Structural Timber Design 0632050918

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Blackwell Science

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0 1999by Blackwell Science Ltd Editorial Offices: Osney Mead, Oxford OX2 OEL 25 John Street, London WClN 2BL 23 Ainslie Place, Edinburgh EH3 6AJ 350 Main Street, Malden MA 02148 5018, USA 54 University Street, Carlton Victoria 3053, Australia 10, rue Casimir Delavigne 75006 Paris, France Other Editorial Offices:

Blackwell Wissenschafts-VerlagGmbH Kurfurstendamm 57 10707 Berlin, Germany Blackwell Science KK MG Kodenmacho Building 7-10 Kodenmacho Nihombashi Chuo-ku, Tokyo 104, Japan The right of the Author to be identified as the Author of this Work has been asserted in accordance with the Copyright, Designs and Patents Act 1988. All rights reserved.No partof thispublication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical,photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without prior permission of the publisher. First published 1999

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zy zyxwv For further information on Blackwell Science, visit our website: www.blackwel1-science.com

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Preface 1

Timber as a Structural M aterial 1.1 ~ntroduction 1.2 The structure of timber 1.3Defects in timber 1.3.1 Natural defects 1.3.2Chemicaldefects 1.3.3Conversiondefects 1.3.4Seasoning defects 1.4Typesof timber l .4.1 Softwoods 1.4.2 Hardwoods 1.5Physical properties of timber 1.5. 1 Moisture content 1.5.2 Density 15.3Slopeof grain 1.5.4Timberdefects 1.6 References

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S 5268 :Part 2 :11996 2.1 Introduction 2.2Design philosophy 2.3Stress grading of timber 2.3.1Visual grading 2.3.2Machine grading 2.4 Strength classes 2.5Design considerations (factors affecting timber strength) 2.5.1 Loading 2.5.2Serviceclasses 2.5.3 Moisture content 2.5.4 Duration of loading

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Contents

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2.5.5Sectionsize 2.5.6 Load-sharingsystems 2.5.7 Additional properties 2.6 Symbols 2.7 References

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3 UsingMathcad@ for Design C ~ c u l a ~ o n s 3.1 Introduction 3.2WhatisMathcad? 3.3WhatdoesMathcaddo? 3.3.1 Asimple calculation 3.3.2Definitions and variables 3.3.3 Entering text 3.3.4 Workingwith units 3.4 Summary 3.5 References

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4 Design of FlexuralMembers(Beams) 4. l Introduction 4.2 Design considerations 4.3 Bending stress and prevention of lateral buckling 4.3.1EAFective span, L, 4.3.2 Form factor, KG 4.3.3Depth factor, K7 4.3.4 Selection of a suitable section size 4.3.5 Lateral stability 4.3.6An illustrative example 4.4 Deflection 4.4.1Deflectionlimits 4.4.2 Precamber 4.4.3Bendingdeflection 4.4.4Sheardeflection 4.5 Bearing stress 4.5.1Lengthand position of bearings 4.6 Shear stress 4.6.1Shear at notched ends 4.7 Suspended timber flooring 4.8 References 4.9 Design examples Example 4.1 Example 4.2 Example 4.3 Example 4.4

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esign of Axially Loaded Members 5. l Introduction 5.2Designofcompressionmembers 5.2. l Design considerations 5.2.2 Slenderness ratio, h 5.2.3 Modification factor for compression members, K12 5.2.4 Members subjected to axial compression only (Clause 2.1 1.5) 5.2.5 Members subjected to axial compression and bending (Clause 2.1l .6) 5.2.6 Design of load-bearing stud walls 5.3 Design of tension members (Clause 2.12) 5.3.1Design considerations 5.3.2Width factor, K14 5.3.3 Members subjected to axial tension only 5.3.4 Combined bending and tensilestresses 5.4Designexamples Example 5.1 Example 5.2 Example 5.3 Example 5.4 Example 5.5

6 Design of GluedLaminatedMembers 6.1 Introduction 6.2 Design considerations 6.3 Grade stresses for horizontally glued laminated members 6.3.1Single-grademembers 6.3.2 Combined-grademembers 6.3.3 Permissible stresses for horizontally glued laminated members 6.4 Grade stresses for vertically glued laminated beams 6.4.1Permissiblestresses for verticallyglued laminated members 6.5 Deformation criteria for glued laminated beams 6.6 Curved glued laminated beams 6.7 Bibliography 6.8 Design examples Example 6.1 Example 6.2 Example 6.3 Example 6.4 Example 6.5

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Contents

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7.1 Introduction 7.2 Transformed (effective) geometrical properties 7.3 Plywood 7 '4 Design considerations 7.4.Bending l 7.4.2 Deflection 7.4.3 Panelshear 7.4.4 Rollingshear 7.4.5 Lateral stability 7.4.6 Web-stiffeners 7.5 References 7.6 Design examples Example 7.1 Example 7.2

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8 Design of (Spaced) Built-up

Columns 8.1 Introduction 8.2 Spaced columns 8.3 Design considerations 8.3.1 Geometricalrequirements 8.3.2 Modes of failure and permissible loads 8.3.3 Shear capacity ofspacerblocks 8.4 Compression members in triangulated frameworks 8.5 Reference 8.6 Design examples Example 8.1 Example 8.2 esign of Timber Connections

9. l Introduction 9.2 Generaldesignconsiderations 9.3 Joint slip 9.4Effectivecross-section 9.5Spacingrules 9.6Multipleshearlateralloads 9.7Nailed joints 9.7.1 Improvednails 9.7.2 Pre-drilling 9.7.3Basicsingleshear lateral loads 9.7.4Axiallyloadednails(withdrawalloads) 9.7.5 Permissible load for a nailed joint 9.8Screwed joints 9.8.1Basicsingle shear lateral loads 9.8.2Axiallyloadedscrews(withdrawalloads) 9.8.3 Permissible load for a screwed joint

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Contents

9.9 Bolted and dowelled joints 9.9.1Basicsingle shear lateral loads 9.9.2 Permissible load for a bolted or dowelled joint 9.10 Moment capacity of dowel-type fastener joints 9.1 1Connectored joints 9.1 l. l Toothed-plate connectors 9.1 l .2 Split-ring and shear-plate connectors 9.1 l .3 Metal-plate connectors 9.12 Clued joints 9.12.1 Durability classification 9.12.2 Design considerations for glued joints 9.13 References 9.14 Design examples Example 9.1 Example 9.2 Example 9.3 Example 9.4 Example 9.5 Example 9.6 Example 9.7 Example 9.8

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179 180 184 185 188 189 191 193 195 195 196 196 197 197 199 20 1 204 208 210 213 216

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esign to Euroco~e5 10.1 Introduction 10.2 Design philosophy 10.3 Actions 10.4 Material properties 10.4.1Designvalues 10.5 Ultimate limit states 10.5.1 Bending 10.5.2 Shear 10.5.3 Compression perpendicular to grain (bearing) 10.5.4 Compression or tension parallel to grain 10.5.5 Members subjected to combined bending and axial tension 10.5.6 Columns subjected to combined bending and axial compression 10.5.7 Dowel-type fastener joints 10.6 Serviceability limit states 10.6.1Deflections 10.6.2 Vibrations 10.6.3 Joint slip 10.7 Reference 10.8 Bibliography

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10.9Designexamples Example 10.1 Example 10.2 Example 10.3

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Appendix A: Section Sizes for Softwood Timber Appendix B: Weights of Building ater rials Appendix C: Related BritishStandards for TimberEngineering

257 259 260

Index

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The increasing recognition of timber as a structural material is reflected in the inclusion oftimber design in many undergraduate courses. majority of design textbooks for undergraduate engineering students neglect, to a large extent, the importance of timber as a structural and building material. As a consequence, relativelyfew textbooks provide information on the designoftimber structures. Structural TimberDesign is intended to address this issue by providing a step-by-step approach to thedesign of all the most commonly used timber elements and joints illustrated by detailed worked examples.This is an approachwhich is recognisedto be beneficial in learning and preferred by most students. The book has been written for undergraduate students on building, civil and structural engineeringand architectural courses and will be an invaluable reference source anddesign aid for practising engineers and postgraduate engineering students. It provides a comprehensive source of information on practical timber design and encourages theuse of computers to carry out design calculations. Chapter 1 introduces the nature and inherent characteristicsof timber such as defects, moisture content and slope of grain, and discusses the types of timber and factors that influence their structural characte includes a comprehensive review of the recently revised t 2: 1996: Structural Use of Timber. The design philosophy of its new approach to the strength classsystem and also the factors affecting timber strength are explained. Chapter 3 gives an overviewofMathcad@,acomputer software programmeused to carry out mathematical calculations, and details its simplicity and the advantages that it provides when used for design calculations. Theaimis to encourage readers to usecomputing as a tool to increasetheir under-standing ofhowdesign solutions vary in response to a change in oneof the variables and howalternative design options canbe obtained easily and effortlessly. The design of basic elements is explained and illustrated in Chapters 4 and 5, whilst the design of more specialised elements such as glued laminated straight and curved beams and columns, ply-webbed beams and built-up columns isillustrated in Chapters 6, 7 and 8 using numerous worked examples.

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InChapter 9thedesignoftimberconnectionsisdetailed.The new approach adoptedby the revised BS 5268:Part 2 in 1996, i.e.the Eurocode 5 approach for the design of timber joints, is described.The chapter includes a comprehensivecoverageofthedesignrequirements for nailed,screwed, bolted and dowelled joints, and the design of connectored joints such as toothed-plates, split-rings and shear-plates and glued connections is also detailed. Several step-by-step worked examples are provided to illustrate the design methods in this chapter. Chapter 10 provides a comprehensive review of the proposed European code for timber, Eurocode 5: Design of Timber Structures. The limit states design philosophy of EC5 is explainedand the relevant differences with the design methodology of BS 5268 are high~ghtedand discussed. This chapter also provides comprehensive coverage of EC5 requirementsfor the design of flexural and axially 1o.aded members and dowel-type connections such as nailed,screwed,bolted and dowelled joints. Again,step-by-stepworked examples are provided to illustrate the design methods in the chapter. Alldesignexamplesgiveninthisbook are produced in theform of worksheet files and are available from theauthor on 3 r disks to run under Mathcad computersoftwareVersion6, or higher, in eitherone of its editions: (Student, Standard, Plus or Professional). Details are given at the end of the book. The examples are fully self-explanatoryand well annotated and the author isconfident that thereaderswhether students, course instructors, or practising design engineerswill find them extremely usefulto produce designsolutions or prepare course handouts. In particular, the worksheets willallowdesignengineers to arrive at themost suitable/ economic solution(s) very quickly. Extracts from British Standards are reproduced with the permission of BSI under licence no. PD\1998 0823. Complete editions of thestandards can be obtained by post from BSI Customer Services, 389 Chiswick High Road, London'W4 4AL. The cover illustration was kindly supplied by MiTek Industries Ltd.

