:'*aj' dh **;ffai: ff"***r:5" F*'- by leading experts rn the field, including one of of Eurocode 5, this practical book provides a '$@w 1Si" rsive guide to the design of to the latest EuroPean and UK timber structures standards. of timber slruclures to Ettrocode 5 begins with a description of timber, its strength, stilfness, moisture behavour, rheology and durablity, before descrbe the production and relevant properlies of materas used for tmber wrll learn the theory behind the design of structural elements, such and walls, as well as how to ensure these structures conform to ru es. practitioners as wel as students at postgraduate and undergraduate evel, of timber slructures to Eurocode 5 wil equip readers with the necessary al skills to design any t mber structure wth conlidence and coverage: desion requirements accord ng to Eurocode 5 are illuslraied wtl^ ryo heo P(amplcs specificatons and European standards to Eurocode 5 coverage ol trmtler related nratenals and therr relevanl of beams, columns, panels, trussed structures. frames, arches floors and Joints of UK and European design standards and practices astelford.com/books rsBN 978-0-7277 -3609-3 ,ltll illilxliltl|ltltl]l ilt tnoru{r,r.\
Transcript
:'*aj'
dh
**;ffai:
ff"***r:5"
F*'-
by leading experts rn the field, including one ofof Eurocode 5, this practical book provides a '$@w
1Si"rsive guide to the design ofto the latest EuroPean and UK
timber structuresstandards.
of timber slruclures to Ettrocode 5 begins with a description of timber,
its strength, stilfness, moisture behavour, rheology and durablity, before
descrbe the production and relevant properlies of materas used for tmber
wrll learn the theory behind the design of structural elements, such
and walls, as well as how to ensure these structures conform toru es.
practitioners as wel as students at postgraduate and undergraduate evel,
of timber slructures to Eurocode 5 wil equip readers with the necessary
al skills to design any t mber structure wth conlidence
and coverage:
desion requirements accord ng to Eurocode 5
are illuslraied wtl^ ryo heo P(amplcs
specificatons and European standards to Eurocode 5
coverage ol trmtler related nratenals and therr relevanl
of beams, columns, panels, trussed structures. frames, archesfloors and Joints
of UK and European design standards and practices
astelford.com/books
rsBN 978-0-7277 -3609-3
,ltll illilxliltl|ltltl]l ilttnoru{r,r.\
Pubhshed by Thomas Telford Limited, 40 Marsh Wall, London E14 9TP, UK.www. thomastelford.com
Distnbutors for Thomas Telford books are
USA; ASCE Press, 1801 Alexander Bell Drive, Reston, VA 7Al9l-4400Ausnalia: DA Books and Journals, 648 Whitehorse Road, Mitcham 3132, Victoria
First published 2009
Also available from Thomas Telford LimitedICEManual of Bridge Engineering,2nd edition. G. Parke and N. Hewson ISBN: 978-0.7277 -3452.5
Concrete Bridge Strengthening and Repdir. Iain Kennedy Reid ISBN: 978-0-7777-3603-lDesigners' Guide to EN 199i-2 Eurocode 3: Design of steel strucnnes. Part 2: Steelbridges. C. R. Hendyand C. J. Murphy ISBN: 978-0-7277-3160-9
A catalogue record for this book is available from the British Library
ISBN: 978-0-7277 -3609 -3
@ Thomas Telford Limited 2009
Translated and updated from the original Danish publicationTra og tr*.konstruktioner I and 2 @ TOP 2007
All rights, including translation, reserved. Except as permitted by the Copyright, Designs and
Patents Act 1988, no part of this publication may be reproduced, stored in a retrieval system ortransmitted in any form or by any means, electronic, mechanical, photocopying or otherwise,without the prior written permission of the Publisher, Thomas Telford Limited, 40 Marsh \Vall,London E14 9TP.
This book is published on the understanding that the authors are solely responsible for thestatements made and opinions expressed in it and that its publication does not necessarily implythat such statements and/or opinions are or reflect the views or opinions of the publishers.'While every effort has been made to ensure that the statements made and the opinions
expressed in this publication provide a safe and accurate guide, no liability or responsibility can
be accepted in this respect by the authors or publishers.
Tlpeset by Academic + Technical, BristolIndex created by Indexing Specialists (UK) Ltd, Hove, East Sussex
Printed and bound in Great Britain by CPI Antony Rowe, Chippenham
Contents
Introduction
L
1.1
72.t2.22.3
2.47..5
.t
3.1
3.2
44.r4.24.3
55.t5.25.3
5.4
Basis of designOverview of UK and European design principles
Construction productsThe treeStructural timberGlulamWood-based panel products
Joints and fasteners
Structural examplesIntroductionMain and secondary members
Straight members and beams with varying depthTension and compressionTapered beamsShear
ColumnsIntroductionAxially loaded columnsLaterally loaded columnsLateral torsional buckling of laterally loaded
88
323Z5Z
596780
969696
106106
rzzt27
134134t34138
columns I43
111
66.r6.26.3
7
7.r7.2
7.3
88.1
8.7.
8.3
8.4
99.1
9.29.39.49.59.69.79.8
1010.1
r0.210.3
References
Index
iv
Curved beams and framesCurved beamPitched cambered beamArches and frames
Trusses and bracingsIntroducdonStructural design of trussesBracings
I, T and box.beamsIntroduction and background theoriesTransformed (composite) cross-sectionsBeams with thin webs
Beams with thin flanges (srress skin panels)
Connections and fastenersDesign of multi-fastener jointsLoad-carrying capacity of dowel-type fastenersNailed connectionsConnections with staplesBolted connectionsConnections with dowelsConnections with screws
Design basis for IBS 5268]f BS 52681, Structural use of timber, is based on permissible stress design,
rind this phrase appears in the title of Pan 2. However, it does notinclude a description of the design principles equivalent to those in
iL,N 1990]. Grade stress values for properties of materials, most ofwhich are given in tabular form in [BS 5268-2] itsell incorporate
safety factors so that they represent the stress that the material is consid-r:red able to bear over the hfe of a building with a reasonable level ofsafety. The grade stresses are considered for 50-60 years' load duration.A series of modification factors are then applied to the mechanicalproperties, generally increasing the load-bearing capaciry for shorterioad durations. The permissible stress in service for a particular typeand duration of load to the element is thus established, and verifiedagainst the sffess applied by the design loads. These design loads are
normally obtained from the parts of tBS 63991.In addition to supporting normal loads, [BS 5268-2] requires timber
structures to withstand accidental damage without catastrophiccollapse. The Approved Document A gives guidance for the require-ments of disproportionate (progressive) collapse design.
tBS 5268-2] has been the key code in the series, covering structuraldesign of timber in general. The other parts provided subsidiary informa-tion. [BS 5268-2l specified how timber structures may be designed towithstand applied loads. [BS 5268] includes several parts as listedbelow:
r Part 2: 2002, Code of practice for permissible stress design, materials
and worl<rnanshipo Part 3: 1998, Code of practice for trussed rafter roofs
o Part 4.1: 1978, Fire resistrmce of timber structures. Recommendntioru
for calcuLating fire resisutnce of timber members
o Part 4 .2: 1990 , Fire resistnrce of timber snuctures. Recommendrttbrs forcabulnting fire r esisturce of timber stuA w alk anl j oiste d fh:or cmstructioru
Practical destg of timber structures to Eurocode 5
o Part 5: 1989, code of practice for the presentatiue tredtment of struc-tural timber
o Part 6.I: 1996, Code of practice for timber frame walls. Dwellings notexceeding seuen storey s
o Part 6.2:2001, Code of practice for timber frame walls. Buildings otherrhan dwellings not exceeding sec.)en storeJs
o Parts 7.1 to 7.7: Recommendations for the calculntionbasis for spantables for c)arious elements
The appropriate loads to be used for design purposes were given in[BS 6399] with three parrs covering dead, imposed and wind loads.
Definitions
Element and componentThere is great confusion in definition of elements and components atEuropean level. The UK's definition of elements and components isreversed in the Eurocode and the rest of Europe. For clarity thefollowing are definitions which the UK musr adopr:
Element is a structure or part of the structure which consists ofmembers or components. For example, a trussed rafter is an 'element'because it includes members/components which are rafters, intemalweb, ceiling tie and punched metal plate connectors. Another examplewould be a wall panel which is termed 'element' because it consists ofelements or components such as studs and sheathing.
Component or member is a part of an element.Sysrem is a structure which consists of elements.
Notation
In1'lroductionThe symbols and notations are very vital and important as the UK isused to different symbols and notations than those given in Eurocode.Many major errors can occur if these notations are mixed when usedin design.
Member axesThe UK has been used to r-x, )-) and z-z being the major, minor andout-of-plane axes respectively. These have been changed into y-), z-zand x-x respectively in the Eurocode (see Fig. 1).
2
Introduction
v
z- z being out-of -plane axis
ln IBS 5268]
Fig. 1 Differences between axes according to IBS 5268] and Eurocode 5
Decimol symbolsThe UK uses a full point (.) to denote a decimal place, whereas in the
Eurocodes this is seen as a comma (,). For example:
aF-
In [BS 5268]1,000.00 means one thousand;
In [EN 1995-r-rl1,000 means one;
z
x-x being out-olplane axis
ln [EN 1995-1-1]
1.000 means one
1.000,00 means one thousand
Symbols
GeneralSymbols usually consist of a main symbol with one or more indices
separated by commas. For example /.,0,1 which is the characteristiccompression strength parallel to the grain (where f is strength, 'c' iscompression, O is parallel to the grain and 'k' is characteristic).
In accordance with Eurocode 5, the following general symbols are
used. Symbols not mentioned are defined where used and their meaningmay vary.
Main symbolsA cross-sectional areaE modulus of elasticityF force, actionG permanent action; 0r
shear modulusI second moment of area, sometimes called moment of inertiaM bending moment
--N0vw
Practical design of timber structures to Eurocode 5
axial forcevariable actionshear force or also sometimes used as volumesection modulus
distancewidthdiameter or also sometimes used as side length (nails)
eccentricitymaterial strengthheightradius of gyration
constantlengthradiusthickness
Introduction
tor tOrSrOn
ult ultimatey shear
vol volume
xrYr z axes
Y Yield
+ Symbol for fibre direction
Axes, forces and momentsFor beams a coordinate system as shown in Fig. 2 is used.
Combined str ess index (a erification)In order to verifii the adequate strength of a structural member, all the
applied stresses should be combined. For example, if a sffuctural timbermember is under bending, compression and tension, for strength verifl-cation the sum of the ratios of stress to strength for particular loads must
be less than or equal to 1.0. For example, if a timber beam is in bothtension and bending, then:
o,lf,* o^lf* 11 (1)
where o, is the tensile stress and /, is the tensile strength, o- is thebending stress and fi the bending strength.
Construction productsBuilding materials and products are covered by the EU ConstructionProducts Directive (Council Directive 89lI06lEEC). The purpose of
Fig. 2 Coordhflte system (axes, forces and moments)
v"
Practical desip of timber structures to Eurocode 5
(€
Fig. 3 CE mark
the directive is to ensure the free market in the building sector that has
traditionally been one of the most nationally regulated.For building products, compliance with the Construction Products
Directive must be demonstrated when they are marketed for permanentincorporation in buildings or civil engineering works and have influenceon:
1. mechanical resistance and stability2. safety in case of frre3. hygiene, health and the environment4. safety in use
5. protection against noise
6. energy economy and heat retention.
National building authorities are only permitted to put requirements inrelation to these six so-called'Essential Requirements'. This means thatit cannot be requested that 'convenience standards' are followed.Example of a convenience standard can be a standard for timber sizes.
Products meeting the requirements of the harmonised standard (see
below) may be marked with the CE mark, see Fig. 3.
Most European countries, but excluding the UK and a few otherEuropean countries, will require manufacturers to mark their productwith the CE mark. However, it is prudent for UK users to specifi' andrequest CE marking which will be proof of compliance with the Harmo-nised Standard, thereby complying with the Construction ProductsDirective.
The CE mark allegedly tells the consumer that the product meets alllegal essential requirements in all EU member states.
The Building Products Directive applies to all products whether theyare produced within or outside the EU. The basis for the CE marking iseither:
o a harmonised European standard, i.e. a standard produced by CEN(Comit6 Europ6en de Normalisation), the European Organisationfor Standardisation, or
6
F_ Introduction
; a European technical approval guideline (ETAG) produced by
EOTA, the European Organisation for Technical Approval.
In both cases they are based on a request called a 'Mandate' by the EU
Commission.A harmonised European standard is compulsory and contains:
r technical requirements for the product
r requirements for initial type testing to ensure that the product may
be able to fulfil the requirements
o requirements for the producers' quality assurance system
o the level of attestation of conformity, i.e. who is responsible for the
initial testing and the tasks in relation to the producers' qualiry
assurance system.
Decisions about initiation of the work, scope, acceptance etc. are taken
by the EU Commission.An ordinary European standard contains normally only the technical
part and its use is voluntary. All decisions about initiation of the work,
scope, acceptance etc. are taken by CEN. For products not expected tobe covered by a harmonised standard in the near future a EuropeanTechnical Approval (ETA) may be granted. An ETA is a favourabletechnical assessment of the 6.tness for purpose of a product for anintended use made by a technical body notified by a member state onthe basis of technical guidelines (ETAGs) produced and adopted byEOTA. An ETA issued in one EU country is automatically valid inall member countries.
The following products may be CE marked:
o fasteners, connectors and nail plateso structural timbero glulamo LVL (laminated veneer lumber)o prefabricated elements assembled with punched metal-plate fastenerso prefabricated wall, roof and floorso light composite wood-based beams and columns (i.e. I-beams, box
beams, others).
F
1
Basis of design
Tablc 1.1 The structural Eurocodes
EN number The structural Eurocodes
EN 1990
EN 1991
EN 1992
EN 1993
EN 1994
EN 1995
EN 1996
EN 1997
EN 1998
EN 1999
Eurocode: Basis of structural design
Eurocode 1: Actions on structures
Eurocode 2: Design of concrete structures
Eurocode 3: Design of steel structures
Eurocode 4: Design of composite steel and concrete structures
Eurocode 5: Design of timber structures
Eurocode 6: Design of masonry structures
Eurocode 7: Geotechnical design
Eurocode 8: Design of structures for earthquake resistance
Eurocode 9: Design of aluminium structures
dmber structures, has three parts:
1. [EN I995-I-l] General. Common rules for buildings
2. [EN 1995-L-2] General rules. Structural fire design
3. tEN 1995-2l Bridges
The introduction of the key Eurocode for the design of timber struc-tures, [EN 1995-I-ll (called Eurocode 5), will have a major impact onthe design of future timber structures in the UK. The Eurocodes are
based on limit state design, while timber is the only principal construc-tion material for which the UK Codes are not limit state design codesbut permissible stress design.
1.1.2 TlwEwocodes
BackgroundThe Commission of the European Community decided in an acrionprogramme in the field of construction that 'The Eurocodes are roestablish a set of common technical rules for the design of buildingsand civil engineering works which will ultimately replace the differingrules in the various Member States'.
Relatirnship between the Eurocodes and National Reg,iationslPublicAutharity Re quir em en t s
There is a clear and vital distinction between design codes and NationalRegulations/Public Authoriry Requiremenrs. Harmonisarion of NationalRegulations is outside the scope of Eurocode development. It is the
Basis of design
1.1 Overview of UK and European design principles
7.1.7 GeneralIn the UK, the design of civil and structural engineering works has
generally been based on a series of Codes of Practice, drafted by
committees within the British Standards Institution (BSI), and
published by BSI. The BSI structural Codes of Practice are widely
respected and used in many other countries. However, most major
countries have their own codes or equivalent documents. As a result,
different design procedures have been required for structures according
to the country in which they are built.As part of the European Union's (EU's) initiative to facilitate trade
within the construction sector, the EU has commissioned a common
set of codes to be used for construction throughout the EU. Draftingof these codes was initially overseen directly by the EU, but later itwas passed to the European Standards Organisation (CEN). Member'ship of CEN includes the National Standards Organisations of countries
belonging to the European Union and the European Free Trade Asso-
ciation (EFTA). Hence, a complete suite of Codes for civil and struc-
tural engineering design has been developed, termed the Eurocodes.
These codes will replace the existing national codes by the end of 2010.
The Eurocodes aim to:
o provide a common basis for the design of structures within EUMember States
o facilitate the exchange of construction services between Member
Statesr facilitate the marketing and use of structural componentso improve the competitiveness of the European construction industry
in countries outside the European Union.
The Eurocodes cover ten main subjects listed in Table 1.1. Many ofthese codes are subdivided into a series of parts. [EN 1995], Designof
B
Practical design of dmber structures to Eurocode 5
objective however that the Eurocodes, together with their appropriateNational Annexes, should be recognised in National Regulations as
one of the routes for meeting compliance. The legal status of the Euro-
codes under the Building Regulations will be exactly the same as that ofthe current National Codes of Practice. In accordance with normal rules
following the introduction of European Standards, Eurocodes will be
called up in public procurement specifications, and to be used for the
design of products for the purpose of obtaining a CE (Conformit6
Europ6en) mark.
The Eurocode programme and the relationship between uarious Eurocodes
The structural Eurocodes are shown in Table I . 1. Each Eurocode gener-
ally consists of a number of parts, which cover the technical aspects of
rhe srructural and fire design of buildings and civil engineering struc-
tures, with specific parts relating to bridges. A list of the various parts
and the publication date of each EN are continuously being updated
on the Thomas Telford website www.eurocodes.co.uk.
The Eurocodes are a harmonised set of documents that have to be used
together. Their linked relationship is shown in Fig. 1.1. In accordance
with Fig. 1.1 tEN 1995-I-ll has to be used with IEN 1990], the head
key Eurocode, the appropriate parts of [EN 1991] and relevant parts of
the other Eurocodes.
i@@@
Frg. l.I Relationship between the Eurocodes
10
TFF- Basis of design
Supporting and related documents (product standards, etc.)
The following standards are required for the use of [EN 1995-1-1]:
General reference Eurocodes:o [EN 1990]: Basis of structural designo [EN l99ll: Actions on structures (all parts)o [EN 1995-l-21: Structural fire design
Other reference standards.
Harmonised standards (hENs). hENs are Harmonised ProductStandards. They give the rules by which products can meet therequirements for CE marking to be placed on the market. hENsreference (call up) all other relevant CEN standards covering a
particular product, including (but not limited to) the following:o fire requirementso test methodso classification standardso production standardso material specifi.cationso grading standards.hENs are written (or being written) for:o solid timber [EN 14081]o all panel products [EN 13986]o glulam tEN 140801o laminated veneer lumber, LVL [EN 143741o fasteners/connecrors [EN 14592] and [EN 145451o trusses/trussed rafrers IEN 14250]o timber frame wall, floor and roof elements [EN 147321.
The following CEN standards are probably also needed, depending onthe sector:
oa
oO
O
O
a
IEN 3381
IEN 19121
IEN 3361
IEN 11941
IEN 12369: Part 1l
IEN 12369: Part Zl
Timber strength classes
Visual grades (assignment to strength classes)
Timber size tolerancesGlulam strength classes
Strength properties of oriented strand board(OSB) /chipboard/fibreboardsStrength properties of plywood
Role of Nado nal Annex - Using EN Eurocod.e at a national leqtelIt rs the responsibility of each National Standards body (e.g. the Britishstandards Institution (BSI) in the UK) to implemenr Eurocodes as
11
Practical desip of timber structures to Eurocode 5
a: National title pageb: Forewordc: EN title paged: EN texte: EN annexesz: National Annex
Fig. 1.2 National Standards implementing Eurocodes
National Standards. The National Standard implementing each Euro-code part will comprise, without any alterations, the full text of theEurocode and its annexes as published by the CEN (Fig. 1.2, boxes c,
d...). This is preceded by a national title page (box a) and nationalforeword (box b), and may be followed by a National Annex (box z).
Rules and contents of National Annexes for Eurocodes
The European Commission, recognising the responsibiliry of regulatoryand national competent authorities in each EU Member State, has safe-
guarded their right to determine values related to safery matters at
national level through a National Annex. These safery matters includedifferent levels of protection that may prevail at national, regional orlocal level and ways of life.
A National Annex may only contain information on those para-
meters whlch are left open in the Eurocode for national choice,known as Nationally Determined Parameters, to be used for thedesign of buildings and civil engineering works to be constructed inthe country concerned. \Uhere a Eurocode clause allows choice, a
recommended value or method is given.
N ational\ determined par(rmeters (NDP$NDPs will allow Member States to choose the level of safety applicableto their territory. The values, classes or methods to be chosen or deter-mined at national level are:
tz
Basis of design
o values and/or classes where alternatives are given in the Eurocode(e.g. levels of safety)
o values to be used where only a symbol is given in the Eurocode (e.g.
partial factors)
. lou.ttry-speci6.c data, e.g. geographical, climatic (snow maps for
instance)
o procedures to be used where alternative procedures are given in the
Eurocodes.
Natianal Annexes
The National standards bodies (i.e. BSI in the UK) publish the NDPs in
a National Annex. In addition to NDPs a National Annex may also
contain:
r decisions on the application of informative annexes
o references to non-contradictory complementary information (NCCI)to assist the user in applying the Eurocode. The NCCI is sometimes
referred to as 'Rump Standards' or'Residual Standards' in the UK.
It should be noted that in Eurocode 5, NDPs are used for situationsother than just to safeguard Member States' rights to define safery. Theyhave been also been used to cover situations where there is no possibilityof a consensus view being reached on an issue (e.g. for most of theserviceabiliry section and the sections on detailing rules in IEN 1995'1-U).
Principles - Application RulesEurocode 5 has two main notations throughout its contents for certainrules and requirements:
1. 'Principle requirements' are annotated by the suffix'P'. This meansthat you must comply with the requirement. They are general state-ments and definitions for which there is no alternative permittedunless specifically stated.
2. 'Application Rules' are generally recognised rules which comply withand satisfy the 'Principle requirements'.
Tlt" Uf National Annex requiremenrs are included in this publicationwhich may diifer from those iequired by other counrries. \Uhen a srruc-ture is designed for countries other than the UK, the National rules ofthat counrry must be adopted.
t3
Practical design of timber structures to Eurocode 5
Informative and Normative Annexes in the Eurocode are defined as
non-compulsory and compulsory requirements respectively. InformativeAnnexes can become Normative if they are recommended by theNational Annexes. For example, Annexes A, B and C of Eurocode 5
for buildings and civil engineering works are recommended for use inthe UK by the UK National Annex.
1.1.3 Basis of st:ru.ctwal design (the use of IEN 1990] fortimber struchnes design)
It is recommended that [EN 1990] is studied separately in detailHowever, this section introduces the principles of [EN 1990] and
describes the objectives of [EN 1990], lists the requirements and
provides information on the representative values of the loads to be
used in the combination of actions for use with the design and detailingclauses of Eurocode 5. It also gives the values adopted by the BSi
National Annex to [EN 19901.
Note: The principal differences between EN 1990 and UK practice are all listed an,i
explained in Gulvanessian, Calgaro and Holicky, 2005, who provide a comprehensir',
description, background and commentary to EN 1990. Guidance on EN 1990 [BRE,2001 describes the background to the selections made in the BSI National Annex ttr
EN 1990.
Design link to IEN 1990]
IEN 19901 is the head key Eurocode for the harmonised StructuralEurocodes and is required for the verifrcation of both ultimate anci
serviceability limit states as it provides the information for safety factors
for actions and combination of superimposed actions.
[EN 1990] establishes and provides comprehensive information andguidance for all the Eurocodes, on the principles and requirements for
safety and serviceability, describes the basis of their design and verifica"tion and gives guidelines for related aspects of structural reliability and
durability of structures. It is based on the limit state concept and used inconjunction with the partial factor method. [EN 1995] does not give
the material-independent clauses required for design. These are onlyincluded in [EN 1990]. Hence it is very important that [EN 1990] is
used with all the Eurocode parts.
The limlt state concept and the partial safety factor method used in
tEN 19951 constitute a big change from the traditional British Standard
r4
Basis of design
approach for timber. In the Eurocode system the safety and reliability
.or."p, is to be chosen and developed by the designer.
Requirements of IEN 1990]
The requirements of IEN 1990] which need to be adhered to by [EN
19951 are:
o Fundamental requirements. These relate to safety, serviceabiliry
and robustness requirements.
o Reliabihty differentiation.
o Design situations. IEN 1990] stipulates that a relevant design
situation is selected taking account of the circumstances in whichrhe structure may be required to fulfil its function. IEN 1990]
classifies design situations for ultimate limit state verification as
follows:o persistent situations (conditions of normal use)o transient situations (temporary conditions, e.g. during execu-
tion)o accidental situationso seismic situations.
o Design working life. For buildings and other common structures therecommended design working life (i.e. rhe assumed period forwhich a structure is to be used for its intended purpose with antici-pated maintenance but without major repair being necessary) is 50years. Design working life needs to be considered for materialproperry deterioration, life-cycle costing and evolving maintenancestrategies.
o Durability.o Quality assurance.
1.1.4 Limit state design
GeneralIn the Eurocodes, the safety requirements for structures are formulatedrn terms of limit states. A limit state is a state where the structure is onthe. point of not fulfilling the required performance requiremenrs.
A distinction is made berween serviceability und ultimate limitstates.
F
$
Practical desip of timber structures to Eurocode 5
S er v ic e ab ili ty limit state sServiceability limit states concern:
o the functioning of the construction works or parts of themo the comfort of peopleo the appearance.
Serviceability limit state failure occurs when:
o deflection of a structure or a member is visually or functionallyunacceptable (e.g. it may result in cracks of ceiling and walls tx.
leakage of roofs)o sway or vibrations are unacceptable or uncomfortableo there are incipient attacks of rot or corrosion that may eventuall,v
contribute towards or lead to failure if remedial steps are nortaken.
Eurocode 5 contains some recommended deflection and vibratiorrlimits, but it is the designer's responsibiliry in consultation with tht.client to detail the requirements.
Uhimate limit states
Ultimate limit states are associated with collapse or with other forms o{
structural failure and concern:
o the safery of peopleo the safety of the structure and its contents.
Ultimate limit state failure occurs when:
uplift, overturning or sliding of the whole or part of the structur(takes place
o failure of materials is evidento instabiliry of members or structures (i.e. column failure, lateral tor"
sion instability, overturning, etc.) occurs.
1.1.5 The partial coefficient method
GeneralThe basic elements are characteristic actions (commonly known as
loads in UK) and characteristic material parameters (mechanical prop-erties). The basic principles are that:
I6
Basis of design
design actions are found by multiplying the characteristic actions by
partial safety factors (load factors); the design action effects are
found from prescribed combinations of design action
design material parameters are found by dlvidlng the characteristic
parameters by other partial coeffi.cients (material factors) and
design resistance is calculated with these design parameters
it shall then be verified that the design resistance is not less than
the design action effects.
Actions
A distinction is made between four types of actions that are classified by
their variation in time:
1. permanent actions (G), ".g.
self-weight, fixed equipment and
actions caused by shrinkage and uneven settlements
2. variable action (Q), ".g.
imposed loads, wind and snow
3. accidental actions (A), e.g. explosions or impact from vehicles
4. seismic actions.
In addition to the characteristic value of an action (Gl, Ql and Ar)which is similar to the British Standards'definition, other representativevalues are specified in [EN 1990] for variable and accidental actions.Three representative values commonly used for variable actions are
the combination value ,!oQu, the frequent value t!1Q1, and the quasi-perrnanent value t!2Qp. The factors ,bo, rl\ and r!2 are reduction factorsof the characteristic values of variable actions, and each are definedbelow, and their numerical values are given in Tabte 1.2.
Table 1.2 Factars for the representatiue values of actions
tbztbr4to
Imposed loadsA: Domestic and residential areasB: Office areasC: Congregation areasD: Shopping areasE: Storage areas, including loftsH: Roofs*
Snow loads on buildings
_ Situated up to 100m above sea level\7ind loads on buildings
0.70.7
0.7
0.71.0
0.7
0.50.5
0.5 0.30.5 0.3
0.5 0.6
0.5 0.60.9 0.8
00
0.2 00.2 0
'Th. roof
t7
Practical design of timber structures to Eurocode 5
The combination value *oQr. is associated with the combination ofactions for ultimate and irreversible serviceability limit states (theserviceability limit states where some consequences of actionsexceeding the specified service requirements will remain when theactions are removed) in order to take account of the reduced probabilityof simultaneous occurrence of the most unfavourable values of several
independent actions.The frequent value /rQr. ir primarily associated with the frequenr
combination in the serviceability limit states and it is also assumed tobe appropriate for verification of the accidental design situation of tht:ultimate limit states. In both cases the reduction factor {1 is applied
as a multiplier of the leading variable action.The quasi-permanent value {2Q1,is mainly used for the assessment oi
long-term effects, for example in checking cracking or deflection. But
they are also used for the representation ofvariable actions in accidental
and seismic combinations of actions (ultimate limit states) and for
verification of frequent and quasi-permanent combinations (long ternr
effects) of serviceability limit states.
}r Basis of design
I. Fundamental (persistent and transient) design situations (strength
or equilibrium):
! to,,Gu,, -t tBlQr,l + t tB,i{o,iQr,,ii>l pl
tEN 19901 Expression (6.10) : (1.3)
where Qr.,r it the so-called leading variable action (live load). For
most materials the leading action is that which results in the largest
acdon effect, but this is not necessarily so for timber structures
because of the factor k-o,i, see below.
Where it is not obvious which is the leading action, each action
should in turn be taken as Ql,r to determine the combinationwhich produces the worst effbct.
2. Accidental design situations ({ire, impact or explosion):
Design actions
For permanent actions (dead load):
Ga : ?cGl
For variable loads:
Qa: laQu
The load factors are different for permanent actions (76) and variablc
actions (lB) - otherwise the method would be identical to the permis'
sible stress method with a load factor of i.0 which has been used untilnow in the UK.
Action (load) combinations
In most cases permanent actions and one or more variable actions act
simultaneously. According to [EN 1990] the following combinationrules shall be used (a part of the equation in [EN 1990] prestressing
has been omitted because this is never applicable for ordinary timberstructures).
There are two main design situations: fundamental and accidental.These are now discussed in turn.
18
(1.1)
(r.2';
D cu,, + (Aa) -t 1'rtQr,,r + t ,b2,,Qr,,1
i>I j>l
tEN 19901 Expression (6.11a) : (1.4)
The accidental action is in parenthesis because it should only be
included when considering the direct effects on the sffucture ofan explosion or impact. It should not be included when consideringthe situation after the event or after a fire.
Expression (1.3) may, if it is less demanding, be replaced by thefollowing equations:
f €r",,Gu,, * ryo,rQr.,r + t ta,i4to,iQr,,ri>1 j>1
tEN 19901 Expression (6.10b) :where { :0.925.
Expressions (1.5)-(1.6) may only be used:
(1.6)
for fundamental (not accidental) design situarionsfor strength (not equilibrium) verificarionswhen the leading variable action is wind or snow and it isunfavourable and its characteristic value exceeds l3.5o/o ofthe characteristic value of the permanent actions, or when
ooo
t9
Practical design of timber structures to Eurocode 5
the leading action i, u.ry orher rype of variable action exceprstorage and its characteristic value exceeds 22.50 of the char-acteristic value of the permanent actions.
Material parcuneters (mechnnical properties)
For strength properties, modulus of elasticity and density, the character"istic value m1 is taken as rhe 5 percentile, i.e. a probability of 5olo of gettinrlower values is accepted. For stiffiress values (e.g. modulus of elasticity).the mean value E-"o, is normally taken as the characteristic value.
Design mnterial pdrdmeters
Design material parameters, md, are determined as:
,ffikffid: k^od-
'liu(1 i
where:
k^od is a modification factor taking into account different conditions such as load duration, moisture content, temperatur{.and size. In Eurocode [EN 1990] rhe norarion 4 is used insreaciof k*4;
mk is the characteristic value of the material parameter m;'yu is the partial coefficient covering the uncertainry in deter"
mining of m.
Similarly, for stiffness:
trrLkEd: K^rd-
^lu
For 1y the values in Table 1.3 are to be used in the UK.
( 1.8.r
The calculation of the design action effect is the same for all material,rand reference is made to [EN 1990]. On the resisrance side of the equa-tion there are several features that are material dependent. Th,:following describes how the design resisrance is determined for timberstructures.
Service classes
To take into account the moisture content in the timber- and wood-based materials, structures shall be assigned to one of the three serviccclasses given below.
70
Basis of design
Partial coefficients for actiorc (load factors), uhimate limit states
Permanent actions, 76 Variable actions, 7p
Unfavourable Favourable Favourable Unfavourable
VTable 1'3
Strength verification
Equilibrium verification
Combined strength and
equilibrium verifi cation*
t.351.10
r.35
1.000.90
1.00
1.50
1.50
1.50
00
0
ITh" .o*bin.d check is an optional alternative to separate calculations for
equilibrium and strength verifications when both have to be carried out. However, ifitis employed then it must also be verified that setting 76 to 1.00 for both the
favourable and unfavourable parts of the permanent load does not produce a less
favourable effect.
o Service class 1 is characterised by a moisture content in thematerials corresponding to a temperature of 20"C and the relativehumidiry of the surrounding air only exceeding650/o for a few weeksper year. In service class 1 the average moisture content in mostsoftwoods will not exceed 12olo.
o Service class 2 is characterised by a moisture content in thematerials corresponding to a temperature of 20"C and the relativehumidity of the surrounding air only exceeding 85% for a few weeksper year. In service class 2 the average moisture content in mostsoftwoods will not exceed 20olo.
o Service class 3 is characterised by climatic conditions leading tohlgher moisture contents than in service class 2.
Examples of assignments to service classes in the UK is given inTable 1.4.
Table 1.4 Sercrice classes
Service class Type of construction
I V/arm roofsIntermediate floors
, Internal and party timber walls of buildings" Cold roofs
Ground floorsExternal timber-frame walls
, External uses where member is protected from direct wetting' Exlernal uses, fully exposed
-
21
Practical desip of timber structures to Eurocode 5
Tahlc I.5 lLtarl-duration classcs
"F Basis of design
Tabte 1.6 Values of k^,,,1
Load-durationclass Duration Examples of loads Material Standard Serviceclass
Lt>ad-duration class
Permanent
Long-term
Medium-term
Short-term
Instantaneous
More than 10 years
6 months to 10 years
1 week to 6 months
Less than 1 week
Perm- Long-anent termaction action
Medium- Short- ]nst:rn-
term term taneousaction action action
Self-weight
Storage loading (including in bfts)Water tanks
Imposed floor loading
Snow
Maintenance or man loading on r(xrl .
