 180

140

104

226

187

155

115

HEA 200

130

97

211

174

145

108

HEA 220

120

90

195

161

134

99

HEA 240

110

82

178

147

122

91

HEA 260

106

79

171

141

117

88

HEA 280

102

76

165

136

113

84

HEA 300

94

70

153

126

105

78

HEA 320

88

67

141

117

98

74

HEA 340

85

65

134

112

94

72

HEA 360

82

63

128

107

91

70

HEA 400

78

61

120

101

87

68

HEA 450

75

60

113

96

83

66

HEA 500

72

58

107

92

80

65

HEA 550

71

59

104

90

79

65

2.6 Section factor A/V (m–1) for commonly used IPE, HEA and HEB sections. For the two unprotected sections (see the two left-hand colums), the correction factor for the shadow effect ksh according to equation (2.9), see section 2.2.2, has been included in the section factor. The section factor for the complete range of IPE, HEA, HEB and HEM profiles is given in table 4.5 of Fire 4.

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unprotected

contour encasement

hollow encasement

section

four-sided heating

three-sided heating

four-sided heating

three-sided heating

four-sided heating

three-sided heating

HEB 140

117

88

187

155

130

98

HEB 160

106

80

169

140

118

88

HEB 180

99

74

159

131

110

83

HEB 200

92

69

147

122

102

77

HEB 220

87

65

140

115

97

72

HEB 240

82

61

131

108

91

68

HEB 260

79

59

127

105

88

66

HEB 280

77

58

123

102

85

64

HEB 300

72

54

116

96

80

60

HEB 320

69

52

110

91

77

58

HEB 340

67

52

106

88

75

57

HEB 360

66

51

102

86

73

56

HEB 400

64

50

97

82

71

56

HEB 450

62

50

93

79

69

55

HEB 500

60

49

89

76

67

54

HEB 550

60

50

88

76

67

55

2.6 Section factor A/V (m–1) for commonly used IPE, HEA and HEB sections (continued).

Section factors can be calculated (see fig. 2.4 and 2.5), but are generally provided by tables within section booklets, like table 2.6 (see also table 4.5 in Fire 4 (Design tables).

2.1.5 Critical steel temperature The critical steel temperature θa,cr is the steel temperature at which structural failure occurs and this temperature depends on the degree of utilization. The degree of utilization µ0 in the event of failure is equal to the reduction factor on the yield strength of steel ky,θ for tension members, see equation (2.2). For beams that are not sensitive to lateral torsional buckling, the degree of utilization must be corrected, see section 2.4. The critical steel temperature is also shown in figure 2.2: for example θa,cr = 600 ˚C for ky,θ = 0,47.

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unprotected

c

t

c

t

t

c

t

t

c

t

The classification of cross-sections according to EN 1993-1-1 for normal conditions is not automatically valid in case of

t

t

fire, because the modulus of elasticity decreases faster than c

c c

the yield strength. As a result, the local buckling resistance

c

of steel parts under compression is reduced, which in some

cross-section class

loaded in bending

loaded in compression

1

c/t ≤ 72ε

c/t ≤ 33ε

2

c/t ≤ 83ε

c/t ≤ 38ε

situation. Some of the sections, which can develop their

c/t ≤ 124ε

c/t ≤ 42ε

plastic moment resistance under normal conditions (class 2),

3

fall into class 3 in case of fire and must then be calculated

outstand flanges t

c

c

t

t

cases leads to a higher cross-sectional class in the fire

c

elastically.

c

In the cross-section classification according to EN 1993-1-1, table 5.2, the factor ε is used to determine in which class

t

a cross-section falls at normal temperatures, depending on loaded in compression

cross-section class

the ratio between the plate width and the plate thickness

1 (plastic)

c/t ≤ 9ε

2 (compact)

c/t ≤ 10ε

under compression (fig. 2.7). In the event of a fire, ε must

c/t ≤ 14ε

be multiplied with a factor of 0,85 to take account of the

3 (semi-compact)

influence of temperature on the local buckling behaviour:

other sections h

t

d



b angle

circular hollow secion

(2.5)

cross-section class

loaded in compression

1

–

d/t ≤ 50ε2

Table 2.8 shows the cross-sectional class of a number of

2

–

d/t ≤ 70ε2

3

h/t ≤ 15ε and

d/t ≤ 90ε2

rolled sections in the event of a fire.

loaded in compression and/or bending

b+h ≤ 11,5ε 2t

For sections in class 4, EN 1993-1-2, cl. 4.2.3.6, gives a conservative value for the critical steel temperature of 350 ˚C.

value of ε at fire

Alternatively, the calculation method from Annex E can be

steel grade

S235

S275

S355

S420

S460

ε ε2

0,85

0,79

0,69

0,64

0,61

0,72

0,62

0,48

0,40

0,37

used, resulting in higher critical steel temperatures than 350 ˚C.

2.7 Cross-section classification in the fire design situation.

2.8 Cross-section class of commonly used IPE, HEA and HEB sections in bending and compression under normal temperature conditions and in the fire situation for steel grades S235, S355, S420 and S460. The cross-section class for the complete range of IPE, HEA, HEB and HEM sections and for readily available hollow sections is given in table 4.13 and table 4.14 of Fire 4 respectively.

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2.1.6 Cross-section classification in the fire situation

internal compression parts

section

bending

fire

compression

bending

S235 S355 S420 S460 S235 S355 S420 S460

compression

S235 S355 S420 S460 S235 S355 S420 S460

IPE 270

1

1

1

1

2

3

4

4

1

1

1

1

3

4

4

4

IPE 300

1

1

1

1

2

4

4

4

1

1

1

1

3

4

4

4

IPE 330

1

1

1

1

2

4

4

4

1

1

1

1

4

4

4

4

IPE 360

1

1

1

1

2

4

4

4

1

1

1

1

4

4

4

4

IPE 400

1

1

1

1

3

4

4

4

1

1

1

1

4

4

4

4

IPE 450

1

1

1

1

3

4

4

4

1

1

1

1

4

4

4

4

IPE 500

1

1

1

1

3

4

4

4

1

1

1

1

4

4

4

4

IPE 550

1

1

1

1

4

4

4

4

1

1

1

1

4

4

4

4

IPE 600

1

1

1

1

4

4

4

4

1

1

1

1

4

4

4

4

HEA 160

1

1

2

2

1

1

2

2

1

2

3

3

1

2

3

3

HEA 180

1

2

3

3

1

2

3

3

1

3

3

3

1

3

3

3

HEA 200

1

2

3

3

1

2

3

3

2

3

3

3

2

3

3

3

HEA 220

1

2

3

3

1

2

3

3

2

3

3

3

2

3

3

3

HEA 240

1

2

3

3

1

2

3

3

2

3

3

3

2

3

3

3

HEA 260

1

3

3

3

1

3

3

3

2

3

3

3

2

3

3

3

HEA 280

1

3

3

3

1

3

3

3

3

3

3

4

3

3

3

4

HEA 300

1

3

3

3

1

3

3

3

2

3

3

3

2

3

3

3

HEA 320

1

2

3

3

1

2

3

3

1

3

3

3

1

3

3

3

HEA 340

1

1

2

3

1

1

2

3

1

3

3

3

1

3

3

4

HEA 360

1

1

2

2

1

1

2

2

1

2

3

3

1

2

3

4

HEA 400

1

1

1

1

1

2

2

2

1

1

2

3

1

3

4

4

HEB 160

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

HEB 180

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

HEB 200

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

HEB 220

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

HEB 240

1

1

1

1

1

1

1

1

1

1

1

2

1

1

1

2

HEB 260

1

1

1

1

1

1

1

1

1

1

2

2

1

1

2

2

HEB 280

1

1

1

1

1

1

1

1

1

1

2

3

1

1

2

3

HEB 300

1

1

1

1

1

1

1

1

1

1

2

3

1

1

2

3

HEB 320

1

1

1

1

1

1

1

1

1

1

1

2

1

1

1

2

HEB 340

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

2

HEB 360

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

2

HEB 400

1

1

1

1

1

1

1

1

1

1

1

1

1

1

2

2

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normal temperature

EN 1993-1-2, cl. 4.2.5 describes a simple calculation model of the heating of a steel section according to the standard fire curve. This heating depends on the net heat flux to the steel member, the section factor (see section 2.1.4) and – for protected members – the thickness and thermal characteristics of the protection material (see section 2.2.4). The thermal response of steel during standard fire exposure is treated in four parts: – net heat flux to the steel member (section 2.2.1); – heating of unprotected steel sections (section 2.2.2); – heating of unprotected galvanized steel sections (section 2.2.3); – heating of protected steel sections (section 2.2.4).