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ructural

1.1 Introduction

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Timber has always been one the of more plentiful natural resources available and consequently is oneof the oldest known materials used in construction. It is a material that is used for a variety of structural forms such as beams, columns, trusses, girders and is also used in building systems such as piles, deck members, railway foundations and for temporary f o m s in concrete. Timber structures can be highly durable when properly treated and built. Examples of this are seen in many historic buildings all around the world. Timber possesses excellent insulating properties, good fire resistance, light weight and aesthetic appeal. A great deal of research carried out since the early part of this century has provided us with comprehensive information on structural properties of timber and timber products'. A knowledge of engineering materials is essential for engineering design. Timber is a traditional building material and over the years considerable knowledge has been gained on its important material properties and their effects on structural design and service behaviour. Many failures in timber buildingsin the pasthaveshown us the safe methods of construction, connection details and design limitations. This chapter provides a brief description of the engineering properties of timber that are of interest to design engineersor architects. But it should be kept in mindthat, unlike some structural materials suchas steel or concrete, the properties of timber are very sensitive to environmental conditions. For example, timber is very sensitive to moisture content, which has a direct effect on the strength and stiffness, swellingor shrinkage of timber. A proper understanding of the physical characteristics of wood aids the building of safe timber structures"

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1.2 The structure of timber *

Mature trees of whatever type are the source of structural timber and it is important that users of timber should have a knowledge of the nature and growth patterns of trees inorder to understand its behaviour undera variety 1

Structural TimberDesign

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of circumstances. Basically, a tree has three subsystems: roots, trunk and ow^^ Each subsystem has a role to play in the growth pattern of the tree.

Roots, by spreading through the soil as well as acting as a foundation, enable the growingtree to withstand windforces.They absorb moisture containing minerals from the soiland transfer it via the trunk to the crown. Trunk provides rigidity, mechanical strength and height to maintain the crown, Alsotransports moisture and minerals up to the crown and sap down from the crown. Crown provides as largeas possible a catchment area covered by leaves. These produce chemical reactions that form sugar and cellulose which cause the growth of the tree.

A s engineers we are mainly concerned with thetrunk of the tree. Consider a cross-section of a trunk as shown in Fig. 1.1. Wood, in general, is composed of long thin tubular cells. The cell wallsare made up of cellulose and the cellsare bound together by a substance known as lignin. Most cells are oriented in the direction of the axis of the trunk, except for cells known as rays which run radially acrossthe trunk. Rays are present in all trees but are more pronounced in some species, such as oak. In temperate countries, a tree produces a new layer of wood just under the bark in the earlypart of every growing season. This growth ceases at the end of the growing seasonor during winter months. This process results in clearly visible concentric rings knownas annular rings, annual rings or growth rings. In tropical countries where trees grow throughout the year, a tree produces wood cells that are essentially uniform. The age of a tree may be determined by counting its growth rings'.

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Fig. 1.l

Cross-section of a trunkof a tree.

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Timber as aStructuralMaterial

3

The annular band of cross-section nearest to the bark is called sapw ood. The central core of the wood which is inside the sapwood isheartw ood. The sapwood is lighter in colour compared to heartwood and is25-170mm wide, depending on the species. It acts as a medium oftransportation for sap from the roots to the leaves, while the heartwood functions mainly to give mechanical support or stiffness to the trunk. In general, the moisture content, strength and weights of the two are nearly equal. Sapwood has a lower natural resistance toattacks byfungi and insectsand accepts preservatives more easily than heartwood', In many trees, each annular ring can be subdivided into two layers: an inner layer made up of relatively large cavities called springw ood, and an outer layerofthickwallsandsmallcavitiescalled sum m erw ood, Since summerwood is relatively heavy, the amount of summerwood in any section is a measure of the density of the wood.

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e fe c t s in t im b e r2

Owing to the fact that wood is amaterial which is naturally occurring, there are manydefectswhich are introduced during the growing period and during the conversion and seasoningprocess. Any of these defects can cause trouble in timber in use either byreducing its strength or impairing its appearance. Defects may be classifiedas: natural defects, chemical defects,conversion defects and seasoning defects. t ~ r a defects J

These occur during the growing period. Examplesof natural defects are illustrated in Fig. 1.2(a). These may include: Cracks and3ssures. They may occur in various parts of the tree and may

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even indicate the presence of decay or the beginnings of decay. Knots. These are common features of the structure of wood. A knot is a portion of a branch embedded by the natural growth of the tree, normally originating at the centre of the trunk or a branch. Grain defects. Wood grain refers to the general direction of the arrangement of fibres in wood. Grain defects can occur in the form of twisted-grain, cross-grain, flat-grain and spiral-grain, all of which can induce subsequent problems of distortion in use. Fungaldecay. This may occur in growingmaturetimber or even in recently converted timber, and in generalit is goodpractice to reject such timber. \ Annual ring w idth. This can be critical in respect of strength in that excess width of such rings can reduce the density of the timber.

Structural Timber Design

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Cross-grain

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(a) Natural and conversion defects

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Springing Twisting

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Bowing (b) Seasoning defects

Defects in timber.

These may occur in particular instances when timber is used in unsuitable positions or in association with other materials. Timbers such as oak and western red cedar contain tannic acid and other chemicals which corrode

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These are due basically to unsound practice inthe use of milling techniques or to undue economy in attempting to use every possible piece of timber converted from the trunk. A wane is a good example of a conversion defect.

Seasoning defectsare directly related to the movement that occurs in timber due to changes in moisturecontent. Excessive or uneven drying, exposureto wind and rain, and poor stacking and spacing during seasoning can all produce defects or distortions in timber. Examples of seasoning defectsare illustratedinFig. 12(b). Allsuchdefectshave an effect on structural strength as well as on fixing, stability, durability and finished appearance.

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Trees and commercial timbers are divided into two groups: softwoods and hardwoods. This terminology hasno direct bearing on the actual softness or hardness of the wood.

Softwoods are generally evergreen with needle-like leaves comprising single cellscalled tracheids, which are likestrawsinplan, and theyfulfil the functions of conduction and support. Rays, present in softwoods, run in a radial direction perpendicular to the growth rings. Their function isto store food and allow the convection of liquids to where they are needed. o ft w o o ^ c h a ra c t e ris t ic s 0

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Quick growth rate; trees can befelled after 30 years, resulting in low density timber with relatively lowstrength. Generally poor durability qualities, unless treated with preservatives. Due to speed of felling, they are readily available and comparatively cheap.

1 .4 .2 ~ ~ r d w o o d s

Hardwoods are generallybroad-leaved(deciduous)trees that losetheir leaves at the end of each growing season.The cell structure of hardwoods is

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Structural Timber

Design

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more complex than that of softwoods, with thick walled cells, calledJibres, providing the structuralsupportand thin walledcells,called vessels, providing the medium for food conduction. Due to the necessity to grow newleaveseveryyear the demand for sap is high and in some instances larger vessels may be formed inthe springwood - these are referred to as rig porous woods. When there is no definite growingperiod the pores tend to be more evenly distributed, resulting in dzfuse porous woods. r d w o o d c h a ra c t e ris t ic s

Hardwoods grow at a slower rate than softwoods. This generally results in a timber of high density and strength which takes time to mature over 100 years in some instances. There is less dependency on preservatives for durability qualities. Due to time taken to mature and the transportation costs of hardwoods, as most are tropical, they tend to be expensive in comparison to softwoods.

ysical p ro p e rt ie s o f t im b e r3

Dueto the fact that timber issucha variable material, its strength is dependent on many factors which can act independently or in conjunction with others, adverselyaffecting the strength and the workability of the timber. Amongmanyphysical properties that influence the strength characteristics of timber, the followingmaybe considered the most important ones.

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is t u r e c o n t e n t

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The strength of timber isdependent on its moisture content, as is the resistance to decay. Most timber in the UK is air-dried to a moisture content of between 17% and 23% which is generally below fibre saturation point at which the cell wallsare still saturated but moisture is removed fromthe cells. Any further reduction willresult in shrinkage4. Figure 1.3highlights the general relationship between strength andlor stiffness characteristics of timber and its moisture content. The figure shows that there is an almost linear loss in strength and stifkess as moisture increases to about 30%, corresponding to fibre saturation point. Further increasesin moisture content have no influence on either strength or stiffness. It should be noted that, although for mostmechanical properties the pattern of change in strength and stiffness characteristics withrespect to change in moisture content is similar, the magnitude of change is different from oneproperty to another. It is also to be noted thatasthe moisture content decreases shrinkage increases. Timber is described as being hygroscopic which means

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Fig. 1.3 Generalrelationshipbetweenstrengthand/ orstiffnessandmoisture content.

thatit attempts toattainan equilibrium moisture content with its surrounding environment, resulting in a variable moisture content. This should alwaysbeconsideredwhenusing timber, particularly softwoods which are more susceptible to shrinkage than hardwoods.

Density is the best single indicator of the properties of a timber and is a major factor determining its strength. Specific gravity or relative density is a measure of timber's solid substance. It is generally expressed as the ratio of the oven-dry weight to the weight of an equal volume of water. Sincewatervolume varieswith the moisture content ofthe timber, the specific gravity of timber is expressedat a certain moisture content. specific gravity of commercial timber ranges from 0.29 to 0.8 1, most falling between 0.35 and 0.60. '

Grain is the longitudinal direction of the main elements of timber, these main elements being fibres or tracheids, and vessels in the case of hardwoods. In many instances the angle of the grain in a cut section of timber is not parallel to the longitudinal axis. It is possible that this variation is due to poor cutting of the timber, but more often than not the deviation in grain angle is due to irregular growth of the tree. This effectisoflesser consequence when timber is axially loaded, but leads to a significant drop in bendingresistance.Theangleof the microfibrilswithinthe timber also affects the strength of the timber, as with the effects ofthe grain, if the angle of deviation increases the strength decreases.

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1-5.4 Tim b e r d e fe c t s

As described earlier, defects in timber, whether

natural or caused during conversion or seasoning, will have an eEect on structural strength as well as on fixing, stability, durability and finished appearance of timber.

1 .6

Re fe re n c e s

Somayaji, S. (1990) StructuralWoodDesign. West Publishing Company, St. Paul, U.S.A. Illston, J. M . , Dinwoodie, J . M. and Smith, A.A. (1979) Concrete, Timber and Metals - The Natureand Behaviour of StructuralMaterials. Van Nostrand Reinhold International, London. Illston, J.M. (1994) Construction ater rials - Their Nature and Behaviour. E.& F.N. Spon, London. Carmichael, E.N. (1984) Timber Engineering. E.& F.N. Spon, London.

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Strength capability of timber is difficultto assess as we have no control over its quality and growth. The strength of timber isa function of severalparameters including the moisture content, density, duration of the applied load, size of members and presence of various strength-reducing characteristics such as slope ofgrain, knots, fissures and wane. To overcome this difficulty, the stress grading method of strength classification has been devised'. Guidance onthe use of timber in building and civil engineeringstructures is given inBS 5268: Structural use of timber. This was originally divided into seven parts:

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Part 1: Limit state design, materials and workmanship. Part 2: Code of practice for permissible stress design, materials and workmanship. Part 3: Code of practice for trussed rafter roofs. Part 4: Fire resistance of timber structures. Part 5: Preservation treatments for constructional timber. Part 6: Code of practice for timber framed walls. Part 7: Recommendations for the calculation basis for span tables.