Residual loading after accidental evr. r ,
WindImpect loading rnd expl,rsion
Timber, [EN 14081'1]
glulam [EN 14080]
and LVL [EN 14]741,
IEN 142791
Plywood [EN 636' Part 1l
[EN 636, Part 2]
[EN 636, Part 3]
1
2
3
0.60 0.i00.60 0.i00.50 0.55
0.60 0.i00.60 0.700.50 0.55
0.30 0.450.40 0.50
0.30 0.40
0.30 0.45
0.20 0.100.40 0.50
0.30 0.40
0.30 0.45
0.20 0.30
o.za 0.40
0.20 0.40
0.20 0.40
0.90 1.10
0.90 1.10
0.70 0.90
0.90 1.10
0.90 1.10
0.70 0.90
0.85 1.10
0.90 1.10
0.70 0.90
0.85 1.10
0.60 0.800.90 1.10
0.70 0.90
0.85 1.10
0.60 0.80
0.80 1.10
0.80 1.10
0.45 0.80
0.80 1.10
0.45 0.80
0.80
0.80
0.65
0.65
0.70
0.55
0.65
0.45
0.70
0.55
0.65
0.45
0.60
0.60
0.60
Iz
3
1
I
0.80
0.80
0.65
To take into account the influence of load duration on strength, lolt' !
shall be assigned to one of the five load'duration classes of Table f .iThe factor k*o6 as a function of service class and load duration
given in Table 1.6.
VerificationFor static equilibrium (EQU-), it shall be verified that:
Sa,ar, 5 Ra,r,a (1't)
where:
Sa,a., is the design value of the destabilising actions;
R,r,,,b is the design value of the stabilising actions.
. EQU limit states. These involve loss of static equilibrium in the considered structul.,
either as a whole rigid body or in any one ofits constituent parts. In such situations, tii'mechanical and resistance properties of the material are not generally determining
factors, while even modest geometric variations in the distribution of actions or the ir
points of application may be crucial.** STR limit states. These concern the failure or excessive deformation of a structure t',
its constituent members. In such cases, it is the resistance of the materials that is tl-rt
determining factor in verification.f GEO li-it srares. These involve failure or excessive deformation of the soil. The
critical factor in ensuring safety for such limit states is the rnechanical characteristics i'i
the ground. In the case of the design of structural members (footings, piles, basemerrr
walls) involving geotechnical actions and resistance of the ground (STR and GEO),
three separate approaches are recommer-rded.
27
OSB-
Particle-board
2
1
Fibreboard,hard
Fibreboard,medium
Fibreboard
MDF--
1
z
1
\]JLi, oriented strand board. ** MDF, medium density fibreboard.
For verification for internal failure or excessive deformation of thestructure or structural members, including footings, piles, basement
Io*l:'-.r.., where rhe strength of consrrucrion materials governs
l,t t R"); and for failure or excessive deformation of the g.urrrrJ wherethe strength of soil or rock is significant in providing resistance
IEN 3001, osB/2IEN 3001, osB/3and OSB/4
IEN 3001, osB/3and OSB/4
[EN 312, Part 4and 5l[EN 312, Part 5]
[EN 312, Part 6and 7l
[EN 312, Part 7]
IEN 622-21 HB.LA,HB.HLAI or HLA.2IEN 622-21
HB.HLAI or HLAZ
IEN 622-31
MBH.LAI or 2,
MBH.HLSI or 2MBH.HLSl or 2
IEN 622-51 MDF.LAand MDF.HLSMDF.HLS
2
1
23
Practical destgn of timber stntctures to Eurocode 5
(GEOr), it shall be verified that:
Sa < Ra (1.1i:
where:
S,1 is the design value of the effect of action such as internal fortmoment or a vector representing several internal forces , ,
moments;Ra is the design value of the corresponding resistance.
Note: [EN 19901 used symbol E with various subscripts for desr,. '
actions and design resistance. To avoid confusion with modulus of e1',
ticity the symbols S and R have been preferred.
1.I.6 Serviceability
D esign stiffness u alues
For serviceablhry limit states, mean stiffness values are used directll'obtain the best estimates of expected deformations. In Eurocodes thlexpressed more formally as follows:
The mean values should be used with a partial coefficient:
t,IM -
I
S ervic e ability limit stntes v erific ation
For the serviceabiliry limit states verification [EN
Sa < Ca [EN 1990] expression (6.1) :
(1.1r
where:
S,1 is the design value of the effects of actions specified in Li ,i'
serviceability criterion, determined on the basis of the relevl-'r i.
combination;Ca is the limiting design value of the relevant serviceabiliry criterit':
Combination of actions for the serviceability limit stntes
For serviceabllity limit states verification, [EN 1990] requires the thrr ',:
combinations to be investigated which are shown below. [EN 199' j
gives three expressions for serviceability design: characteristic, frequeriand quasi-permanent.
24
1. The characteristic (rare) combination is
when exceedance of a limit state causes
or permanent unacceptable deformation.
DCu,r * Qr.,i +\r,qiQr.ij>l i> I
IEN 19901 Expression (6.14b) :
Basis of dcsign
used mainly in those cases
a permanent local damage
(1.13)
The frequent combinations are used mainly in those cases when
exceedance of a limit state causes local damage, large deformations
or vibrations which are temporary.
Icu,, * |;r,rQr,,t +lr[z,iQr,,ii>l i>1
IEN 19901 Expression (6.15b) :The quasi-permanent combinations are
term effects are of imPortance.
Icu,, +\,l,z,iQr.,j>l
'> 1
tEN 19901 Expression (6.16b) : (1.15)
Creep
When a structure is loaded it will get an instantaneous deformation u;,,,which should be calculated with mean values determined by standar-dised short-term tests.
'When a load is maintained constantly (e.g. a permanent load), the
deformation of the structure or member will increase in principle asshown in Fig. 1.3. This phenomenon is called creep. During the earlystages of loading, the deformation increases fast, but with time therate of increase will decrease asymptotically to a final value u6. Thedeformation at dme t may be e*pr"rr"d urt
u(4 : il'^,[l + p(r)] (1.16)
)
3.
19901 stipulates ttr. rr
(1.1i)
(1.14)
used mainly when long-
(1.17)
wh,ere <p(r) is called the creep function.ln Eurocode 5, Expression (1.16) is written as:
$n : a;^,(1 +kat)wiere k2"1 is a modification factor for deformation which depends on thernaterial, the moisture content and the load-duration class. Examples oftrdej. are given in Table 1.7.
z5
Load, F
Practical desiffi of timber structures to Eurocode 5
Time
Fig. 1.3 Constdnt load F and deformation u with time t of a simply suDp()i.,d
beam followed b1 wrloading at time T
If a load after a time T is removed, the deformation will be reduce' I ',ythe same u;,r1 2s when it was loaded. This will be followed by a cli,.'p
recovery deformation until the deformation stops at a permanent dci, i"-
mation. It should be noted that if the stress level is less than about 'ir.",i,of the characteristic strength (and this will most often be the case), t';t-
permanent deformation will be small and may in practice be disregar' r, J
if the total loading period is smaller than the unloaded period, e.g. snt 'u,/
loading in the UK.Over a period, the deformations depend on the average load tir'rt
in most cases is considerably smaller than the characteristic 1,','i.
The average load is called the 'quasi-permanent' part of the load' 'i i,e
deformation from a variable load is, therefore, calculated as:
u1i,, : u^rt(l + r/,Zkaq) (1 i r)
where ry'2 is given in Table 1.2 and Table 1.8.
If two or more constant loads are applied at different periods, ':r'e
Fig. 1.4, they will each induce deformations as described above. I rr
more than one load, the deformations calculated for each load shoi,id
be added together.
Shear deformationsIn most cases only deformations from bending are of importance, [.'ltsince the shear modulus is rather low there are situations where it is
also necessary to take shear deformations into account, e.g. for tlrinwebbed I-beams - see Example 6.1 in Chapter 6.
26
Notes: For timber which is installed at or near its fibre saturation point, and which islikely to dry out under load, these values shall be increased by 1.0. It is a known facrthat dried timber is stiffer than wet timber. However, when a timber structure or amember with high moisture conrenr is loaded, the deformations will not be reducedduring drying of the structure or the member. In fact the deformation will increasefurther. In addition, if a timber beam which is near irs fibre saturation moisturecontent, is exposed to alternating load, the deformations will continue to increase.
Deformation contributions from j ointsJoints in timber structures are rather flexible and in trussed structurestheir contribution to the deflections may be larger than those fromdeformations of the timber part.
The slip g for a load F should be calculated from:
C: F/K ( 1.1e)
FTable 1.7 The factor kp1
Basis of design
NlaterialStandtrrd Service class
Structural timber
Glulam
LVL
Phwood
OSB
Particleboard
Fibreboard, hard
Fibreboard, medium
IEN 14081-ilIEN 140801
tEN 143731 and [EN 142791
IEN 336-11
tEN 316-21
IEN 336-31
tEN l00lOSB/2
OSB/3 and OSB/4
tEN llzlType P4
Type P5
Type P6
Type P7
IEN 622-31
MHB.LAI and MHB.LA2MHB.HLSI and MHB.HLS2
IEN 622-21
HB.LAHB.HLAl and HB.HLA2
0.60
0.80
0.80
0.80
0.80 2.0
1.00
1.00 2.50
2.25
1.50 2.25
2.25
2.25 3.001.501.50 2.25
z.t52.25 3.00
3.003.00 4.00
where K is the slip modulus. Table 1.9 contains expressions for thesllP modulus for some common fasteners. Reference is also made toLhapter 9 for further informatir.rn.
Deformation, u
llh
27
Practical design of timber structures to Eurocode 5
Table 1.8 Quasi-permanent factor--
Basis of design
Table 1.9 Slip moduh.c K in N/mm for dowel-type fasteners with diameter d
4tz DowelsScrews
Tight-{itting bolts*
Nails with pre-drilling
Nails without pre-drilling
Staples
#,
1.5P. to.8
l0'
Imposed loadsA: Domestic and residential areasB: Office areas
C: Congregation areas
D: Shopping areas
E: Storage areas, including loftsH: Roofs*
Snow loads on buildingsSituated up to 100m above sea level
\7ind loads on buildings
0.30.30.6
0.60.8
0 t.5Pm :0.8g0"
* The roof imposed load should not be applied at the same time as wind or snow.
Limiting values for defection of beams
The serviceability criteria should be specified for each project andagreed with the client. In the UK National Annex, the values inTable 1.10, which take into account creep deformations, are given forguidance.
VibratioruLoads applied on structures should not cause vibrations that can impairthe function of the structure or cause unacceptable discomfort to theusers.
Load, F
Deformation, u
Fig. 1.4
loads
ZB
Time
period with two different constant
* For bolts the clearance should be added separately.
Note: p- is the density of the wood (mean value) in kg/ml.
For residential floors with a fundamental frequency h 18H", a
special investigation should be made.
For floors, unless other values are proven to be more appropriate, a
modal damping ratio of e :0.02 (i.e.2o/o) should be assumed.
The fundamental frequency for a rectangular floor, I x b, simplysupported along all four edges and with timber beams having a span I,
can be calculated as:
. 7r [(EI),Ir:rtV;where:
m is the mass per unit area in kglmz;I is the floor span in m;
Table 1.10 Limiting ualues of indiuidual beams
Type of member Limiting value for flnal deflections ofindividual beams, tu6^
A member of span I A member withbetween two supports a cantilever I
0
0
(1.20)
Roof or floor member with a plastered
or plasterboard ceilingRoof or floor member without a
plastered or plasterboard ceiling
Ilz5o
rlr50
t1125
tl7 s
Deformatinns for a structure ouer a
Note: cu6 should be calculated as &/'n in accordance with [EN 1995-l-1],2.2.3(5).
29
Practical design of timber structures to Eurocode 5
(EI), is the equivalent plate bending stiffness of the floor about anaxis perpendicular to the beam direction, in Nm2/m.
For residential floors with a fundamental frequency /r < B Hz, Euro-code 5 gives very advanced design methods. The UK National Annexhowever states that floors with a span up to 6 m will normally behavesatisfactorily provided the deflection a under a point load is smallerthan:
F- Basis of design
- 0.325 for floor decking nailed or screwed, and glued tothe joists at standard centres and glued in accordance
with the manufacturer's recommendations(EI)t is calculated as the flexural rigidity of the floor decking
perpendicular to the joists, using E^"on1iot E. Discontinuitiesat the edges offloor panels or the ends offloor boards may be
ignored. (EI)6 may be increased for plasterboard, struttingand strongbacks as follows:
add 0.34 . 10e N/mm2/m for standard plasterboard
add 0.53 . 10e N/mm2/m for standard struttingadd for a single continuous strong-back fastened to all joists
within 0.11 of mid-span its bending stiffness in Nmm2
dlvided by the span lin metres.
1.1.7 RobustnessAll structures are required to be reasonably robust, i.e. they should notbe sensitive to unintended incidents or small deviations from the design
assumptions, e.g. small deviations from the intended geometry due toexecution errors, or foundation settlements.
Robustness (sometimes called safety against disproportionate or
progressive collapse) requirements are those that, in the case of an
accident, the structure does not fail disproportionate to the cause ofthe accident, i.e. failure in a small part of the structure must notresult in failure of the whole structure.
Robustness may be ensured by the design of the statical system, e.g.
by choosing statically indeterminate structures where there is more thanone path for the loads to the supports, by choice of materials and joints
and by conffol of the construction execution. It should be noted thatincrease of the safety factors, by itself rarely has an important effect,
even though the safety codes sometimes accept this as a possible way
of compliance.The codes are rather vague regarding implementation of the robust'
ness requirements into practice and it is usually left to the designer' Inthe UK, Building Regulations Approved Document A (Communities
and Local Government, 2000) provides some design guidance forrobustness (disproportionate collapse or progressive collapse), whichshould be used.
d<1.85 mm/kN for I ( 4500mm68 200
lti- mm/kN for / > 4500 mm(1.21)
(1.72)
where the floor deflection should be calculated as:
k7,,,11u2k4,"o,o:ffi mm/kN
where:
kau, is proportion of point load acting on a single joist
( o.+z- o.oe h I l4(EI)h l:maxi L s+ I
t 0'i5I"n is equivalent floor span in mm
: 1.0lfor simply supported single span joists: 0.91for the end spans of continuous joists: 0.851 for the end spans of continuous joists
krh"u, is amplification factor to account for shear deflectionskro p is factor to account for composite action between joist and
floor decking(EI)ru, is bending stiffness of a joist in Nmm2 (calculated using
E^run)(Ef)a is floor flexural rigidity perpendicular ro rhe joists in Nmm2/ms is joist spacing in mmI is span between supporrs in mmk,h,o, : 1.05 for simply supported solid timber joists
: 1.10 for continuous solid timber joists: 1.15 for simply supported glued thin-webbed joists: 1.30 for continuous glued thin-webbed joists
k,o p : 0.3 for floor decking nailed or screwed to the joists inaccordance with the decking manufacturer's recommenda-tions
3t30
z
Construction products
2,I The tree
2.1.1 Structure of the *eeLiving trees consist of foliage, stem, branches and roots. The foliage(leaves or needles) contains chlorophyll that, with energy from rhe sun,can decompose rhe carbon dioxide (COz) in the air inro oxygen andcarbon which are the basic elements in cellulose, hemicellulose andlignin as the main chemical components of wood. The stem and branchescarry the foliage and contain vessels for transport of liquids between theroot and top of rhe ffee and is a store for nourishment (see Fig. 2.1).
PithThe pith is a narrow wood bar (about 10 mm in diameter) in the cenrreof the stem. It consists of loosely bounded dead cells rhar are orientedalong the tree. Pith rays from the pith to the bark are able to rransporrliquids and nourishmenr.
BarkThe stem and the branches are covered by the bark which protecrs thewood against drying out, attacks of fungi, beetles and physical damage.Under the bark there is a thin growth layer called the cambium wherenew bark cells are formed outward and new wood cells inward. Everyyear the ffee produces a new annual ring.
Annual rings
The inner part of the annual rings is called early wood or spring woodand is formed during the spring, often with relatively high growthrate. Its purpose is to ensure an early transport of liquids. Early woodis light in colour and has relatively low density, stiffness and strength
32
Sap wood
Heart wood
Fig. 2.1 Cross-section of a tree stem
because of thin {ibre walls and big lumens (cell holes/voids). The outerpart of the annual rings is called late wood and is formed relatively slowlyduring the summer. It is darker than the early wood and has higherdensity, stiffness and strength.
For conifers the thickness of late wood is almost constant and trees withnanow annual rings are preferred because the amount of spring wood is
relatively small. For deciduous trees (often a little misleadingly calledhardwoods) the thickness of early wood is almost constant and trees
with broad annual rings are prefened because the amount of late woodis relatively large. The width of the annual rings is in the range 2-10 mm.
Wood cells
The basic element of wood is the wood cells. They consist of cell wallssurrounding the cell lumen. The cells are oblong and orientedessentially in the lengthwise direction of the tree and grow at lengthsof 2-4 mm and their thickness varies between 10-50 trrm. The cellsare squeezed between each other and connected through pores so
that long tubes, called wood fibres, are formed, serving in the livingtree to transport liquids.
Tree growthThe growth of a tree is shown schematically inFig.7.7.
'J
Practical destgn of timber sfiuctures to Eurocode 5
Fig. 2.2 Schematic growth of a conifer
Early in the spring a top shoot grows lengthwise and creates a narrowyear shoot on the top of the tree. similarly, side shoors grow out from thepith as small individual trees. The side shoots become branches andtheir anchorage in the stem form knots. Branches that are overgrownso that they do nor get sunshine die and will eventually break off.
KnotsA knot is the embedded part of a branch. At areas close ro the knots thewood fibres in the stem change direction and continue into the branches.The fibre direction can be heavily distorted as shown in Fig. 2.3. \Uhen a
Fig. 2.3 Radial qoss-sectbn in a tree stem anl. knots: (a) Iiuing knot; (b) Icrwtfrom a dead brarch - nedr to the surface the knot will become lnose; (c) embeddedknot
3+
branch dies it often breaks off close to the surface of the tree. \When thetree continues to grow, the knot becomes embedded into the stem. Adistinction is made between dead and living knots.
o Dead knots are the dead part of a branch and are not integrated
with the stem. They will often become loose and fall out when
the tree stem is cut up because the wood in the branches shrinks
more than ordinary wood.r Living knots are integrated into the stem and will usually not fall
out, but can crack during drying.
The knots in pine wood are concentrated at the same height around
the trunk and spaced corresponding to a year's growth, typically 250-800 mm. For spruce the knots are more randomly dispersed along thetree stem. When the tree is cut, the knot pattern on the board surface
will vary (see Fig. 2.4) . The knots are denoted after their location such
as edge knots, (narrow) side knots and (wide) face knots. Furthermore,they are denoted after their shape as round, horn or leaf knots.
Wide face
Edge knot
External side
Narrow side
Annual ring
Fig. 2.4 Different types of knots
V_
Narrow side knot
35
Practical design of timber structures to Eurocode 5
Sapwood atrd heartwoodThe outer material in the tree stem is denoted sapwood. It containsmany living cells that can transport liquids f.oro th. bottom to thetop of the tree. \x/hen the rree becomes old, the old woocl cells dieand resin, sugar composites, tannin and oils are deposited in the cavities.This is when a heartwood core is formed in the central area of the tree(see Fig. 2.1). The heartwood is often darker and more durable than thesapwood. It is' however, not always the case. As an example, it is notpossible with the naked eye to detect rhe core uf ,pru.e and it haspoor durability.
DensityThe density of the wood cell wall is about l55Okg/nJ. The density ofwood is smaller due to the voids within the ce[s. The density ofspruce and pine is typically in the range 300-600 kgim3 correspondingto a void percenrage of 80-60.
Cracks and shakes
cracks and shakes ofren arise during drying of solid timber products, bursometimes they may be initiated in the living tree be.nur" of growthstresses.
Main directions of woodDue to the wood structure with annual rings, three main material direc-tions may be identified, i.e. longitudinal (L), tangential (T) and radiar(R) (see Fig.2.5). The longitudinal direction refers to the fibre directionand the radialdirection radiares from the pith to the bark and finally thetangential direction is perpendicular to these two.
2,1.2 Moisture content
Generalwood always contains water in the cells, either as free water in the celllumens or as bonded water in the cell walls. The weight of the water as apercentage of the weight of the dry wood is called the moisture content:
weight of water
Construction products
Longitudinal directionI
. Cross-sectionExternal side
Pith side
.rTangential direction
.,-- Annual rings
"'* Radial direction
Fig, 2.5 Material directions and side definitions in tree stem and solid board(Courtesy Erik Serrano, SP, Screden)
The moisture content may be determined by weighing a piece of wood,drying it at 105"C until weight equilibrium is reached and then weighingit again. The moisture contenr is found as the weight loss (i.e. weight ofwater) relative to the weight of the dried wood:
(2.2)
In practice the moisture content is determined by an electric moisturemeter. The principle is that the electric resistance is measured betweentwo electrodes pressed into the wood. Electric moisture meters can,however, only be used for moisture contents between about 6 and 307o.
Just after felling of the ffee rhe moisrure contenr is high; in somewood species higher than 100%. When the wood is dried, the freewater in the cell lumens disappears lirst, followed by rhe warerbonded to the cell walls. The moisture content when all free warerhas been removed is called the fibre sarurarion point. This point differsbetween wood species and varies normally between 25 and 30%. Themoisture content in dried wood may be increased again, by placing itin a moist atmosphere or by exposing it directly to water. In theformer case the moisture content cannot exceed the fibre saturationpoint.
If a piece of wood is placed in a constant climate for long time themoisture content in the wood will reach an equilibrium moisturecontent (EMC). As an approximation it may be assumed that the
u(o/o) :,OOwet weight - dry weight
dry weight
36
u(%) : 1ggweight of dry wood (2 1)
37
Practical desiffi of timber structures to Eurocode 5
Relative humidity (RH), %
Fig. 2.6 Influence of RH and ternperdture on EMC in Nordic conifers
EMC in wood only depends on the relative humidity (RH) and thetemperature of the surrounding air as shown in Fig. 2.6.
It may take some time for wood to reach the equilibrium moisturecontent, especially for members with large cross-sections. For anordinary floorboard it will take some days to reach equilibrium, whereasit may take months for a large timber member. The moisture content atthe surface of a glulam beam follows the short-term climatic variation,but the moisture content inside the member will correspond to the long-term variations over the year. For large glulam members, the insidemoisture content will be almost constant, corresponding to the averageRH over the year.
The indoor EMC of wood will typically vary between 12 and I5o/o
during summer and between 7 and 10% during winter because of theheating. The outdoor EMC of wood is about 15olo during summer andit increases during the winter t():
o l\-25o/o if the timber is exposed to the wearhero 16-200/o if the timber is protected against direct weather exposure,
e.g. by a roofl4-l7o/o in faEades, windows and doors
M oi s tur e - r eI ate d def ormationsMoisture variation above the {ibre saturation point will not cause dimen.sion changes in wood products because it is only the free water content inthe lumen that is changed. Moisture changes below the fibre saturation
3B
Construction products
Table 2.1 Shrinkrtgelswelling strains for Nordic conifers for euery unit change in
point will on the other hand result in dimensional changes. Wood shrinks
when it is dried and swells during wetting. The shrinkage/swelling strains
in the longitudinal, radial and tangential directions of wood are assumed
to be proportional to the values shown in Table 2.1.
The longitudinal strain is relatively small compared to the otherstrain components. However, the effect cannot always be disregarded,as for a 30 m long beam the length change will be about 30 mm for a
change in the moisture percentage of 10.
In practice the direction of the sawn cut wood relative to the annualrings is random and usually an average strain value of 0.2o/o is used forthe shrinkage/swelling strains perpendicular to the fibre direction.The difference between the tangential and radial strains results indistorted cross-sections when solid timber is dried (see Fig.2.7). Thedistortion is highly affected by the annual ring pattern of the individualpiece - see Fig. 2.7 where:
(a) the growth rings are running in the radial direction and perpendi-cular to the wide faces, therefore the board will keep its shape butbecome thinner and shorter;
Fig.2.7 Sawncutp(ilternsandshapedistortionof timber cross-sections causedb\shrinkage being larger in the tangential than in the radial direction
Ooc
LIJ
3zocoo9155.aoE 10Ef'tr!a'5u
LrJ
0
O1525950E1FO o100 EoF
0.3
(a)(b)
i9
Practical design of timber structures to Eurocode 5
(h) the growrh rings at rhe ends are running in the tangential directiclnbut in the radial direction in the middle, thus the thickness changesare largest at the ends;
(c) this cross-section will shrink less in the radial direction than in thetangential and it becomes skew, and timber cut in this way shouldnot be used in structures;
(d) the wide growth rings are running more 'tangential' in the outer sidethan in the inner, so the outer side will shrink more than the innerand the cross-section will become concave with the concave sideoutwards. If this cross-secrion is pressed flat (e.g. when planed)the outer side will crack.
Solid timber will often crack during drying, especially if it is driecl fast.The drying srarrs in the ourer layer and the shrinkage will be prevenredby the inner core that is still wet. This internal constraint can result inhigh tensile stresses that can cause significant crack damage of thematerial. Due to unavoidable changes in the temperature ancl RH,wood will always be changing irs size and shape during its service lifeand it is necessary to take this into consideration in the design oftimber strucrures. To reduce the problems, timber should be condi-tioned to the climatic conditions where it is going to be used. Thefollowing maximum moisture content values should be specified:
o indoor l0-l3o/oo outdoor, under cover 14*18%o outdoor exposed to weather ZO-Z5o/o.
If higher moisture contents cannot be avoided, shrinkage should beallowed to take place freely to avoid damage to the sffuctuie. Eurocode5 permits the use of wood with high moisture content during con-struction but only if it is ensured that the wood can dry without riskof attack from fungi and that it is possible to replace members subjectto unacceptable distortions.
2.1,3 Densitysince both mass and volume vary with moisture content, different densirymeasurements are used. The two most common density definitions are:
o dry density, po: ma,tlVdo determined from mass and volume ofcompletely dried wood
o moist (r"t) density, pr,: mu/Vu determined from mass andvolume at the moisture content u (o ).
40
Construction products
Often p12 determined from mass and volume at a moisture content of12olo (corresponding to a climate of about 20"C and 657o RH) is
taken as reference. For spruce and pine the following expression may
be used for u between 8 and 1B%.
ptz: pull -0.05(u -l})l (2.3)
2.1.4 DurabilityIf wood is not treated correctly it is a perishable material. It can be
destroyed by insects, bacteria and fungi. On the other hand wood is
resistant to many chemicals and is often used in storages for aggressive
agents such as salt and soda and in swimming halls (chlorine). However,in these cases it is often necessary to use fasteners of stainless steel orother especially durable materials.
Fungi
In buildings it is possible to lind about 30 species of wood-destroyingfungi. This number is much hlgher in woodlands and forests. Althoughsome of the fungi are harmless, their presence should be regarded as a
warning sign. They indicate that the moisture level is high and thatthere is risk of attack by wood-destroying fungi. Fungal spores are
found everywhere in the air. They are minute (thousandths of a
millimetre) and are carried by the air movement until they find a
place where the growth conditions are favourable. The spores shootwith a so-called hypha that takes root, grows into the wood and
develops into a mycelium. From the tip of the hypha, enzymes are
secreted. They convert the wood to food substances that can nourishcontinued growth of fungi. Under the right conditions mushroom- orchanterelle-like fruits may develop from the mycelium. In these,
spores may be formed, and the life-cycle begins again.
Fungi growth requires food, oxygen, a reasonable temperature and
moisture. Most fungi prefer temperatures around 20-30"C but some
require higher temperatures. At temperatures below 5'C all fungigrowth stops. In saturated wood (moisture content above about75%) , the oxygen content is insufiicient for most fungi to grow. Thisexplains why timber pile foundations below the groundwater table do
not rot.Fungi do not attack sound wood at moisture contents below 20%
and the attack will normally stop if the moisture content is reduced
4t
Practical destp of timber structures to Eurocode 5
below 207o. There are, however, some fungi that can attack wood atlower moisture contents when the wood has been affected by fungipreviously.
Ror
The result of a fungi attack is rot. often no distinction is made berweendry rot and brown (wet) rot.
o Dry rot is the result of a normally slow destruction of the woodcaused by fungi or bacteria under prolonged high moisture conrenr,e.g. due to insufficient maintenance or inappropriate structuraldetailing. Building insurance may nor cover dry rot because ircould be taken by insurers as a sign of lack of proper maintenance.
o Brown (wet) rot normally results from a sudden influx of warer orentrapment of water during the building process.
Mould and discolouring fungtwood exposed to moisture may be attacked by mould or discolouringfungi, e.g. blue stain. These attacks are harmless and the sffength andstiffness are not reduced but the appearance is impaired and i.,dicat"sthat the moisture level is so hlgh that there is risi of anack of wood-destroying fungi. Mould live on the surface of the wood and growthmay start if the air moisture content at the surface is higher than 16%in the wood itself. Mould has been attracting increased attentionbecause it may be carcinogenic and allergenic, even when the fungiare dried out and dead. Therefore, wood with visible mould shouldnot be used indoors.
Blue stain fungi creare black or blue discolouring on rhe surface whichcannot be removed easily without extensive planing. In the trade, bluestain is regarded as a blemish that should be avoided if the surface is rostay unrreated. Blue srain can be avoided if the wood is driedimmediately after cutting or sprayed with or dipped in a fungicide.
Insecrs and marine borersInsects normally pose only small problems, with the exception of houselonghorn beetles which may cause great damage to the structure. Houselonghorn beetles are most commonly found in the south-west area ofLondon (mainly surrey) where special Building Regurations exisr roprotect structural timber and prevent further spread. The best way to
42
Construction products
avoid problems is to keep the wood dry as house longhorn beetlescannot live in wood with moisture contents below 10o/o. For all otherinsects the limit is about 157o.
Attacks from shipworm that live in saltwater may be disastrous formarine structures.
Natural durabilityAccording to the European standard [EN 350-1] a five-class system is
used to describe the natural durability of wood and wood-basedproducts to wood-destroying fungi:
1. very durable2. durable3. moderately durable4. slighdy durable5. not durable.
tEN 350-2j lists the natural durability of solid wood for selected woodspecies which are important for design and construction. Examplesare shown inTable 2.2.
Table 2.2 Natural durability classes for certain species
Wood species Durability class
AshAzob6BirchBeech
Douglas
Oak, European
Oak, AmericanGreenheartLarchMerbauScots pine
FirSitkaThuja, North AmericanThuja, EuropeanWestern Red CedarWallabaSapwood, all species
5
2
5
5
3-43
4
1
3-41-23-44
4,sz
3
2
1
5
43
od" 5
Table 2.3 Definition of haTard classes according to EN 335.1
F Construction products -]
Table 2.4 Examples of design for durabilitl
Hazard classes Typical service conditions(biological use class)
Vood indoor in dryconditions
Wood not directly exposed tooutdoor climate or groundcontact, but brief wetting ispossible
Vood exposed to outdoorclimate and condensation,but without ground contactand not permanently wet,provided damaged wood maybe replaced withoutsignificant problems andprovided consequences offailures are small
Vood in permanent contactwith ground or freshwater orespecially exposed to weather.Parts critical to safety thatmay be difficult to replace
Wood in saltwater and partshaving special requirementsfor strength and durability
Poles for overhead lines,sleepers, fence posts, woodfl"g rton"r, exterior stairs andbalconies, beams in crawlspaces, sills on foundationwalls
Quay wharfs, moorings, poles
Protect outdoor structures ftomgetting wet, e.g. by effective roofoverhangs and eaves
Ensure external surfaces are
treated properly to repel waterand dirt
Slant-cut top of members
exposed to weather so that watercan run off
Cover ends of posts and
cantilevered beams
Examples
)t
IEN 335-11 defines fiveclasses. They are describedhazard classes are not theaccount only the influenceand stiffness properties.
hazard classes, also called biological usein Table 2.3.It should be noted that thesame as service classes which take intoof the moisture content on the strength
W
W
6-i
hffiffi&
hffi
wW
Desigtt for durabilityFungi attacks can be avoided if the wood is dried immediately aftercutting and kepr dry during all phases of the construcrion and in use.This is possible by proper design and consrruction which is called'Design for durability'. Examples are given in Table 2.4.
44 4s
Table 2.4 Continued
Use drip trays or ledgers so watercan run off
Min.8 mm
-t'2
Min. 10 mm
Keep wooden members awayfrom ground and vegetation
Make sure the pith side isoutwards as the heartwood is
more durable than sapwood, thepith side gets fewer fissures and itis a better base/surface forpainting
Construction products
Table 2.4 Continued
Use vertical claddings so watercan run off and not become
trapped
Ensure that the wood can move
freely; use overlap joints ratherthan butt joints
Nail correctly in order to reduce
cracks around the nailsNail heads shall just be flush withthe surface of the wood member
Heartwood
46 47
Practical destgn of timber structures to Eurocode 5
Chemical wood protection'Where it is not possible by other means to prevent decay of timber byfungi and insects etc., wood should be chemically treated by pressureor vacuum impregnation.
Pressure impregnationPressure impregnation is a process whereby wood is placed in a pressurecylinder and a vacuum is created to extract air out of the cells before thecylinder is filled wirh preservative liquid and exposed to high pressurefor a period of time. The wood is then dried and rhe preservativeagents are fixed to the wood and become insoluble. Note: The woodshould not leave the plant before the preservative agenrs are fully fixed.
The active preservative agents are organic fungicides and heavymetal salts dissolved in water. In the past the active agents werebased on copper, chromium and arsenic (CCA). Nowadays however,arsenic and chromium are prohibited in most European countriesbecause they may cause allergies and cancer. They are replaced byless harmful copper compounds.
Creosote is also used to preserve timber, especially for poles andrailway sleepers. However, impregnation with creosote is no longerpermitted in some European countries, although the creosote treatedproducts may be used.
Vacuum irnpregwtionThe penetration of the preservative thar is decisive for the protectiondepends on the preservative and the wood species. For some speciesit is possible to fully penerrate the wood or at leasr the sapwood. Thisis the case for the sapwood of fir, larch and Douglas, but not forheartwood that has high natural durability.
Spruce is very difficult to treat because the penetration both in itssapwood and the heartwood (which is not very durable) is only a fewmillimetres; therefore spruce is not normally treated.
Pressure-impregnated wood shrinks and swells as untreated wood.Therefore, it should be dried to a moisture content corresponding tothe environmental conditions of its end-use and service life. It shouldbe noted that pressure treatment may reduce the strength of wood.The producers shall declare the reduction if it is more rhan l0%.
Vacuum impregnation is a process developed for components (i.e.doors, windows, faEade elements, etc.).
In the vacuum treatment, the penetration in the sapwood is about5-10mm from the surface and about 50mm from the ends.
48
Construction products
Sapwood
Heartwood
Fig. 2.8 The extent of penetration by (from top): pressure tredtment, uecuumtreatment, surf ac e tr edtment
Vacuum-impregnated structures should not be processed or shaped(machined) after treatment. The same applies in principle to pressure-
treated wood, because there is a risk of exposing small unprotectedzones in the border between the pith and the core.
Figure 2.8 shows the extent of penetration by pressure, vacuum andsurface treatment.
The recommended protection depending on the hazard classes anddurability classes in accordance with tEN 4601 is shown in Table 2.5.