2.2.1 Net heat flux to the steel member The net heat flux

reaching the steel member is calculated with EN 1991-1-2, cl. 3.1, consi-

dering the heat transfer by convection

(due to movement of gases) and by radiation

(emission of energy through a space) (fig. 2.9). The equations (3.1) to (3.3) of EN 1991-1-2 can be presented in a simplified way by: (2.6) 2.9 Heat transfer mechanisms: radiation, convection and conduction.

Where: αc coefficient of heat transfer by convection (25 W/(m2K) for exposure during the standard fire curve); θg gas temperature (in the fire) around the member (K); θm surface temperature of the steel member (K); εm surface emissivity of the steel member;

σ Stephan Boltzmann constant (σ = 5,67·10–8 W/(m2K4)). The surface emissivity of carbon steel is 0,7 and 0,4 for stainless steel, according to EN 1993-1-2, cl. 2.2(2). For galvanized steel a value of 0,35 can be adopted up to 500 °C and 0,7 beyond 500 °C. This has been derived from research and will be incorporated in the future version of EN 1993-1-2.

2.2.2 Heating of unprotected steel sections In most simplified cases, the temperature distribution in a steel cross-section is uniform. For unprotected steel sections the increase of the steel temperature Δθa,t during a time interval Δt can be determined from EN 1993-1-2, equation (4.25):



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(2.7)

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2.2 Calculation of the thermal response

Am/v section factor of an unprotected the steel member, see section 2.1.4; c a

specific heat of steel (in J/(kgK)), being temperature dependent (see EN 1993-1-2, cl.

ρa

unit mass of steel (7850 kg/m3);

ksh

shadow factor explained below.

3.4.1.2) and showing a strong peak due to changes in the crystallic structure at 735 °C;

Equation (2.7) is better understood if rewritten to the equation of equilibrium of energy between the energy transferred to the steel section and the energy stored in the section (causing an incease of temperature in the steel section): (2.8) In the case of I shaped sections, the so-called ‘shadow effect’ plays a role. The shadow effect means that the radiative heat to the web and to the inner side of the flanges is partially shielded by the flanges. This effect is taken into account by the correction factor ksh according to EN 1993-1-2, cl. 4.2.5.1:

(2.9)

Where (Am/V)b is the box value of the section factor for an imaginary rectangle that fits around the I shaped section. Figure 2.10 shows the relationship between the (corrected) section factor and the steel temperature of an unprotected steel section after 20, 30 and 60 minutes of fire following a computation

2.10 Relationship between the corrected section factor ksh·Am/V and the steel temperature θa of an unprotected I-section after 20, 30 and 60 minutes of fire. The graphs are given in tabular form in table 4.4 of Fire 4).

with the ‘simple’ calculation model of EN 1993-1-2. For a fire resistance of 30 minutes and a critical temperature of 600 ˚C – corresponding to a degree of utilization of μ0 = ky,θ = 0,47 (see fig. 2.2) – a section factor

(were relevant corrected with the shadow factor ksh ) of up to 35 m–1 is required. The section factor is usually greater than 60 m–1 for conven-

tional rolled and hollow sections and even greater than 140 m–1 for IPE sections (see table 2.6). As a result, a fire resistance of 30 minutes is generally not feasible for an unprotected steel structure. Usually, a fire protection measure – an insulating covering or the application of a composite steel-concrete construction – is necessary to obtain a fire resistance of 30 minutes (see section 2.2.4). A requirement of 30 minutes fire resistance can only be met with an unprotected steel structure at a low degree of utilization in combination with a low section factor. The choice of the section plays an important role here.

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Where:

Since the surface emissivity of galvanized steel is lower than that of non-galvanized (carbon) steel up to 500 ˚C, as described in section 2.2.1, it heats up slower as can be seen in figure 2.11 and table 4.4 of Fire 4, in which the temperature development during the first 30 minutes of standard fire exposure is compared as a function of the section factor. As a result, it can be derived that up to 20 minutes about 5 minutes difference in fire resistance is achieved up to a section factor of 80 m–1 and a critical steel temperature θa,cr up to 525 °C (θa,galvanized,20 ≈ θa,non-galvanized,15 ). At 30 minutes the difference depends on the section factor Am/V: – 8 minutes for Am/V = 40 m–1

beam HEM 240 or a hollow section with t = 25 mm and θa,cr = 500 °C;

– 4,5 minutes for Am/V = 60

beam HEB 260 or a hollow section with t = 16 mm and θa,cr = 670 °C;

m–1

– 2,5 minutes for Am/V = 80 m–1 beam HEA 260 or a hollow section with t = 12,5 mm and θa,cr = 730 °C; . – 1,5 minutes for Am/V = 100 m–1 beam HEA 200 or a hollow section with t = 10 mm and θa,cr = 750 °C

2.11 Nomograms for the temperature development of non-galvanized and galvanized carbon steel during 30 minutes exposure to the standard fire curve as a function of the section factor.

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2.2.3 Heating of unprotected galvanized steel sections

An insulating plate material, a sprayed mortar or an intumescent coating slows down the heat transfer to the steel profile, enlarging the time to reach the critical steel temperature. For protected steel sections the increase of the steel temperature Δθa,t during a time interval Δt can be determined from EN 1993-1-2, cl. 4.2.5.2, equation (4.27):

(2.10)

Where: Ap/V section factor of a protected steel member, see section 2.1.4; λp

thermal conductivity of the fire protection system (in W/(mK));

dp

thickness of the fire protection material (in m);

cp

specific heat of the fire protection system (in J/(kgK)), being temperature dependent;

ρp

unit mass of the fire protection material (in kg/m3);

θg,t

gas temperature (of the fire) at time t;

θa,t steel temperature (of the fire) at time t; Δθg,t increase of gas temperature (of the fire) during the time interval Δt. In protected sections there is no shadow effect. The insulating properties of fire protection material depend not only on its thickness dp, but also on the thermal properties of the protection material and in particular on the thermal conductivity λp. This coefficient generally depends strongly on the temperature, so that its value changes during the fire exposure. For this reason, it is not permitted to use the value of the thermal conductivity at normal temperature in calculations. The structural element to which the protection is attached may deform or deflect in the event of a fire. Therefore, the mechanical behaviour of the protection material is also important to prevent the protection from falling off, detaching and/or serious cracking. The constructional details – such as the number and type of mechanical fasteners and the shielding of the seams in case of plate protection – are important in this respect. The effects of the method of application cannot be theoretically assessed in advance. Therefore, EN 13381-4 and EN 13381-8 prescribe tests with protection materials on both loaded and unloaded steel sections. This enables the determination of the governing thermal properties of the protection during fire, depending on the temperature development and the thermal and mechanical deformations (the so-called ‘stick­ability’).

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2.2.4 Heating of protected steel sections

which show the required protection or coating thickness for a given fire resistance, section factor and critical steel temperature.

Manual calculation Without performing tests or taking the test reports into account, it is still possible to get an impression of the required protection thickness with a simple manual calculation (see example 2.3). The conservative values of the material properties according to table 2.12[3] can be used for this purpose. These values apply within the temperature range for which fire tests have been carried out. The manual calculation is not indicated in EN 1993-1-2, but generally provides a safe approximation of the required protection thickness at the design stage. Depending on the critical steel temperature, the fire resistance requirement and the section factor, the graphs in figure 2.13 can be used in the design stage to select an insulation material with a required thickness. The graphs do not take into account the influence of the thermal capacity and the moisture content of the covering material, so the approach provides a conservative solution. These graphs are a simplification of the nomogram[3] in figure 2.14.

λp

ρp

cp

(W/mK)

(kg/m3)

(J/kgK)

gypsum, fibre-reinforced

0,20

800

1700

silicate

0,15

600

1200

vermiculite

0,15

800

1200

mineral wool

0,20

150

1200

mineral fibres

0,12

300

1200

vermiculite

0,12

550

1100

protection material

plated hollow encasement

sprayed contour encasement

2.12 Material properties of some commonly used protection materials.

2.13 Relationship between the section factor Ap/V and the critical steel temperature θa,cr, depending on the thermal resistance dp /λp of the fire protection material for a required fire resistance of 30, 60, 90 and 120 minutes.

