neer Basis of design, material properties, structural components and joints
Edited by H.J. Blass P. Aune B.S. Choo R.Gsrlacher D.R. Grifiths B.O.Hilson P. Racher G . Steck
First Edition, Centrum Hout, The Netherlands
Contents
Preface AcknowIedgements AII~/ZOI'S National Representative Organisations . Contract im~zpleinentat~ . . . .
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. . . . . . . . . . . . .
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A
Basis of design and material properties
A1 A2 A3 A4 A5 A6
A17 A18 A19
European standardisation Limit state design and safety format Actions on structures . . Wood as a building material . . . . . . Timber in constmction . . . . . . Strength.grading . .. Solid timber Strengtl~classes GIued laminated timber - Production and strength classes Laminated veneer lumber and other structural sections Wood-based panels - Plywood Wood-based panels - Fibreboard, particle board and OSB Adhesives Behaviour of timber and wood-based materials in Are Detailing for durability Durability - Preservative treatment Environmental aspects of timber Serviceability limit states - Deforn~ations Serviceability limit states - Vibration of wooden floors Creep
B
Structural components
A7 A8 A9 A10 A1 l A12 A13 A14 A15
AXG
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Volume and stress distribution effects Tension and conlpression Bending Shear and torsion Notched beams and lloies in gluIail~beams Columr~s Buckling lengths Tapered, curved and pitched cambered beams Glued thin-webbed beams Srressed skin panels Mechanically jointed beams and colutnns Trusses Diaphrag~l~s and shear walls Franles and arches STEPEUROFORTECI-I - an iiiitiativc ur~der[he EU Come~tProgramme
Foreword This publication is the first major output from the Structural Timber Education Programme (STEP) work initiated by Eurofortech and supported by the Comission of the European Communities under the Comett programme. It represents a commendable effort by about 50 people from 14 European countries to make Eurocode 5 operational and accepted by the users. Eurocode 5 is a legal document aimed at the qualified engineer wit11 a basic knowledge of timber and timber structures. It gives the requirements for design, but not their background. It cannot stand alone. It has to be supported by textbooks explaining the general philosophy of the Eurocodes, especially Eurocode 5, and giving the background for its requirements and detailed design rules. The STEP lectures are such a textbook for direct use by instructors at engineering schools and a basis for writing national textbooks.
The STEP project is closely linked to Eurocode 5, the European code for the design of timber structures (ENV 1995-1-1 and 1995-1-2). Work on Eurocode 5 began in 1973 when John Sunley - at that time at the UK Forest Products Laboratory, later director of TMDA - initiated the drafting of a model code for the design of timber structures in Working Commission W18 of CIB (The international council for building research, studies and documentation). The initiative of John Sunley was very timely; the result the CIB Structural Timber Design Code - was published in 1983 and was immediately accepted as the basis for the timber part when the Commission of the European Communities in 1985 initiated drafting a set of European design codes: the Eurocodes.
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Eurocode 5 is the result of tremendous cooperative efforts involving people from industry and most timber researchers in Europe (with substantia1contributions from Australia, Canada and USA), The main forum for this cooperation has been C B Wl8; most of the technical details have been discussed in this working group, and the background has been reported in the proceedings from its meetings: so far 26 volumes, about 1OOOO pages. Devoted and qualified authors are one reason for the successful outcome. Equally bportant is the management of the project. In this respect STEP has been extremely lucky. The management and reviewing committees headed by Hans J. Blass have done an outstanding job.
Hans J~rgenLarsen, Chairman, Eurocode 5 Drafting Committee
STEPiEUROF0RTECI.I - an initiative under the EU Comett Programme
Preface European harmonisation The unification process in the European Union (EU)has led, and will continue to lead, to changes which will impact on n b y aspects of life in the member countries, including industrial practice. A key objective of the EU is the creation of a stronger and more competitive industrial base. This is being achieved in a number of ways including technological innovation, intensification of training, and the standardisation of key practices and operations within industry. The l~armonisationof component and product quality standards is an important elenlent of this process. Such harmonisation facilitates not only for freer movement of goods and services within the EU but also for enhanced col~esion and competitiveness in the presentation of the products of EU industry in external markets.
New standards require adjustments in training Within tile industrial sectors of timber processing, manufacture and utilisation, new European standards are being prepared. In the specific area of the utilisation of timber for structural purposes a series of standards is being developed in support of Eurocode 5. It is anticipated that the European stadards will eventually replace the various equivalent national standards. The introduction of the new standards will require adjustment both'in education and training institutions and on the part of practising professionals in the architectural, engineering, building and manufacturing sectors. A lead-in time is required to facilitate a smooth transition for industry to the changed environment of a transnational harmonised market.
STEP/Euroforteeh, background In its role as the transnational EEU network for training and education for the forest and wood industries, EUROFORTECB has recognised the educational implications of the changes being experienced by Europe's forest and wood sector industries. During the past three years it has helped to create STEP, the Structural Timber Education Programme and assisted a large team of European experts to prepare the STEPfEUROFORTECN teaching materials relating to the use of timber in structural applications. The two volumes of this cotnpendium of technical inforlnation were made possible througl~the financial contributions of the European Union and 14 participating countries. It will assist teachers, students and practising professionals in applying and implenlenting new European standards for the structural use of timber. This pool of information wilI both contribute to the structural use of timber and increase technical expertise within the industry. Thiber Engineering - STEP 1 is the first volulne of the STEP cornpendium and will be complemented by the second volume, Timber Engineering - STEP 2. In additiol~a supporting slide collection is available.
The purpose of the compendium is to assist engineers, lecturers and students to implement Eurocode 5 Design of timber structures - Part 1-1: General rules and rules for buildings and Part 1-2: General rules - Supplementary rules for struchiral fire design. Since the Eurocodes are not yet available in their final fonn at the time of printing, minor discrepancies between Eurucode 1 and Eurocode 5 still exist and are addressed in the relevant lectures. The chapters of the book contain timber engineering lectures and were written by specialist lecturers and experienced civil engineers, and correspond to tile best available knowledge in 1994. Lecturers using
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STEPlEUROF0RTECI-I at'i initiiltive under the EU Comctt Programme
Acknowledgements Authors Timber Engineering - STEP 1 T.Alsmarker, Lund University, Division of Stmctural Engineering, P.O. Box 118, 5-221 00 Lund, Sweden
L. Andriarnitantsoa, Centre Experi~nenraldu Batiment et des Travaux Publics, Departement Batiment, Domaine de St. Paul, F-78470 St. Remy les Chevreuse, France
P. Aune, University of Trondlleim, The Norwegian Institute of Technology, Dept. of Structural Engineering, Rich. BirkeIands vei la, N-7034 Trondl~eirn,Norway H.J. Blass, Delft University of Technology, Faculty of Civil Engineering, Timber stnrctures, P.O.Box 5048, 2600 GA Delft, Netherlands
H. Briininghoff, Gesamthochschule Wuppertal, Pauluskircfistrasse 7, D-42285 Wuppertal, Germany
A. Ceccotti, Universirh degli Studi di Firenze, Dipartimento di Ingegneria Civile, Via di S. Marta 3, 1-50139 Firenze, Italy
B.S. Choo, University of Nottingham, Dept. of Civil Engineering, University Park, Nottinghanl NG7 2RD, United Kingdom F. Colling, Deutsche Gesellschaft fiir Holzforschung e.V., Bayerstrasse 57-59, D80335 Miinchen, Gern~any
B. Edlund, Chaimers University of Technology, Dept. of Structural Engineering, Sven Hultins gata 8, S-41296 Goteborg, Sweden J. El~lbeck, Universitat KarIsrul~e, Lehrstuhl fiir Ingenieurholzbau und Baukonstruktionen, Postfach 6980, D-76128 Karlsruhe, Gemlany W. Ehrl.lardl, Universitat Karlsruhe, Letlrstuhl fir Ingenieurlmlzbau und Baukonstruktionen, Postfach 6980, D-76128 Karlsruhe, Germany
E. Gel~ri,ETHZ, Professur fiir Holztechnologie, ETH Honggerberg, CH-8093 Ziirich, Switzerland P. Glos, Universitat Miinchen, Institut f i r Holzforschung, Winzererstrasse 45, D80797 Miinchen, Germany
R, G~rlacher, Universitiit Karlsruhe, Lel~rstuhl Er Ingenieurholzbau und Baukonstruktionen, Postfach 6980, D-76128 Karlsruhe, Gemany
D.R. Griffiths, University of Surrey, Dept. of Civil Engineering, Guifd ford, Surrey GU2 SXN, United Kingdom
STEPIEUROFORTECE-I- m initiative under the EU Cornett Programme
F. Rouger, Departement Structures, Centre Technique du Bois et de I' Ameublement, 10, Avenue de Saint-Mand6, F-75012 Paris, France
G . Sagot, Consultant Industriel, 9, Rue de Ren6ville. F-75400 Fecamp, France
K.H. Solli, The Norwegian Institute of Wood Technology, P.O. Box 113, Blindern, N-03 14 Oslo 3, Norway G. Steck, Fachhocl-rschule Miinchen, Kartstrasse 6, D-80333 Miinchen, Germany P.J. Steer, Consultant Structural Engineer, 28 Aslbourne Road, Derby DE3 3AD, United Kingdom
S. Tfieiandersson, Lund University, Division of Structural Engineering, P.O. Box 1 IS, S-221 00 Lund, Sweden
T. Vihavainen, VTT Building Technology, Wood Technology, P. 0.Box 1806, FIN-02044 VTT, Finland .
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H. Werner, Universitat Karlsruhe, Lehrstul-rl fiir Ingenieurl~ofzbau und Baultonstruktionen, Postfacfi 6980, D-76128 Karlsruhe, Germany
L. Whale, Gang-Nail Systems Ltd., Christy Estate, Ivy Road, Aidersfiot, Hants GU 12 4XG, United Kingdom
STEPIEUROFORTECII.- an initiative under d ~ eEU Comctt Programme
Nerherlcznds NRO: Centrun1 Hout, Almere Supporting organisations: Delft University of Technology, Delft; Stichting WESP, Woerden; Stichting Opleidings- en Ontwikkelingsfonds voor de Timmerfabrieken, Bussum; TNO Building and Construction Research, Rijswijk
Nowcry NRO: Thte Norwegian Institute of Wood Technology (NTI), Oslo Supporting organisations: University of Trondheim; The Norwegian Institute of Wood Tecfinology, Osf o
Porfi4gal NliO: Laborat6rio Nacional de Engenl~ariaCivil, Lisboa
Sweden NRO: Triiinf'ormation, Stockl~olnl Supporting organisations: Cllalmers University of Technology; Lund University; Swedish National Testing and Research Institute
Switzerland NRO: Lignum Schweizerische Arbeitsgemeinschaft f i r das Holz, Ziirich Supporting organisations: ETH, Ziirich; EPF, Lausanne; SIA Schweizerischer Ingenieur- und Architekten-Verein, Ziirich
United Kirzgdom NRO : TRADA, High Wyconlbe, Buckinghanlsl~ire Supporting organisations: Timber Research and Development Association; GangNail Systems Ltd.; Brighton University; University of Nottingham; University of Surrey; Meyer International; SCOTFI; institute of Wood Science; MiTek Industries Ltd .; Sin~psonStrongtie International Incorporated; James Donaldson & Son; Donaldson Timber Engineering
Contract implementation Centrum Hout, STEP/EuroforiechSecretariat, Westeinde 8, 1334 BK Alrnere, The Netlterlands Cornnlission of the European Comlunities Taskforce, Human Resources, Education, Training and Youth, COMETT Programme, Contract No 92/ 1/6960 Eurofortech, International Office, Roebuck Castle, Be1field, Dub1in 4, f reland
STEPIEUROFORTECN - an initiative under the ELI Co~~lert I>rograrnme
The following loadslload combinations are possible, see Figure 4:
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Selfweight alone. Penaanent. Due to the low value of k,,,,,,,, this load may be decisive in theory, but rarely in practice.
I.
Selfweight -t snow, short-term. This combination gives the greatest axial force in the columns.
2.
Selfweight + wind, short-term. This combination may be decisive For anchoring against uplift.
3.
Selfweight -t- snow c (wind, combination value), short-term. This cornbination gives the greatest axial force in the columns combined with bending in the columns.
4.
Selfweight c wind + (snow, combination value), short-term. This combination gives the greatest ~nornentit1 the columns.
STEPIEUROF0RTECI.i - an initintivc under thc EU Comeli Prograrnnic
Communication 94lC 62/01 requirements listed.
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each of them referring to one of the essential
Tecllttical speci$cntiorts wittzbz the scope of the Cu/tstr.uctiot~Prod~tcts Directive The CPD lays down that, in order to be placed on the market, the products shall be fit for their intended use, that is, they shall have such characteristics that the construction works, in which they will be incorporated, can satisfy the applicable essential requirements. The CPD also establishes that the EU Member States shall presume that the construction products are fit for their intended use if they bear the CE marking. The CE marking is not a quality mark; it demonstrates only that products meet the legal requirements necessary for them to be placed on the market by co~nplying with the applicable technical specifications, which can be of three types:
- national standards transposing harmonized standards, i. e., standards prepared by the European Committee for Standardization (CEN) or by the European Committee for Electrotechnical Standardization (CENELEC), on the basis of mandates given by CEC;
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European technical approvals;
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national technical specifications accepted by the CEC, where harmonized standards do not exist.
The first two types of technical specification will be the normal methods used to obtain the CE marking and further detaiis are given below. The Members of CEN are the eighteen National Standardisation Bodies of EU and EFTA Member States. In order to respond to the request included in the CPD, for the existence of harmonized European standards, more than sixty CEN Technical Committees are currently dealing with around 2000 work items (corresponding to EN Standards or Parts of EN Standards to be drafted) in the area of building and civil engineering. The standardisation work concerning timber and related products will be summarized later in this lecture. It is outside the scope of this lecture to give details about the procedures followed to prepare and approve an EN Standard. It is, however, important to state that when a CEN Member adopts an EN Standard, this will acquire the status of a national standard and the i~ationalstandard(s) covering the same subject shall be withdrawn. The European techrlical approval (ETA) is a favourable technical assessment of the fitness for use of a construction product, based on the fulfilment of the essential requirements of the construction work where the products are incorporated. The ETAS are basically applicable to those products for which there is neither a harmonized standard, nor a mandate from the CEC for the production of one covering those products. So, this type of technical specification is reserved for innovative products and corresponds to an extension, to a European scale, of the national Agrement Certificates currently issued in different countries. European technical approvals are issued by approval bodies designated by the EU Member States which are presently associated to the "European Organization for Technical Approvals" (EOTA), that coordinates these activities, and will ensure that STEP/EUROFORTECH - an initiativc under tllc EU Cotnett Programme
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There are three Service Classes, denoted 1, 2 and 3. The classes 1 and 2 are characterised by the moisture content of the surrounding air. In Service Class 1 the average equilibrium moisture content in most softwoods will not exceed 12%; in Service Class 2 it will not exceed 20%. There are no limits for Service Class 3. There are five Load-duration Classes. They are characterised by the order of accumulated duration of the characteristic load, see Table 4, where also examples of loading are given.
It is generally assumed that the relationship between the resistance (R) and the strength paraineters V), the stiffness parameters (4 and the geornetricai data (a) is known. If this is the case, design values should be used to determine the design resistance:
The design value R, can also be determined directly from characteristic values (R,) determined from tests:
For structures where the resistance depends on Inore than one material - e.g. timber and steel or wood-based panels - it can be difficult to select tile right value of k,",,,. It is of course always on the safe side to use the lowest value for the materials used. Geoructrical dain
The geornetricitl design values correspond genenlly to the characteristic vaIues, i.e, to the values specified in the design. In cases where the influence of deviations are critical the geometrical design values arc defined by
where Act takes account of the possible deviations from the characteristic values. Values of Aa are given in the appropriate clauses of EC5. Load-duration Class Permanent Long-term Medium-term Short-tcnn Instantaneous
Duration'
more than 10 years 6 months - 10 years 1 week - 6 months less than one week
Exarnples of loading self weight storage irnposcd load snow" and wind accidental load
A,,,,, for Service Classcs 1&2
3
0,60
0,50 0.55 O,G5 0,70 0,90
0,70
0,80 0,90 I , 10
a Thc Load-duration Classes are charncleriscd by the effect oP a constant load acting for a ccriain period oC time. For variable action the appropriale class depends on the erfecl of tlie typical variation of tile load in the life of the structure. The accumulated duration of' the characteristic load is orten very sliort compwcd with the total loading time. b In areas with a heavy snow load for a prolonged period of time, par1 of the load should be regarded as medium-term. Table 3
Loctd-tlrtmdnrz Closs~sund k,,,,,! for solid rinrbcr attrl glr~lcim.
STEPIEUROFORTECM - un initiative undcr 1l1c EU Comctt Programme
"Greeni~ouses".Further, and with special relevance to this Iccture, is, obviously, tile work of CENtTC 250 - "Structural Eurocodes", where ECS concerning ille design of tiinber structures will be finalised, as will be described later. Apart from the work on the EC5, the major interest for timber structures is focused on the EN Standards that will be produced by CENJTC 38, CEN/TC 112 and CEN/TC 124. Tlie programme of work of these three TCs was established taking into account the need for supporting EN Standards for Eurocode 5. Briefly, the activity of these Technical Comlnittees is now referred to.
CEN/TC 35 is the oldest, was created prior to the pubtication of the CPD and, in former times, produced EN Standards concerning test methods for preservative proclucts. The work was gredtly enlarged and accelerated recently and a coherent set of new EN Standards concerning this subject is in the final phase of production (see STEP lecture A 15). CENITC 112 currently has a worlc programme that includes around 80 items covering particleboarcis, oriented strand boards, fiblzboards, plywood, cernentbonded particleboards, together with general test rnethods and forl?ialdehyde eiuissioti. CENITC 124 was created in 1987 and t11e work programme involves around 40 items dealing with solid timber, glued laminated timber, connectors and test nlethods, which are obviously closely related to Eurocode 5. Finally, some words ribotit the work concerning EC5. CENITTC 250 - "Structural Eurocodes" was created in 1990 and took over the previous work, that had been started around 1977 under t11c auspices of the CEC, of' drafting a systein of Eiiropean structural design codes: the Eurocodes. Sub-committee 5 of TC 250 (CENmC 2SOlSCS) is in charge OF EC5 and established a work programme that anticipated the publication of three documents. Tlie first, for general application, was published in 1993; it is referenced as ENV 1995-1-1 : 1993 -"Eurocode No.5 Design of timber stnictures. Part 1.1: General rules and rules for buildings". The second, ENV 1995-1-2 - "Eurocode No.5 - Design of timber structures. Part 1-2: Structural fire design" tias been finalized. Drafting of the third document, dealing with bridges, has beer1 started. In coinrnot~with Eurocodes dealing with other materials, Eurocode 5 will be published as an ENV, i.e., as a European Prestatidard. This rneans that - as opposed to the status of an EN Standard - existing conflicting nationat standards may be kept in force (in parallel with the ENV) until the filial decision about the conversion of the ENV into a EN is reached. In order to implement these ENVs, Member States are expected to publish National Application Documents (NADs), namely to assign certain safety levels that are set out as iildicative levels in the ENVs.
STEPIEUROFORTECH -
i1n
ir~iliativcunder thc EU Co~ilettProgrimme
Action
\lf~
'\'I
Imposed load in buildings Snow loads Wind loads
0.7- 1 ,O 0,6 096
0,5-0,9 02 0,s
K! 0,3-0,8 0,O
0,o
MrttcriaI plopcrties
The material properties correspond either to the rnean value or to the 5-percentile determined by standardised tests ~lndel-reference conditions: duration of test 5 tninutes at 20 "C and relative humidity 65%. The lnean values are used for serviceability limit stnte verifications. The 5-percentiles are used for all properties (strength, stiffness and density) related to illtiinate limit states.
Gcornetriciil dilta
The characteristic geometrical values, such as spans, dimensions of cr-osssections, deviations from straigl~tness,usually correspond to the values specified in the design or to nominal values.
Actions
The design actions may be different for the different limit states and are found as described below. Firstly, the possible load cases are identified, i.e. compatible load arrangements, sets of deformations and imperfections. A load arrangement identifies the position, magnitude and direction of an action.
Design values
Secondly, the actions are colnbined according to the following sy~nboiic expsessio~~:
where y are partial factors (load factors) for Lhe action considered, tc&ing account of: the possibility of i~nf'avourable deviations of the actions, the possibility of inaccurate nod el ling of the actions and uncertainties in the assessnient of effects of actions. Values of the load factors are given in Table 2. Reduced partial factors may be applied for sit~gle-storeybuildings of inoderate span that are only occupied occasionally (storage buildings, sheds, greenhouses, and buildings and small silos for agricultural puq~oses),lighting masts, light partition walls, and sheeting.
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~ The representative values multiplied by the y-values y, G,, yQ Q, yQ ! l ~ Qk are called design actions. The principle is thus that one variable action with its characteristic value in turn is combined with the permanent actions and all other variable actions with their colnbination value yf, Q,, Finally, the effects (S) of actions - for example internal forces and moments, stresses, strains and displacernents - are determined from the design values of the actions, geometrical data and, where relevant, material properties (X):
As a simplification it is permitted instead of (7) to use the more adverse of tile following combinations4.
''
Thc sinlptiftcd exprcssioris are on the irnsnfe sidc for
Q,less than 30-507h oof Q,.
STEPIEUROFORTECI-I- an initiative undcr thc EU Cornclt Programme
Limit state codes The Eurocodes are limit state codes, meaning that the requirements concerning stmctural reliability are linked to clearly defined states beyond which the structure no longer satisfies specified performance criteria. In the Eurocode system only two types of limit state are considered: ultimate limit state and serviceability Limit states. Ultimate limit states are those associated with collapse or with other forms of structural failure. Ultimate limit states include: loss of equilibrium; failure through excessive deformations; transformation of the structure into a mechanism; rupture; loss of stability. Serviceability limit states include: deformations which affect the appearance or the effective use of the structure; vibrations which cause discomfort to people or damage to the structure; damage (including cracking) which is likely to have an adverse effect on the durability of the structure.
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Safety verification The partial coefficient method In the Eurocodes the safety verification is based on the partial coefficient method described below.
Figure 2
Statistical distributiotu (idealised)for action effects (S)and resistance (R). Tile c~miulativeprobability is detroted P.