Table 2.5 Guide for selection of materials according to IEN 460]
Hazard classes
(biological
use class)
Durability class
1
2
3
4
5
a
a
a
a
a
a
a
a
(.)(i)
a
a
(.)(i)(i)
a
(.)(.) - (i)ii
a
(.)(.) - (i)ii
r Durability acceptable(r) Durability normally acceptable(o)-(i) May be acceptable(i) Impregnation normally advisablei Impregnation necessary
Nore: Judgement depends on the degree of exposure and the surface treatment
V
49
Practical design of timber stntctures to Eurocode 5
CEN has published srandards for rreared timber where nine classesare distinguished and are very open to methods and preservatives.Guidance should be sought from the producers.
Heat treatmentHeat treatment with temperatures about 200'C in closed tanks mayincrease durability. Heating causes sugar ingredients in the wood to bebroken down and changed to tar compounds colouring the wood brownand increasing moisrure stability and durability againsr fungi. The strengrhand stifftress are reduced by 10-30o/o. Heat-treated wood is marketed as
an environmentally friendly product for faEades, playgrounds andgarden fumiture and accessories. As understanding of its durability andperformance in use is still in its infancy, the suppliers recommend usinga surface treatment similar to those used for untreated wood for thetime being until more experience is gained from its performance in service.
2.7.5 Fire\Wood is classed as a combustible material but it has in many respects good{ire properties because its behaviour is predictable and the reduction ofstrength and stifftress is slow. With the introducdon of performance-based building regulations it is now possible to build wooden houses upto four, five, six and seven stories hlgh in certain European countries.The UK Standard [BS 5268: Part 6] now provides guidance for buildingtimber-{iame dwellings up ro seven sroreys high, which is the result of aprestige research project called TF2000 (see Enjily, 2001) carried outjointly by the Building Research Establishment (BRE), Timber Tech-nology Ltd (TTL) and industry.
To be able to assess rhe behaviour of building producrs during fire,they are classified based on their contribution to lire, smoke generationand giving off of droplets and parricles:
o their reaction to fire, which is specially important for cladding andwood-hased panels
o their resistance to fire.
Reaction to fire is determined according to [EN 138231. According tothis standard, building producrs are classifi.ed in the following classes,based on:
o Classes A to F (Class A covers products that do not contribute tofire (i.e. non-combustible materials)).
50
Construction Droducts
o Classes s1 to s3 for their smoke generation (where s1 is the best i.e.generates less smoke).
o Classes d0 to d2 for the giving-off of burning droplets and particles(where d0 is the best i.e. gives less burning droplets and particles).
Structural timber with a minimum mean densiry of 350 kg/m3 and a
minimum thickness of 22mm is, without further testing, classi{ied as:
o Class D: Building products whose contriburion to fire is acceptable.o Class s2: Limited smoke generation.o Class dO: No burning droplets or particles.
The following notations are used for European reaction to fire interms of their performance criteria:
o R for structural resistanceo E for inregriryo I for isolation.
The measured time for maintaining the required performance undera standardised fire test is expressed in minutes, e.g.30,60,90, 120. Itis also possible to combine the classes, for example RE30 means thatboth load-carrying capacity and integrity are maintained for 30 minutes.
Wood and wood.based panels can be classilied as Classes O, 1 and 2(Classes 0 and 1 can be achieved by trearing them with lire-retardanrchemicals). European classification can be obtained in accordancewith [EN 13501.21using the fire resisrance resr data.
The fire resistance may be verified by testing and calculationsaccording to [EN 1995.1./], [BS 476], and [EN 13501.21. However,there are other ways of demonstrating fire resistance by calculationsto [BS 5268-41, Section 4.2 arrd [BRE Report BRl28].
Reaction to fire may be verified by testing according to [BS 476.61,tBS 4i6-il and [EN 13823].
Joints with steel parts may be weak spots in the structure if notdesigned properly, not only because the steel strength is temperaturesensitive but also because the steel transmits the heat into the wood.Joints with unprotected steel parts cannot be assumed to have a fireresistance of more than 15 minutes. However, steel parts in joinrsmay be protected by countersinking them into the wood or by coveringthem with plasterboard or other board materials.
The fire resistance and reaction to fire of timber may be improved bysurface or pressure treatment using fire retardants which delay the firerather than prevent the wood from burning completely. It should be
V
5t
I'ractical desigt of timber structures to Eurocode 5
noted that it is cheaper to increase the sizes of timber members (forhigher fire resisrance) rather than using fire retardants, especially inheavy structures. Fire-retardant impregnation reduces the strengthand stiffness of timber, especially in some products thar are hygroscopic,and they may cause damp and salt spots in rooms with varying RH.
2.2 Structural timber
2.2,1 Sac,r.,ing and marketing
SawingStructural timber (i.e. solid timber that has been strength graded) hasin most cases a rectangular cross-section (sawn/cut on four sides), seeFig.2.9.
The sawing starrs wirh two or more parallel cuts along the rength ofthe log, giving waste side-boards and a cenrre block. The centre block isthen turned 90' and split with two or more parallel cuts into waste side-boards, boards and planks. other sawing patterns may arso be used toobtain cut members with certain shrinkage or appearance properties.Examples are shown in Fig. 2.10.
Construction products
Quarter sawing
Star sawing
Fig. 2.10 Sawing pdtterns
Standard sizes
specifications of sizes for structural timber are based on target sizes andtolerances. Target sizes are the actual sizes used in design calculationsand are therefore the size required from the supplier, with no deviarionsoutside the specified tolerance class being permitted. Two toleranceclasses are specified in EN 336:
1. For tolerance class 1 the acceptable deviations are -1mm to*3mm for thicknesses and widths less or equal to than lOOmmand -2 to *4 mm thereafter.
2. For tolerance class 2 the acceptable deviations are -lmm toflmm for thicknesses and widths less than or equal to lOOmmand -1.5 to +1.5 mm rhereafrer.
If graded timber is machined beyond rhese limits, it should be regradedand its size reclassified.
Timber structures can be designed using any size of timber. However,since producers are not normally aware of the specific end use of timberat the time of production it has become practice to produce a limitedrange of sizes, which have therefore become the most readily availablesizes in the UK. These commonly available sizes are listed in Table2.6. Unless otherwise specified, sawn timber will meet the requirementsof tolerance class 1.
Timber is often machined (processed) on two opposing sides or on allfour sides to get more precise dimensions meeting tolerance class 2.
V
Fig. 2.9
52
A tlpical sawing practice for solid timber
53
VPractical design of timber structures tct Eurocode 5
Table 2.6 Commonly aq.)ailable nrget siTes of sawn softwood timber
Note: Certain sizes may not be obtainable in the customary range of species and grades.
Timber is often planed (processed) on one or more sides for the sake
of appearance, use and more uniform sizes. Planing on two oppositesides will result in the following size losses:
o 22-100 mm: 3 mm (4 mm) or where the surface quality is especiallyimportant 4 mm.
o 120-300: 5 mm.
The number in brackets applies if there are special requirements to thesurface quality and straighhess. If only a thickness adjustment is
needed, the loss will be about 2 mm for all sizes.
Boards for formworks or underlay boards for roo6.ng felt are often onlyplaned on one of the wide sides. The planing shall only ensure that theboards have a uniform thickness.
A complete specification of sizes may read: 35 (TZ). 100 (T1) or 38(Tr) .r45 (r2).
Commonly available North American timber (lumber) sizes (to toler-ance class 2) are shown in Table 2.7.
Standard lengths are a multiple of 0.3 m, with a minimum length of1.8m. Lengths up to 5.4m are common, but lengths up to 72m canbe obtained at cost. Lengths of 5.7 m and over may not be readilyavailable without finger jointing. Minus tolerance on lengths are notpermitted.
For special purposes, timber boards are only cut on the two wide sides.
They have higher bending strength than ordinary sawn boards because
54
Construction products
Table 2,7 Commonll auailable softwood structural timber surfaced to the
Canadian Lumber Standard (CLS) lAmerican Lumber Standard (ALS) srzes
Thicknessmm
Width: mm
285
38(,/,/((,/Note: CLS/ALS surfaced structural timber has rounded arises not exceeding 3 mmradius.
the wood fibres are not cut and are often used in scaffolds. Tongue-and-groove edging is used to ensure connection between boards. The tongueand grooves for planks used in sheet piling may be shaped as shown bythe left diagram in Fig. 2.11.
Normal planks and timber often have wanes. In cases when this is notacceptable it is necessary to specifu square-edged cross-section, whichcan be expensive.
2,2.2 Strenghclcsses
GeneralWood is a natural material with strong variation in its material proper-ties such as density, stiffness and strength. To ensure a more uniformquality, timber is graded. The aim of the grading may be ro achieve a
desirable appearance; this is relevant for joinery, or to ensure a specihedstrength and stiffness.
The grading may be either visual (i.e. based on an assessment of thegrowth defects visible on the surface) or mechanical (machine). Thetwo methods may also be combined. The most common mechanicalstrength grading methods are based on the sirnple statistical fact thatstrength and stiffness are correlated. Machine grading may thereforebe performed by loading a piece of timber in bending (for practical
Thickness:mm
Width: mm
300275250225200175150t2510075
235184Lt489672Z
75
38
47
63
75
100
150
7.54
100
Fig. 2.11 Planks for sheet piling and ordinary tongue-and-grooue plank
55
r ooo oo qi1 > o---la,llcaFr3 E+:r,F7gt"2< :1 ;'='= qgta To dHi FrF$f;at?i;;:iFg;*al:€=_il+<;isa i3tr?E rf Fis g 3l6 *1i6 s tILeillgrA allE;3 ?i;-sil I+;i=iZ E; ni,ft"4 e] fte d.Fa?sHer;H' ."a'-o*EEiEiFl;ii*if
Fi*i ;= jil ;*S?Slf 1f ei EE6tl*'ix=c.i;'_7=iti !t:; T* =;; li +?;€JiTjl= iv: Fa rii=: r; at; as i i; iJ +"8 *"+ il-. -',.i n r q *o - 4 =, =.'4 = i I L-d = 6'''rii F." ls m:$ir93s5;f; ii^i,*vlHfirFEF3F ;ai i*!ei:A 1]i,i$+is=-f=r;i=EL?77=ltiqi+g; irrsa -=- -, ;ZiF-q;Zf ;E!E6J;e:Fil*:i ii1;lE 5 : ;il ry;#{-?FE1Us :1nU'.= Hy,g vas== 6=-
Table 2.8 Softwood, characteristic strength srlffness and density values
Strength class ct4c18c30 c2.7 cz4 c16
Strength values in N/mm2bendingtension in the fibre directiontension perp. to the fibre directioncompression in the hbre directioncompression perp. to the fibre directionshear
Stiffness values in N/mmzE parallel, meanG, mean
Density in N/mm2mean
characteristic
"f,.o.lri r.o0.l,
"f..o.lJc.q0.[
fa,
JU
l80.6
23
2.7
1.0(4.0)
-
12 000800
460380
2.0(3.4)r
1.8(3.2).
t.7(1.0)-
t610
0.5L7
2.2
z7
l60.6
zz
l,o
8000500
370310
9000
600
380) Ll)
18
11
0.518
2.2
24t40.5
2t2.5
t48
0.4
r67.0
2.8
(4.0)-
115001)a
7<(4.0;-
11 000700
4ZO350
450374
trL(J
G
Ptz
Pt2.k
7000
500
350290
Nore: The most common grades in the UK are in bold.* The values in ( ) are under discussion in CEN at the time of publication and will probably be accepted as the linal figures by the end of 2009
o
Ioc
Ic\o\Jt\]
Practical design of timber sttuctures m Eurocode 5
Table 2.9 Hardwoods, characteristic strength sti.fhess and density ualues
Strength class D40 D60 D70
Examples of species Oak
Constructinn products
Fig. 2.12 Example of a mark
2.3 Glulam
2.3.1 IntroductionGlulam (glued laminated timber) is produced by gluing thin woodlamellas together on their wide faces to produce members with sizeslimited only by the production facilities and transport considerations.
Since the starting-point is thin flexible lamellas, it is possible toproduce curved members that would be expensive for other materials.Examples of structures and typical beam sizes are given in Chapter 3.
Production and deliveryProduction is shown schematically in Fig. 2.13.
The basic material is strength.graded boards dried to a uniformmoisture content of about lTo/o.The boards are planed and their endsare finger-jointed and glued to produce long boards (laminations orlamellas), see Fig. 2.14.
The end-jointed lamellas are cur in lengths corresponding to themember length. Glue is applied on rhe faces of lamellas and these areplaced in a jig and pressed rogether. For curved members, the jig ismade by bolting vertical posrs to the base, corresponding to rhe formof the component (Fie. 2.I5) and the clamping pressure is applied bybolts. Straight beams are normally pressed by hydraulic presses instationary jigs.
D30
Beech Azob6 GreenheartBasralocus
Characteristic sffength values N/mm2bending f^ltension in the fibre direction ft,o,k
compression in the fibre direction /,,99,1
compression perpendicular to the f,,9,Lfrbre direction
Mean stiftiess values N/mm2E parallel to the fibre direction Eo
Density kg/#Characteristic ptz,t
1l 000 17 000 20000
590 700
30 40 60 7018 74 32 3223 26 32 34
8888
10 000
530 900
o Grading condition. Dry if the timber has intentionally been graded
at a mean moisture content of 20o/o or less, without any measure-ment exceeding24o/o.
o Bending strength, compression strength, tension strength, shearstrength and modulus of elasticity. Normally by reference to oneof the strength classes of [EN 338], e.g. Cl6, C24.
o Reaction to fire. For softwood with a minimum density of 350 kg/m3and a minimum thickness of 22mm: class D-s2,d0.
o Durability. For timber not rreared against biological atrack, one ofthe classes 1-5 in [EN 350.2] or NPD (no performance determined)which means that the durability is not determined. For treatedtimber, information about the treatment can be found intEN 152881.
An example of a mark is shown in Fig. 7.12; the markings are explainedas follows:
Grading company (EHAB).General structures (GS).
Strength class (C16).Reference number (S1 1 1V).Species of timber (E\U/ER - European whitewood or redwood).The British Standard on which the grading has been based [BS 49781.
58 59
&Practical des1gn of timber structures to Eurocode 5
Fig. 2.13 Production process for glulan members
The clamping pressure shall be maintained until the glue is cured. Toobtain a shorter curing time and a more reliable curing, the temperaturein the curing chamber is normally increased to about 40'C or the glue
lines are heated by high-frequency excitation. After curing, the compo-nents are finished by clean cutting on depth, planing on the wide faces,
shaping, surface treatment, mounting of {ittings, etc. Most glulammembers are produced from Norway spruce because it has good strengthproperties and a light and uniform appearance. Also its moisture
Fig. 2.14 Finger joint. p : pitch, l: finger length, b, - tip width, l, - ti1 gaD
The top board has finger joints with colourless glue on the wide face
60
Co'trstr uctio'n pr o ducts
Clean cutting
Clean cutting
Fig. 2.15 Plan uiew of production of curued structure and beam with varyingheight
changes are rather slow, and shrinkage and swelling are moderate.However, spruce has low natural durability and is difiicult to impreg.nate. For moist environments, pressure-treated lir is sometimes specifiedbut the improvement is only small and rarely worth the extra cost. Theheartwood and the impregnated parts of the sapwood are of coursedurable but there is a risk that small unprotected areas of sapwood inthe border areas are exposed by planing of the lamellas.
The glues used in glulam are at least as durable against weather,moisture and fire as the wood used and they do not give off harmfulagents, even when burned. Traditionally, resorcinol glues that give a
dark glue line have been regarded the best and most durable, but theuse ofcolourless polyurethane glues is increasing because ofappearancerequirements by architects. In service classes 1 and 2, it is also permittedto use the cheap melamine-urea glues if it can be guaranteed that thetemperature in the structure will not exceed 50'C. They also givealmost colourless glue lines.
In principle, glulam beams can be produced with any rectangularcross-section and even l-shaped. In most cases the most economicalsolution is, however, a solid rectangular cross-section with one of thestandard widths 65,90, l15, 140, 160 or 185 mm (Scandinavian prac-tice, based on Imperial sizes) or 60, 80 . . .).00 m (Continental Europeanpractice). They correspond to the widths of boards with a planing loss oflOmm for widths up to 150mm and 15mm for wider boards. Beams
wider than 185 mm are normally produced by gluing two or moreboards side by side (see Fie.7.16). The top and bottom laminationsare edge glued; the others are just placed side by side. Wide beams
are more dif{icult to produce and therefore more expensive. Beams
Part of the manufacturing rig for producing camber
61
Vertical glulam
Practical desig't of timber structures to Eurocode 5
Fig. 2.16 Cross-seclons of glulam beams
with width 65 mm or less are normally produced by sawing of widerbeams along their lengths. This gives an unfavourable knot patternand the sffength values should be reduced by 2Oo/o.
For beams it is economical to choose a high rario berween depth h andwidth b. The higher thehlb ratio, rhe more importanr it becomes withan effective bracing to avoid lateral instability. With a normal bracing, aratio up to 6-7 may be used.
To reduce moisture stresses the laminations should be used with theirpith in the same direction through the thickness. However, because ofthe increased risk of splits of the sapwood, both top and bottom lamina-tions are normally placed with their pith outwards.
To reduce stresses in curved beams when the laminations are pressedin place, the lamination thickness r should not exceed fm,rx:
Table 2.11 Glulam tolerances according ro IEN 390] at
V Construction products
12o/o moisture content
$7idth
Depth
Length
Cross-section angle
+2 mm
-2 mm*4mm-2 mm
I 7o/o
-0.50/o*2mm-2mm+0.1%
-0.IVo*20mm-20mmDeviation from right angle
All widths
h < 40Omm
h > 400mm
l< 2.0m
2.0m<l<20m
20m< I
< 1:50
(2.4)
where r is the radius and fi,1 rhe characeristic bending strengrh of rhelamination. The maximum lamination thicknesses depending onbending radius are shown in Table 2.10.
T able 2. 1 0 Maximum lamination thickness(t) depending on bending radius r
Glulam max t
Unless otherwise agreed, glulam is delivered with the tolerances givenin Table 2.11.
The sizes of glulam members are limited by the production equipmentand the time permitted from glue application on the first lamination tofinished clamping. Normally members with volume over about lOmland more than 25 m long will require special measures. The size mayalso be limited by transport restrictions. The height from the road rothe top point of the load is normally limited to 4.95m, see Fig.2.l7,and normal allowable overhang is 3.5m, 2.00m and 1.00m at rear,front and sides respectively. Anything outside these limits and lengthsover 35-40m require special permissions.
Camber may be used for beams to compensate for the deflections.Since the correct camber depends on factors normally not known bythe producer, beams are delivered without camber, i.e. with straightunderside, unless otherwise speci{ied by the client.
Glulam factories shall be subject to third-parry external control. Thecontrol shall comprise:
o grading and moisture content of the laminations
r,,n*: h(t.k)
GL36GL28GLI4
0.006r0.0055r0.0052r
62
Fig. 2.17 Size limirs by road trdnsport
63
Practical design of timber structures to Eurocode 5
. strength of {inger jointso quality of the lamination planingo mixing and application of glueo gluing times and clampingo curing conditions, temperature and air moisture contento glue line quality.
The strength of finger joints shall be controlled regularly by bendingtests to failure. The glue line quality is controlled by so-called delamina-tion tests where 100 mm long cut-offs are impregnated with water underhigh pressure and then dried fast. The length of delaminated glue lines is
taken as an indication of the glulam quality.
Deliuerl and handling on site
Glulam beams are normally delivered on trucks with a crane that may beused to offload and also to erect light structures. Glulam shall behandled with care on site and checked to ensure it has not beendamaged during transport and handling. Glulam is often deliveredwrapped in plastic as a protection against water and soil. If there iswater under the plastic, e.g. from condensation, the glulam may be dis-coloured due to mould and the plastic should be removed so the woodmay dry. For outdoor storage the glulam shall be stacked on a flat anddry support base and protected against the rain. To ensure ventilation,battens shall be placed between the glulam beams and under thecovering. The battens shall be placed vertically above each otherotherwise the members may be permanently deformed by prolongedstorage.
2.3.2 Properties
Mo istur e - r el at e d pro pe r t i e s
Glulam is regarded as more moisture stable than timber because itis delivered dry and moisture changes are slower due to the largerdimensions.
Sun exposure may result in a rapid drying out at the surface. Thismay lead to surface cracks and with time to desffuction of the surface.Cantilevered beam-ends, especially south facing, require specialprotection (see Fig. 2.18).
The moisture content at delivery is about lZo/o.If glulam is exposed tomoisture, e.g. if stored outdoor during winter, the moisture content may
64
7 Construction products
Kmm
i,__
Fig. 2.18 Examples of protection
metal plates
Ventilatron
of cantileuered beams by profiIed boards or
increase to 18-20%. If glulam is built in with this high moisrure conrenrit is important that the building is not suddenly heated to hlgh rempera-ture since this may lead to severe cracking because the wet core willprevent shrinkage of the outer part of the members.
DensityA density of 500 kg/m3 or more should be assumed when calculatingdead load from glulam structures.
Srrength and stiffness
Glulam has higher mean strength and smaller variation than ordinarytimber. EN 1194, Timber structures - Gluedlaminated timber - Strengthclasses and determination of characteristic vdlues, gives strength classes forglulam. There are four classes for so-called homogeneous glulam andfour for composite glulam. In homogeneous glulam the laminationquality is the same in the whole cross-section. In composite glulamthe lamination quality in the middle two-rhirds may be of a lowerclass than outer laminations. The classes are denoted GL (glulam)followed by the characteristic bending strength in N/mm2 and by hfor (homogeneous) or c for (composite).The characteristic strengthand stiffness values are given in Table 2.12.
For rectangular cross-sections the reference depth in bending andwidth in tension is 600mm.
65
Practical desip of timber structures to Eurocode 5
Table 2.12 Characteristic strength and stffiess ualues for glulam
v
Glulam class GLL4 GLZS GLJ2
Construction products
2.4 Wood.based panel products
2.4.1 IntroductionWood-based panels play an important role for timber structures, forexample as:
o floors and roofsr underlay for flooring and roofingo stabilising walls and roofs (bracing)
o webs and flanges in I- and box-beamso gusset plates
o diaphragms.
The first wood-based panel product produced was plywood in about1900. Plywood was in the beginning produced with joiner's glues suchas animal and casein glues, which had little moisture resistance.Later, around 1930, particleboards were produced using the firstsynthetic glue (urea formaldehyde). Wood fibreboards were inrroduceda short while after particleboards.
2.4.2 Plywood
ProductionPlywood is made by gluing together 1.5-3mm rhick plies (veneers),
usually with their grain direction perpendicular to each other (see
Fig.2.l9). The direction parallel to the grain direction of rhe ourerplies is called the panel grain direction. The plies perpendicular tothis direction are called cross-plies. In plywood with an even numberof plies, the {ibres in the two middle plies are parallel.
For smaller depths and widths, h,may be multiplied by:
the bending and tension strengths
(2.5)
( 1.1
kh:mi"t (#l'since the bending properries depend especially on the properties of theouter laminations it is assumed that the load-carrying capacity of aglulam column is the same for homogeneous and .omporlte glulam.
For glulam loaded in tension or compression without column effectthe strength of composite glulam is smaller than for homogeneous.Normally the producers will deliver composite glulam. If the higheraxial sftength is needed, it is necessary to specify homogeneousglulam.
Specifications
In addition to requiring that glulam shall be produced according toIBS EN 140801. The following should be specified:
o special requirements to wood species, e.g. firo any special requirements to glue, e.g. colourless glue to finger joints
or in generalo any special requirements to moisture content. any special requirements to lamination thicknesso any special requirements to protection against biol0gical attacks.
66
,""", Jveneers
I
Fig. 2.19 A tlpical layout of p$wood
67
Practical desigr of dmber structures to Eurocode 5
Structural plywood is rnainly made from spruce, fir and birch.Different species and qualities are also used, e.g. one species for theouter plies and another for the inner (combi plywood) or a better qualityfor the outer plies. To avoid bow, plywood shall be symmetric about themiddle plane, both with regard to thickness of the veneers and theirmaterial properties.
Plies are rotary peeled from straight logs with large diameter. The logs
are cut in lengths that correspond to the final pressing plate length.After softening by water storage, timber logs are mounted in the millso that they can rotate about their central axis. By pressing a knifeagainst the log a long thin veneer sheet is cut out. The veneer is
dried and cut in smaller lengths that are graded in different qualityclasses. If necessary, defects are cut out and repaired by glued-inpatches. Glue is apphed on veneers and the sheem are pressed togetherin a hot press. After pressing, the panels are climatised and cut to thedesired dimensions. The panels may be sanded to improve appearance.For structural plywood, sanding may be a doubtful advantage because itis often made so imprecise that one of the outer plies is removed partiallyor cornpletely.
According to [EN 314.2], a distinction is made between three gluingclasses:
o class 1: only for use in dry indoor condition (Service class 1)
o class 2: for use in outdoor condition if protected against directweather and water, and in moist indoor climate (Service class 2);the glue is resistant to direct water exposure for a limited periodof time, e.g. Juring construction
o class 3: for use in outdoor conditions (Service class 3).
Plywood is produced in three corresponding classes according to stan-dard IEN 6361.
Properties
Because of the crossing fibres, moisture-related deformations in thepanel plane are only slightly larger than for wood in the grain direction.The following free shrinkage/swelling strain values may be used for a
unit percentage change in moisture content:
o in the thickness direction: about 0.2%o in the length direction: about 0.010o/o (-g.1mm/m)o in the cross direction: about 0.015o/o (-9.15 mm/m).
6B
Construction products
In principle the strength and stiffness properties for plywood may be
estimated by the usual rnethods for composite materials based on the
geometry, the material properties and {rbre orientation of the individual
veneers. It can, however, only be a rough estimation and the structuralproperties shall be verilied through tests.
Plywood products
The panel surfaces are normally untreated, but they may be sanded,
sandblasted or profiled. The top ply may be plugged or lilled to make
the surface smooth; this is important if the plywood is to serve as
underlay for thin flooring or roofing. Plywood may be surface treated
or coated and the outer plies may be impregnated with polymers.
Peeled plywood has a tendency to acquire li.ne surface fissures. Theyhave no influence on the strength properties of the final product butmay be visible through paints; this, however, may be counteracted by
applying a film to the outer surfaces during production. Structuralplywood is mainly imported from Scandinavian countries, Canada and
the USA. With the exception of Finnish birch plywood there are onlysmall differences between the products from these countries.
The standard dimension for European plywood is 1200.2400mmand for plywood from the USA is l2Z0 .2440 mm. Panels withtongue-and-groove edges are about 15 mm smaller. Normal thicknesses
vary from about 8 to about 30 mm.
Strength and stffiessThe properties vary considerably and it is necessary to obtain the specific
properties from the producer. As an example, for Europly p\wood,available throughout most of Europe, the values in Table 2.13 may be
used.
The shear strengths and stiffnesses for all thicknesses are:
f,t, - 3'2N/mm2
fu.rolliw,k: 0'9 N/mmZ
G:5OON/mm2
The mean density is 400 kg/m3.
There are two essentially different shear types. One of the shear types
is when plywood acts as a panel or diaphragm (see Fig. 2.20). The panel
shear strength is denoted fi. The other type is when the plywood is
7
69
{O
Table 2.13 Characteristic strength and mean stiffness values for Europly
Thickness:mm
No. of plies/veneels
Characteristic strength values: N/mm2
Bending Tension and compression
.f'.0.I f^.90./, /'.0,1
f..o.r
Mean stiffness values: N/mm2
l
_l
oos
q
q9
ln
I
oiG
otrIooolq
E,.o
E.,o
Bending Tension and compression
Er.9o
Ec.90
tr-IJr.90.lfJ..90.i.
E^.90
5t5
5t55t5
7t7715
7t77t79t99t7
9t9717
9t9tUrl
915070009440
7000080006400
710082008900
60008900
76005700
1800
3 100
2800
3900180026005 100
37002300
3000
450048003300
6000
59006100
470473005800
58005700
68005700
58005i005500
3850
4650
4100444029a0
4400
44004500
4740
4500
440045004600
10
15
t215
11
t2t4lz10
I2t2T4
17
l515
l5I418
t4r413
16
14
14
T4
13
10
13
10
10
7
10
10
11
t211
10
11
11
20
2618
'U29
22
25
z5
18
zz23
17
9
t7t515
t616
18
18
t919
zl2l2l
* If number of plies are bigger than number of veneers, the two outer veneers on both sides are glued together with parallel grain directions.
F
Co
Ioo
ioo6
E-------lllttL___l
;"tr----Tl
'd =1 N)q) o-=.!r 5 .)'o 5'd = r/'iJ N i aH J- J u=o./ 5 - 5Dr::I: +gii.3;IirH€iiF=€* i HTEE :
TE.EYqgq3FLTFEg*5 Fu rfEts 5
7a{-}'tei!=irr3)-E = i =*: SgEIa€tsIiE;;iif $ ilr; $;rf ; f ;-: r" F =
a =;is._4=-{d;ilt==i'g;-* R sxl.' :Fg53rE1':!"FE|Sf h &aF =__rL2Z-o-"eg+Q;*fi3iE 5=='-6r-,=i-^.,d tri'q.;6.A_ ==ii t-
?A=E-: f la-= 116 H F*i ?=EAtr-=e,a- ? ,E6[j'-ci^4 3'A'.i'j-c33a- ==T;22i{;!3 _p-HF3;sii'B'*iqE-''Fd6 EE":f g-i I f Fpi ?g-*: yE T B 6(J'.1 | LL') q o k al,: = Hii-ra- * ! g -(D ) - s A; / - Q,-=c!= t.der=ltriart6 :il#g't Yanir=4=e{T' ': v,
*;: li?i[H'tEeB=.# f il
rlOC
t-Ji!
I
3o
0a
A
{
vPractical destg of timber structures to Eurocode 5
Table 2.14 Minimum qualities of particleboards in Seruice classes I and 2. (Notethat particleboards are not allowed to be used under Serqtice class 3 conditions)
Service class
Construction products
Table 2.15 Characteristic strength values cmd medn stiffnesses in N lmm2 forparticleboard type P7 according to IEN 312]
Thickness, Plate
t: mm bending,It^1,
Tension, Com- Shear Plate
/,.0.1 pression, bending,
.f..o.a f ,J, f ,.*t.t E^
Tension/com-pression,
E,.6, 8..9
Density,p:
kg/m3
EN312Type P4
Type P5
Type P6
Type P7
EN 3OO
OSB 1
OSB 2
OSB ]
6<t<1313<t<2020<t<2525<t<3232<t<4040 <t
t5.5 8.6 2.4
t4.7 8.r 2.2
13.7 7 .9 Z.A
t3 .5 7 .4 1..9
r3.2 7.7 1.9
13.0 7.0 1.8
Load-bearing boards for use in dry conditionsLoad-bearing boards for use in humid conditionsHeavy-duty load-bearing boards for use in dryconditionsHeavy-duty load-bearing boards for use in humidconditions
General-purpose boards for use in dry conditionsLoad-bearing boards for use in dry conditionsLoad-bearing boards for use in humid conditions
(oriented strand board), a board rype developed especially for the buildingindustry. OSB is made with relatively long fibres normally placed in threelayers, where the particles in the outer layers are oriented mainly in theboard direction whereas the middle layer is oriented mainly perpendicularto them. OSB is thus in principle similar to plywood.
The standard dimension of OSB is 1 200 . 2400 mm but it is possible toget board up to 2.7.12m. The thickness range is 6-40mm. Therequirements for ordinary particleboards are given in [EN 312] andfor OSB in [EN 300]. The different panel types may be used as
shown in Table 2.14.
Properties
The average density varies between 500 and 650 kg/m3 and is highestfor thin boards. The moisture-related deformations are considerablyhigher than for wood and they are only partly reversible because some
of the bonds between particles are broken during moisture expansion.This is especially pronounced for the thickness direction. By repeatedwetting and drying the boards become thicker and thicker. It is there-fore essential that the boards are conditioned to the climatic conditionswhere they will be used during their service life.
The size changes are almost proportional to the changes in therelative air humidity RH. A change of 10% in RH results in lengthand width changes of 0.06% (0.6 mm/m) and thickness changes of
7Z
0.3-0.4o/o (3*4 mm/m). By soaking in water for 24 hours, the thickness
may increase by about 107o.
Strength and stiffness
Examples of strength and stiffness values are given in Tables 2.15 to2.17. There are, as for plywood, two shear strength values corresponding
to panel (panel shear) and plate behaviour (rolling shear).
Further information about particle boards and OSB can be found in
[Digest 477,Pan2,2003] and [Digest 477,Part 1,2003].
2.4.4 Wood-fibreboards
ProductionThe raw materials are the same as those for particleboards. There are
two production methods: the wet method (the original and most
common method) and the dry method. In the wet method, the hbres
Tabte 2.16 Density (inkslm3) and characteristic snength values (inNlmm2) forOSBI2 and OSB/3 according ro IEN 3O0J
Practical desig of timber structures to Eurocode 5
Table 2.17 Snffness ualues (mean ualues) h N/nvnz for OSBI2 and OSBI3according ro IEN 300j
Construction products
Table 2 .18 Minimum qualiry cf fibreboard for use in Seruice classes 1 and 2.
(Fibreboards should not be used in Seruice class 3)
BS EN Service classThickness,t:
mnl
Bending Tension and compression
E-o E-.90
>6 to 25 HB.LAHB.HLAMBH.LAMBH.HLSMDF.LAMDF.HLS
are kept and transported in water after the raw material has beendecomposed into fibres. Two decomposition processes are used:
1. The'masonite'method. wood chips are steamed under high pres-sure. A sudden removal of the pressure makes the chips 'expiode'into fibres.
2' The 'defribrator'method. wood chips are decomposed by grinding.The fibre mass that contains about 70yo water is placed or', , ,r"tconveyor belt with a layer of sawdust or paper mass on top. Themass is pressed in a stack press. Normally the net is only removedafter pressing which leaves a characteristic surface pattern on oneside, with the other surface being smooth.
No glue is added but the lignin in the cell wails acts as a thermo-setting glue which is cured by the heat in the press at abour 200.cfor 5-10 minures followed by curing in a chamber at abour 165.c forabout 5 hours. when leaving the curing chamber the moisture contentis very low and the boards are, therefore, conditioned in a normal-useclimate followed by cutting into the required dimensions. Hard oiltempered boards are dipped in or sprayed with oil before curing.
- The production of porous fibreboards is simpler. The woocl-rrbi"
^urr,after being pressed to the chosen thickness, is cured at a temperature of165- 180'c and the moisrure contenr is adjusted by sprinkring warer onboth sides. It is possible ro impregnate the boards during the ptcess, e.g.by adding asphalt to the fibre mass or by giving them a *rrn." rreatmentafter curing.
Fibreboards are marketed in many sizes where length and width aremultiples of 610mm, with a maximum dimension of 2.44 x 6.10m.For structural boards a distinction based on density is made betweenhard and medium boards:
o Hard boards have a density above B00kg/m3. standard thicknessarc 3.2,4.8 and 6.4mm. The requiremenrs for their productionare given in [EN 622-2l.