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Suppliers of fire resistant materials have test and classification reports for each of their products,

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15 | fire 2 calculation of the fire resistance |

60 50

40

30

20 10 2000

Ap λp · V dp (W/m3K)

800 80

1500 1200

100

1000

700

900

200

800

κ1·κ2 (–) 0,60

400 700

0,70

600 600

1,00

500

0,5

450

500

400

0,7

350 a (–)

400

1,0

300

250

300

200

150 200 100

100

0,7

0,6

0,5

0,4

0,3

0,2

0,1

0

10

20

degree of utilization μ0 (–)

30

40

50

60

70

80

90

fire resistance (min)

2.14 Nomogram for the graphical determination of the fire resistance of unprotected and protected sections according to EN 1993-1-2.

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100

110

120

protected steel section

0,85

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section factor Am /V (m–1) unprotected steel section

temperature (˚C) 900

EN 1993-1-2, cl. 4.2, describes a simple calculation model, based on heating according to the standard fire curve and a uniform temperature distribution in the steel section. The latter is the case of sections that are fire exposed from four or three sides. The simple calculation model is applicable to the following structural steel members, both unprotected and protected: – tension members (see section 2.4); – beams of cross-section class 1, 2 or 3 in bending, distinguishing between beams without lateral torsional buckling and beams with lateral torsional buckling (see section 2.5 and 2.7 respectively); – columns (members under compression) of cross-section class 1, 2 or 3 (see section 2.6); – members of cross-section class 1, 2 or 3 loaded by a combination of bending and axial compression (not covered here). For each of these steel members the fire resistance can be determined, taking into account the decrease of the yield strength and the modulus of elasticity as a function of the temperature. The equations in EN 1993-1-2 look a bit complicated, because they also contain the material factors γM,0 and γM,fi. If both factors are equal to 1,0, the equations can be simplified, as is presented in this

NA

section. In addition to the simple calculation model, EN 1993-1-2 also allows the use of advanced calculation models. These models take into account temperature variations over the steel cross-section, which always occurs with sections that are fire-exposed from one side, such as integrated floor beams (see sections 2.8 and 2.9). Advanced models can also take into account the behaviour of a natural or physical fire – possibly in combination with the system behaviour of an entire structure – instead of individual components. The use of such physical models is known as ‘fire safety engineering’, see Fire 3 (Fire safety engineering).

2.3.1 Connections EN 1993-1-2, cl. 4.2.1(6), indicates that the fire resistance of bolted and welded connections need not be checked if the following two conditions are met: – the thermal resistance (dp/λp)c of the fire protection of the connection is at least equal to the thermal resistance (dp/λp)m of the fire protection of the connecting elements; – the degree of utilization Ed/Rd of the connection is equal to or less than that of the connecting members. The background to the first requirement is that there is usually more steel volume at the location of the connection than at the location of the connecting members. This leads to a lower steel temperature. The second condition is evident, noting that this condition should be verified on the basis of the design at normal temperature. If both conditions are met, the connections may

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2.3 Calculation of the mechanical response

connections do not need to be protected when the connecting members do not need to be protected. Alternatively, bolted and welded joints may also be checked using the simple calculation rules in appendix D of EN 1993-1-2. Basically, these calculation rules mean that the calculation rules for the strength of the joints are applied at normal temperatures, taking into account the temperaturedependent reduction factor for the yield strength kb,θ (for bolts) and kw,θ (for welds). The values of this reduction factor are given in table D.1 of EN 1993-1-2 (see table 2.16 in example 2.1). The thermal response of the connection may be based on the section factor A/V at the position of the connection. As a further simplification, a uniform temperature distribution in the connection may be adopted, provided that this temperature distribution is determined on the basis of the largest section factor of the connecting members (a conservative assumption). For the development of the steel temperature, the rules of EN 1993-1-2, cl. 4.2.5 (see also section 2.1.4), may be used. Annex D of EN 1993-1-2 gives separate rules for the temperature development in beam/column and beam/beam connections where there is a concrete floor on the beams. These empirical rules take into account a non-uniform temperature distribution over the height of the beam as a result of heat losses to the concrete. The starting point is the temperature of the bottom flange of the beam θo at such a distance from the connection that this temperature is not affected by the connection. The temperature θo can be calculated on the basis of EN 1993-1-2, cl. 4.2.5. The temperature of the bottom flange of the beam at the connection is assumed to be 0,88θo due to heat losses to the connection and due to shielding effects. This can then be used to determine the temperature distribution over the height of the beam. NA

Annex D of EN 1993-1-2 can also be applied to derive the specific section factor of the connection in cases where the connecting members are protected (e.g. offsite applied intumescent coating) and the bolts and nuts are not protected.

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be protected in the same way as the (decisive) connecting member. This also means that the

• Given. A beam splice connection in which both members HEA 400 are provided with intumescent coating (fig. 2.14). The required fire resistance is 60 minutes. Both beams have welded end plates 300x360x20 mm with intumescent coating (except for the connection surface and the bolt holes) and 6 bolts M30. The moment in the fire design situation is ME,θ = 115 kNm. The moment resistance at normal temperature is MR,20 = 253 kNm. • Question. Is protection of the bolts and nuts needed to reach the required fire resistance of 60 minutes? • Answer. The section factor A/V of the unprotected part of the connection is calculated in three steps. Step 1. The fire exposed area of the bolts is A = 6·2π(2r)2 = 6·2π·(2·15)2 = 33929 mm2 (assuming the radius r of the fire exosed nut and the bolt heads are twice that of the bolt and the sides are protected after intumescing of the coating on the end plates, leaving only the upper surface of the bolt and nut unprotected); Step 2. The volume of the bolted connection is V = 2Lend platebend platetend plate

2.15 Beam splice connection of example 2.1. Both HEA 400 sections have welded end plates which are fire protected by an intumescent coating. The nuts and bolts can be left unprotected for 60 minutes fire resistance.

+ 6πr2Lbolt = 2·300·360·20 + 6·π·152·(2·20 + 2·30) = 4744115 mm3

(two end plates and the bolt extending 30 mm from the plates on both sides and neglecting the extra steel mass in the nut and bolt head outside the bolt diameter); Step 3. The section factor is A/V = (33929·10–6)/(4744115·10–9) = 7,2 m–1. From table 4.4 of Fire 4 it follows that after 60 minutes the connection temperature for A/V = 7,2 m–1 is θa,con,60 = 433 °C. Linear interpolation from EN 1993-1-2, table D.1 (table 2.16) provides the

temperature

bolts

welds

carbon steel

θa (°C)

kb,θ (tension and shear)

k w,θ

k y,θ

20

1,000

1,000

1,000

kb,θ = 0,700.

100

0,968

1,000

1,000

The moment resistance in the fire design situation MR,θ is checked:

200

0,952

1,000

1,000

300

0,903

1,000

1,000

400

0,775

0,876

1,000

500

0,550

0,627

0,780

600

0,220

0,378

0,470

700

0,100

0,130

0,230

800

0,067

0,074

0,110

900

0,033

0.018

0,060

1000

0,000

0,000

0,040

1100

0,000

0,000

0,020

1200

0,000

0,000

0,000

strength reduction factor for bolts (tension and shear) for θa,con,60 = 433 °C:

Since MR,θ = 221 kNm > ME,θ = 115 kNm, the connection complies without protecting the bolts and nuts.

2.16 Strength reduction factors for bolts and welds, compared to that of the effective yield strength of carbon steel as a function of the steel temperature.

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Example 2.1

For tension members, the resistance in the fire design situation Nfi,θ,Rd follows directly from the resistance at normal temperature NRd with the reduction factor ky,θ according to equation (2.2): Nfi,θ,Rd = ky,θNRd (2.11) In addition to a verification of the resistance according to equation (2.11), it is also possible to verify whether the steel temperature at the required fire resistance time is lower than the critical steel temperature. The calculation method for determining the fire resistance of a tension member thereby consists of three parts: – calculation of the critical steel temperature θa,cr as a function of the degree of utilization; – calculation of the steel temperature θa as a function of time; – determination of the fire resistance as the time for which θa = θa,cr (fig. 2.17). In practice, it is usually not necessary to determine the exact fire resistance in minutes, but to check whether the fire resistance requirement of 30, 60, 90 or 120 minutes has been met. In principle, the approach consists of the same three parts, with a total of eight steps. See section 2.5 for further details. Wind (X-)bracing can usually be left unprotected at a required fire resistance of 30 minutes due to the low degree of utilization. Let us consider a practical bracing strip 150x8 mm2, designed with NA

a unity check of 0,7 at normal temperature. During fire the ‘normal’ load factor for wind γQ = 1,5 is lowered to γfi = 1,0. Furthermore the combination factor ψ1 = 0,2 has to be applied in the fire design situation. Thus, the degree of utilization μ0 = unity check·γfi/γQ·ψ1 = 0,7·1,0/1.5·0,2 = 0,093. Table 4.1 of Fire 4 provides the critical steel temperature θa for this value of μ0: θa,cr = 840 °C. The section factor of the bracing strip (heated on four sides) is Am/V = 2000/8 = 250 m–1. Table 4.4 of Fire 4 provides the steel temperature after 30 minutes θa,30 for this value of Am/V: θa,30 = 834 °C. Since θa,cr = 840 °C > θa,30 = 834 °C, the X-bracing complies without protection.