The main parameters are the actions, the material properties and the geometrical data. Normally, these parameters are stochastic variables with distribution functions as shown in principle in Figure 2 for the action effects (S) and the corresponding resistance (R): e.g. bending stresses and bending strength or the axial force in a centrally loaded column and the buckling Ioad. The distributions have the mean values S,,, and R,,,, and they can be assigned characteristic values S, and R, defined as fractiles in the distribution. For actions an upper fractile is nomalty used; in some cases, a lower value may be appropriate, e.g. for counteracting uplift. For resistance a lower fractile or the mean value is normally used; in exceptional cases an upper resistance value may be appropriate. The purpose of the design is to get a low probability of failure3, i.e. a low probability of getting action values higher than the resistances. This, in the partial coefficient method, is achieved by using design values found by multiplying the characteristic actions and dividing the characteristic strength parameters respectively, by partial safety coefficients. TItc prubability of failttre cat1 be esti~natedby statistical ntctlrods, attd in the future srtclt rt~etlrodsrrtay be rcsed by dcsigrrers. Torlay, tlicy arc only rised for very special stricctrrrcs, c.g. for bridges with very lorge sparrs or for rlte calibration of tlic safety cletrrerrrs (e.g. partial coeflcients) of tlte sirrtplc ver#catiurr sysfenls rrscd in practice.
iSTEPlEUROFORTECH - an initiative under the EU Comctt Programme
Limit state codes The Eurocodes are limit state codes, meaning that the requirements concerning structural reliability are linked to cIearly defined states beyond which the structure no longer satisfies specified performance criteria. In the Eurocode system only two types of limit state are considered: ultimate limit state and serviceability Limit states. Ultimate limit states are those associated with collapse or with other forms of structural failure, Ultimate limit states include: loss of equilibrium; failure through excessive deformations; transformation of the structure into a mechanism; rupture; loss of stability. Serviceability limit states include: deformations whiclt affect the appearance or the effective use of the structure; vibrations which cause discomfort to people or damage to the structure; damage (including cracking) which is likely to have an adverse effect on the durabiiity of the structure.
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Safety verification The partial coefficient method In the Eurocodes the safety verification is based on the partial coefficient method described below.
Fig~trc2
Statistical distri6~aiotu(idealised) for action effects (S) arid resistance (R). The cr&nialath~e probability is detroted P.
The main parameters are the actions, the material properties and the geometrical data. NormaIly, these parameters are stochastic variables with distribution functions as shown in principle in Figure 2 for the action effects (S)and the corresponding resistance (R): e.g. bending stresses and bending strength or the axial force in a centrally loaded column and the buckling load. The distributions and R,,,, and they can be assigned characteristic have the mean values S, values S, and R, defined as fractiles in the distribution. For actions an upper fractile is normally used; in some cases, a lower value may be appropriate, e.g. for counteracting uplift. For resistance a lower fractile or the mean value is normally used; in exceptional cases an upper resistance value may be appropriate. The purpose of the design is to get a low probability of failure3, i.e. a low probability of getting action values higher than the resistances. This, in the partial coefficient method, is achieved by using design values found by multiplying the characteristic actions and dividing the characteristic strength parameters respectively, by partial safety coefficients. .' Tffcprubalrility
of faillrrc carr be esti~tiatedby statistic01 f?f&I/tod~, and in the fultrre sircli ttrcthods may be rcscd by desigrrcrs. Torlay, rlicj~arc only used fur very special sfrrccr~rrcs,e.g. !or. bridges lvirh \ler)*large sparrs or for rhe calibratiort of the safety elctnmts (e.8. partial cocJJ?cictrts) of the sirrtple veriJcafio~rsysren~sused in practice.
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ISTEP/EUROFORTECH an initiative under the EU Cornet1 Programme
Action
\I'o
\If,
'lfz
Imposed load in buildings
0.7- 1,O 0,6
0,s-0,9
02
06
0,s
0,3-0,8 0,O 0,o
Snow loads Wind loads
ivlnccriat p~.opcr[ies
The material properties correspond either to the mean value or to the 5-percentile determined by standardised tests tinder reference conditions: duration of test 5 rninutes at 20 "C and relative humidity 65%. Tile mean values are used for serviceability limit state verifications. The 5-percentiles are used for all properties (strength, stiffness and density) related to ultirnate limit states.
Gco~nctricaldata
The ctlaracteristic geo~netrical values, such as spans, ditnellsions of crosssections, deviations from straightness, usually correspond to the values specified in the design or to no~ninalvalues.
Actions
The design actions may be different for the different limit states and are found as described below. Firstly, the possible load cases are identified, i.e. compatible load arrangements, sets of deforrnatiorls and imperfections. A load arrdngement identifies the position, magr~itudeand direction of an actiot~.
Design values
Secondly, the actions we cornbined according to the following syrnbolic expressiorl: CYG.IG~,~ "+ " Yo,r Qt, i
"+ " ~ ~ ~ , i ' ~ i ~ , , , Q t i
where y are partial factors (load factors) ibr L11e action considered, taking account of: the possibility of unhvourable deviations of the actions, tile possibility of inaccurate modelling of the actions and uncertainties in the assessnlent of effects of actions. Values of' the load factors are given in Table 2. Reduced partial factors may be applied for single-storey buildings of inoderate span that are only occupied occasionally (storage buildings, sheds, greenhouses, and buildings and small silos for agricultural puq~oses),lighting masts, light partition walls, and sheeting. The representative values multip1ied by the y-values - y, G,, yQ Q,, yL, \yo Qt are called design actions. The principle is thus that one variable action with its characteristic value in turn is combined with the permanent actions and all other variable actions with their coinbination value ~hQ,. Finally, the effects (S) of actions - for example internal forces and tuoments, stresses, strains and displacements - are determined from the design values of the actions, geometrical data and, where relevant, material properties (X):
As a simplification it is permitted instead of (7) to use the more adverse of the following combinations . J
''
Thc sin~plificdcxpressioris are on tlie i~nsnfcside for
Q,icss than 30-50%1of Q,.
STEPIEUROFORTECI-I - an iniliativc i~ndcrthc Ell Cornell Progriimmc
"Greenhouses". Further, and with special relevance to this lecture, is, obviously, the work of CEN/TC 250 - "Stnictural Eurocodes", where EC5 concerning the design of tiinber structures will be kiiialised, as will be described later. Apart froin the work on the EC5, the major interest for timber structures is focused on tlie EN Standards that will be produced by CEN/TC 38, CEN/TC 112 and CEN/TC 124. Tile programme of work of these three TCs was established taltirig into account the need for supporting EN Standards for Eurocode 5. Briefly, the activity of these Technical Comlnittees is now referred to. CEN/TC 38 is the oldest, was created prior to the pubiication of the CPD and, in for111er times, produced EN Standards concerning test methods for preservative proclucts. The work was greatly enlarged and accelerated recently and a colierent set of new EN Standards concerning this subject is in the final phase of production (see STEP lecture A15). CENfrC 1 12 currently has a worlc programme that includes around 80 itenis covering particleboards, oriented strand boards, fibreboards, plywood, cetnentbonded particleboards, together with general test {nethods arid fornialdehyde e~nission. CENRC I24 was created in 1987 and the work programme involves around 40 items dealing with solid timber, glued laminated timber, connectors m d test mettiods, which are obviously closely related to Ei~rocode5. Finally, some words about the work concerning EC5. CENtTC 250 - "Structural Eurocodes" was created in 1990 and took over tlie previous work, that had been started around 1977 under the auspices of the CEC, of drafting a system of Etiropeilti structural design codes: the Eurocodes. Sub-committee 5 of TC 250 (CENfTC 250/SC5) is in charge of EC5 and established a work programme that anticipated the publication of three documents. The first, for general application, was published in 1993; it is referenced as ENV 1995- 1-1: 1993 -"Eurocode No.5 Design of timber stnrctures. Part 1.1: General rules and rules for buildings". Tlie second, ENV 1995-1-2 - "Eurocode No.5 - Design of timber structures. Part 1-2: Structural fire design" has been finalized. Drafting of the third document, dealing with bridges, has been started. In common with Eurocodes dealing with other materiais, Eurocode 5 will be published as an ENV, is., as a European Prestandarcl. This means that - as opposed to the status of an EN Standard - existing conflicting national standards may be kept in force (in parallel with the ENV) until the final decision about the conversion of' the ENV into a EN is reached. In order to i~nplementthese ENVs, Mernber States are expected to publish National Application Docunients (NADs), namely to itssigrl certain safety levels that are set out as indicative levels in tlie ENVs.
-
-
-
There are three Service Classes, denoted 1, 2 and 3. The classes I and 2 are cliaracterised by the moisture content of the surrounding air. In Service Class 1 the average equilibrium moisture content in most softwoods will not exceed 12%; in Service Class 2 it wilI not exceed 20%. There are no firnits for Service Class 3 . There are five Load-duration Classes. They are characterised by the order of accumulated duration of the characteristic load, see Table 4, where also examples of loading are given. It is generally assumed that the relationship between the resistance ( R ) and the strength parameters 0, tlie stiffness parameters (E) and the geolnetrical data (u) is known. If this is the case, design values should be used to determine the design resistance:
The design value R , can also be detcnnined directly froin characteristic values (R,) determined from tests:
For structures where the resistance depends on Inore than one material - e.g. timber and steel or wood-based panels - it can be difficult to select the right value of k,,,,,,,. It is of course always on the safe side to use the lowest value for the materials used. The geometrical design values correspond generally to the characteristic values, i.e. to the values specified in the design. In cases where the infIuence of deviations are critical the geometrical design values are defined by
where Aa takes account of the possible deviations from the characteristic values. Values of Aa are given in the appropriate clauses of EC5. Load-duration Class
Permnncnt Long-term Mediurn-term S hort-tenn Instantaneous
Duration"
Bxatnples of loading
more than 10 years 6 months 10 ycars 1 week - 6 months less than one week
-
self weight storage irnposcd load snow" and wind accidental load
k,,,,, for Service Classes 1 &2
3
0,60
0,50
0,70
0,55
0,80 0,90 1.10
0,65 0,70 0,90
a The Load-duration Classcs are charac~eriscdby tlie effect of a constant load acting for a ccrtain pcriod of time, For variable action Ltic appropriate class depellds on the effect of the typical variation of the load in the life of the structure. The accumulated duration of the characteristic load is onen very sliort comparcd with the total loading Lime. b In areas with a heavy snow load for rt prolonged period or time, part of the load should bc regarded as rncdium-term.
Table 4
Load-dtlmtion Classes arrd k,fl,,,tfbrsolid tittrber ar~dgltllnnr.
STEPIEUROFORTECM - an initialive under ll~cEU Cotnclt Programme
Communication 94/C 62/01 requirements listed.
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each of them referring to one of the essential
Tecllrlical specifications within tire scope of dle Corlstluction Prociucts Directive The CPD lays down that, in order to be placed on the market, the products shall be fit for their intended use, that is, they shall have such characteristics that the construction works, in which they will be incorporated, can satisfy the applicable essential requirements. The CPD also establishes that the EU Member States shall presume that the constnlction products are fit for their intended use if they bear the CE marking. The CE marking is not a quality mark; it demonstrates only that products meet the legal requirements necessary for them to be pfaced on the market by complying with the applicable technical specifications, which can be of three types:
-
national standards transposing harmonized slandards, i. e., standards prepared by the European Committee for Standardization (CEN) or by the European Committee for Electrotechnical Standardization (CENELEC), on the basis of mandates given by CEC;
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European technical approvals;
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national technical specifications accepted by the CEC, where t~armonized standards do not exist.
The first two types of technical specification will be the normal methods used to obtain the CE marking and further details are given below. The Members of CEN are the eighteen National Standardisation Bodies of EU and EFTA Member States. In order to respond to the request included in the CPD, for the existence of harmonized European standards, more than sixty CEN Technical Committees are currently dealing with around 2000 work items (corresponding to EN Standards or Parts of EN Standards to be drafted) in the area of building and civil engineering. The standardisation work concerning timber and related products will be summarized Iater in this lecture. It is outside the scope of this lecture to give detaiIs about the procedures foIlowed to prepare and approve an EN Standard. It is, however, important to state that when a CEN Member adopts an EN Standard, this will acquire the status of a national standard and the ilatio~lalstandard(s) covering the same subject shall be withdrawn. The European technical approval (ETA) is a favourable technical assessment of the fitness for use of a construction product, based on the fulfilment of the essential requirements of the construction work where the products are incorporated. The ETAS are basically applicable to those products for which there is neither a harmonized standard, nor a mandate from the CEC for the production of one covering those products. So, this type of technical specification is reserved for innovative products and corresponds to an extension, to a European scale, of the national Agrement Certificates currently issued in different countries. European technical approvals are issued by approval bodies designated by the EU Member States which are presently associated to the "European Organization for Technical Approvals" (EOTA), that coordinates these activities, and will ensure that STEPJEUROFORTECH- an initinlivc under the EU Cornctl Programme
The following loadstload cotnbir~ationsare possible, see Figure 4:
-
Selfweight alone. Periuanent. Due to the Iow value of A,,,,,,,, this load [nay be decisive in theory, but rarely in practice.
1.
Selfweigllt t snow, short-term. This combination gives the greatest axial force in the columns.
2.
Selfweight + wind, short-term. This combination may be decisive for. anchoring against uplift.
3.
Selfweight + snow -I- (wind, combination value), short-term. This combii~ationgives the greatest axial force in the columns combined with bending in the columns.
4.
Selfweight c wind + (snow, combination vnIue), short-term. Tltis combination gives the greatest rnornent in the columns.
STEP1EUROFORTECI.I - an initiative under the EU Comelt Programme
Actions on structures STEP lcciurc A3 P. Racllcr CUST Civil Engineering Blnisc Pascal University
objectives To give an overview of the classification of the actions applied to structures. To define the cl~aracteristicvalue for the n~oslcolnrnon actions applied to buildings. T O present the design situations and the associated values for combined actions.
Summary In accordance with ECI, tl.iis lecture deals with the evaluation of the actions used in EC5 design calculations. Regardless of dynalnic effects, the representative values of the actions on buildings depend on their variation wit11 dme. These values are established for permanent, imposed, snow and wind actions. Then, the combined value of actions is calculated for the various design situations. A typical example of the calculation of the actions for a fralne complen~entsthe lecture.
Introduction For the intended col~slructionwork, tile designer is first faced wit11 the conceptual design of the structural system. This stage will consider the type of structure and on construction material to be used. The structural design then starts with an analysis of the actions that may be applied to the chosen structure. Account should be taken of direct actions that are the applied external forces as well as tile indirect actions that result from imposed deformations (e.g. settlement of supports or dimensional change induced by moisture variations). Regardless of the constnlction material, the design requires the evaluation of tile actions that may act during the life of the structure. These depend on the strucrural form, on the type of construction work and on the method of construction. At this stage, it is necessary to consider tlie nature of the actions or action-effects, i.e. either static or dynamic, to achieve an accurate slnrciural analysis. For example, the quasi-static assu~nptionmay nor be acceptable in the Sotlowing cases:
-
floors srtbjected lo human or machine-induced vibrations,
-
flexible plale-like structures such as suspension-bridge decks tliat could flutter wile11subjected to wind velocities above a critical value,
-
structures loaded by ground ncceleration due to seismic action.
In these cases, a dynamic itnalysis model should be used to find the action-effects of the force-time history, considering the stiffness, Lhe inass and the damping ratio or structural members. However, the resonant component of tile action-effect is small for most structures. Therefore the static calculations are made, and an equivalent dytia~nicamplification factor applied to the static value of action. This lecture, therefore, deals will1 the assessment of direct actions and their combination for static analysis only. These calculations will also need to consider the National Application Documents and current regulations applicable to the colinlly where the structure is cotistructed.
STEPIEUROFORTECI-I - on initiative undcr thc EU Comett Programme
General concepts
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Strifcturcrl c1as.siJcaiio~z.s The design Eurocodes (EC2 to EC7) are based on a calibration of successf'ul traditional design methods. Nevertheless, a mention should be made of the criteria to which the reliability concept of ECI referred. Regarding human hazard and economic losses, the stmcturai safely and serviceability requirements consider the working life and the design siliiations of the structures (C.E.B., 1980). Class
Working life (ycars) Example 1 to 5 Temporary structures 25 Replaccablc structul-al elements Buildings and common structurcs 50 Bridges or other engineering works 100
I
2 3 4
The working life corresponds to tile period for which the structure is to be used for its intended purpose. Table 1 gives a classification of the construction works. In addition, the design situations refer to events that may occur during tlte working life of tlle structure. Therefore, the actions are evaluated for the relevant design situations that are classified as:
-
In addition to the previous classifications, differentiation of the actions has to be considered according to the variation of their magnitude in space and with tirne. For common design, the actions or action-effects are defined as:
-
-
persistet~t,sitiratio~r.srelated to the conditions of normal use, trarz.sierri sitlrntiort.~related to temporary conditions, e.g. during execution, accidctltnl sitrrntiotts related to exceptional conditions like fire or impact,
Load clnss~ficcition
-
-
perrnnrletlt nctiotrs (G), e.g. self-weights of the construction works, vat-iabke ncrions ( Q ) , e.g. imposed actions, snow and wind actions.
Other actions like accidental ( A ) and seismic (S) actions are outside the scope of this lecture (see STEP lectures A2, B17 and (217).
Figrrre I
Tirrte-voriution of ihc total appliecl actiorrs on
-
-
LI floor.
The permanent actions have negligible variation in magnitude with time, except when changes to a construction are made (see Figure I). For the variable actions (Hendrickson et al, 1987, Rackwitz, 1976), the variations are modelled as a discontinuous process (i.e. snow or wind) or as a process resulting From a sustained part, Q,.,and a transient part, Q7.(i.e. imposed load). For timber which is more *STEP/EUROFORTECH :In initiative undcr thc
-
EU Comctt Progrnmmc
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time-dependent than other construction materials, the temporal variation of the actions must be emphasised. According to EC5, the design criteria must lake into account the load-duration effects. Therefore, the designer must classify the variable actions in relation to the specified load-duration classes (see STEP lecture A2). In terms of spatial variations, the actions are considered either as fixed or free. Free actions could have any spatial distribution over the structure or part of it. Then, the design is carried out using the worst load arrangements of the free actions.
Representative vnlues of nctiorzs The basic value of an action is the chnracterisric vnltte, denoted G, or Qp Usually, the permanent actions G, cotrespond to the nominal value. However, if the structure is sensitive to variation in G or if the coefficient of variation (COW of G is greater than 1096, two characteristic values are considered, n lower value Gk*i4and upper value G,,,,. Assuming a Gaussian distribution for G, these vaIues are given by: (1) G,,, = G,,,,, ( 1 - 1,64 COV ) ; G,, = G,,,,,, ( 1 + 1,64 COV ) The characteristic variable actions Q, are related to a given return period of N years, corresponding to a probability of exceedance p = 1/Nin a year. According to ECI, the actions Q,are defined for N=S0 years or p=0,02. For other probabilities of exceedance p, (with p, 5 0,2), the characteristic value QN is estimated as:
6
1 - COY - [ In(-h(1-p,))+ 0,577221
QN
=
X
Qfi
1
+
2,5923 COV
(2)
where COV is the coefficent of variation of Q. If permitted by National regulations, this relation may be appropriate to define the characteristic value of a variable action:
-
from values related to a return period Iess than 50 years (e.g. snow or wind),
-
for structural design with an acceptable higher risk of exceedance (i.e. temporary structures) or, conversely, with a greater safety @N<0,02).
In addition, the designer needs to consider other representative values for variable actions given as:
-
the combination value (!v0Q,),
-
the quasi-permanent value (I~I~Q,), which is related to the time average value.
the frequenl value (yf,Q&, which is exceeded for 5 percent of the time,
and (\yrQk) are usually considered when In practice, the values Gk, Qh (I@,) checlcing the ultimate limit states. For the serviceability Iimit states, these values are used for the calculations of short-term effects only. The long-term effects (e.g. creep on the loading side, deformations) are assessed considering the values G, and (y2Qk) and the deformation factor k,,/ on the material side.
Permanent actions Tlte permanent actions are due to the self-weight of structural members and the weights of all components to be supported permanentIy by the members. These dead loads comprise fixed partitions, insulation, cladding or finishes. The estimation STEPIEUROFORTECH - an initiative under the EU Comctt Programme
A313
of the permanent actions requires knowledge of the structural configuration and the constnlction materials. TIie values of the permanent actions are established using the nominal dimensions of the components and the rnean weight density of the constituent materials (in kNh-I). For many building products, the designer should refer to the weights given by the manufacturer.
In order to si~nplifytlie calculations, the dead loads due lo framing mernbcrs and lightweight partitions are conveniently defined as unifortnly distributed loacls over tlie bttilding area. A reasonable estin~atemay be obtained by referring to similar structures. The self-weight of the flooring (sheet and joist) or roofing (sheet, rafters and purlins) lnelnbers ranges usually between 0,25 and 0,45 kN/rn2. For coitinlon framing members, the overall weight could be estimated as g=(15+1)/100 kN/t>12 where 1 is the span of the inembers in metres. Depending on the weight P of the partition per tti2 of will1 area, the partitions may be taken into account as a uniform load equal to 0,75 P per r?lZ of floor area. This estimate is used for partitions up to four rnctres in height if P is less than 1,0 kN/rtt2 and less tlian 40% of the iniposed actions.
Imposed actions The imposed actions in buildings are due Lo occupancy. They correspond to loads that niove by themselves (i.e. people, trucks) and to moveable loads ( i s . f~trniture, light partitions, stored materials). Distinction is niade between the lortded areas according to the intended use. In common buildings, three classes havc to be considered: 1 - clwcllings, offices, shops . . ., 2- roofs and 3-produclion areas. Cutcgory
Type of use
Ex:unpIe
A
Residential activities
Aprtrtmcnts, bedrooms in Ilotels
B
Offices
Classroo~ns,operating rooms in hospital
C
Congregation areas
Assembly ilalls, theatres, dining roorns
D
Shopping
Areas i n warehouses
E
Storage
Archives, storage area of goods
Table 2
Clrlssificatiorr c~Jfloora~.easin brtiklirr,~.~.
For production areas, the design is achieved with imposed actions on floors depending on the specific use of the buildings. Otherwise, the values of the imposed actions take into account the density of occupation and the degree of public access to the area. Thus, the first class is subdivided into five categories (Table 2). Roofs are categorized as not accessible except for maintenance or repair (Category H) or as accessible. For accessible roofs, the design is inade wit11 the occupancy corresponding to the floor classification.
ECI: Part 2-1
A 314
Referring to this classification, tlie design of a floor or roof takes into account either a uniformly distributed load q, or a concentrated load Q,as imposed action. The free load Q, acts on a square area with a 50 mnr side. TIiis load is intended lo ensure adequate design of secondary members. It may be also critical on small spans. Table 3 gives tile minimum values of these imposed actions as specified in ECI. Reduction coefficients can be applied to these values depending on the floor area and the nunlber of storeys.