7+
6IL-J
622-5
Hard boards
Mediurn bo'.rrds
MDF
Notes: HB: hard board; MB: medir.rm board; L: for structural use (load bearing); A: al1
load durations; H: also Service class 2 (humid);S: only short term.*Not
as underlay for rooling felt or foil or in crawl spaces.
o Medium boards have a density of between 600 and 800kg/m3.
Standard thicknesses are 9, 11 and 12mm. The requirements for
their production are given in IEN 622-3].
A new board type is MDF (medium-density {ibreboard) which ls
produced in a similar way to particleboards by mixing glue and a dry
fibre mass that is pressed between two hot steel plates. The result is a
homogeneous panel with two smooth faces. These boards were origin'ally aimed for the furniture industry but have also found a market inthe building sector. The boards may be produced with thickness
between 9 and 50 mm. The requirements to their production are
given in tEN 622-51. The density of these boards is about 7O0kg/m3.
A board type called HDF (high-density fibreboard) is a traditionalwet process board, but with two smooth sides.
Fibreboard and MDF are produced in many qualities (see Table 2.18,
which also indicates where they may be used according to Eurocode 5).
Properties
The moisture-related deformations are quite similar to those ofplywood. Traditional boards will bow if the moisture content is changed
and it is necessary to condition them under pressure to the service life
conditions.
Strength and stiffness
Examples of strength and stiffness are given in Tables Z.l9 andZ.20.
zza0
75
?ractical desip of timber structures to Eurocode 5
fable 2.19 characteristic srrengrhr and mean sri/Fnesi and density ualues fornedium-density board
Construction products
Table 2.21 LVL, characteristic strength and stiffness ualues inNlmm2 for Kerto
V
fhick-less,
:mm
Density:kg/ml
f..o.r.IJm,0.k
/r,o.r.
f,,so,tIJc.0./.Ii c.a0.k
/..so.lIiv.k
f ,,rol.k
Eo
38
35
tt7
27
t23.5
5.5
1.5
10 000
Plate Tension, Com-bending, f .1 pression,
f^.t f ,.n
Shear Bending, Tension,
Iu.n't,k hr.A
f,.t f,.",tt
Strength value: N/mm2
Bending, flatwise
Bending on edge
Tension in the flbre direction
Tension perpendicular to the fibre direction
Compression in the fibre directionCompression against narrow side
Compression against wide face
Panel shear
Rolling shear
Mean stiffness values: N/mm2Bending flatwise or on edge
Strength values in N/mm2 Stiffness values in N/mnr2
Com-pression,
E..i.
l0 7.4
r0 6.5
2.4 A.B 31001.9 0.11 2900
3.9
3.5
3.9
3.5
I 100
2900
3 100
2900
650
600
Further information about fibreboards may be found in [Digest 427,)art 5l and [Digest 477,Parr 6,20031.
,,4,5 LW ond other wood.based products
.vL-vL (laminated veneer lumber) is mosr often made of z_3mm thickpruce veneers wirh a length of 25m and a width of goomm. The'eneers are dried, graded and placed after glue application on aonveyor belt with the fibres essenrially parallel to the panel direction.n some types there are, however, also some cross-plies to improve thehear strength. The veneer package is fed into a hot press to cure thelue and a conrinuous panel with thickness of 25-75 mm is formed.'he outer veneers are scarf end jointed whereas the inner veneers areutt jointed. Finally, the panels are cut into either paners or beams,ith depths up to 900 mm and lengths up to Z0 m.
'able 2.20 characteristic strengths and mean stiffness and density ualues forIDF.LA
In Europe, LVL is produced under trade names; for example, inFinland the brand name is Kerto while in Sweden the brand name is
Swedlam. They are produced in accordance with tEN 143741. LVL isused in line with structural timber and glulam. Due to the glued thinveneers, the strength properties in the fibre direction are rather high,
typically between 35 and 50N/mm2, as shown in Table 2.21.
Examples of structures made with Kerto are shown inFig.2.7?..
hickness,
mmStrength values in N/mm2 Stiflness values in N/mm2 Density:
kg/tr-trBending, Tension, Com- Shear Bending,
f^l f ,1, pression,
-.f,,*,i.1
f,t, f,t f,.n,t.t
Tension/
compression,
8,11E,.1
t7 17.4t.<t<19 12.4| <t<30 12.4
)< r 11.8
9.7
8.4
7.6
6.0
9.2,
8.4
7.6
6.0
3.2
3.2
3.2
3.0
3 100
2800
270a
2400
690
600
550
500
4.8 3700
4.8 J200
4.8 32A0
3.6 Z 100
Fig. 2.22 Structures made with Kerto products
77
Pructical tlesip of tintber structttres to Eurocode 5
Fig. 2.23 Geometry of typical l-beams and metal web beams
I-beams
I-beams with flanges made of tirnber LVL and web made of hard libre-board or OSB are produced as a standard product in the UK and othercountries (see Fig. 2.23).
The depths of the I-beams vary between 200 and 5OO mrn and thestandard lengths are 61719ll2m.
Parallel strand lumber and laminated strand lumberParallel strand lumber (PSL) is produced from slender ply strips thar aremixed with glue. A strip bundle is pressed ro the desired shape in a hotpress until the glue is cured. Laminated strand lurnber (LSL) is producedsimilarly from long chips. Both products are used in line with structuraltimber (see Figs 2.24-2.26).
7B
7
Fig. 2.24 (a) Parallelproprietary products
(b)
lumber; (b) Iaminated strand lumber
C ons tr uc tiot't pr o ducts
Both are
Fig. 2.25 PSL column andbeam
Fig. 2.26 LSL beam
Practical desip of timber snuctures to Eurocode 5
2.5 Joints and fasteners
2.5,1 IntroductionIn timber structures there are generally many joints and they are often
crucial points and part of design' because they take up considerable
space and have a tendency to become complex. Normally joints dictate
the final size of timber members and components. Joints are often made
as lap joints or with gusset plates of steel, or wood-based panels fastened
either by glue or by laterally loaded mechanical fasteners. The
load-carrying capacity of glued lap joints is limited due to stress concen-
trations at the glue line borders'Traditional timber joints have been out of use for some time but due
to the introduction of computer numerically controlled (CNC) wood-
working machines some traditional joint types may again become of
interest because of their fire resistance, or for use in structures with
many similar compression members, e.g. lattice shell structures.
Examples are shown inFtg. 2.27.
In the following the most common fasteners will be described with
examples of their load-carrying capacity. A more detailed description
of strength and stiffness and requirements for spacing and end and
edge distances is given in Chapter 9.
2.5.2 NailsNails consist of a metal rod or shank which is usually made of steel,
although it can be made of aluminium, brass or many other metals, or
even plastic. The shank is usually designed to be round and smooth.
The most common nail types are smooth nails with circular cross-section.
Shanks with annular grooves, spiral, or helical threads are used when a
stronger, more permanent grip is required. There are nails specific to
their end-use, e.g. tile roofing, flooring, shingles, guttering' panel
products, gypsum panels, sheet metal and concrete. Some nails are
designed to be driven by air-powered nail guns rather than by a hammer.
Steel wire is usually drawn from coils of metal wire and fed into a nail-
making machine. They can be further twisted or formed to the desired
type. According to the European standard IEN t4592], a minimum
ultimate tensile strength of 600 N/mmr is required. The head is
normally round with a diameter of about 2.5d, where d is the diameter
or side of a square cross-section shank. For brads the head is only a littlelarger than d.
Nails other than smooth nails are produced from special steel so thatthey have the same bending strength as smooth nails.
80
Construction products
Fig. 2.27 Traditional timber joints
The sizes for some commonly used nails are given in Tables 7.72 and
2.23. Annular ring shank nails are especially aimed at joints with thinsteel plates and are less slender than common nails. Square twisted
nails are also used, but they have poorer properties than screw and
ring shank nails (see Fie.2.28).In some countries, round nails with a rolled thread with high pitch are
also used. They rotate when they are hammered in and act to some
extent similar to screws. Staples, although used to a lesser extent inthe UK, may be used to join thin wood members (see Fig. 2.28).
v
B1
Prnctical design of timber structures to Eurocode 5
Table 2.22 Commonly used snooth round wire nails
Diameter,d: mm
Length, l: mm
2.36
2.65
3.0
3.25
3.7 5L<
5.0
5.66.0
Table 2.23 Annular ring shank nails (Strongtie). Dimensions: diameter, d;
length, L; ringed length, L1; and head diameter, D. The point length is about 1.5d
The characteristic load-carrying capacities of some round nails aregiven in Table 2.24.It is seen that strength-wise it is advantageous touse slender nails, but the labour cost becomes higher. Even though theload-carrying capacity of one nail is small, nailed joints are very effectivebecause they do not require shaping of the timber and because nails canbe placed close to each other (minimum net pattem 5d x l)d).
Nails are flexible fasteners with a slip in the order of 0.1d at theserviceability load.
The tensile load-carrying capacity of smooth nails is small and notreliable. The characteristic tensile load-carrying capacity of onesmooth nail 3.4.90 is about 0.15kN and tensile loaded smooth nailsshould only be used in secondary structures (possibly as skew nailing),otherwise annular ring shank nails should be used. The tensile load-carrying capacity of an annular ring shank nail4.0 x 75 is about 1.2 kN.
Nailed joints are common in light structures such as truss structures,see Fig. 2.29.
Table 2.24 Load-carrying capaciq Fu.l "for one laterally loaded nail in Cl8 and
the area Aneeded to transfer lkN (shear) force
d: mm F1: kN A needed per nail, mmZ A needed for 1 kN: mm2
Practical desigt of timber structures to Eurocotle 5
Fig. 2.29 Nailed joints in a truss
Nails used indoors (service class 1) are normally not corrosion protected
but the Eurocode 5 has protection requirements for other service classes as
listed in Table 2.25. For specially corroding environmentsFelZn 40, hot-dip zinc coating or stainless steel should be used. This also applies for nails
in contact with conoding material, e.g. some wood species (oak, westemred cedar and thuja for instance) and some types of preservative.
2.5.3 BoltsBolted joints are often used in heavy timber structures, e.g. glulamstructures. The most common bolts are M10-M24 bolts which are
normally hot-rolled, with coarse threads. They are available in totallengths and thread lengths almost as desired. They are always used
Table 2.25 Minimum corrosion protection requircments of nails and screws
Descnption Service class
Construction products
(a) (b)
Fig. 2.30 Bolt types: (a) machine bohs without and with washers; (b) coachbohs
without and with washers under the nut
with washers with side length 3d and thickness 0.3d under both head
and nut and may therefore be used for lateral as well as axial loads.Coach bolts or carriage bolts are used in secondary structures. They
have a smooth curved head and a square part under the head to preventthe bolt from turning when tightening. It is thus not possible to use
washers under the head unless washers are purpose-made with a
square hole. Different bolt types are shown in Fig. 2.30.Examples of bolted structures are shown in Fig. 2.3 1.
Eurocode 5 requires bolts to be litted tighdy in the holes in thetimber; however, in practice, to ease the {itting, the holes are always
drilled about 1 mm larger than the diameter of the bolts. Bolts may be
placed in a pattern about 4d . 10d. Examples of load-carrying capacitiesfor bolted timber-to-timber joints are given in Table 2.26 and theminimum requirements to corrosion protection are given in Table 2.27.
2.5.4 DowelsDowels with diameter B-20 mm are often used instead of bolts. Theyshall fit tight in the holes and are therefore often made from turnedspecial steel with bevelled ends (see Fig.2.32) . The use of dowels usually
Practical destgn of timber structures to Eurocode 5
Tabla 2.26 Characteristic knd-carrying ccrpc.cities Fp for boked timber-to-timberjoints and the necessary .treds to transfer a load of I kN. The vdlues are per shear
for double-shear joints where the thlckness of the side members is r : 47 mm andthe thickness of the middle member is 2t
d: mm F1: kN A needed per 1 bolt, mm2 A needed for 1 kN: mm:
screws with diameter d between 2 and 6 mm, length between 3d and lLdand with threaded length about 600lo of the total screw length. Coach
screws/lag screws with hexagonal head and diameter between 6 and
20 mm are often used for larger timber connections. Examples of lag
screws and slotted screws are shown in Fig. 2.34. For diameters above
5 mm pre-drilling is required.Screws have advantages where small members have to be fastened to
large timber members as shown in Fig. 2.35(a) and (b). Bolts would be
more expensive and become less effective when shrinkage of timbermembers takes place if no retightening is scheduled.
A new development is long (up to 1000 mm) sel0drilling and self-
tightening screws that can be screwed in by light electric hand tools;these screws are made from high-strength steel. Examples are showni\Fie.2.36.
These screws have slightly hlgher lateral load-carrying capacitythan corresponding nails but their main advantage is their high axialload-carrying capacity, making them suitable for anchorages and
reinforcements (see Fig. 2.35(c) and (d)).
(a)
(a) lag screws; (b) slotted screws
3
8
L5
2ZA0
9000
z0 000
750I 100
1300
Table 2.27 Minimum corrosion protection requirements for bohs and dowels
Service class
Bolts and dowels None Fe/ZN25czi5a
results in a nicer appearance and a stiffer joint because the slip due tothe oversized holes is avoided. An example of a dowelled joint is
shown in Fig. 2.33. The holes should be drilled in one operationunless CNC equipment is used.
The lateral load-carrying capacity of dowel joints are the same as for acorresponding bolted joint, but the spacing along the grain may bereduced to 7d. The required corrosion protection is the same as for bolts.
2.5.5 Screq.us
Screws are often used instead of nails in joints where appearance is
important, where it should be possible to separate the timber partsagain and where higher load-carrying capacity is required than couldbe achieved by using nails. The most common screws have been slotted
None
Fig.2.32 Dctwels
B6
Y2d- d+
Fig. 2.34 Screw types
(b)
B7
Practical design of timber structures ta Eurocode 5
(c) (d)
Fig. 2.35 Screwed joints: (a) a post fastened n a glulam arch withlag screw withhexagonal head; (b) column fastened to a steel anchor; (c) joist fastened by a longscrew; (d) screw used as reinforcement of rctcfud beam
tlvead both wder the head and at tfu end (the pitches are a little different resuhingin the pm* being draum tight ngether). Bottom: self-drilling screw 6 x 300 mm
88
Constntction products
(a) (b)
Fig. 2,37 (a) Suews used to fasten a joist to a header beam; (b) lateral loads
transfened fo inclined screws
The high axial load-carrying capacity means that many laterallyloaded joints may be made as screwed tension/compression joints (see
Fig. 2.37(b)).Steel plate connectors (i.e. joist hangers, brackets, etc.) are known in
Europe as 'three-dimensional connectors'. They are usually fastened
with 3.7 mm or 4-5 mm connector screws with a cone under the
head (see Fig. 2.38). The cone causes the nails or screws to be rigidlyheld in the plate.
The requirements for corrosion protection are given inTable 2,27.
2.5.6 Glued-inboltsSteel rods glued into holes in solid timber may obtain a high load'carrying capacity both laterally and axially. These joints, often called
Fig. 2.38 Angle bracl<et with cornecnr sctew
89
Practical destgn of timber structures to Eurocode 5
Fig. 2.39 Joints made with glued.in bohs in end grain
glued-in bolts (sometimes referred to as glued-in rods), may be madewith the hole direction parallel, perpendicular and at an angle to thegrain direction. Glued-in bolts give several structural possibilities andare being used more and more in glulam structures (see examples inFigs 7.39 and 2.40). Smooth rods may be used but normally threadedrods are preferred. The most frequently used glues are polyurethaneor epoxy glues, which (as opposed to resorcinol glues) also bond to steel.
The axial load-carrying capacity of glued-in bolt joints increasesapproximately with r/ where I is the glued-in length. The joint is rela-tively stiff and failure is often brittle and stress redistribution betweenthe bolts not possible. In joints with several bolts there is a risk for
Fig. 2.40 Joints made with glued-in boh
90
Construction products
Fig. 2.41 Punched metal plate fasteners
uneven load distribution over the bolts: if a bolt is overloaded and fails,progressive failure may take place (zipper failure). The anchorage lengthshould be sufficient to ensure that initial failure is ductile yielding in thesteel and normally mild steel is recommended.
2.5.7 Punched metdl plate fastenersPunched metal plate fasteners (also called nail plates) are 1-2mmthick steel plates with protruding teeth on one side. The plates onthe market differ regarding the shape of the teeth and their pattern(see Fig. 2.41). Some plates have only one tooth type whereas othershave two or more, e.g. short and stiff for high shear load and some
long and slender that serve to anchor the plate into the wood. Nailplates are mainly used as gusset plates pressed into the surfaces of thetimber sections they join. A typical area of usage is light trussed struc-tures, e.g. roof trusses (an example is shown in Fig. 2.42), but theplates are also suitable for other structures made of boards and plankswith the same width.
Fig. 2.42 Truss rafter with punched metal plate fastener joints
91
VPractical desip of timber structures tct Eurocode 5
Fig. 2.43 Reinforcement of end notched beam
A typical shear load-carrying capacity is about 5 N/mmz, i.e. the area
,-r""d"J to transfer a load of 1 kN is about 200 mmz.
The external pressure needed to press the plates into the wood is
considerable - about 5-6N/mm2 - and the whole plate should be
pressed into the timber in one operation, which requires special press
equipment. The punched metal plate connectors are normally produced
in special factories operated by organisations which provide sophisti-
cated design and detailing software for the trusses. On some occasions
however, it is possible to mount the plates on site by hammering on a
stiff steel plate * see Fig. 2.43 for an example.
Normally the plates are electro-zinc-plated before punching. Experi'ence shows that there are no corrosion problems even though the edges
and sides of the teeth are unprotected. The general requirements toprotection of thin steel plates are shown in Table 2.28.
2.5.8 Nailing platesIt is possible to nail through 1- 1.2 mm steel plates without drilling. For
thicker plates it is necessary to pre-drill the steel plate. Nailing plates
with pre-punched 5 mm holes spaced at 10-20 mm are available up
Table 2.28 Minimum protection requirements for nail plates and thin steel plates
Description Service class
Construction products
Fig.2.44 Gusset plate cut from plate with pre-punchedholes (4mm ring shank
nails or 5 mm connector screws are placed in the marked holes)
to 1.3.3m2 from which plates or strips may be cut as desired. Anexample is shown in Fig. 2.44.
2.5.9 ConnectorsBolt and screw joints may be reinforced by connectors located between
the faces of two timber parts. There are two connector types: inlaid and
pressed-in connectors. The first type consists of cylindrical rings or discs
placed in milled cut-outs. The second type consists of plates with teethalong the perimeter pressed into the wood. Inlaid ring connectors are
shown inFig.2.45.Pressed-in connectors are marketed under the brand name Bulldog.
They are made from thin steel plates from which triangular teeth are
pressed up along the edge(s) (see Figs 2.46 ar'dT-.47).Therc are twotypes: two-sided and single-sided tooth-plate connectors. The two-sided tooth-plate connectors are used in wood-to-wood joints. Themiddle hole for the two-sided connectors is larger than the boltdiameter, i.e. the shear force in the joint is transferred from the
timber parts through the teeth. The single-sided tooth-plate connectors
are aimed at steel-to-wood joints but may also be used for timber-to-timber joints, making it possible to separate the parts if desired at
some stage. They may also be used in pairs (back to back) where it is
not possible to press the parts together during execution. The hole forthe single-sided connectors is 0.5 mm larger than the bolt diameter,
and the bolt edge is reinforced by a bulb, making it possible to transfer
load from the connector to the bolt. Typically the lateral krad-carrying
capacity of the bolt connection is increased by a factor of 2-3.
Fig. 2.46 Single-slded Bulldog connector. One connector js used in steel-to-woodjoints. In wood-to-woodjoirrrs, rwo conncct{rrr ure used if the parts need to be
Bulldog may be round, square or oval with diameter/side lengths
between 50 and 130mm (see Table 2.29).
In most cases connectors are delivered unprotected just oiled or oil
varnished. It is, however, recommended to use hot'dip zinc treated
connectors in severe environments.
V
Fie.
94 95
3
Structural examples
3.L IntroductionThis chapter gives examples of timber structures. The purpose is not tocover all structural possibilities but merely to give a survey of often-usedsimple structures with typical dimensions as inspiration and help fordrawing and design. More complicated structures made by combiningstraight and curved beams and panels are only dealt with briefly.
3.2 Main and secondary membersIt is often possible to distinguish between a main and secondarymembers. In the example shown in Fig. 3.1 the main members arethe glulam beams supported by concrete columns and the secondarymembers are the structural timber joists. In the example shown inFig.3.2, the main members are trusses with punched metal plateconnectors, spanning from faEade to faEade and the secondary membersare the members spanning between trusses. In the example shown inFig. 3.3 the glulam arches are rhe main members and the glulambeams are the secondary members.
The secondary members themselves may in some cases be regarded as
main members with secondary members. For example, in Fig. 1.1 thedeck may be regarded as a secondary member relative to the joists.
If the distance between the main members is not determined by thelayout of the structure, the following may be used as a guide. It is normallyeconomical to have a large distance, d, between the main members. Themoments and consequently the required section moduli increase propor-tionally to a, but.tlle required section dimensions increase as an approx-imation only by a1l3 and the required timber volume by s2l3 .The n,rmberof ioints and foundations are the same, i.e. the costs per unit area willdecrease with the distance. on the other hand, the costs of the secondarymembers increases as the distance between main members increases, asshown in Fig. 3.4 where an optimum distance can be found.
As an alternative, an often-used optimum distance is:
aopr: tfl
The above expressions are illustrated in Fig. 3.5.
Cost per m2
Optimal main members
3.4 The optimlon distance is the one thnt resuhs in mtnimum total costs
05101520SPan, / in m
Frg. 3.5 Optimum distance between main structures
Examples of structural members are shown below.
Solid beams
Beams of srrucrural timber with a distance o( l-2 m may be used for
spans up to 7 m. Normally hlb ts 4 to 8 where h is the depth and b is
rhe width or rhickness. Beams deeper than about 6b require special
bracing to avoid lateral instability.Glulam beams may be produced with any length but longer spans
may utilise other rypes of structural components such as trusses'
Simply supported single.span beam
b>bl7h - tl70 to IlIT
Continuous beam
b>bl7h - ll25 to ll20
Continuous beams of structural timber may be made as coupled
beams with the double cross-section over the support' where the
moment is the largest. The beams are joined by nails or screws'
7 Structural examples
9
8
7
6
E5
2
1
0
Structural timber
(1.3)
^^itllt
t
Frg
98 99
Practical desigt of tintber structures to Eurocode 5
Glulam beams may be tapered or pitched.
hmiddre * Il20 to llIA
Glulam beams may have one or several curved parts.
An architecturally interesting structure is called a boomerangbeam, i.e. a pitched beam with curved underside. With downwardload the moments will try to straighten the beam, which results intension stresses perpendicular to the grains thar weaken the beamconsiderably.
The problems may be avoided by using a rension rie,space utilisation.
but it limits the
In houses it is common to use collar ftusses with roof inclinations of35-55" and spans up to 12 m. The horizontal reaction shall be takenby the deck or a tension tie. These are somerimes called raised tietrusses or 'A'-frame trusses.
100
F Structural examplcs
Tru.s.se.s
Countless types of trusses are produced' Slender closely spaced
trusses (usually at 0.6 m spacings) with spans up to about 20 m are
almost always produced with punched metal plate fasteners.
The roof inclination forspans up to 25 m shouldbe greater than 15', i.e.
h - I17.
--<<K1 -=.2<-<l
The mid-depth h should be
about If 7 for mono pitchbeams.
Scissor trusses are made
with roof/ceiling inclina-tions of:
Q5-3A")100*15"), i.e.
f - tlr0 and (f +h) - ll5
For parallel N- or V-TTUSSCS:
h - I19 to ll14
Large trusses are produced with flanges of glulam or LVL and steelgusset plates or brackets with bolts or dowels.
101
Prttctical desig of titnber structures to Euxtcode 5
V-girder trusses supporting sports hall roofTypes of trusses.
because of the problems withand arches are often made as
.,,:t;1.
,l'!i'ltIi
Portal {rame
Typical dimensions forspan l:
Maximum depth:h - 0.031
Depth at foot: hf - 0.9hDepth at top: h, - A.5h
\X/idth: b - 0.18h
Vaulted
Practical desig of timber structures to Eurocode 5
The curved corners that limit the usability may be avoided by joiningstraight beams with 6nger joints. The joints weaken th" ,tr"rrgth-urrdthe required depth is increased by z0o/o. To reduce th" ,ir"r,gtr,reduction a middle piece is ofren used. The two straight parrs mayalso be joined by gusset plates with mechanical f"rt..rJrr.
Middle piece
Arches and" cupolasw_ith large-span (up to rzom) arches with depths of about 0.02-0'011are required. The closer the centre line is to the line of thrustthe smaller the required depth, but the bigger the problems withunintentional deviations from the assumed geometry.
Beams - straight and curved - can be brft togett er to form pyra_mids and cupolas.
85m
A glulam arch lna
r04
sports hall
105
vStructural examples
Erection of glulam poral frames
4
o,.6,,1 is the design tensile stress parallel to grain and f.g,a is the designtensile strength parallel to grain. Ar., is the effective cross-sectionalarea, i.e. the total area reduced by areas of slots, notches, boltand nail holes. Reductions of the cross-sectional area may be ignoredfor nails and screws with a diameter of 6 mm or less driven withoutpre.drilling. When assessing the effective cross-sectional area at ajoint with multiple fasteners, all holes within a disrance of half theminimum fastener spacing measured parallel to the beam from agiven cross-section should be considered as belonging to that cross-section.
It should be remembered that for srrucrural timber the designstrength may be increased by the factor
Straight members and beams with uarying depth
Example 4.1
=30 >40 >30#bt_---- 1
The tension member shown in the figure above is loaded in the
member (grain) direction by a dead load of 8 kN and an imposed
load of 25 kN.The tension member is made of material C16 and it has a
rectangular cross-section with thickness 75 mm and width b. The
load is transferred ro rhe member through an 8 mm thick steel
plate in a 10mm slot by four lOmm dowels in 10mm holes' The
minimum width due to the required dowel distances is
30+40*30:100mm.
Service class 1 (indoor)
Find: The member width b.
The design tensile strength parallel to grain .f,,o,a it with f,.s.1 : 10 N/mm2 and 'yu: I.3:
Dead load (k*od":0.6): /,,e,4 : 0.6' lOll'3 : 4'6lN/mm2
4.1,1 Tension parallel to grainFor beams loaded by concentric tensile force parallel to grain F,9,; itshall be verified that:
orr,o., a I"fr,o.J
io -oiilll=zol i
lliio roi
I
Fr,o,d
An",ot,Ad:
(4 1)
(4.2)
kn:-i"{ (+l'
106
(4 3)
Fa : 1.35. 8 + 1.5 . 25 :48.3 kN
r07
Practical desien of timber structures to Eurocode 5
For an estimated width b :175 mm the effective area becomes:
A"ff : (75 - 10) . (125 - Z.tO): 6.83 . 103 mmz
t: (i#)o':ro4<The combined stress index:
for dead load:
(10.8 . 103)/(6.83 . 103)
(1.04 . 7.38)
where:
, /V*l\o'"_l
_\V/
os.9g,4 is the tensile stress perpendicular to the
reference volume for which f 96 is defined:
o for glulam: Vuf :0.01 : 10 ' 10 3 m3
o for structural ti-b"r, V,"{ :0.57 ' 1O-3 m3.
Oc9O.d . 1-..:-\I
/c,90,,,1
oc.eolf .J a 1
kc,oO.fc,90,d
F..90.,1ut.9a.e{f d - ""ff
where:
A41 is an effective contact area;
Srrarghr members and beams with uarying depth
(4.7)
grain and V,"1 is the
(4.8)
(4.e)
(4.10)
V
r.3
:#:0.21 <
for dead load and imposed load:
98.1jo'_)/g.8L1o') i.o8(t.04.9.g5)
-------1 : toJT: o'69 ( I
4.1.4 Compression perpendicular to the grain
Block be aring compression
Where a large surface area of a timber member is exposed to a uniformcompression stress o.,9g.4 perpendicular to the grain (e.g. at continuoussupports), it shall be verified that:
4.1.2 Compression parallel to grainFor a short column (with no risk of instability failure) loaded by a com-pressive concentric force F.,s,; parallel to the grain, it shall be verifiedthat:
() ^ I-'" ( 1
/.,0,a -
where:
F.,,JO^):-
An",
RaiI bearing compr ession
Where a beam is exposed to a concentrated pressure over a small surface
area, e.g. at a support, it has been shown experimentally that thecompression capacity becomes larger than the pure material strengthperpendicular to the grain. This is especially the case if the structureis not sensitive to the effect of deformations due to the compression.
The reasons for this effect are that not only the wood fibres directlyunder the load carry the load but also the neighbouring material and
that the resistance increases with increasing compressive deformation.To take this into account, Expression (4.8) is replaced by:
The effective area Ar,", is calculated similar to a tension member.However, also holes in the compression area may be disregarded ifthey are filled with a material stiffer than the wood. For columns, reduc-tions from symmetrically placed holes may also be disregarded.
4.1.3 Tension perpendicular to the grainWhere a volume, V, is exposed to a uniform tensile stress perpendicularto the grain (as in a curved beam), it shall be verified that:
or.9Ad , 1
-\l
kvol I t.9a d
108
(4 4)
(4 s)
where the effective design stress perpendicular to the grain is calculatedAS:
(4.6)
t09
Practical desig of timber structures to Eurocode 5
lra>30mm
A"n> b(l + 60 mm)(b)
Fig. 4.1 Beam loaded perpendicular n the grain
k..96 is a factor taking into account the load configuration, thepossibility of splitting and the degree of compressivedeformation.
The effective area should be calculated as the actual compressionlength I increased at each end by 30 mm, but not more than a, I or\12 (see Fig.4.1(a)).
Unless otherwise specihed in the following ke6 shall be assumed to beunity.
For members on continuous full supports, provided that 11 > 2h (see
Fig.4.1(a)):
o kso : 1.25 for solid softwood timber. kqo : 1.5 for glued laminated softwood timber.
For members on simple supporrs, provided that h > 2h (see
Fig. 4.1 (b)):
. kso : 1.5 for solid softwood timbero kso : 1.75 for glued laminated softwood timber
where h is the depth of the member and I is the contact length.
110
Srrarghr menibers and beams with uaryhtg depth
4.1.5 Load at drl orngle to the grain
TensionFor a timber beam that is loaded in tension in an arbitrary directiondefined by the angle o between the load and grain, it shall be verified that:
-nffiA"t 2
,b,t-- t
nffi
o:'"'o < lt,,n,a -
where the tensile
(4.11)
AS:
(4.t2)
111
strength in the load direction should be taken
f t.o,rtf t,eod
b(/ + 30 mm)
Example 4.2A timber frame wall is made of studs with cross-sectional dimensionst x b : 44 x 145 mm and a centre-to-centre (clc) distance of600 mm. The bottom sill has the same width and is supported on aconcrete foundation. The load on each stud is 2 kN from dead load
and 8 kN from imposed load.
Seruice class I (indoor)
Verify that the load from the studs can be carried by the bottom chord.The characteristic compression strength perpendicular to the grain
is f.,so,L:2.2N/mm2. Th" design strength for load group M(hoa:0.8) and with 1a : 1.30 for structural timber is given by:
For dead load * imposed load, the design load for each stud is given
by'
F4 : 76G + ?0Q : I.35 .Z + 1.5. 8 : 14.7 kN
With an effective compression length of 1"6 : t + 2 . 3A : 44 *60: 104 and k.,96 :1.25 for structural timber on a continuoussupport the combined stress index is:
F6 14.7 .rO3oc,90,eff d
k,,sof ,,so,a
0.97:-1.69k,,esbl"ff f ,,es.4
:0.58 < 1
r.25 .r45 .r04.1.35
f t,o,af,,s.,r sinz a t ft,sodcos2 rr
Practical desip of timber structures n Eurocode 5
..'.N7 \>/ I
Fig. 4.2 Compressiue stress dt an angle a to the grain
CompressionFor a timber beam that is loaded in compression, as shown in Fig. 4.2, itshall be verified that;
oc,ad - ,
-\
lJr,od -
Straight members and beams with varying depth
angle. It is seen that for tension even small angles reduce the strengthconsiderably.
4.1.6 Bmding
Bending about one main axis
For beams loaded in pure bending about one of the main axes it shall be
verified that:
omd _MalW - ,
I^d l^d(4.r5)
where the compressive strength in the load direction should be taken as:
where:
o^,4 is the maximum stress caused by the design bending momentMa;
\(/ is the section modulus;
f^,a is the design bending strength.
Bending about two main axes
For beams loaded in biaxial bending it shall, except for rectangularcross-section, be verified that:
"P :2e *"+4 < r g.t6)lmd lmd Jmd,
where the bending stresses omd, om,yd and o^,",4 are calculated as:
(4.13)
(4.r4)
Figure 4.3 shows how the tensile and compressive strength properties
for the material classes C16 and GL24h are influenced by the load
1.00
0.90
0.80
o.70
0.60
0.50
0.40
0.30
o.20
0.10
a"
Fig. 4.3 Variation of tensile and compressiue snength at an angle a to the grain
directicn for C16 and GL24h for angla between 0' and 90'. In the insert: angles
between 0" wtd 5" . c : com|ressian, t: tensiorl
rt7.
t-fr,o.dk,,sofr,go.dlc,ad-ffi
(4.t7)
where W, and W. are the section moduli.For rectangular cross-sections and for other angular cross-sections it
shall however only be verified that the following two conditions are
fulfilled:
omd: o^.1.d * om,zd:H . H
o:o'o *u-?4 < tImtd Im,zd
k^?t! +"]A s tlm1d Jm,zd
where the coefficient k- equals 0.7.
(4.18)
(4.1e)
113
Practical design of timber structures to Eurocode 5
t Stress distribution in the y-yplane
Fig. 4.4 Stress distribution in a rectangular beam subjected to biaxial bending
The background for the modification is that for these cross-sections
the maximum stresses only act at small volumes close to the corners(see Fig. 4.4), and it is unlikely that the whole cross-section will fail ifthe bending stress exceeds the bending strength just in these small
volumes. The bending strengths for bending about the axes may be
different due to the depth factor k6.
Lateral instability
High slender beams can fail due to lateral deflection and torsion whenthey are loaded in pure bending as shown in Fig. 4.5.
Example 4.3
The purlins in a roof with slope 1:3 (a : 18.4') are spaced at L.Zm(measured in the roof plane) and have a span of 4.8 m.
rt4
Straight members and beams with varying depth
Timber C16. Serq.)ice class l.Loads:
o dead load: g : 0.3 kN/mz (meas,rred along the roof )
. snow: s : 0.4 kN/m2 (measured horizontally)r wind pressurer w : 0.5 kN/m2 (measured along the roof).
Find: an appropriate purlin size.
