Structural Timber Design

im Sc, MSc, PhD, FIVVSc ~ a ~ i ~niver~ity, er Edinbur~~

Blackwell Science

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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Preface 1 Timber as a Structural Material 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 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

xi

1 1 3 3 4 5 5 5 5 5 6 6 7 7 8 8 9 9 10 12 12 12 13 14 14 14 16 16 V

vi

Contents

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

17 18 18 19 20

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

21. 21

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

26 26 26 27 28 29 29 30 30 31 32 32 33 33 34 34 35 36 36 37 39 40 40 43 46 50

21 22 22 22 24 24 25 25

Contents

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

vii

56 56 56 56 57 58

60 61 62 63 64 64 64

65 66 66 69 73 75 79

82 82 84 84 84 84 86 87 89 90 90 92 93 93 97 102 113 119

viii

Contents

esign of P l y - w e b b ~Beams 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

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

123

123 l 24 125 127 128 129 130 130 131 131 132 132 132 137 143

143 144 145 145 145 147 148 148 148 148 152 159

159 160 161 162 163 165 166 167 167 169 172 173 175 176 177 178

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 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

ix

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

219 220 22 1 22 1 223 224 225 227 228 229 230 230 23 1 239 239 240 24 1 242 242

x

Contents

10.9Designexamples Example 10.1 Example 10.2 Example 10.3

242 242 248 25 1

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

257 259 260

Index

263

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. xi

xii

Preface

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.

ructural

1.1 Introduction 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"

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

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'.

Fig. 1.l

Cross-section of a trunkof a tree.

Timber as aStructuralMaterial

3

The annular band of cross-section nearest to the bark is called sapwood. The central core of the wood which is inside the sapwood isheartwood. 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 springwood, and an summerwood, Since outer layerofthickwallsandsmallcavitiescalled summerwood is relatively heavy, the amount of summerwood in any section is a measure of the density of the wood.

efects in timber2 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

e

e

e

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 width. This can be critical in respect of strength in that excess width of such rings can reduce the density of the timber.

Structural TimberDesign

Shake

Diagonal-grain

Cross-grain

Flat-grain

(a) Natural and conversion defects

End

Cupping

Springing Twisting

~oneyco~bing

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

Timberas a StructuralMaterial

5

metals. Gums and resins can inhibit the working properties of timber and interfere with the ability to take adhesives.

1.

o ~ ~ e r sdefects io~

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.

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. oft woo^ characteristics 0

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

6

Structural Timber

Design

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. rdwood characteristics

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 properties of timber3 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.

l' .5.1

isture content

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

Timberas a StructuralMaterial

7

100 h

E

80

U) U)

S U)

60

ti

I

Fibre saturation point

%

-0

40

5

P ; 20 0

0

15

30

45

60

75

90

Moisture content(%)

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.

8

StructuralTimber Design

1-5.4 Timber defects 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 References 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.

hapter

r

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: 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

l' 0

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 for 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:

BS EN 518 :1995 Structural timber. Grading. Requirements for visual strength grading standards. BS EN 519 ;1995 Structurul t i ~ b e rGrading. . 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~cationfor softwoods graded for structural use. S 5756 :1997 Spec~cationfor tropical hard 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.

Introduction to BS 5268: Part 2:1996

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 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 To modify Emin for deflection in trimmer beams and lintels 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 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

12

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

ual g r a ~ i n g

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.

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 his 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 conBS 5268 :Part 2, as they siderably larger than the grade stress values used in 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

Structural Timber

Design

Table 2.2 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

CS

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

GS

ss

GS

ss ss

ss

CS CS

GS GS

GS CS GS

ss ss

ss

ss ss

GS

GS

GS

ss

ss

ss ss

ss

ss

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.

erations (factorsaffecting tim 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 Service classes Due to the effects of moisture content on mechanical properties of timber, the permissible property values should be those corresponding to one of the

introduction to BS 5268: Part 2: 1996

15

16

Structural Timber

Design Table 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%. 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 ~content re 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

Introductionto BS 5268: Part 2: 1996 Table 2.5 Modification factor K3 for duration ofloading(Table