According to the load-duration classes of EC5, a medium-term duration is usually considered for the load q, on areas A to D. This loading is taken as long-term for category E and ns short-lenn for categoly H. Lastly, tllc concentratecl action QLis related to the sl~ort-tern1duration class. Type of area
Category Floors, accessil~leroufis:
A
q
General stairs
(IcN)
Balconies
2 2 2
General Stairs,balconies
3 4
2 3
5
4
areas with tables
3
4
areas with fixed seats
4
4
possibility ol' co~~centralions
5
7
5
4
5
7
5
7
Department store
E General
Table 3
(2,
3 4
D Shops
13
)
2
C General
Norr-accessible roofY:
I
slope: < 20' z 40"
I~rlposedloods on floors arrd r-oo/iit; brti1dir1g.c
Apart from tile previous gravity loads, account may also be taken of horizontal imposed actions on partition walls and barriers. They are short-term actions applied at the height of t l ~ ehand rails (0,S to 1,2 111). Table 4 defines the characteristic values of the line action q,. Category
Tablc 4
A
B
C,D
Public events in C or D
Horizontal imposed acrioris orr pnrririons nnd barriers.
Snow loads The snow loads are based on mensurernents of snow depths on the ground and snow density. Depending on the surrounding terrain and the local weatlter, the specilic density of snow varies from 0,l (fresh snow) to 0,4 (old or wet snow). From a statistical analysis 01' these records, the characteristic snow load on the ground (s,) is defined for a return period of 50 years. As they depend on the geognaphical location and the altitude of the site, the characleristic values s, are given in the national loading codes. In addition, the designer should also consider local effects tllat may modify the specified value s,. For example, significant increase in the snow load on a member can result from snow turning into ice or min falling on the snow. For structurnl calculations, the designer has to consider the load arrangements on the roofs stich as:
-
balanced distributions resulting from unifonn snow falls,
-
and unbalanced loads due to drifting under windy conditions or snow sliding.
STEP/EUROFORTECI.I- :In iniiialivc under the EU Cornelt Progr:bmmc
A 3/5
From the analysis of snow falls on the ground, the snow loading is generally treated as a variable action of short-term duration (less than one week). Referring to the horizontal pro.jection of the area, the characteristic value of the roof snow load is calculated as:
-
The shape coefficient pi takes into account the roof exposure and geometry. Three coefficients pi are defined in ECI, depending on the roof slope a (Figure 2).
0 Figrire 2
15
30
a ("1
GO
Strorv shcri~ccoeflcients orr roofi
Assuming that the snow could slide off the roof, Figure 3 describes the design patterns S, and Sz for the snow load on pitched (a, b and c) and curved roofs (d).
-
Figrire 3
-
Stzonv loncl CII-mngettterrtsorr roofs.
In addition, the designer should pay attention to the possible increase in the snow load due to the shape and the location of the structure. For example, the design has to take into account the additional loads due to filling of roof valleys or formation of drifts against walls.
Wind actions Wind actions fluctuate with time and these variable actions are related to the shortterm load duratiori class. The structural response could be considered as the STEP/EUROFORTECl-I - an initiative undcr thc EU Comett Prograinme
-
-
coinbination of a quasi-static coinponent and a resonant component. This component could be significant for flexible (e.g.buildings with a height lo width ratio greater than 3) and elongated vertical structures. In these cases, detailed wind analysis is required. However, the resonant component is of minor importance for most structures, and wind actions are defined using the simplified method described in this section. The wind actions are represented by static pressures on the surfaces of the structure or by global pressure and friction wind forces (E.C.C.S., 1987).
Wind \rnrintions The design calculations are based on the reference wind velocity vrF, and pressure qref.Referring to a mean return period of 50 years, 1 1 , ~ is defined as the average wind velocity over a ten minutes period at I0 nt above terrain category II (see Table 5). The geographical location is taken into account using the basic wind velocity vr,./;, at sea level given in national wind maps. From this value, v , , ~ and q,,, are defined as: "rcj
= CDIR CTEMCALT " r c h ~
(4)
1111s
C,,, is a factor related to tlie wind direction (e.g. C , , R ~ l ) , C,,,, is a reduction factor for temporary structure, C,, is tlie altitude factor specified in the wind maps, p is the air density taken as 1,25 kg/r,13.
where
As the wind pressure varies with height above the ground, the designer has to consider the reference height z,, of the external building surfaces. Depending on the shape of the building and the crosswind dimension b,,, Figure 4 specifies the reference height for walls and roofs.
B
I.
1.
4,
1
1.
b,,,A< l
(4
(11)
4,.
1.
Ic/>,,, //1<2
(4
De$tzitioa oJ rlra rcfcrance lreiglrf ,; .for btrildi/rgs: p1m1 ntrd cross\t7irtd dir~re~r.siol~ (a) rrlalls ( bf .flat ( c ) pirched ((d) c~trclvnril~ed( e ) roojk.
Figure LC
The effect of height and ground roughness on the wind velocity is first considered with the roughness coefficient cr(z,). With the classification and the values given in Table 5, this coefficient is defined by the logarithmic wind profile as: C,
(~1,)
where
=
K, In f max(
2,"
zmin)1 zol
(6)
z,, is the roughness length, z,, is the height of' the ground layer where the wind velocity is
STEPIEUROFORTECH - an initiative under the EU Comett Programme
A3/7
constant, K, is the terrain factor. Category I
Terrain
- Rough open sea, lakes (fetch upwind >5km) -
I1
Kr
,
I
)
Z~ (NI)
0,17
2
0,0 I
0.19
4
0,05
Smooth flat country without obstncies
- Farmland with hedges,
occasional houses or
[arm structures
Ill
- Suburban and industrial areas and forests
022
8
0,30
IV
- Urban areas covered with buildings of
0,24
16
1,o
average height greater than 15n1
The resultant adjustli~entfor the environmental effects on the wind is then covered by the exposure coefficient C,,.Considering the reference height z,,,and the site conditions of the designed structure, the exposure coefficient is determined frorn:
where c, is the topography coefficient talcing into account local terrain variations such as hills or escarpments (e.g. c,=l).
Pressuw coqficictzts The pressure coefricients define the wind pressures acting normally to the surhces or the buildings. The external (C,,,) and inlernal (C,,,) pressure coeff cients are defined as positive ifthe wind pressureacts towards the surface. A negative valuedenotes suction on the walls or uplift of the roofs. The effect of the wind direction 8 is taken into account by twoseparatesets ofcoefficientsconsideiing the windward sideaseitherthe gable (8= 90") or the long-side (8= 0 or 180"). The external pressure coefficient also varies with the shape of the stntcture. In addition, wind runnel tests have sllown that larger pressures occur at the edges and the corners of structures (Lusch, 1964). These observations result in pressure distributions as shown in Figures 5 and 6. According to EC1, tlie specified coeflicien~svary on the structure as specified in the Following sections For commori shapes of' rectangular buildings. These values cor~espondto the upper value for all wind directions + 45" from the normai to the side under consideration. Figure 5 gives the coefficient C,,,for wall areas greater than I0 n z 2 and bnilding dimensions such as: cl/ir(B=O') or UIr(8=9O0)$1. These pressure distributions relate to the aspect windward dirnensian c,,.,where el,= rnin (h1,,,2/ I ) . For stnaller wall areas, higher values of the pressure coefficient have to be used. On tile windward side, the coefficient C,,,.is reduced to +O,G l'or an elongated building area (UAor cl/ft) 2 4.
a3 t0.X
It'
-6R=c)O'
Figrcrv 5
Presslira
[email protected] vertical tttalls.
STEP/EUROFORTECH -
:ti>
initiative under the EU Coinett Progrnmmc
In addition to the wall pressures, the wind actions applied to roofs require special attention as wind uplift may affect the design of the joinls. In the case of flat roofs, Figure 6 defines tile pressure coefficient for the wind directions 8= 0 or9O".
Figure 6
Pressrtrc coqfficierrt.~ forflar roojk.
For windward sloping roof surfaces, the wind actions are pressures or suctions depending on the pitch angle a. Both pressure and suction have to be considered when a varies between 15 i\nd 30" (see Tables 6 and 7).
4 1 1 re 7
k\'itld nr-eczsotr nronopitcll (a,b,c) atld d~topilcfr (d,e,.flroof.ffforrltc&fferet?t~ c t i r ~ c l direcrio)rs8.
~ 5
~ -1,7
F -1,2
-0,G
G F -2,3
G H H -1,3
-0,8
F
G
H
I
- 1 ,G
-1,8
-0,6
-0,5
STEPtEUROFORTEC1-1- nn initiative under thc EU Comctt Programrnc
A319
Table 7
E.t-terttalpre.ss~trecoeficienrs C, for rlnopitcl~roofi.
The presence of openings and the porosity of the external surfaces greatly affects the internal wind pressure in buildings. Considering the influence ofthe wind direction, the internal pressure coefficient C,,ivaries with tile opening ratio of the windward side. For normal closed buildings with opening windows ordoors, the valueof C,,,.is taken either as 0,8or-0,5 forall the internai surfaces, whicheverresults in the Inoresevere loadcase.
Desigtl \~iirrclnotiolts For building design, the wind action effects are generally estimated using the wind pressure distribution on the surfaces. It results from thecombination ofthe external (we.) and internal (wi) pressures given by: where ziis equal to the relerence height of the walls for closed buildings or the mean height of the openings. According to EC1, structures are designed for all wind directions taking into account the characteristic value of tlie wind actions (kt!,). They correspond to the net pressure distribution defined as:
For some structures, the wind forces resulting from pressure and friction effects [nay need to be considered. The pressure force (F,,,)is the su~nmationof pressures on the projected structural area normal to the wind. For structures which are sensitive lo torsion, the resulting force F, is assumed to act with art eccentricity e=b,)lO. The friction force (l;l,)has to be considered in the case of large surfaces swept by the wind (e.g. free standing roofs).
Combination of actions After the estimation of the actions, the design requires the structural analysis of the actioneffects. This stageinvolves theselectionofreaIistic loadarrangements for which the structure ar the structural cotnponents are to be designed. Then, the design valrres result froin tlle following con~binationsof the actions. Firstly, at the ultimate limit states, the colubiriation for persistent or transient situations is:
where
yG>iis the partial factor for the permanent loads (see STEP lecture A?). Q,,represents the dominant variable action.
Secondly, the cornbination at the serviceability limit states depends on the action effect being checked considering both: STEP/EUROFORTECI-I -
;in
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the characteristic combination:
c G~
; +
q,
Q ~ ,
( 1 1)
i ~1
i
and the quasi-permanent combination:
C
+
C
Gk,i
+
i
C@?,jQkj jt I
According to EC1, the £'' factors for buildings are given in Table 8 where Y ,-values refer to accidental load combinations. Actions Imposed loads
'IJ,, Cntegory
A,B C,D E H
0.7
0,7 1,o 0
II*,
0,s 0,7
0,3
0,9
0,a
0
0
0.6
Snow loads
0,6
0,2
0
Wind actions
0,6
0.5
0
Tobit 8
Y1fac~or3for var'inblc noions otr brtiidiags.
For timber structures, the designer must pay special attention to finding out the critical load cases as they depend on the material load-duration factors. At the ultimate limit states, thecombination (10) is related to the use ofthe k,,, factor. For eachcombination including variable actions, the appropriate k,,,, factor corresponds to the dominant action Q,,,. At serviceability lin~itstates, thecombination (I 1 ) applies to thecalculation of the instantaneous action effects in service. In addition, the combination (12) refers to the calculation of the long-term action effects using the relevant factors k,,/ior the materials and the service class of the structure (Racher and Rougcr, 1994). According to EC 1 calculalions, the k,,,, factors related to ttic perinanent load-duration class have to be used (see STEP lectures A 17 and C18). Considering the different limit states, tile combination of the actions is calculated for each critical load case. The designer's judgement could lead himliier to consider a few worse-case load arrangements. These are commonly:
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(dead + in~posecl)for floor me~i~bers or (clead + s n o ~ vfor ) roof' members, (dead i- \c~it?ri + SIIO\Y SJ2 or.S?)(see Figure 3) for the structure.
Unifor~lilydistributed loads usually control the design of members, while unbalanced load cases car1 induce more critical effects for connections or in some framing systems (i.e. lattice structures).
Example In the example, the design values or the combined actions are calculated for the frame shown in Figure 8. The building is 48 metres long and the frame spacing s, is 4,8 nt. Referring to national snow and wind maps, the location of the projected building provides the following cliaracteristics for:
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snow loads on tile ground: reference wind velocity: terrain classificalion:
s, = 1,5 kN/rt12 I,,,,= I J , , ~ , ~ = 24 t ~ / s .
ground category I11 (industrial area).
According to the national regulations, the snow and wind actions are classified in the short-term duration class. As the structure is located at an altitude greater than 500 111 a combination of wind and snow sllall be considered. Tlie Y factors for snow are: STEP/EUROFORTECH - nn initiative under (he EU Comctl Programme
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YJos=0,67, Y,,,=0,3 and YIZ,..= 0,l.
The preliminary choice of the designer results in the values of the characteristic permanent loads as:
-
-
self-weight of the frame: ge,= 0,70 kN/n7 roofing elements: gkz= 0,55 M/171z
-
Geotrtetry of rile fiutt~e(a) nrrd up/~lirrlgravity loucls (b): pernlnrrerrt (g,G), i~c~riuble ((I, Q)and st~otv(S,. 3,) lurrds.
Figtlre 8
Pertnnnent loczcis The uniformly disti-ibuted load on the horizontal projection of the rafters, due to permanent actions is:
g, = ( gk,l'. S~
g,,2
1cos a
= (
OJ
4.
4.8 * 055 )
cos 13.5 '
=
--
3/43 W / I ~
The self-weight of the vertical members results in the load: Gk = h g k , l = 4,5 0,7 = 3,15 kIV
Ilrtposed 1oad.v Tfle design requires only consideration of the imposed loads corresponding to the maintenance of the roof. As the slope of the roof a(a= 13,5") is less than 20°, tire uniformly distributed and the concentrated imposed loads are: q, = 4,8 , 0,75 1 cos(13,5) = 3,7 liN/m Q, = 1,5 IN
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These loads belong to the short-term duration class and they do not act simultaneously with otlier variable actions.
S~ro\,vloads Figure 2
For a slope LX less than 1 .So, the shape coefficients p of the snow are defined as:
P
=
=
=
0,8
The design considers two characteristic snow loads on the horizontal projection of the structure: the symmetrical snow load S,:S,,, = ( p s,) sF = 0.8 1,5 4,8 = 5,76 W/nt - the snow on halrthe frarne S,,: = ( 0,5 p sk ) sF = 2,88 kN/m
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Wind cictiorts The value of the reference wind pressure is: qrcf=0.5 p v,>
= 0.5
. 1,25 .242= 0.36
STEPIEUROFORTECH - an initiutivc uncicr thc
k ~ / ~ n ~
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Considering the frame geometry, the reference heights for the walls (zlv=4,5 111) and the roof (z,,.= 7,5 rn) areless than the groundlayer height z,,,,,,=8 rn.Therefore, llle roughness and exposure coefficients are constant for all the external and internal surfaces. Equation (6)
Equation (7)
If74
E.~'~enraCpr.e.~.srrtre coeficieiru for 6 =Oa(n)a~rd8 =90°(11).
The distribution of the external pressure coefficients (Figure 9) is defined with the aspect dimension e,,, that takes the value of t 5 m for all wind directions. For the roof, these coeficicnts are calculated by iuterpolation between the values of same sign given for 5" and 15". Equations (8) and (9)
The characteristic wind actions are obtained as:
The wind effects on the frame result fiom aconstanl internal pressure (C,,?+O,8 or-0,5) combined with the external pressures for each wind direction. The design of the frame considers three distributions resulting from the wind acling on the gable (lz,,,,) or on the long side ( w 2 ,and HI^,^). Figure 10 shows lhe wind actions for the Srarnes in the middle of tile building.
STEPIEUROFORTECI-t- nn initiative undcr the EU Comci( Prograrnmc
i r eI
Distrihlrfiotrso f ~ h ~~~itidacriotls e on rhe.fi.nnle(kN/ttt): w , , ,~(6) ~ I J atld ~ , ~ (c)
(ct)
Cot?tbitlntionof actions: ullincate limit stntes Depending on the effect being checked, the design of the frame refers lo the load combinations with one variable action: C I : 1,35 ( g k + G,) C 2 : 1,35 (g, + G,) + 1,5 (q, or Qk) C3: 1,35(g, + G,) + 1,5 S,,, C4: (gk + G,) 1. 1,5 n ~ ~ , ~ and the cornbinations of snow and wind actions:
SI k or Sll,, 1 fy5lJio,,y 2 where Y, and Y,,,,, are the combination factors associated with snow and wind. C 6 : 1,35 (g,
+
Gk) + 1,s [
-&
+
With the prescribed k,,(,,factors, the combination C1 can be critical if the permanent loads represent more than 70% of the total loads. In this example, the first two combinationsas well as thecombinations ofsnow and wind do notcausccriticaleffects. In practice, the design of the frame depends on the design ofthe moment-resisting joint (2 or 4) which is achieved using load case C3. This case also gives the critical cornbination forthe members in combined bending andcompression. Thecombination C4 defines the worst reversal forces due to wind uplift: bending and tension in the members, and tension in the hinges. Preliminary design values of forces and moments are given in Table 9. 1
Section Combination Wind actions
C3
C4
N (m)
171
1' (kN) h4 (kN.tt1)
138 0
-22,1 -16,3
0
Tcrltle 9
C3
2(column) C4 C4 11~,,~
\tJz,k
C4
134 32,3 0
-41,1 -9,9 0
tthk
) L ~ ~ , ~
138
-26 -25,8
-25,3 -20, t
-622
60,2
82
156
3
C3
Design vafric.~ of forces arrd ttiorrlents at tlre rclrimnte littrit states.
STEP/EUROFORTECI-I - an initiativc undcr tlic EU Comett Programme
Cor~tbirrntior~ qf actio17s:seiviceabi1it-y liritit states As snow is the rnain variable action, the instantaneous effects of {he actions are calcuIated froin the combinations:
Depending on Lhe shape and the span of the frame, the limitation for tile horizontal detleclion of the column is checked using either the combination C7 or C8. Tile combination C7 gives tile maxilnuln value of the vertical deflection in section3. In addition, the calculalion of the long-ten11 effects such as creep deformations refers to the quasi-permanent combinations: = (gk Gk)4. O,l s,,k c9 : (gk Gk) @?+J sI,k +
(gk
+
+
+
Gk)
+
@2,sSll,k
@2,,9
Wi,k
= ( ~ k
+
'9'
+
Tocalculatethe final deflections, it is therefore necessary to considertl~ecornbinations:
-
(C7,Cg) for the vertical displacements, (C7,Cg) or (C8,ClO) whichever causes the greater horizontal displacements.
References C.E.B. (1980). S1ruciuraI sarety. Bulletins d'information N"127 and 128, Brussels, Belgium. E.C.C.S. (1987). Kecornmendations for calcuiating the cffects of wind on constructions. European Convention for Constructional Steelwork, Technical commitlee 12,Rcporl N"52,Brusscls, Bclgium. I-lendrickson, E.M., Ellingwood, B. ilnd Murphy. J. (1987). Limit stntc probabilitics for wood structural membcrs. ASCE, J, of Slructur~lEngineering, USA, Vol. 1 13 N"1, p. 88-1 06. Lusch (1964). Wind tunnct invcsligationson buildings withreclangulnrbnsc and with flat and duo-pitchcd roofs. Rcpon of Bauforschung Ne41,Germany. Rachcr, P. and Rougcr, F.(1994). Scnticcabilily limit states - A proposal for updating Eurocode 5 with rcspcct to Eurocodc 1. in: CIB WI 8~-27"'Mecting,Sydney, Australia, July 1994. Rackwitz, R, (1976). Pr;~cticalprobabilistic approach lo design. C.E.B., Bullelin d'inforrnation Brusscls. Belgium.
STEPIEUROFORTECN - on initiiitivc under the EU Comclt Programme
N' 112,
Wood as a building material
STEP lecture A4
Objectives
P. I-ioffmcycr
To provide the concept of wood as a cellular, anisotropic material. To present the basic definitions of moisture content and density. To introduce shrinkage and swelling and their implications in structural engineering. To present the necessaly background for the understanding of ECS's modification factor, k,,,,,.
Technical University of Dentnark
Summary The concept of wood as a cellular composite material is presented. The microstructure of the wood cell wall is discussed with a view to explaining the anisotropic nature of the physical and mechanical properties of wood. Important features of macrostructure are included; keywords are growth rings, juvenile and reaction wood, sapwood/heartwood, grain deviation, knots. Density is the single most important physical characteristic of wood. The higl~ variability is discussed and the concept of characteristic density presented. Water is always present in wood. The amount of water has a profound influence on almost all wood properties. Moisture content and the fibre saturation point are defined and the sorption isotherm presented. Anisotropic shrinkage and swelling are introduced and their engineering implications discussed. Different types of distortio~~s caused by drying ace presented. An overview of rnoisture strength relationships and the influence of moisture level on the failure mechanisms of wood and wood based inaterjlils is discussed. Wood and wood based inaterials experience a significant loss of strength over a period of time. For permanent loads, wood and wood based materials are assigned strength values that are 60% or less of their short term strength. This duration of load effect is discussed and its moisture dependency is described.
Introduction Wood is a natural, organic cellular solid. It is a composite made out of a chemical complex of cellulose, helnicellulose, lignin and extractives. Wood is highly anisotropic due mainly to the elongated shapes of wood cells and the oriented structure of the cell walls. In addition, anisotropy results from the differentiation of cell sizes throughout a growth season and in part froin a preferred direction of certain cell types (e.g. ray cells). The minute structure of cell walls, the aggregation of cells to form clear wood and the anomalies of structural timber represent three structural levels which all have a profound influence on the properties of wood as an engineering material. For instance, the ultrastructure level of the cell wall provides the explanation of why slirinkage and swelling of wood is normally I0 to 20 times larger in the transverse direction than in the longitudinal direction. The microstructure of clear wood holds the key to understanding why wood is 20 to 40 rimes stiffer in the longitudinal direction than in the transverse direction. The macrostructure of knots, fibre angle etc. provides the explanation of why tensile strength along the grain may drop from more than 100 N/ltrnz2 for clear wood to less than 10 NAlrrn' for structural timber of low quality. STEPlEUROFORTEC11 - an initiative undcr thc EU Comett Progrnmine
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The structure of wood Wood is obtained from two broad categories of plants known comrnercidly as hardwoods (angiosperms, deciduous trees) and softwoods (gymnosperms, conifers) (Figure I).
Figitre I
Corirrrrerciul finrbe~.i.s obtnirierffrotn (a)lrard~~~oods (ongiospertns) orfronl ( b ) sofr~voocls(gymrro.spemw)(Cottrfesyof W.A. C6tC). LeJr: octk (Qltet-clutaoBfir), right: spruce (Picea abies).
The observation of wood without optical aids shows not only differences between softwoods and hardwoods and differences between species, but also differences within one specimen, for example sapwood and heartwood, earlywood and Iatewood, the arrangement of pores and the appearance of reaction wood. All these phenomena are the result of the development and growth of wood tisstte. Softwoods and hardwoods differ in cell type (Figure 2).