1000

1000

standard fire

800

temperature (˚C)

800 15 mm protection Ap / V = 100 m–1

600

600

400

400

200

200 steel temperature

0

20

40

60 time (min)

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80

100

120

0,0

0,2

0,4

0,6

0,8

corrected degree of utilization (–)

1,0

0

critical steel temperature (˚C)

2.17 Graphical determination of the fire resistance of tension members and beams that are restrained against lateral torsional buckling.

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2.4 Tension members

does not need protection, e.g. in the case of a building subdivided into two fire compartments where each compartment is stabilized individually and the reduced loading in the fire design situation can be carried by the bracing in the cold compartment, assuming the braces in the hot compartment carry no loading anymore. The forces are transferred form the hot to the cold compartment by the diaphragm action of the floor and/or roof, in which possible torsional forces have to be taken into account.

2.5 Beams not sensitive to lateral torsional buckling For beams that are not sensitive to lateral torsional buckling, the moment resistance in the fire design situation Mfi,θ,Rd follows directly from the moment resistance at normal temperature MRd with the reduction factor ky,θ according to equation (2.2): Mfi,θ,Rd = ky,θMRd (2.12) The moment resistance at normal temperature MRd may be determined for class 1 sections with a plastic moment distribution. For class 2 and 3 sections, an elastic moment distribution has to be used. For class 1 and 2 sections, the plastic moment capacity of the cross-section is used, and for class 3 sections, the elastic moment capacity is used. Class 4 sections must be calculated in accordance with annex E of EN 1993-1-2 if the conservative value of the critical steel temperature of 350 ˚C is not used. The simple calculation method is based on the assumption that the temperature of a steel section is uniformly distributed, both over its cross-section and its length. This assumption is correct for sections that are exposed to fire at all sides. However, this assumption is incorrect for beams that are exposed to fire at three sides – for example, a steel floor beam under a concrete floor – because the upper flange has a lower temperature than the bottom flange. The latter has a positive effect on the load-bearing capacity. A similar effect occurs, for example, with continuous beams, where the bottom of the beam is locally shielded and has a lower temperature at intermediate supports. In order to compensate for the simplified assumption and to align the results with the results of fire tests, the adaptation factors κ1 (non-uniform temperature distribution across the cross-section) and κ2 (non-uniform temperature distribution along the longitudinal axis) have been introduced for beams that are not sensitive to lateral torsional buckling. For members that are not sensitive to lateral torsional buckling subject to bending and with a nonuniform temperature distribution, equation (2.12) takes these factors into account:

(2.13)

Besides the verification of the moment resistance according to equation (2.13), it is also possible to verify whether the steel temperature is lower than the critical steel temperature. The calculation method for determining the fire resistance consists of the same three parts as for tension members.

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Depending on the design, sometimes even for a required fire resistance of 60 minutes, the bracing

load in the fire design situation qθ,d

In practice, it is usually not necessary to determine the exact fire resistance in minutes, but to check whether the fire resistance requirement of 30, 60, 90 or 120 minutes has been met. In principle, the approach consists of the same three parts as given in section 2.4, with a total of

2 load-bearing capacity at normal temperature qd

eight steps (fig. 2.18): – calculation of the critical steel temperature θa,cr as a function of the (corrected) degree of utilization (steps 1-5);

3 degree of utilization μ0 = qθ,d / qd 4 correction factors κ1 and κ2

– calculation of the steel temperature θa after 30, 60, 90 or 120 minutes (steps 6-7); – check whether θa ≤ θa,cr (step 8). • Step 1. Determine the load on the structure in the event of fire qθ,d (Nθ,d for tension members).

• Step 2. Determine the load bearing capacity at normal temperature qd (Nd for tension members). • Step 3. Determine the degree of utilization:

5 critical steel temperature θa,cr depending on μ0, κ1 and κ2

(2.14)

6 section factor A/V

The equations (2.3) and (2.4) can also be used as a safe approach of the degree of utilization of, for example, office buildings. • Step 4. Determine the adaptation factors κ1 and κ2, depending on the heating conditions of

7 steel temperature θa

the beam. For beams that are fire-exposed form three sides under a composite or concrete floor, κ1 = 0,7 (unprotected beams) or κ1 = 0,85 (protected beams) applies. For statically un­determined (continuous) beams, κ2 = 0,85 applies. In all other situations, κ1 = κ2 = 1,0.

8 check θa ≤ θa,cr

2.18 Flow chart for the assessment of the fire resistance of tension members and beams that are restrained against lateral torsional buckling.

• Step 5. Determine the critical steel temperature θa,cr, represented by the red curves in figure 2.2 and figure 2.17 (righthand side):

(2.15)

Equation (2.15) can be derived from equation (2.2) with κ1κ2μ0 = fy,θ/fy = ky,θ and θa,cr = θa. • Step 6. Determine the section factor depending on the type of section, the way of heating (from three or four sides) and the fire protective covering, if any (see fig. 2.4 and 2.5). The section factor is given in table 2.6 for the most common I sections. For unprotected hollow sections Am/V = 1/t, where t is the wall thickness (in m). • Step 7. Based on the standard fire curve, determine the steel temperature θa after the fireexposure time corresponding to the fire resistance requirement. In the case of unprotected sections, the development of the temperature in the steel section depends on the section factor, the thermal properties of steel (the steel surface emissivity εm, the specific heat ca and the unit mass ρa) and on the heat transfer characteristics of the fire compartment (the emissivity of the flames εf and the coefficient of heat transfer by convection αc). In the case of protected steel sections, the thickness and material properties of the protective material also play an important role. The calculation of the steel temperature θa is based on a time step method and is not possible manually. However, with a suitable computer program or available design tools, it is easy to calculate the steel temperature. • Step 8. Check that θa ≤ θa,cr.

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1

• Given. A single-storey industrial building has a storage area with an intermediate floor. The HEA 550 floor beams in grade S235 steel are simply supported with a span L = 10,5 m and a centre-to-centre distance of a = 3,0 m. The load on the floor beams is Gk = 4,5 kN/m2 and Qk =

5,0 kN/m2 with ψ2 = 0,8. The beams support a prefabricated concrete floor and are heated on

NA

three sides in the case of fire. The required fire resistance is 30 minutes. • Question. Design a structural solution to avoid protection of the steel beams. • Answer. The load in the fire design situation (step 1) is: qθ,d = (Gk + ψ2Qk)a = (4,5 + 0,8·5,0)·3,0 = 25,5 kN/m and the maximum load bearing capacity at normal temperature (step 2):

In the case of fire, the section complies with class 1 (see Fire 4, table 4.13), which means that the plastic moment capacity can be taken into account. The degree of utilization (step 3) follows from equation (2.14):

For a statically determined beam, that is unprotected and heated form three sides, κ1 = 0,7 and κ2 = 1,0 (step 4). Equation (2.15) is used to find the critical steel temperature (step 5):

The section factor (step 6) for an unprotected beam HEA 550 heated form three sides (and corrected with the shadow effect) is Am/V = 59 m–1 (see table 2.6). This results in the steel temperature (step 7) after 30 minutes of fire θa,30 = 721 ˚C (see fig. 2.10, fig. 2.11 and tables 4.4, 4.5 and 4.6 of Fire 4). This value is higher than the critical steel temperature (step 8), so that this unprotected beam does not satisfy the requirement. The same conclusion also follows from the nomogram in figure 2.14. For μ0 = 0,32, κ1κ2 = 0,7·1,0

= 0,7, θa,cr = 705 ˚C and Am/V = 59 m–1 can be read after linear interpolation between the curves for unprotected steel with Am/V = 50 m–1 and Am/V = 60 m–1. For Am/V = 59 m–1, read θa,30 = 720 ˚C.