17

14,

BS 5268 :Part 2)

~~~

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 Section size

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

Structural TimberDesign

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.

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.

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 5 3

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

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 ~ , ~ ~ , ~

Introduction to BS 5268: Part 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. ~eometrical and mechanical properties n a

A b d E Emean Emjn

G h l

I L Le

m n

h

e Pk Prnean

z

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

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

Structural Timber Design

A m As

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,,g,

o,lg,l

grade compressive stress perpendicular to grain

C F ~ , permissible , ~ , ~ compressive stress perpendicular to grain

Tension

applied tensile stress parallel to grain CJt1g,// grade tensilestress parallel to grain atlU~ permissible , ~ ~ tensile stress parallel to grain

CF~,~,/I

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

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

22

Structural Timber Design

computer screen in a format similar to the way it would be done manually with paper and pencil.WhileMathcademploys the usualmathematical -, /,=) for algebraic operations, it also uses the convensymbols (i.e. tional 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 What does Mathcad 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 A simple calculation’ 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).

signispressed,

Mathcad computes and shows the

3.3.2 Definitions and variables2 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

15"-

23

\

-14.923

Fig. 3.1 A simple calculation.

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 ["I] to 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

t 2 type acc/ expressions. For example, to calculate the magnitude of 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

acc :=-g%

Fig. 3.2 Calculating with variables and functions.

24

Structural Timber

Design

acc :=-9.8

Fig. 3.3 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

M = 20 *kN.m

Fig. 3.4 Equations using units.

Using Mathcadfor Design Calculations

25

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

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.

1. Wieder, 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.

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)

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

4.3 Bending stress and prevention of lateral buckling 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

1

Y Fig. 4.1 Cross-sectionof a rectangular beam,

28

Structural Timber Design

where: amla,//= 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 Ixx= 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). amla&,// is calculated as the product of The permissible bending stress grade bending stress parallel to grain am,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,//= Om,g,// x K2

x K3 x K6 x K1 x Kt3

(4.4)

KZ?K3 and 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

Clear span Effective span Span to centres of actual bearings I

i

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

DesignofFlexuralMembers(Beams)

29

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.For 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: for h 5 72mm, for 72mm

h he

uspended timber flooring

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

Structural Timber Design

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 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

Solid blocking wall between Masonry joists v

(e) A typical support arrangement

Fig. 4.8 Suspended timber flooring-typical components.

Design of FlexuralMembers(Beams)

39

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

Books, Oxford.

40

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.

4.9 Design examples Example 4 7

Design of a main beam

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.

Dimensions inmm Fig. 4.9

Beam details (Example4.1 ).

Definitions

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

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

'1. Geometricalproperties 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

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. Loading Applied uniformly distributed Total load, W

load,

W

:= 3.9 kN m-* W:=weLe W = 11.11 okN

W

3. K-factors

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 rsubjected s to axial tension only

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

where:

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

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:

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. o t , a , / / , should

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

not exceed the

5.3.4 Combined bendingand tensile stresses

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

xK~K~K~KM

M

-z

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

Structural Timber Design

xamples

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 !

L, = 1.0 x L

Cross-section Fig. 5.6

Column details (Example 5.1).

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

N :=newton

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

1. ~ e o ~ e properties t r ~ ~ a ~

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 *

+

Design of AxiallyLoadedMembers

Secondmomentof

area, Iyy

h

Iyy := h b3 lYy = 1.1 X io7 o

67

*

m 4

For a rectangular section

Radius of

gyration, iyy

Section modulus, Zxx

2. Check slenderness ratio, h

b

ZYY

:= J12

iyy= 28 o mm b h2 zxx:= 6 Zxx= 339 904.17o mm3 *

h : = G? _ lYY

h = 142.85 300mm NO load sharing (Kg, clause 2.9)

K5

:= l

K6 := 1

h1

:= h

mm" h; 92 300 0.81 h; + 56 800

K7

*

+

K7 = 0.89 := 1

Glulam m o d ~ c a t ~ factors on (Table 21): Single-grade, 15 laminates in C24 timber Bending // to grain, K15 Compression perpendicular to grain, K18 Shear // to grain, K19 Modulus of elasticity, K20 4.

Gradestresses

BS5268 : Part 2, Table 7 Timber strength class, C24 Bending // to grain Compression perpendicular to grain Shear // to grain Mean modulus of elasticity

Gm,g.// :=

cF,.g.pp

7.5 N mm-2 mm-2

:= 1.9N

:= 0.71 N . mm-2

Emean :=

mmm2

10800N

5. ~ e ~ d stress j ~ g

Applied bending moment = 57.61 o kN b h2 zxx:= 6 Zxx= 6.01 X lo6 o mm3

Mmed

Section modulus

Applied bending stress Permissible bending stress

*

*

95

96

Structural Timber Design

. ~ateraJ st~bi~ity Clause 2.10.8 and Table 16

Maximum depth-to-breadth ratio, h/b

h -= 4.87 b Ends should be held in position and compression edges held in line by direct connection of t & g decking to the beams

7. Shearstress

Applied shear force

wmed Fv:=7

Applied shear stress Permissible shear stress

8. Bearingstress

Applied load

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

9. Deflection

Modulus of elasticity of glulam, E Deflection due to bending Am

Deflection due to shear Total deflection

= 34.02 o mm

Design of GluedLaminatedMembers

Permissible deflection

97

Aah := 0.003 Le Aah = 31.5 omm *

Camber required =deflection under permanent (long-term) loading:

Deflection under live load

Along = 13.67 o mm Provide 15 mm camber Alive := A t o t a l - Along Alive 21.83 o mm Deflection satisfactory

Therefore 115 mm x 560 mm glulam sections in single-grade C24 are satisfactory €xample 6.2 Design of a combined-grade glued laminated beam selection of a suitable section size