Part l of BS 5268wasnevercompleted and, with the introduction of Eurocode 5: DD ENV 1995-1-1: Design of timber structures, the development of this part was completely abandoned. Part 2 of BS 5268, on which the design of structural timber is based, was originally published as CP 112 in 1952 and revised later in 1967 and, with extensive amendment, in 1971. The 'basic stresses' introduced in CP 112 were determined from carryingout short-term loading tests on small timber specimens free from all defects. The datawas used to estimate the minimum strength which was taken as the value below which not more than 1% of the test results fell. These strengths were multiplied by a reduction factor to givebasicstresses.Thereduction factor made an allowance for the 9

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StructuralTimber Design

reduction in strength due to durationfor loading, size of specimen andother effects normallyassociated with a safety factor, such as accidental overloading,simplifyingassumptionsmade during designanddesign inaccuracy, together with poor workmanship. Basic stress was defined as the stress that could be permanently sustained by timber free from any strength-reducing characteristics'. Since 1967 there have been continuing and significant changes affecting the structural use of timber. Research studies in the UK and othercountries had shownthe need for a review of the stress values andmodification factors given in the original code. the concept of 'basic stresses' was With theintroduction of BS 5268 in 1984 largely abandonedand the new approach forassessing the strength of timber moved somewhatin line with 'limitstates' design philosophy. In 1996, Part 2 of BS 5268 was revised witha clear aimto bring this code as close as possible to, and to run in parallel with, Eurocode 5: DD ENV 1995-1 -1: Design of timber structures, Part 1.1 General rules and rules f o r buildings. The overall aim has been to incorporate material specifications and design approaches from Eurocode 5, while maintaining a permissible stress code with which designers, accustomed to BS 5268, will feel familiar and be able to use without difficulty. The first step in this process involvesstrength grading of timber sections. Thereare two Europeanstandards which relate to strength grading:

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BS EN 518 : 1995 Structural timber. Grading. Requirements for visual strength grading standards. BS EN 519 ;1995 Structurul t i ~ b e r.Grading. Requiremen~s for ~ a c h i n ~ strength graded timber and grading machines. dance for stress grading of the two typ hardwoods, are given in the following

timber, namelysoftwoods

S 4978 :1996 Spec~ cationf o r softwoods graded for structural use. S 5756 :1997 Spec~ cation f o r tropicalhard woo^ gradedfor str~cturaluse. The current revised versions

of these standards conform with

the

The structural design oftimber members is related to Part2 of BS 5268, and is based on permissible stress design philosophyin which design stressesare derived on a statistical basis and deformations are also limited. Elastic theory is used to analyse structures under various loading conditions to give the worst design case. Thentimber sections are chosen so that the permissible stresses are not exceeded at any point of the structure.

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11

Permissible stressesare calculated by multiplying the ‘grade stresses’, given in Tables7 to 12a ofBS 5268 :Part 2, by the appropriate modification factors, K-factors, to allow for theeffectsofparameterssuch as load duration, moisture content, loadsharing,sectionsize,etc.Appliedstresseswhich arederived from theserviceloadsshouldbeless than or equal to the permissible stresses. A summary of the K-factors used for the calculation ofpermissiblestressesisgiveninTable2.1.Owing to changes made to BS 5268 : Part 2 in 1996, some K-factors which were used in the previous editions, such as IC1,K10, etc., have been withdrawn. The permissible stress design philosophy, asBS in5268 : Part 2, is different from the limit states design philosophy of Eurocode 5 which has two basic requirements. The first is ultimatelimitstates (i.e. safety) which is usually

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Table 2.1

Summary of K-factors used for calculation of permissible stresses

K-factor Description

or application

5268BS

Timber grade stresses and moduli for service class 3 Duration of loading Bearing stress K4 Shear at notched ends K5 Form factor: bending stress for non-rectangular sections K6 Depth factor: bending stress for beams other than K7 300mm deep Load sharing systems K8 for deflection in trimmer beams and lintels To modify Emin K9 Slenderness in compression members K 12 Efktive length of spaced columns K1 3 Width factor for tension members K1 4 Single grade glued laminated members and horizontally K1 5-20 laminated beams Vertically glued laminated members K27-29 Individually designed gluedend joints in horizontally K30-32 glued laminated members Curved glued laminated beams K33-34 Stress factor in pitched cambered softwood beams K35 Plywood grade stresses for duration of loading and K36 service classes Stress concentration factor for ply-webbed beams K37 For tempered hardboards K3841 Fastener slip moduli K,,, Nailed joints K43-50 Screwed joints K52-54 Bolted and dowelled joints K56, 57 Toothed-plate connector joints KS,C,58-61 Split-ring connector joints KS,C,D,62-65 Ks,C,D,66-69 Shear-plate connector joints K70 Glued joints

K2

K3

: Part 2 : 1996

Table 13 Table 14 Table 15 Clause 2.10.4 Clause 2.10.5 Clause 2.10.6

z

Clause 2.9 Table 17 Table 191Annex B Table 20 Clause 2.12.2 Table 21 Table 22 Table 23 Clause 3.5.3 Clause 3.5.4.2 Table 33 Clause 4.6 Section 5 Table 52 Clause 6.4 Clause 6.5 Clause 6.6 Clause 6.7 Clause 6.8 Clause 6.9 Clause 6.10

zyxwvutsrqpon

12

zyxwvut

zyxwvu zyxwvuts zyxwvu zyx

Structural Timber

Design

expressed in terms of load-carrying capacity and is achieved byfactoring-up of load values and factoring-down of material strength properties by partial safety factors that reflect the reliability of the values that they modify. The secondis servi~eabilitylimitstates (i.e. deformationandvibrationlimits) which refersto the ability of a structural system and its elements to perform satisfactorily in normal use. It is important to note that inpermissible stress design philosophy partial safety factors (i.e. modification factors) are applied only to material properties, i.e. for the calculation of permissible stresses, andnot to the loading.

Once timber has beenseasoned it is stress graded; this grading will determine the strength class of the timber to satisfy the design requirements of BS 5268 : Part 2. Strength grading takes into account defects within the timber such as slope ofgrain, existence and extent of knots and fissures, etc. All timber used for structuralwork needs to be strength graded by either visual inspection or by an approved strength grading machine. Clause 2.5 of BS 5268 :Part 2 deals with strength grading of timber.

3.1

zyxwvutsr ual g r a ~ in g

zyx zyxwvu zyxwv

Visual grading is a manual process carried out by an approved grader. The grader examines each piece of timber to check the size and frequency of specific physical characteristics or defects, e.g. knots, slope of grains, rate of growth, wane, resin pockets and distortion, etc. The required specifications are given in BS 4978 and BS 5756 to determine if a piece of timber is acceptedinto one of the two visualstressgrades or rejected. These are General Structural (GS) and Special Structural ( SS)grades. Table 2 of BS 5268 : Part 2 (reproduced here as Table 2.2) refers to main softwood combinations of species visually graded in accordance with BS 4978,

Machine grading of timber sectionsis carried out on the principle that strength is related to stiffness. The machine exerts pressure and bending is induced at increments along timber length. The resulting deflection is then automatically measured and compared with pre-programmedcriteria, which leads to the grading of timber section. BS 5268 : Part 2, Clause 2.5 specifies that machine graded timber, other than thatcarried out by North American Export Standard for Machine Stress-rated Lumber (e.g. 1450f-1.3E), should meet the requirements of BS EN 519. To this effect timber is graded directly to the strength class boundaries and marked accordingly.

zyxw zyx z z zyxwv zyxwvu zyxwvu Introduction to BS 5268: Part 2: 1996

13

In general less material is rejectedif it is machine graded, however timber is also visually inspectedduring machine gradingto ensure major defectsdo not exist.

The conceptof grouping timberinto strength classes was introducedinto the UK with BS 5268: Part 2 in1984~~trength classes offer a number of advantages both to thedesigner and the supplier of timber. The designer can undertake hi s design without the need to check on the availability and price of a large number of speciesand grades which he might use. Suppliers can supply any of the specieslgradecombinations that meet the strength class calledfor in a specification. The concept also allows new species to be introduced onto the market without affecting existing specificationsfor timber. The latest strength classes used in the current version of BS 5268 :Part 2 : 1996 relate to the European strength classes which are defined in BS EN 338 : 1995 Structural timber. Strength classes. There are a total of 16 strength classes, C14 to C40 for softwoods and D30 to D70 for hardwoods asgiven in Table 7 of BS 5268 : Part 2 : 1996 (reproduced here as Table 2.3). The number in each strength class refers to its ‘characteristic bending strength’ value,forexample,C40timberhasa characteristic bending strength of 40N/mm2. It is to be noted that characteristic strength values are considerably larger than the grade stress values used in BS 5268 :Part 2, as they do not include effects of long-term loading and safety factors.

oftw wood grading: Softwoods which satisfy the requirements for strength classes given in BSEN 338 when graded in accordance with BS4978 and American timber standards NLGA and NGRDL are given in Tables 2, 3 , 4 and 5 of BS 5268 :Part 2. The new strength classes for softwoods are C14, C16, C18, C22, C24, TR26, C27, C30, C35 and C40. However it is likely that the old strength class system (i.e. SC1to SC9) may be encountered for some time. A comparison of the lowest of the newstrength class (C classes) against the most common old SC classes can be made: SC3 compares with C16, SC4 with C24, and SC5 with C27. TR26 timber, which is commonly used for axially loaded members (i.e. trussed rafters), is equivalent to the superseded M75 European redwood/whitewood. ~ a r d ~ o grading: od Tropical hardwoods which satisfy the requirements for strength classes given inBS EN 338 when graded to HS grade in accordance with BS 5756 are given in Table 6 of BS 5268 :Part 2 : 1996. The strength classes for tropical hardwoods are D30, D35, D40, D50, D60 and D70. Grade stresses: Grade stresses and moduli of elasticity for service classes l and 2 (described in Section 2.5.2)are given in Table7 of BS 5268 : Part 2 for

14

zyxwvu zyxwvutsrq zyxwvutsr

Structural Timber

Table 2.2

Design

zyxwv zy zyxwvu zyxw zyxwvu zyxwv zy

Softwood combinations ofspecies and visual grades whichsatisfy the requirements for various strength classes. Timber gradedin accordance withBS4978 (Table 2, BS 5268 : Part 2) Timber

Strength classes

C27 C24 . C22 C18 C16 C14 C30

Imported: Parana pine Caribbean pitch pine Redwood Whitewood Western red cedar

GS

ss ss

GS

GS

CS

Douglas fir-larch (Canada and USA) Hem-fir (Canada and USA) Spruce-pine-fir (Canada and USA) Sitka spruce (Canada) Western white woods(USA) Southern pine (USA) British grown: Douglas fir Larch British pine British spruce

ss

CS

ss

ss

CS

GS GS

CS

ss

ss

ss

ss

GS

ss

GS

ss

GS

GS

CS GS

ss

ss

ss

ss

zyx zyxwv zyxw zyxw zyxwvut 16 strength classes, and in Tables 8 to 12a for individual softwood and hardwood species and grades. Table 7 is reproduced here as Table 2.3.

e ra t io n s ( fa c t o rsa ffe c t in g t im

As mentioned previously, there are several factors which influence timber strength and hence theyshould be considered in the analysis-design process of all structural timber members, assemblies and frameworks. The main design criteria recommended by BS 5268 : Part 2, Clause l .6 for consideration are listed below.

For the purpose of design, loading should be in accordance with BS 6399 : Parts 1, 2, and 32 and CP 3: Chapter V : Part 23 or other relevant standards, where applicable.