SoJFnvood shows a relatively simple structure as it consists of 90 to 95% tixcheids, which are long (2 to 5 nmr) and slender (10 to 50 prn) cells with flattened or tapered, closed ends. The tracheids are arranged in radial files, and their longitudinal extension is oriented in the direction of the stem axis. In evolving from earlywood to latewood the cell walls become thicker, while the ceIl diarlieters become smaller. At the end of the growth period tracheids with small cell Iumina and small radial diameters are developed, whilst at the beginning of the subsequent growth period tracheids with large cell lurnina and diameters are developed by the tree (Figure I(b)). This difference in growth ]nay result in a ratio between latewoad density and earlywood density as high as 3:1. STEPIEUROFORTECH - an initiative undcr thc EU Comctt Progmrnme
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Resin
Figure 2
Models of a softl-t)oociorrd a Irard~voociblock, sho~virlgthe inair1 plnires for (~1riso1rop)f (adaptedft-on1 Fc~tgrel~ i l dWcgcr,er; 1983).
The storage and the transport of assimilates take place within parenchyma cells which in sofhvoods are predominantly arranged in radially running rays (Figure 2). Resin canals are longitudinal and form radical cavities within the tissue of most softwoods. The tree sap stream from one cell to another is facilitared by small openings or recesses in the fibre wall known as pits. A predominant type in softwoods is the bordered pit. These not only let water move freely but they also act as valves to prevent the spread of air into sap filled cells, in which case the water columns, extending from the roots to the crown, would rupture and the tree would evenh~ally die. Uilfortunately, pits perfom] tile same function during drying of timber. Capillary forces are developed upon water retreat from the cell lumens tltrough the pits, and the pit membranes ltlove effectively to seal off the pit openings. This not only impedes the drying of wood; it also may impede greatly the susceptibility to later i~npregnationtreatment. Such pit aspiration is the nuin reason why spruce, for example, is nonnally very difficult to impregnate.
Hnrdrvood anatomy is Inore varied and coraplicated than that of softwood, but most structural concepts are analogous. Hardwoods have a basic tissue for strength containing librifor~nfibres and fibre tracheids. Within this strengthening tissue, conducting vessels are distributed, often with large lunlina. These vessels are long pipes ranging from a few centimctres up to Inany metres in length and consisting of single elernents with open or perforated ends. Diffuse-porous and ring-porous hardwoods can be distngoished by the arrangement of the diameter of the vessels (Figure 3). Hardwood fibres have thicker cell wnlIs and smaller lumina than those of the softwood twcheids. The differences in wall thickness and lumen diameters between earlywood and latewood are not as extrelne as in softwoods. The number of parenchyma cells in hardwoods is higher than in softwood. Hardwoods often have very large rays and particularly in tropical hardwoods there are high percentages of longitudinal parenchyma. Some basic features of the wood cell waH are found to be co~nlnonamong many different wood species. The basic skeleral substance of the wood cell wall is cellulose which is aggregated into larger units of structure called elementary fibrils. These, in turn, are aggregnted to form threadlike entities known as microfibrils. The number of cellulose chains contained in each rnicrofibril has been estimated to be STEPtEUROFORTECH -
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irlitiaiivc tinder the EU Co~ncilProgramme
A413
in the range of 100 Lo 2000. The cellulose in a microfibril is embedded in a rnatrix of hemiceiluloses and er~velopedby lignin.
Light tiricrogrupli of rhc /firre f)jpes of pore pcitrenrs rtfgrowth irtcrerrretrrs it1 har~l\~loods as scctl in cross section. Key: A, riitg-porotrs (red onk); B, serrti-
The layered structure of the fibre cell wall is illustrated in Figure 4. Between the individual cells there is a layer, the tltidrile lamella (ML), which glues the cells together to forin the tissue. The middle lainella is rich in lignin and pectic substances and virtually free of cellulose. In the pritt~aty\call ( P ) the cellulose microfibrils are arranged in a rnndorn, irregular network. In normal wood tissue, the s e c o ~ ~tvall ~ l uconsists ~ ~ ~ of three fairiy distinct layers S,, St and 3,. The outennost layer, S,, is very thin (0, I to 0,2 pnr) and exhibits an average tt~icrofibrilangle (for the layer as a whole) of about 50 to 70". The bulk of the secondary wall is ~nnde up of the S, layer, which is typically several ~nicrometresthick. The microfibrils are usually oriented to the fibre axis at a relatively small angle (5 to 22'). Within the S, layer the microfibrils are arranged with a gentle slope but not in a strict order.
,.e 4
Schenicrric clffltegetter01 ~crallnrcllirecfrcre ofirortt~nl~vuod.fit~ers. Key: L,cell ltrnretl; ML. tt~icdlelanlella; P, prinraiy ~ i ~ c r lurrcl l ; S,, St utld S.,, 1ayer.s of tl~c secoirdcity \i~all(udaprccl frarrt Pnr-han! urlcl G r q , 1984).
From an engineering viewpoint, the celI wail structure is an ingenious construction. The dominant S2 layer OF allnost axially oriented bundles of rnicrofibrils very STEPfEUROFORTECH - an initiative under !he EU Comcit Progrnmrnc
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effectively takes up tension forces. In compression the bundles of tnicrofibrils are turned into Iong slender columns which are then prevented from buckling by the inner and outer reinforcing layers of S, and S, microfibrils having a more gentle slope.
Growth rings For most softwoods and ring-porous hardwoods there is a relationship between the width of growth rings and density, Softwoods tend to produce high density Iatewood bands of a relatively constant thickness. Most of the variation in growth ring width is caused by a variation in the thickness of the low density early wood bands. For most softwoods, therefore, density decreases with increasing growth ring width. This explains why ring width is included as a grading parameter in many visual grading rules currently used in Europe. However, caution sl~ouldbe exercised when using such refationships. The density level for a given ring width is dependent on soil type, cli~nateconditions, sifvicultural practice etc. Therefore, for softwood timber of mixed origin, ring width does not predict density with any real accuracy (Figure 5).
300
&--+---1---t4___ill_i-~
0
I
2
3
4
5
6
7
8
\vr (nlm)
F ~ ~ I I5I - E De~uify,p , , (kg/~~t') as afirttctiorr of groivrl~ring lvidtlr .
,
MJ, (r~rirr). Resuits froiir 1600 spccirrrens of nvo . . sorl~plesof Swedislr grorolr nlrcl Dartislz grows sprtlcc.
Ring-porous hardwoods such as oak and ash are characterized by a high concentration of open vessels produced during spring. The width of these rings is relatively constant and the variation in growth ring width is caused by a variation in the thickness of the high density latewood bands of fibre tracheids. This is why density increases with increasing ring width for most ring-porous hardwoods. There is no such relationship for diffuse-porous hardwoods such as poplar itnd beech.
Sapwood and heartwood The young outer part of a tree stem conducts the upward flow of sap from the root to the crown. This part of the bole is known appropriately as sapwood. As the cells grow old, they stop functioning physioiogically; this inner part of the bole is known as heartwood. In most species heartwood is darker in colour due to the inc~ustationwith organic extractives. These chemicals provide heartwood with a better resistance to decay and wood boring insects. NorrnalIy heartwood formation results in n significant reduction in moisture content. This results in pit aspiration. In many hardwood species the vessels become plugged. This causes a marked reduction of perrneabilSTEP/EUROFORTECI-1 - Bn initiative under Lhc EU Comet1 Programme
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ity. In some species (e.g. spruce, beech) the heartwood is not coloured, nevertheless the extractives and physical alterations result in a difference between sapwood and heartwood.
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For the purpose of wood preservation, sapwood is preferred, since the heartwood rs is virtually impermeable. of a species such as pine ( P i ~ ~ i,~j~lvestris)
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Juvenile and reaction wood The wood of the first 5 to 20 growth rings (juvenile wood) of any stem crosssection exhibits properties different from those of the outer part of the stem (mature wood). This is particularly significant for softwoods. In juvenile wood, tracheids are relatively short and thin-wailed with a gentle slope of the microfibrils of tile S2 layer. Juvenile wood therefore typically exhibits lower strength and stiffness and much greater longitudinal shrinkage than mature, normal wood. Heartwood often holds all the juvenile wood, which possesses inferior quality with respect to lnechanical properties. Therefore, in young, fast grown trees with a high proportion of juvenile wood, heartwood may be inferior to sapwood. Juvenile wood is not normally considered a problem in terms of timber engineering. However, with the increasi~~g proportion of fast grown, short rotation plantation trees being used in the industry, the problems attached to juvenile wood will increase. A tree reacts to exterior forces on the stem by forming reaction wood. Softwoods develop compression wood in areas of high conlpression, whereas hardwoods develop tension wood in high tensile regions. While the occurrence of tension wood is of minor importance to timber engitleering, conlpression wood often creates problems. Compression wood has the appearance of wider growth rings and a I~igherlatewood proportion than normal wood. In addition, the contrast between earlywood and latewood is less dislinct than in normal, mature wood (Figure 6). The microfibrifs of the S2 layer are arranged with a 45' slope which results in excessive longitudinal shrinkage, similar to juvenile wood.
Figlclz. 6
Cortlprcssion woocl irr sprttce (Picea ubies). (a)cot~tpressiori~~loocl; (bj rlurrrrcrl I~~OOC~.
Timber containing compression wood is liable to excessive distortion upon drying. Compression wood is normally of higher density so there is no loss in mechanical properties, however in a dry condition it tends to break in a brittle manner. Most visual strength grading rules limit the amount of compression wood in high quality grades.
Grain deviation Some trees grow with a cell orientation forming a helix around the stem. This spiral grain is common in certain timber species and rare in others. It is particularly STEPIEUROFORTECH - an initiative undcr the EU Comett Programme
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pronounced in young trees. Timber sawn from these trees often exhibits grain deviation which will severely impair its use. Limits to grain deviation are included in most visual strength grading rules; typically a grain deviation of I in 10 is accepted for high quality timber while 1 in 5 or more is accepted for low quality timber.
Knots IOlots are the parts of branches that are embedded in the main stem of the tree. Tlle lateral branch is connected to the pith of the main stem (Figure 7). As the girth of the trunk increases, successive growth rings form continuously over the stem and branches and a cone of branch wood (the intergrown knots) develops within the trunk. Such knots are termed tight knots because they are intergrown with surrounding wood. At some points he limb may die or break off. Then subsequent growth rings added to the main stem simply surround the dead limb stub and the dead part of the stub becomes an encased knot. It is not intergrown and often has bark entrapped and is called a loose knot.
Figure 7
Tire lateral (Irarrc growtlt rirq or lr
conrrecrcd to the pith of fhc rtrairr stern. fon~tscontir~rtortslj~ over the sret,~nnd
Figrtre 8 A sofnctood board niny skatv k~tots i~rclrrsters scparcited by t11eofrerr clear it~oorlof tl~eir~~erjrodes.
Figllre 9 Teltsior~fuilrirc of a sprttce board cntcseri IJJ' fibre itrcliitntion aro~ntrl cr brrtt.
STEPIEUROFORTECH - an initinlive under the EU Cornclt Programme
Softwoods are characterized by having a dominant stem from which whorls of lateral branches occur at regular intervals or nodes. Softwood boards therefore sl~ow knots in clusters separated by the often clear wood of the internodes (Figure 8). Knots are, by far, the single most important defect affecting mechanical properties (Figure 9). ICnots are termed according to their appearance at the surface of the timber (Figure 10).
Fig~trc10
K~lofs o1.e terttred accordi,rg to tltcir appearance ut the srttfclce of tlic rittrber; (a) spike krrot; (6)ticirralv face knot; ( c ) tlirorcgh k~ror;(d) orris ktjot;(c) \vide
face ktjot; Cfl knot cluster.
Density Density is the most important physical characteristic of timber. Most mechanical properties of timber are positively correlated to density as is the load carrying capacity of joints. Limits to density are therefore incorporatecl directly in the strength class requirements of prEN 338 "Structural timber - Strength classes". Density is defined as
where n i is the inass (kg) of timber and V its volume (nl3]. Density is moisture dependent, because moisture adds to the mass and may cause the volume to swell. Density p , at a moisture content, w (%), is expressed as 111,
p,=--
v,
-
rrro(l +oyolo) 1 +O,Olw = Po V,(l +oYOlP,~) 1 +0,01p ,o
(2)
where m,, V, and p, are the mass, volume and density at zero moisture content, p, is termed oven-dry density or simply dry density. P,, is the coefficient of volumetric swelling and has the units of percentage swelling per percentage increase of moisture content. As explained in detail later, swelling only occurs when water is penetrating the cell wall layers. The moisture content corresponding to saturation of the cell wall is tenned the fibre saturation point a,, This corresponds to a moisture conrent of about 28%. Above this no swelling occurs. Below fibre saturation, swelling may for practical purposes be considered Iinear wit11 moisture content. In wood science and engineering, dry density p, and density p,, at 12% moisture content are most frequently used. Density values given in EC5 are defined with mass and volume corresponding to an equilibrium at a temperature of 20 "C and a relative humidity of 65%.
The values of p,? referred to in EC5 relate to the average density pl,,,,nt,r and the characteristic density p , , , , defined as the population 5-percentile value. For a given STEP/EUROFORTECH - an initiative undcr the ELI Comcu Programme
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strength grade of timber, density is assumed to show a r~ormaidistribution with a coefticient of variation of 10%. Therefore:
In forestry, density is expressed as the ratio of oven-dry rnass to the green volu~ne.
This density (p,,), often terined basic density, is preferred by foresters, because it gives direct information about how much wood (dry mass production) is present in a given volume as it appears in the forest. An additionat advantage of using waterswollen, or green volume, is that it can be determined by the simple technique of water displace~nenteven for irregular shaped sarnptes. A further wood density reIated term is specific gravity (G). Basic specific gravity is defined as: Ino !h= -
Go,;
p ,"
plYV,
dry Inass mass of displaced water
where p,,. is the density of water. The terms basic density and basic specific gravity contain the same information, and they are different only in the fundamental sense that basic specific gravity is a number (0 < G < 1,5) and basic density has the unit of kS/in3. The densities p,, and P , are ~ related to basic density p,
P12
=
Po s 1-16.10-~p,
by
,
(7)
All the various expressions for density are used frequently in literature on timber properties. Often no specific mention is made of which variant of density is being used. Caution should therefore be exercised when using such information. The density p, of the cell wall is about 1500 kg/~n?Tile density of wood, therefore, is dependent on its porosity, defined as the volume fraction of ceIl lumina. Structural timber typically shows dry density values in the range from 300 to 550 kgha3,which gives fractional void volu~nesin the dry condition from 0,80 down to 0.63. The density of timber., even of a particular sample talcen from a single location, varies within wide limits. prEN 338 "Structural timber - Strength classes" defines characteristic density values plZ,kfor softwood in the range from 290 kg/~n3for the low strength class C14 to 420 fig/nz3 for the high quality strength class C40. For visual grading, growth ring width was earlier shown to be of limited value (Figure 5). Therefore alternative methods for density assessment are needed. This topic is covered in STEP iecture A6.
Wood and moisture Moisture content is defined as the ratio of the mass of removable water (I?z,,.) to the dry mass (m,) of the wood (Equation 8). The dry mass is obtained by oven drying at 103 + 2 "C. Moisture content may be expressed as a fraction or in percentage STEPIEUROFORTECH - nn inirialivc under thc EU Cornctt Programrnc
terms. Througliout this chapter, wood moisture content is expressed in percentage terms.
For moisture contents in the range 6 to 28%, electric moisture meters are available, which are easy and quick to use. The accuracy of the best meters is of the order -c 2% which is quite sufficient for practical engineering applications. The two principles currently in use are, firstly, a DC based measurement of the moisture dependent resistivity between two electrodes hammered into the wood and secondly an AC based assessment of the moisture dependent dielectric properties of wood in an electric field created by two electrodes resting on the wood surface. Both types of meter require calibration and the AC meters only measure the moisture content in the top layer of the wood. When wood is dried from a green condition, water is first lost from the cell lumens. This water is not associated at the molecular level with wood and is termed free water. The water held within the cell wall is termed bound water. as it is held to the cell wall substance with hydrogen bonds and van der Wads forces. The removal of water from the cell wall thus requires greater energy than reruoval of free water. The moisture content, w,, when the cell wali is saturated with moisture, bur no free water exists in the cell lumen, is termed the fibre saturation point (FSP). The FSP for most species is in the range of 25 to 35%; for most practical purposes 28% is a convenient average. The fibre saturation point is of considerable engineering significance since below this point there will be dramatic changes in most physical and ~nechanical properties. Above the FSP most properties are approximately constanl. Wood is hygroscopic and thus continually exchanges moisture with its surroundings. For any combination of temperature and humidity in the environment there will be a corresponding moisture content of the wood where the inward diffusion of moisture equals the outward movement. This moisture content is referred to as the equilibrium moisture content w,. Wood, however, is rarely in a state of' moisture equilibrium as the climatic conditions of the environment are constantly changing. The levet of moisture content and even the magnitude and speed of moisture fluctuations have a profound influence on almost all engineering properties of wood. A sorption isotherm represents the relationship between moisture content o ,and relative humidity yr at constant temperature T. At a specific relative humidity yr the equilibrium moisture content w,, depends on whether equilibrium is reached as a result of desorption or as a result of adsorption. The adsorption isotherm (A) is always lower than the corresponding desorption isotherm (D). The AID ratio at room temperature generally ranges between 0,8 and 0,9. Sorption hysteresis in timber is beneficial from an engineering viewpoint. This is because wood exposed to cyclic humidity conditions shows smaller changes in moisture content for given humidity changes than would be the case if there were no hysteresis. Sorption hysteresis reduces the effective slope dwlclyr of the actual sorption isotherm and the dimensional changes associated with humidity changes. Figure 1 1 shows sorption isotherms for spruce; these curves may also for practical purposes be taken as representative of pine and fir. The equilibrium moisture content of panel products like plywood and particIeboard are also adequately STEPIEUROFORTECM - an iniliativc undcr the EU Comclt Programme
described by Figure 11. However, extensive chemical treatment or heat treatment during production of panel products like fibreboards may significm~tlyreduce the equilibrium n~oisturelevel of such products.
y' [%I
Figrrw 11
Sorpliori isothe~.r~u for sprrtce at 25 'C (Sfurrrnz 1964). Moistrtre corlterrf (a) I ~ E ~ S Ire/atitre ~S hunriciit)~ fly). A: n~fsorptioil;D: c~esorpfioit;0: osciffatittg sorj~tio)~.
Considerable time is required before timber wiil come to equilibrium with a surrounding constant climate. For example, 50 x 100 H I I ) ? spruce timber at w = 20% may need more than 4 weeks at 20 "C and yr = 54% before the centre will reach the corresponding equilibrium moisture content of o = 10%. Therefore, the moisture content of a component in a timber structure will approach the equilibrium moisture content corresponding to the average temperature and relative humidity over a period of weeks rather than being affected by short cycles of high or low f~umidity.
Shrinkage and swelling Moisture has such an affinity to the wood celi wail substance that i t can force its way into this virtually non-porous material. By so doing, it pushes the ~nicrofibrils apart. The resultant swelling of the cell wall can for practical purposes be assu~ned to be equivalent to tlre volr~rneof the adsorbed water. During sweiling the volume of the cell lumens stays constant. This implies that the volumetric swelling of timber equals the volume of rlle adsorbed water. When moisture is removed from the cell wall, timber shrinks. Shrinkage and swelling within the normal moisture range for timber structures are termed movements. The directional movements are first and foremost dependent on the microfibrillar orientation ofthe dominant S, layer of the fibre cell wail. Since the microfibrils are normally inclined at a low angle to the longitudinal direction (Figure 4), almost all ntovements show in the transverse directions. The anisotropy between transverse and longitudinal ~nosernentsis of the order 20: I . Juvenile wood and compression wood exhibit microfibrillar angles much larger than normal wood, which result in much larger longitudillal movements. In compression wood the helical angle is often STEPIEUROFORTECH - an initiative undcr the EU Cotnett Programme
A411 1
of the order 45" which results in equally large movements in the longitudinal and transverse directions (Figure 12). Anisotropy in timber's water relationships exists even within its transverse direction. The tangential movelnents may, for practical purposes, be taken as twice the radial movements. Therefore, although microfibrillar angle is of major importance, it is quite apparent that other factors are also important. For most engineering purposes, however, it is unnecessary to differentiate between the two transverse directions, and transverse movement is often taken as the average value.
Figlrre 12
Lotlgitudirtal (L) orld tarlgctrticll (7') s1lrirzkage.s (%) j'rorrr greet1 ro over~-dty cotzrli/ion irr rclariotr 10 nrerrrt jiDt.il angle (0). Species is Pirrtts jeffre~e?fi (Maylotr, 1968).
Changes in dimensions tend to be linear with moisture in the range of 5 to 20% moisture content. In this range movelnents may be calculated from
where h , and It, are the dinlensions (thicknesses) at moisture contents o,and o, respectively. P is the coefficient of swelling (positive) or shrinkage (negative). Units are %I%.
If no species-specific value of the coefficient of movernent is known, an approximation may be used. The coefficient of volumetric movelnent P,, can be considered to be equal to the numeric value of the density rimes 10'" In other words, the volurne of timber of a density equal to 400 I g / 1 1 1 ~s~vells0,4% for each 1% increase in moisture content. This is based on the volumetric sweIling equaling the volurne of water uptake. Tile coefficient of longitudinal movernent, Po, is usually negligible, in which case the coefficient of transverse movement, P,, is equal to half the coefficient of voiurnetric rnovemenr. For most species, including spruce, pine, fir, larch, poplar and oak, engineering values of Po and J,f can be taken as p, = 0,Ol and p, = 0,3,where flis given as percentage movement for I % change of moisture content. For dense species like beech (Fagus syh~atica)and eklii (Lol~hir-aalatn) a P,, = 0,3 should be used. In plywood, the movements in the pane1 plane are of the same order as the longitudinal movemcnts of timber. For other composite wood products, such as particleboards and fibreboards, these movements are very dependent on the particular panel type and production technique. In the transverse direction of panel products, the reversible movemcnts are of the same order as those of timber. However, many panel products, which have been subjected to high compression STEP/EUROFORTECH-
an initiative under rhc
EU Co~ncttProgramme
stresses during production, will show additional, irreversible tllickness swelling or"spring back". When wood is restrained from expanding (e.g. in bolred joints), the uptake of moisture induces intetnal stresses. Due to the viscoelastic/plastic nature of wood such stresses will eventually relax and irreversible di~nensionalchanges occur. When wood returns to its original moisture content the dimensions have shrunk, and the bolted joint may then be a loose fir and have lost some of its capacity. It is therefore ilnportant in engineering design to retain access to sucll construction details which may need tightening up. timber should In order to mini~nize the problems of dimensional ~nove~nents preferably be used at a moisture content corresponding to the relative humidity of its envil.ontneni. Within buildings, timber of a moisture content higher than 20 to 22% should only be used as an exception and only in suc1.t cases where adequate and quick drying of the structure is obtained witt~outrisks of biological degradation or perlnanent set due to mechonosorptive creep.