Design of a glued laminated timber beam for the roof of a restaurant is required. The beam is to span 9.8 m centre to centre on 125 mm wide bearings under service class 2 conditions. It is proposed to use a combined-grade lay-up using softwood timber in strength classes of C18 and C16 with laminations of36mm finished thickness. The beam is subjectedto a dead load of 0.67 kN/m excluding self-weight,from t & g boarding and roofing, and an imposed medium-term load of 2.25 kN/m. Definitions

Force, kN Length, m Cross-sectional dimensions,mm Stress, Nmmm2 1.

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

Geometrica/properties

Eflt'ective span, L, Bearing width, bw Beam dimensions: Breadth of section, b Depth of section, h Cross-sectional area, A Second momentof area, I,,

Le := 9.8 m bw := 125. mm

2. Loading

Dead load: Self-weight of beam (kN/m), Swt

-

Swt := 0.3 kN .m"

assumed

Structural Timber Design

Prescribed dead load (kN/m), PDL Total dead load, DL Imposed load: Prescribed imposed load (kN/m),Pi1 Total imposed load, IL

PDL := 0.67 kN

+

m-'

+

DL := (Swt PDL) Le DL = 9.51 o kN pi1 := 2.25 kN m" +

IL :=pi1 Le IL = 22.05 o kN *

Total load ( k N ) : Long-term,

Medium-term, Wmed 3. K-factors

Service class 2 (K2, Table 13) Medium-term loading (K3, Table 14) Bearing: 125 mm (K4, Table 15) (bearing position not defined) Notched end effect (K5, Clause 2.10.4) Form factor (K6, Clause 2.10.5) Depth factor (KT,Clause 2.10.6)

:=1 K3 := 1.25

K2

K4 := 1.0

K5 := 1 K6 := 1

Since section size is not known, at this stage assume, K7 := 1 Kg := 1

No load sharing (Kg,Clause 2.9)

Glularn ~ o d ~ c a t i factors on (Table ?l): Stress values for the higher-grade timber apply BS5268 : Part 2, Clause 3.2 Since number o f laminations is not known, Table 7, for C18 timber ignore at this stage Bending // to grain, K15 Compression perpendicular to grain, &g Shear // to grain, K19 K20 := 1.17 Modulus o f elasticity, K20 L

4.

Gradestresses

BS5268 : Part 2, Table 7 Timber strength class, C18 Bending // to grain Compression perpendicular to grain

Design of GluedLaminatedMembers

Shear // grain Mean modulus of elasticity

99

zg.i := 0.67 N mm-2 Ernean := 9100 N mm-2 *

*

Selecting a trial section

Using deflection criteria: Modulusofelasticity for glulam, E Permissible deformation under imposed load

E := Emean - K20 E = 1.06 x lo4 o N.mmF2 0.003 L, = 29.4 o mm

&h : =

0

5 I;.t."ed L2 Required second moment of Zxx,rqd := 384 * E . &h area, Zxx using &h underimposed load Zxx.rqd = 1.24 X 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 300mm

G l u l a ~ ~ o d ~ cfactors at~on (Table Part 2, Clause 3.2 BS5268 : 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):

:= 1.52 K18 :=1.69

K15

K19 :=2.73

K20 :=1.17

-

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 )".l1

K14 = 1.13 Clause 2.10.10 Tension // (&, Table 22)

Compression // (K2gC,Table 22)

K27 := 1.l

for twoglued timber sections per flange := 1.14 for twoglued timber sectionsper flange

Modulus of elasticity for deflection Table 22) K28E := 1.24 for a total of four glued timber sections in both flanges

Design of Ply-webbedBeams

Clause 4.5 Plywood grade stresses ( K ~ GTable ~ , 33) Plywood moduli ( K 3 6 ~Table , 33) Plywood rolling shear (K37, Clause 4.6) 3.

K36s

:= 1.33

K36E := 1.54

K37 := 0.5

Gradestresses

BS5268 : Part 2, Table 7 Strength class, C18 timber Tension // to grain Compression // to grain Shear // to grain Mean E value Minimum E value BS5268 : Part 2, Table 41 Finnish conifer, 9-plies 12 mm plywood with face grain perpendicular to span Tension perpendicular to Dply.t.g.pp:=7.44 N mm"2 face grain c ~ ~ ~ := ~ 9.8 . ~ N. mmM2 ~ . ~ Compression perpendicular to face grain Panel shear // and perpendicular ?;ply.g := 3.74 N mm-2 to face grain Rolling shear := 0.79 N mmm2 Modulus o f elasticity in tension Eply := 2950 N mm-2 and compression perpendicular to face grain G, := 270. N mm"2 Modulus of rigidity (shear modulus) +

-

e

4.

Geometrica/Properties

Transform section to an equivalent o f all timber. Using Erneanfor timber Plywood thickness Transformed web thickness,

Etimber := Etimbermean

tply := l:!

mm

tply.tfd := tply

*

APlY Etimber

tply, tfd

tply.tfd

= 3.89 o mm

~

139

1

Structural Timber

Design

Transformed section: ~ross-sectionaldimension:

b := 47 .mm

+

l? := tply.tfd b .2 B = 97.89 o m m H := 580 mm h :=97 -mm +

Second moment of area, I,,

a:=H-:!.h a = 386omm B -H 3 ( 2 . 6 ) . a 3 zx, := 12 12 = 1.14 X io9 0mm4

Section modulus, Z,,

Second moment of area, ZYY

zyy= 1.52 X

io7 o mm4

The ma~imumapplied bending stress in transformed section should not be greater than the lesser of: Timber tension // to grain Timber compression// to grain Transformed plywood tension perpendicular to face grain Transformed plywood compression perpendicular to face grain

~qd.ply.c.adm.pp:= 0ply.c.g.pp *

timber

Thus, the lowest value is taken as the permissible stress in bending G#d.ply.t.adm.pp = 3-21 N mm-2 *

&

K368

Design of Ply-webbedBeams

Applied load,

W

W

Applied bending moment, M

CFm.a.1

Applied bending stress,

= 1.72 0 kN m-' *

L: M ;= 8 M = 12.39 o kN * m M W

'

om.u.1 :=ZXX

N mm-2 Bending stress satisfactory C F ~ .= ,.~ 3.15 o

BS5268 : Part 2, Clause 2.10.10 E Etimber.min ' K28E E = 7 . 4 4 ; ~1 0 3 ~ N * m m " 2 5.W.L: Am := 384 E .IXX A, = 8.78 o

Modulus of elasticity for deflection Deflection due to bending

*

*

A , :=H

Web area, A,

*

tply

A , = 6.96 x lo3o mm2 M A, :=G, A , A, = 6.59 o Atoral := A m a s Atoral = 15.37 o mm A a h :=0.003 L e A,& = 22.8 o Deflection satisfactory

Deflection due to shear

*

+

Total deflection P e ~ i s s i b l edeflection

Applied shear force,

*

Le

F,, := 2 Fv = 6.52 o kN W

F,,

*

First moment of area above neutral axis, Q

Q = 2.37 x

Applied panel shear stress,

za

Fv

, z :=

lo6 o mm3 *

e

(2 tply) , z = 0.56 o N mm-2 IXX

*

*

141

142

Structural Timber Design

:=zp1y.g K8 K36s z a h . / = 4.9’7 ~ N . m m - ~ Panel shear satisfactory

Permissible panel shear

Tach./

*

8. Rolling shear

Applied shear force, F,

F, = 6.52 o kN

First momentof area of upper flange above neutral axis, Qr

Qr

:=(2

Qr

= 2.2 X lo6 o mm3

Applied rolling

shear stress,

zu :=

Fv

a

b

*

Qr

BS 5268 :Part 2, Clause 30

2 h Zxx = 0.06 o N K37 := 0.5

permissible panel shear

zuh

*

*

:= %.g K8 K36s K37 z u h = 0.53 o N mm-2 *

*

*

Rolling shear satisfactory 9. Lateralstability

Clause 2.10.10

Check Zxx/Zyy ratio

zxx

-75.24

”

ZYJJ

Condition (f) applies, i.e. compreSsion flanges should be fully restrained, for example, by direct fixing of roof sheeting Therefore the section is adequate

Timber columns maybe classified as simple or built-up, depending on their method of construction. Simple columns are fabricated from sawn timber or from gluedlaminated sections (glulam)to form one piece, for example,a rectangular section, The design requirements for simple columns are discussed in detail in Chapters 5 and 6 for sawn solid sections and glulam members respectively. ~uilt-upcolumns are those composed of two or more sections of timber connected together either by gluing or by means of mechanical fasteners (such as nails, bolts, etc.)Suchcolumnscan provide considerably more strength than the sum of the strength of the sections acting alone. Built-up columns can beconstructed in a great variety of shapes, see Fig. 8.1, to meet special needs or to provide larger cross-sections than are ordinarily available, or purely for architectural applications. While glued built-up columns can be assumed to behave as a single member, the full composite strength developmentinmechanically fastened columnsis doubtful.In general mechanically fastened columns may not possess adequate composite action by the connectors to make them act as a unit. In such cases designers are recommended to revert to prototype testing or conservative designsolution.' BS 5268 :Part 2 :1996 providesguidance for design of a special type of builtup column known as a spaced column which is detailed in this chapter.