2.5.2 S e rv ic e

c la s s e s

Due to the effects of moisture content on mechanical properties of timber, the permissible property values should be those corresponding to one of the

15

zyxw

introduction to BS 5268: Part 2: 1996

16

zyxwvut zyxwvuts zyxw zyxwvu zyx

zyxwvu zyxwvu zyxwv zyx zyxwvuts zyxwvut zyxwvu

Structural Timber

Design

Tabl e 2.4 Modificationfactor K2 forobtainingstresses and moduli applicable to service class 3 (Table 13,

BS 5268 : Part 2) Property

parallel Bending to grain parallel Tension to grain Compression parallel to grain Compression perpendicular to grain parallel Shear to grain Mean and minimum modulus of elasticity

K2

0.8 0.8 0.6 0.6 0.9 0.8

three serviceclassesdescribedin Clause 1.6.4 and given in Table 1 of BS 5268 : Part 2 : 1996. These are summarised below:

(1) Service class I refers to timber used internally in a continuously heated building. The average moisture content likely to be attained in service condition is 12%. (2) Service class 2 refers to timber used in a covered building. The average moisture content likely to be attained in service condition if building is generally heated is 15%, and if unheated, 18%. (3) Service class 3 refers to timber used externally and fully exposed. The average moisture content likely to be attained in service condition is over 20%.

zyxwv zyxwvuts zyxwvu Grade stressandelasticmodulivaluesgiven in Tables 7 to 12aof BS 5268 : Part 2 apply to various strength classes and timber speciesin service classes1 and 2. For service class3 condition they should be multiplied by the modification factor K2 from Table 13 of the code (reproduced here as Table 2.4).

2.5.

j ~ t ~c or net e n t

A s moisture content affects the structural properties of timber significantly,

BS 5268 : Part 2 : 1996 recommends that in order to reduce movement and creep under load the moisture content of timber and wood-based panels when installed should be close to that likely to be attained in service.

Duration of load affects timber strength and therefore the permissible stresses. The grade stresses (Tables 7 to 12a) and the joint strengths given in BS 5268 :Part 2 are applicable to long-term loading. Because timber and wood-based materials can sustain a much greater load for a short period

zyxw zyx zyxwvut zy zyxwvu zyx zyx zyxw zyxwv zy zy zy zyxwvu zyxwvutsr Introductionto BS 5268: Part 2: 1996

Table 2.5 Modification factor K3 for duration ofloading(Table BS 5268 :Part 2)