A purlin cross-section of 75 x 200mm is estimated. The design
moments from dead load (76 : 1.35) and snow load (18 : 1.5)
For the snow load where the load is given for the horizontal area
the final deflection is calculated as:
us,fin:5'9 'cos l8'4'0'910'3 : 16'5mm <ll26A
To calculate the load-carrying capacity of a straight elastic and simply
supported beam, it is assumed that the torsion is prevented at the end
supporrs and that the beam is loaded by two equal bending moments
M-: Mr ar the beam end. Under these conditions the beam will be
stable for loads below a critical value M : M.,. If this value is exceeded
the beam will suddenly deflect as shown in Fig. 4'6' Solving the
governing differential equations the following expression for the critical
Fig. 4.5 Lateral torsional buckling deformation of a simp\ supported beam
116
106 /-Mt I I ).
Fig. 4.6 Beam deflected in torsion and lateral deflection instabilitl
buckling moment is found:
M : M., :I lrr,or,,, [r
+ (;)'#| (4.20)
where I,r, is the moment of inertia for torsion and I* is the so-called
warping constant. The last term in the bracket is only of importancefor open thin-walled cross-sections. For the majority of cross-sectionsin timber structures I*f (lzl,",) - O and the expression becomes:
M*:;Expression (4.21) applies to beams with equal end moments. For othercases numerical methods, e.g. based on strain energy methods (virtualwork), are required. The results can always be written in the form:
M.r: Il,lf (4.22)
where 141 is an effective length of the beam. Eurocode 5 gives some
approximate values as shown in Table 4.1. As is apparent from Figs 4.5
and 4.6, the critical moment depends on the location of the load in
Stralghr members and beams with uarying depth
(4.2r)EI,GI,,,
EITGI"'
t17
Practical design of timber structures to Eurocode 5
Table 4.1 Effectiue length l"s as a function of beam length I and beam depth h(see Example 4.4)
Load acts in:
the bottom of the beam the cenrreline the top ofthe beam
/ R_-______________1 \*B
0.91
O.Bal
0.91 + Zh
0.8a1+ 2h
u.6l
E-tl-[q oer-o5h2B
I.-nc+AU.( tnl - 0.5h
ffin-41/'-i\
I \ r)
0.61 - 0.5h a.6l + 2h
the cross-section. The higher the location, the bigger the driving effectand the smaller the critical load. Loads acring below the axis ofrotation will even have a stabilising effect. This is taken inro accountin Eurocode 5 by reducing/increasing 141 as shown by 0.5h and 2hrespectively.
The torsion moment of inertia lru, of a rectangular cross-section withside lengths b and h(>b) is given by:
1",-+(t -ourl)
, zb'(h - h1))rror :6 _ 1i,
" ,r G* -t
For a closed box cross-section as shown in Fig. 4.7 , I,o, is given by:
For a rectangular cross-section, Expression (4.22) canbe rewritten as:
(4.23)
(4.24)
(4.25)
relative beam slenderness ratio has been
o^', M., 1
f^:wk: lt^*,
whereas for columns a
introduced.
118
Srrargfrr members and beams with uarying depth
b
Fig. 4.7 Box beam geometry and notation
From Expression (4.22) with characteristic values inserted:
M., 7To^'": fr: WIE;JF;il ('76)
For typical strength and stiffness values for structural timber:
n nnt )u. /o0 _o^.,: #Eo.ot g.Z7)
trffh
Until now linear elastic behaviour has been assumed, i.e. o^gf f^1 Iabout 0.5 and ),n,,"; > about 1.4.
Tests to determine bending strength are normally performed onbeams with )^.,.1 - 0.75.|n Eurocode 5 the following expression foroudlf^d is given:
_ (lk,,:\4: { 1.56_ 0.75^^,,,.t forI^d
It/^1",,.,Expression (4.28) is shown in Fig. 4.8.
k",'I
0.8
0.6
0.4
0.2
00 0.5 1.5 2 2.5 3 3.5 4
1r.r"t
F
k.
),"1 ( 0.75
0.75 < ).^.,"11 1.4 (4.28)
1.4 1\^,,"1
Fig. 4.8 k* : o-,al f^.d ds d function of the relatiue slenderness ratio ).*,,"1
IT9
Practical design of timber structures to Enrocode 5
Example 4.4
IFt
ffi loz'rt' 2.S, 7.5m | 0.14 mN-'- + "-" + H
A simply supported glulam beam (GU2c) with cross'section dimen'sions 115 x 700mm has a lengthof 10m. The load is a short'term
load F acting on the top of the beam' The ends of the beam are
restrained against torsion.
Service class 1.
Find: the maximum value Fn ".
For a load acting at the centreline the effective length according toTable 4.1 is:
Ly : (0.8 '4'A.75 '0.75) ' 10 +2 '0.7 :7.4m
'!(ith Ee.s5 : 11100 and f^1,: 32N/mm2:
0.78b2 - : g 19. 1rloo : 22.rN/mm,om.c,: Irnh "o.ot
where the bending coefficient k- is equal to 0.7 for rectangular cross-
sections.Combined bending, axial compression and buckling are dealt with in
Chapter 5.
Practical design of timber structures to Eurocode 5
Fig. 4.9 Single taperedbeam
4.2 Tapered beamsBeams are sometimes tapered in order to obtain a suitable geometry (e.g.
roof slope) or to tailor the size to the force distribution or architecturallybe attractive. Figures 4.9 and 4.10 show two types of beams commonlyused in practice, namely single tapered and double tapered beams. It is
common practice to cut/taper the {ibres on only one side of the beams,
normally the top/compression side and that the fibres on the other side(normally the bottom/tension face) are parallel to the span.
In derivation of some of the following equations, it is assumed thatthe beams are simply supported, but the equations may also be used
as an approximation for other cases, e.g. for the calculation of thestraight parts of arches, see Chapter 6.
4.2.1 Single tapered beamThe stress distributions in tapered beams differ significantly from thoseof beams with constant depth. Both the normal stresses and the shearstresses vary significantly over the cross-section depth and along itslength (see Fig. 4.9).
In single tapered beams, the bending stress increases slightly at thebottom face and reduces at the top face. A lateral load also inducesnot only axial stresses but also stresses perpendicular to the {ibres.The reason for this is that the normal stress parallel with the top surfacerequires a vertical stress colnponent to fulfil the equilibrium conditions.These effects are taken into account by reducing the bending strength
Fig. 4.10
r22
0.5/
hr,n,-l @iA
---!I| 'ma\ I
Double tapered beam
t23
7 Straight members
by a factor k- and it shall be veri{ied that:
.t-'1 alk,,n1,,, l-
where:
t'*m.{r.t
a-.,1 is the design bending stress:
6MaOm.J- ttl
Dn'
For tensile stresses parallel to the tapered side:
and beams with warying depth
(4.35)
(4.36)
For compressive stresses parallel to the tapered side:
k-.,r..
(4.37)
(4.38)
shown infactors for
The reduction factor k,n', for compression and tension is
Fig. 4.11 for glulam GL32h and GL24c. The reductionother grades of glulam will fall between the rwo grades.
1.00
0.90
0.80
0.70
0.60
6 0.50
0.40
0.30
0.20
0.10
0.0001234567
a: degrees
Fig. 4.11 Reduction factors k,,,.n for glulam GL32h and GL24c
Practical desip of timber structures to Eurocode 5
For single tapered beams, the maximum bending stress is often at across-section near the shallower end of the beam. The critical cross-
section may be found analytically but it is often easier to calculate thestresses in several cross-sections along the beam. For a simply supportedsingle tapered beam with a uniformly distributed load q, the distance xfrom the shallower end of the beam to the critical section is given by:
, l-,r,v
- I-
h*l h^in
where the stress is calculated as:
O.75qtz
bh,^h*The deflection may be found by the principle of virtual work. For thebeams mentioned above, the largest deflection becomes:
umtx.: kdtfl"ruo
where the deflection constant k4"p, is given in Fig. 4,I2. The deflectionu6 is the deflection in a corresponding beam with constant depth equalto h^"on : 0.5 (h.in + h,,,^),
4.2.2 Double tapered beomsFor a simply supported beam (see Fig. 4.10) with uniformly distributedload, q, the distance x from the shallower end to the critical cross-
section with the maximum sffesses is:
(4.42)
and the maximum bending stress is:
O.75qt/(4.43)om:
bh^i"Qh.,,r -h^^)The bending deformation of the beam results in tension stresses perpen-
dicular to the grain direction under the apex point (cross-section C inFig.4.10). The distribution of the tension stress, or,9o, is as shown inFig. 4.10. The normal stress at the top becomes zero because of thediscontinuity in the slope of the upper surface. The maximum tensilestress may be calculated by the expressions given in Chapter 5. Theywill, however, rarely be of any importance.
For the deflections, Expression 4.41 applies.
t24
Straight members and beams with varying depth
1.20
1.15I
*E l.to
1.05
1.00
n*1dln*
1.4 1.6 1.8 2 2.2 2.4h^rJh^n
Single tapered beam
(4.3e)
(4.40)
(+.4r)
1.2
Fig. 4.12h*lh^
Relation between
, h^inx: L zh*
1.4 1.6 1.8 2 2.2 2.4 2.6 2.8h*Jh,i,
Double tapered beam
the deflection factor kp11", and the (taper) ratio
125
Practical desip of timber structures to Eurocode 5
Serqtice class LShow that the load-carrying capacity is sufficient.
The cross-section with the maximum stress is placed at a distance xfrom the middle towards the shallower end.
The moment is 0.5Fx, the depth is h(x) : 0.40 -10.6x19, and thebending stress is:
0.5Fo(x\: -_:bh(x)'16
The maximum stress is found in the middle of the beam, see thetable below.
With a:3.8" the reduction factor on the top surface where thefibres are cut becomes k^.o,r:0.936
The instantaneous deflection in the middle of a
constant depth of 700 mm is calculated as:
FPua:4gFil
12.90. 103(9. 1o',)',
beam with a
: 30.4 mm48 .r3.7. 103 . 115 . 7003
From Fig. 4.12 with h*o*/h^n: 1000/400 :2.5, the deflectionfactor is found to bek6"n",r: 1.18 and the deflection:
u^,t : 1.18 ' 30.4 : 36 mm
The deflection for the characteristic load is approximately 70% ofthis value.
t26
Fig. 4,13 Illustration of shear force H acting on an arbitrary cross-section
r27
Straight members and beams with uarying depth
4.3 Shear
4.3.1 GeneralTimber beams can be subject to large shear stresses, especially close toconcentrated forces and near supports. Shear stresses can also be caused
by a torsion moment applied to the beam.
The effect of an external shear force V. in the z direction of a beam isillustrated in Fig. 4.13.H is the horizontal shear force induced bv %on the cross-section with unit length. H is equal to:
4.3.2 Shear stresses cdused by bendingFor beams with shear forces it shall be veri{ied that:
!.rJ,,,t -
SH:)VI)
.s. __S,.,,T,: jV, andott '' - hl, u,
The resultant shear stress is found by vector addition as:
where S, is the static moment of the shaded area about the y-y axis. Theformula applies irrespective of how the cut is made.
To determine the corresponding shear stresses it is necessary toestimate the distribution over the cutting surface. For thin-walled cross-sections a uniform distribution over the thickness may be assumed. Thesame applies for rectangular beams for cuts parallel to one of the sides.
For a rectangular beam with the shear forces V. and V, and the cuts1-1 and 2-2 shown in Fig. 4.l4,the shear stresses are calculated as:
(4.44)
(4.45)
(4.46)
(4.47 )
'l ,z
I
I
I
I
I
I
I
I
!
I
I
I
I
I
v
2 t
vy
ffid1i]]@*si* *
A
v.
Practical design of timber structures to Eurocode 5
1 tzTFig, 4.14 lllusnation of notation used for determination of sfuar stesses for abeam with rectang.llar cross. section
For a beam with rectangular cross.section with depth h and width b,and with a shear force V in the direction of h, it shall be verified that:
Straight'members and beams with varying depth
4.3,3 Beans with end rwtclwsFor a beam with a notch at the support, there may be a risk of crackingfailure along the paths shown in Figs 4.L6(a) and (b), due to stress
concentrations at the notched corner. Initially the crack is stable, butwith increasing load the crack propagates and results in total collapse.
For the notched beams shown in Fig. 4.t6, it shall be verified that:
,{)t){-,\Jz''
/r/x\'-z tn,'ui"'
where krrorl, is a factor that takes into account the effect of end cracks:
3V--<. 1
2 hk,,*1,b = '
( 0.67 for strucrural timberk,,o,k : { O.OZ for glulam
I t for other wood.based products
(4.48)
(4.4e)
According to Eurocode 5, loads within a distance h from the end maybe disregarded (see Fig. 4.15). For beams this reduction applies onlywhen the notch is on the opposite side of the support.
Fie. 4.15 For calculation of the shear force V, Ioads closer to the support edgethnn the beam depth h or h41 may be disregarded
r28
For a beam with the end notch at the compression side (see Fig.
4.I6(c)) the reduction coeffi.cient ku:1, whereas for a beam withthe notch at the tension side (see Fig. 4.I6(a) and (b)), the reductioncoefficient factor should be calculated as:
rd -r5
vd <1ef*- ''' btknhf,n -
k": '"i"{ ir,}(t;- +oBp\/;-t - az)-,
(4.50)
where:
ahh"tropi
(4.51)
is the distance from the reaction to the comer of the notch;is the beam depth (in mm)is the effective depth (in mm): h"ff lh: alhis the notch slope.
Practical design of timber structures to Eurocode 5
+,"t
(a) (b) (c)
Fig. 4.16 Rectangular beam with end notches: (a) sharp notch at the tension side;
(b) inclined notch at the tension side; (c) inclined notch at the compression side (it
should be noted that there is no crack pattem as the notch is in compression)
0.40
0.20
0.000.3 0.5 0.7 0.9
c
Fig. 4.17 The influence of beam depth and notch depth on the factor ke forglulam beams. The figures are beam depth in mm
1.00
0.80
0.60
for structural timber
for glulam.1.5
k,:l+1.11:t/t
The influence ofthe beam depth and the notch depth on the factor k"
is illustrated in Fig. 4.17 that corresponds to k, :6.5 (for glulam) anda A<
u,: {z u
(4.52)
(4.53)
Example 4.7
130
:0.44
13r
Straiglit members and beams with lzrying depth
A concrete form is supported by beams of class CIB with 500mmcentres. The beam span, measured between the centre points ofthe supports, is 2.5 m. The depth of the end notch is limited to75 mm. The short-term desi.gn load is 4a:3.OkN/mz.Service class 3 (outdoor).
Find a beam with sufficient strength and stiffness.
The design bending and shear strengths for C18 are:
f^d: O-7 '18ll.3 :9'69Nlmmz
f,,a - 0.7' 3'4 I I.3 : 1'83 Nlmm2
The design bending moment is:
Ma : 0.5 .3.0 .2.52 /8 - 1.17 kNm
The necessary section modulus:
w :1.1.7 .ra6 p.6g : t|r. 103 mm3
Possible cross.sections:
for 38 x 200: W - 253. 103 mm3, A : ?600mm2
for 47 x 175: W : 24A. 103 mm3, A : 8225 mmz
va : 0.5 . 3.0 . 1.7. : 1.80 kN
For 38 x 200:
h: 200mm
h"r : 75 mm
a:50mma:h41fh:0.375
0 : alh: 501200 - 0.25
,-V
l.nKi-v
L -<,!n-J
According to Expression (4.51) the reduction facror is:
k,:5h (A:r;: t:C+ o.B . o.zsl$- a*)-'
Practical design of timber stnrctures to Eurocode 5 Straiglit members and beans with uarying depth
For a circular cross-section with a radius r the maximum torsion shear
stress is:
2Trto,.mox: i- where T is the twisting moment (or torque) (4.55)
7fr
For a rectangular cross-section h x b with h > b the maximum torsionshear stress is:
Pure torsionFor beams loaded in torsion, the torsion shear stresses 4o".2 must fulfilthe following condition:
,rlr,O < l.zIu,a -
t32
(4.54)
133
5
Columns
5.1 IntroductionA member loaded by a compression force is normally called a column.
5.2 Axially loaded columnsFor a column with cross-section area A, loaded by an axial compressionforce F. that induces a compressive stress o{ or:Frf A, it rn"U b"verified that:
-c
/.J. = I (5.1)
where k. is a factor (/.. < l) called the corumn factor, is derived in thefollowing Expression for k.
For the column shown in Fig. 5.1 it is assumed that it may deflect inone of main axes directions. The corresponding second moment of areais I and the elastic buckling stress is equal to the Euler stress op:
nzEI nzE
I2A - ^z
(5 2)
where ): lli,-l is rhe free column length, i is the radius of gyration:
= /IlA and I is the second momenr of area (moment oflnertia).
Traditionally, the slenderness ration ) is used to describe the slender-ness of the column. In the following it is, however, found more conve-nient to use the so-called relative slenderness ratio defined by:
TT\ \ I lr:Ar.t: Ar/;+ (5.1)
With this relative slenderness ratio, Expression (5.2) becomes:
(5.4)
In practice, all columns have certain imperfections. They are oftennot perfectly linear, and the load can act with some eccentricity due
134
opIl, ).'.'
Columns
Fc = ocA
I
Fis. 5.1 Simp\ supported, axially loaded coltunn
to knots. As an approximation it is, therefore, assumed that the column
in the initial situation has a sinusoidal defection with the eccentricity e
in the middle of the column (see Fig.5.2). Thrs means that the axial
force will give a moment M^iy: F.(ef u^i1) in the middle of the
beam where u^i4 is the deflection of the beam.
The governing differential equation for static equilibrium of an initi'ally deflected column is given by:
^-d|u ^/ 7rx\O, al: -f,l - -f. ltt + e tr"T
)The resulting centre deflection is given by:
ocUmid:
oE*o,
e*umid-s1s-o' kE
orl:'k' - o*
(5.5)
(5.6)
(5.7)
where kp is de{ined from the Euler stress as kr: oplf,. In the mid-height of the column the normal stress is a. and the bending stress is:
o^:F,(e lu^i,t)lW :# C:mFailure corresponds, see Expression (4.29) to:
oc om
f,n' f-giving:
oc . orAe_r_
f,o' wf.o',jf, : k,
kE-1 (5 8)
kp - o,lf,
I
Fig. 5.2 Simply supported, axial$ Ioaded column with initial deflection
t35
Prttctical design of timber structures to Eurocode 5
that is:
t(t*eAL'o I \:,
from which with:
(5 e)
then:
k,:u+r,F-\ (5.10)
Since all grading rules for srrucrural timber resrricr the initial deflec.tion to a fraction of the length l, and since ),"1 is proportional to I, itwould seem natural to set e proportional to ),"1; but this results ink. ( 1 even for small values of ), which is in contradiction to the factthat the compression strength is found by specimens with a slendernessratio, A, of about 15, corresponding to )ret.o : 0.3. It is instead assumedthat:
r Columns
(5.11)
(s.r7)
(5.13)
(5.r4)Figure 5.3 shows k. as a function of ),"i. For ),.1 < 0.3, k. - 1.0.
The load-carrying capacity of columns depends very much on rhestiffness of the column as a whole and local reductions in the cross-section area have only small effect. k. is, therefore, calculated withthe properties of the toral cross-section. The stresses shall however becalculated for the reduced cross-section. The biggest reductions arenormally found at the ends where it shall be verified that:
eA {.
w i:6()"1 - )"'16)
where:
. ( 0.2 for srrucrural rimberl): <"
I O.t for glulam
,\r.1.3 : 0.3
that is:
k : 0.5[1 -t g(\,a - 0.3) + ^7,a]
or.nrt( F.
f, frAn"u' '
t36
1
0.9
0.8
0.7
0.6
r" 0.5
0.4
0.3
0.2
0.1
0
2.Ol>2.51
Fig. 5.4 Theoretical free column lengths and recommended effectiue lengtlr for
,iir^n with restraint support conditions made b1 mechanical fasteners
I
I1.0/1.0/
k =05('.# #;)
Fig. 5.3 Relationship between column factor k, and )',r1 for strucmral timber and
glulam
where Ar.,, is the reduced cross-section area. If the cross-section varies
over the iength, the calculations are normally made with the smallest
cross-section over the middle third of the length'
For types of support (boundary) conditions other than simply
supportJ, the same expressions are used as an approximation' with
the free column lengths (effective lengths) corresponding to the support
conditions. Where support restraints depend on mechanical fasteners
the effects of slip in lhe joints shall be taken into account by using
conservative ,rulu", for the column length' see Fig. 5.4 unless a more
stringent analYsis is made.
k
I
Io.7l0.85/
I
TI
I
I
)_0.5/o.7l
TheoryRecommended
(5.15)
t37
Practical desigrL of timber structures to Eurocode 5
Example 5.1A simply supported column of timber class C16, with length 4.0 mand cross-secrion dimensions of 150 x 150mm is loaded by rho.t-term load under service Class 1 conditions.
5.3 Laterally loaded columnsA simply supporred column that in addition ro an axial force is loaded bya lateral load inducing a moment with a maximum value M6 at themid'height is considered. The bending srress from M6 is o.. Ftr prac-tical reasons o- is defined differently from that than in Expression(5.8) where o^ for the axially loaded column is the bending stress inthe initially deflected column.
It is initially assumed that the column is loaded in the plane of one ofthe main axes and restrained against deflection perpendicular to thisplane (see Fig. 5.5).
138
Columns
o.W = Ms
+
Fig. 5.5 Laterally loaded, simp\ supported colwnn with initial moment Ms in the
mid-hetght of the column
In principle, the calculations are the same as for the concentrically
loaded column, but with a formal initial eccentricity in the middle of
(e + M6/F.). Due to the axial force this moment is increased by the
factor o,f (o, - op).
For a laterally loaded columns it shall be verified that:
@
#,,**Ttt (5.16)
(5.1 7a)
(5.1ib)krro^,y I on' <lf,,
Fc
#
[lllllL_l
@
If the column is not simply supported or if the moment is not maximum
in the middle, o- should be taken as the moment that is increased
substantially due to the deflection.For the general case with bending abour rwo axes ir shall be verified
that:
or_k..,.f..0 '
where:
k.., is the column factor for deflection in z axis direction (bending
about the y-y axis);k.,, is the column factor for deflection in the y axis direction
(bending about the z-z axis);
k,n is the factor taking into account that it is unlikely that total
failure takes place when the strength is exceeded in one cross'
section corner only. Normally a value o{k^:0.7 is used'
1i9
Tractlial desigrl of timber structures to Eurocode 5
Note that even when the bending moment acts about the y-y axis bothconditions shall be fulfilled to take into account u.,y .orrpiing effectsbetween the deflections. In practice the main axes are ri, ,r...rr"ryparallel to the sides of the cross-section because of knots etc.
V Columns
Example 5.2
A simply supported rectangular column of c16 with praned cross-section 44 x I45 mm and length of I: Z4OOmm, wirh a permanenrconcentric load of Fa: l7.0kN and a uniformly distributed lateralwind load inducing a design moment of Ma: l.5kNm at mid_height about the sffong axis is used outdoJs to support " ,oof.The column is in a service class 2 condition. The comjression sideof the column is braced in its full length.
Show rhat the column has sufficient load.carrying capacity.f ^ 17
?: #o :0.00314
For axial compression load alone:
Permanent load:
12 000o a,: - 1.88N/mm2" c'u'd 44 . 145 -
hoa: A'6
'Yu: L'3
fc,od:0.6' 17 lI'30 : 7.85 N/mm2
i:4[.9mm
^:74A0141.9 : 57.3
,T")*, : I
^1ry -s7 '3 ,/dn6r4 : r.oz4lT'V Ep 7r
From Expression (5. 14) :
lc : 0.5[1 + 0.2 . (I.oz+- 0.3) + t.oz42] : 1.097
From Expression (5.10):
,1l'-:-Al'1 1- 1.097 + \/1.097t - 1.0242
From Expression (5.16):
ocd 1.88
Cffi: d.6?1 . zs5 : o'36 < 1
For axial load and momenr:
The wind, which is classed as instantaneous, determines k_o4.service Class 2, k^oa: l.l:
fc,od : I.I0 ' (17 /L 3) : 14.38 N/mmz
f^d - |.rc' 0611.3) : l3.54Nfmmz
o^d :1.5 . 106 .6194 .r45\ :9.73N/mm2
From Expression (5.16) :
oc.d *o^.d - 1.88 _L 9.73
- n ro )_^ 1.)k,,tf,,a' f^,a 0.671.14.J9' 13.53-
v't' ' v'IL
cEJ76oa)E'6
.oqoo
Eoodo)coE
c0
Ma = 1'5 kNm
r40
:0.91 < 1
r4r
Practical design of timber structures to Eurocode 5
Example 5.3The same column as that in Example 5.2 is held against deflection inthe weak direction in the mid-height only.
Show that the column has sufficient load-carrying capaciry.
M= 1.5 kNm
1200 mm
The column may deflect in both main directions. Deflection abourthe strong axis is already covered by Example 3.2. Only checkingof deflection about the weak axis is required.
Therefore the load-carrying capacity of the column is adequate.
5.4 Lateral torsional buckling of laterally loaded columnsIn the examples above it has been assumed that the failure takes place
due to bending in the main direction. For deep, narrow cross-sections
loaded in bending about the strong axis a failure mode with combined
lateral deflection and torsion is possible or more likely. To take this
into account it should for \^.,"1> 0.75 be verified that:
(5.18)
where k.,, is the column factor for deflection in the weak direction and
k., is the factor for lateral instability, see Expression (4.28).
oc.J / o.,r,.t \2
[J.*-*(.ffi/ <r
r43
6
Curued beams and frames
Fig. 6.1 Stress uariation in a plane curued beam with constant bending moment
this effect. It is assumed that the normal stresses vary linearly over thebeam depth (see Fig. 6.2), i.e. the influence of the non-linear srress
distribution is disregarded. The force resukanr F on one half of thecross-section is F : l.5Mlh. Equilibrium of the marked elemenrloaded by F on both cross-sections and the stress o9o requires:
Curved beams and frames
6.1 Curved beamLoading a curved beam in bending will result in stresses both paralleland perpendicular to the beam (see Fig.6.1). The normal stresses inthe convex side of the beam are smaller than the stresses at the concaveside and the stresses at the concave side are larger than the stresses in a
corresponding straight beam. The reason for this is that even ifthe deformations vary linearly, the sffains will not do so because ofthe varying fibre lengths. Normally these e{fects are disregarded,i.e. the stress is for a rectangular cross-section calculated as for a straightbeam: lr r
oout: on: 6Mlbhz (6.1)
The bending stresses o- developed during the fabrication when thelaminations with thickness I are formed to a curvature I f r are theoreti-cally rather high. In the outermost fibres:
o^ : Etl(2r) (6.2)
These internal stresses reduce the load-bearing capacity of the cross-
section.For an elastic modulus E:l2O00N/mm2, a lamella thickness
t : 33 mm and a radius r : 5000 mm, the bending stress becomeso- : 4ON/mmZ, i.e. corresponding to the characteristic strength.Experimental results show, however, that the built-in stresses becomesignificantly smaller, probably due to creep that occurs during thehardening process where moisture from the adhesive is added.According to Eurocode 5 the strength values for bending, tension andcompression {or rf t < 240 should be reduced by the factor:
k.,,,. : 0.76 I O OOI I(<l)t
(6.3)
The bending moment results also in stresses perpendicular to grain.The following simpli{ied derivation of the transversal stresses illustrates
t44
Fd? : oesbr^dd0
FMogo:, :1.5,,DTmid Dhr^,4
(6 4)
where b is the thickness (widrh) of the beam.When the moment distribution tends to reduce the curvature, as is
the case in Fig. 6.3, the stresses perpendicular to the grain are tensilestresses and it is necessary to take into account that the strengthperpendicular to grain depends on the stressed volume. The relevant
\\
Fig. 6.2 Internal forces and rension srresses perpendicular to the grain direction ina curt,ed beam
111
/_l'/ \a--
/ ogo\
r45
Practical design of timber structures to Eurocode 5
Fig. 6.3 For a curued beam consisting of two straight parts joined b1 a curuedpart the strength perpendicular to grain depends on the uolume of the curved part
volume, V, is shaded in Fig. 6.3. To take into account the variation ofstresses over the depth, the volume should not be taken higher than2Vrurolf 3, where V,,,ol is the total volume of the beam. It shall be veri{iedthat:
(6.5)
The reference volume for glulam is V,"f : 0.O1mr. The factor k1;, takesinto account the stress variation over the depth. For a parabolicvariation from zero at the surface to a maximum value in the middleka^: 1.4.
Example 6.1
A glulam beam carrying a roof structure is supported by a doubleglulam column as shown in the figure above. The glulam is GL32hwith a thickness of 160mm. It has two straight parts AB and CDjoined by a 633 mm deep curved part BC. The fibres of the straightparts are cut at the bottom. The radius is 17 m. The beam is simplysupported at A and B and it is assumed that the roofing provideslateral stability.
t46
m=r^(Y)"
Curued beams and frames
The design load (dead load and snow) is 5 kN/m measured horizontallyand the beam is in a service Class 2 (i.e. outdarr protected) condition.
Show that the beam has sufficient strength.
Reactions and internal forces:
Ra.d : -5 ' lZ ' (Z 14) : -30 kN (uplift)
Rs,,] : 5 . IZ . (614) :90kNMbd:5 .$2lD: 160kNm
,, [5.8:40kNuu':t40-90:-5okN
Since r/r : 17 000133.3 : 51A.5 > 240, the strength is not reduceddue to the curvature, see Expression (6.3).
The design strengths are found using k-o1 : 0.9 (for snow) and
1u: I.25 (for glulam):
f^,,1 : 0.9' 32 I l.Z5 : 73.04N/mm2
f,,a : 0.9' 3.8 I 1.25 : 2.?4N/mmZ
f,,ead: 0.9 '3.311.25 : 7.38N/mm2
freod : 0.9' 0.36 1 1.25 : 0.26N/mm2
Bending calculations are relevant in B. The angle of taper is calcu-lated from:
tana : (633 * 300)/4000 : 0.083(a :4.76")
At the top where the cut fibres are loaded in rension:
6. 160. 106o :14.97 N/mm2"m'd rco .$32
k^,o
1
:0.667
t47
Practical desip of timber structures to Eurocode 5
om.d -
l+.97 : o 94 .< 1
h.,f^.a 0.695 .23.04
The maximum stresses perpendicular to the grain in the curvedpart are:
, _ Ma 160. 106 .)
ot.9r.d:t.f- -15 -:0.137N/mm2onr,61
- ''- 160 .633 .17 3l t
The stressed volume (corresponding to B*C) is approximately;
V - 0.160. 3.0. 0.633 - 0.30m3
f,,godkds(Yl'
The shear strength is adequate since:
ra_ 1.5.50000 _o)7f,,a 160 -633 .2.74
, 6Mot}m.i: l(O
-6nio
148
,_,(Y)"ot,9ad
6.2 Pitched cambered beamThe pitched beam shown in Fig. 6.4 consists of two single tapered beamsA-B and D-E joined by a'triangle'with curved underside with radius r.The fibres are cut on the top side of the beam.
The stresses in the triangle correspond in principle to those in a
curved beam - the axial stresses do not vary linearly and the momentalso induces stresses perpendicular to grain - but these effects aremuch more pronounced, especially near the apex where the normalstresses are zero because of the apex point. It is, therefore, notunusual to replace the construction by a curved beam with a separate'triangle'.
The maximum normal stress is found in the bottom side of the apexsection and should be calculated as:
Curued beams and frames
Fig. 6.4 Pitched beam with curved underside. B and D dre tangent. points
The maximum tensile stress perpendicular to the grain direction isfound just under centreline in the apex section and should be calculatedAS:
a- Ll," 6M,n
ot.ea.mu: kso;;# (6.i)onip
where Moo is the moment in the apex section where the beam depth ishoo. The factors k6 and k9e are:
ko : k, ., (*) ., (*)' . u- (*)'
kso:ks,*(H) .r(*)'where:
kr :1f 1.4tana +5.4tan2 a
kz:0.35-8tana
kt : 0.6 * 8.3 tan a - 7.8 tanz a
k+:6'u'-'2 o
ks:)2tana
ka:0.25 - 1.5 tan ct -f2.6tanz a
kt:2.ltana - 4tanz a.
(6 8)
(6.e)
(6.10)
r+
ld
(6.6)
r49
Practical design of timber structures to Eurocode 5
h.,
Fig. 6.5 Double tapered beam with straight underside
For a curved beam with a : 0: ks : O,ka : 0.25 and k7 : O and, inaccordance with Expression (6.4) , the transversal stress becomes:
o t,ea : 0.25 . 6M I (r-1abh)
For a double tapered beam with straight underside (see Fig.6.5),r : o( and the normal stresses in the apex section are, since a is
small, given by:
o^:
and
6Mdt)
6hlo
6M.-ot.9a:0'2a -lt
bh;D
The bending stress in Expression (6.6) shallrequirement:
Om.mux,J - 1,
r ) KcurvrJ rr.J
where k,,,," is found from Expression (6.3) with the curvature of theinnermost lamination.
For the tensile stress perpendicular ro grain it shall be verifiedthat:
- /11 r 0.2ot.9A.d lvr"{\7:<k;',(r7 I (6.14)Jr.9O,,l \ v ,/
where V is the volume corresponding to the shaded areas in Figs 6.4 and6.5, and
kai,: 1.4 for curved beams and for a tapered beam with straightunderside (see Fig. 6.5)
kau : 1.7 for pitch cambered beams (see Fig. 6.7).
150
(6.1 1)
(6.t2)
fulfil the following
(6.13)
Curued beams and frames
Example 6.2
A pitched cambered glulam beam of class GL28h is laterally braced.
It is in a service Class 1 condition. The lamellas are cut at the top
side. The beam thickness is 115mm. The design load from dead
load and snow is a short-term load q: 10kN/m measured on thehorizontal.
Show that the strength is sufficient.
The dimensions h,n;n:400mm and h :667 mm are estimated.