Fig. 8.1 Typical cross-sections for built-up elements. 143

1

Structural Timber

Design

Spaced c o Z ~ ~ nare s thosebuiltup as two or more individualmembers (shafts) with their longitudinal axes parallel, and are separated at the ends and mid-points with spacer bZocks and joined together by gluing, nailing, bolting or other means of timber connectors.A typical make-upof a spaced column is illustrated inFig. 8.2. "he spacer blocks are provided to restrain differentialmovementbetweenthe shafts and to maintain theirinitial spacing under the action of load. The end connectors provide partial fixity to the individual members of the column, thus effectively restraining their buckling tendency. Spaced columns are often used in architectural applications, in trusses as compression chords, and in frame construction. A spaced column, due to the geometry of its cross-section, could haveat least 25% more load-carrying capacity than a single solid member with a similar volume of timber. Spaced columns, apart from being economical, can providesuitable construction through which other piecessuch as bracing or column to truss connections can be inserted conveniently.

Suitable connections (mechanical or glued)

Spacer blocks

294mm

Try a gusset of 350mm in length along the bottom edge of the ceiling tie. 8. Design of the plywood gusset

A free-body diagramof the non-concurrent forces actingon the joint, with reference to the centre line of the members, is shown in Fig. 9.24(b). Since the three forces are not

Design of TimberConnections

Fig. 9.24( b)

207

Free-body diagram.

coincident the free-body isnot in full equilibrium (i.e. the sum of the moments of the forces (sayabout point 0) is not equal to zero). Thus, the applied non-concurrent force the systemwillinduce a moment of M, at the joint, whichshouldberesistedby plywood gusset plate. In addition, the plywood gusset should also be able to resist a shearing force of F = 4.7 kN acting along an axis parallel to the rafter and passing through the interface between the ceiling tie and the rafter (i.e. along x-x). Therefore, the balancing moment, M , is Plywood thickness, t

M := (2.13 kN) .(106. mm) M = 0.23 o kN m t:=9.mm

Length of the gusset along the rafter, h

Section modulus, z

Stress due to bending moment

h = 392.81 o mm t h2 z := 6 z = 2.31 x lo5 o mm3 M G m :=-

z

= 0.98 o N mm-2 4.7 kN G, := t*h CY, = 1.33 o N mm-2 D t o t a l := G m t- Gs G t o t a l = 2.3 0 N mm"2

Gm

Shearing stress along x-x Total stress acting along x-x

*

~

208

Structural Timber Design

BS5268 : Part 2, Tuble 41 Grade shear panel zg := 3 . 7 4 - ~ * m m - ~ Modification factor for plywood K36 := 1.33 grade stresses for medium-term (K-36, Table 33) Permissible panel shear in T&n :=Tg K36 plywood l;,&= 4.97 0 N m m - 2 *

*

Plywood size is $ a ~ s f a c t o ~ Rafter member:

Plywood gusset: 9 mm 7-ply Finnish conife Ceiling tie: 47 x 9 7 m C18 ti

@ 42 m centres along tie

/ /350m-> Fig. 924(e)

Designed joint details.

.5 ~ e s i of ~ ansimple t w o - m e ~ ~ e r

er

~ o l tconnection e ~

The bolted connection shown in Fig. 9.25 is subjected to medium-term tensile loading under service class 2 conditions. The joint comprises a singleM12 bolt acting in single shear with C18 timber sections. Determine the load capacity of this connection.

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

Bolt diameter, d bolts, Thinner member thickness

NO. O f

N :=newton kN := lo3 * N

Direction parallel to grain, ,l/ Direction perpendicular to grain, pp

d:= 12.mm nbolt

:= 1

tthinner

:=33 .mm

Design of Timber Connections

P

47 m

33 m

P Fig. 9.25 Bolted connection (Example9.5).

. Basic v a l ~ e ~ BS5268 : Part 2, Table 64 Strength class, C18 timber, load parallel to grain Basicsingleshear lateral load Fbafic :=1.22 k N under medium-term loading, by interpolation, Fbmic

-

BS5268 : Part 2, Clause 6.6 Timber-to-timber connection K46 does not apply Moisture content, K56, service class 2 No, of bolts one inline, n = 1, K57

BS.5268 : Part 2, Clause 6.6.6 Permissibleshear lateral load per bolt Loadcapacity of the connection, Pcapacity

K46 := 1

K56

:= 1

K57 := 1

Fadm := Fbasic

*

&6

*

K56 ' K51

F a h = l .22 o kN Pcapacity:= Fa& nb& Pcapacity = 1.22 0 kN

209

210

Structural Timber Design

5 . ~ i n i m bolt ~ m endand edge distances

BS5268 : Part 2, Table 75 loaded distance End End distance unloaded Edge distance loaded distance Edge unloaded

7-d=84omm 4 d = 48 o m m not applicable 4 d = 48 o m m not applicable 1 . 5l.8d0=m m

-

+

6. Joint slip

BS5268 : Part 2, Clause 6.2 and Table 52 Strength class, Cl8 timber Characteristicdensity(Table 7 ) p := 320 .kg m"3 Slip modulus: Since the equation for slip modulus is an empirical one (i.e. with hidden units in the coefficient part), for Mathcad to produce correct units, muliply it by the units shown inside the parentheses; or alternatively, use the equation without units for p and d. Thus, slipmodulus, K,,,

h.

K,,, := p1.5 .d . (kg"5 .m2.5 .N . 106) Kser = 3.43 X lo3 o N mm-' *

Slipperboltunderpermissible load, U

U :=

&er

= 0.36 o m m := U 1 .OO mm Ujoint = 1.36 o mm

U

Allowing 1 .OOm m additional slip due to oversize bolt hole

r;,,, -

Ujoint

+

Therefore the load capacity of the joint is 1.22 kN with a joint slip of 1.36mm Example 9.6 Design of a three-member timber-to-timber bolted connection

The boltedconnectionshown in Fig. 9.26 issubjected to along-term loading, as indicated, under service class conditions. 2 The joint comprises a singleM16 bolt acting in double shear with C22 timber sections. Checkthe adequacy of the connection. Definitions

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

Bolt diameter, d bolts, nbolt

NO. O f

N :=newton

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

Design of TimberConnections 5.8 kN

\r,

211

members: Rafter 2 of 35 x 194mm C22timber

,/'k"

5.2 kN

I

72 x 194m C22timber Fig. 9.26

2.63 W

Boltedconnection (Example 9.6).

Side member thickness Inner member thickness Check adequacy o f the section Distance from loaded edge to furthest fastener

touter

:= 35 mm

tinner :=72

*

mm = 72 0 mm >2 194. mm := 2 = 97 o mm *

tinner he he

*

touter

= 70 0 mm okay

2. Basic vafues BS5268 : Part 2, Clause 6.6.4 and Table 70 The support reaction acting on the ceiling tie makes the load in the rafter act parallel to grain, and in the ceiling tie to act at 27" to grain direction. Therefore Hankinson's equation should be used to determine the appropriate basic shear load values. Strength class, C22 timber (Table 70) FraYter.1 :=3.09 kN For 35 mm outer members (rafters), long-term load parallel to the grain for a M16 bolt For 72mm inner member (ceiling tie) corresponding to 72/2= 36 mm outer members for a M16 bolt:

Ftje.l:= 3.18 kN long-term load parallel to grain, by interpolation long-term load perpendicular Ftie.pp := 2.64 kN to grain, by interpolation

212

Structural Timber Design

For load at angle a where a := 27.-

Ftie.8

n

180 (3) Grade shearstressforC22 timber (Table 7)

Ftie.8 Ftie.pp

Ftie :=

+

*

Ftie.pp

*

COS(CX)~

= 3.05 o kN 1cg.8 := 0.71 N mm-2 Ftie

3. ~ o d i f i c a t i o factors n

BS5268 : Part 2, Clause 6.6 Timber-to-timb,er connection, K46 does not apply Moisture content, K56, service class 2 No.of bolts one inline, n = l, K5, Serviceclass 2 (K2, Table 13) Load duration, long-term (K3? Table 14) Clause2.9) Loadsharing (K8,