17

14,

~~~

loading

Duration of

K3

Long-term: dead i.e. + permanent imposeda Medium-term: i.e. dead +temporary imposed snow Short-term:i.e.dead + imposed+wind:dead imposed + snow +windb Very short-term: i.e. dead + imposed +wind (gust)” 1.75

+

+

1.oo 1.25 1S O

___~

For uniformly distributed imposed floor loads K3 = 1except for type2 and type 3 buildings (see Table 5 of BS 6399 : Part 1 : 19842) where, for K3 may be assumed to corridors, hallways, landings and stairways only, be 1.5. For wind, short-term category applies to class (1 C5 S gust) as defined of in CP3 : Chapter V :Part 23or, where the largest diagonal dimension the loaded area a , as defined in BS 6399 :Part 2,2 exceeds50 m. c For wind, very short-term category applies to classes A and B (3 S or 5 S gust)asdefinedinCP 3 :Chapter V : Part Z3 or, wherethelargest diagonal dimensionof the loaded area a, as defined inBS 6399 :Part 2: does not exceeds 50m.

a

(a few minutes) than fora long period (several years), the grade stresses and the joint loads may be increased for other conditions of loading by the modification factors given in the appropriate sections of BS 5268 : Part 2. Table 14 of BS 5268: Part 2 (reproduced here as Table 2.5) gives the modificationfactor K3 by whichall grade stresses(excludingmoduliof elasticity and shearmoduli)shouldbemultiplied for various durations of loading.

.5 .5 S e c t io n s iz e

The bending, tension and compression and moduli of elasticity given in Part 2 of BS 5268 are applicable to materials 300 mm deep (or wide, for tension). Because these properties of timber are dependent on section size and sizerelatedgradeeffects,thegradestressesshouldbemodified for section sizesother than 300 mm deep bythe modification factors specifiedin the appropriate sections of the code. In general, it ispossible to designtimberstructuresusing any sizeof timber. However, since the specific use is normally not known at the time of conversion, sawmills tendto produce a range ofstandard sizes known as ‘customary’ sizes. Specifying such customary sizes will often result in greater availability and savings in cost4. The customarylengths and sizesproducedbysawmills in the UK, normally available from stock, are given in Tables NA.1 to NA. 4 of the

zy

Structural Timber Design

zyxwvut zyxwvu zyxwv

National Annex to BS EN 336 : 1995 which usestarget sizes as the basis for the standard. Furtherinformation and details of the customarylengths and sizes are given in Appendix A.

zyxw zyxw zyxwv zyxwv zyxwv zyx zyxw zyxwvu zyxwv zyx zyxwv zyxw

The grade stresses given in Part 2 of BS 5268 are applicable to individual pieces of structural timber. Where a number of pieces of timber (in general four or more) at a maximum spacing of 610 mm centre to centre act together to support a common load, then the grade stressescanbemodified (increased) in accordance with the appropriate sections of the code. In a load-sharing systemsuch as rafters, joists, trusses or wall studs spaced at a maximum of 610 mm centre to centre, and which has adequate provision for the lateral distribution of loads by means of purlins, binders, boarding, battens, etc., the appropriate grade stressescanbemultiplied by the load-sharing modification factor K8 which has avalueof1.1. In addition, BS 5268 :Part 2 recommends that the mean modulus of elasticity should be used to calculate deflections and displacements induced by static loading conditions. Therefore in a load-sharing system: K8 = 1.l ~odificationfactor Modulus of elasticity E = E m e m

It is to be noted that special provisions are provided in BS 5268 :Part 2 for built-up beams, trimmer joists and lintels, and laminated beams; these are given in Clauses 2.10.10,2.10.1 1 and Section 3 of the code. It is also important tonote that the provisions for load-sharing systems do notextend to the calculation of modification factor K I 2for load-sharing columns.

zyxwv

BS 5268 :Part 2 recommends that in the absence of test data, the following grade stress and moduli of elasticity values may be used: tension perpendicular to grain, Ot&l torsional shear, Ttorsjon rolling shear, Tr

= 5 x shear stress parallel to grain, Tg,11 = 5 x shear stress parallel to grain, l"s, // = x shear stress parallel to grain, zg ,11 = 1 X Ernean or min

3

modulus of elasticity Ito grain, E L shear modulus, G = B1 X Ernean or min permissible compressive stress = CFc,ah,//- (CFC,ah,//- G c , a h , l ) sin a where the load is inclined at an angle a to the grain, C T ~ , ~ ~ , ~

zyx zyx zy zy zyxw zyxw zyx zyxw zyxw zyxwvu zyxwvutsr Introduction to BS5268: Par t 2: 1996

1

The following symbols andsubscripts are used to identify section properties of timber elements, applied loading conditions, type of force and induced andpermissiblestresses.Symbols and subscripts are kept as similar as possible to those given in Part 2 of BS 5268 : 1996. ~ e o m e t r i c aaln d n a

A b d E

Emean Emjn

G h l

I L Le

m n

h

e Pk

distance angle of grain area breadth of beam, thickness of member diameter modulus of elasticity mean value of modulus of elasticity minimum value of modulus of elasticity modulus of rigidity or shear modulus depth of member radius of gyration second moment of area length, span effective length, effective span mass number slenderness ratio first moment of area characteristic density average density section modulus

zyxwvuts zyxwvutsrq

Prnean

z

m e c h a n ic a l p ro p e rt ie s

bending moment applied bending stress parallel to grain grade bending stress parallel to grain permissible bending stress parallel to grain

applied shear force applied shear stress parallel to grain grade shear stress parallel to grain permissible shear stress parallel to grain applied rolling shear stress pernhssible rolling shear stress

28

zyxwvutsr zyxwvuts

zyxwvutsrq zyxwvu zyxwvu zyxw

Structural Timber Design

A m As

zyxwv zyxw zyxwvutsrqp zyx zyx zyxw zyxw

Atotal

A,&

bending deflection shear deflection total deflection due to bending and shear permissible deflection

CF,,,,~/ appliedcompressive stress parallel to grain

I/ gradecompressive stress parallel to grain C T , , , ~ ,permissible / / compressive stress parallel to grain C F , , , , ~ appliedcompressive stress perpendicular to grain o,lg,l grade compressive stress perpendicular to grain C F ~ , permissible , ~ , ~ compressive stress perpendicular to grain O,,g,

Te n s io n CF~ ,~ ,/ I

applied tensile stress parallel to grain

CJt1g,/ /

grade tensilestress

parallel to grain

atl U ~ permissible , ~ ~ tensile stress parallel to grain

zyxwvu zyxw zyx zyxwvu zy

1. Arya, C. (1994) Design of structural elements. E. & F. N. Spon, London. 2. British Standards Institution (1984, 1995, 1988) BS 6399: Loading for buildings. Part 1 : 1984 : Code of practice for dead and imposed loa&. Part 2 : 1995 : Code of practice for wind loa&. Part 3: 1988 : Code of practice for imposed roof loads.BSI, London. : Chapter V : Loading. Part 3. British Standards Institution (1972) CP 3 2 : 1972 : Wind loads. BSI, London. 4. BritishStandardsInstitution(1995)BS EN 336 : Structural timber. Coniferous and poplar. Sizes. Permissible deviations. BSI, London.

apter

zyxwv

Many academic institutions and designoffices are turning to computer assisted instructions. This is especially true in scienceand engineering where courses are being introduced to teach the use of computers as analysis and design tools. Mathcad’s potential as a powerful and easy to use computational tool has already been recognised by most academicinstitutions and many design offices. The aim of this chapter is to demonstrate how the analysis and design calculations for structural timber can be incorporated into simple-to-use electronic notepads or worksheets. Access to a personal computer (PC)and the associated software Mathcad is not a prerequisite for understanding the designcalculationsin the examplesprovidedinthis book. Alldesign examples given are fully self-explanatory and well annotated. They have been produced in the formof worksheets to run under Mathcad,version 6, or higher,ineitherone of itseditions,i.e. Student, Standard, Plus or Professional. Details are given at the end of this book. The design worksheets given are intended as a source of study, practice and further development by the reader. They should not be seen as complete and comprehensive design worksheets but rather as the foundations of a design systemthat can be developedfurther. The aim isto encourage readers to use computing as a tool to increase their understanding of how design solutions vary in response to a change in oneof the variables and howalternative design options can be obtained easily and effortlessly, allowing the design engineerto arrive at the most suitable/economic solution very quickly. It is important to note that this chapter is not intended to teach Mathcad. It aims only to familiarise the reader with the Mathcad worksheet formats that are used to produce design examples in this book.

Mathcad (developedby MathSoft, Inc.)is an electronic notepad (live worksheet) that allows ath he ma tical calculation to beperformed on a 21

z

22

zyxwvu

zyxwvu zy zyxwvut Structural Timber Design

computer screen in a format similar to the way it would be done manually with paper and pencil.WhileMathcademploys the usualmathematical symbols (i.e. -, /, =) for algebraic operations, it also uses the conventional symbols of calculus for differentiation and integration to perform these operations. It preserves the conventional symbolic form for subscribing, special mathematical and trigonometrical functions, series operations, and matrix algebra. When expository text is added, Mathcad’s symbolic format leads to reports that are understood easily by others. Data can be presented in both tabular and graphical forms. Mathcad can also be used to answer, amongst many others, the ‘what-if’ questions in engineering problems. With a well structured worksheet, design calculations can be performed whereby parameters can be changed and the results viewed almost immediately on the computer display and/or printed.

+,

3 .3 W h a t d o e s Ma t h c a d do ?*

Mathcad combines the live document interface of a spreadsheet with the WYSIWYG interfaceof a word processor. WithMathcad, equations can be typeset on the screen in exactly the way they are presented intextbooks, with the advantage that it can also do the calculations. Mathcad also comes with multiplefonts and the ability to print what you see on the screen on any Windows supported printer. This, combined with Mathcad’s live document interface, makes it easy to produce up-to-date, publication-quality engineering reports and/or design solution sheets. The following subsections demonstrate how some simple operations are carried out in Mathcad. This is to illustrate the formatlmeaning of the operations used to produce the examples in this text.

3.3.1

zyx zyxwvuts zyxw A s im p le c a lc u la t io n ’

Although Mathcad can perform sophisticated mathematics, it can just as easily be used as a simple calculator. For example, Click anywhere in the worksheet; you will see a small crosshair. Type 15 - 81104.5 =

As soon as the equal result (see Fig. 3.1).

3 .3 .2

signispressed,

Mathcad computes and shows the

D e f in it io n s a n d v a ria b le s 2

Mathcad’s power and versatility quickly becomes apparent when the variables and functions are being used. By defining variables and functions, equations can be linked together and intermediate results can be used in further calculations.

UsingMathcadforDesignCalculations

23

z

zyxwvutsrq \

- 14.923

zyxwv zyxwv zy

15"-

Fig. 3.1 A simple calculation.

zyxw zyxwv z

For example, to define a valueofsay 10 to a variable, say t, click anywhere in the worksheet and type t: (the letter t followed by a colon). Mathcad will show the colon as the definition symbol := and will create an empty place holder to its right. Then type 10 in the empty placeholder to complete the definition for t. To enter another definition, press [ "Ito ] move the crosshair below the first equation. For example, to define ace as -9.8, type acc:-9.8. Then press [J] again. Now that the variables ace and t are defined, they can be used in other ace

expressions. For example, to calculate the magnitude of - t 2 type acc/ 2 2*tA2.The caret symbol represents raising to a power, the asterisk * is multiplication, and the slash / is division, To obtain the result, type =. Mathcad will return the result (as shown in Fig. 3.2). A