There are three possibilities to meet the fire resistance requirement of 30 minutes with an unprotected beam: – use a heavier section (overdimensioning); – apply a higher steel grade; – design the beam statically undetermined. calculation of the fire resistance |

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Example 2.2

Take a heavier section, for example a HEB 550, which increases the maximum load bearing capacity at normal temperature (step 2):

In the fire design situation, the section complies with class 1 (see Fire 4, table 4.13), which means that the plastic moment capacity can be taken into account. The degree of utilization (step 3) decreases to μ0 = 25,5/95,3 = 0,27. The corresponding critical steel temperature (step 5) is then θa,cr = 736 ˚C. The corrected section factor (step 6) for an unprotected beam HEB 550 (heated form three sides) is Am/V = 50 m–1 (see table 2.6). For this section factor the steel temperature after 30 minutes (step 7) is θa,30 = 693 ˚C. This value is lower than the critical steel temperature (step 8), so an unprotected HEB 550 uncoated satisfies the requirement.

Higher steel grade Use a higher grade of steel, e.g. S355, which increases the maximum load bearing capacity at normal temperature (step 2):

In the fire design situation, the section complies with class 1 (see Fire 4, table 4.13), which means that the plastic moment resistance can be taken into account. The degree of utilization (step 3) decreases to μ0 = 25,5/119 = 0,21. The corresponding critical steel temperature (step 5) is then θa,cr = 768 ˚C. Since the section factor does not change, the steel temperature remains after 30 minutes θa,30 = 721 ˚C. This value is lower than the critical steel temperature (step 8), so an unprotected HEA 550 in S355 satisfies the requirement.

Design the beam statically undetermined Assume that the beam is continuous over three supports. According to the plasticity theory, the maximum load bearing capacity at normal temperature is (step 2):

The degree of utilization (step 3) decreases to μ0 = 25,5/114 = 0,22. For an unprotected, statically indeterminate beam (heated form three sides), κ1 = 0,7 and κ2 = 0,85 (step 4). The corresponding critical steel temperature (step 5) is then θa,cr = 789 ˚C. Since the section factor does not change, the steel temperature remains after 30 minutes θa,30 = 721 ˚C. This value is lower than the critical steel temperature (step 8), so that an unprotected, continuous HEA 550 beam satisfies the requirement.

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Overdimensioning

• Given. A simply supported floor beam HEA 400 in grade S235 steel in a six-storey office building with a span L = 8 m and a centre-to-centre distance a = 5,6 m. The load on the beam is Gk = Qk = 4 kN/m2 with ψ2 = 0,3. The beam is heated on three sides. The fire resistance requirement is 60 minutes.

NA

• Question. The required protection thickness for a sprayed, contour encasement. • Answer. The load in the the fire design situation (step 1) is : qθ,d = (Gk + ψ2Qk)a = (4 + 0,3·4)·5,6 = 29,1 kN/m and the maximum load bearing capacity at normal temperature (step 2):

In the fire situation, the section complies with class 1 (see table 2.8), which means that the plastic moment capacity can be taken into account. The degree of utilization (step 3) follows from equation (2.14):

For a protected, simply supported beam (heated form three sides), κ1 = 0,85 and κ2 = 1,0 (step 4). Applying equation (2.15), the critical steel temperature (step 5) is found: θa,cr = 649 ˚C. The section factor (step 6) for a HEA 400 beam heated on three sides with a contour encasement is Ap/V = 101 m–1 (see table 2.6). The required thermal resistance of a sprayed coating material for a fire resistance of 60 minutes (step 7) and θa,cr = 650 ˚C follows from figure 2.13: dp/λp ≈ 0,04. This means that a protection thickness dp = 0,04λp = 0,04·0,12·103 = 5 mm of sprayed vermiculite or mineral fibres

is required (the value for λp is given in table 2.12). A similar result is found with the nomogram in figure 2.14. For μ0 = 0,39 and κ1κ2 = 0,85·1,0 = 0,85

it can read: θa,cr ≈ 660 ˚C and (Ap/V)(λp/dp) ≈ 2000 m–1. The result is an approximation of the required coating thickness:

This protection thickness can be reduced slightly because of the thermal capacity (thermal active mass) of the insulation, but that has hardly any effect in this example. The reduction factor equals to 1/(1 + φ/3) – see equation (2.10) – with:

The index p stands for ‘protection’ and the index a for ‘steel’. The reduction is then 1/(1 + 0,078/3) = 0,97, so 3%. In practice, the thickness remains unchanged.

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Example 2.3

The calculation of the fire resistance of steel columns is different from that of tension members and beams without lateral torsional buckling: the load-bearing capacity in the fire design situation cannot be determined directly from the decrease in strength as a function of the temperature. The reason is that the buckling factor depends not only on the temperature, but also on the slenderness. In addition, in the fire situation, the modulus of elasticity of the steel decreases faster than its strength (see fig. 2.2). The critical steel temperature for columns can be determined by means of an iterative calculation, in which, after a few iterations, the temperature is found at which the bearing capacity (resistance) of the column corresponds to the compressive force acting on the column during fire. To avoid this iterative calculation, table 2.19 can be applied instead. EN 1993-1-2, cl. 4.2.3.2 gives an equation for the buckling curve in fire for class 1, 2 or 3 sections, see equation (2.22). The non-dimensional slenderness

(for the temperature θa), in which the

effect of the faster decrease of the modulus of elasticity (and thus of the stiffness of the column) is taken into account, is used for this purpose: (2.16) The non-dimensional relative slenderness

is according to the buckling calculation at normal

temperature: (2.17)



Here λ is the slenderness for the considered direction (y or z) and λ1 is the slenderness value to determine the relative slenderness for the applied steel grade. The slenderness is equal to: y

=

ℓ fi,y

and

iy

z

=

ℓ fi,z iz

(2.18)

Where ℓfi is the buckling length in case of fire and i is the radius of gyration in the considered direction. The slenderness value to determine the relative slenderness λ1 according to EN 1993-1-1, cl. 6.3.1.3 applies: (2.19) With two auxiliary parameters α and φθ according to EN 1993-1-2, cl. 4.2.3.2 the buckling factor

χfi in the fire design situation is determined and then the design buckling resistance Nb,fi,t,Rd: 235 fy

= 0, 65 = fi

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=

(

1 1+ 2

(2.20) +

2

–

2

1 2

+

calculation of the fire resistance

Nb,fi,t,Rd =

fi

Ak y, fy

)

(2.21) (buckling curve)



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2.6 Columns

S235

S275

S355

0,05

0,10

0,15

0,20

0,25

0,30

0,35

0,40

0,45

0,50

0,55

0,60

0,65

0,0

950

820

767

725

692

671

650

629

608

590

574

558

542

0,2

918

796

745

697

673

649

625

601

582

564

546

528

509

0,4

892

777

714

678

650

622

595

574

553

532

512

485

452

0,6

867

747

685

651

617

588

564

539

515

483

441

391

164

0,8

829

699

657

615

581

552

522

486

430

320

117

–

–

1,0

784

674

621

578

542

506

437

316

124

–

–

–

–

1,2

738

645

585

541

492

385

197

–

–

–

–

–

–

1,4

694

611

552

495

346

127

–

–

–

–

–

–

–

1,6

674

582

516

364

116

–

–

–

–

–

–

–

–

1,8

652

554

436

169

–

–

–

–

–

–

–

–

–

2,0

628

524

294

–

–

–

–

–

–

–

–

–

–

0,0

950

820

767

725

692

671

650

629

608

590

574

558

542

0,2

921

797

747

698

675

651

627

603

584

566

548

530

512

0,4

894

780

718

680

653

625

598

578

557

536

516

493

460

0,6

871

752

688

655

622

592

568

544

520

494

453

411

246

0,8

835

703

660

619

585

557

528

499

444

367

186

–

–

1,0

788

677

625

582

547

512

452

353

177

–

–

–

–

1,2

743

648

589

545

502

407

234

–

–

–

–

–

–

1,4

695

614

556

503

370

162

–

–

–

–

–

–

–

1,6

676

585

520

384

147

–

–

–

–

–

–

–

–

1,8

654

557

447

195

–

–

–

–

–

–

–

–

–

2,0

630

527

312

–

–

–

–

–

–

–

–

–

–

0,0

950

820

767

725

692

671

650

629

608

590

574

558

542

0,2

924

798

749

700

677

653

630

606

587

569

551

533

515

0,4

897

783

724

684

657

630

603

582

562

542

522

502

472

0,6

878

758

692

660

628

598

575

552

529

506

470

431

356

0,8

845

713

666

627

591

564

537

509

466

413

278

–

–

1,0

795

681

632

588

555

521

474

403

250

–

–

–

–

1,2

752

653

594

552

511

430

288

101

–

–

–

–

–

1,4

698

620

562

511

403

213

–

–

–

–

–

–

–

1,6

679

589

526

409

191

–

–

–

–

–

–

–

–

1,8

658

562

465

230

–

–

–

–

–

–

–

–

–

2,0

634

532

337

–

–

–

–

–

–

–

–

–

–

2.19 Critical steel temperature (˚C) of centrically loaded compression members in grades S235, S275 and S355 steel, depending on the relative slenderness and the degree of plastic utilization μpl (the compressive force on the column in case of fire divided by the plastic normal force at normal temperature). More detailed values are given in table 4.8 (for S235), table 4.9 (for S275), table 4.10 (for S355), table 4.11 (S420) and table 4.12 (S460) in Fire 4.