&6

:= 1

K56 := 1

K57 := 1

K2 := 1

K3

:= 1

K8

:= 1

4. ~ e r ~ i s loads s i ~ l ~

(1) For rafter: Permissible load per shear plane actual load (per shear plane)

(2) For ceilingtie: permissible load per plane shear actual load (per shear plane)

Fadm.rafter := Fra8er.l

k;6

' K56

= 3-090 UJ 5.80 kN Prafter := 2 Prafter = 2 -9 0 kN Satisfactory Fadm.mafter

*

Fadmetie := Ffie * &6

K56 ' K57

3.05 o kN 5.20 kN Prafter := 2 Prafter = 2.6 o kN Satisfactory

Fah.tie

*

(3) Shear stress in jointed timber BS 5268 : Part 2, Clause 6.1 and Figure 6 Permissible shear stress zadm Zg.// K2 K3 Kg Z a h = 0.71 o N mm-2 Permissible shear force vu* .- 2. 3 Z a h he tinner V a h =L 3.31 0 kN >2.63kN Satisfactory *

S-"

*

*

*

K57

Designof Timber Connections

BS5268 : Part 2, Table 75 For rafter: end distance loaded end distance unloaded edge distance loaded edge distance unloaded For ceiling tie: end distance loaded end distance unloaded edge distance loaded edge distance unloaded Thereforethe connec~onwith ~ be a d ~ u a t e

7 d = 112 o mm not applicable 4-d=64omm 4 d = 64 o mm not applicable 1.5.d=24omm 7 . d = 1120mm 4 .d = 64 o mm not applicable 4.d=64omm 1.5.d= 24omm N edgeand ~enddistances u detailed ~ abovewill

esign of a t ~ r e e - m e m ~ e r ~ ~ moment f t e ~ connection

st~ef-to-tim~~r

The bolted connection shown in Fig.9.27 is subjected to a long-term eccentricload of 12.5 kN asindicated. Thejoint comprises two4mm thick steel side-platesand an inner timbermemberinstrengthclassC22joined together usingeightM12 bolts under service class 2 conditions. Check the adequacy of the connection.

Two member: 4side-plates mm Innersteel (

Fig. 9.27 Eccentric loaded connection (Example 9.7)).

timber

214

Structural Timber

Design

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

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

1. Geometrical details

Bolt diameter, d NO. of bolts, nbolt Bolting pattern: horizontal spacing, x vertical spacing, y Side member thickness (Clause 6.6.5.1) Inner member thickness Distance from loaded edge to furthest fastener

2.

d:= 12.mm nbolt :=8

x :=90mm y := 85 -mm tsteel :=4 mm

>2.5mm or 0.3 d = 3.6 o mm okay

:= 72mm

he:=294.m-62*mm he = 232 o mm

lied loading

Applied vertical load, P Eccentricity, ep No applied horizontal load, H Eccentricity will induce a moment of M and a shear force of V at C, the centre of geometry of the connection Distance from C to each bolt, r

Sum of squares of distances fromC to each bolt, J= Force acting on furthest bolt (i.e. bolt a) due to applied moment M Force acting on bolt a due to applied shear force V

r;!

P := 12.5 kN *

ep :=45 mm H:=O*kN M:=P.ep M=0.56okN-m V:=P Y = 12.5okN a

ra := ~ x T ra = 123.79 o mm rb :=x rf := x rc :=ra re :=ra rg := ra rh :=y rd := y J:=4.r~+2*r~+2.r~ J = 9.2 X 1040mm2

Design of Timber Connections

21 5

Force acting on bolt a due to applied horizontal load H = 0 For the rectangular fastener pattern, the total force on bolt a is given by

[(F.+

F:=

J ( x 2+3 ) X

Fa.M

'

F = 2.18 o kN This force is acting at an angle o f a to grain of timber, where

a = 76.18 o deg

3. Basic load vaiues

BS5268: Part 2, Clause 6.6.4 and Table 70 72 mm inner member corresponding to 72/2 = 36 mm outer members for a M12 bolt: Long-term load // to grain, by interpolation Long-term load perpendiuclar to grain, by interpolation

Fpp:= 2.105 kN *

F1 FPP F1 sin(a)2 Fpp COS(^)^ F=2.12okN Grade shear stress for C22 timber ~ ~:=-0.71 1 N mmm2 (Table 7)

For load acting at angle a

F :=

4. ~odification factors

BS.5268 : Part 2, Clause 6.6 Steel-to-timber connection (&fit Clause 6.6.5.1) Moisture content, K56, service class 2 No. o f bolts in one line, n = 3, Service class 2 (KZ, Table 13) Load duration, long-term (K3, Table 14) Load sharing (Kg, Clause 2.9)

&6

:= 1.25

K56 :=

l

K57 := 1 K2 :=

K3

+ *

*

l

:= 1

K8 := I

BS5268 : Part 2, Clause 6.6.6 Permissible load per shear plane

-

:=F . &6 K56 = 2.64 o kN nshear :=2

Fadm

K57

Fadm

Number of shear planes Permissible load for bolt

Fadm.bolt := Fadm * nshear

= 5-290 kN Satisfactory

Fadm.bolt

Shear stress in jointed timber: BS 5268 : Part 2, Clause 6.1 and Figure 6 Permissible shear stress Permissible shear force Hence the timber section can sustain an applied shear force at the connection of Fadm.y 6. ~ i n i ~ bolt u mspacings

BS5268 : Part 2, Table 75 end distance loaded end distance unloaded edge distance loaded edge distance unloaded spacing parallel to grain spacing perpendicular to grain

7 .d = 84 o mm 4 .d = 48 o mm 4 .d = 48 o mm 1.5 .d = 18 o mm 5 .d = 60 o mm 4 .d = 48 o mm

not applicable not applicable 56mm providedokay not applicable ]

(10.33)

242

Structural Timber

Design

Table 10.14 Values of slip moduli k,,,, per fastener per shear plane (in N/mm) (Table 4.2, EC5)

Fastener type Timber-to-timber Panel-to-timber Steel-to-timber Bolts and dowels Screws Nails (pre-drilled) Nails (no pre-drilling)

pk5d

& pk5d0.8

Staples where Pk is the joint member characteristics density, given in Table 1, BS EN 338 :1995 (in kg/m3) d is the fastener diameter (in mm).

(4) For joints made with bolts, EC5 permits 1mm oversize holes which should be added to joint slip values. Thus: Uinst,bolt

-&er

=1 -

kSW

(10.34)

(10.35)

1. Timber Engineering -STEP I (1995) Centrum Hout, The Netherlands.

Timber Engineering -STEP 2 (1955) Centrum Hout, The Netherlands. Page, A.V.(1993) The new timber design Code :ECS. The Structural Engineer 71, No. 20, 19 October.

e s i p of floor joists

A timber floor spanning 3.8 m centre to centre is to be designed using timber joists at 600 mm centres. The floor is subjected to an imposed load of 1.5 kN/m2 and carries a

Design to Eurocode 5

243

dead loading, excluding self-weight, of 0.30 kN/m2. Carry out design checks to show that a series of 44mm x 200 mm deep sawn section timber in strength class C22 under service class l is suitable.

Section A-A Fig. 10.7 Timber floorjoists (Example 10.1).

Force, kN Length, m Cross-sectional dimensions, mm

Stress, Nmm"2 N :=newton kN := lo3 N

1. ~ e o ~ e t r properties i~af

Breadth of beam section, b Depth of beam section, h Span between support centres, L Bearing length, I Joist spacing, Js Cross-sectional area, A Second moment of area about y-y axis, Iy Section modulus about y-y axis, Wy

b:=44+mm h := 200 mm L := 3.8 mm I := 75 mm Js := 600 mm A :=b.h A = 8.8 X lo3 0mm2 b h3 Iy := 12 Iy = 2.93 x lo7 o mm4 b h2 := 6 W y = 2.93 x lo5 o mm3

wy

+

Cross-section

2

Structural Timber

Design

BSEN338 : 1995, Table l Characteristic bending strength Characteristic shear strength Characteristic compression perpendicular to grain Mean modulus of elasticity // to grain 5%tile modulus o f elasticity // to grain Mean shear modulus Average density 3. PartiaJ safety factors

EC:Part 1.1, Table 2."33.1 Permanent actions Variable actions EC:Part 1.1, Table 2.3,3.2 Material factor for timber

Applied dead load, DL Self-weight, Swt Total characteristic permanent load/m length, G k Imposed load, ZL Characteristic variable (imposed) load/m length, e k Design action, F d

A. U l t i ~ a t elimit states

5 . Mo~jfjcatjon factors

Factor for medium-duration loading and service class 1 (kmod, Table 3. l .7) Size factor (kh,Clause 3.2.2) for h > 150mm

&.O'j

:= 6.7 kN mm-2

:= 0.63 kN mm-2 pmean := 410 kg mm-3

Gm,,,

*

*

*

Design to Eurocode 5

Load sharing applies (kls, Clause 5.4.6) Lateral stability (kcrit, Clause 5.2.2): ffective length, Lef for full restraint against rotation

245

kls := 1.1