a cc :=-g%

Fig. 3.2 Calculating with variables and functions.

24

Structural Timber

Design

zyxwvut

zyxwvutsrq zyxwvutsrq

zyxwvutsr zyxwvut a c c :=- 9.8

Fig . 3 .3

zyxw zyxw zyxw z

Enteringtext.

Mathcad handles text as easily as it does equations. To begin typing text, click in an empty space and choose Create Text %ion from the Text menu or simply click on the icon on the menu bar. Mathcad will then create a text box in which you can type, change font, format andso on asyou would when using a simple Windows based word processor. The text box will grow as the text is entered. Now type, say, ‘Equation of motion’ (see Fig. 3.3). To exit text mode simply click outside the text box.

Units of measurement, while not required in Mathcad equations, can help detect and enhance the display of computed results. Mathcad’s unit capabilities take care of many of the usual chores associated with using units

zyxwv zyxwvu zyxwvutsr M = 20 *kN.m

Fig . 3 .4

Equations using units.

Using Mathcadfor Design Calculations

25

z

zyxwvut zyxw zyxw zy zyxw z zyxw

and dimensions in engineering analysis and design calculations. Once the approp~atedefinitions are entered, Mathcad automatically performs unit conversions and flags up incorrect and inconsistentdimensional calculations. Although Mathcad’s latest edition recognises most common units, you maywish to defineyourown units. For example,N =newton,and kN = IO3N. Toassign units to a number, simply multiplythe number by the name or letter(s) which defines the unit. To illustrate this, calculate the magnitude of the bending moment M at the built-in end of a cantilever of length L = 2m induced by a force of P = 10 kN acting at its free end. To do this, click anywhere in a worksheet and type: N :=newton kN : = 103*N L : = 2*m P : = 1O*kN

M

: =P*L

zyxw

Then type M=.As soon as the = sign is typed, Mathcad will compute the result and also display the units of M (as shown in Fig. 3. 4).

Thepreviousexamplesaimed to demonstrate the simplicityofusing Mathcad in producingthe design examples givenin the proceeding chapters of this book. To learn more about Mathcad, refer to the next section in this chapter.

zyxwv zyxwvutsr zyxwvut

1. W ieder, S. (1992) Introduction to ~ u t h c u for d Scientists and Engineers. McGraw-

Hill, Inc., Hightstown.

2. ~ a t ~ c User’s a d Guide, ~ a t h c u d6.0 (1996) Mathsoft, Inc.,

MA.

Flexural members are those subjected to bending. There are several types and forms of flexural timber members that areused in construction. Typical examples are solidsection rectangular beams, floor joists, rafters and purlins. Other examplesinclude glulam beams (verticaland horizontal glued laminated beams), ply-webbed beams (I-beams and box-beams) and beams of simple composites (Tee and I shaped beams). Although the design principles are essentially the same for all bending members of all materials, the material characteristics are different. Steel for example is ductile, homogeneous, and isotropic. Concrete is brittle and can be assumed homogeneous for most practical purposes. A s for timber, the material properties are differentin the twomain directions: parallel and perpendicular to the grain. Even though the normal stresses due to bending are parallel to grain direction, support conditions may impose stresses that are perpendicular to grain direction. Thesestresses, in addition to the primary stresses, should be checked in the design against the permissible values, which include the effects of environmental conditions, material and geometrical characteristics. This chapter deals in detail with the general considerations necessary for the designofflexuralmembers and describes the design details ofsolid section rectangular timber beams.Designmethods for glued laminated beams and ply-webbed beamsare described in Chapters 6 and 7 , respectively.

zyx zyx zyx zyxwvu

The main design considerations for flexural members are: (1) bending stress and prevention of lateral buckling (2) deflection (3) shear stress (4) bearing stress. 26

Design of FlexuralMembers(Beams)

z

27

The cross-sectional properties of all flexural members have to satisfy elastic strength andservice load requirements. In general,bendingis the most critical criterion for medium-span beams, deflection for long-span beams and shear for heavily loaded short-span beams. In practice, design checks are carried out for all criteria listed above. In Chapter 2 it was mentioned that the design oftimber elements, connections and components is basedon the recommendations ofBS 5268 : Part 2 : 1996 which is still basedon 'permissible stress' design philosophy. The permissible stress value is calculated as the product of the grade stress and the appropriate modification factors for particular service and loading conditions, and is usually compared withthe applied stress in a member or part of a component in structural design calculations. In general:

zy zy zyxw zyx zy zyxw zyxwvuts zyxwvu zyxwvu zy

permissible stress ( =grade stress x K-factors ) 2 applied stress

4 .3

Be n d in g s tre s s a n d p re v e n tio n o f la t e ra l b u c klin g

The design of timber beams in flexurerequires the application of the elastic theory of bending as expressed by: 1M.Y ff=I

The term Z/y is referred to as section modulus and is denoted by Z . Using the notations defined in Chapter 2, the applied bending stress about the major ( x") axis of the beam (say) (see Fig. 4.1), is calculated from:

I

zyxwvutsrqponmlkjihgf

1

Y Fig. 4.1 Cross- sectionof a rectangular beam,

28

zyxwvutsrq zyxwvut zyxwvu zyxwvutsrqpon zyxw Structural Timber Design

zyxw zyx zyxwvu zyxwv zyx zy zyxwv zyxwv zyxwv

where: a m la ,/ / = applied bending stress (in N/mm2) M = maximum bending moment (in Nmm) Zxx=sectionmodulus about its major (x- x) axis(inmm3). angular sections

For rect-

bh3

2

I x x = second moment of area about x-x axis (in mm4) y = distance from the neutral-axis of the section to the extreme fibres

(in mm) h= depth of the section (in mm) b = width of the section (in mm).

am la&,/ / is calculated as the product of The permissible bending stress grade bending stress parallel to grain a m ,g ,/ / and any relevant modification factors (K-factors). Theseare K2 for wet exposure condition (if applicable), K3 for load-duration, K6 for solid timber members other than rectangular sections (if applicable), KT for solid timber members other than 300mm deep, and K8 for load-sharing systems (if applicable). Hence:

am,adm,//=

O m ,g ,/ /

x K2 x K3 x K6 x K1 x Kt3

(4.4)

KZ?K3and K8 are general modificationfactors, which were described in detail in Chapter 2. K6 and K-, specifically relate to the calculation of permissible

bending stress, am,a&,// and are described in the following sections.

Clause 2.10,3 of BS 5268 : Part 2 recommends that the span of flexural members should be taken as the distance between the centres of bearings. Required bearing length

Beam orjoist

zyx zyx zyxwvutsrq Clear span

Effective span

Span to centres of actual bearings

I

i

ig. 4.2 Effective span(Baird and Ozelton').

DesignofFlexuralMembers(Beams)

29

z

zyxw zyxwvu zyxwv zyxwv zyxwvuts zyxwv zyx

Where members extend over bearings, which are longer than is necessary,the spans may be measured between the centres of bearings of a length which should be adequate in accordance withPart 2 of the code (see Fig. 4.2). In determining the effective span, Le, it is usually acceptableto assume an addition of 50 mm to the clear span, between the supports, for solid timber beams and joists and 100mm for built-up beams on spans up to around 12m, but longer spans should be checked.'

Grade bending stress values given the in code applyto solid timber members of rectangular cross-section.Fo r shapes other than rectangular (see Fig. 4.3), the grade bending stress value should bemultipliedby the modification factor K6 where: &j

= 1.18 for solid circular sections, and = 1.41 for solid square sections loaded diagonally (see Fig. 4.3).

The grade bending stressesgiven in Tables 7-12a of BS 5268 :Part 2 apply to beams having a depth, h, of 300 mm (Clause 2.10.6). For other depths ofbeams,thegradebendingstressshouldbemultiplied by the depth modification factor, K7, where:

zyxwvut

for h 5 72mm, for 72mm

K7 = 1.17

h he

u s p e n d e d t im b e r flo o rin g

zyxw

A suspended flooring system generally comprises a series of joists closely

spaced, beingeither simply supported at their ends or continuous over loadbearing partition walls. The floor boarding or decking is applied on the top of the joists and underneath ceiling linings are fixed. A typical suspended floor arrangement is shown in Fig. 4.8(a) The distance between the centres of the joists is normally governed bythe sizeof the decking and ceiling boards, which are normally available in dimensions of 1200 mm wide x 2400mm long. The size of the decking and ceilingboardsallowsconvenient joist spacingsof 300 mm, 400mm or 600mm centre to centre. In addition, the choice of joist spacing may also be afYectedby the spanning capacity of the flooring material, joist span and other geometrical constraints such as an opening for a stairwell.

38

zyxwvuts

Structural Timber Design

zy zyxwv

Header joist Joists

38 or 50 mm

Trimer joists C \

\

Tongued & grooved boarding

( b) Solid timber tongued&

grooved decking

Load-bearing partition wall& spreader beam

zyxwvu zyxwv zyxw zyxwvuts Masonry wall

Header joist

Trimer joists A

Stairwell

Joists

T r i m e r joists Joist-hanger nailed together

(a) A typical suspended floor arrangement

trimer (c) A typical joist to joists connection

10 m bolts staggered at 600 m centres

Joists

6 to 1 O m thick steel plate, 10 m less in depth than timber joists

Joists

(d) Flitched beam Fig. 4.8

Solid blocking wall between Masonry joists v

(e) A typical support arrangement

Suspended timber flooring- typical components.

Design of FlexuralMembers(Beams)

39

z

zyxwvu

The most common floor decking in domesticdwellings and timber-framed buildingsusessomeformofwood-based panel products, for example chipboard or plywood. Solid timber decking such as softwood tongued and grooved (t & g) decking is often used in roof constructions, in conjunction with glued-laminatedmembers, to produce a pleasant, natural timber ceiling with clear spans between the main structural members. The solid timber tongued and grooved boards are normally machined from 150mmwide sections with 38-75 mm basic thicknesses [Fig. 4.8(b)]. The supports for joists are provided in various forms depending on the type of construction. Timber wall plates are normally used to support joists on top of masonry walls and foundations, Fig. 4.8(e). In situations where joists are to be supported on load-bearing timber-frame walls or internal partitions, headerbeams or spreader members are provided to evenly distribute the vertical loads. Joist-hangers are often used to attach and support joists onto the main timber beams, trimmer members or masonry walls [Fig. 4.8(c)]. Timber trimmerjoists are frequently used within timber floors of all types of domestic buildings, seeFig. 4.8(a). There are two main reasons for which trimmer joists may be provided2.First is to trim around anopening such as a stairwell or loft access (Trimmerjoists A), and to supportincoming joists (Trimmer joists B), and second isto reduce the span of floor joists over long open spans (Trimmer joists C), as shown in Fig. 4.8(a). Trimming around openings can usually be achieved by using two or more joists nailed together to form a trimmer beam,Fig. 4,8(c), or by using a single but larger timber section if construction geometry permits. Alternatively, trimmers canbe of hardwood or glued laminated timber, boxed ply-webbed beams, or composite timber and steel flitched beams2, Fig. 4.8(d). All flooring systems are required to have fire resistance from the floor below and this is achieved by the ceiling linings, the joists and the floor boarding acting together as a composite construction3.For example, floors in two storey domestic buildings require modified 30 minutes fire resistance (30 minutes load-bearing, 15 minutes integrity and 15 minutes insulation). In generala conventional suspended timber flooring systemcomprising 12.5 mmplasterboard taped and filled, tongued and grooved floor boarding with at least 16mm thicknessdirectlynailed to floor joists, meets the requirements for the modified 30 minutes fire resistance providedthat where joist-hangers are used they are formed fromat least 1 mm thick steel ofstrap or shoe type. Further details and specific requirements for fire resistance are given in BS 5268 : Part 4: ‘Fire resistance of timber structures’.