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plastic degree of utilization μpl

steel grade

= fi

=

(

1 1+ 2

+

2

–

2

)

1 2

+

Nb,fi,t,Rd =

fi

(buckling curve)

Ak y, fy

(2.22)



(2.23)

In a braced frame, the buckling length ℓ fi of columns may, under certain conditions, be reduced in the fire design situation compared to the buckling length at normal temperature. The reduction applies to continuous columns or to columns that are connected rigidly (moment connection) or semi-rigidly (flexible connection). The fire must be confined to a single storey. In addition, the floor below and/or above the fire compartment shall form a separation between two fire compartments and shall also have a fire resistance at least equal to that of the column under consideration. Under these conditions, the column in the fire compartment can be considered to be fixed by the adjacent column in the upper and/or lower fire compartment. Figure 2.20 shows that the buckling length may then be reduced to 0,7 times the system length for the top column and 0,5 times the system length for the other columns, see EN 1993-1-2, cl. 4.2.3.2(5). The stiffness of the connecting, non-heated column(s) is high in relation to the column in the fire compartment, which has become weaker due to the heat. For the same reason, for example, a base plate connection of a column on the ground floor can also be regarded as a rigid connection under certain circumstances. The condition for this is that the eccentricity of the load is not too great; this is usually the case for columns in a braced frame. The rotation of the base plate is then negligible compared to the column deformations that occur in the case of fire. For centrically loaded columns with a relative slenderness of 0,5 ≤ ≤ 1,4, the reduction of the buckling length in the fire design situation by 50% means that the critical steel temperature increases by 50-150 °C (see table 2.19). This is the case with conventional wide flange sections up to a height of 300 mm and square hollow sections up to 200 mm with a yield strength of 235-355 N/mm2 and a storey height of 3,5 m.

2.20 Reduction of the buckling length of columns in braced frames.

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235 fy

= 0, 65

• Given. A four-storey office building, each with a storey height h = 3,6 m. All floors, including the roof floor, have been designed identically. The steel structure is braced and consists of façade columns at a centre-to-centre distance a = 3,6 m and floor beams with a span L = 7,2 m. The columns – square cold formed hollow sections 120x120x10 mm in S275 – are not protected against fire by the façade. The permanent floor and roof load is Gk,floor = Gk,roof = 5,0 kN/m2 and

the variable floor load Qk = 4,0 kN/m2 with ψ2 = 0,3. The weight of the façade, attached to the

NA

columns, is Gk,façade = 2,5 kN/m2. The connection of the columns to the beams is designed in

such a way that the columns are loaded centrically (e0 = 0); there is no transverse load on the façade columns. The required fire resistance of the entire structure, including the floors, is 60 minutes. • Question. The required thickness of a fire protection of the façade columns. • Answer. The calculated value of the load on a façade column in the fire design situation per floor level is Nθ,d,floor = a(Gk,floor + ψ2Qk)L/2 = 3,6·(5,0 + 0,3·4,0)·7,2/2 = 80,4 kN and of the roof Nθ,d,roof = a(Gk,roof + ψ2Qk)L/2 = 3,6·(5,0 + 0·4,0)·7,2/2 = 64,8 kN. The weight of the columns is

neglected. The façade load on each column is Nθ,d,façade = ahGk,façade = 3,6·3,6·2,5 = 32,4 kN per floor.

The columns on the ground floor are critical. The total centric compressive force in a façade column in the fire design situation due to the floors, the roof and the façades is Efi,d = 3Nθ,d,floor +

Nθ,d,roof + 4Nθ,d,façade = 3·80,4 + 64,8 + 4·32,4 = 436 kN.

The cross-section classification for the square hollow section column loaded in compression is based on the widt-to-thickness ratio c/t:

The section complies with class 1 (see Fire 4, table 4.14), therefore the simple calculation method may be used. For the reduced buckling length associated with the buckling mode in the fire design situation and the resulting slenderness, the following is found: ℓ fi = 0,5h = 0,5·3600 = 1800 mm 1

= 93, 9

=

ℓ fi

i

= 1

235 235 = 93, 9 = 86, 8 fy 275

=

1800 = 41,1 43, 8

=

41,1 = 0, 47 86, 8

The plastic degree of utilization μpl is:

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Example 2.4

by interpolation. This critical steel temperature – for which the the design buckling resistance Nfi,t,Rd equals the actions in the fire situation Efi,d – can alternatively be determined after a few iterations (550 °C/489 kN; 600 °C/360 kN; 575 °C/425 kN and 562,5 °C/457 kN) with the equations (2.16) and (2.20) to (2.23), for θa = 570 °C:

The section factor for a square hollow section 120x120x10 mm heated from four sides is Ap/V

= 1/t = 1/(10·10–3) = 100 m–1. The required thermal resistance of the protection material for a fire resistance of 60 minutes and θa,cr = 570 ˚C is read in figure 2.13: dp/λp = 0,058. This can be

achieved, for example, with a silicate board with a thickness dp = 0,058λp = 0,058·0,15·103 = 9 mm. The application of the nomogram in figure 2.14 is as follows. Assume θa,cr = 570 ˚C (vertical axis).

Read horizontal to the right the intersection point for t = 60 minutes: (Ap/V)(λp/dp) = 1450 m–1. The result is an approximation of the required protection thickness:

This thickness can be reduced slightly, but in this example this has little effect, also because of the minimum thickness of 12 or 15 mm that is available on the market. The reduction factor is 1/(1 + φ/3) with:

The reduction is then 1/(1 + 0,153/3) = 0,95, so 5%.

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From table 2.19, the critical steel temperature θa,cr = 570 ˚C follows for μpl = 0,39 and

For beams that are sensitive to lateral torsional buckling (fig. 2.21), the determination of the fire resistance is different from that for tension members and beams in bending that are not sensitive to lateral torsional buckling. As in the case of columns, it is not possible to determine the load-bearing capacity (or the resistance) in the fire design situation directly from the decrease in strength as a function of the temperature. The reason is that the reduction factor for lateral torsional buckling in the fire design situation χLT,fi not only depends on the slenderness, but also on the temperature. The modulus of elasticity of steel decreases faster than its strength, see the graph for kE,θ in figure 2.2. In order to determine the critical steel temperature, an iterative calculation must therefore be carried out. After a few iterations, the temperature is found at which the loadbearing capacity corresponds to the bending moment in the fire design situation. To avoid an iterative calculation, table 2.19 may be used also for lateral torsional buckling. EN 1993-1-2, cl. 4.2.3.3, gives a lateral torsional buckling curve for fire, which is identical to the buckling curve in the fire design situation. It uses a non-dimensional slenderness for lateral (LT stands for ‘lateral torsional buckling’ and com for ‘compression’),

torsional buckling

in which the effect of the faster reduction of the stiffness is taken into account:

(2.24)



With two auxiliary parameters (α – see equation (2.20) – and φLT,θ,com) the reduction factor for lateral torsional buckling in the fire design situation, χLT,fi is determined and then the design lateral torsional 2.21 Example of a beam (rafter) – in a single-storey building – that is sensitive to lateral torsional buckling.

bucking moment resistance at time t Mb,fi,t,Rd: (2.25) (2.26)



(2.27a) (2.27b)

The relative lateral torsional buckling slenderness

has to be determined with a lateral torsional

buckling calculation at normal temperature in accordance with EN 1993-1-1, cl. 6.3.2.2.