Critical bending stress (NAD, Clause 6.5) Relative slenderness for bending Lateral instability factor Bearing factor (kc,90,Clause 5.1.5): Bearing length, I No overhang at beam ends, a Distance between bearings, II

-

I := 75 mm a := 0 - m m 21 :=L I zI = 3.73 x 103

mm

In order to make Mathcad accept the following empiricalequation, the indicated units have been added. Bearing factor

kc.go := 1

-I ) + a -17(150000- mm mm2 *

Factor for shearinmembers with notched end (kv, Clause 5.1.7.2)

Design bending moment

Design bending stress

Design bending strength

kc.90 = 1 kV :=l for no notch

246

Structural Timber Design

7 . Shearstrength

Design shear stress = 0.53 O N Illm"2

0V.d

Design shear strength

*

fV.d :=

Kmod

*

kV

'fV.k

Kls

YM

fV.d = 1.62 o N mm-2 Shear strength satisfactory 8. Bearingstrength

Design bearing load Vd = 3.12 o kN Design bearing stress oc.9o.d

Design bearing strength

= 0.94 O N lllm-2

fc.90.d := fc.90.d

*

kmod kc.90 *

kls

'fc.90.k

YM

= 3.45 o N mm-2

Bearing strength satisfactory

B. Serviceability limit states Clause 4.3, EC5 For serviceability limit states (Table 2.3.3.2, EG5) Bending moment due to permanent loads, MG Bending moment due to variable loads, MQ

(1) Instantaneous deflection:

For bending and shear due to permanent action, Gk, using equations (4.6) and (4.9)

yM

MG

:= 1.0

= 0.39 o kN m

Qk L2 M Q := -

8

Design to Eurocode 5

247

For bending and shear due to variable action, Q k Maximum allowable deflection due to variable action (Clause 4.3, EC5) %.inst

c U2.inst.adm

Satisfactory (2) Final deflectiondue to variable actions: Modification factor for deformation, for medium-term under service class 1 (kde$ Table 4.1, EC5)

Maximum allowable deflection (Clause 4,3, EC5) (3) Final deflection due to all actions (permanent and variable): Maximum allowable deflection (Clause 4.3, EC5)

In general, for beams without precamber, it is not necessary to check ~ 2 . f i nas unet.fm is always greater. IO.

~ibration

The UK NAD re: EC5 Clause 4.4.1 Total instantaneous deformations should be less than the lesser of

(&

= 11.41 o m m

and14mm

Therefore 44 mm x 200 mm sawn timber sections in strength class C22 are satisfactory

2

Structural Timber

Design

2 Design of an eccentrica//y/ o a ~c eo ~t ~ ~ n

For the design data given below, check that a 100mm x 250 mm sawn section is adequate as a columnif the load is applied40 mm eccentric about its y-y axis. The column is 3.75m high and has its ends restrained in position but not in direction. Design data Timber: C22 Service class: 2

Permanent load: 15kN Variable (medium-term): load

17 kN

40

~

m

Y

I

Cross-section

Lq= 1.0 x L

Fig.10.8 Column details (Example 10.2).

Force, kN Length, m Cross-sectional dimensions, mm

Stress, Nmm” N :=newton kN :=lo3 N

1. G e o ~ e t r j cproperties a~

Column length, L, EEective length, Ley Width of section, b Depth of section, d Cross-sectional area, A Second moment of area about y--y axis

L = 3.75 rn

L, := 3.75 Lef := 1e 0

m L Ley= 3.75 o m b :=100 mm d :=250 mm A := b - d A = 2.5 X lo4 0 m m 2 I y : = J12” . b . d 3 Iy = 1.3 x lo8 o mm4

-

a

*

Design to Eurocode 5

Section modulus axis

about y-y

b d2 wy:= 6 *

Wy = 1.04 x lo6 o mm3

35 :=

Radius of gyration about y-y axis

ly

Slenderness ratio about y-y axis

hy :=

Secondmomentof z-z axis

Ay = 51.96 I, := h d b3 Iz = 2.08 x lo7 o mm4

iy = 72.17 o mm

% IY

area about

Radius of gyration about 2-2 axis

a

-

l, := *

v

%

iz = 28.87 omm

h, := L;,f

Slenderness ratio about 2-2 axis

iz

h, = 129.9 2. Timber strength properties

BS EN 338 : 1995, Table l Characteristic bendingstrength Characteristic compression parallel to grain 5%tile modulus ofelasticity parallel to grain

fm.k := 22

N mmm2 N

fc.o.k :=20

Eo.05 := 6.7 - k N .mm-2

3. Partial safety factors

EC5 : Part l .l,Table 2.3.3.1 actions Permanent actions Variable EC5 : Part l .l, Table 2.3.3.2 Material for timber

:= 1.35 Y Q := 1.5

yw := 1.3

4. Actions

Characteristic permanent load, G k Characteristic variable load, Qk Design action, N d Eccentricity, er

G k := 15

kN

Q k := 17 * kN

Nd:=YG'Gk+YQ.Qk N d = 45.75 o kN

ey := 40mm

249

250

Structural Timber

Design

Design moment due to eccentricity about y-y axis

5. ~odifjcation factors

Factor formedium-duration loading and service class 1 (kmod, Table 3.1.7) Load sharing does not apply (kis, Clause 5.4.6)

kt, :==1.0

6. Bending strength

Design bending moment about y-y axis Design bending stress about y-y axis

kid

= 1.83 o k N . m

No bending moment about z-z axis, thus Design bending strength

7. Compressionstrength

Design compressive stress 0C.O.d

Design compression strength

-

= 1.83 o N mm-2 kmod kls

*

fc.0.k

fc.0.d

:=

fc.0.d

= 12.31 o N.mm-2

YM

Buckling resistance (Clause 5.2.1, EC5): Euler critical stresses about y-y and z-z axes

Design to Eurocode 5

251

fc.0.k

Relative slenderness ratios

0c.crit.y 5el.y

=Z

0.9

Both relative slenderness ratios are >0.5, hence conditions in Clause 5.2.1 (4) apply: For a solid timber section, For a rectangular section (Clause 5.1.6), Thus

pc := 0.2

k m := 0.7

and Hence

kc, := kY

+ J-h:,.

kc., = 0.81

and

l

kc., :=

kc., = 0.18 Check the following conditions:

0c.O.d kc., ‘fc.0.d

-+

0m.z.d fm.z.d

+km”

Gmyd fm.y.d

-0.91 < 1.0 Satisfactory < 1.0 Satisfactory

Therefore a l00 mm x 250 mm sawn section timber in strength class C22 is satisfactory

Example 70.3 Design of a timber-to-timber nailed tension splice joint

A timber-to-timber tension splice joint comprises two 47mm x 120mm inner members and two 33 mmx 120 mm side members ofstrength class C22 timber in service class 2. It is proposed to use 3.35 mm diameter, 65mm long round wire nails without predrilling. The joint is subjected to a permanent load of 2 kN anda medium-term variable load of 3 kN. Determine the required number of nails with a suitable nailing pattern.

Structural TimberDesign

A Nailing zones

(a)

Splice joint (Example 10.3).

Force, kN Length, m Cross-sectiQna1dimensions, mm eo~etri~af

Stress, Nmmm2 N :=newton kN := lo3 N +

prope~ies

Thickness of side members, tl Thickness of inner members, t2 Width of timber members, h Cross-sectional area of side members, A, Cross-sectional area o f inner members, Ai, Nail diameter, d Nail length, Inail Nail pointside penetration, tpoint

:= 33 .mm :=47 mm h := 120 mm A, := h * tl A, = 3.96 x lo3 o mm2 Ai, := h t2 tl

t2

*

*

Ai, = 5.64 X lo3 o mm2 d := 3.35 mm Inail := 65 mm

-

+

$point

tpoint

Clause 6.3.1.2, EC5 Minimum allowable pointside penetration For overlap nailing without pre-drilling

. ~

= 32 o mm

tpoint.adm := 8 d tpoint.ah = 26.8 o mm t2 -tpoht= 15 o mm >4 d = 13.4 o,mm Both pointside penetration and overlap nailing are satisfactory

is t r e ~ ~properties t h~ ~

BS EN338 : 1995, Table I Characteristic tension parallel to grain Characteristic density

:= haif -tl

r

ft.0.k := 13

N mm-2

Pk := 340 * kg

*

m-3

Design to Eurocode 5

253

~ i asafety l factors

EC5 : Part 1.1, Table 2.3.3.1 Permanent actions Variable actions

YG :=1.35

EC5 : Part I J , Table 2,3,3.2 Material factor for timber Material factor for steel

yjl.l.timber

YQ :=1.5

YM.steel

Characteristic permanent load, G k Characteristic variable load, (& Design action, N d

A. ~ltimatelimit states

:= -3 :=1.1

:= 2 kN Q k :=3 kN

Gk

+

Nd:=YG'GkS'YQ*ek N d = 7.2 o kN

difi~ation factors

Factor for m e d i ~ - d u r a t i o n loading and service class 1 (kmod, Table 3.1.7) Size factor ( k h , Clause 3.2.2) for h S50mmis the lesserof:

kmod

kh

:=0.8

:= 1.3 and

k h ==

.

k h :=

1.05

~ e n ~ strength i o ~ of t i ~ b e r

Designtensionstressparallel grain in side members

to

cft.0.d :=

*

cft.0.d