In the case of large timber members, it is not always possible to neglecl longitudinal movements. If, ils an example, the ~noisturecontent of the upper and lower part of a glulam beam varies, it may result in significant vertical movements. A roof beam laid in insulation may, during winter, experience the warm, dry climate of the heated room in its lower part and the moist, cold climate of the unheated loft in its upper part (Figure 13(n)). The deflection ri of the beam is catculated from
where I is (he span of the beam and the curvature K = -(E,~-C,)/J~ and
E,,
and
E,
K
is
are t.he strains of the outermost upper and lower parts of the beam.
Similar examples of importance ta timber engineering are for example l u g e stressed skin roof elements or roof trusses with the lowel- chord placed in insulation in a relatively drier climate (Figure 13(b)).
STEPIEUROFORTECII - an initiative under the EU Cornclt Programme
A411 3
Deflections may also occur in structures where the moisture distribution is homogeneous but different from the original moisture content. An example of such a case is given in Figure 14 which illustrates a three-hinged frame wit11 finger jointed corners.
i
t 1
Honroger~eoltsmoisntrz. cllrrtrge it] n ~/~rz.e-hirrgedfinttzc irti~lrjittger- joitrted comers rvill cnrtse nlovemtetrts due to tile charzge of (Ire atlgle Oer~t~cetl fibres arld the cross sectiarls of the 1argefitrgerjoir~r.r( f j ) (adupteclfrort~Larse~lutld Xiherhalf, 1994).
A Iio~nogenousincrease in moisture content results in an increase of dimensions in the transverse direction corresponding to the moisture induced strain E. The longitudinal dimensions are assumed to stay constant. This results in a change of the angle between fibre direction and the finger joint from a to a - A a where A a is calculated from
The total change of angle in a two-finger-joint corner amounts to 4Aa. In a symmetrical three-hinged frame with 2 joints in each corner the total vertical movement of the top of the Frame is
In statically indeterminate structures, the above movements will give rise Eo increased stresses.
Distortions The anisotropy of transverse swelling may cause cross sections to distort upon drying (Figure 15). The fact that tangential shrinkage is about twice the radial shrinkage explains the tendency for the growth rings to straighten out. The internal stresses developed by the anisotropic shrinkage may be released primarily in the development of radial cracks. The tendency to cracking is more pronounced the larger the cross section and the faster the drying rate. The presence of compression wood, juvenile wood or even knots in only part of a cross section may cause lengthwise distortions known as bow, spring and twist. Twist may also result from sawing timber from a tree exhibiting spiral grain. Cup is the result of the different movements in the tangential and radial directions (Figure 16). STEP/EUROFORTECH - an ini~iativcundcr thc EU Camctt Programme
Figrire 15
Distorriotrs oj'>lariorlsci.oss seclioizs aficr r h y i ~ ~critfioiiz g, dijJcerent iocntiozi.~ i~ra log.
The degree of distortion is often given maximum limits in national strength grading rules. The CEN standards for visual and machine strength grading contains recommended limits to distortion (Table I). Such limits do not reflect an exact relationship between distortion and strength but rather define limits beyond which the handling and assembling of timber in structural co~nponents becomes unacceptably complicated. There may be occasions when the structural design calls for tighter limits than given in Table I and such Iimits (hen must be agreed with the producer. Type of distortion
Grade fitting into strength clnss
CIS and below
Higher classes
Bow
20
10
Spring
12
8
Twist
2 rrniiJ25 tr~niwidth
1 rrriiz/25 itrni width
CUP
No restrictions
Moisture content and mechanical properties The mechanical properties of wood are dependent on moisture content. An increase in moisture produces lower strenglh and elasticity values. Tf~iseffect is partly explained by the cell wall swelling, whereby less cell wall material per unit area is available. More important, however, is that water, when penetrating the cell wail, weakens the hydrogen bonds responsible for holding together the cell wall. Moisture variations above fibre saturation point have no effect on n~echanicalpropel-ties, since such variations are related to free water in the cell lumens.
STEPIEUROFORTECJI- an iniliativc under rl~cEU Corncir Programme
A4115
The effect of moisture change varies for different mechanical properties. For example, failure in compression parallel to grain is caused by fibre buckling where moisture sensitive hydrogen bonds play an important role and is inore sensitive to rnoisture than tension strength which atso includes rupture of covalent bonds when tearing apart the cell wall microfibrils. Values for the effect of moisture on the mechanical properties of clear wood properties are given in Table 2. For practical purposes a linear relationship between moisture content and properties may be assumed for 8% < w < 20%. Property
Change (%)
Coinpression strength pamllcl to the grain Compression strength perpcndiculnr 10 tlie grain Rending strength parallel to the grain Te~lsionstrength parallel Lo Lhe grain Tcnsion strength pcrpcndicular to tile grain Shear strength parallel lo the grain [nipact bending strength parallel to the grain Modulus of elasticity panIIeI to thc grain Tcible 2
5 5 4
2,s 2 3
0s
13
A ~ [ ~ ~ I J . ~ Ici~arrgc ' I ? I C (%) ~ I E of clear lltood pro[)erfie.s for cr orle percerrmge cirur~gcof rr~oisttcrz.corlterll. Bc~sisis properties uf 13% uroistcrre coriterrl.
For some mechanical properties the influence of moisture is less significant for timber rhan for clear wood (Hoffrneyer 1978; Madsen 1975; Madsen et al. 1980); tensile strength of low quality timber is virtually independent of tnoisture content. Figures 17 and 18 are based on results from an investigation (Hoffrneyer 1978) of 50 x 150 rlntt spruce (Picell ubie.~),where samples of equal strength distribution were subjected to coinpression, tension or bending failure at each of three different moisture content levels. All figures show strength against the percentile values.
Figtire 17
Strerlg/ll (Nhrrtr~')agairrsr perccritile for trlcrfched sctrt~plesof spruce (Picea nbies) .strbjccietl to a: comprcssioti, 1): te/rsiotr arld c: be~rc/ir~g at rjloisrirre corilcrtt levels 12%, 20% uad >2S%.
The influence of moisture content on compression strength is seen
LO be independent of timber quality, since the relative strength difFerences stay almost constant throughout the whole range of percentile values (Figure 17a). Tensile strength, however, seems to be very inodestly influenced by moisture and no difFerence is seen at the 5-percentile level. In fact, dry timber strength (a-12%) drops below moist timber strength (w-20%) for the lower half of the timber quality ((Figure 17b). Bending strength represents a mixture of the co~npressionand tension behaviour,
STEP/EUROFORTECf-I- an initiative undcr thc EU Comctt Progr:irnmc
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-
and at a timber quality level corresponding to the 5-percentile, bending strength is only very- modestly influenced by moisture (Figure 17c). Bending strength is rrorn~ailyhigher than both cornpression strength and tensile strength, wi.~ichis partly explained statistically by the fact that the bending test subjects only a small amouni of the individual specimens to high stresses. The failure mode of timber subjected lo bending is moisture dependent. In bending at low moisture content, failure is governed by areas of high tension, tvhereas at high inoisture content failure is governed by areas of high compression. Tensile failures are brittle whereas compression failures exhibit extensive yield resulting in zones of compression creases.
Figure 1S
EC5: Part 1-1: 3.1.5
Slrz.rlg/lr(N/~irrrr')ogaitrsfpe~.ccrlti/eI%) foi-i~1ntcheci.sc~17ip/es of slmrce (Picea obits). The resrrlts sholvr~iit Fig1tt-e I7 Irave beeti r.enmitged to ill~rsrrntc[he i r l t e r . a i o / i i of co~iipressioit-,reiisiorz- uiiri boidirtg .strerigrli nl eqrml moislrrre cnriterlr I~I>L'/.S.
Timber subjected to the moisture conditions of service class 1 of EC5 shows higher co~npressionstrength than tensile strengtll for a given percentile (quality) (Figure I8a). Such timber subjected to bending will always fail in a brittle manner and Iinear strain distribution may be assuined ail the way to failure. Timber in service class 3 condition behaves differently; here compression strength is lower tIinn tensile strength for all quality levels (Figure 18c). Such timber will initiate bending failure by developi~lgvisible compression creases in tile outermost compressed zones. As the bending stress increase, the neutral axis moves towards the tension side allowing the increased compression stresses to be carried over a larger cross section. The strain distribution is no longer linear. Eventually the tensile stress reaches the ultimate tensile strength and the bean1 fails. Timber in service class 2 conditions shows brittle failure for low quality beams arid ductile Failure, associated with co~npressioncreases, for higher quality beams (Figure 18b). When comparing tnechanicai properties, a standard reference moisture condition consistent with an environment of 20 "C and 65% relative Ilumidity is to be used for timber and wood based panels. For structural timber tested at a different condition, the mechanical properties must be adjusted in accordance with prEN 384 "StructuraI timber - Determination of characteristic values of mechanical properties and density".
Duration of load Timber experiences a significant loss of strength over a period of time. The strength values to be used in design of timber members for long-term permanent loads are app~.oximatelyonly 60% of the strenglh values found in a short-term iaborato~ytest. STEPIEUROFORTECH - an initiative t~nderthe EU Con~ettProgramme
A4/17
The background to this 0,60 modification factor dates back to the 1940's. when duration of load experiments were carried out at the Forest Products Laboratory in Madison, Wisconsin (Wood 1947, 1951). On the basis of rests on small clear specimens subjected to bending for up to seven years, a stress-lifetime relationship was established, which predicts the lO-years strength to be slightly less than 60% of the short term strength. Tile relationship, termed the "Madison curve", is illustrated in Figure 19 and is a plot of stress ratio against logarithmic time to failure, where stress ratio (SR) is the actual long term load over estimated short term failure load. Most countries have since ir~cludedthe resulting modification factors in their timber design codes. The Madison curve was regarded as being valid not only for bending, but for all strength properties, grades and species. The basis for regarding results obtained on srnall clear specimens as also being valid for stn~cturaltimber is rather tenuous considering that the failure mechanisms are quite different taking account of, for example knots, inclined grain or fissures.
Figlire 19
Srrass ratio (a) as cr firrictioir cf logcrrilnric tirrte lo .foilrrre (holrrs)for srrrall clear specbnerrs subjecfed to l~encli~ig (IVood 1951).
The first duration of load tests to include structural timber were initiated twenty years ago in Canada, and suggested a much less severe modification of load factor for timber than for clear wood (Madsen and Barrett, 1976). The Findings also suggested a timber quality dependency for the duration of load effect similar to that already found for the effect of moisture. A large number of duration of load tests on structural timber have since been carried out both in North America and in Europe. From these it may now be concluded that, except for the eariy Canadian results, there is no general evidence of a much less severe duration of load modification factor for timber than for clear wood. In fact, some resufts (Gerhards, 1991, Soltis et al., 1989) suggest the Madison curve to be non-conservative for timber in bending. Furthermore the duration of load behaviour of timber in tension and compression is reported to comply with the Madison curve (Glos, 1987; Lackner, 1990; Soltis et al., 1989). Moisture content has a marked influence on the duration of load behaviour (Hoffmeyer, 1987 and 1990; Fridley et al., 1991). For a given stress ratio, beams STEPIEUROFORTECM - an initialivc under thc EU Cornctt Prograrnmc
at a liigiler ~noisturecontent wilI fail before beams at a lower moisture content. However, the drier beams will have been subjected to higher loads because their short term strength is higher. Moisture variations are known greatly to increase creep in limber. This effect is terrned rnechanosorptive because it is only apparent during simultaneous mechanical stress and moisture sorption cycling. The mechanosorptive effect has been shown also to shorten the time to failure of timber (Hoffmeyer, 1990; Fridley et a]., 1992). Surf~lcetreated timber or glulam members of large volume experience relatively less moisture variation than untreated timber or small volume timber. The evidence of a mechanosorptive effect suggests that surface treated tilnber and large volume glulam members should be allowed a more modest duration of load modification factor. An exanlple of the effect of moisture on duration of load behaviour is shown in Figure 20, where results from Hoffmeyer ( I 990) have been updated to cover seven years of load duration.
f;iS,rrc 20
Stress rntio (9'0) agaiirsi loguritlrt~tictinre rojiiil~tre(Iror4r~)for50 x 100 t111)r beut~rsr.sp~-rrce (Picen L ~ ~ I ' C Ys~ibjecred ) to bel~~tilrg CII o = 10%, o = 20% ntrcl err w cycling bet wee^^ 10% nrrd 20%. +: varyitzg ~~~oistrtrc. co~~terif; A: 20% trroist~ireco~rre~rr; .r = 10% trroistrrre co~rte~rt. Y = otle ycrit: M = orre 1?7otrth. M' = otrc ~t~eek (r.cprorirtccd @cr Hqfl;rs)ler; 1990).
400 beams of spruce were subjected to bending at either 10% nloisture content, 20% moisture content or a rnoisture content varying between the two levels in a 2 monthly cycle. Matched samples were used for both short-term tests and long-term tests. AII specimens of a particular sample for long-term testing were subjected to the same load and the specimens were ranked in order of ascending time to failure. The results from short-term tests on a matching sample were ranked in order of ascending failure load. The stress ratio, SR, of n particular specimen, was then predicted as the ratio between the actual Ioad and the failure Ioad of the short-term specimen of the same rank and moisture content. T11e results show the Madison curve to describe tilnber at 10% moisture content conservatively, while timber at 20% moisture content is adequately modelled. A significant inechanosorptive effect is displayed under the conditions of varying moisture. Tile latter beams are STEPIEUROFORTECH - an ioitii~tiveur~dcrthe EU Cornett Progr;~rnlne
AW19
subjected to the same loads as the beams at constant high rnoisture. They are therefore only at a high stress ratio during the high moisture half-cycle; during the half-cycle of low moisture they are loaded to a lower stress ratio because the corresponding short term strength increases as a result of drying. Nevertheless, the mere change of moisture content results in a significant shortening of the lifetime.
The results indicate a lifetime at the 60% stress ratio level of '/2 year and 4 years for the beains of varying moisture content and 20% moisture content respectively. The Madison curve predicts a corresponding lifeti~neof five years. An extrapolation of the test results for the beams of 10% n~oisturecontent predicts a lifetime of 30 years at SR = 60%. The duration of load behaviour of panel products varies within a very wide range. Structural ply wood is considered to behave like solid wood. Particleboard behaviour is intirtiate1y linked to particle size and particle orientation, and for both particle0 term board and fibreboard, glue quality is of the uttnost importance for the loneproperties. While the best particleboard products may be assigned a O,4O duration of load modification factor for pennanent loads, fibreboards may rzlte as low as 0,20.
Modification factors for moisture content and duration of load EC5: Part 1 - 1: 3.1.7
111 timber design, the influence of moisture and duration of load is taken into consideration by assigning timber structures to service classes and actions to loadduration classes. EC5 then defines tnoditication Factors, k,,,,, for each combination of the two classifications.
References Rngel, D. and Wegener, G.(1984). Wood. Walter clc Oruytcr. fidlcy, K.J.;Tnng, R.C.; Soltis, L.A. (1991). Moisture cf'fccts on load-durdtion bchaviour of lumber. Part I. Effect of constant relative humidity. Wood and Fibcr Science 23(1):114-127. Pridlcy, K.J.; Tdng, R.C.; Soltis, L.A. (1992). Moisture effects on load-duration behaviour of lumber. Part 11. Effect of cyclic relative humidity. Wood and Fiber Science 24(1):89-98. Gerlrards, C.C. (1991). Bending crccp and load duration of Douglas-fir 2 by 4s under constant lox~d. Wood and Fibcr Science, 23(3), 1991, pp. 384409. Glos, P.; Hcirncs!~off,B.; Kellckshot'cr,W. (1987). Load durdlion effcct in spruce lumber loaded in tcnsion and comprcssion. ilolz als Roh- und Wcrkstofl', 45(5):243-249. Hoffmcycr, P. (1978). Moisku-c Content-Strength Relationship for Spmcc Lumber Subjcc[ed to Bending, Compression and Tension along the Grain. Proceedings of IUFRO Timber Engineering Conference, Vancouver, B.C.. Canada. FIoffmeyer, P. (1987). Duration of load cl'fects for spruce timber with spccial rcfercr~ccto moisture content. Proceedings of CEC Seminar on Wood Technology, Munici~,Germany. floffmcycr, P. (1990). .Failure of wood as influcnccd by moisture und duration of load. Doctoral dissertation. College of Environmental Sci. and Forestry. S.U.N.Y., Syracuse, N.Y., U.S.A. Lackncr, R. (1990). Duration-of-load Effcct on Tensile Strength for Structural Softwood 45 x 145 nrrrt. Norsk Treteknisk tnstitutt, Mcddelelse (rcpon) no. 76. Larsen, H.J. and Riberholt, 1-1. (1994). Trrekonsrruktioner, beregning. SBI-Anvisning 135. Stntcns Byggeforskningsinstilut, Denmark.
STEPIEUROFORTECH - an initiative under the EU Corncrt Programme
Madsen, B. (1975). Moisturc Contcnt-Strength Relalionship for Lumbcr Subjected to Bending. Struc:urat Rcscarch Scries Report No. I I. Dcpt. Struc. Eng., U.B.C., Vnncouvcr, Canadn. Madsen, B.; Barrctt, J.D. (1976). Time-slrcngth rciationsliips for lumber. Struct. Rcs. Series. Report No. 13. Univ. British Columbia, Vnncouvcr, Canadn. Mndscn, B.;Jarrzen, W.; Zwnagstra, J. (1980). Moisture Effects in Lumber. Str~cturalRcseard~Series Report No. 27. Dcpt. Slruct. EIIE.. U.B.C., Vnncouvcr, Canada. Mnylan, R.A. (1968). Cnuse ol' high longitudinal shrinkage in wood. For. Prod. J. 16f4): 75-78. Pnrham, R.A. nnd Grity. R.L. (1984). Formation and Srructure of Wood. In Ro\\tcil, R.M. (ed.). The Chemistry o l Solid Wood. Advnnccs in Cllcmislry Series 207. Soltis, L.A.; Nclson, W.; iiillis, J.L. (1989). EI'recl of lo:iding mode on durn:ion-of-lo;~d fdciors. Proceedings, Second Pacific Timber Engineering Confcrence. Aucklnnd. Next1 Zealnnd.
Stnmm, A. (1964). Wood and cellulose science. The Ronald Press Comp:lny. N.Y., U.S.A. Wood. L.W. (1947). Bchaviour of wood unclcrcontint~cd1o:lding. Eng. Ncws-Record 139(24):t 08-1 1 1. Wood, L.W. (1951). Relation ot' strength of' wood to duration of stress. U.S.Fores~ Products Laboratory, Report No. 1916.
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STEPlEUROMRTECM an initiative under the EU Comett Programme
Timber in construction STEP Icclure A5 P. J. Steer Consultani Structural
Objective To focus attention on the essential properties of tirriber which have to be considered in the design, detailing and construction of timber stmctures.
En,'olneer
Summary The production of timber and otlter wood-based structural materials is described. Two metl~odsto counteract the high variability of timber properties, namely grading and reconstitutjon are outlined. The essential properties of timber in service are summarised including the effects of moisture content, long-term loading, creep, shrinkage and swelling and the bel~aviourin fire. General guidance for the design of timber structures is given.
Introduction Wood is a natural resource that is widely available throughout the world. Wit11 proper management, there is a potential for an endless supply of timber and other wood-based materials. Due to the low energy required and the low pollution during manufacture timber has a far less detrimental i~npaclon the environmenl than other building materials. One example is the process of photosynthesis, in which trees absorb carbon dioxide, store the carbon as wood and release oxygen. Growing trees tl~ereforereduce the carbon dioxide in tile atmosphere. Timber is a live material. Its properties are anisotropic, they change wit11 changes in environmental conditions and load duration has also a significant effect upon strength and deformation. The properties not only vary from species to species but even within a particular species. Due to climatic differences and different forestry practices, spruce from Northern Europe, for example, has different properties than spruce from Souffzem Europe. To be able to design timber structures successfully, the practising engineer needs to be aware of the particular properties of the timber being specified.
Production of timber and wood-based materials Historically (he size of trees in tile forest detern~inestile size of the timber that may be produced. One lrundred years ago timber with cross-sections of 150 x 450 n r l i t and lengths u p to 20 171 were commonly available. Today, in many countries, timber over 75 x 225 ~ i l t l tand more than 5 nz long attracts a cost premium due LO scarcity. However, if larger sizes are required, several timber members can be combined to fonn a con~positemember, for example a glulam member. Because timber is produced by nature, strength and stiffness properties are highly variable. There are basically two ways to counteract variability and hence provide il refiabie structural material. Timber can be graded and classified into different quatities. These different qualities can then be used to satisfy different uses or requirements. Reconstitution is also possible. Elere, trees are divided into s~naIler parts which are then reformed, normally with the addition of glue.
Clcrssification o f ri~~iberTin-tbercan be assigned to a particular strength class by grading procedures, either machine strength grading or visual grading. Grading is based on established relationships between measured parameters and the strength of the timber. In machine strength grading procedures, the tnain grading parameter is the ~noduius of elasticity (see STEP lecture AB). Visual strength grading is mainly based on Iinot sizes and positions. Classifying timber by strength classes simplifics the design process. Once a strength class is selected, a number of timber species from different geographical sources may be available to meet the designers' requirements. However, otlier factors can have an influence on the choice of the material; for example, visual appearance, durability of the timber in relation to the environment in service and whether it can take the preservative treatment, facility for jointing and gluing and the ability to receive decoration. Additionally all these facets must be related to material cost. Standardised cross-section sizes are more economical to use because they can be bought froln stock and preference should be given to their specification. In certain circiimstances specification of species, grade and even the mill producing the timber may be necessary to achieve the particular properties required. An a~ialogyis the specification of a concrete requiring particular sands, aggregates and cement together with a closely controlled waterlcernent ratio to satisfy a particular end use.
Xecor~stitritcrl~t~oocl-Dcisccl p~oclricts The natural growth of wood causes a distinct inl~omogeneityof the material. Knots, pitch pockets and other growth characteristics influence the strength and hence cause a considerable variability within the members. By dividing large pieces of wood into smaller units ilnd then rejoining thern, the defects are distributed within the material and consequently the variability of the material properties decreases. The larger load-bearing capacity of glued laminated timber compared to sawn timber is not caused by a higher average capacity of glularn, but by the decreased variation in strength proper-ties and hence higher characteristic strengths. Generally, the strength variability of the wood-based materials rioted below decreases with increasing amount of processing:
Pi.on'llct -
-
-
-
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pole timber sawn timber glued laminated timber laminated veneer lumber plywood parallel strand lumber oriented str'and board particleboard fibreboard
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-
-
-
Coinponent pltrts logs planks planks veneers veneers veneer strips flakes chips fibres
Poles are the exception since they are hardly processed at all but nevertl~elessare particularly strong because the wood fibres are not cut leading to the fact that the continuous fibres guide the stresses smoothly around the knots.