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2.7 Beams sensitive to lateral torsional buckling

• Given. The beam HEA 400 in S235 of example 2.3, where in this case it is assumed that the floor does not support the parts of the beam under compression against lateral torsional buckling. The relative lateral torsional buckling slenderness at normal temperature is • Question. The required protection thickness for a sprayed, contour encasement. NA

• Answer. The load in the fire design situation is qθ,d = 29,1 kN/m and the sections complies

with class 1 in the fire design situation (see example 2.3). The plastic degree of utilization μpl is:

From table 2.19 it follows by interpolation that for μpl = 0,39 and

the critical steel

temperature θa.cr = 498 ˚C. (For the beam without lateral torsional buckling in example 2.3 θa.cr = 650 ˚C was found.) Alternatively, the critical temperature θa,cr = 500 ˚C (for which the bending resistance in the fire design situation Mfi,t,Rd becomes equal to the bending moment in the fire design situation Efi,d) can also be determined after some iterations (400 °C/287 kNm and 600 °C/131 kNm) with the equations (2.24) to (2.27), for θa = 500 ˚C:

The section factor (step 6) for a beam HEA 400 that is heated from three sides with a contour encasementis Ap/V = 101 m–1 (see table 2.6). The required thermal resistance of a sprayed protection material for a fire resistance of 60 minutes and θa,cr = 500 ˚C follows from figure 2.12: dp/λp = 0,075. (For the beam without lateral torsional buckling in example 2.2 dp/λp was found to be 0,04). This means a layer of sprayed vermiculite or mineral fibres with a thickness dp = 0,075λp = 0,075·0,12·103 = 9 mm.

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Example 2.5

Read horizontally to the right the intersection point for t = 60 minutes: (Ap/V)(λp/dp) = 1120 W/(m3K). The result is an approximation of the required protection thickness:

This thickness may be reduced slightly. The reduction factor is 1/(1 + φ/3), with:

The reduction is 1/(1 + 0,140/3) = 0,96, so 4%. In practice, the thickness remains unchanged.

2.8 Integrated beams, unprotected The structural integration of steel floor beams in a concrete floor (fig. 2.22) – or, for example, steel columns in the cavity of the façade (see Fire 1 (Fire safety), fig. 1.17) – improves the behaviour of the structure in the event of fire. Due to their protected position, the steel structural components are only heated on one side instead of on three or four sides. As a result, the heating process is slower and the critical temperature is reached later. Without additional protection, such integrated beams (and columns) achieve a fire resistance of 30 minutes or even 60 minutes. See section 2.9 for protected integrated beams. This section deals with the following aspects of unprotected integrated beams: – thermal behaviour; – calculation methods (simple and advanced); – temperature distribution in the cross-section; – verification of the capacity of the bottom plate (for IFB, SFB and THQ beams); – verification of the plastic moment capacity of the cross-section (for IFB, SFB and THQ beams).

2.8.1 Thermal behaviour In the case of integrated beams, a distinction is made between closed and open beam sections (see fig. 2.22). • In the case of closed beam sections (THQ or ‘hat’ beams), radiation and convection to the top flange and to the web plates take place in the hollow space. As a result, the temperatures in these parts are higher than with open profiles, where the upper flange and the web are completely surrounded by concrete. However, computer calculations show that the temper-

2.22 Types of integrated beam: (a) closed section with increased fire resistance provided by means of protection to the bottom flange; (b) open section with increased fire resistance provided by means of reinforcement or protection to the bottom flange.

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The application of the nomogram in figure 2.14 is as follows. Assume θa,cr = 500 ˚C (vertical axis).

the upper flange and 100 ˚C in the middle of the web. The strength of the steel (see fig. 2.2) and the moment resistance have hardly decreased. Integrated beams without protection therefore have a fire resistance of 30 minutes. Due to the protective effect of the concrete, the temperature of the bottom flange is considerably lower than when the girder is below the floor. For comparison, figure 2.10 shows that the temperature after 30 minutes of fire for standard beam sections is in the order of 800 ˚C. After 60 minutes of fire, the influence of heat transfer in the cavity has increased significantly, causing the temperature of the top flange to rise to almost 300 ˚C and that of the web to 500 ˚C. The temperature of the bottom flange rises to more than 800 ˚C. The moment resistance is therefore reduced to less than 20% of that at normal temperature. In most cases a fire resistance of 60 minutes is not feasible for unprotected closed sections; the bottom flange must then be protected (see fig. 2.22a). • With open beam sections, no internal radiation or convection occurs, so that the temperatures of the web and the top flange remain low. A fire resistance of 60 minutes is often achievable for SFB beams and only in certain cases for IFB beams[1]. The fire resistance can be increased by adding reinforcement or by protecting the bottom flange (see fig. 2.22b). In the first case, for example, stirrups must provide the transfer of shear forces between the reinforcement and the steel section. Calculation rules to determine the influence of additional reinforcement on the fire resistance have recently been developed to be incorporated in the next generation of Eurocodes. Integrated beams are heated on one side, so that the temperature distribution in the cross-section is not uniform. As a result, one of the conditions of the calculation method in EN 1993-1-2 is not met. However, it is easy to calculate the fire resistance of structural members heated on one side. The calculation method can be used for both integrated beams and integrated columns. The structural engineer can use two models to calculate the fire resistance of an unprotected integrated beam: a simple and an advanced method.

2.8.2 Simple calculation method In order to use the simple calculation method in EN 1993-1-2 a number of simplified, conservative assumptions have to be made. This determines the critical steel temperature for the entire beam, based on the temperature of the hottest part: the bottom plate. The section factor of a bottom plate with width b and thickness t is: (2.28) This results in a section factor of Am/V = 45-80 m–1 for standard integrated beams. Although this is low compared to the section factor of rolled sections that is placed below the floor, it is not always low enough to achieve a fire resistance of 30 minutes with unprotected integrated beams. The steel temperature after 30 minutes is about 650-750 ˚C (see fig. 2.10). It therefore

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atures in a closed profile are low after 30 minutes of fire: about 500 ˚C in the bottom flange, 50 ˚C in

of fire resistance with the simple method. The reason is that the method with section factors does not take into account the heat capacity (accumulation) of the concrete and the relatively low temperatures in the web and in the upper flange. This leads to an underestimation of the fire resistance and thus to a non-economical design. However, tests have shown that a fire resistance of 30 minutes can easily be achieved without protection[4].

2.8.3. Advanced calculation method A better determination of the fire resistance of unprotected integrated beams is possible with a more advanced calculation method, which is well applicable depending on the country and

NA

tools available. In this section, the general principles are treated and illustrated with an example. Dependent on the country an equivalent method is possible. The advanced calculation method does not assume a uniform temperature distribution in the beam (as in the simple calculation method in EN 1993-1-2), but a more realistic temperature distribution. This allows the advantages of integrated beams to be better exploited. With this calculation method, a plastic cross-section calculation can be used to check the resistance to fire. The structural engineer calculates the bending moment capacity at mid span and checks the transverse load-bearing capacity of the bottom plate/flange. The shear force capacity (web) is not decisive if this is not the case at normal temperatures. The following aspects of the advanced calculation method are discussed: – temperature distribution in the cross-section; – verification of the bottom plate; – verification of the plastic moment capacity.

Temperature distribution in the cross-section The temperatures can be obtained from finite element calculations. From these, temperature rules have been derived for specific parts of the cross-section[4]. The most important part is that of the bottom plate, for which the following equation is available: (2.29) The parameters A, B and C are given in table 2.23.

2.23 Parameters or calculating the bottom plate temperatures in equation (2.29).

C

θa,max (˚C)

–12,8

760

414

–11,8

980

712

0

–2,6

990

–

0

–1,25

1025

–

time (min)

A

30

0,113

60

0,130

90 120

B

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depends on whether the critical steel temperature is sufficiently high to demonstrate 30 minutes

2.24 Definition of plate thicknesses to be used in the calculation of temperatures for an SFB beam.

Aw

Bw

Cw

Dw

30

–140,7

832,4

0,00317

–0,0230

60

–103,8

968,6

0,00232

–0,0182

90

–108,6

1146,7

0,00198

–0,0154

120

–70,4

1124,4

0,00158

–0,0134

2.25 Parameters for calculating the web temperatures in equation (2.30).

For SFB beams two zones have to be considered: a zone with plate thickness tp,1 (bottom plate and bottom flange together) and a zone with plate thickness tp,2 (only the bottom plate), see figure 2.24. This method can be used when at least 85% of the bottom plate is covered by the concrete or composite floor or when the cannelures of the composite floor are filled with mineral wool. If not an alternative method has to be used to calculate the heating of the cross-section. The temperatures in the web θw are much lower and can be determined from equation (2.30) as a function of the distance z to the top of the bottom plate or bottom flange (in case of a SFB beam). θw = k1ek2z with k1 = Aw·ln tp + Bw k2 = Cw·ln tp + Dw

(2.30)

The parameters A w, Bw, Cw and Dw are given in table 2.25. From equation (2.30), the point in the web where the temperature of 400 ˚C is reached, can be calculated. Above this point no strength reduction is necessary; below this point the strength is reduced. The top flange temperature is always below 400 ˚C (for every type of beam and even for the smallest section after 120 minutes), and no strength reduction is necessary.