Designtensionstressparallel grain in inner members

Nd 2 As

to

cft.0.d := Dl.0.d

Designtension strength parallel to grain

= 0.91 o N mm-2 Nd A in

= 1.28 o N mm-2

ft.0.d :=

kmodkh

'ft.0.k

YM.timber

= 8.37 o N .mmw2 Tension strength satisfactory

ft.0.d

7 . ~ ~ ~ e d strength d i n g of timber

Characteristic embedding strength without pre-drilling Since the following is an empirical equation (with hidden units inthe coefficient part), for Mathcad to produce the correct units, multiply it by the units shown inside the parentheses; or alternatively use the equation without units for Pk and d. Thus:

254

Structural Timber

Design

pk d-Ov3 (sec-2 .m2-3 1.26 lo5) = 19.42 o N mm-2

fh.k := 0.082 fh.k

Design embedding strength for headside timber

8.

+

fh.1.d :=

kmod ' f h . k YM.timber

fh.1.d

for pointside timber

*

= 11.95 o N mm-2

fh2.d Z"fh.1.d f h 2 . d = 11.95 0 N

*

Yield momentof nails

Yield moment o f a nail (using a similar treatment for the units as above) Design yield moment

-

My.k

d2*6.(kg. m-*6 s e c 2 n6.31 io4) = 4.17 x lo3 o N mm

1My.d

:=kmod

M y . k := 180

*

My.k

YM.stee1

= 3.03 x lo3 o N mm

My.d

9. Load-carryingcapacity

EC5, Clause 6.2.1 For a timber-to-timber joint with nails in single shear, design resistance per shear plane, R d , is the lesser of to R d f (see Table 10.6),where: is the pointside penetration length and the ratio, P

t2 := tpoint

Failure mode (a)

&.a

t2

fh.1.d

P:=fh.2d p=1

Rd.a

Failure mode (b)

:=fh.l.d

*

= 1.32 X

Rd.b :=fh.l.d t2

d io3 0 N d .P

$1

*

*

Rd.b

= 1.28

Rd.c

= 538.94 o N

X

lo3 0 N

Failure mode (c)

Failure mode (d)

Design to Eurocode5

Failure mode (e)

Failure mode (f) Rd.f

Therefore the design resistance per nail is the ~ n i m u mof:

= 542.17 0 N

R d := [Rd.aRd.bRd.cRd.dRd.e

&.f]

min(Rd) = 538.94 o N

Number o f nails per side required is For a symmetrical nailing pattern adopt 16 nails per side. Thus,

Nnails := 16

l 0. NaiJ spacing EC5, Table 6.3.1.2 Nail diameter Angle to grain Minimum spacing parallel Minimum spacing perpendicular

d := 3.35 a :=0

+

a1 := ( 5 5 lcos(a)l). d a1 = 33.5 o mm +

a2 := 5 . d a2 = 16.75o mm a3.t := (10 5* ( c x ) ~* )d Minimum loaded end distance ~ 3 =, 50.25 ~ o mm . 10 ~ d Minimum unloaded end distance ~ 3 := ~ 3 =. 33.5 ~ o mm not required ~ 4 . 1:= (5 5 lsin(a)l) d Minimum loaded edge distance ~ 4 =. 16.75 ~ o mm not required Minimum unloaded edge distance ~ 4 :=. 5 ~ d ~ 4 =. 16.75 ~ o mm

+ ICOS

+

+

B. Serviceabilitylimitstates 11. Joint slip EC5, Clause 4.2 Nail diameter Timber characteristic density

d :=3.35 mm pk = 340 o kg

+

255

56

Structural Timber

Design

Slip modulus (kser, Table 4.2, EC5) and using a similar treatment for the units of this empirical equation, for nails without pre-drilling Design load for serviceability limit states Load per nail

~nsta~taneous slip Uimt

= 0.47 0

Assuming allnails to slip by the same amount,eachinner 0.47mmrelative to side members. Therefore the total instantaneous slip is: ~ o d i ~ c a t i ofactor n for deformation due to creep ( k d d , Table 4.1, EC5) for ~ e ~ a n e load, nt for medium-term variable load, Final slip per nail is calculated as

Final slip of joint

Fig.10.9(b) Nail spacings and distances.

member willmove

by

In the previous versions ofBS 5268:Part 2 the softwood timber section sizes for sizes of sawn and processed were specified to BS4471: 1978 Spec~cation softwood, which gave sizes and tolerances for three types of surface finish: sawn, planedand regularised. BS 5268 :Part 2 :1996 requirements for timber target sizes are those given in BS EN 336 :1995 Structural timber. Coniferous andpoplar.Sizes.Permissibledeviations and in its National Annex. This standard specifies two tolerance classes: tolerance class 1 (Tl) is applicable to sawn surfaces, and tolerance class 2 (T2) applicable to planed timber. Regularised timber can be achieved by specifying T1 for the thickness and T2 for the width. The commonly available lengthsand cross-section sizes are also listed in the National Annex of BS EN 336, and are referred to as target sizes. The targetsize is defined as the desired timber section size (at 20% moisture content) whichcanbeused, without further modification, for design calculations.

A1 Basicsawn softwood timbersectionsizeswhosesizesandtolerances comply with BS4471: 1978, at 20Y0 moisture content

Table

Width

Thickness

(-1

300

250 225 200 175 150 125 100 75 36 38 44

47

50 63 75

100

150

200 250 300

X

X

X X X X

X X X X

X X X

X X X

X X X X

X X X X X X

X X X

X X X X X X

X X X X X

X X X X

X X X X X X

x x x

x x x

x x

x x X

x X

257

258

Structural Timber

Design

Table A2 Customary target sizes of sawn structural timber (Table NA.2, BS EN 336 :1995)

Thickness (to tolerlance class 1) 0 225 200 (mm) 175 150 125 100 22 25 38 47

Width (mm) (to tolerance 1) class 300

75 X X X

63

75 100 150 250 300

X

X

X

X

X X X X X X

X X X X X

X X X X X X X

X X X

X X X X X X X

X

X

X

X

x

X

x X X

X

X X

Note I Certain sizes may not be obtainable in the customary range of species and grades which are generally available Note 2 BS EN 336 has a lower limit of 24 mm. However, as thinner material is used in the UK the customary sizes of such material are also listed here

Table A3 Customary lengths of structural timber (Table NA. 1, BS EN 336 :1995) Length (m) 2.10 1.80 2.40 2.70

3.005.10 4.20 3.30 4.50 3.605.70 4.80 3.90

5.40

6.00 6.30 6.60

7.20

6.90

Note Lengths of 5.70m and over may not be readily available without finger jointing

In general, the differences between BS 4471 and BS EN 336 are minor and should not present any problemsto specifiers and suppliers in the UK.'For comparison purposes, in Table A1 the basic sawn softwood timber section BS 4471 are given.The sizeswhosesizes and tolerancescomplywith customary target sizes, whose sizes and tolerances comply with BS EN 336, for sawn strucural timber are given in Table A2. Table A3 gives the range of lengths of sawn softwood structural timber.

Reference 1. Fewell, A.R. (1997) Changes to the requirements and supply of timber structural materials, UKTEG Seminar, I. Struct. Eng., London, February.

Appendix B

Weights of Building Materials

Some typical building material weights,for determination of dead loads, are tabulated in Table B 1. The values are based on BS 648 :1964. Table B1 Weights of building materials (based on BS 648 :1964) Material

Asphalt

Roofing 2 layers, 19mm thick Damp-proofing, 19 mm thick

Bitumen roofing felts

Mineral surfaced bitumen per layer

Glass fibre

Slab, per 25 mm thick

Gypsum panels andpartitions Building panels 75 mm thick

Lead

Sheet, 2.5mm thick

Linoleum

3 mm thick

Plaster

Unit mass 42 kg/m2 41 kg/m2 44 kg/m2

2-5 kg/m2 44 kg/m2

30 kg/m2

6 kg/m2

Two coats gypsum, 13mm thick

22 kg/m2

Corrugated

4.5 kg/m2

Plastic sheeting Plywood

per mm thick Rendering or screeding Cement :sand (1 :3), 13mm thick

0.7 kg/m2

(depending upon thickness and source)

24-78 kg/m2

Slate tiles Steel

Solid (mild) Corrugated roofing sheet per mm thick

Tarmacadam

25mm thick

Tiling

Clay, for roof

Timber

Softwood Hardwood

Water Woodwool

Slab, 25mm thick

30 kg/m2

7850 kg/m3 10 kg/m2

60 kg/m2 70 kg/m2 590 kg/m3 1250 kg/m3 1000 kg/m3 15kg/m2

259

itis i

BS 52 Part 2 :1996 Part 3 :1998 Part 4 :1978 Part 5 :1989 Part 6 :S996 Part 7 :1990

EC5

t

Structural use of timber Code of practice for permissible stress design, materials and workmanship. Code of practice for trussed rafter roofs. Fire resistance of timber structures. Preservation treatments for constructional timber. Code of practice for timber frame walls. Recommendations for the calculation basis for span tables.