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Properties of timber and wood-based materials Wood as a. natural material has vely different properties in ciif'ferent directions. Parallel to the grain, i.e. in die direction of the trunk of the tree, the strength of the material is particularly high, whereas perpendicular to the grain the strength properties are low. The tension strength of wood parallel to the grain is for example about 40 limes greater than the tension strength perpendicular to the grain. It is quite easy to split wood along the fibres using an axe, but it is mucll more difficult to cleave a piece of wood perpendicular to the grain. These large differences of strenglh and stiffness properties in different directions are overcome in most woodbaed panels. Since the wood fibres in Inany panel types have randoin orientations, the in-plane properties depend much less on the direction than in solid wood. Timber is a hygroscopic n~aterial,Consequently the moisture content depends on the surrounding climate and changes accordingly. If' timber dries below about 30% moisture content, it shrinks perpendicular to the grain whereas the shrinkage along the grain is sn~alIenough to be ignored. The sl~rinkagecan amount up to about 7% of h e cross-sectional dimensions. Therefoorc, timber sllould be installed at a ~noisturecontent close to the equilibriu~nmoisture content likely to be achieved in service. Hindered shrinkage defonnations in service can, for example in cont~ections,cause tension perpendicular to the grain and hence potential failure. Because of tile different shrinkage in radial and tangential directions, spIits can occur if large cross-section timber dries too fast. In general, spIits do nor reduce the strength of the timber members. They can be rainimised by kiln drying.
In timber frame construction drying shrinkage can affect other materials. Brickwork, for example, tends to expand after consrruction so interfaces between timber and masonry m ~ ~accommodate sr the differential movements. Similar effects can occur with plastic pipework installed in winter and expanding with the heating of the building. For similar reasons, the installation of lifts in multi-storey timber frarned buildings requires special consjdention. Another result of inoisture content changes is the c11a11ge in mechanical properties. Wit11 decreasing rnoisture content, the strength and ~nodulusof elasticity values increase. Timber under load shows an increase of deformation with time. In a constilnt cli~nnte,creep deformations only exceed the elastic deforlnations by about 50% in 20 years. If [he moisture contenr of the wood varies, however, the creep deformations may exceed severai l~undredpercent of the initial deforn~ations.Creep deformations are not only important because of possible excessive deformations but also because they can lead ro a reduction in load-carrying capacity due to creepbuckling effects. Apart from the rnoisture content, the duration of the load significantly influences the strength and defonnations of timber and timber structures. With increasing lond duration, the strength of timber decreases. The designer therefore has to assign each lond to a load duration class and subsequently rnodify the characteristic strength properties based on the duration of the co~~lbination of loads. The influence of load duration on the deformations is taken into account by an increase in creep deformations. The thermal properties of timber are good; tlle low thennal conductivity means that cold bridging is nor n problem to the building designer and Iow expansion across and along the grain wilh temperature change is n particularly beneficial attribute in fire conditions.
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STEP/EUROFORTECl.l an iniiiativc under \llc EU Cornetr Programme
A513
Fire doors made of wood are expected to be a barrier between a fire at close to 1000°C and an escape corridor that is at n temperature of 30°C. The general perception of timber in a fire is poor, it can be ignited and will sustain and spread fire due to the volatile gases it gives off when hot. However its combustion is a predictable process and the spread of flame can be minimised by treating or finishing the wood. In fire conditions the exposed timber surfaces of sections with dimensions exceeding about 50 rn~trwill char and deplete at a constant rate. Within the depleted section the strength and stiffness of the timber remain essentially unchanged and hence the strength of a timber member after a period of fire can be assessed from the residual cross-section. Consequently, large glulam cross-sections show an excellent behaviour in fire whereas smaller sections, for example, trussed rafter members, have to be protected. Because of the predictable behaviour of timber in fire, steelwork is sometimes protected by a layer of sacrificial timber. Steel fasteners in timber connections may also have to be protected to achieve an adequate fire resistance of the structure. Timber as a natural material is part of a natural growing-decaying cycle. Once trees are felled they are prone to biological decay but the onset of decay and the rate of decay can be controlled by the design and use of the wood. There are three approaches to this problem:
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design the construction and the details to eliminate the high moisture conditions likely to lead to decay and/or insect attack,
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select timbers that are naturally durable in the service environment or
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preservative-treat the timbers.
Examples of the good durability of timber can be seen in old buildings throughout Europe. However the changes in use of timber nowadays means that much greater care is necessaly in detailing the construction and in treating timber.
Design of timber structures In several respects, timber as a structural material is similar to steel. Both materials are available in similar shapes and even jointing of timber or steel members, respectively, is often comparable. On the other hand, there are marked differences between both materials leading to different design problems. Table 1 shows an overview of similarities and differences regarding steel and timber. Timber members are particularly capable of acting as tension, compression and bending ~nembers.If tension perpendicular to the graii~occurs, however, timber is prone to cleavage along the grain. Because o.f its high strength to weight ratio, it is widely used as a structural material for roofs and pedestrian or bicycle bridges. Compared to steel or concrete, the modulus of elasticity is low. This is often counteracted by choosing a stiff structural form, for example I-beams instead of rectangular cross-sections for bending members. Another example would be the use of folded plate and shell structures as roofs. Due to the ease of workability, timber members can be produced in many sizes and shapes. However, designing timber structures often requires more effort than designing comparable steel or concrete structures. This is caused by the orthotropic properties of timber and by the requirements of mechanical fasteners used to connect timber members. In the fabrication of trussed rafters using punched metal plate fasteners, the design process is automated using Computer Aided Design thus substantially reducing design costs and resulting in very competitive structures. STEPiEUROFORTECH - an initiative under tire EU Cornctt Prognrnmc
Steel
Timber
Similarilics hollow sections
poles
bars, angles
sawn timber
sheets
panels
welding
gluing
hol~ing
boiri~rg
Differences
isotropic
anisotropic
manufactured
grown, graded
uni fo1-111
varirtble, hetcrogerieous affected by moisture
affected by telnperature
Toblc 1
Sinliiari~ie~ and c l ~ ~ c ~ - ~bef~vee~z r ~ c e , ssteel orlcl lintbere as str.rtctrrra1 itloteriuls.
Because timber is a sympathetic, warin material it is not only used as a struclural material but also as internal finishing and is much appreciated by architects. The texture and appearance of timber makes it very suitable for use in visually exposed structures. Since timber and wood-based panels can be visually exposed it is possible lo make econon~icsavings by utilising the same timber for both structural and visual functions. The combination of steel and timber often produces light and competitive structures with timber as compression and steel as tension members. Because of the necessary cross-sections for timber co~llpressionmembers, buckling is often only a minor problem in design when compared with steel compression members. Alti~oughmost timber is found in buildings having a simple rectangular form used, for example, in floor joists, rafters and oll~erroof components or for walls in timber framed housing, large structures can be built econolnically in other forms such as domes and examples exist spanning over I00 metres. Timber may also be used coinpositely with concrete. For instances in bridges the concrete may provide a strong wearing surfwe and protecting the timber structure below. The timber then provides the tensile reinforcement and may act as a permanent formwork.
Concluding Summary Because timber is a natural material the essential properties vary considerably. In order to use timber efficiently as a reliable structural material, strength grading is necessary.
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It is a lightweight nlaterial with a high strength to weight ratio.
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The strength and stiffness properties of timber are highly dependant on the angle between Ioad and grain. Timber is strong and stiff parallel to the grain whereas it is prone lo cleavage along the grain if tension stresses perpendicular to the grain occur. It ltas a low shear strength and shear modulus.
STEPIEUROFORTECH - an initiative under the EU Comell Programme
A515
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Timber strength and stiffness properties change with changing moisture content. Especially creep deformations are increased by varying moisture content. Shrinkage and swelling have to be considered during the detailing of timber structures.
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AItllough timber is combustible and ignitable its performance in a fire can be calculated and it is very suitable for use in large sections without protection and in specialist situations e.g. fire doors.
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Timber acts well compositely with both steel and concrete.
STEP/EUROFORTECH- nn initiative under the EU Cotriett Progr~rnn~e
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Strength grading STEP I C C ~ L ~ SAG C P. Glos Ludwig-h4;1simiIi;1nsUt~ivcrsitBtMiincl~cn
Objective To develop an understanding of the imporiance of strength grading in the process of converting wood, a natul-a1 raw material, into timber. for structural use.
Prerequisite A4
Wood as a building material
Summary The lecture explains why siructurnI timber ]nust be strength graded, how the grading process affects tlie characteristic values for strength and stiffness and hence why strength grading is a prerequisite to making timber a reliable and cotnpetitive slructural material. Visual and machine strength grading are outlined and the European grading standards for visual and machine strength grading are explained.
Introduction Wood is a nat~lral product of trees which exhibits great variations in qualily according to species, genetics, growth and environmental co~~ditions. Wood properties valy not only from tree to tree but also within a tree, over the cross section and along the stern axis (see STEP lecture Ad). The process of converting roundwood into sawn timber interferes wit11 tile structure of the naturally grown wood. For exanlple wood fibres rnay be cut due to sloping grain and distortions around knots. This leads to considerably greater variations in the strength properties of sawn tiniber than in roundwood. In general, the smaller the cross-section, tile greater the variability. Thus, the strength properties of ungraded rirnber of any one species may vary to such a11 extent that the strongest piece is up to 10 times tile strength of the wealcest piece (see Figure I ).
Since the use of structural timber is based on its characteristic strength value, i.e. the lower 5-percentile of the population, the high strength of tlie majority of the pieces cannot be utilised unless the timber is graded. This shows that for economic S7'EP/EUROl;ORTECIi - an inilialive llndcr the EU Come11 Progr:tmmc
AG/1
reasons timber has to be divided into classes of different quality on a piece by piece basis. I-Iowever, strength can only be determined indirectly by parameters which can be determined visually or by other non-destructive methods. Since, there exists only a limited correlation between these parameters and the strength, the variability widiin these classes cannot be reduced as much as would be liked. The lower the predictive accuracy of the grading method, the greater the overlapping of clilsses will be, see Figure 2. This demonstrates the impact of the applied grading method on the economic use of timber.
Figtire 2
Sclre~rtcof rcrrsilc srrertgrll dis~ribittiortof strrtcttiml ritr~bernssigrled to tifree gracles a, b, c ctccor.diit~gm Dicbolcl atrd Clos (1994).
Moreover, it is a necessary prerequisite that timber is available in qualities and quantities that are desired by users and that it meets all user requirements, the most important being that timber qualifies as a reliable material with defined properties. Traditiondly, strength grading was done by visuafly assessing timber, taking into account strength reducing factors that could be actually seen, mainly h o t s and a~lriualring width. Up to the beginning 20th century visual strength grading was essentially based on tradition m d local experience. Detailed grading rules were introduced for the first time in 1923 in the USA and, fro111 the 1930s onwards, successively in various European countries. Due to the great variety in wood species, timber qualities and different building traditions, for example different crosssectional dimensions, it is hardly surprising that the grading rules developed over the last 50 years differ widely in the grading criteria as well as in the number of grades and grade limits. All these grading rules, however, have in common the general deficiency of visual grading methods: for practical reasons only visually recognizable characteristics can be taken into consideration and only simple combination rules are possible. Important strength determining cllaracteristics such as density cannot be assessed satisfactorily. The predictive accuracy of visual grading therefore has its limitations. Since the grading decision depends on the judgement of the grader it can never be totally objective. To improve the accuracy of strength grading with the aim of achieving a better utilization of the available timber quaiities machine grading processes were developed from the 1960s onwards in Australia, USA, UK and, later, in other countries.
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The increasing importance of' quality assurance and the rising demand for high quality timber have led to a growing interest in machine strcngch grading and iniiiated the development of new machines with greater predictive accuracy. In tin~bergrading a general distinction must be inade between the so called appearance grading and strength giading. In the former, wood is assessed according to its appearance, i.e. decorative criteria, which is important wherever timber is intended to remain visible. Appearance is the main consideration for non-structural timber, such as boards for cladding, but may also be important for structural timber where it is exposed in use. In strength grading, limber is mainly assessed according to criteria which are relevant to its strength and stiffness. Frorn this, it follo\vs that where stn~cturaltimber is exposed in use and the appearance is important, timber may have lo be graded for both strength and appearance. However, this lecture will deal oniy with the strength grading of sawn timber.
General requirements for strength grading Strength grading is intended to ensure that the properties of timber are satisfactory for use and in particular that the sirengtl~and stiffness properties are reliable. Therefore grdding rules have to define grade limits for characteristics which are sufficiently correlated to the strength and stiffness of timber. In traditional visuaI strength grading the most important strength determining factors are rate of growth, indicated by the annual ring width, and the strength reducing factors such as knots, slope of grain, fissures, reaction wood, fungal and insect damage and mecl~anical damage. In machine strength grading it is possible to determine other characteristics sucll as bending modulus of elasticity, which are better correlated with strength properties. In addition to grading rules for strength and stiffness, it is also necessary to define grade limits for geometric properties, for example wane and distortion such as bow, spring and twist which may also affect the structural use of wood. Since the wood moisture content influences distortion, fissures and wood dimensions, the grade limits have to be related to a reference moisture content, which is set at 20%. Moisttire content is also important in machine strength grading when moisture-dependent properties of tile timber are being measured. European grading rules require that a piece of timber be graded based on its most unfavournble cross-section. The grade will at least be on the safe side if the tirnber is cut into shorter Iengths later on. However, the grade may change if tile cross sectional dimensions are reduced after grading, for exa~nplcby re-sawing or planing. This reduction in size may affect the average density or the knot ratio of the piece. The grading rules should therefore state the amount of dimensional change that is permissible to avoid the need for re-grading. Graded tirnber should be marked. This rnariting shall as a minimum give the following information: grade, wood species or species combination, producer and the standard to which the timber is graded. The ininiinum requirements for visual grading standards have been laid down in EN 51 8 "Structural timber - Grading - Requirements for visual strength grading standards". Requiremenls for machine grading can be found in EN 519 "Stn~chiral timber - Grading - Requirements for machine strength graded timber and grading machines".
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Visual strength grading T1.1ereare currently many different visual strength grading ruIes for timber in use in Europe. They differ in the number of grades and grade Iimits and, also, in the way grading cllaracteristics are measured. In particular, there is a wide range of methods for determining knots. Knots in sawn timber vary greatly in shape. They vary with sawing patterns and tin~berdimensions and are diflicult to determine and classify. Strength is mainly reduced by grain deviations around knots rather than by the actual .knots. This is also evident from the Pact that, in general, failure starts from extreme fibre deviations in the vicinity of knots and not from the knots themselves. Wood structure may be even more affected when several knots are situated close together in a piece of timber. Thus knot ratio is usually calculated from the sutn of knots within a defined section along the lertgtll of a piece of timber rather than merely from the biggest knot. Edge knots and knots in tensile zones have a greater effect on strengtli than centre knots or knots in compression zones. Therefore, the position of knots within cross-sections of timber is often also taken into account in grading rules. Efforts to harmonize visual grading rules throughout Europe were not successful because no single set of grading rules would cover the different species, timber clirnensions and uses in an econorllically salisfactory manner. Therefore, EN 5 18 merely gives the minimum requirements for visual strength grading of both softwoods and hardwoods and permits the use of all national standards which li~lfilthese requirenienls. According to these limitations, the following characteristics have to be taken into account:
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li~nitatiorisfor strength reducing characteristics: knots, slope of grain, density or rate of growth, fissures
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linlitations for geometrical characteristics: wane, distortion (bow, spring, twist)
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limitations for biological characleristics: fiingal and insect damage
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other characteristics: reaction wood, ~nechanicaldamage.
In order to determine these cliaracteristics, all four faces of each piece of timber rnust be examined. Economic restraints, however, do not allow for a slow, deliberate examination. For example, in a sawtnill a piece of timber is graded in two to four seconds. This clearly shows that visilaI grading rules should be as sitnple as possible and under tliese conditions only a rough estimate can be made of these characteristics. Since the reliability of the grading process has to be guaranteed, the grader will tlteref'ore generally introduce a f~rrthersafety margin to the required grade timits, thus further reducing the efficiency of visual grading. In summary, the advantages and disadvantages of visual strength grading are as follows:
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it is simple, easily understood and does not require great technical slcill
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it does not require expensive equipment
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it is labour intensive and rather inefficient in that wood structure and density which influence strength (see Figure 3) are not sufficiently taken into con-
STEPIEUROFORTECI-1 - an ini[iative i~ndcrthc EU Comctt Progra~ntne
sideration.
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it laclcs ob~ectivitywhich rnakes it even more izrefficient
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it is an effective method, if correctly applied.
Figure 3
Effect of blof ratio A and ricnsity oti terrsile str-etrgtl~j;.,,of sr~~~ictrrml tintbar accolzlirrg to Glos (1963).
Machine strength grading The above disadvantages of visual strength grading can be overcome by machine strength grading. Most of the grading machines in use to-day are the so-called bending machines which determine average bending modulus of elasticity over short lengths (Fewell, 1982). Timber is fed continuously through the grading machine. The machine bends each piece as a plank (i,e. about the wealier axis) between two supports which are some 0-5 Lo 1,2 m apart and either measures the applied load required lo give a fixed deflection or measures the deflection under a particular load. From these values it calculates local modulus of elasticity taking into account rhe cross-sectional di~nensionsand natural bow of the piece of timber which is either measured or eliminated by deflecting the piece in both directions. Since ilte introduction of machine strength grading about 30 years ago research work has been conducted to furlher improve the grading process. Numerous investigations have dealt with the determination of modulus of elasticity by methods other than bending, such as vibration, inicrownves and ultnsound. The latter have the advantage of not mecltnnically stressing the timber and hence avoiding damage. Furthemlore, the maxirnum thickness of tilnber need not be limited to about SO mnt as in bending machines. Recent research has shown that predictive accuracy of machine grading can be further inlproved by tecl~nicalnlodifications of the machine and by a combination of severai grading parameters. For example, the cornbination of lnodulus of elasticity (E) and knots has a better correlation with strength than E by itself (Table 1). The incorporation of density into the grading process can also contribute to the grading results, as tiis can be used to produce grades with higher characterislic density and also to reject timber with significant portions of reaction wood. The presence of knots may be determined by optical scanning across the four surfaces or by radiation, while density may be determined by weighing or radiation (see Figure 4). STEP/EUROFORTECI-1 - an inilialive under the EU CornctL Programme
A615
Grading paratncter
Correlation with f;,
fro
f;..,,
Slope of grain
02
0,2
0,i
Density
0,s
0,s
0,G
Ring widtii
0,4
0,s
0,s
Knots + ring width
0,5
0,G
0,5
Knots
+ density
0,7 - 0,8
0,7
-
0.8
0,7 - 0.8
Modulus of clasticily E
0.7
- 0,8
0,7
-
0,8
0.7
- 0,8
+ density E + knots
0,7
- 0,8
0,7
-
0,8
0,7
-
E
Table /
> 0,8
> 0.8
0,8
> 0,s
Correlntiotr coefficierrts betwcetr possible gracfittg clrarnc~eristicsarrd srrcr~gtll properties accorrlirrg to Glos (1993). Species: Errropearr sprtlce.
In radiation, for example by tnicrowaves or gamma rays, part of the irradiation is being absorbed. The greater the Inass that is being irradiated, i.e. the higher the density, thickness and moisture content of the piece of timber, the higher the absorption will be. Knots can be determined by radiation since knot density, on the average, is 2,5 times higher than that of normal timber. In optical scanning the four timber surfaces are monitored by video cameras. Knots are detected via shades of grey and may be differentiated from other effects not related to strength such as dirt or stain by analysing the surrounding texture. Values for knot ratio may be determined via image analysis. NaturaIly, the higher efficiency of machine strength grading is more costly. The grading machines currently available vary greatly in performance and price. When comparing different machines or machine grading and visual grading the cost, efficiency and speed have to be taken into account.
Fignrc 4
Scilenre of a Eliropearr gracfirg ntaclrirre wit11 rrrrrltiple setrsing &vices for rtteaslrritrg defo1t11atioti(a), load (b), mdiafiott absorptiorr (c), b o ~ v(d), tfiicktress (e) nrtd rtroistlrre corrtetlt
m.
One important difference between visual and machine grading is that with visual grading, it is possible to check at any time the correctness of the grade assignment STEPlEUROFORTECH - an initiative under tile EU Comett Programme
even with timber which is in use. In contrast, in machine grading this check is not possible by visual measures. For this reason there has to be frequent and regular control of the reliability of machine grading. In various parts of the world two distinct control methods have been developed, the so called olrrpi~tconrr-ollerlsysrem and the ninct7irze c*oratr-olied s)rstenr. The output controlled system was developed in North America. Control is based on the frequent destructive strength testing of samples of the machine graded timber. This system is relatively costly but permits a modificatjon of machine settings in order to optimize yield. To be economical, this method requires great quantities of titnber of the same size and grade. These conditions rareIy exist in Europe, where a great variety of sizes, species and grades in smalier quantities are typical. For these conditions the machine controlled system was developed. With this system mills generally do not have to test the graded timber but rather rely on the strict assessment and control of the tnachines as well as on considerable research efforts in determining the machine settings which remain consrant for a11 machines of the same type.
EN 519 outlines the requirements for the machine strength grading operation and for grading machines. Both output controlIed systems and machine controlled systems are allowed. The acceptance of grading machines and machine settings requires a ~horoughexperimental and theoretical examination of the machine's principle of operation, performance and reliability, involving hundreds of strength tests to establish the effects of a11 variables that may affect the machine's performance, such as timber sizes, tolerances, surface finish, moisture content, tetnperature, throughpt~tspeed, timber orientation, etc. Independent test data must be provided to verify that tlie machine graded timber has characteristic strength and stiffness properties that meet tlie specifications of the grade.
Machine proof-grading In some countries, such as Australia, machine proof-gnding has been adopted instead of machine strength grading. In the former, a piece of timber is loaded on edge to a level corresponding to the design load of the desired grade liines a predetermined safety factor. If the titnber sustains this proof load without failure, excessive deformation or other signs of damage it will be allocated to the desired grade. Cornpared to rnachine strength grading this method is straightforward and, in particular, requires little a priori data about the timber source to be graded. However, it: per~nitsa yes/no decision only, i.e. the grading into one specific grade. It is also wasteful, as with low proof loads, timber is not efficiently being utilized whereas, with high proof loads, a certain percentage of the timber will be damaged and discarded. Therefore, proofgrading is not considered adequate for the European market.
Concluding summary Structural timber must be strength graded in order to ensure that its strength and stiffness properties are reliable and satisfactory for use.
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Strength grading can be based on a visual assessment of the tirnber (visual strength grading) or on the non-destructive measurement of one or more properties (machine strength grading).
STEPEUROFORTECH - an initiulivc under
lllc
EU Co~nctlProgrnnlme
A617
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Machine grading is Inore expensive but has greater predictive accuracy. I1 results in higher yields of higher grades and in the allocation of timber to higher strength classes.