Vith the tangent points placed approximately 1m from themiddle, the angle of taper is found from:
rana : (667 - 400)/4000 :0.0668
a :3.8"ault:10-a:6.7Vd : (0.51 -h^;n)qcosc': (l0lZ - 0.4)cos3.8o : 46kN
f,,a : 0.9' 3.2 I 175 : 2.30N/mmz
17 t.5 'Vd 1.5 . 46 000 1.49
fr: m- ns 4so. Ln: fr: o'65
It is necessary to take into account the influence ofthe taper: For
the zone between A and B with compressive stresses parallel to the
tapered side. Therefore, over the length A-B, it should be verifiedthat:
om1 qax(l - x) , ,
f^,a-wf^,ak^,,='where:
f*d: O'g ' (ZBll'75) : 20'16N/mm2
and from Expression (4.38)
hrp:0'937
151
Practiccrl desip of timber structures to Eurocode 5
The calculations are given in the following table.
x: mm h: mm M: kNm \X/: 103 mm3 o-,4: N/mm2 o^1l(ln'f^d)
01000
2000
25003000
3500
40005000
400
467534
567
600
634667
843
3067
41805445
6t626900
76808530
t3622
0.0010.?8
t4.66t5.221.5.20
14.78
14.07
9.18
0.000
0.57 4
0.780
0.810
0.809
0.787
0.74e0.488
Vith a camber of the curved side of about 50 mm:
hop - 4A0 + 5000 tan 10o - 4000 tan6.7 - 50 : 797 mm
rrnid - rin + 0.5hdp : 11 000 + 0.5 ' 797 - 11 390 mm
hoplr^ta: 0.07
Lr : 1 * 1.4tan lO' + 5.4t"rr2 10o - I.415
kz : 0.35 - 8 tan 10" : *1.061
k: : 0.6 * 8.3 tan l0' - 7.8 t"nz loo : L82I
k+: 6t"r,2 10o : 0.187
ks:0.2tan 10o : 0.035
ko : 0.25 - 1.5 tan lo" + 7.6ranz 10o : 0.065
kt : 2.1tan 10o - 4 tanz IO" : A.746
ko : k, .*, (*) .u,(*)' .r(*)' : 1 346
kso : ks . *(*) ., (*)' : o o4t4
6.r25 ,rc6
0
4s80
94
105
tr4tz}125
om,mo&d - 1. 6Mrp
tr:towffi:r.346-0.72<l
t52
tr5 .7972 . 19.38Therefore, the strength for the changed structure is suffi.cient.
t53
Curcied beams and frames
ot,e,,rwx: t no# : a.04146 t'i?11*0: : 0.420N/mmz
6nip
ft,eod : O'g' 0'45 I l'25 : 0'32N/mmz
The volume loaded in tension perpendicular to the grain is:
V : 0.115 . {0.797 + 0.66?) . 1 : 0.17m3
\fith V,,f :0.01m3'
o,: (ffi)o' :0,,kr,.: L7
ot,90d *f \so,akrotkx
ot,90d *ft,solk*tka*
0.420
0.32-0.57 . t.7
0.r40.32 .0.58 . r.4
: L.35
Therefore the strength is inadequate because the ratio is >1.0.If the top triangle is rnade separately and fastened with nails or
screws, the stresses in the curved beam with depth 667 mm andmean radius 11.33 m are reduced to:
n5 .to6:0.14N/mm2
tt5 .667 .tt333
and the stressed volume is reduced to:
V - 0.1 1,5 .0.667 . 2 : 0.15 m3
that is:
u*,: (ffi)':orukai,: !'4
Practical design of timber structures to Eurocode 5
6.3 Arches and frames
6.3.1 GeneralIt is relatively simple to produce curved glulam structures and therebyarches and frames. In some cases these structures may, however, pose
instability problems out of the plane (lateral instability) and in theplane (buckling). The in-plane instability problems increase when thecomponent centreline is close to the line of thrust.
In most cases the design requires effective frame computer programs.
An exception is the popular three-hinge arch with curved corners, as
shown in Fig. 6.6. Three-hinged arches are very stable in their ownplane and a simple but sufficiently precise design method is described
below, provided lateral instability is prevented by holding the compres.
sion side by a bracing.
6.3.2 Tlvee-hinged arch with curved cornersThe determining load combination for the corner is normally dead loadand symmetrical snow. The cross-section D with maximum momentmay be found by trial and error. At the curved corners, it is usual toignore the vertical loads as they are taken by the rafters and columns.In this case, the moment may be determined from the maximumdistance e from the resultant reaction line of thrust to the centreline:
M:eR:r\M*N* (6.15)
The frame corner is designed as a laterally loaded column with the axialforce N - -R and with the distance lap from point A to point E (where
M : 0). For out-of plane deflection the column length corresponds to
Fig. 6.6 Three.hinged (A, B and C) symmetrical arch with curqLed conters
t54
Curued beams and frames
the distance between thc bracing points. lt shall be veri{ied that
::!-+":f( kb"..t (6.16)k. -1..0.J I^.d
provided lateral instability is prevented.
The straight parts, for which the decisive load combination normally
is unsymmetrical snow, are designed as tapered beam columns with an
in-plane column length equal to the distance lctc from point C to point
G (where M : 0). The column depth is taken as the mean depth on the
distance C-G. For out-of-plane deflection the column length corre-
sponds to the distance between the bracing points. If the fibres are
cut, the strength reduction should be taken into account (factor k,n,,,,
Expressions (4.37) and (4.38)).
The support cross-section should be designed for shear. At point Athe design shear stress is given bY:
(6.r7)
where a1 is the angle between the grain direction and the vertical axis,
At the top hinge the shear stress is:
, - Rng,J cos oi - R4y.1 sin rl1rJ: I t
bi-,
. - Rcv..t c()s r} - R6g..1 sin nT,l:l')T (6.18)
where a is the angle between the grain direction and the horizontal.
6.3.3 Tlvee-hinged arch with shnrp conters (ttiffigulflted comers)
By finger-jointing glulam beams it is possible to make three-hinged
arches with triangulated corners (see Fig.6.7). The tirnber volume is
Fig. 6.7 Three-hinged slmmetrical frame with triangulated corners
finger-jointing
formed by
t55
Practical design ctf timber structures to Euroatde 5
larger than for curved corners because the moments become largerand because the finger joints have relatively low load-carryingcapacity.
Finger-jointed arches are normally designed by the producer of theglulam.
Example 6.3The glulam arch shown in Fig. 6.7 is made of glulam class GL24h inservice Class 1 condition and has the following dimensions; I - 25 m,hrid":4m, htup:7.2m, r: 3.0m, Qroof :15" and laminationthickness of t:22mm. Dead load is g - 2.5 kN/m and snow loadis either sr :4kN/m uniformly distributed over the whole roof orsz :2 kN/m uniformly distributed over one side of the roof.
Find; adequate dimensions of the structure.
The following dimensions are estimated: corner depth h -0.031-0.748m corresponding to 34 laminations of thickness22mm, h,,p - 0.5h - 300mrn, beam width b - 0.18h - 140mm.In practice there may also be loads from cranes etc. These loadsmay normally not be decisive for the frame but may be importantfor steel parts used for anchorage and fittings. In rare cases windmay result in an opening moment and related tension stressesperpendicular to the fibres.
Since the span is moderate, the frame is placed directly on rhefoundation and supported laterally by a concrered-in steel U-beam.The span will be reduced slightly because the vertical reacrion is
placed a little inwards from the edges of the frame. This is disregardedbecause of the opposite effect of the horizontal reaction acting at asmall distance from the top surface of the foundation.
Dead load:
RAv,d : RBv,,J : gll2 :31.25 kN
Rari,,J : R6H,,J : glz 118hr"r1: 27.1kN
Snow s1:
Rav,d : Rsv,,l : sllf 2:50kN
RaFr,d : RsH,,1 : srlz 118hr"r1:43.4kN
t56
Curued beams and frames
Snow s2 on the right-hand side:
Rav,,t: s2lf8- 6.3kN
Rnv,,l:3s2fl:1B.BkN
Ras,d : RAv dllT fh,"p : 10.9 kN
Rna,a : RaH,a
The maximum forces at the corners are found for g * s1:
Rav,d : 31.3 + 50.0 : 81.3 kN
Rau,,r : 27.I + 43.4 :70.5 kN
R,c.,r :
Based on the frame drawing and the action line for the reaction,the maximum eccentricity is measured to be approximatelye - 1.4 m, i.e.:
v:0The deformations will increase the moments calculated for the
initial geometry. This is taken into account by treating the corneras a column with length l4s where E is the point between C-Awith zero moment (see Fig.6.6). The taper means that the anglebetween the system line and horizontal is a little larger than theslope of the roof. The angle of the system line is estimated to be16".
M : Rslixp tan cy * (g + ilxLlT : 92.2xrtan 16u
- (2.s + Ox\lzsince RsH : RaH
xg corresponds to M : 0; xE :6.22m
laE : 8'3 m
Riu,,i * Rir-r,a : 107.6 kN
r57
Practical desrgrl of timber structures to Eurocode 5
For glulam of class GL24h
Arel.z -8300\,47 f Uw VF o+oo
: 0.618
It is assumed that deflection of the frame out of plane is prevented bythe fagade at about 0.5 m over the support and about 2.5 m from thevertical line of stanchions, i.e. the column length for deflectionperpendicular to the plane of the frame is approximately 5.0m.
. 5ooo/12 I )4),./r:fflFo4oo:1.99k,,z: 0.982 and trc.,, : 0.241
rlt:3000172:136krrrr":0'90
For glulam GL24h and short-term load the design strengths are:
f.,o,a : 0.9' 24 I 1.25 : 17.28N/mm2
f*l - 0.9 ' 24ll.25 : 17 .28N/mm2
For deflection about the strong axis it shall be verified that:oc.Od , or,,t /1
The shear force at point A with depth 500mm and a1 : 14o is:
Va : ReH,,; cos 14o - Rav,a sin 14' :70.5 cos 14o - 81.3 sin 14"
: 48.8 kN
\(/irh 1,,,r
Td*
f ,.a
: 0.9 . 2.711.25
1.5 . 48 800
: 1.94N/mm2:
#:0.54 < t
r5B
v0.504.r.94
t59
Curued becrms and frames
The axial force Ra,a : 107 kN and the moment M : 107 .0.5/Z :27 kNm can easily be carried.
The straight beam parts correspond to tapered columns withcolumn length ls6 eeual to the distance from the top hinge (C) tothe point with zero moment (G). For dead load and one-sidedsnow load:
Rcv,,J : 6.3 kN, RcH,d : 27 .l + 10.8 : 37.9 kN
MG : 0 for x6 :7.62m
In point G the cross-section depth is calculated or measured ro be620mm.
The cross-section with maximum bending stress is, according toExpression (4.39), found at a distance x from the symmetry linethrough C:
, : 1-_ h"'^- : 7 .93=
= -'oo, - - : 2.59 m^*'h^,nlh*,* t'/J
1gg1 *620- z't
where the bending stress (see Expression 4.40) is:
7.1 IntroductionFor lightweight structures with moderate spans it is common to usetrusses made of timber members using punched metal plates as gussets(see Fig. 7.1).
Almost all punched metal plate truss rafters are fabricated in factoriesand the fabricators are usually responsible for the design of the trussesusing a particular system owner's design software. System owners areusually organisations that fabricate punched metal plate connectors inaddition to producing sophisticated design software that is licensed tothe truss fabricators in retum for using the punched plate connectorsof the system owner. However, it is in principle possible for others todesign them using Eurocode 5.
Trusses may also be produced traditionally from srructural timber,glulam and LVL with gusset plates of wood-based panel producrs suchas plywood or steel. These gusset plates are usually nailed, screwed orbolted to timber members at nodal points.
Fot many trusses it is necessary to prevent out.of-plane bucklingof the top chords (rafters) and often also the compression webmembers.
160
Fig. 7.1 Punched menl plate roof truss
161
Practical desigt'L of timber structures to Eurocode 5
7.2 Structural design of trusses
7.2.1 GeneralTrusses are normally statically indeterminate, even when the reac-tions are statically determinate. Eurocode 5 requires in principle thattrusses are designed as frame structures taking into account the effectof deformations, slip in joints and eccentricities, e.g. at supports andnodal points. A full calculation may be very complicated and ofren a
simple linear first-order calculation is used and the non-linear beha-viour is taken into account by the design of the individual members(column effect). A simplified design merhod is described in thefollowing.
7.2.2 Simplified designThe method is based on the following assumptions:
. part of the support length is placed verrically under the end nodeo the height of the truss is grearer than 0.15 times rhe span and
greater than 10 times the chord depth, i.e. the truss is relativelysriff.
The structure is modelled as beam elements placed at the sysrem lines ofthe truss members. Apart from the top and bottom chords where thecentre/system lines shall coincide, it is only required that the systemlines fall within the cross-section, but any eccentricities shall be takeninto account in the design of individual members.
The axial member forces are found by the normal equilibrium condi-tions (e.g. framework analysis) assuming that the members are joined byfrictionless hinges. All the loads are transformed into point loads at the
Top chord, usuallycompression chord
Centreline
\\Bottom chord, usually in tension
Fig. 7.2 llotation for trusses. Nodes are connected by slstem lines thut on\ forthe bottom and top chord lwue to coincide with member centrelines
r62
Fig. 7.3 Reduction of bending moments at nodes for continuous members
nodes. Experience has shown that this method resulm in very precise
estimates of the axial forces.Eurocode 5, however, requires that for strength verification of
members in compression and connections, the calculated axial forcesshould be increased by 10%.
The bending moments in members spanning one bay should be deter-mined assuming frictionless hinges at the nodes.
For continuous elements, the effect of deformations should be takeninto account by a 10o/o reduction of the bending moments over thesupports. These reduced moments should also be used in calcularionof the bay moments. An example is shown in Fig. 7.3.
Often the load from the roof is transferred through tiles or roofingonto battens which have equal centres hence creating equally distancedpoint loads on rafters. If the batten spacing is less than 0.4 times the baylength, the row of point loads may be assumed to act as a uniformlydistributed load.
For trusses that are loaded predominantly at the nodes the sum of thecombined bending and axial compressive stress areas should be limitedto 0.9.
For compression members, the free column length is generally takenas the distance between adjacent points of contraflexure. For fully trian-gulated trusses, the effective column length for members in compressionshould be taken as the bay length, if:
o members are only one bay long, without rigid end connectionsr members are continuous over two or more bays and are not loaded
laterally.
When a simplilied analysis of a fully triangulated rruss wirh punchedmetal plate fasteners is used, the following effective column lengths, as
shown in Fig. 7.4, may be assumed:
1. For continuous members without signilicant end moments andwhere the bending stresses of the lateral load are at least 40o/o ofthe compressive stresses:
Trrlsses tnrd bracings
r63
Practical desig of timber structures to Eurocode 5
o 6.6 o 0.6 0.6N 1.0 i\wlYIYYFig. 7.4 Colrunn length reduction factors
. in an outer bay: 0.8 times the bay lengtho in an inner bay: 0.6 times the bay lengtho at an internal node: 0.6 times the largest adjacent bay
length.7. For continuous members with significant end moments where the
bending stresses of the lateral load are at least 4Oo/o of the compres-sive stresses:
o at the beam end with moment: O (i.e. no column effect)o in the penultimate bay: 1.0 times the bay lengtho remaining bays and nodes: as described above in (1)o all other cases 1.0 times the bay length.
It is best practice to place gusseted joints in the top and bottomchords where the moments are zero and further to ensure that thecomponent does not become unstable if all joints act as hinges. It isassumed that the top chord (rafters) is held against lateral deflecrionby bracing and battens, i.e. the column length corresponds to thebatten spacing. Laterally deflection of web members should also beprevented by the end nodes and additional bracing.
The strength variation of rrusses is reduced because of the loadsharing of members for which the strength may be increased by aload-sharing factor (system factor) k.,r., : 1.1 provided the trusses arelaterally connected by a continuous'load distribution system capableof transferring the loads (assumed to be short-term) from onemember to the neighbouring members. It should be ensured that theload distribudon members are continuous over at least two trussesand the joints are staggered.
Trusses and bracings
Example 7.1
0.8
2.25 2.25
A W-truss in service Class 1 with geometry and member dimensions,as shown in the figure is used at centres c : 600 mm.
Verify that the ffuss using C16 has sufficient load-carrying capaciryfor the following assumed design loads:
o dead load on the top chord measured along its length:
B,,p : 0.5 kN/*t (including the self-weight)o dead load on the bottom tie (bottom chord):
Euo,: O.4kN/mz (including the self-weight)o roof snow load, measured horizontally):
s : 0.405 kN/mz (characteristic snow load on groundso : 0.45 KN/m2 and form factor 0.9).
Note: The assumed load in the example is very much simplifredbecause the purpose is to demonstrate the design principles of trusses.
The determining load case is dead load * snow.
Etopd:1.35 '0.5 :0.675 kN/mZ
*bot.d : 1.35 '0.4 : O'54kN/mz
s,r - 1.5 .0.405 :0.608kN/mZ
,lr,V
lF.
,+
164
I 1.2m l+
t65
PracticcLl design of timber structures to Eurocode 5
All calculations of forces and moments are for design loads. Theuniformly distributed loads are replaced by point load at the nodes:
Fr : 0.5cllr*2 cos 20"(g opf cos 20' + s) * lr-zgao,] : 1.38 kN
The axial forces and moments are summarised in the followingtable.
N: kN(*ve tension, -ve compression)
M: kNm
Middle
1-Z2-3
1-76-7
z-73*7
* 10.69
-9.38
r0.056.69
*1.82t.t 1
0.280.28
0.260.10
*0.45
-0.45
-0.76-0.26
F
t66 167
Trzsses and bracings
For the main members the load combinations with snow are
critical. For some of the secondary members the dead load alone
may be dominating, but this is not investigated since the stress
index is small. The required increase of the forces and moments by
10% and the system factor k,o, - 1.1 compensate each other.
\X/eb member diagonal 3- 7Tension member C16 with ft,o.d:0.9 .l0ll.3 :6.92N/mm2:
o,.d: ll30 nRq
fl,o d +7 . 75 . 6.gt: ffi.: o' 13 < I
Diagonal2-7Centrally loaded column with l: 1.10m:
f,,ad:0.9 '17lL3 : 11.77 N/mm2
\r"I:
oc,Od
k,f ,,od
noo.Jn47r
r *-IUV s+oo
1820
1.45; k,:0.403
0.52
47 .75. 0.403 .rt.77 4.74: 0.11
Top flange 1-2The top flange is a laterally loaded column. For deflection in theplane of the ffuss the column length is equal to the node distance.Perpendicular to the plane, the flange is held by the battens. Theirdistance is determined so that deflection in this direction is notcritical.
fc,ad:0.9 '17ll.3 :11.77 N/mmz
f^.d:0.9 16ll.3 - 11.08N/mmz
Midd\e: l, : 0.8 . 7.25lcos 20o : 1.92m
W :47 .r2oz 16: 112.8- 103 mm3
. I1ZO.Jn T 11
A,,, : #/rtr : o.eBB; k, :o.6ee
Practical desip of timber structures to Eurocotle 5
ord , omd
k,f,,o,a ' f^,a
0.45 . 106l_
11.77' 112.8. lO]. 11.080.699 . 47 .t20
10 690
10690
: 0.73 + 0.36 : 0.59
: 0.6 . 2.25f cos20" : 1.44m
- 1440.\/TI4,"1 - 12gn ffi:0.742; k : 0.857
ocd , o^d
4f,pt- f*0.45 . 106
0.857.47.1201t.77
: 0.19 + 0.36 : 0.55
rtz.8 .103 . 11.08
To avoid deflection perpendicular to the ffuss planedecisive it is required that:
deflection e2u laterally supported at mid'height b1 a spring with stiffness C, where
u is the resulting deflection and F the reaction force perpendicular to the colwnn
in the elastic support
C:k.\:z(,*.or")\4 \ m/a
Structuraltimber 11300
Glulam I l5A0
Practical design of timber structures to Eurocode 5
Table 7.1 Theoretical requirements to the strength F expressed as F/N for k. - 4
e1,,l2a F/N
Theoretically UK National Annex to Eurocode 5
Trusse.s and bracings
The strength and stiffness of the bracing should as a minimum be:
Ra: 30.5160 : 0.51 kN
C : 4N ala : 4 ' 30 400/3000 : 40'6 N/mm
Only one of the bracings is assumed to be active when the column
starts to buckle (the one with tension)'
For 3.35 mm diameter round nails the design load-carrying capa-
city with k^o,t:0.9, ?u:1.3 is (see Chapter 9) about 600N'
Therefore, at least one nail is required.
The stiffness for a nail is found from Table 1.7. For p* :370kgl1m:
*,:!**,:', *or :t-"roo" r.rt' 8 :4r6N/mm
The stiffness of the bracing is Ca : Faful where u1 is the lateral
deflection of the column at mid'height (bracing positions) for a
force F1 acting at the same Point.The force in the active bracing member is rtF t. Since the elonga-
tion is small compared to the slip in the two joints (one in each end):
^F 't/l - 2Lll:V, "rc_:flnn
c : nK*12 : c : nhl| : 2OBN/mm
Therefore, the stiffness is also sufficient' In practice the minimum
number of nails to be used is two, even if one nail is sufficient.
7.3.2 Bracing of a structural systemA system of n identical parallel columns shall be braced by a structure
that may be loaded by an external load q (see Fig. i.6). An example
is where the rafters (top compression chords) of a trussed rafter roof
are braced by a beam at the gables. In Fig. 7'6 the bracing beam is
shown as a separate truss, but the columns may act as flanges in the
bracing truss.It is required that the bracing shall be able to take a uniformly distrib-
uted load (additional to any external load) of:
t 137.5
| /63
1 /60
i/100
Example 7.2
kr:0'258
f,,od:0.9 ' 17lI.3 : 11.77 N/mmz
Na :0.259 .11.77. 10Oz . 10-3 : 30.5kN
170
A 6 m long column of C16 timber in service Class 2 condition withcross.section 100 x 100mm is braced at mid.height by two timberC16 members 38 x 75 nailed to either face of the column with nnails of diameter 3.35 mm and length of 75 mm, that are in turnnailed to a stiff top beam.
Find the required number of nails when the load on the columncorresponds to its design load.
Note: It is assumed that the two bracing members are only forpreventing the column from buckling and they should not be consid-ered as a part of the main structure.
The slenderness ratio of the column is:
r'
//e^// 38x75
. 1000./12 TnA'"1 : roo, V s+oo-
:krNa
4, : n k,.rr
(7 3)
t7t
Practical design of timber structures to Eurocode 5
Fig. 7.6 Sysrem of n columns supported b1 a common bracing truss
where:
N4 is the mean (taken over the length) design compression force inthe column;
I ls the length of the columns.
In the UK National Annex to Eurocode 5 the following value isgiven:
k, :min {f*
- ( 50 for members spaced at 600 mm or lesskr': {t ') L 40 for members spaced at more than 600 mm
Fur,u^ulu,rd: O, 't"{ f
t72
(7.4)
(7 .5)
The factor k; allegedly takes into account that for large structures youmay expect a more careful erection. On the contrary, srricter require-ments should apply, because secondary strength increasing effects willbe relatively less important.
It is also required that the lateral deflection for any external loadshould be less than l/500, a requirement that will only in exceptionalcases be decisive.
It is best practice that the force on the bracing, F,1, from each columnshould be necessary to hold the column in place as given by Expression(7.1). These forces are added over the length but since not all will get
the maximum force the required support load may be estimated to be
not more than:
Trusscs ,nd brucitrgs
Further, it should be possible to use the bending stiffness and strengthof the columns to take and distribute part of the line load, e.g. half ofthem with B or more columns and nz f 16 for half of them for less than8 columns.
Trusses should be checked for straightness and vertical alignmentbefore {ixing to the permanent bracing.
When trusses are fabricated, the members should be free from dis-tortion within the limits given in EN 14250. However, if memberswhich have distorted during the period berween fabrication anderection can be straightened without damage to the timber or thejoints and maintained straight, the ffuss may be considered satisfactoryfor use.
The maximum bow a6u* tn any truss member after erection should,according to the UK National Annex to Eurocode 5, be limited to10mm provided that it is adequately secured in the completed roof roprevent the bow from increasing.
The maximum deviatiofi d7r, of a truss from true vertical alignmentafter erection should, according to the UK National Annex to Eurocode5, be limited to:
. f l0+5(H- l)mmader.ptrmiu,,J: mrnt
25 mm
where H is the height of the truss in metres.
(7 7)
(i.B)
7.3,3 Bracing of the compression side of abeamThe compression zone in a beam with moment M and depth h may beregarded as a column with a compression force I.5Mlh. This is,
however, very much conservative because Iirst, a bracing placed atthe top of the beam is more effecdve than the bracing placed at mid-depth of the beam; second, this means that the lateral and torsion stiff-ness is disregarded. It is, therefore, suffi.cient to design the column for:
N,J:(1 -k.,)Y
(7.6)
t73
8
I, T and box.beams
8.1 Introduction and background theoriesThis chapter covers glued beams symmetrical about theirthin webs and or flanges loaded by an axial force N,moment M : M, and a shear force V : V. (see Fig. 8.1).
ffitrffiru&ffi
z-axis witha bending
Fig, 8.2 Cross'sectinn composed of layers with different E'values
The transformed area is defined by the integral:
At:
where the index r denotes
frsf moment of area about
(8.2)
transformed cross'section' The transformed
the 11-axis is defined bY:
I^*^
I^*,",,0o
I^*,,0oFrg. 8.1 Cross-section of 'I','T' andbox-beams. The plate-Iike structures to theright are often called stressed skin elements
Normally two or more material types with different stiffness proper-ties are used in these structural members, e.g. solid timber and wood-based panels. The distribution of the bending stress is highly dependenton the elastic modulus in the beam direction. The srress distribution is
calculated by using the theory for'transformed' cross-sections.
8.2 Transformed(composite) cross,sectionsA cross-section composed of n layers (see Fig. 8.2) is regarded. Themodulus of elasticity of layer I is denoted E; and the modulus of elasticityof one of the layers is taken as reference modulus E."g. Two coordinatesystems are used: )1-21 and )-z through 01 and O respectively. Therelationship between the x-coordinates is given byr
S1,: (8.3)
The transformed first moment of area about the 1-axis is defined by:
(8.4)
(8.5 )
S,:
It is assumed that the ]-z coordinate system is located in the centre of
gravity, O, for the transformed cross-section defined by the first moment
of area being 0:
Sr : o : I^*ot,i - e)dA: sr, - eA,
and the distance between the coordinate systems becomes:
St,,:1The transformed moment of inertia (second-order moment of area)
about the )1-axis is defined bY:
t,,: L f,ri,,ae (8'6)
z:zl-e
174
(8.1)
t75
Prctctical desip of timber structures to Eurocode 5
The transformed second momenr of inertia about the y-axis is definedby,
r,:J 8,,,1
oo:l#,., ,-ef dA
: I ^fi,i,
dA + ez I ^*^
* r, I o{z,,de
-I n.2
- rk - I1te
where S, : 0 has been used.The axial stress from a normal force N acdng at O is:
E.N-t *\u\(/ -;- .Errl A,
(8 7)
The stress distribution is a stepwise constant for each material layerand the stresses are larger for the stiffer layers.
The sftesses from a moment M are calculated as:
(8.e)
(8. i0)
(8.11)
I, T and box-beams
8.3 Beams with thin webs
8.3.7 GeneralThis section covers beams with cross-sections as shown in Fig. 8.3. The
flanges may be solid timber or laminated veneer lumber (LVL)' It is
assumed that the cross-section is symmetrical about a vertical plane
and that the load acts in this plane. If thls is not the case it is necessary
to take the resulting torsion into account.
In the following it is assumed that the cross-sections are double-
symmetrical and use the same materials for top and bottom flanges. Itmay in some cases be convenient to use different material for the
tension and compression flanges but this requires very careful installa'
don in construction practice so that they are not utilised inappropri-
ately, which could result in failures.
Cr o s s - s e ction c onstants
The modulus of elasticity of the flanges is E and the modulus of elasticity
of the webs is called E,.The transformed cross-section constants are:
nl,\ - Et S-" \\/ - Errf I, ,
and the related curvature is:
M,h
-_- Er"fl,
The distribution of rhe srresses does not depend on the absolute E-values, but only on their relative values u.td it is therefore importantthat the ratios are as correct as possible. If a too low value i, ured in alayer, the stresses in this layer will be underestimated which may leadto premature failure. Therefore, the mean values are arways used forall materials such as timber and wood-based panels.
If the materials have different creep properties the stress distributionwill change with time. In the materials with large creep rate, the stresseswill be relieved, whereas they will increase ir-r th" oth", purtr. Fo. ,r..yimportant structures it may be necessary to det"rmine the stressdistribudon with both the initial (short-term) values and the valuescorresponding final values Ep after creep. In analogy with deformationcalculations Ep may be estimated to:
tr.ELnn - TTGAccording to Eurocode 5 it is only required to calculate with Ep,.
176
(8.8)
A, : zbh +E;u-u
r,:Tftz + 3(H- r,)tl + u*nt
(8.12)
(8. 13 )
bw= t
0.5b r 0.5bdP
1
I o.si,
Frg. 8.3 Cross-section notations for double'symmetrical beams and tlpical bend'
ing stress distribution
l
t,.
l--'--__-{
t77
Practical design of timber structures to Eurocode 5
8.3.2 Axial sfressesThe stresses in the flanges from an axiar force N and a bending momentM, : M are:
NMor:E*t'and for the web:
_ E*/N M\u: E \A-
*tti (8.15)
The sffesses in the top and bottom of the flanges are determinedasi
N MH*lu{ - -' A, 1,2
and they shallfulfil the following condition:
l"rllf^ < t
The stresses in the centre of the flanges are:
(rs6:I*MfH-h\"J.U A,*I,\ 2 )and they shall fulfil the following conditions:
o1,olf, < 1 (in the tension side)
lot ollk,f, < I (in the compression side)
where k. is the column factor correspondingmetrical slenderness ratio:
'/TIt,
I, T and box-beams
and they shall ful{il the following condition'
lo*llf*,- < I (8.27)
where /*"_ i, the bending strength of the web material for in-plane
b""dn!.'ii this strength property is not available the value may be esti-
*nt"dls the smallervalue of 1.25f*.,andl'Z5f*,rwherefi,. andfi,, are
the tension and compression strengths of the web material'
8,3.3 Panel shecr sfresses
I-sections
The shear stresses are also calculated by using transformed cross'section
properries. For cross-section 1-1 in the I cross-sections in Fig. 8.3, the
(8.14)
(8.16)
(8.17)
(8.18)
(8.1ea)
(B.1eb)
to the following geo-
(8.20)
shear force is given bY:
c
H, ,:Vr1-1'rlr
where S1-1,, is the transformed first moment of area about the axis
through lh" ."r-,tt. of gravity of the flange area outside the cross section
1-1:
Ebhe-Jl l,r-E l-teJ t
If h < 4t, the shear force H1-i may be assumed to be uniformly distri-
buted over the thickness of the flange and the panel shear stress is
given by:
Hr-r,l-I
h(8.2 5 )
lf h > 4t, the shear stress will vary over the thickness and the maximum
panel shear stress should be calculated as:
ryl r /h \o'/mux - h \4f/
H-h
(8.23)
(8.24)
(8.26)
)-b*b*
where l. is the distance between the cross-section where the flanges areheld against lateral deflection, i.e. the compression flange is ,r"u,!d n, ucolumn, that can deflect laterally. For box beams in particular, this is avery crude simplification and it is normally possible to find a higher load-carrying capacity by making a proper lateral instability calculation.
The stresses in the top and bottom of the webs arer
o*:EEo(i.Ti)
L7B
For the I cross-sections, the maximum panel shear force occurs in cross'
section 2-2 and is found as:
Sr t.H't-t:V--
t,
lu
(8.2 I )
t79
Practical design of timber structures to Eurocode 5
Fig. 8.4 Web buckling due n shear srresses
where S2-2,, is the transformed first moment of area about the axisthrough the centre of gravity of the cross-section above the cross-section 2-2:
Sr.,,:25, ,,* E tH!'" E624
If the shear force H2-2 is assumed to be uniformly distributed, the panershear stress becomes:
H.'t-l - t
Box cross-sections
By making rhe cur as shown in Fig. 8.3 through the symmetry axis wherethe shear stresses are zero, the beam can be treated as two I-beams.
Web bucklingBeams with high thin webs can fail in rateral (shear) buckling as shownin Fig. 8.4.
Buckling may be disregarded if h* < z0r, provided it is verified that:
Practical design of timber structures to Eurocode 5
1. For domestic flat roofs without any access with spans 600mm:o plywood l5-l6mm thicko particle boards types P5 or P7: 18 mm thick.
2. For domestic floors with spans 600mm:o plywood: generally 18 mm thick; however, for Canadian Douglas
{ir and Swedish and Finnish spruce plywood 15.5*16mmo particle boards types P5 and P7: 22 mm thick.
The elements are calculated as a number of I-beams that each takes theload directly on the web and on half the web distance to each side.
Cross-sectlon constants
The modulus of elasticity E of the webs is taken as reference modulus ofelasticity.
The calculations are made for an effective cross-section as shown inFig. 8.5. The reason why the full plate width is not used is that thenormal stresses vary due to the low shear stiffness of the panel material.The stresses are maximum at the web junctions and minimum in themid-span of the panel. This is taken into consideration by using an effec-tive width b"6,1.
In the compression side the effective width becomes:
b,."ff : b* + b, (exterior web: bf + 0.5b.)
and for the tension side:
b,,rff :b* +b, (exterior web: bf + 0.5b,)
The effective web width depends on, for example, the ratio E/Gbetween the axial modulus of elasticity and the panel shear modulusand on the span. Small variations in the effective width have no greatinfluence and normally very simplified rules are used. According toEurocode 5, the values given in Table 8.1 should be used.
The maximum limit shall ensure that the failure will not be due tobuckling and it therefore only applies for the compression side wherethe free distance between the webs is also limited to Lb,.-u,. The trans-formed cross-section constants with the modulus of elasticity of the webmaterial as reference are given below.
Double symmetrical cross-section:
b"ff :br,"ff :br,"ff
t:tr:t,
186
(8.31)
(8.32)
I, T and box-beams
Table 8.1 Effectiue lTange width for beams with thin flanges where I is the plate
spdn
Panel material b. and b, b.,mn*
Plywcxrd with the libres in the outer veneers oriented:
in the web directionperpendicular to the web direction
OSB
Particleboards and fibreboards and MDF
0.11
0.11
0.151
0.21
Z)t,?.5t,
/0t,
30t,
E1 : E,: E,
g:0E.A,: h*b* i 27b,11t
t,: |u;-,1* +Elu*t1t * + t12
Single symmetrical cross section:
A, : hrb* +E,trb,."11 I 8,t,b,,,y1
" _Ertrbr.rff(h* + t,.) - E,t,b,.rL(h* I t,)- 2EA,
T:#f ro tn, *0 5t, -Fe) < I
where f is the tension strength of the flange panel.
t, : |uJ,l .t+b,"tr(h*+ r.)z + Ho,,"utn*
r t,)z - A,ez 18.t77
8.4.2 Axial sfresses
For moments alone it shall be verified that the stresses in the web fulfilthe following condition:
oM-
-
-q
I I
-fr-1,/r'''
(8.33)
(8.34)
(8.35)
(8.36)
In the flanges the stress variation over the thickness is disregarded and itshall be veri{ied that the tension stress of,r in the middle of the plate
fulfills the following condition:
(8.38)
(8.3e)
187
Practical design of tirnber structures to Eurctcode 5
In the compression side it shall be verified that the srress o/.c i'themiddle of the panel fulhls the following condition:
o{" E- Mi:i U,Q.sh*r0.5r.-e)
<1 (8.40)
where f, is the compression strengrh of the flange material.