DD EN77 1995-1-1 : 1994 E~rocode5: structures General rules and rules for buildings (together with United Kingdom National Application Document)

BS EN 384 :1995 Structural timber. Determination of characteristic values of mechanical properties and density.

BS EN 385 :1995 Finger jointed structural timber. Performance requirements and minimum production requirements.

BS EN 518 :1995 Structural timber. Grading. Requirements for visual strength grading standards.

BS EN 336 :1995 Structural timber. Coniferous and poplar. Sizes. Permissible deviations.

BS EN 338 :S995 Structural timber. Strength classes. BS EN519 :1995 Structural timber. Grading. Requirements for machine strength graded timber and grading machines. 260

RelatedBritishStandardsfor

Tmber Engineering

261

BS EN 301 :1992 Adhesives, phenolic and aminoplastic, for load-bearing timber structures: classification and performance requirements.

BS EN 386 :1995 Glued laminated timber. Performance requirements and minimum production requirements.

BS EN 390 :1995 Glued laminated timber. Sizes. Permissible deviations.

BS EN 20898Mechanicalproperties

of fasteners.

This Page Intentionally Left Blank

actions, 221, 244, 249, 253 adhesives, 82, 195 additional properties, 18 axial compression, 56-63, 86, 89, 119, 148, 229 axial compressing and bending, 61-2, 68, 71, 78,122,157,230-31 axial loading, 56-81,119,151,153 basic stress, 10 beams axes, 27, 225 circular, 29 curved, 90-92, 113-18 flitched, 38, 39 glued laminated, 26, 82-122, 225 notched, 36-7,46, 227-8 ply-webbed, 26, 123-42 rectangular, 26, 28-9 solid section, 26, 225 straight, 83 trimmer, 38, 39 bending deflection 33, 90, 129, 239-40 strength, 225-6 stress, 27-8, 61-2, 65, 86, 128, 157, 225-6 bearing length, 35-6, 228-9 bearing stress, 34-6, 96, 101, 118, 228 bolts, 160, 163, 165, 179-88, 231, 235, 238 boxed beams, 123 British grown timber, 14 camber, 33, 83, 90, 239 cantilever, 239 ceiling tie, 204, 21 1 centre of geometry, 185 characteristic values, 220, 222 clear span, 28-9

columns, see Chapters 5, 6, 8 and 9 built-up, 143 combined stresses, 56, 61-2, 65, 230 effective length 57-8, 145-6, 230 glued laminated, 83, 119 load sharing, 63 permissible stresses, 60-62, 64-5, 86, 89, 146-7 rectangular solid, 56-64, 230, 231 slenderness ratio, 56-60, 145-6, 230-31 spaced, 143-58 spacer blocks, 144-8 combined stresses, 56, 61-2, 65, 230 computer, 2 1 compression, 56-64, 86, 89, 121, 147,228-31 concentric load, 60-61 connections, see Chapters 9 and 10 bolted, 163, 179-88, 231, 235, 238 dowelled, 163, 179-88, 231, 235, 238 glued, 195-6 nailed, 146, 163, 164, 166-75,231,235,238 nail-plates, 194 punched metal-plates, 160, 193-4 screwed, 146, 163, 165, 175-9, 238 shear-plates, 160,163,165,191-3 split-rings, 160,163,165,191-3 toothed-plates, 160,163,165,189-90 conversion, 3, 4, 5, 8 creep, 220, 240, 241 decking, 37,39 defects in timber, 3-5 deflection bending, 33, 90, 129, 239-40 camber, 33, 83, 90, 239 cantilever, 239 creep, 220, 240, 241 final, 240-41 263

264

Index

deflection ( c o ~ ~ ~ ~ ~ e ~ ) instantaneous, 239-42 limits, 32, 239, 241 modification factor, 240 permissible, 32, 239, 241 shear, 34, 90, 129 slip in joints, 161-2, 241-2 slip modulus, 162, 241-2 depth to breadth ratio, 30 depth factor, 29, 87, 224 design philosophy permissible stress, 10- 1 1 limit states, 11-12, 220 Douglas fir, 14, 164 dowels,160,163,165,179-88 dowelled joints, 163, 179-88, 231, 235, 238 durability, 195 duration of load, 11, 16-17, 127, 174, 179, 180-82 eccentric load, 61, 69, 248 effective cross-section, 162-3 effective geometrical properties, 124-5 effective length, 57-8, 145-6, 230 embedding strength characteristic, 234-5 design, 234-5 end rotation, 226 European, 2 19 Eurocodes, 2 19 Eurocode 5, see Chapter 10 factor of safety, 221, 223 Finnish plywood, 133, 204, 216 flexural members, see Chapter 4, see also beams floorboards, 37-9 form factor, 29 geometrical properties, 124-5 geometric centre, 185 glued joints durability classification, 195 pressure, 196 strength, 195-6 stress, 196 glulam, see glued laminated glued laminated, see also Chapter 6 assembly, 82 bending deflection, 90 bending stress, 86, 89

column, 119 combined-grade, 84-5 curved beams, 90-92 horizontally laminated members, 84-7, 121 modification factors, 85-87 radial stress, 91-2 shear deflection, 90 single-grade, 84 vertically laminated members, 87-90, 120 grade stresses, 13, 15 hangers, joist, 39 Hankinson’s equation, 180, 185, 188 hardwoods, 5-6,13,15,167 holes bolts, 162, 179, 231 dowels, 179, 231 pre-drilled, 164,167,175 I-beams, 123,124,131,137 imposed loads, 17 improved nails, 167, 174 instantaneous deflection, 239-42 joint slip, 241-2 Johansen’s equations, 23 1 joinery joints, 159 joints, see Chapters 9 and 10, see also connections bolted, 163, 179-88, 231, 235, 238 dowelled, 163, 179-88, 231, 235, 238 glued, 195-6 nailed, 146, 163, 164, 166-75,231,235,238 nail-plates, 194 punched metal-plates, 160, 193-4 screwed,146,163,165,175-9,238 shear-plates, 160,163,165,191-3 split-rings, 160,163,165,191-3 toothed-plates, 160,163,165,189-90 joists, 18,37-9 hangers, 39 trimmer, 38, 39 knots, 3 lateral support, restraint, 30-31, 131, 226 lateral stability, 30-3 1, 13 1 length, see effective length limit states, design philosophy, 11-12, 220

index

load duration, 11,16-17,127,174,179, 180-82 load sharing, 18, 63, 226 long-term loading, 17, 127, 174, 179, 180-82 224 machine stress grading, 12 Mathcad, see Chapter 3, 21-5 mechanical fasteners, see connections,joints medium-term loading, 17,127,174,179, 180-82,224 metal-plate fasteners, 193-4 modulus of elasticity minimum, 15, 58, 60 mean, 15, 87, 222 5th percentile, 222 moisture content, 6-7, 16, 224 nails, 160, 162, 231, 235, 237 nailed joints, 146, 163, 164, 166-75,231, 235, 238 National Application Document (NAD), 219, 226,240,241 noggings, 62,63 notched beams, 36-7,46,227-8 panel shear, 127, 130 panel bending, 126 partial coefficients for actions, 221 for material properties, 221, 223 permissible stresses solid section timber, 27, 28, 35, 36, 60, 61, 62, 65 glued laminated, 86-7, 89, 92 plywood, 127,128,130,131 ply-webbed beams, see Chapter 7 plywood boarding, 39,126 properties, 125,127 permissible stresses, 127, 128, 130, 13 1 punched metal-plates, 160,193-4 radial stress, 90-92 radius of gyration, 57 redwood, 14 rolling shear stress, 130-31 scarf joints, 159 screws, 160, 162, 231, 235

265

screwed joints, 146, 163, 165, 175-9, 238 second moment of area, 33, 57, 131 section size, 17, 30, 257 serviceclasses, 14-16, 127, 175, 179, 185, 190, 193, 223-4 serviceability limit states, 12, 220, 239-42 shear deflection, 32, 34, 90, 129 shear modulus, 18, 129-30 shear-plate connectors, 160, 163, 165, 19 1-3 shear stress, 15, 19, 36-7, 86,89, 130-31, 161, 227-8, 236 short-term loading, 16-17,127,174,179, 180-82, 224 Sitka spruce, 14 slenderness ratio, 56-60, 145-6, 230-3 1 slip, in joints, 161-2, 241-2 slip modulus, 162, 241-2 spaced columns, see Chapter 8 span, clear, design, effective, 28-9 species, 14 staples, 235 steel plates, gusset plates, 170, 174, 177, 184, 189, 233, 235 stiffeners, 131-2 strength classes, 13-15, 222 strength properties, 221-2 studs, 62-3 tapered beams, 83, 98 tension members, 63-5, 229, 230 thickness, plywood, 125 tongued and grooved (t & g) floorboards, 38, 39 toothed-plate connectors, 160, 163, 165, 189-90 transformed section method, 124-5 ultimate limit states, 12, 220, 224-38 variable loads, actions, 221 very short-term loading, 17, 127 wane, 4, 5 web-stiffeners, 13 1-2 whitewood, 14 width factor, 64 wind loading, 17, 63, 224 yield moment characteristic, 234-5 design, 234-5

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