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Current research shows that grading methods can be further improved. Strength grading must be developed further in order to ensure that timber remains an economic and coinpetitive structural material.
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Requirements for strength grading are set our in EN 518 (visual strength grading) and EN 5 19 (machine strength grading). Both standards leave room for future technical developments.
References Dicbold, R, and Glos, P. (1994). lrnprovcd tirnbcr trlilization through novel machine strcngth grading. flolz als Roh- und Wcrkstorf 52: 222. Fcwell, A.R. (1982). Macl~incstress grading of timber in the United Kingdom. Iiolz als Roh- urtd Wcrkstoff 40: 455-459. Glos, P. (1983). Technical and econon~icalpossibilities of titnber strcngth grading in small and incdium sized compsnics. In: SAH-l3ulletin 198311. Zurich: Schweitcriscl~cArbci~sgemeinsclaftfiur Holzforschung.
STEP/EUROFORTECH - an initiative undcr tllc EU Cornelt Programme
Solid timber - Strength classes STEP lcck~reA7 P. GIOS Ludt~tig-h~lusimili3nsUnivcrsitiit Miinchen
Objective To describe the system of strength classes standardised in EN 338 wIlic11 simplifies and improves both supply and use of stix~ct-uraltimber.
Prerequisite A 6 Strength grading
Summary The lecture describes the advantages of n strength class system which aims at reducing the number of species/grade/source choices in order to simplify timber specification for the designer of timber structures and reduce restrictions on the supplier of structural timber, for example, reduce his need to stock a large range of species. It describes the strength classes established in EN 338 "Structural timber Strength classes" and explains how gradelspecies combinations are assigned to these strength classes and how characterislic design values other than those included in EN 338 can be determined.
f ntroduction EC5 in common with the other Eurocodes provides no data on strengtll and stiffness properties for structural materials. It ~nerelystates he rules appropriate to the determination of these values to achieve compatibility with the safety format and the design rules of ECS. The following requirernenls apply for structural timber:
-
It shall be visuaIly or machine strength graded.
-
Visual grading shall be carried out according to standards which fulfil tlle tninirnum requiren~ents of EN 518 "Structural timber - Grading Reqt~ire~nents for visual strength grading standards".
-
Machine strength grading inust meet requirements given in EN 519 "Structural timber - Grading - Requirements for machine strength graded Lirnber and grading machines" (see STEP lecture AG).
-
Characteristic values for strength, stiffness and density shall be deter~nined according to EN 384 "Structural cirnber - Determination of characteristic values of mechanical properties and density".
Any timber, regardless of origin can therefore be used for timber structures designed according to EC5 rules provided it has been strength graded according to the rules of EN 5 I8 or EN 519, t l ~ echaracteristic values for strength, stiffness and density Raving been determined according to EN 384 and this has been certified in an "attestation of conformity". However, as yet, there are no directives as to tile procedure. In individual cases this procedure of assigning characteristic values to separate grades will always be possible. However, i t inay be impractical and confusing STEP/EUROFORTECtl - an illiriativc ~lnciertlic EU Comctt Progrnmlnc
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where marly timbers of different qualities, different sources and graded to different rules, are available. This is usually the case with structural timber. In a typical tirnber importing country such as the UK over 100 different species/ source/grade combinations are offered (Fewell, 1991). There will be a growing tendency towards a more varied timber supply in nil EU and EFTA countries due in particular to the fact that about half the sawn timber used in these countries is being imported. Furthermore it is to be expected that timber presently used in single grades onIy will be assigned to a larger number of grades due to growing market demands and the use of improved grading methods. Greater cornpetition in the supply of timber will reduce costs. However the increasing numbers of grades and characteristic values will cause confusion and limited specifications may lead to problems in supply. To avoid these problems it was decided to introduce a strength class system as a result of the success of similar systems in the UK and Australia.
A strength class system comprises a limited number of classes each with its own set of strengtl~properties, to which species/grade cornbinations of similar strength ate allocated. This makes the entire process of timber specification ~nuchrnore simple. In principle, a strength class sysrern rnay create econotnic losses for grades which have just failed to meet the specifications of one class and have to be allocated to the next lower one. This problem, however, only occurs in visual grading, whereas in machine grading, timber can be directly graded to a strength class by appropriate n~achinesetting. Economic losses for visual grades may be minimized by adjusting strength class boundaries to the characteristic values of the most econoinically important grades. The introduction of strength classes is advailtageous boll1 to the timber user and the timber supplier. The designer does not need to acquaint himself with a multitude of different grades and related characteristic vaIues, no matter in which European country his project will be built. instead, he can simply choose the strength class suitable for his project from a concise tabla, similar to those used for other structural materials. The litnber producer has the advantage that he can achieve higher prices for his timber since the better the grading process applied, the higher the strength classes to which his tiinber is allocated. Grading tnachines can be used to grade the tirnber directly into strength classes and also into classes which could not be achieved by visual grdding. The timber supplier has the advantage that he can select the most econornic source for a specific grade.
The EN 338 strength class system The strength class system established in EN 338 "Structural timber - Strength classes" is shown in Tables l and 2. It consists of 9 classes for coniferous species and poplar (Table 1) and G classes for deciduous species (Table 2). It ranges from the weakest grade of softwood, C14, to the highest grade of hardwood, D 70, currently used in Europe.
EN 338 gives characteristic strength and stiffness properties and density values for each strength class and provides rules for the allocation of timber, i.e. combinations of specieslsourcelstrength grade, to the classes.
STEP1EUROFORTECI-l - an initiative under the EU Comctt Programme
14
16
18
22
24
27
30
35
40
-6.e.a
8
10
11
13
14
16
18
21
24
f;.wl,e
0,3
0,3
0,3
0,3
0,4
0,4
0,4
0,4
0,4
f;:cu
16
17
18
20
21
22
23
25
26
f;;wr.~
4,3
4.6
4,B
5,l
5,3
5,G
5,7
6,O
6,3
L.L
1,7
1,8
2,O
2,4
2,5
2,s
3,O
3,4
3,s
f;lLk
in kN/tirnrZ
Table I
Strer~grhclasses am! clmmc(eri.rfic vulrtcs riccurdirrg to EN 338. Conifcrorcs species arid Poplar:
Table 2
Strr~igtltC~CISSL's and charuc~eri,sticvcibes nccorrli~igfo EN 335. Dccidiro~cs. .specie.s.
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The estilblishment of slrength classes and related strength and stiffness profiles is possible because, independently, nearly all softwoods and l~ardwoodscommercially available exbibit u similar relationsllip between strength und stiffness properties. Experimerital data sl~owsthat all important characteristic strength and stiffness properties can be calculated frotn either bending strength, modulus of elasticity (E) or density (see Figures I to 3). However, further research is required to establish tlie effect of timber quality on these relationsl~ipsand to decide whether accuracy could be ilnproved by modifying these relationships for different strength classes. Deciduous species have a different anatomical structure from coniferous species. They generally have higher densities but not correspondingly higher strength and stiffness properties. This is why EN 338 provides separate strength classes for coniferous and deciduous species. Poplar, increasingly used for structural purposes, sliows a density/strength relationship closer to that of coniferous species and was therefore assigned to coniferous strengtl~classes.
i r e 1
Relutio~ulripbett~~eetr terrsiorr, corrrpression arid sfiectr stretigth artil beiidirrg srrz'rrgth.
Fire 2
Relrrtiot~.shipbetn~eeacnrrrpre.vsion perllet~diciticirmid terrsinir pelpc,tidicrllnr strcrrgt/i NIICIderrsity.
S'I'EPEUROFORTECI-I
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i r e3
Relntiotrslrip Oettveerl lower 5 - p e r r o ~ t i l c ntodjcl~ts of elc~sticity parnliel, nrod1111csof ekasricir.y perpenrlicitlar- arid sl~ear/nod~(lusm ~ drnod~rl~rs of e/asficify pnrnlfe!.
Due to the relationships between strength, stiffness and density shown in Figures 1 to 3 a species/source/grade combination can be assigned to a specific strength class based on the characteristic values of bending strength, modul~isof elasticity and density. According to EN 338 a timber population can thus be assigned to a strength class provided
-
the timber has been visually or machine strength graded according to the specifications of EN 5 18 or EN 5 19.
-
the characteristic strength, stiffness and density values have been determined according to EN 384 "Determination of characteristic values of mechanical properties and density".
-
the characteristic values of bending strength, modulus of elasticity and density of the population are equal to or greater than rhe corresponding values of the related strength class.
-
The European Standard CENlTC 124.215 "Structural Limber Strength classes Assignment of visual grades and species" lisls visual strength grades and species of timber, and specifies the strength classes from EN 338 to which they are assigned. The grades and species included are those which have been used for a long time andfor for which satisfactory test data exist (see Table 3). Timber graded by machine to EN 519 may be graded directly into tile strength classes and marked accordingly and is therefore not referenced in this Standard.
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Strengtl~ Grading rule publishing Class country (Grading standard)
Gradc Species
C24
Austria
G.BH Spruce, Pine, Fir, Larch
CNE Europe
Francc (NFB 52001-4)
CF22
Whitewood, Douglas fir
France
Germany (DIN 4074-1)
SIO
Spruce, Pine, Fir, Larch
CNE Europe
Nordic Countries (INSTA 142)
T?,
Redwood, Whitewood
NNE Europe
The Netlterlands (NEN 5466)
B
Spruce
UK (BS 4978)
SS SS
Redwood, Whitewood Douglas fir, Larch, Hem-fir, S-P-F Southern pine Parana pine Pitch pine
ON OR^^ B 4100-2)
Commerciai name
SS SS SS USA -t Canada (NGRDL+NLGA)
Table 3
Source
J
+P
Scl
+ fir
NC Europe
CNE Europe USA -+ Canada USA Brazil Caribbean
Douglas fir, Larch, Hem-fir,USA + S-P-F Canada
S~reng~lr class C I?, cr.ssigtrment of visrtal grucles nttd s/~eciesnccordit~gto CEN/l'C 124.2 15. CNE Ei~rc~pe: Centrcil, Nor111 d Eastertr Eliropr NNE Elirwpe: Northe~-n& North eusrent Ertrupe NC Er~upe:Norti~euru ~ Cetztral d Eatr*opc.
For combinations of species and visual grades which meet the requirements of EN 518 but are not listed in this standard, the assignment to strengtli classes can be made according to EN 338 using characteristic values determined in accordance with EN 384.
Determination of characteristic values A characteristic strength value is defined in EC5 as a population lower 5-percentile value which rnust be evaluated experimentally. The results depend, inter alia, on the following (see also Figure 4):
-
The definition of the population including the difficulty encountered when linking one sub-population (the sample) to other sub-populations (the timber lilcely to be obtained from one source and used in one structure),
-
the sampling plan. Due to its limited size no sample represents its population exactly, and the smaller the sample, the less accurate the model,
-
the testing methods including systematic differences between different test standards,
-
the data analysis including the statistical lnodels used,
-
the adjustment to standard reference conditions, such as moisture content, inember size, rest configuration.
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Figure 4
Dete17llinatiorrof characteristic strcngfli ~~alries. Po;ct~riulirlfl~ietlcing factors.
EN 384 specifies the methods that must be used when determining characteristic values in order to ensure comparabiIity when assigning different combinations of grades and species to strength classes. Important points are:
-
The population shall be defined in terms of species, source and manufacturing process. The population definition shail also include the stress grade, except where the information on the total range of strength is required to determine relations between the mechanical properties used in deriving settings for grading machines.
-
San~plesshdl be selected from the population. Any known or suspected differences in the mechanical properties of the population distribution due to growth regions, sawmills, tree size, method of conversion etc. must be represented within the number of samples selected, by a similar proportion to their frequency in the reference population. This requirement sllall be the major influence in determining the number and size of samples.
-
-
Testing shall be carried out in accordance with EN 408 "Timber structures Structural timber and glued laminated timber - Determination of some physical and mechanical properties".
-
Sample lower 5-percentiles are determined for strength properties by ranking, and for density from a normal distribution.
-
Characteristic values are determined as the weighted means of the sample lower 5-percentiles for strength properties and density, and ns the weighted mean of the sample means for modulus of elasticity.
-
The characteristic strength values are adjusted for small andlor few samples and for extreme between-sample variability. Few samples and a small sample size are taken into account by a reduction factor ks (see Figure 5). To cover between-sample variability the characteristic value must not be greater than 1,2 times the lower 5-percentile value of the lowest sample (f,, I1,2 min f,,).
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liigltrr 5
-
T11e effects of tlie rt~lnrber.of sr~t~rples ( 1 . 3 ) ~ticlfile rirrmber of pieces in snlaiiest snn~ple(40. ..250) on tltc ,factor k,.
The reference conditions are as set our in EC5, for example 20C/65% r.h. for all properties, and 150 ttrtrt depthlwidth for bendingftension properties respectively.
Concluding summary
-
The European Con~monMarket will lead to a more varied timber supply in most EU and EFTA countries, with a correspondingly Larger number of grades and characteristic values. To keep the specification process of timber simpIe and to avoid confusion, n strength class system is being introduced, to which species/ grade combinations of sirnilar strength and stiffness nlay be allocated.
-
A strength class system has been established in EN 338. It consists of 9 classes for coniferous species and poplar and 6 classes for deciduous species. It provides characteristic strength and stiffness properties and density values for each strength class and gives rules for the allocation of timber to these classes.
-
Characteristic values of individual speciesfgrade cornbinations shall be determined according to specific rules, defined in EN 384. <
References Fewell, A.R.. Glas, P. (1988). T i ~ cdetermination of cltaracleristic slrength values lor stress grades of slruclural timber. Part I , In: Ptoc. of' the C[B WIS Meeting, Parksville, Canada, Paper 11-6-2. Fewcll, A.R. (1991). CEN Stnndard (or strength classes and the determination or characteristic values. In: Proc. of' the 1991 Int. Timber Eng. Conf., London, UK, 1.122-1.128.
Glued laminated timber Production and strength classes STEP lecture A S F. Coiling Deuiscl~eGescllschafi I'iir Holzfbrschung
Objectives To describe the production of glued laminated timber and to discuss its advantages in construction. To explain the strength determining factors and the background of tile European regulations.
Prerequisites A7 Solid timber - Strength classes A1 2 Adhesives
Summary The prodrlction of glued lalnjnated timber is described and the performance and minimum production requirements are discussed. The resulting advantages compared to solid timber are demonstrated. The factors influencing the strength and stiffness properties of glulam beanls and tl-re background to the regulations in CEN-standards are explained.
Typical Production Process The production process may vary slightly between different countries. A typical sequence of operations for the production of glued laminated timber (glulam) is shown in Figure 1 .
Prepat-atioi~of the planks (oreci A ) Planks with a maxirnurn thickness of approximately 50 mr11 and lengths ranging from about 1,5 to 5,O m are taken from an outdoor stockyard and kiln dried (1). One reason for this is that the adhesives used require the moisture content of the wood Lo be 15% maximu~n(see STEP lecture A12). After drying the planks are pre-planed (2) and strength graded (3). The vnoisture content is controlled, the ends of the planks are cut off in preparation for finger jointing (4) and the planks stock piled (5). STEP/EUROFORTECN - an initiative ~ ~ n dthc e r EU Cornell Progra~nnlc
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Firrger jointing (area B) The planks are joined lengthwise by Ineans of finger joints to produce a continuous lamination. A typical finger joint is shown in Figure 2 with the notation given in prEN 385 "Finger jointed structural timber".
Figlire 2
Finget joint (1 = firrgcr l o l g t l ~ p, = pitch, 6, = rip ividth, I, = rip go!)).
The joint profile is cut into the end-grain and the adhesive is applied (6). The planks are then pressed together for at least two seconds (7) such that the resulting friction between the fingers keeps the planks together during handling. The continuous section is then cut into laminations of the required lengths (8) and stored (9) for a minimum of eight hours to ensure the curing of the glue before the further handling of the laminations.
Gluir~g(area CJ The laminations are planed (10) to remove the remaining rough surface and the unevenness at the finger joints and the glue is applied (I 1) usually by running it beneath a glue curtain. For horizontal glulan~,the laminations are placed on edge one beside the other - giving the final cross-section lying on its side - and pressed together. The gluefine pressure generally is between 0,4 and 1,2 Nhlrtr?. Higher values are necessary for curved members or hardwood laminations. The jigs and pressing devices allow the production of straight (12.1) and curved (12.2) beams. The gluelines are kept under pressure in a controtled climate at a temperature of 20°Cand a relative humidity of 65% for at least six hours before the clamps are released and the beams are stacked (13) ready for finishing. Figure 3 shows the layout of a pitched cambered beam with the correspor~ding lamination lengths and its final form.
Finislzing {area D) Tfie beams are planed on their sides (14) in order to remove residual adhesive squeezed out of the joints and to ensure smooth surfaces. Finally the beams are finished (15). These operations include various treatments and preparation work which benefit from being carried out under controlied conditions (e.g. drilling of holes for connections, the application of coatings). Son~etimesthe glulam is wrapped to protect it against damage and dirt.
Preparatiort of the aclliesives (area E ) Unless resin and hardener are pumped directly from storage tanks and mixed automatically during application, a separate room for the preparation of the adhesives (mixing of resin and hardener) is required. There should also be suitable resin and hardener storage facilities and an area with access to adhesive cleaning equipment. STEP/EUROFORTECH - an inilialive under the. EU Comctt Programme
Performance and production requirements
11.1prEN 386 "Glued laminated timber - performance requirements and minimum production requireinenls" procedures are specified in order to obtain reliable and durable bonding, so that the glue lines in the laminated timber maintain their integrity throughout the intended life of the structure. The most important requirements are described below.
Cenet.nl Requii-ements prEN 386 specifies the fo'ollowing requirements for the components of glued laminated members:
-
The rittlbel- shall be strength graded (see STEP lecture AG) to conform requirements for visual with prEN 518 "Structural timber - grading strength grading standards" or prEN 519 "Strucmral timber grading requirements for machine strength graded timber and grading machines".
-
-
-
The odlzesives (see STEP lecture AI2) s11alI meet the requirements for adhesive type 1 or 11, as appropriate, listed in prEN 301 "Adhesives, phenolic and aminoplastic, for load-bearing timber structures: classification and performance requirements".
-
The characteristic bending strength of the end joints obtained from flatwise bending tests according to prEN 408 "Timber structures Solid timber and glued laminated timber - Determination of some physical and lnechanical properties for structural purposes" shall meet the following requirement:
-
fnt.j.k
'Z fmj.k.r
(I)
where Jl,,,.kr is a required characteristic bending strength. prEN 1194 "Timber stnictures - glued laminated timber - strength classes and determination of characteristic values" specifies STEPIEUROFORTECH - an initiative under thc EU Comctt Progm~nrnc
A813
where j;,,,,,is (he characteristic bending strength of a glulam beam with a given strength class (see Table 2). The factor 1,3 is valid for homogeneous, and the factor 1,4 for combined, glulam. -
The requirements for ghlc litfe iiftcgril)~are based on the resting of the glue line in a full cross-sectional specimen, cut from a manufactured member. Depending on the service class, delaminatiorl tests (according io prEN 391 "Glued laminated timber - delamination test of glue lines") or block shear tests (according to prEN 392 "Glued laminated timber - glue line shear test") must be performed.
Munrtfcrctrving reqriirentents Minimum require~nents for the production of glued Iaminated members for structural use are given in prEN 386, especially those concerning production conditioris (equipment, climate in production halls), the treatment, sizes and species of timber, the adhesives, and the manufactur.ing process itself (positioning of the laminations, tolerance limits, cramping). Examples of manufacturing requirements are the lengthways grooving of wide laminations to reduce cupping effects or the layout of wide cross-sections with layers consisting of two boards arranged parallet to each other.
Qtrality corztrol Quality control is of particular importance in glulain production due to the nature of its manufacture and end use. Since the quality of the glue lines cannot be appraised in the produced members, special attention lias to be give11 to quality control during production. Generally, quality controi consists of an internal part carried out by the producer and an external part by an independent third party. Quality control includes daily bending tests of finger joints and either delamination tests or block shear tests to check glue line integrity. Furthennore, records have to be kept giving the details of every production run including the date and the number of members produced, their species, timber quality, dimensions, moisture content of the timber, time for start of adhesive application, lime for s h r t and end of the cramping process, cramping pressure, type of resin and hardener, amount of adhesive per m h n d calibration of the moisture meter as well as the temperature and relative humidity of the different production halls. Quality coi~trolalso relates to the training of the personnel and the strength grading of the timber.
Large finger joints If large finger joints are used to join entire glulam members (as, for example, in the case of frames), special performance and minimurn production requirements have to be fulfilled. These requirements are given in prEN 387 "Glued laminated timber - Production requirements for large finger joints. Performance requirements and minimum production requirements". Tl-rere may be additional nationaI requirements.
Advantages of glued laminated timber in use Glued laminated timber is an highly engineered building material, extending in many cases the traditional use of timber. The main reason for this is that the production process with integral quality control as described above, provides a number of advantages compared with solid timber. The most important are described below. STEPIEUROFORTECH -
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Beall? sizes Due to the production of continuous laminations, unlimited beam sections and lengths are theoretically possible. Giula~nbeams with depths of 2,O m or lengths of 30 to 40 lrt are not exceptional. Limitations however, are imposed by the open time of the glue, the sizes of planing machines and production halls or for architectural reasons. During the transportation of glularn beains if the dimensions exceed IG t i ? in length, 2,5 111 in widti1 or 3,5 rti in height, supplementary actions such as the application of blinker-signal equipment, police escorts or exceptional permissions ]nay be necessary. Also the routes have to be cl~eckedcarefully in order to avoid sharp bends and low bridges.
Beall? shapes The possibility of curving the single Laminations before gluing allows the production of exciting beam shapes (see also STEP lecture B8). This also ailows beams to be precambered to accoinmodate dead load deflection. The production of curved beams requires the adaption of jigs and pressing devices for every new beam geometry; thus the production time is higher in comparison with straight beams. The resulting cost difference depends on the number of similar members and is often negligible. Tapered ~nemberscan be produced by simply varying the length of single laminations or by sawing two tapered members from a straight element.
Higher stretlgth and srrfl7ess Because of the production process, knots are spread more evenly within the volume of the beam leading to a more homogerreous material. The influence of single potential failure areas due to lcnots is reduced, resulting in a lower variability and, in lower quality timber, a higher mean strengtll. A more detailed description of strength influencing factors is given below.
Cor~rbiitedg1111a172 The use of iaminations makes it possible to match the lamination quality to tile level of stress. In the case of a bending member for instance, Iaminations of a higher strength class are positioned in the outer highly stressed regions, whereas in the inner zones laminations of a lower quality mily be used. This aIlows a inore economical use of the available wood material.