8,4.3 Sheor sfressesThe shear stresses may be assumed uniformly distributed over the cross-sections 1-1, z*2 and 3-3 shown in Fig. 8.5. The condirions that shallbe fullilled for the compression side are given below. For the rension sidesimilar conditions apply. The design shear srrength for webs of wood is
/",,1 and for flange panels fu,panet.dfor panel shear andfi,,o11{or plate shear(rolling shear).
For cross-section 1-1, panel shear stress in the flange:
I, -f and box-beams
(skins) are more significant. If the moisture content in the bottom isreduced by Au the curvature becomes n : erLulh' where h is the
distance between the panels and a simply supported element with
length i will get nr-, .tp*urd deflection o{ u : n128.
Example 8.2
r##45 s33 45 533 45
't200
0.5/= 2600
The stressed-skin element shown in the figure above is simply
supported with a span of 5.2m. Both flanges are l}mm thick Cana'
dian spruce plywood glued to webs of timber C16. The grain direction
of the outer ply is parallel to the web direction. Due to the limited
panel length the webs are spliced by a single gusset plate placed on
the inner side. The top plate roofing felt is placed directly on the
panel and consequently this panel shall be assumed to be placed in
service Class 3. For the other parts of the element service Class 1
applies.' the d*rigr',load from dead load and snow is 2'0 kN/m2 (short-term
load).
Verifu the strength and stiffness of the component.
For plywood, the following characteristic values are assumed:
f,.o,k:20N/mm2
.f,,o,L : 15 N/mm2
f v,panel,k: 3 '0 N/mm2
f ,,rol,k : 1'0 N/mm2
E*"on:7000N/mm2
Y
T12I 145*12
For cross-se ction 2-2, rolling shear at the joint between panels andweb:
,,70;,.(d,'-.), o__ I,+[*
E,, (t,+h*. \r) 2.d ,, Eo'''fr \ t - t/h;: '''-- th [*, 't I
If b* > 8r, b* shall be replaced by:
^ /8'\ou"" \a,/For cross-section 3-3, the shear stress in the web:
,f r r2
r\ \.d rt la*U,'bff' ,.
-..
Ju.J Jt.d
Tt,t.dIJ u.d
<l (8.41)
(8.42)
(8.4i)
(8.44)
8.4.4 DeflectionsThe deflections are calculated with the bending sriffness EI,. Normallyany contribution from shear stresses is disregarded. often the deflec-tions due to moisture differences between bottom and top panels
1BB r89
Practical desip of timber structures to Eurocode 5
For the compression flange with ^b,t : I .2 and k*4 : 0.7 :
fc,o,r):0.7 '2011.2 : 11.67 N/mm2
fupanetd: 0.7 ' 3.011'2:1.75N/mm2
f,,,,t,k : 0'7' I'0 I I.2 : 0.58 N/mmz
The stiffness should be reduced by a factor:
E : 0.9. ?000 : 6300N/mmz
For the tension flange with kn o6 : 0.9:
fqod:0.9 '15I1r.2 : IL25N/mm2
fc,od : ft,od : 0'9' 15 II.2 : ll.25N/mm2
fv,panetd: 0.9 ' 3.011.2 :2.75N/mmz
f,,,ot,k : 0.9' 1.0 I l'2 : 0.7 5N/mm2
E^"*,: ?000N/mmz
Webs:
f^d : 0.9' 16 I 1.3 : 1 1.08 Nfmm2
f,,a : 0.9' 3.2 I L3 : 2.22N/mm2
E: 8000N l^ t
The design moment and shear force for an interior l.beam are,respectively:
Practical design of timber structures to Eurocode 5
Axial stress in the compression flange (see Expression (8.40)):
.rc6.04s12+12+15.8)of ,"d :E^"^ Md "
_ 6300.3.91
f ,,od E I,f ,,0,a' 8000 60.3 . 106 .10.77
: 0.48
Flange splice
The moment at the splice in the quarter points is reduced by a factorof 0.75. Since the utilisation factor of the tension web is 0.26, therequired strength of the splice is 0.75.76:2001o of the tensilestrength. Experience has shown that the strength is adequate.
Shear srresses
285 mm
Cross-section 1-1, panel shear stress in the panel (see Expression(8.41)):
ffi no (Y-t:45-(-16s))!t-r'a : 30o6 .
Iu,Paneld 50.3. 106 .t2.t.75
:0.21 < 1
Cross-section 2-2, rolling shear at the joint between the flange
and the web (see Expression (8.42)):With b. :45mm { 8r:96mm:
295 t)rz-z.d : rr-t.dffi
*:0.284N/mmrTl _l s : H:0.4e < r
565 mm
192
f u,,oI
t93
The calculation is a little on the safe side since the maximum
,otttrrU shear stress takes place in the second veneer glue line (i'e'
one veneer from the Panel face)'"- Crorr-r".tion 3-3, shear stress in the web (see Expression (8'44)):
0.284 +300645 '[14'5 - 2'(-16'8)]2
T-3d- '@--ff - - 2.75
- o'48 : o.z1 < 1
7.25
I, I Ano oUx'ueutttJ
0.28 + 0.20
2.75
Cross-section 5-5, panel shear stress in the tension flange (see
Expression (8.41)):
7ooo. 260.12.8000
-168)rz + 145
rs-sd :3006.fv,Paneld
Cross-sectio n 4-4,rolling shear at the joint between the web and
compression flange (see Expression (8'42)):
565-.lz : o.4rN/mmz14- 4.d : r5-5.d' 260 B-
v', r
r4-4d *0.41 _ 0.55 < If,,*r 0'75
60.3 . 106 . lz .2.?.5
0.70
2.75
9
Connections and fasteners
9.1 Design of multi.fastener jointsNormally several fasteners such as nails, screws and bolts are used intypical timber connections. Initially the distribution of the internalforces between the individual fasteners is determined.
9.1.1 Concentrically loaded connectionIf the external load is acting in the geometrical centre of gravity of thetimber connection, the forces acting on the individual fastener are equaland parallel to the external load. An example is shown in Fig. 9.1.
9.1.2 Eccentrically loaded joint
Known line of actionThe external force R acting on the structure shown in Fig. 9.2 is trans-ferred by n identical fasteners with coordinates (xi,y;). The coordinaresystem used is chosen in such a way that the origin is located in thegeometrical centre of gravity, defined by:
i', :o ir, :oi:1 i:l
The external force R : (R,, Rr) acts at a distance r from the origin. It isassumed that the deformation in the joint corresponds to a translation(uo,qro) of the origin and a rotation d. The rranslation of fastener i isdenoted (rt,r,) and calculated as:
ui: uA - 9Ji ui: ng I )xi (e.2)
Assuming that the force acting on a fastener is proportional to its totaltranslation (linear elastic behaviour), the force components become:
F;." : K(us - 0y,) F;,, : K(o,s f dx;)
194
(e.1)
Fig. 9.1 Example of a centrally loaded comtection
Static equilibrium requires that:
(b)
Fig. 9.2 Plane connection with known
(b) model ol a ioint with rutations
Connections and fasteners
(e.4)
line of action: (a) examPle of joint;
R": )iF;'": Knusi-1
Ui
(e.3)
195
Practical desip of timber structures to Eurocode 5
n
R, : IF;., : Knt'si:1
nnRr : I (F,,rr, - Fi,,),) : Kdt 6! +y?)
F,,:&-frr, 0,,:In'+f",
(e.5)
(e.6)
where Expression (9.1) has been used.By determiningus, up and d by these equations and using Expression
(9.3), the forces on the fasteners are found as:
(e.7)
(e.B)
where In is the fastener group's polar moment of inertia de{rned by:
Io: I $? +v!)i:1
The force acting on fastener iparallel to the external force R
Fp; : R/n (e.10)
and a force from the moment acting perpendicular to the radius vectorTi:
t-,, : f ', (e. n)
Unknown line of forceAn example with two groups of fasteners is shown in Fig. 9.3. Arigorous analysis of the load on the individual fasteners may bedifficult, and it is often simpler to esrimate the line of action an'd takethe load'carrying capacity as the smaller of the values calculated forthe two groups. If the values were very different, the calculationsshould be repeated with a new estimate of the line of action. For thestructure shown in Fig. 9.3, where the external load, R, is assumed tobe parallel to the top chord, it is, however, possible to give a precisesolution. The final force expressions will be given below withoutdetailed calculations.
196
(e e)
may also be expressed as a force F,.;
Flo + F!,
Connections and f astener s
Fig. 9.3 Truss connection between the top md the bottom chord with two groups
of fasteners, one in the top chord, the other in the bottom chotd
The distance between the centres of gravity of the fastener groups is
(er,"u).The load on each fastener is a force Fp acting in the direction of
R and a force F- perpendicular ro the line from the individual fastener
to the centre of the fastener group. For group 1 with n1 fasteners and a
polar moment of inertia Io,r:
F :R F -R(e,+eu),. g.rz\'r'/-nr 'mr Ip.1 -flpz
For group 2 with n2 fasteners and a polar moment of inertia Io.z:
9,1.3 Plasticload-carrying capacity of timber connectionBy a linear elastic calculation, the load'carrying capacity is determined
by the most heavily loaded fastener. As shown below, fasteners typically
display pronounced plastic behaviour and it is normally possible to
increase the load beyond the elastic limit. It may be difficult to find
the exact plastic load-carrying capacity but it is relatively easy to deter'
mine a value on the safe side by estimating a load distribution fulfillingthe equilibrium conditions (i.e. a srarically permissible load distribution)
with the forces on all fasteners less than the yield load'carrying capacity(i.e. a safe load distribution).
t * Centre of gravity
197
Practical desip of dmber structures to Eurocode 5
Example 9.1
A cantilever beam carries a load R acting at distance e : 10a fromthe centre of gravity of the connections, The cantilever is, as
shown in the above figure, fastened to the column with 16 fasteners.The fasteners are assumed to have an elastic-plastic behaviour withthe yield capacity Rr.
Find the elastic load-carrying capacity and the yield capacity of thejoint.
The maximum force on a fastener is found for the fastener in theupper right or lower right corners, where vector addition (notshown) gives F-o* : 0.58R : R",. The elastic load-carrying capacityis:
R"R"lrr,:^-iA:1'72R)
u.)6
Plastic calculationIt is assumed that the vertical load is carried by the four centralfasteners and that the other fasteners take the moment. The plastic
t98 199
Connectians and f astener s
load-carrying capacity is limited by:
Rplorr : 4R,
and
Rplo,,(8.1.5a+4.1.5at/1
l0aRra : 2.05Rj
The load-carrying capacity is thus increased by at least I7o/oby taking
the plastic behaviour into account. A marginally higher value may be
found by also using the central fasteners to take part of the moment.
9.2 Load-carrying capacity of dowel'type fasteners
9.2.1 General theoryThis chapter describes the theoretical basis for the Eurocode 5 expres.
sions for the load-carrying capacity of dowel-type fasteners (i.e. nails,
bolts, dowels and screws) loaded perpendicular to their axis (laterally
loaded).The principal behaviour is illustrated in Fig. 9.4 fot a so'called double
shear connection (two side members and one middle member). The
main part of the load is transferred by contact pressure between the
Fig. 9.4 Double shear dowel connections. Thick dowels remain straight and the
loarl is transferred almost solely by shear in the dowel. Slender dowels bend and
pdrt of the load may be taken by tension in the inclined dowel patts and b1 frictionbetween the timber parts that are pressed together by the tension forces
-t--t-?-?--+,+-+-{'
ltll-t-+-1.-t--j-+-i.-i-
Load per unit length1c)1b)
Connections and lastenersPracticul design of timber structures tct Eurocctde 5
Fy
Fig. 9.5 Dowel pressed into a timber member, dndIo ad - def ormation cur v e
"'i,-]T'[___ rltL]
t 2)Bearing deformation, u
the real and ideul-plastic
rywtimber members and rhe dowel that is exposed ro shear and bending. Apart of the load may be taken by direct tension in the inclined dowelsand by friction between the timber members.
A simple theory for calculation of the plastic load-carrying capacitywithout the effect of rension force in the dowel (and thereby alsofriction) was proposed by K. W. Johansen. k was published in Danishin l94I and in English in 1949 (Johansen, 1949). The theory is oftencalled the European Yield Model (EYM). It is only valid if the fairureis ductile and not brittle (e.g. caused by splitting). This is normallyensured by the structural detailing rules and minimum requirementsto member thicknesses.
It is assumed that the dowel acs as a beam laterally loaded by aconstant contact pressure 4 per unit length. The relation between thecontact pressure and the deformation may be found by the test ser-upsketched in Fig. 9.5 where a sdff steel cylinder in a hole in a timbermember is loaded by a force F. The figure shows a typical load-deformation curve. At the beginning there is a linear relationshipthat is followed by a curved parr afrer which the load falls slightly byincreased deformation. In practice a fully plastic behaviour with yieldvalue F, may be assumed.
The so-called embedding is defined by:
,4,In: iwhere 4, is the external load (N/m) acting on rhe dowel when the woodmaterial starts to yield (permanent deformation because of some type offibre damage) and d is the dowel diameter. The embedding srrengthdepends first and foremosr on the compression strength (and therebyon the density p of the wood) and on the angle a berween the load
200
and the fibre direction. Also the dowelform and diameter play a signif-
icant role.The load-carrying capacity also depends on the yield momen'Y' 9f
the dowel. Assuming iieal-plastic behaviour of both wood and dowel,
the clowel behaves either as a stiff unit without bending deformation
or as stiff dowel parts that are joined by yield hinges' The possible failure
*oi", for single and clouble shear joints are shown in Fig' 9'6'
Inthesingleshearjoint,thedowelwilleitherremainstraight(failuremodel)o.b",',dinoneortwoyieldhinges(failuremodes2or3respec.,'t*frl.'ett the double shear joint failure' mode 1 corresponds to a
rnou"*"rl, of the dowel either in the side members or the middle
member. In failure mode 2, two yield hinges occur in the middle
memberwhiletheclowelremainsstraightinthesidemembers.Infailure;;; t, four yield hi,',g"' u'" fu'*J within the dowelr two in the
middle member and one in each outer part'
It is relatively simple to derive expressions for the load'carrying
*p".Ut", for the described failure modes using only the equilibrium
conditions. As an example, the load-carrying capacity of a dowel canti-
l*"r.d from a timber member baded by a force R acting at a distance e
from the surface i, ,rJ. with e : o this situation is the same as failure
mocle 3 for a single shear joint because of symmetry'
(e.t4)
tvvvqF
la)lzF 1/eF 1b)
Fig. 9.6 Failure modes for smgle (upper row) and double (lower row) slrcur
joints
z0t
Practical desip of timber structures to Eurocode 5
arntr
Fig. 9.7 Geometry and the contact load distribution between wood end dowel fora dowel loaded by a force R, acting at a distance e from the sw-t'ace of a timbermember
with the ideal assumptions the dowel will remain straight unril ayield hinge is formed ar a disrance z from the surface. since themoment M, is a maximum moment, the shear force is equal to O inthat point. vertical equilibrium and moment equilibrium about theyield hinge would give:
Rr: zf6d
Rr(zfe)-zdf1,lT:M,
Rr: I
Cormections and lastene$
9.2.2 Wood'to'wood or wood'based panel'to'wood
connections
Single shear joints:
Rr,1 : min
I,
fnl,,{ifn.zl.tzd
(9.19a)
(e.1eb)
(9.1ec)
(e.1ef )
(e.15)
(e.16)
(e.r7)
r joints:
fnJ"!i0.5 f 1,,2.pt2d
If the force R, acrs at the surface of the member (e:0), the load-carrying capacity of the dowel becomes:
(e.18)
For the failure modes a,b, g and h, the load can be increased afteryielding. The reason is that because of the large deformarions therewill be tension in the dowel that will act as a rope and part of theload can be taken directly by the tension componenr p"rull"l to rheload. Further load can be transferred by friction. The friction conrribu-tion is proportional to the tension force and the sum of the two contri-butions is, for short, called the rope conrribution. The biggestcontribution is of course obtained for dowels with head and nut andfor screws, but it can also be substantial even for smooth nails anddowels.
202
to5+#lr,lo * o.!PEW - 4*' (e Zoc)
,--t.$\f:+\f2M,tfn,*d*r
vI-t,r'with:
d
.|I-
fn,z,t
f t ,t,u.
Ro",k
4
(e.20a)
(e.2ob)
(e.20d)
(e.7t)
(e.27)
where:
R",i. is the characteristic load-carrying capacity per shear plane per
fastener;
Double shea
-'r:l
703
Practical desip of timber structures to Eurocode 5
is the timber or wood-based panel thickness or penerrationdepth, with I either I or 2;is the characteristic embedding strength in timber member i;is the fastener diameter;is the characteristic fastener yield moment;is the ratio between the embedding strength of the members;is the contribution from the rope effect;is the characteristic axial withdrawal capacity of the fastener.
Correction factorsIn Expressions (9.19) and (9.20), the first rerms on the right-hand sidewithout the factors 1.05 and 1.15 are the load-carrying capacitiesaccording to rhe Johansen yield theory, while the second termT : F*/4 is the contribution from the rope effect.
The factors are correction factors to compensate for the very simpleway the design values are derived from the characteristic vaiue, criz.
Rr,,t: k^oaRr1.llu (see Section 9.2.8), whether the load-carryingcapacity depends solely on timber properties or partly also on the steelproperties. In the latter case It would be more correct to introducek-o,1 and the partial safety factors directly on the material parameters:
R, = 1fi,fi': MTypically 1u,*,od/^1u,,,".1 is about 1.2 and k-,,4 about 0.9, i.e.:
R'; = 1 15!4*ffilM.wood
For the other failure modes with bending in the dowel, the effect issmaller and a factor of 1.05 has been chosen.
Limitation of rope effectThe contribution to the load-carrying capacity due ro the rope effectshould be limited to rhe following percenrages of the Johansen part ofthe load-carrying capacity:
r round smooth nails l5Yo. square smooth nails 25Yoo other nails 50Yoo screws 1007oo bolts 75Voo dowels 0o/o.
204
Connections and fasteners
If Rur,L is not known, then the contribution from the rope effect
should be taken as zero.
For single shear fasteners the characteristic withdrawal capacity,
R*.1, is taken as the lower of the capacities in the two members'*For th" withdrawal capacity, Ro".1, of bolts, the resistance provided by
the washers may be taken into account.
9.2.3 Steel-to-wood connections
GeneralThe characteristic load-carrying capacity of a steel'to-timber connec-
tion depends on the thickness of the steel plates. Steel plates of
thickness less than or equal to 0.5d are classified as thin plates and
steel plates of thickness greater than or equal to d with the tolerance
on hole diameters being less than O.ld are classified as thick plates'
The characteristic load-carrying capacity of connections with steel
plate thickness between a thin and a thick plate should be calculated
by linear interpolation between the limiting thin and thick plate
values. The strength of the steel plate shall always be verified.
Thin steel plate in single shear:
(9.23a)
(e.23b)
Rr,k :
(e.24a)
(e.24b)
(e.24c)
in a double shearSteel plate of any thickness as middle member
connection:
fnttti (9.25a)
(e.2sb)
(e.lsc)
7.05
( 0.4 t'nuttdR^.,. : min{").k - ""'^
| t .ts r/Tfrr.1,f 1fi r T
Thick steel plate in single shear:
t1
fn,t,
dM-,.
BTRo",k
r) +r
+T
r) *r
M1 k*od*oudf h,k
Ru.k
Practical design of timber structures to Eurocctde 5
Thin steel plates as the outer members in a double shear connection:
n . f o.51n.r.rtrd (9.26a)f(. ,. : mln<-'!'K -----[t.tsrtrVrpffi+r
e.z6b)
Thick steel plates as outer members of a double shear connection:
(9.27a)
(e.27b)
(e.28)
where:
Ry,t is the characteristic load.carrying capacity per shear plane perfastener;
fnl is the characteristic embedding strength in the timber member;11 is the smaller of the thickness of the timber side member or rhe
penetration depth;t2 is the thickness of the timber middle member;d is the fastener diameter;Mr,t is the characteristic fastener yield moment;T is the rope effect contribution;Ro,.L is the characteristic withdrawal capacity of the fastener.
Failure modes
The failure modes for steel to dmber joints are illustrated in Fig. 9.8.The contribution from the rope effect is limited to that for wood-to-
wood joints.
Fig. 9.9 Notations for spacing between fasteners.and distances from fasteners to'rrii
oa edges of th" tr*L* i^b"r. a is the angle between the force direction for
the fastener and the wood grain ditection
It shall be taken into consideration that for joints close to an_end, the
load-carrying capacity may be reduced because of failure along the
perimeter of the group of fasteners'
9.2.4 Minimum spacing ond distutces
The expressions given uboi" pr"r.rme that failure is ductile, which can
l" ".rr,rr"d
by sufficient timber dimensions, spacings, and distances to
end and edges of timber members' The detailed requirements are
given in the specific chapters with basis in Fig' 9'9'
9.2.5 SPlittingWhen *ood i, ioaded with a tension component perpendicular- to the
gruir-, ,l-rrough bolts or nails, in order to prevent splitting failure' it
shall be verified that:
Connections and lasteners
i r '.-t r I
1.^ | 1-' 1r?- tk,'42 - Fo *
1"" , + l-f 1,. ;1*a,la1ll -+
R.,,. : -i.l 0'5fi z'r'tzd
[ 2.]/M,r ft td + T
T: I,"t4
-'lqf
dddddffillllnrRfin ffi ffiFl-l-t(s) (h) (jY(r)
Failure modes for steel to timber joints
3s.tts ---1
Va 5 Rso,a
where:
R96,4 : 14b
(e.ze)
(e.30)
V I is the maximum design shear force caused by the fasteners (V1
or V2);
('-Y)
F,g. 9.8
206
lra.la.Ll_+
207
Practical design of tirnber structures to Eurocode 5
Iv1
F,g. 9. I0 Joints with a load component perpendicular to grain
b is the thickness of the timber member loaded perpendicular tothe grain, in mm;
h"tr is the effective depth, taken as the distance perpendicular to thegrain from the loaded edge to the centre ofthe furthest fastener
inmm, as shown in Fig. 9.10. Note that the shear force Vdepends on the load configuration; see as an example Fig. 9.1 1.
For a load outside the supports, V : F. For a load in the mid-spanbetween supports, V : 0.5F, i.e. the splitting load-carrying capacity is
doubled.
Y connections and fasteners
I
1 g.z.A Multiple sheat plane connections
i i" multiple ,h.n. plutt" connections the resistance of each shear
1 ;;rirtance from individual shear planes in a_ multiple shear plane
connection,thegoverningfailuremodeofthefastenersinthelespec-dve shear plur";shouldle compatible with each_other and should
not consisr of a combination of failure modes 1 with the other failure
modes'
9.2,7 MultiPle fastener iointsThe arrangement, sizes of the fasteners and the fasteners' spacings,
"dg" ur-rd e-r-rd distur-r.es shall be chosen so that the expected strength
anl stiffness can be obtained in a joint. It shall be taken into account
that the load'carrying capacity of a multiple fastener joint' consisting
of fasteners of the ,u-" iyp" and dimension, may be lower than the
summation of the individual load'carrying capacities for each
fastener.\when a connection comprises different types of fasteners, or when
the stiffness of the connections in respective shear planes of a multiple
shear plane connection is different, their performance as a group of
fasteners should bE verified.
For one row of kasteners parallel to the grain direction, the charac'
teristic load-carrying .up^.ity parallel to the row, Rr."6,k' should be
taken as:
FI F*]bl2 b/2
Fig. 9.11 Loads acting on fasteners dt dn ouerhctnglcantileuer (top)
position within the supports (bottom)
208
Rr,.f/,k : n.fRi,l
where:
(e. r 1)
n"ff is the effective number of fasteners in a line parallel to the grain
direction;Rn.k is the characteristic load'carrying capacity of each fastener-
parallel to the grain direction'
For a force acting at an angle to the direction of the row' it should be
verified that the force componerrt parallel to the row is less than or equal
to the load-carrying .npn.iry calculated according to Expression (9'31) '
It should also be rreiifi"i thut the force perpendicular to grain is less than
or equal to the perpendicular load-carrying capacity calculated
according to Expression (9.79).
b
Crack
and at ,t
209
be used
Connections and fastenersPractical design of timber structures n Eurocode 5
9.2.8 Design valuesThe design load-carrying capacities should be found from the characrer-istic values as:
R1 : k,,olRyf 11.1ul (e.32)
9.3 Nailed connections
9.3.1 Laterally loaded wood.to-wood
Lo ad- c arrying c ap acity
The symbols for the thicknesses in single and double shear connecrions(Fig. 9.12) are defined as rl which is:
for a single shear connection: the head side timber thicknessfor a double shear connection: the head side timber thickness or thepoint side penetration whichever is smaller
and 12 which is:
o for a single shear connection: the point side penetrationr for a double shear connection: the central member thickness.
Yield momentFor square and grooved nails, the nail diameter d should be taken as theside dimension. For smooth nails produced from wire with a minimumtensile strength of 600N/mmz, the following characteristic values for
(e.33)
where:
M, i. is the characteristic value for the yield moment' in Nmm;
d "
is the nail diameter, in mm;-f,,0 ; ;il :h;;;.,eristic tensile strength of the wire, in N/mmz'
Embedding strength
For nails *lth dlu*"rers up to 8 mm, the following characteristic embed'
ding strengths in timber and LVL apply:
without predrilled holes:
/r,l: o.o8z prd-a3 N/mm2
with predrilled holes:
fn,r. : 0.082(1 - o.o1d)Pp N/mm2
where:
pt" is the characteristic timber density' in kgim3;
d is the nail diameter, in mm.
the yield
M., r. :for round nails
for square nails
moment should
I# ruud'o
I# r.ud2o
oo
(e.34)
(e.3s)
ffi\tz
Effective number of nails
Fo. or-r" row of n nails parallel ro the fibre direction the load'carrying
capacity parallel to the {ibre direction should be calculated using the
effective number of fasteners n"6.
If the nails of the row are staggered perpendicular to grain by at least d
(a)
Fig. 9.12 Definitions of q and t2 for:shear joint
2r0
(b)
(a) a single shear joint;
(see Fig. 9.13):
,rff:l
otherwise:
k",,nrff : n,"
(e.36)
(e.37)
2ll
and (b) a double
Practical desip of timber structures to Eurocode 5
- Grain direction' -----?
Fig. 9.13 Nails rri a rant parallel to grdin stdggered perpendicular to grain directionby d (1 : nail,2 : grain direction)
where:
is the effective number of nails in the row;is the number of nails in the row;is given in Table 9.1.
Nalls in end grain
Smooth nails may be used in secondary structures as, for example, infascia board nailed to rafters. The design values of the load-carryingcapacity should then be taken as ll3 of the values for nails installedat right-angles to the grain.
Nails other than smooth nails may be used in structures other thansecondary structures. The design values of the load-carrying capacityshould be taken as ll3 of the values for smooth nails of equivalentdiameter installed at right-angles to the grain, provided that:
o the nails are only laterally loadedo there are at least three nails per connectiono the pointside penetration is at least 10d. the connection is not exposed to service Class 3 conditionso the prescribed spacings and edge distances given in Table 9.2 are
satisfied.
Table 9.1 Values of k"11
Spacing
Not pre-drllled Pre-drilled
n"ffnk"ff
k"ff
a1 > 14d
ar : l]dar :7dat-4d
1.0
0.85
0.7
1.0
0.850.7
0.5
zI2
- For intermediate spacing, linear interpolation of k"y is pennitted
7t3
Connectiorts and f astener s
(e.38)
Fig. 9.14 OuerlaPPing nails
I
Demiling rules
Timberlhould be pre-drilled with holes not exceeding 0'8d where d is
the nail diameter, when:
o the characreristic density of the timber is greater than 5OO kg/m3
o the diameter d of the nail exceeds 8 mm'
In a three-member connection' nails may overlap in the central member
provided (t - tz) is greater than 4d (see Fig' 9'14)'
There should be at least two nails in a connection'
For smooth nails the point side penetration length should be at
least 84. For other nails, ihe point side penetration length should be
atleast6d.Unlessotherwisespeci{ied,nailsshouldbedriveninatright-angles to the grain and to such depth that the surfaces of the
nail heads are flush with the timber surface'
RulesfortheminimumspacingandminimumdistancesshowninFig. 9.9 are given in Table 9'2'
iirob". should be pre-drilled when the thickness of any timber
members is smaller than:
where:
t is the minimum thickness of timber member to avoid pre-
drilling, in mm;
is the characteristic timber density in kg/m3;
is the nail diameter' in mm'
(7dt : max{ (Bd - }O)lL" -'400
Pt
d
Practical desip of timber structures n Eurocode 5
Table 9.2 Minimum distances for nails where the notdtion is defined h Fig. 9.9
Distance(Fie. 9.9)
Angle, a' Minimum spacing or end/edgc distance
\Without predrilling \7irhpredrilling
p1, < 420kglm) 42A < pk < 50Okg/mr
Spacing, a1
(parallel)
Spacing, a2
(perpendicular)
o3.t'
loaded end
d\.,'
unloaded end
a4.r'
loaded edge
d4r'
unloaded edge
0<a<360
0<n<360
d<5mm: (7+8 coso)d(5 + 5lcosol)d
d)5mm:(5+7 cosril)d
5d 7d
(4+lcosal)d
(3 + | sintrl)J
(7+5coso)d
7d
d<5mm:(3+2sina)d
d)5mm:(3+4sin<r)d
3d
-90< a < 90 (10+cosrr)d (15+5coso)d
90<o<270 10J
0''<a<lB0' d<5mm: d<5mm:(5 + 2 sin o)d (7 + Z sin a)d
d)5mm, d)5mm,(5 + 2 sin rr)d (7 * 5 sin o)d
180'< o < 360" 5d 7d
t5d
Sl,p
The instantaneous slip should be determined as:
K.,: aa8fi51lo(N/mm) (e.3e)
where:
d ls the nail diameter (in mm);p* is the characteristic wood density (ln kg/m3).
With typical values inserted, a slip value of about 0.1d is found at theserviceability limit.
9.3.2 Laterally loaded, wood.based panels,to.wood
Embedding strength
For nails with a head size of at least 2d, the characteristic embeddingstrengths are:
2t4
Connections and faxeners
For plywood:
fr,t,: O.!Iprd-o tt
where:
fnl, is the characteristic embedding strength, in N/mm2;"i; is the charactedstic plywood density, in kg/m3;
d is the nail diameter, in mm.
For hardboard in accordance with EN 622'2:
f4,:3Od-a'310'6
where:
fn,t, is the characteristic embedding strength, in N/mm2;p; is the characteristic hardboard density, in kg/m3;
d is the nail diameter, in mm;
t is the wood-based panel thickness in mm.
For particle board and OSB
ft J,: 65d-o'7 o'r
where:
fnl, is the characteristic embedding strength, in N/mm2;
d is rhe nail diameter, in mm;
t is panel thickness, in mm.
(e.40)
(e.41)
(e.42)
Detailing rules
Minimum nail spacings for all nailed wood'based panel-to'timber
connections are those given in Table 9.2 multiplied by a factor of
0.85. The end/edge distances for nails remain unchanged unless other'wise stated below.
Minimum edge and end distances in plywood members should be
taken as 3d for an unloaded edge (or end) and (3 + 4 sina)d for a
loaded edge (or end), where o is the angle between the direction of
the load and the loaded edge (or end)'Hardboards should be predrilled to avoid damage on the underside
caused by the piercing of the nail point which may reduce the load-
carrying capacity by 70-25oh.
zl5
Practical desip of timber structures to Eurocode 5
9.3.3 Nailed steel-to-timber connections
Detailing rulesThe minirnum edge and e^d distances for nails given in Table 9.2 apply.Minimum nail spacings are rhose given in Table 9.2 multrphed by afactor of 0.7.
SID
The slip for joints with thin steel plates should be taken rhe same as forwood. For thick steel plates the slips are reduced by a factor of 0.7.
9.3.4 Axially loaded nails (withdrawal)
W ithdr aw aI Io ad - c ar ry ing c ap acityThe withdrawal capacity for smooth nails is mainly caused by frictionforces between the nail and the wood. For annular ring shank nailsthere is also a mechanical effect.
Smooth nails shall not be used to resist permanent or long-term with-drawal loads. For threaded nails, only the threaded pu.t should beconsidered capable of resisting withdrawal load. Nails in end grainshould not be considered capable of resisting withdrawar loads.
The characteristic withdrawal capacity of nails, Ro,.tr , for nailingperpendicular ro the grain (Fig. 9.r5a) and for slanr (skew) nailing(Fig.9.15b), should be taken as the smaller of the values found fromthe following expressions.
For smooth nails:
R ., : If".'d'r,,,|. /", ud' -t [n,'"a.r,']i
tI to""
+TIrI
(a)
15 (a) Nailing perpendicular to the
(e.43a)
(e.43b)
t min toai
(b)
fibre direction and (b) slant (skew)Fig. 9.
nailing
2r6
Y Connections and Jastenets
For other nails
(e.44a)
(e.44b)
f o*.k: 20 ' 10-6 P?L
fh,od,k: 7O ' 10-6 Pf,
where:
gt is the characteristic density in kg/ml
For smooth nails with a point side penetration tp.' smaller than 12d
the withdrawal capacity should be multiplied by:
For threaded nails with a poinr side penetration fpen smaller than 8d,
the withdrawal capacity should be multiplied by:
The friction decreases with time and with moisture content changes,
"rp".iutty for smooth nails. However, hot'dip zinc coating increases the
withdrawal resistance of smooth nails' For annular ring shank nails
11o,,udtp",R"'r' :
t fn-r,^ai
where:
{, '. is the characteristic point side withdrawal strength;'in'",r, is the characteristic head side pull-through strength;
d is the nail diameter;
r^-- is the point/side penetration length or the length of the
thteaded part in the point side member;
r is the thickness of the head side member;
dn"od is the nail head diameter'
The characteristic values of the parameters fo*.1 and f1,.u,1,1 sholld be
determined by tests according to [EN 1382]' tEN 13831 and
IEN 14358], unless otherwise specified in the following''
Fo, ,*ooth nails with a point side penetration of at least lTd the
characrerisric values of the withdrawal and pull-through strengths
should be found from the following expressions:
(e.45a)
(e.45b)
(o's7-z)
("t-')
217
Practical design of timber structures to Eurocode 5
hot-dip coating may result in a reduction in the load-carrying capacitybecause the gap between the rings is {illed with zinc material. Therefore,electro zinc coating should be used.
Slant (skew) nailing (see Fig.9.15) may be used to take smallanchorage loads. By slant nailing, the force acts ar an angle to thenail axis and the nails are loaded in both tension and bending.
Detailing rules
The spacing and end and edge distances for laterally loaded nails apply.For slant (skew) nailing there should be at least two nails in a connec-tion and the distance to the loaded edge (see Fig. 9.15) should be ar
least 10d.
Moisture movements
By repeated wetting and drying, the nails will move out, resuldng inprotruding nail heads (sometimes called popping up of nails). Theeffect is most pronounced for long nails. After the first moisture cyclethere is no difference between smooth nails and other nails, but afterseveral cycles the effect is most pronounced for smooth nails. Annularring shank nails and screw nails are, therefore, preferable not forgettingthat shorter nails can be used.