Verification of the bottom plate The purpose of assessing the bottom plate is to determine whether the bottom plate (and in the case of an SFB beam, also the bottom flange) is sufficiently strong in the transverse direction to transfer the floor loading to the beam web. This is because the force transmitted from the support of the hollow core slab via the bottom plate to the web causes stresses due to bending and shear in the transverse direction in the bottom plate (and, in the case of an SFB beam, also in the bottom flange).

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time (min)

2.26 Additional reinforcement used with an IFB beam to improve the transverse bending resistance.

for IFB-beams) these forces can be transferred by additional reinforcement, see figure 2.26. If only the bottom plate is considered, it is assumed that the force of a hollow core slab is acting halfway along the length of the slab on the bottom plate. The verification of the bottom plate is as follows: 1. Calculate the temperature of the bottom plate with equation (2.29). 2. Determine the reduced yield strength fy,θ of the bottom plate using

equation (2.2).

3. Assess the C-value (unity check) according to:

(2.31)

Where: qmax maximum value of the transverse shear force (of the slab) of the

two sides of the integrated beam in kN/m or N/mm;

e1, e2 distances in mm according to figures 2.27, 2.28 and 2.29; fy,θ

reduced yield strength of the bottom plate in N/mm2;

tp

thickness of the bottom plate in mm.

Equation (2.31) is conform the mechanical equation for the ultimate limit state of an integrated beam at normal temperature. However, the yield stress of the steel is now reduced as a function of temperature. The application of equation (2.31) for the three types of girders mentioned above is discussed below. • IFB beam. The force distribution in the bottom flange of an IFB beam is shown in figure 2.27. Equation (2.31) can be used with e2 = 0. Furthermore, qmax = qΘ,d /2 applies.

2.27 Force distribution in the bottom plate of an IFB beam.

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When the thickness of the bottom plate is not sufficient (as is usually the case

2.29 Force distribution in the bottom plate of a THQ beam.

• SFB beam. The force distribution in the bottom flange and the lower plate of an SFB beam is shown in figure 2.28. For the SFB beam, both the bottom flange and the bottom plate must be checked according to equation (2.31). For both the bottom plate and the bottom flange, qmax = θθ,d /2 applies. From the geometry it follows that for the bottom flange in equation (2.31) the term

e1 – e2 should be replaced by e2 and tp by tf. The temperature of the bottom plate is higher than that of the bottom flange due to the lower thickness, see equation (2.29), where tp is equal to the summation of the thicknesses of the bottom plate and the bottom flange for calculating the bottom flange temperature. • THQ beam. The force distribution in the bottom flange of a THQ beam is shown in figure 2.29. The cross-sectional check is done with equation (2.31), where qmax = θθ,d /2 applies.

Verification of the plastic moment capacity of the cross-section The contribution of the bottom plate (and flange in case of a SFB beam) to the moment capacity of the beam must be reduced due to the transverse stresses. The stress distribution in the bottom plate by bending and shear in the transverse direction must be determined by considering the plate as a cantilever beam with the connection to the web as a fixed support. For the assessment of the positive moment capacity (in the span), the plastic stress distribution in the bottom plate can be assumed, because this plate has a tensile force in an longitudinal direction.

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2.28 Force distribution in the bottom flange and bottom plate of a SFB beam.

plate must be reduced by Aσ- and Aτ. In the remaining area, the entire yield strength can be al-

2.30 Reduction in cross-sectional area to be used for determining bending resistance, due to bending and shear forces in the transverse direction (section not drawn to scale).

lowed in the longitudinal direction.

The cross-section is divided into several parts, each with a characteristic temperature and corresponding reduction of the strength. After the reduced cross-section has been determined, the plastic moment capacity can be calculated by dividing the cross-section into the top flange, the web, the bottom flange (in the case of a SFB beam), and the bottom plate. For each part, the calculation is based on a uniform temperature. The yield strength is determined according to equation (2.2). With the reduced areas, it is now possible to calculate the position of the neutral axis in the cross-section in order to determine the plastic moment. The force in each part of the cross-section is: Nθ,pl = Aefffy,θ (2.32)



Where: Nθ,pl resulting force in this part of the cross-section;

Aeff effective surface area of this part of the cross-section; fy,θ

reduced yield strength in this part of the cross-section, depending on the steel temperature in that section.

The position of the neutral axis is such that the resulting force above this line (compression) and below this line (tension) are equal, so that the total normal force is equal to zero: ∑Nθ,pl = 0.

When the location of the neutral axis is known, the plastic moment Mpl is determined as the summation of the contributions to the moment capacity by the different forces in the cross-section.

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Without exceeding the yield criterion according to Huber-Hencky, in area Aσ+ the entire effective

yield strength can be allowed in longitudinal direction (fig. 2.30). The cross-section of the bottom

• Given. An office building with integrated beams SFB 200-HEB 200-400x15 (fig. 2.31) in S355 with Wpl = 822·103 mm3 and hollow core slabs with a support length of 80 mm. The weight of the integrated beams is Gk = 1,1 kN/m; they have a centre-to-centre distance a = 7,2 m spanning L = 4,5 m. The weight of the hollow core slabs is Gk = 5,5 kN/m2. They are designed for a variable

NA

load Qk = 4 kN/m2 with ψ2 = 0,3.

• Question. Check whether a fire resistance of 60 minutes is achieved. • Answer. The load on the beam in the event of fire is qθ,d = (Gk,floor + ψ2Qk)a + Gk,beam =

(5,5 + 0,3·4)·7,2 + 1,1 = 49,3 kN/m and the corresponding bending moment Mθ,d = qθ,dL2/8 = 49,3·4,52/8 = 125 kNm. The load from the floor on the beams on one side is qθ,max = 0,5qθ,d =

0,5(Gk,floor + ψ2Qk)a = 0,5·(5,5 + 0,3·4)·7,2 = 24,1 kN/m.

For a fire resistance of 60 minutes, the temperatures of the bottom parts are calculated with equation (2.29), see figure 2.32:

2.31 Integrated beam SFB 200-HEB 200-400x15 supporting hollow core slabs.

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2.32 Temperature in three characteristic points.

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Example 2.6

k1 = Aw·ln tp + Bw = –103,8·ln 30 + 968,6 = 615,6 k2 = Cw·ln tp + Dw = 0,00232·ln (30) – 0,0182 = –0,0103 θ3 = k1ek2z = 615,6·e–0,0103·z With this equation for θ3, the point in the web where a temperature θ3 = 400 °C is reached can be derived: hℓ = (1/k2)·ln(400/k1) = (1/–0,0103)·ln(400/615,6) = 42 mm above the bottom flange. Above this point no strength reduction is necessary; below this point the strength is reduced. Equation (2.2) defines the yield strength for each of these parts, see table 4.1 of Fire 4 (Design tables): – part 1 (where the bottom flange is above the bottom plate): fy,θ1 = 0,177·355 = 62,8 N/mm2 (743 ˚C); – part 2 (the extending bottom plate):

fy,θ2 = 0,098·355 = 34,8 N/mm2 (832 ˚C);

– part 3 (lowest 42 mm of the web):

fy,θ3 = 0,540·355 = 192 N/mm2 (for 572 ˚C, the average between 400 and 743 ˚C). Other parts are not reduced in strength.

Verification of the bottom plate For fy,θ2 = 34,8 N/mm2, Cp follows from equation (2.31):

Verification of the bottom flange For fy,θ1 = 62,8 N/mm2, Cf follows from equation (2.31):

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The web temperatures are calculated from equation (2.30):

The reduction of the cross-section is:

For each part of the cross-section, the plastic normal force can be determined (table 2.33). The total plastic normal force is the sum of the plastic normal forces in the individual parts and amounts to 2038 kN. Half of this force (1019 kN) is slightly less than the force provided by the top flange (1065 kN). Therefore the neutral axis is in the bottom part of the top flange. The location of the neutral line from the top of the profile zna is:

The sum of the contributions to the plastic moment of the normal forces multiplied by the distance z to the neutral axis results in Mθ,pl = 127 kNm > Mθ,d = 125 kNm.

Conclusion Both the transverse load-bearing capacity (of the bottom plate and bottom flange) and the longitudinal moment capacity Mθ,pl are sufficient in the fire design situation. The SFB 200-HEB 200-400x15 beam has therefore a fire resistance of 60 minutes, without protecting the bottom plate.

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Nθ,pl

z

M θ,pl

θ

(mm2)

(˚C)

top flange (compression)

2870