4 .8

zy zyxwvu

zyxwvu zyxwvut

References

1. Baird and Ozelton (1984) Timber Designer’s Munual, 2nd edn. BSP Professional

Books, Oxford.

40

zyxwvut zyxwv zyxw zyx zy zyxw

Structural Timber Design

2. TheSwedishFinnishTimberCouncil (1988) Principles of Timber Framed Construction, Retford. 3. TRADA (1994) Timber Frame Construction, 2ndedn.TimberResearchand Development Association (TRADA), High Wycombe.

zyxwv zyxwvuts zyxw zyxwvutsr

4 .9

Design examples

zyxwv zyxwvuts

Ex a m p le 4 7

D e s ig n o f a m a in b e a m

A main beam of 3 m lengthspans over an opening 2.8 m wide (Fig. 4.9)and supportsa flooring system which exerts a long-duration loading of 3.9 kN/m, including its own self-weight, over its span. The beam is supported by 50mm wide walls on either side. Carry out design checks to show that a 75 mm x 225 mm deep sawn section whitewood grade SS under service class 1 is suitable.

zyxwvu Dimensions inmm

Fig. 4.9

Beam details (Example4.1 ).

De fin it io n s

zyx zyxwvut zyxw

Force, kN Length, m Cross-sectional dimensions, mm Stress, Nmm"2

' 1.

N : = newton kN:= lo3 .N Direction parallel to grain, // Direction perpendicular to grain, p p

Ge o m e t ric a l p ro p e rt ie s

Span (clear distance), L Bearing width, bw Effective span, Le

Beam di~ensi5ns: Breadth of the section, b Depth of the section, h

L := 2.8 m bw : = 50-mm Le := L+bw Le = 2.85 o m b : = 75. mm h : = 225. mm

zyx

zy zyxwv zyxw zyx

zyx zyx zyxwvut zyxwvu zyxw zyxwvuts zyxw zyxwvu zyxwv zyxwvu zyx Design of FlexuralMembers (Beams)

A:=b*h A = 16 875o mm2 Zxx : = b h3 Zxx = 7.12 x lo7 o mm4

Cross-sectional area, A

h.

Second moment of area, ,,Z

2. Lo a d in g

Applied uniformly distributed Total load, W

3.

load,

W

*

: = 3.9 kN m-* W:=w eLe W = 11.11 okN

W

K - fa c t o r s

Service class 1 (K2,Table 13) Load duration (&, Table 14) Bearing: 5 0 m , but located 72mm

K14 =

(y )

0.11

5 .3 .3

M e ~ b e r ssu b j e c t e d t o a x ia l t e n s io n o n ly

An axially loaded column hasits line of action of load passing through the centroidal axis of the column. (1) The applied tensile stress, o t, a , / , in an axially loaded timber member is calculated from the following equation:

where:

T = tensile force A,,, = net cross-sectionalarea.

z zyxwvut zyxwvu zyxw zyxw Design of AxiallyLoadedMembers

(2)

65

The p e r ~ i s s i ~tensile le stress, G,,,&,// , is calculatedas the product of the grade tensile stress, and any relevant modification factors (K-factors) as follows:

z zyxw zyxw zyxwvuts zyxwvu zyxwvu zyx zyxw zyx z where K2,K3 and & are general modificationfactors for service class3, load-duration and load-sharingsystemsrespectively,which were described in detail in Chapter 2. K14 is the width factor as described earlier.

In general, the value of applied tensile stress, permissible tensile stress, C T ~ , ~hence: ~ , I,

o t , a , / / , should

not exceed the

5 .3 .4 Co m b in e d b e n d in ga n d t e n s ile s t re s s e s

In members that are subjected to lateral loading as well as the axial tension, the position of maximum stress occurs at the point of maximum bending moment (Fig. 5.5). Clause 2.12.3 of the code requires that the sum of the ratios of the applied tensile and bending stresses to those of the permissible ones (i.e. interaction quantity) must not exceed unity: (5.10)

w,Mie: Applied tensile stress,

permissibletensilestress, applied bending stress,

T

Ut,a,ll

=A,,,

cFt,ah,// = "ts,//

=m,a,//

-" =

May

x K~K~K~KM

M

-z

L -Fig. 5.5 Tension member subjected to lateral loading.

zyxw zyxwvutsr zyxwvuts Structural Timber Design

xamples

zyxwv zyxw zyxwvutsr zyxwvutsrqp

A timber column in strength class C18 is4m in height with a rectangular cross-section of 97mm x 145mm as shown in Fig. 5.6. The column is restrained at both ends in

position but not in direction and is subjected to service class 2 conditions. (a) Determine the maximum axial long-term load that the column can support. (b) Check that the column is adequate to resist a long-term axial load of 12kN and a bending momentof 0.8 kNm about its x-” axis. Y !

zyxwvu zyxw zyxw zyx zyxwv zyxwvu zyxwvut zyxwvut zyxwvut zyxwvu zyxwvu zyxw Cross-section

Fig . 5.6

Column details (Example 5.1).

Force, kN Length, m Cross-sectional dimensions, mm Stress, Nmm-2 1.

L, = 1.0 x L

N :=newton

k~ := 103 . N Direction parallel to grain, // Direction perpendicular to grain, pp

~ e o ~ e pt ror p~e rt~ie sa ~

133’5268 :Part 2, Table 18 Column length, L Effective length, L, Width of section, b Depth of section, h Cross-sectional area, A

Second moment of area, I,,

L : =4.0 m Le : = 1.0 L Le=40m b : = 97-mm h : = 145 mm A.1”b-h A = 14065 omm2 I,, : = L. b . h3 12 I,, = 2.46 x l O7 o mm4 *

+

zyxw zyxw zyxwvut

z zyxwvu zyxwv zyxw zyxw zyx Design of AxiallyLoadedMembers

Secondmomentof

area, Iyy

For a rectangular section

*

m 4

zyxwv zyxwv zyxwvu zyxwvu zyxwvu zyxw zyx zyxwv zyx

Radius of

gyration, iyy

Section modulus, Zxx

2.

h

Iyy : = h b3 lYy = 1.1 X io7 o

67

b

ZYY

: = J12

iyy= 28 o mm b h2

z xx: = *

6 Zxx= 339 904.17o mm3

Ch e c k s le n d e rn e s s ra t io , h

h : = G? _ lYY

h = 142.85 300mm K7 : =0.81 h: K7 = 0.89 *

+ 92 300 + 56 800

zyxwv

Glulam modtjication factors (Table BS5268 :Part 2, Clause 3.2 Combined-grade, 8 laminates in Cl8 timber, by interpolation Bending // to grain, K15 Compression perpendicular to grain, K I8 Shear // to grain, K19 Modulus elasticity, of

21): Stressvalues for the higher-graded timber apply

K15

: ==1.32

K18 :=

1.69

K19 := 2.73 K20 : = 1.17

1

zyxwvutsr zyxwvutsr zyxwvut zyxwvut Stru~turalTimber Design

Applied bending moment

Section modulus

zyxwvu zyxwvutsr zyxwvutsr zyxwvu zyxwvuts zyxwvut zyxwvuts

Applied bending stress

Permissible bending stress

Check self-weight: BS5268 :Part 2, Table 7 Density Beam self-weight (kN/m): Actual Assumed

7 . ~ a t e ra l s t a ~ ilj t y

Clause 2.10.8 and Table 16

Maximum depth-to-breadth ratio, hlb

8.

h b Ends should be held in position and compression edges held in line by direct connection of t & g decking to beams

- = 4.91

S h e a rs t re s s

Applied shear force

Applied shear stress Permissible shear stress

wmed

zyxwvut

F,, : = 2 F,, = 15.78 o kN

z zyxwvu

zyxwvut zyxw zyxw zyxwvut zyxwvu zyxw zyxwv zyxw zyxwvu z zyxw zyxwv Design of Glued LaminatedMembers

Applied load

F:= -" w m e d

Applied bearing stress (bearing area = b bw)

0c.a.pp :=

2 F = 15.78 o kN

(3%)

zyxwvutsr

= 1.15 o N mm"2

0c.a.pp

Permissible bearing stress

0c.adm.pp := 0c.g.pp * K2 K8 K3

= 4.65 o N.mm-2 Bearing stress satisfactory

0c.ah.pp

Modulus of elasticity for glulam, E

E := Emean K20 E = 1.06 x lo4 o N - mm-2

Second moment of area

b h3 rxx: =12

zXx= I .U x io9 o mm4

Deflection due to bending

Deflection due to shear

101

A,, = 25.16 0 mm 19S2 '

A, : =

(b h) E *

*

A, = 1.17 o mm

K18

z

zyxw zyxw

1 Cl 8 timber

I

Cl 6 timber

C18 timber

Fig. 6.7

Cross- sectionof glulam beam (Example6.2).

I

zyxwvutsrq zyxwvuts zyxwvut zyxw zyxw

4 02

zyxwvut zyxw zyxw zyxwvuts zyxwvuts zy zy

StructuralTimberDesign

Total deflection

Atotal := A m +. Atotal = 26.34 o

Permissible deflection

As

zyxwvutsrqpon

mm A a h : = 0.003 L, A a h = 29.4 o mm Deflection satisfactory and no pre-cambering is required *

Therefore adopt a 110 mm x 540 mm glulam section in combined-grades of C18 and C16

€ x a m p / e 6 .3

D e s ig n o f a f/ o o r in g s y s t e m

Design of aflooring system using gluedlaminated timber beams for the first floor of an art gallery is required. The flooring arrangement comprises main beams with effective span of 9.6 m at 4.5 m centres supporting secondary beams at 0.8 mcentres and 38 mm tongued and grooved(t &g) flooring using hardwoodtimber. The secondary beamsare simply supported on 100mm hangers attached to main beams which are in turn supported on load-bearing walls providing a 1'75 mm bearing width at each end. It is proposed to use softwood timber in strength class of C24 with laminations of 38 mm finished thickness, single-grade and horizontally glued laminated throughout. The floor is subjected to a dead load of0.4'7 kN/m2, excluding self-weight, and an imposed medium-tern load of 3.25 kN/m2. De fin it io n s

zy zyxwvu zyxwvuts zyxwvut zyxwvu zyxwvu

Force, kN Length, m Cross-sectional dimensions, mm Stress, Nmm"2 A.

N :=newton kN : =lo3 N Direction parallel to grain, // Direction perpendicular to grain, pp

-

De s ig n o f t o n g u e d a n d g ro o v e d b o a rd in g

Assuming t & g boarding comprises 100mm wide timber beams of thickness (depth) 38 mm simply supported on joists.

' 1. Lo a d in g

Secondary beam spacing, Js t & g width, b t & g thickness, t Dead load: BS5.268 :Part 2, Table 7 Average density, D30 hardwood t & g boarding, self-weight ( W m 2 ) , tg

J s : = 0.8 m b : = 100. mm t : = 38. mm

pmean: =640 kg m"3 tg := pman tg v

*

tg = 0.24 o kN m-2

zy zyxwv zyxwvutsrqp zyx zyxwvutsrqponmlkjih zyxwvutsrqp --"--? ! -.

4.5 m

.

I

1

4.5 m F

I

! !

! ~! .-

I

! !

! ! ...

!

,!

l

!

- _ _ e _

4.5 m

1

b

-.

zy zyxwvu zyx v-4 v-4

-.

.-

'

Secondary beams Main beams

(a) Support structure layout

300 m

(b) Section A- A: secondary beam details

t & g hardwood

4 details (c) Main beam Fig . 6 .8

9.60 m

Details of flooring system (Example 6.3).

zy

zyxwvutsrqponmlkjih 300 mm

I

I

Section C- C

104

zyxwvut zyxwvu zyxw zyxw zyxwvu zyxw Structural Timber

Design

Prescribed dead load (kN/ m2),PDL Total dead load (kW , DL

DL := PDL + tg DL = 0.71 o kN m-2 : = 3.25 kN . me2 W:=(DL+IL)*b*Js

zyxwvuts zyxwvut zyxwvutsr zyxwv zyxwvutsr

Imposed load (kN/ m2), IL IL Total load (kN), W

W = 0.32 o kN

2.

K - fa c t o rs

Service class 1 (K2, Table 13) Medium-term loading (K3, Table 14) Bearing (G ,Clause 2.10.2) Notched end effect (K5, Clause 2.10.4) Form factor (KG, Clause 2.10.5) Depth factor (K?, Clause 2.10.6) for h 5 72mm Load sharing applies (K8, Clause 2.9) 3.

zyxw zyxwv

PDL : = 0.47 kN - m-2

Gra d e s t re s s e s

:= 1 K3 := 1.25

K2

K4 := 1 . O assumed

K5 : =1

:= 1 K7 : =1.17

K6

zyxwvuts zyxw zyx zyxw zyxwv Kg

: = 1. 1

&S135268 :Part 2, Table 7

Strength classification Bending /I to grain Mean modulus of elasticity

4. Be n d in g s t re s s Applied bending

moment

Permissible bending stress

Strength class D30 : =9.0 N Emean := 9500 N mme2 *

CT,.~ ,/ /

+

W *JS

M :=- - - - ”

8 M = 0.03 o kN m

om.adm./l : = om.g.1 K2

K3 K6 K7 ’ K8

= 14.48 o N mm-2

CT,.,~ .,J

Since Z = t2, therefore 6 *

trqd = 1 1.46 0 mm Thickness satisfactory

*

zyx zy

zyxwv zyxw zyxw zyxw zyxwvuts zyx zyxwvutsr zyxw zyxwvu Design of GluedLaminatedMembers

Load sharing system Permissible deflection

Second moment of area

zyxwvutsrqpo

E := Ehean A a h : = 0.003 JS A a h = 2.4 o mm *

b . t3 zxx: = 12

zXx= 4.57 x

io5 o mm4 5. W *J s 3 A := 384 E Zxx A = 0.49 o mm Deflection satisfactory

Deflection

*

zyxwvutsrq zyxwvutsrq *

Shear and bearing stresses are not critical in decking arrangements.

Therefore 38 mm t & g boarding in D30 timber is satisfactory

B . De s ig n o f s e c o n d a ry b e a m s 1.

Lo a d in g

EfTective length, L, Bearing width, bw Beam dimensions: Depth, h Breadth, b Total dead load from flooring (kN/m2), DL Self-weight of beam (kN/m), Sw t Imposed load (kN/m2), ZL

Le : = 4.35 m bw : = 100 m m *

-

Not known at this stage

DL = 0.71 o kN m-2

Sw t : =0.3 kN m-'assumed ZL : = 3.25 kN mW 2

Total load (kN): Long-term,

?VIong

Mediumterm, Wmed

2. K - fa c t o rs Service class 1 (K2, Table 13) Medium-term loading (K3, Table 14) Bearing: l00 mm (Ka, Clause 2.10.2)

105

K2 := 1 K3 : =1.25

K4 : = 1

1

zyxwvut zyxwvut zyxwvu zyxwv

zyxw zyxwvuts zyxwv zyxwvu zyxwvut zyxwvut zyxwvutsr zyxw i zyxw zyxwvut

Structural Timber

Design

Notched end effect (K5, Clause 2.10.4) Form factor (&, Clause 2.10.5) Depth factor (KT, Clause 2.10.6) No load sharing (Ks, Clause 2.9)

K5

:= 1

:= 1 K7 : = 1 assumed Kg := 1 K6