9.3.5 Combined laterally and axially loaded nailsFor connections loaded with a combination of axial load (Fu,.;) andlateral load (F",a) it should be verifred that:
For smooth nails:
F,".d*1g.,Rrr.,i Rn.J - -
For other than smooth nails:
(*)'_'(#)'='
(e.46)
(e.47)
where:
Ro,.,1 and Ru,,1 are the design load-carrying capacities for axial load andlatereal loads respectively.
2t8
Connections and fasteners
Example 9.2
, lr , tz -r
Two dmber members C24 and C16 with thicknesses t1 and t2 are
.irr"d with an ordinary smooth nail with diameter d: 4'7mm and
f, : 600 N/--2. Th" nail length is I : rt -l tz : 90 mm'
Calculate the load-carrying capacity for t1 between
The joint between a purlin and a beam both of cz4 is made with a2 mm thick Simpson strong-Tie universal bracket as shown in thefigure. The fasteners used are annular ring shank nails 4.0 x 40 mm.
Determine the design load-carrying capacity for a short-term loadin the direction of the purlin in Service class 1.
Elastic solutionThe centre of gravity of the nail group is placed zg I 3 : 9.2 mm fromthe left line of nails, and 3a + rc/3: 33 mm over rhe lowermosrnail. The polar moment of inertia is calculated to I, : 3455 mmz .
The load-carrying capacity is found from Expression (9.22).Normally Expression (9.23) {or thin plates should be used bur tests
Tea+t20
I*
220 22r
Y Cont'tections and f asteners
have shown that these nails will be held rigidly by the plate and that
Expression (9.24) rlraY be used.
My,k : O-3fdz'6: O'3 ' 600'42'6: 6620N/mmz
fr,: o.allpud*ot * 0.082 ' 350'4-0'3 : 18'9N/mm2
Without roPe effect;
R"': ^ \ii,iir)
:"n**
The withdrawal parameter is (determined by tests): f,',1rn*2. Th. effective penetration depth is with a point
By a rigorous plasdc analysis a load-carrying capacity of about 2200 Nmay be calculated.
Connections and fasteners
(OS- fOa); and the minimum disiance to the plywood end is 4d'
I
I
i
I
I R,,o
I
n"!
60
50
40
30
20
assumed that the nails are staggered so that n"ff : n'- it. nails may be placed as shown in the figure' The distances are
determined by rir. botto* flange; the theoretical distances in the top
flurrg" are slightly smaller b"tu"t of the inclined grains' The
*ir-lirrr,r* .dg" dirturr.e is 5d : 16 mm; the minimum end distance
is 15d : 57 mm; the minimum spacing in the grain distance is Bd
g.4 Connections with staPles
9.4.I GenetalFo. ,o.,r-rd or nearly round or rectangular staples with
- bevelled or
,i^"rrt."f poi.rt.i legs the rules for nails apply with the following
273
Design the joint berween top and bottom flange in the truss fromExample 7.1.
Proposal
I I",'
222
Pructical design of dmbcr structures to Euror-oJ., 5
F ig. 9. 1 6 Staple dimensio^T
exceptions:
r pre-drilling is not requiredo the characteristic yield moment Mr,;, for staples with diameter d made
from wire with a characreristic rensile sffengrh of 800 N/mm2 shoulclbe taken as:
Mr,k : 240d2'6 (e.48)
For staples with rectangular cross-section, d should be taken equal tothe square root of the product of the two dimensions, i.e. d: t/abwhere a andb are the sides of the rectangle.
The lateral design load-carrying capacity per sraple per shear planeshould be considered as equivalent ro that of rwo nails with the staplediameter, provided that the angle between the crown and the directionof the grain of the timber under the crown is greater than 30o, seeFig. 9.16. If the angle between the crown and the direction of thegrain under the crown is equal to or less than 3O', then the lateraldesign load-carrying capaciry should be multiplied by a factor of O.Z.
9.4.2 Effective number of staplesFor n staples in a row parallel to the grain, the effective number n.yshould be calculated as for nails.
9.4.3 Detailing rulesThe width b of the staple crown should ar leasr be 6d, and the point sidepenetration length t2 should be at least 14d, see Fig. 9.16. There shouldbe at least two staples in a connection. Minimum staple spacings, edge
224
-r-+t1
I'
Connections and Idsteners
Tabte g.3 Minimwnspacings and end and edge distances for snples (see Fig. 9-17)
Angle, n." Minimum sPacings
and distances
d1 parallel to the {ibre direction
For 0 2 30'
For d < 30'
d2 perpendicular to the libre direction
aj,,, loaded end
aj.., unloaded end
a4.,, loaded edge
a4.., unioaded edge
O<a<360
0<a<360
-90<a<909A<a<270
0<a<180180<a<360
(10 + 5l cos al)d(15 + 5l cos al)d
t5d
(15 + 5l cos al)d
15d
(15 + 5lsinrrl)d
10d
Fig. 9.17 Definition of distances between stuples
and enil distances are given in Table 9'3' and illustrated in Fig' 9'17
where g is the nr-rgl" b"it""n the staple crown and the grain direction'
9.5 Bolted connections
g,5.1 Laterally loadedbolts in wood'to'wood iotnts
Yield moment
The yield moment Mr p should be calculated as:
Mr,tr : O.3f,,vdz'6
where:
f,.t is the characteristic tensile strength in N/mmz;
d is the diameter in mm'
(e.4e)
Staple centre
775
Practical desip of timber structures to Eurocode 5
Embedding strengthThe embedding strength , for d .-30 mm, should be calcurated using:
fn.o.t is the characteristic srrengrh parallel ro rhe grain direction inN/mm2;
pt is the characrerisric wood density in kg/ml;a is the angle berween the load and grain direction;d is the bolt diameter in mm; and
ko and fn,...l, as a funcrion of a and d in mm are shown in Fig. 9.1g.
Effective number of bohsFor n bolts in a row parallel to rhe grain direction the effective boltnumber should be taken as rl"yl
(e.51)
where:
d.1 is the spacing between the bolts in the grain diection in mm;d is the bolt diameter in mm.
Some examples of the factor nry are given in Table 9.4.For load perpendicular to the grain direction, the effective number is:
n"ff :' (e.54)
For angles a between the load and grain direction of between o' and99", n"ff may be determined by linear interpolation using Expressions(9.53 and (9.54).
226
(e.50)
(e.51)
(e.52)
("tr"f : mrnl
"r'il#
Connections and fasteners
1.00
0.90
0.80
0.70
0.60
*" 0.50
0.40
0.30
0.20
0.10
0.00
20.0EE) ts.o
*:10.0
5.0
a"
(b)
Fig. 9.18 The factor k," (a) anl the embeddings strength fn.'l' -(b) as a fmctim of
thi dio^rt", d anl the angb a between the't'orce direction and the gram direction
Tabte 9.4 The factor n41 depending on the number
of boks n after each other and their spacing a1
al
l1d10d7d
2
3
5
8
10
1.60
7..30
3.65
5.57
6.80
1.75
7.523.99
6.09
7.44
1.87
2.69
4.266.507.94
0.0
227
Y Connecri{)ns and .fastcners:tical design of timber structures to Eurocode 5
9.19 Mulwshedr ioints
krple shear joints
e load-carrying capacity of multiple shear joints can often be deter-
red by treating the joint as several double shear joints.
\s an approximation, the joint in Fig.9.19 may be treated as tworble shear joints. The middle members with thickness tj limits the
J-carrying capacity to:
lFr.r : 4dfn,o,t (e.55)
?re:
rr,t is the characteristic load transferred per shear in the bolts.
rctural detailing:rimum spacing and end and edge distances as de{ined in Fig. 9.9 are
en in Table 9.5. Bolt holes in timber should have a diameter of notre than 1mm larger than the bolt diameter. Bolt holes in steel
tes should not exceed the bolt diameter d by more than 2 mm ord (whichever is greater). This is for ease of fitting.Vashers with a side length or a diameter of at least 3d and a thickness ofleast 0.3d should be used under the bolt heads and nuts. Washers,uld bear fully on timber. Bolts should be tightened so that the members
:losely, and they should be retightened if necessary when the timberreached equilibrium moisture content to ensure that the load-
rying capacity and stiffness of the structure are maintained.
e following embedding strength, in N/mmz, should be
;les to the grain of the face veneer:
i,o,r : 0.11(1 - 0.0ld)p1
l
Table 9.5 Mirrimum spacing ancl end and edge distances for boks
1ilf,
a1 parallcl t(' rllc gririn Jirecti"n
d2 perpendiculi'rr to the grain direction
a3., loaded end
aj,- unkraded end
0<rr<1600<rr<360
-90<o<90
90<cr<150
150<a<210
210<a<270
0<a<180
180<ri<160'
(4+lcosol)d
4d
( 7,1max <
| 80 mn'r
f(1*6sintr)d'tn*1 4,1
4d
[ (1 +6sino)J"tt*t 4,'l
f(2+Zsin.r)dnto*1 lJ
1d
CF
a4., loaded edge
a4.. unioaded edge
used for all
(e.56)
where:
pt. is the characteristic density of the plywood in kg/ml;
d is the bolt diatneter in mm'
Particle boards and OSB
Th" follolving embeclding strength' in N/rnmz' should be used:
fi.,o,r,:5od o'6t02 (9'57)
where:
d is the holt diameter in mm;
t is the wood'based panel thickness in mn'
g.5.3 Laterally loaded bohed ioints, steel'to'woodjoir-r,, u, ,ho*'ri't Fig. 9.19 u'" to*"-'o''tly used in wind bracings for
glularn structures.
9.5.4 AxiallY loaded bolts
BoLt strengthg.fr, -"r, have sufficient strength according to Eurocode 3 for steel
structures (EN 1991)' i'e':
N, . I (9'58)A,f u.dc -
229
Practical desig of timber structures to Eurocode 5
t-L -l
Fig, 9.20 Non-sJmmetric double-shear joint
where:
N is the concentric tensile force;A, is the cross-section area of the bolt;f,.a is the design tensile strength of the bolt marerial;
f 0.90 for rolled threadC:{
|. 0.85 for cur thread
WashersAdequacy of the bending srrength of washers musr be checked and thebearing stress under the washer should ful{il the following condirion:
o,.dlf,.eo.d 4 3 (e.5e)
The bearing load-carrying capacity of bolts under a steel plate shouldnot exceed that of a circular washer with the diameter of:
o lZt, where r is the plate thicknesso 4d, where d is the bolt diameter.
9.6 Connections with dowels
9,6.1 GeneralThe dowel diameter should be greater than 6 mm and less than 30 mm.
9,6.2 Detailing rulesThe rules for bolts apply, except that Table 9.5 should be replaced byTable 9.6.
230
Connections and f asteners
Table 9.6 Minimum spacing and end and edge distances for dowels (see Fig. 9.9)
a1 parallel to the grain direction
a2 perpendicular to the grain direction
a3., loaded end
a3,. unloaded end
a4,, loaded edge
a4.. unloaded edge
0<a<3600<o<360
-90<ri<90
90<a<150
150<a<210
210<a<274
0<a<180
180<a<360
(3 + 2l cos crl)d
Jd
(7dmax {
|80mm
f .r3.,lsinnldmax <
[]d3d
I a3,l sin old-u*l rd
f(2+2sina)d*'*t -],r
ttl,
9.7 Connections with screws
9.7.1 l-aterally loaded screcrs
Lo ad- c arry ing c ap acity
The effect ofthe threaded part ofthe screw shall be taken into account
in determining the load-carrying capacity, by using an effective diameter
d41.For smooth shank screws, where the outer thread diameter is equal
to the shank diameter d, the effective diameter d.6 should be taken as
the smooth shank diameter provided that the smooth shank penetrates
into the member containing the point of the screw by not less than 4d,
otherwise d.11 should be taken equal to 1.1 times the thread rootdiameter.
For smooth shank screws with a diameter d > 6 mm, the rules forbolts apply.
For smooth shank screws with a diameter d < 6, the rules for nails
applv.
Detailing rules
For all screws in hardwoods and for screws in softwoods with a diameter
d > 6 mm, pre-drilling is required, with the folbwing requirements:
o The lead hole for the shank should have the same diameter as the
shank and the same depth as the length of the shank.
2i1
Practical desip of timber structures to Eurocode 5
o The lead hole for the threaded portion should have a diameter ofapproximately 70o/o of the shank diameter.
For timber densities greater than 50okg/#, the pre-drilling diarnetershould be determined by tests.
9,7.2 Axially loaded screu's
Inad-carrying capacity
The following failure modes shall be taken into account:
r withdrawal failure of the threaded part of the screw
o tear-off failure of the screw head when screws are used in combina-
tion with steel plates; the tear-off resistance of the screw head
should be greater than the tensile strength of the screw
o pull-through failure of the screw head
o tensile failure of the screw
o buckling failure of the screw when loaded in compression
o failure along the circumference of a group of screws used in con-junction with steel plates (block shear or plug shear). It should be
noted that block shear or plug shear cannot be verified for nails
and screws using Annex A of Eurocode 5.
For screws according to EN 14592 with 6 mm ( d < 12 mm and
0.6 < drld < 0.75, the characteristic axial load-carrying capacity
R*,o,d should, provided a ) 30o, be taken as:
F*k:
with:
(e.60)
Cornections and f astener s
is the active number of screws acting together;is the effective number of screws;
is the penetration length of the threaded part, in mm;
is the characteristic densiry, in kg/m';is the angle between the screw axis and the grain direction.
other screws, the characteristic axial load'carrying capacity
be taken as:
nneff
I
P,"
a
For
where:
d is the outer thread diameter;
il is the inner thread diameter;
f*,u i, the characteristic withdrawal strength perpendicular to the
grain direction, in N/mmz;
232
(e.63)
fLt, it the characteristic withdrawal strength perpendicular to thegrain direction determined in accordance with EN 14592 forihe associated density of po, inN/mm2;
pa is the associated density (i.e. the density used in testing) in kg/m'.
characteristic pull-through resistance Rh"od.o.k of a connectionaxially loaded screws should be taken as:
(e.64)
3 is the characteristic head pull-through capacity of theconnection at an angle o that should not be less than 30o, tothe grain direction, in N;is the characteristic head pull.through parameterdetermined in accordance with EN 14592 for the associateddensity po in N/mm2;is the diameter of the screw head, in mm.
characteristic tensile resistance ofthe connection (head tear.of{capacity of shank) should be taken as:
,k = nsffRr,p (e.65)
I is the characteristic tensile capaciry of the screw determined inaccordance with EN 14592;is the effective number of screws determined according toExpression (9.63) n4 : no'e
f *l : o.5zd*o 5t;f t pf;8
(dI
ka : min{ 8
Ir
(e.6r)
Q.62)
n41f o,,1dlqk6
L.7 cosz a * sin2 a
233
Practiccrl desigr of timber structures to Eurocode 5
Az.CC 22 €Iz cet.-ts-t*l
t-l| ","n I
dz,ce
8z,cG
dt.ce
Fig. 9.21 Spacings and distances to end and edge
Detailing rules
o The angle tl between the screw axis and the grain direction shouldnot be less than 30".
o The timber thickness should nor be less than 12d.o The point side penetration should not be less than 6d.
The minimum spacings and end and edge distances as shown inFig.9.2l are given in Table 9.7.
Table 9.7 Minimum spacing and distances to end and edge
Minimum spacing Minirnum spacingin a plane parallel to perpendicular to a
the grain direction plane parallel to thegrain direction
Minimum enildistance of thecentre of thethreaded part of thescrew in themember
Minimum edge
distance of thecentre of thethreaded part ofthe screw in themember
.Lz
5d
tl1
7ddt.cc10d
42.cc
4d
234235
Connecrions and fasteners
Example 9.5
-rlolCf)lxlsI
A roint in a tension member 75 x 120mm of C74 with density
,r': lSOkg/mr is made as shown with gussets 47 x l20mm and
1) ,.r.t, 8 x 160mm with an inner thread diameter of 6mm
made of steel4.6 service Class 1'
Calculate the load'carrying capacity for a short-term load'
The lateral load'carrying capacity is determined as the capaciry of
ffio double shear joints, one with \: 47 mm and tz:75 and one
with 11 : 160 * 47 * 75 : 38mm and tz : 75 mm'
Th; calculations are made with an effective diameter
duff : l.I '6:6.6mm'"'the yield moment with fi :400N/mm2 is
Mr,k : A3fdlf : 0'3 ' 4OO '6'62'6 : 16 2OONmm
The embedding strength for load parallel to grain is:
The characteristic load-carrying capacity per shear, R1, for a connection
consisting of one plate and one bolt should be taken as:
Rk:Ro.u*R..1
where:
(e.76)
R1,,l is the load'carrying capacity of the bolt;
n_,i " the load-carrying capaciry conrribution from the tooth-plate.
The characteristic load-carrying capacity of each tooth plate should be
taken as:
for single-sided types
for double-sided types(e.77)
where:
k, are modification factors, with i : 1 to 3' de{rned below
d, is:
o the tooth-plate connector diameter for circular types' in mm;
o the tooth-plate connector side length for square types, in mm;
o the square root of the product of both lengths for rectangular and
oval types, in mm.
The minimum rhickness of the outer timber members should be2.75h",
and minimum thickness of the inner dmber member should be 3.75h",
where h. is the tooth penetration depth (see Fig. 9 '24) '
. _ltSklkzkrdl5'v'k - \ zsLrLrtralt
The factor k1 is:
Ii,I
kr : min{ Jh.
t+where:
(e.iB)
t1
t2
h"
is the side member thickness, in mm;
is the middle member thickness, in mm;
is the tooth penetration depth, in mm.
Practical desig of timber structures to Eurocode 5
Fig. 9.24 Joints with pressed-in tooth-plate connectors
The factor k2 should be taken as:
(e.7e)
(e.80)
where:
d is the bolt diameter in mm.
The factor k3 should be taken as:
( 1.5kr : min{ pr. (9.81)
l;so-
where:
pt, is the characteristic density in kglm3.
Structural detailingFor bolts used with tooth-plate connectors, the rules for bolts applybut the minimum spacings and minimum end and edge distancesshould be those given in Table 9.9 with the symbols illustrated inFig. 9.9.
242
I,I'
with:
k, : -1r-r{ 1or,,
l. 1 5,1.
( r.td,ol, : -i,,{ 7d
Iso*-
Connections and f asteners
Table 9.9 Minimum spdcing and end and edge distances for tooth'pldte
connectoTs
Angle a" to the6bre direction
Minimum spacings
and distances
a1 parallel to the grain
a2 perpendicular to the grain
a3., loaded end
a3.. unloaded end
a4,, loaded edge
aa. unloaded edge
0<o<360
0<n<360
-90<a<9090<aci50150<a<210210<a<270
0<a<180
180<o<360
(1 .2 + 0.3 | cos rr | )d.
t.2d,
7.Ad,
(0.9 + 0.6lsinal)d.t.2d,(0.9 + 0.6lsinol)d.
(0.6 + 0.2lsin al)d.
a.6d,
when circular tooth-plate connectors are staggered Expression
(9.73) applies.Toothed connectors shall be pressed into the wood without cutting
excepr that it is permitted to mill for the plate with a depth slightly
,mali", than the plate thickness. The mill is performed to avoid a gap
in the joint.Because the force needed to press the connector in is rather high,
bolts with diameter of 16mm or less must not be used for pressing in
the connectors. For smaller diameters special bolts should be used for
pressing in the connecrors first and then replaced by the specified
tolts. Washer with rhe same size as the connector (d.) and thickness
of not less than 0.ld. shall be used. If needed, tooth-plate connectors
can be pressed in by hammering using a stiff steel plate provided that
care is taken not to damage the tooth'plate.
DeformationsFor do,rble-sided and single-sided tooth-plates the initial slip is
about lmm and (1 + O.OO5d) respectively, where d is the bolt
diameter.
243
Practical design of timber structures to Eurocode 5
Example 9.7Design the joint between top and bottom flange in the truss designedin Example 7.1 with 16mm spruce plywood gusset plates and boltsand pressed-in connectors (Bulldog), when the reaction is actingon the bottom flange as shown in the figure below.
The joint shall transfer the tension force in the bottom flange:
FtTd:10.05kN, the compression force Fr,z,d: 19.69kN and
the reaction R - 3.66kN (short-term loads).
Since the joint has a pronounced plastic behaviour there is great
freedom to choose how the forces in the joint are distributed. Asone extreme it may, as shown to the left in the figure below, be
assumed that the force in the top flange is transferred to the gusset
plates acting as cantilevers fastened to the bottom flange. Anotherextreme is shown to the right in the figure; here it is assumed thatthe reaction and the force in the bottom flange are transferred tothe gusset plates acting as cantilevers fastened to the top flange.
In the following figure it is assumed that the forces are transferredin the joint line.
Force transfer
62 mm round Bulldog connectors with 12 mm bolts 4.6 are chosen.
244z+5
Connecttons dnd ldsrcners
[',,- 16 :o.z1lo':*'"i
T:t4:;r, IItt -5'
kz: I(r.5 )
kj : *in{ pk - 110 : 0.89 I : o'89
I lso: 350 -F-,1 : ?sk,.^zk/d:s :75'0'?1'1 '0'89' ezrs ltooo:7'72kN
: 0.71
Q,1) 1.5d.'
and
For the bolts with f' : 4ooN/mm,'
Mr : O'31,d76 : A3 '400' !?2'6 :76 750Nmm
A density of 400 kg/# it assumed for spruce plywood:
fn,u = 0.1lpkd-o'3 : 0'11 '400 'lZ*03: 20'9N/mmz
The angle between the force and grain direction in the bottom
Practical design of timber stntctures to Eurocode 5
14.2kN { R; * 2' 8.1 : 16.2kN
The load componenrs on bolt 1 in the grain direction (x) andperpendicular to this direction (y) arer
F4 = 10.0 5/2 :5.03 kN
Fy,d : 3.66.5101120 : 13.3 kN
The angle between {brce andtana : L3.315.03 :2.64
graln direction is found from
a : 69o, i,e. close to the estimated value.
Fl,n+ Fl, *
246
Fig. 10. I Diaphragms m a simple building
247
10
Diaphragms
10.1 IntroductionDiaphragms are often fart of timber structures where one of their roles is
to resist lateral fo,.""'l"t'-u' ''"i"a' Diaphragms are-normally parts of
the structure with toJJ"'"d panels o'-gypttrtn plasterboards fixed
to a dmber framing ";; ;t both sides' In most cases the panels are
fastened by mechani."ii^r,"""rs, but gluing may also.be. used which
can enhance the stiffness of the structures' Structural gluing should
only be dor," .tnd"'"i;;;;'t;""t1".d conditions' Site gluing for
structural purposes is not recommended'
Figure 10.1 shows ';t;;i" t"iqing where the lateral loads from wind
or earthquakes are rransferr"d to the supports by help of both horizonal
and vertical diupt',,"g'n'' it'Jouat o" 'h"
faEades are-transferred by the
wall structur" ,o ,t " roof diaphrug* u,'j from that to the gable
diaphragms urrd do*'i t" 'ft"
gt"""al fn" roof diaphragms may be flat
or pitched.
Practical design of timber structures to Eurocode 5
lO.2 Roof diaphragm (simply supported diaphragm)For I betweenzb and 6b (Fig. 10.2), it may assumed that the moment isresisted as tension/compression by the edge beams:
( 10.1)
where v is the uniformly distributed (wind) load on the edge beam.Provided the strength is determined by the fasreners and not thepanels, the shear forces may be assumed to be evenly distributed overthe width b, i.e. the load per nail becomes:
t)_ qJIL^ stgeoeum
Bb
nFVr:aT:a,
t)
where a is the nail spacing, r is the shear stress and Q is the shear force.The nail load-canying capacity may be taken 20% larger than the valuescalculated according to section 9.3, because the large number of nailsreduces the variation. All nails shall be rhe same rype at equal spacingsof not more than 150mm along the perimeter of the boards and300 mm within the boards. All square-edges of panels must be supportedand nailed to the supports (i.e. joists, beams or noggings) as shown inFig. 10.3.
Theloacl.carryingcapacityofawallmadeofnwallpanels(seeFig.10'5)should be calculated as:
R,.,r : I0",r,,
b+
Fi,r.a
Fig. 10.4 A tlPical wall Panel:
stress on sheathing
(b) (c)
(a) extemal loads; (b) timber framing;
(10.3)
(c) shear
249
Practical design of timber structures to Eurocode 5
F,g. 10.5 Wall consisting of seueral wall panels of which panel (2) has openingsund panel (3) has d smdller width than the others
The load-carrying capacity of the panel i with wood-based panel on oneside should be calculated as:
. 1 .ZRS.,tbiciAu.d.i :'a
where:
Rl,, is the design lateral load-carrying capacity of one nail calculatedas in Chapter 9;
( I ftrr b; > 0.5h
'' :
\zu,1t for bi < o.5h (10'5)
a is the fastener spacing.
The contribution from panel elemenrs wirh openings should be dis-regarded.
For wall panels with wood-based sheathing on both sides thefollowing rules apply:
If the sheathing and fasteners are of the same type and dimension, thenthe total load-carrying capaciry of the wall should be taken as rhe sumof the load-carrying capacity of the individual sheathing on both sides.If different types of sheathing are used, 75% of the load-carrying capa-city of the weaker side may be taken into consideration if fastenerswith similar slip moduli are used. In other cases not more than 50%of the load-carrying capaciry of the weaker side should be used.
The external forces
Fj...,j : Fr.r,,l: Fi.r.dhlb (10.6)
can either be transmitted to the sheathing in the adjacent wall panel ortransmitted to the structure situated above or below. When tensile
250
(10.4)
DiaPhtagms
forces arc transmitted to the structure situated below, the panel should
be anchored by stiff fasteners'
Buckling of wall studs should be checked. where the ends of studs
bear on h,xir.rr-rtal framing members (i.e. bottom rail) ' the compression
p"rp."a."far to the grain stre'ses in the bottom rail should be assessed''
1-n" external forces that arise in wa|l panels containing door or
window openings and in wall panels of smaller width (see Fig. 10.6)
can similaily be transmitted to th" stluctures situated above or beklw'
The buckling stability of the sheathing shall be veri{ied. However, a
buckling investigarion may be omitted for the wood-based panels if the
.^tio of'the cleai stud disiance b,,., and the sheathing thickness r fulfil
the condition:
b,,,,rf t < 100 (10.i)
10.3.2 MethodB
IntroductionThe uK National Annex recommends the use of Method B, instead of
Method A, in the UK.Figure 10.6 shows a wall assembly consisting of walls (6, 7 and 8) each
madJ of wall panels (I,2,3,4 and 5)' Some of the panels (3 1d {) have
op"rlrlg, for windows (12) and doors (13) fespectively. The wall panels are
made o?timber frames covered by sheathing of wood-based panel products.
Th" \Mull panels are linked by a head binder across the wall panel joints.
For a rvall panel to contribute to the in-plane (racking) strength of a
wall, the width of the wall panel should be at least the panel height
I
@ o@
Flg. 10.6 \X/all assembll
@
z5l
Practical desip of tintber structures to Eurccode 5
dlvided by 4. The fasteners of the sheathings to the timber frame shouldbe by either nails or screws, equally spaced around the perirneter of thesheathings (wood-based panels) ar not more rhan 15Omm cenrres fcrrnails and 200 mm for screws. The spacing of fasteners within the peri-meter of sheathings should not be more than twice the perimeter spacing.
'Where an opening is formed in a wall panel, the lengths of the wallpanel on each side of the opening should be treated as separate wallpanels.
The required connection strength between the vertical joints ofadjacent wall panels should be evaluated but should have a designstrength of at least 2.5 kNim. The wall panels when joined rogerherto form a wall should be able to resist overrurning and sliding forcesby either anchorage to the supporting structure or the permanentactions applied to the wall or a combination of both effects. T'l-re wallis loaded at the top by a horizontal racking force Fu.,1.
Load-carrying capacity
The racking strength Ru.; should be calculated as
Rr,,J : I Rr.",a
The contribution from wall i is:
^ R".
fo ,rrn"rdb,R,.n'.J : -_:t;": u4k,.rk,k,,
where:
R"Ja.v",.,,d is the lateral design load-carrying capacity of an individualfastener;is the wall length, in m;is the basic fastener spacing, Expression (10.10) in mm;is the dimension factor for the panel, see Expression( 10.1 1);is the uniformly distributed load factor for wall l, see
Expression (10.12);is the fastener spacing factor, see Expression (10.13);is the sheathing material factor, see Expression (10.14);
9700d( r0.10)
is the fastener diameter, in mm;is the characteristic density of the timber frame, in kg/ml;
(10.8)
(10.e)
bi
s6
kd
k,.,
k,
kn
sO:
d
P*.
752253
,,:l
LaF;.,",r.44i.vert,tl: --q-
where:
bi
h
(?).
(T)'
" bi-tt)f - 1
h-l"
for?>h
I
landb; <4.8m
DiaPhragms
(10.1 1a)
( 10.1 lb)
( 10.1 1c)for\n> 1 and b; ) 4.Bm
where:
h is the height of the wall, t:Tl, _
k,.u - I + (O.O8lqr - 0'O08qi, (?)where q; is the equivalent uniformly distributed vertical load acting on
the wail, in kN/m, see (10.14a) and (10'14b)'
I _ __k,:-- s +0.5/0.86 -sg
IRi,",d.r,o" * 0. 5Ri.",,l.nri'
R,.u,,,l,*o*
( 10.1 2)
(10.13)
for sheathing on one side (10.14a)
for sheathing
on both sides( 10.14b)
( 10.15)
k": t
where:
R, ".,i.^.," is the design racking strength of the stronger sheathing;
ii,;ffi is the desiln racking strength of the weaker sheathing;
;i',;:,;; is the design racking strength of the stronger sheathing'
The equivalent vertical load' q;, used to calculate k;' shouldbe deter'
mined uri.rg o^ly perrnanent actions and any net effects of wind together
with the "q.,irrul"r-rt
actions arising from concentrated forces' including
anchorage forces, acting on the panel' For the purposes of calculating
k;, concJntrated vertica'i forces should be converted into an equivalent
tr"tf.trnfn distributed load on the assumption that the wall is a rigid
loJr, . g. for the load F;.u",,,4 acting on the wall as shown in Fig' 10'7:
is the horizontal distance frorn the force F to the leeward corner
of the wall;is the length of the wall.
Prucrical design of timber structures to Eurocode 5
{TITITIT} O
Lr. lcl,t.c.d l'\t.d
| ,,.0,0
F-- -Fig. 10.7 Determination of equivalent uertical load, qi, and reaction forces fromuertical and horizonnl loads
Fi,r,a<-
l r,oo
The
Fi.r.d
reactions should be calculated as:
- F,.,.ah
- 't.t.d - 0!( 10.16)
where h is the height of the wall.The external forces can be transmitted to the adjacent wall panel
either via the vertical panel-to-panel connections or via the structureabove or below the wall. \x/hen tensile forces are transmitted to thestructure below, the wall panel should be anchored with stifffasteners.
compression forces in the studs should be checked for buckring.where the ends of vertical members bear on horizontal framingmembers (i.e. bottom rails) , the compression perpendicular to thegrain stresses in the horizontal members should be assessed.
The buckling of the sheathings under the action of shear force Fu,,lmay be disregarded provided:
b".; < 100 (10.17)
where:
bn", is the clear distance between studs;t is thickness of the sheathing.
The uK National Annex allows Annexes A, B and c of Eurocode 5 tobe used if required.
254
References
British StandardsBritish Stanclards Institution. General requirements for components used in dis'
charge pipes, drains and sewers for gravity systems' BSI, London, BS 476-6'
Brltish Sian<tards Institution. Fire fesfs on building materials and structures.
Metl'tod of test to determine the classification of the surtace spread of flame of
products. BSI, London, BS 476'7 .
British Srandards Institure. Visual grading of softwood. BSI, London, BS 4978'
British Standards Institution. Structural use of timber. Code of practice forpetmissible stress clesign, materials and workman'shrp' BSI, London, BS5^268'2'
gritist Standards Institurion. Code of practice for trussed rafter roofs. BSl,
London, BS 5268-3.British Standards Institution. Structural use of timber. Fire resistance of timber
stTuctures. Recommendations for calculating fire resistance of timber members.
BSI, London, BS 5268-4.1'
British Standards Institution. Structural use of timber. Fire resisumce of timber
structures. Recommendations for calculating fire resistance of timber stud walls
and joixedfloor construccions. BSI, London, BS5268'4'2'
BritisLr Staniards Institution. Code of practice for the preseruatiue treatmem of
structural rimber. BSl, London, BS5268'5'
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frame walls. Buildings other than dwellings not exceeding /or.rr storels. BSI,
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imposed loads. BSI, London, BS6399-1'
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loads. BSI, London, P,56399'2'
British Standards Institution. Loading for buildings. Code of practice for irnposed
roofloads. BSI, London, BS6399'3'
755
Practical design of timber structures n Eutocode 5
European Committee for Standardisation. LttminatedVeneer Lumber (LVL) -Definitions, classification and requirements. CEN, Brussels, EN 14279.
European Committee for Standardisation. Timber structures - Calculation ofcharacteristic S-percentile ualues and dcceptance criteria /or a sample. CEN,Brussels, EN 14358.
European Committee for Standardisation. Timber structures - Structural
laminated c)eneer lumber - Requirements. CEN, Brussels, EN 14374.
European Committee for Standardisation. Timber structures - Connectors -Requirements. CEN, Brussels, EN 14545.
European Committee for Standardisation. Timber structures - Fasteners -Requirements. CEN, Brussels, EN 14592.
European Committee for Standardisation. Timber structures - Prefabricated
wall, floor and rocf elements. CEN, Brussels, EN 14732.
European Committee for Standardisation. Structural timber - Sluctural timber
treated againstbiologicdl arraclc. CEN, Brussels, EN 15288'
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Document A: Structure. NBS (part of RIBA Enterprise Ltd), London.
Digest 477. \7ood based panels. BRE.
- Part I Oriented smand board' 2003.
- Part 2. Particle board (chipboard). 2003
- Part 4. Plywood. 2003.
- Part 5. Medium density fibreboard (MDF). 2004.
- Part 6. Hardboard, medium board and softboard. 2004.
Enjily, V. The six-storey timber frame building project (TF 2000) at BRE
cardington. Holzbau Forum 6, 6-8 December 2000. Garmisch Patenkirchen
Germany. 2000.
Gulvanesian, H., Calgaro, J.A. and Horlicky, M. Designers guide to EN 1990
Eurocode: Basis of structural design. Thomas Telford Ltd. 2002.
Johansen, K.w. Theory of timber connections. International Association 9fBridge and Structural Engineering (IABSE), Basel, 1949, Publication 9.
Morris, W.A., Read, R.E.H. and Cooke' G.M'E. Guidelines for the construction
of fire-resisting structurdl elements. BRE, 1988, BRE 128, ISBN 0851252931.