Glulam ~ o d ~ c a t ifactors on (Table 21): BS5268 :Part 2, Clause 3. 2

Bending I/ to grain, K15 Compression perpendicular to grain, K Is Shear // to grain, K19 Modulus elasticity, of K2@

3.

Since number of laminations is not known, ignore at this stage

K20

:= 1.07

Em,,,

:= 0.71 N mm"2 : =10 800 N mm"2

Gra d es t re s s e s

13s5268 :Part 2, Clause 3. 2 Table 7, for C24 timber Bending // to grain Compression perpendicular to grain Shear // to grain Mean modulus of elasticity

S e le c t in g

*

zyxwvu

a

t ria l s e c t io n

Using deflection criteria: Modulus of elasticity for glulam, E Permissible deformation

E : = Ernean K20 E = 1.16 X 1 0 ~ 0 ~ . m m - ~ &h

A,*

: = 0.003 L e = 13.05 o mm *

Using lateral stability criteria: In order to achieve lateral stability by direct fixing of deckingto beams, the depthto-breadth ratio should be limited to 5, i.e. h < 5b. Substituting for h = 5b in Ixx = bh3/i2 and equating it to Ixx.rgd: Ixx.rqd

=

*

(5 b)3 will give *

12

and depth of section,

h

b :=

(

12

*

Ixx.rqd

53

)

1/ 4

zyxw

b = 56.64 o mm h := 5.b

h = 283.18 o mm

zy zy zyxwvut

zyxwvuts zyxwv zyxwvuts zyxwvu zyxw zyxwvu zyxwvu zyxwv zyxwvu zyxwvu Design of GluedLaminatedMembers

Try a 70mm x 288 mm section with 8 laminations of 36mm in thickness Trial beam dimensions: Depth (mm), h (mm), Breadth b

h mm : =288 b:=70-mm

Modification factor K7 for section depth: to provide a dimensionless value for K7 in Mathcad, let: h1 : = h mm-l 300 mm for h < 300mm K7 h *

(

+

K7 = 1

Glulam m o ~ ~ c a t ifactors on (Table 21): BS5268 :Part 2, Clause 3.2 Single-grade, 8 laminates in C24 timber, by interpolation: K15 Bending / / to grain, K15 K1g Compression perpendicular to grain, K18 K19 Shear // to grain, K I9 Modulus of elasticity, Kz0 K20

:= 1.40 : = 1.55

: = 2.34 := 1.07

5. g e n ~ j n g stress

Applied bending moment

wmed

M :=

*

Le

8

Section modulus, Zxx

Applied bending stress

Permissible bending stress

Check self-weight:

BS 5268 :Part 2, Table 7

Average density Beam self-weight, (kN/m) Actual Assumed

p : = 420kgm-3

)

'*l1

107

zyxwvut zyxwvuts

zyxwvut zyxwvut zyxw zyxwv zyxw zyxw zyxwvu zyxw zyxw Structural TimberDesign

a t e ra J s t a ~ i Ji t y

Clause 2.10.8 and Table 16

aximum depth-to-breadth ratio, hJb

Q

h - = 4.11 b

Ends should be held in position and compression edges held in line by direct connection o f decking to the beams

e a r s t re s s

Applied shear force

Fv= 7.54 o k N

Applied shear stress

Ta,f/ = 0.56 o

Permissible shear stress, no notch

N mm?

: = zg.i K2 K3 K5 +

Kg K19

zah.i = 2.08 o N . mmv2 Shear stress satisfactory

Applied load

F = 7.54 o kN Applied bearing stress (bearing area = b bw) Permissible bearing stress

Modulus of elasticity for glulam, E

zyxwvut zyxwvuts

Second moment o f area, Ixx

Deflection due to bending

zy z zyxw zyxw zyxwv zyxwvutsrq

zyx zyxw zyxwv zyxwvu Design of Glued LaminatedMembers

Deflection due

to shear

10

zyxwvutsrqp

zyxwvu zyxwv

As: =

19.2 M *

(b h) * E *

As= 0.68 o mm

Total deflection Permissible deflection

+As

Atotal P= Am

Atotal= 10.71 o mm : =I0.003 = Le A ah = 13.05 o mm Deflection okay and no pre-cambering is required

8 mm deep sections with 8 l a ~ n a t of i ~36 mm in thickne~

L e : = 9.6 m EEective length, L e bw : = 175. mm Bearing width, bw Beam dimensions: Depth, h Not known at this stage breadth, b Self-weightofbeam(kN/m), Sw t Sw t : = 0.7. kN . m" assumed Strip of load of width bj = 300 mm, seeFig. 6.8 (b), on the top of a main beamplus its self-weight bj : = 300mm Long-term loading Pstrip.long : = (DL bj Swt) L e Pstrip.long 8-760 kN Medium-term loading Pstrip.med : = (DL IL) bj L e SW t L e Pstrip,med = 18.12 o kN Point (concentrated) loading wlong from secondary beams(kN), PS ps.low := ' 2

}

zyx

zyxw zyxwvu +

+

~

Ps.long

Total load (kN): Long-term, Piong Medium-term, Pmed

K1 to KG are as above No load sharing applies (Kg, Clause 2.9)

L==

3.77 o kN

*

+

*

zyxwvut zyxwvu zyxwvutsr zyxwvu

zyxwvu zyxw zyxwvutsr zyxwv zyxwv zyxwvuts Structural Timber Design

Glularn ~ o d ~ c a t ifactors on (Table 21): BS5268: Part 2, Clause 3.2 Bending // to grain, K15 Compression pe~endicular Since number of lamination^ is not known, to grain, K18 ignore at this stage Shear / I to grain, K19 Modulus of elasticity, KZ-, K20 := 1.07 3.

Gra d es t re s s e s

As for the secondary beams (see above) 4 . S e le c t in g a t ria l s e c t io n

(1) Usingdeflection criteria: For a simply supported beam subjected to a maximum bending momentof M m,,, irrespective of the loading type, the maximum deflection may be estimated using the equation given in Section 4.4.3, as:

Am =

0.104 M m , *

E

*

*

zyxwvutsrqponmlkjih L:

Ixx

zyxw zyx

MmaXfor a simply supported beam carrying (n - 1) point loads of magnitude P, equally spaced, is given by Mmax =

ne P . L: 8

(reference: Steel Designer's Manual) P/ 2

zyxw

P P P P P P P P

P P /2

11111111111 t t + = 10 equal spacings, (n-l) = 9 point-loads along the length 2 @supports. n

zyxwv zyxw zyxw zyxwvut

Number of point-loads, (n- 1)=9 Applied bending moment due to point loads

Applied bending moment due to strip of loading including self-weight Total bending moment

n : = 10

Le MP: = n Ps.med Iz *

*

U

MP= 180.97 o kN m M S:=

Pstrip.med Le *

0

0

MS=21.740kN.m Mtotal : = M S 4" MP

Mtotal= 202.71 0 kN m

zy zyxwv zyxw zyxwvu zyxw zyxw zyxwv Design of Glued Laminated Members

zyxw zyxw zyxw z zyxwvut zyxwvuts zyxwvut zyxwvu

odulus of elasticity for glulam, E ermissible d e f o ~ a t i o n Required second moment of area, I,, using A,h

-

E : = Em,,, K20 E = 1.16 x lo4 o N -mm"2 Au(ifn: = 0.003 L, &h = 28.8 o mm 0.104 Mlotal L:

zyxwvutsrqpon

*

*

0

Ixx.rqd : =

E

*

io9 o mm4 Using lateral stability criteria: In order to achieve lateral stability by direct fixing of deckingto beams, the depthto-breadth ratio should be limited to 5, i.e. h 5 5b. Substituting for h = 5b in Ixx = bh3/i2 andequating it to Ixx,rqd: IxX-rqd

b (5 b)3 will give 12 *

Ixx,rqd

=

*

b :=

= 5.84 X

(

12

*

Ixx.rqd

53

b = 153.86 o mm h:=5*b h = 769.31 o mm ' S,ectionwith 24 laminations of 36mm in thickness Try a 180 mmx 864 mm deep Trial beam dimensions: h : = 864mm Depth (mm), h b : = 180. mm Breadth (mm), b Modification factor K7 for section depth: To provide a dimensionless value for K7 in Mathcad, let: h1 : = h mm" h; 92 300 K7 : = 0.81 for h > 300mm h: 56 800 K7 = 0.85 and depth of the section, h

+ +

~ l u l ~ao~d ~ ~ a t factors i o n (Table 21) : BS5268 :Part 2, Clause 3. 2 Single-grade, 24 laminates in C24 timber K15 : = 1.52 Bending / / to grain, K15 Compression perpendicular to K18 : =1.55 grain, K18 Shear // to grain, K19 K19 : ==: 2.34 K20 : = 1.07 Modulus of elasticity, K20

Total applied bendingmoment Section modulus, Zxx

Mtotal= 202.71 o kN . m b h2

zxx:= -

6 Zxx= 2.24 x lo7 o mm3

112

zyxwvu zyxwvuts zyxwvuts

StructuralTimber Design

Applied bending stress

zyxwvu zyx zyxw zyxwvutsrqp zyxwvutsr zyxwvu zyxwv zyxwvu nilt0taI

0m.a.i

zxx

zyxwvut zyxwvu zyxwvutsr zyxwv zy zyxwv = 9.05 0 N mm-2 Gm.g.1 K2 K3 K6 0m.ah.I 12.05 0 N mm-2 Bending stress satisfactory Gm.a,l/

*

Permissible bending stress

om.adm.(

Check self-weight: BS.5268 :Part 2, Table 7 Average density Beam self-weight, (kNIm) Actual

p := 420 kg m-3

*

*

*

K7

*

K8

*

K15

Assumed

6.

~ a t ~ rsat J a ~ jijt ~

Clause 2.10.8 and Table 16

Maximum depth-to-breadth ratio, h/b

h - = 4.8 b

Ends should be held in position and compression edges held in line by direct connection o f decking to the beams

Pmed Fv :=y

Applied shear force

L

Fv = 84.46 o kN

Applied shear stress

Permissible shear stress, no notch

Applied load

zyxwvu zyxwvu Pmed

F-"

2 F = 84.46 o kN -*

Applied bearing stress, (bearing area = b x bw)

0c.a.pp

:=

(A)

= 2.68 o N mmw2

(T,.,.~ ~

zy z zyxwvu zyxwvu zyx

zyx zyxwvutsr zyxw zyxwvu zyxwvz Design of Glued Laminated Members

Permissiblebearingstress

zyxwvuts zyxwv

: =0c.g.pp K2 K3 ' Kh ' K8 = 3.68 o N mm-2 Bearing stress satisfactory 0c.adm.pp

*

*

0c.ah.pp

113

*

K18

9. ~ e f l e c t i o ~ Modulus elasticity of glulam, E Second moment of

for

E := Emean K20 E = 1.16 x lo4 o N mmm2 b h3 I,, : =12 I,, = 9.67 x lo9 o mm4 a

area, I,,

Deflection due to bending

Deflection due to shear

As= 2.17 o mm

Total deflection

&,tal Atotal

Permissible deflection

Aah : = 0.003 * L e A a h = 28.8 o mm

A m "I= 19.54 o mm

Deflection okay and no pre-cambering is required

Therefore adopt 180mm wide x 8 thickness

m m deep sections with 24 la~nationsof 36 mm in

Design ofa curved gluedlaminated timber beam for the roof of a restaurant is required. The beam is to span 9.0m centre to centre supported on 250 mm wide bearings under service class 1 conditions. It is proposed to use a single grade lay-up using softwood timber in strength class Cl8 with horizontal laminations of 30mm finished thickness. The radius of curvature at mid-span bend is to be 6.5m. The beam is subjected to a dead load of 1.65 kN/m, including self-weight, and an imposed medium-term load of 2.25 kN/m.

Force, kN Length, m Cross-sectional dimensions, mm Stress, Nmm"2

zyxw

N :=newton kN : = l o 3 .N Direction parallel to grain, // Direction perpendicular to grain, pp

4

zy

zyxwvut zyxwvuts zyxw zyxwvutsr zyx

Structural Timber

Design

250 m

**\

1 h

\

250 mtn

zyxwvu

zyxwvu zyxw zyxwvuts

Cross-section A-A

Fig. 6. 9 Curved glulam beam (Example 6. 4).

Effective length, L, Bearing width, bw Beam dimensions: Depth of section, h Breadth of section, b Dead load including self-weight (kN/m), DL Imposed load (kN/m), IL Total load (kN): Long-term, W&

Le : = 9.0 m bw : = 250mm

Not known at this stage DL : = 1.65 kN m-1 IL : = 2.25 kN m-’

zyxwv

Serviceclass 1 (K2, Table 13) Medium-term loading (K3, Table 14) Bearing: 250mm wide (K4,Clause 2.10.2) effect Notched end (K5,Clause 2.10.4)

KZ : = 1 K3 := 1.25 K4 :=

K5

1.0

:= l

zy z zyxwv zyxwvuts zyxwv Design of GluedLaminatedMembers

Form factor (K6, Clause 2.10.5) Depth factor (KT, Clause 2.10.6) No load sharing (Ks, Clause 2.9)

l15

K6 := 1 K7 : = 1 assumed Kg := 1

zyxwv zyxwvu i zyxw zyxwvutsr zyxw zyxwvuts zyxwv zyxw zyxwvu zyxw zyxw zyxwv zyxwv

Glulam mod~ cation factors (Table 21): BS.5268: Part 2, Clause 3.2

Bending / / to grain, K15 Compression perpendicular to grain, Kls Shear // to grain, K19 Modulus elasticity, of 3.

Since number of laminations is not known, ignore at this stage

K20 : ==1.17

Gra d es t re s s e s

IPS5268 :Part 2, Clause 3.2 Table 7 , for C18 timber Bending // to grain Compression perpendicular to grain Shear // to grain Mean modulus of elasticity S e le c t in g

a

Qm .g./ /

: = 5.8

N mmv2

1.7

N mmv2

cT,.g.pp : =

t ria l s e c t io n

Using deflection criteria: Modulus of elasticity for glulam, E Permissible deformation

Required second moment of area, Zxx using A a h

E : = Ernean K20 E = 1.06 x 1040N.mm"2 & h : = 0.003 Le & h = 27 o mm 5 ZL L: Zxx.rqd : = 384 E A ah zxx.rqd = 6.69 X '01 o mm4 *

*

*

*

*

Using lateral stability criteria: In order to achieve lateral stability by direct fixing of deckingto beams, the depthto-breadth ratio should be limited to 5, i.e. h 5 5b. Substituting for h = 5b in zxx= bh3/ 12and equating it to Zx-.rqd: b * (5 Zxx,rqd

12

will give

and depth of section, h

b :=

(

)

12 zxx.rqd 1/4 *

53

b = 89.51 o mm h: = 5 . b h = 447.55 o mm

Try a 105mm x 5 10 mm deep section with 17 laminations of 30 mm in thickness Trial beam dimensions: Depth (mm), h h : = 510 mm b b : = 105 mm Breadth (mm).

-

zyxwvutsrqponmlk zyxwvutsrq zyxwvu zyxwv l’ 1 6

StructuralTimber Design

zyxwvu zyxwv zyxwvut

Modi~cationfactor K? for section depth: to provide a dimensionless value for K7 in Mathcad, let: h1 : = h mm-l +

for h > 300mm

G l u l a ~ ~ o d ~ cfactors at~on (Table BS5268 :Part 2, Clause 3.2 Single-grade, 17 laminates in C18 timber by interpolation: Bending // to grain Compression perpendicular to grain Shear // to grain Modulus of elasticity

BS5268: Part 2, Clause 3.5.3.1 Radius of curvature, r Lamination thickness, t Ratio r/t should not be less than E,ea,J’70

K7

: = 0.81

h; + 92 300 h? -k 56 800

21):

K15

:= 1.52 K18 : =1.69

: =2.73 K20 : =1.17

K19

zyxwvu -

r : = 6500 mm t := 30 mm r - = 216.67 is greater than t 27

&mean

130 o N -mmm2 70 Satisfactory

” _ .

BS5268 :Part 2, Clause 3.5.3.2 Check if ( r / t )