Dry tr~oocl The planks are Iciln dried to a rnoislure content of about 12% since the equilibrium moisture content of wood used indoors amounts to 9 to 12% approximately and hence the danger of damage caused by deformations (such as distortion) occurring during the drying process in the consmction is almost excluded.
Di~~ze~rsionnl accur-acSy The drying of the laminations and the production process aIso allow the production of glulaln beams with accurate dimensions. Since small tolerances are inlportant for the use, and combination, of prefabricated members of different materials, the dimensional accuracy can detennine the use of glufam even if sawn timber would have been sufficient in terms of strength and stiffness. With regard to the increased use of CAD and computer controlled finishing machines, dimensional accuracy is getting more important, If glularn is used in outer walls, wind tightness can be achieved more easily than if using sawn timber with moisture contents above the equilibrium moisture content,
-
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Strength determining factors Glulam is mainly used for bending members. Therefore the main emphasis in this section is put on the factors influencing the bending strength of glued lamiriated timber. Other strength properties are discussed in the next section. Systematic studies (CoHing, 1990a; Colling, 1990b) show that the strength of glulam beams is determined by the strength of the timber and the strength of the finger joints. A lamination consisting of planks connected with finger joints behaves to a certain extent like a series system. Depending on the strength ratio of the timber and the finger joints, respectively, failure will be initiated by either the failure of the timber or of the finger joint. To increase the strength of glulam beams, a balanced strength increase of both planks atld finger joints is necessary. The studies lead to the following conclusions:
-
n more rigorous visual strength grading procedure is not likely significantly to increase the strength of glued laminated timber. Stricter visual strength grading decreases knot sizes and consequently leads to an increase of plank strength without affecting finger joint strength.
-
Machine strength grading based on wood density andfor rnodulus of elasticity contributes to a strength increase of both planlcs ~ r l dfinger joints resulting in increased glulanl strength values.
-
Production related parameters such as sharpness of cutting tools, pressure applied or climate in the production hdls afso influence finger joint strength. Quality control of finger joints to produce reliable strength values is, therefore, essential.
Background to the regulations in CEN
prEN 1194 "Timber structures - Glued laminated timber - Strength cIasses and determination of characteristic values" (September 1993) provides equations for the calculation of the mechanical properties of glued Iatninated timber depending on lamination properties. The equations given in this version of prEN I194 are shown in Table 1 for some of the more important properties. equation according to prEN 1 194
Property Bending strength Tension strength pami/cl to graiir pcrpendiciilar ro gruin Compression strength par~illefto grnirl Density
Table I
(N/rrrrri2) (N/rtlmz)
.f,tL,..~
=
12 4- f;o,,,il
f;,utrc.r
=
9 + 0575 f,,,,.,,~
f,.vc~.~.k
=
7
l5 A.!XI,I,~
(N/~II~I?) f;.~.g.il
(kg/?n3)
Pk.a
= =
(195 - 0,01fr.o,~.r)fc.arr 0*95P,.alarn
Sor~iet~lecllatiicalproperties of glired [aminatrd tirt~ber'.
The equations are valid for homogeneous cross-sections. For combined glulam the equations apply to the properties of the individual parts of the cross-section. As EC5 takes into account the decrease in strength of a material with increasing dimensions (see STEP lecture B1) the equations of Table 1 are related to members having a depth or width of 600 r?lrrt for bending and tension paralieI to grain, and to a reference volume of 0,01 n13 for tension perpendicular to grain.
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The bending strength of glulaln beans is related to the tensile strength of the laminations by an empirical relationship, which is based on tests and analytical investigations. For standard lamination qualities this relationship indicates that the characteristic glulan~ bending strength is 40 to 90% higher than the characteristic tensile strength of the laminations. This may be explained by several effects (Colling and Falk, 1993). The most important are:
-
a difference exists in the tension performance of single laminations as measured by standard test methods and their actual performance in a glulam beam. The test method in prEN 408 for determining the tensile strength provides no lateral restraint to the tension member. Contrary to the situation in a glulam member, off-centre defects such as edge knots consequently induce bending stresses thus reducing the tensile capacity.
-
In glulam beams defects like lcnots are reinforced by adjacent laminations. The reinforcement provides alternative stress paths around the defect.
Also in the case of rcrrrsion and co~?~pl-essio~t parallel lo grain, the characteristic strength values of glulam beams are higher than those of the individual laminations. This may again be explained by load sharing effects as described above. The characteristic tensile strength has been assumed to amount to 75% of the characteristic bending strength. For compression see also STEP lecture B6. In the case of curved and cambered beams, radial stresses occur (see STEP lecture B8). Due to smaller cracks in glula~nbeams, the characteristic tetzsile strcrtgth perpenrlicl~lcrr to the grain is higher than for the laminations acting perperzrliclrfrr to the grain where the alone. The same applies to cor~~prcssiort cllaracteristic values for glulam are higher due to the smaller variation in density compared with the single laminations.
The gluing of an increasing number of laminations leads to a more homogeneous material with low variation of rlerzsity. Therefore, the characteristic density of glued laminated timber is close to the mean value of the density of the single laminations.
Strength classes In prEN 1194 (September 1993) five strength classes for glularn are defined (see Table 2). Tl~elamination qualities needed Lo comply with the required properties may be determined on the basis of the above mentioned equations (see Table 1). GL 20
GL 24
GL 28
GL 32
GL 36
20
24
28
32
36
( N h t ~ t ? ~ ~ ) 10 000 E ~ , ~ , ~ . , (N/JTIITI') 8 000
1 1 000
12 000 9 600
13 500 10 800
14 500 I I GOO
Strengt1.r cfass
XU.~,~
Table 2
(N/NtnrZ)
8 800
Stretlgth c1a.sse.sfor gliicd lnrtli~~~ted tirlzl~er.
STEPlEUROFORTECH - an inilialive under rhc EU Cornell Programme
For homogeneous glulain the design calculations may be carried out by the rnethods described in EC5. In the case of combined glulam, however, the stress analysis may to be carried out using the transformed section method and strength checks shalf be made at a11 relevant points of the cross-section. This means that the different lamination qualities (characteristic strength and stiffness values) have to be taken into account.
The design of composite cross-sections therefore requires additional calculations. Table 3 shows the layup of timbers in accordance with prEN 338 "Structural timber - Strength classes" for homogeneous and combined glulam for the standard gluiam classes. For those beams the design calculations may be carried out as for tzornogeneous cross-sections. If other beam lay-ups are used, they rnust be checked to show that Lhe behaviour of the colnposite beams is at least equivalent to an l~oniogeneousbeam wit11 a target strength class based on Table 2. In the case of shear stresses and stresses perpendicular to the grain - which are normally critical in the core of the beam the applied stress should be checked against the strength of the inner lamination material. Strength class
CL 20
Homageneous glulam combined glulam
'
'
crll icrtnrincrtioas C IS outer. la~tiirmiiat~sC
22 itrrrer ictr~tir~a~iorrs C 16
GL 24
GL 28
GL 32
CL 36
C 22
C 27
C 35
C 40
C 24 C 18
C 30
C 35 C 27
C 40 C 35
C 22
The rctjuirc~nentsfor thc outer laminations apply to the extreme 116 of tllc dcpth on both sides
Table 3
E.t.att~plesc$
heat^^ lay-rcps.
Concluding summary -
Glued laminated timber is a highly engineered building material, providing many advantages over solid timber.
-
Special attention must be given to the strength grading of the laminations, the quality of finger joints, glue line integrity and quality control.
-
Machine strength grading based on wood density and modulus of elasticity is the key to high strength glulam.
References (I990a).TragAhigkcit von Bicgctdgem nus Brettscliiclitholz in Abhiingigkcil von clcn festigkcitsrelcvanten EinfluBgroBen. Dissertation, Universitfit Karlsnlhc, Germany.
Coiling, F.
Colling, F. (1990b). Bcnding strength of glulam l~cams- n statistical modcl. Ln: Proc, of the 1UFRO S5.02 Mccting, St. fohn, Conada. Colling, F, rind Falk. R. (1993). An investigation of laminating cfrects in glucd laminated timber. In: Proc, of' the CIB-W 18 Meeting, Athens, USA.
STEPIEUROFORTECM -
:in
initiativo under t t ~ cEU Conlctt Programme
Laminated veneer lumber and other structural sections STEP lecture A9 A. ~nntn-Maunus Tcci~nicafRcsenrch Ccntrc of Finlilnd (VTT)
Objectives To introduce new high strength wood-based materials not lnentioned in EC5, to describe their use and how they can be designed by following tlte EC5 principles.
Prerequisite A4
Wood as a building material
Summary The leclure begins with a brief description of the fabrication technoiogy of the reconstituted wood ~naterials.IL presents tlie material properties for one type of laminated veneer lutnber including characteristic values as given by the rnanufacturer and accepted for European use. Examples are given of itow the material is used today in load carrying structures. The advantage of using reconstituted wood products is that larger dimensions are available and higher cl~aracteristicstrength values can be achieved than the strength of the raw material used. The dimensions of these products which are, after fabrication, quite dry are more accurate and moisture related distortion of the shape (twisting, warping) is not a problem.
Introduction The strength of timber is determilled more by the weakest cross-sections having defects than by the clear straight grain wood itself, which normally has two Lo four times higher strength than commercial sawn timber. Large defects can be avoided when logs are first cut into thin sections and then glued to a reconstituted product. Especially the tensile strength is increased. Because the co~npressionstrength depends strongly on lnoisture content, the bending failure in service class 2 may take place also on the compression side. Glued laminated timber has a higher strength than its raw material. Still more benefit of the redistribution of large defects into several stnall ones is obtained in tlie fabrication of plywood, in which logs are peeled to veneers with thicknesses of 1 to 5 nlm. PIywood veneers are glued usually in right angles to each other. Laminated velleer lumber (LVL) is a product close to plywood, except that (most) veneers are panllel and larger dimensions are available. The idea of LVL came from the 19GOs and the production has expanded in the 1980s. Today, LVL is produced comn~ercially in the USA by seven companies, in Finland, Japan, Australia and New Zealand. The biggest LVL producer in the US markets LVL under the trade mark Micro=Lam LVL. In Finland the product is called Kei-toLVL. The 1993 production of LVL in 440000 11t3 in America, 51000 m%n Europe and 40000 !n3 in other parts of the world and sliowed a rising trend. Parallel strand lumber (Parallam) is a bcarn-like product made of long wood strands, which was developed in Canada in the 1970's and 1980's. It is now fabricated also in the USA. Anotlier new American structural wood product is Intrailam, which is rnade from large parallel cliips. STEPIEUROFORECI-I - an inilialive under the EU Cornet! Programme
A91 1
Fabrication LVL is mantlfacLured in America from Southern Yellow Pine (Micr.o=Lam) and in Europe From Norway spruce (Kerto). Logs are debarked and heated in hot water for 24 hours. They are rotary peeled into veneers which are clipped into sheets about 2 N I wide. The veneers, having a typical thickness of 3 to 4 nlnr, are graded accordirlg to the density. After drying, pllenol formaldehyde adhesive is applied to veneers which are then laid with the grain running parallel Lo form a continuous rnat of' the desired thickness. Veneers are scarf-jointed except the tniddie veneers which are butt-jointed. These joints are staggered vertically in order to lninimise the effect of joint on the strength of LVL. The ~nsttis hot pressed at a temperature of about 150 "C. After hot pressing, each finished sheet of LVL is cross-cut and rip-sawn to desired dirne~lsions.Lengths exceeding 20 /rz can be pr.oduced. During fabrication the q~~ality control includes regular testing of' the quality of the glue bond and the bending streng~h. ICerZo-LVL is produced as a s~nndardproduct when all veneers are parallel (Kerto-
S) and also as Kerto-Q in which about every fifth veneer is in the perpendicular direction. Standard di~nensionsof cross-section are given in Table 1.
Figttre I
LVL is proditced ns a corlti?tl~o~ls potrel with r~et~clidthqf 1800 rrur[.
STEPIEUROFORTECI-I - an initirrtivc under ttlc EU Cornetc Programrnc
Widths
in
Thicknesses in ~nrn
ltrtlr
27
200 260 300 360
X
33
39
45
51
63
75'
X
X
X
X
X
X
x
x x
x
x
x
x
x x
x x
x
x x
x x
400 450 SO0
x
x
x x
X
X
x x
GOO
900
' ICerto-S only Tahle 1
sf an do^-d rlin~crlsior~s of KCJTO-LVL.Tlrickrie.s.~e.sof Micro=Lnnz LVL cor71pr?'sssfi.0111 19 to 89 n~rn.
Parallarn is made from Douglas fir and Southen1 yellow pine. As in the manufacture of LVL, Jogs are peeled into veneers. The sheets of veneer are then clipped into strands up to 2400 wulr, in length and 2-3 nun in thickness. Tile adhesive is applied to the oriented strands which are fed into a rotary belt press and cured under pressure by microwave heating. The process is motiitored by programmable logic controllers. Parallam emerges f r o ~ nthe process as a continuous billet that can be factory-cut and trjmined to standard sizes up to 20 171 in length. Maximum depth of beam is 480 rltriy and width 285 11im.Square cross-sections up to 180 x 1 SO 11zit1 are co~nmonlyproduced for columns. Intrallam is made froin large chips up to 300 111min length and 30 mm in width. After drying, a polyurethane adhesive is applied and the chips are organised to a direction parallel lo tile panel length. Tile fabricated product is a large panel (2,44 x l0,6 nt), whicll is cut to llte required dimensions.
Examples of use LVL is being used as beams. plates, ~ne~nbers of tlusses and shells. This is done in new buildings as well as in renovation for bealms, joists, truss chords, vehicle decking, concrete formwork, scaffold planking and prefabricated housing. The largest structure made of LVL in Europe is Oulu-don~ewith a diameter of 115 117 (Figure 2). In dome structures, high strength to weiglit ratio, straiglttness and sn~all Fabrication tolerances are important features. The uses of Intrallall~are similar to those of LVL. Parallam is used for beams, headers and columns. In tesidential building construclion in America it is often used in beams when a material wit11 higher slrengtl~is needed. It is suitable also for hall structures and the appearance of material is considered warm and suitable for interior architecture. Both LVL and Parallam are competing with steel in large span structures. The advantages of the wood-based alternatives are good architectural appearance, longer resistance in case of fire and the easy tecl~niquesfor fastening of the secondary structure. Bean and post structures can be built in LVL and in Parallam. An example of a three-storey scl~oolbuilding is illustrated in Figures 3 and 4. A specific feature of this building is that it is built in an area where seismic loads are effective. LVL panels with screwed joints have been used in shear wall stl-uctures in order to STEPfEUROI=ORTECI-1- :In iniiiati\ic unclcr tlic EU Comctl Programme
A913
achieve the racking strength and energy dissi~~alion needed. Wood-based panels connected by rnecharlicaf fasteners to wood frame for111 a structure with high resisiance to eatthqtrakes. Iiigh shear strengll.1 can be achieved by cross-veneered panels.
Fig1tr.c 3
AIBsmdt Centr.e,for Teclrnolagy attd Ec+unott~ics, Get-tiraay: tllr'ee storey LVL-
frame.
STEP/EUROFORTECt~l- an initiotivc under the EU Comcli Programme
-
i r e4
All~stndt Cer1tr.e for Tcclrrrology arirf Ecotmriric.~,GL'I.IIUIIIS: ~(rr~l~(/il(tkc~ rcsistnrlr slrenr 11ja1lsrtlucle oj'C I - O . Y . Y - I ~ L LVL ' ~ Ipatrels. ~L'~C~/
Material properties Durability of LVL, Parallam and 11~tmll;imis companble to nilt~iraltimber. Thcsc products can be impregnated in order to ilnprove durability in moist co~lditions. Also ihe charring rate in fire is close to glued isminoted timber. For LVL uscd as panel, the values for plywood call be used. The moisture content after fabrication is about 10% arid in scrvicc normally 2% less than the moisture content of solid wood. Moisture expansion coefliciellts o l LVL as change of dimension (%) per one per cent change of moisture content iWC given i n Table 2.
Direction
Kerto-S
Kerto-Q
Length Width Thickness
0,OI 0.32
0,O 1 0,03 0.24
0,24
Characteristic values are given in Table 3 for Kerto-S-LVL based on information supplied by the tnanufacturer. These vali~eshave bee11 accepted for use in Sweden. A colnpilation of the ~.esearchresults made in different countries with Kerto-LVL is tnade by Koponen and Kanerva ( 1 992). EC5: Part 1-1: 3.1.7 E C ~ Part : 1-1: 4.1 ECS: Prjrt 1-1: 3.3.2(4)
The lnodification factors for service ctass and load duration k,,,,, and deforrnation factors k,,,? given in EC5 for plywood are aIso valid for LVL and Parallarn. The factor I,, used in glulam design is riot necessaly for LVL because of the smaller statistical variation in strength. Quality control tests of Kerlo-LVL show thc coefficient of variation for bending strength to be less than 10%. Thus a depth factor with an exponent of 0,07would be appropr.iale based on Weibull's theory. However, by using the same partial safety coefficient as for other wood materials,
y,,, = 1,3, extra safety is already included and further reduction is not necessary. Strength and stiffness properties in Nht1~1~ Bending edgewise Bending flirtwise
.LA
51 48
Tension parallel to the grain Tension perpendicular to the grain Compression parallel to the grain Compression perpendicular the grain - parallel to the glue line - perpendicular to the glue line
.6,,1.i
42
f,,~.,
0,6
X:JB.~
42
.[!:J,I.~
9 6
Shear edgewise Shear flatwise Rolling shear 5 % ~nodulus01' elasticity 5 % shear n~odulus
Mean modulus of elasticity Mean shear niodulus
.4,,a,c6rt, 14000 G,r.,t,,,,~
960
Characteristic Density
P1:
500
Average density
P,,,,,,,,
520
Density in kg/ii$
Design of members and joints The design of structiires made of LVL and Parallam follow the general rules of EC5. Bending strength of LVL and Parallam is about the same. In compression and shear Parallarn is stronger. The bending strength of Intrallarn is cotnparable wit11 glulam. Cornparison of strength and stiffness of sawn timber (C24), glula~n(GL32)
-
STEPIEUROFORTECI-I an iniliativc under thc EU Conictt Programme
-
-
and LVL is illustrated in Figure 6. The Figure shows that the stiffness of LVL is somewhat higher but the strength is about twice the strength of average strength graded sawn limber. The bending capacity of the same materials is illustrated in Figure 7 where cross-sections with equivalent bending capacity are shown. Dowel-type fasteners are used with LVL, and the EC5 design equations are as good for LVL as for sawn timber with tile same density. Dowel joints are used also in frame structure with rigid joints as illustrated in Figure 5. Punched metal plate fastener joints are also used and the design principles are the same as for solid wood. Special types of punched ~netalplates have been developed for LVL (see also STEP lecture E6).
Pigrtrz. 7
TItree cr-o,r,c.-,sectiorrs)vidr si17rilnr berldi~rgcapacity: glrtla~~l (GL32)U I I CLVL. ~
snrtltl
tirrzber (C24f,
Summary Engineered wood products LVL and Parallam have higher strength and stiffness than traditional wooden products. They ilre also thoroughly tested because they have entered the market during modern legislation. "Fl~eseindustrial products are well suited for use where high strength and diniensional stability is needed.
Reference Koponcn, S., Kanerva, P.(1992). Summary of European ICcrtn-LVL tests with rnccl~anicalfasteners. Report 29. Helsinki University of Technology. Laboratory or S~rucluralEngineering and building Physics. Espoo, Finland.
STEP/EUROFORTECI-l - an initiative under thc EU Cornett Pragriimmc
A917
Wood-based panels - Plywood STEP lccturc A I0 C. Sicck Fachhnchschule Miincllcn
Objective To explain the critical properties, particularly the st~ucturalbeliaviour, of plywood as an exanlple of layered boards.
Prerequisites A4 Wood as a building ~nalerial A 12 Adhesives
Summary The production of plywood is described and the technical terminology is explained. The essential physical properties of plywood are suminarised. In Inore detail the structural properties and their dependencies on the lay-up are shown. Some exainples of characteristic values of mechanical properties for established products are given.
Introduction Wood in thin layers, known as plies or veneers, has been used since ancient times for example by the Egyptians and Rolnans to fillish wooden surfaces. Since the beginning of the 20th centuty, plywood has been industrially produced. Plywood as a building material consists of an odd number of layers (at least three) which we bonded using various types of adhesives (STEP lecture A12). The suitability of plywood for the aircraft industry initiated intensive research into veneer bonding and the s11-ucluraIproperties of plywood. Initially only natural adhesives were available but today plywood as a constructional material is produced using synthetic adhesives. Plies can be inanuiactured by rotary peeling, slicing or sawing. Plies for the structural plywoods used in building components are produced by the rotary peeling of steamed logs (see Figure 1). This procedure resembles the unwinding of the log to obtain a wooden ribbon of about 2 111111to 4 1rl111 thickness. Tile next step ~ I-ibbon inlo sheets. After kiln drying and gluing, the veneers are laid is to C L I the up with an angle of 90" between the grain direction of adjacent layers and bonded under pressure. Figure 2 sliows the layered con~positionof a plywood cross section. Adjacent veneers provide stability in the panel by reducing the possibility of perpendicular to the grain movements due to swelling and shrinkage. The edge of the panel is protected in all directions since at least one veneer will have the grain rilnning parallef to the panel edge. Plywood is structurally suited for use as a panel material in various components, for example as [he web or flange of beams, in diaphmgtns, as wall panels or as gussets in spaced columns and trusses. STEP/EUROFORTECI.i - an inilintivc undcr the EU Comett Progrnmmc
AIO/I
Figurr 2
Cortlpo.si~iutrof balurlctld 5 layers plylllood cross section, 4 = cj2; cis = dl. --, :grai!~clirection offace veneer'
Physical properties
Deruiv One of the most important physical properties of wood based materials is the density. Depending on the percentage of adhesive and the compression of the bonding, the density of plywood is generally higher than the density of the wood from which it was made. As with solid timber, the elastic properties and strength of plywood are correlated with density. Density values are given in Table 2.
Muisttrre content Like solid wood, the veneers are hygroscopic, and therefore the moistirre content of plywood depends on the climatic condilions of the surrounding air (see Table 1). The moisture content of plywood is less than of solid timber due to the glue lines. Sur.~.oundingair with temperature of 20°C and relative t~umidityof
30%
65%
85%
Equilibrium nloisture content of ply\vood
-5%
-10%
-15%
Equilibrium moisture content of softwood
-G%
- 12%
-17%
Table 1
Eqrtilibrirlnr nloi.vfrtra cot~ferif.
Swelli~lgA~~~ri,lkage Changes in plywood moisture content below fibre saturation point cause changes in the geometrical properties of plywood panels. Because of the grain directions of adjacent layers, the deformations in the plane of the panel are small (about 0,02% per 1% change in moisture content). Perpendicular to the panel plane, in the case of rotary peeled veneers, a radial swelIing/shrinlcage similar to that of the solid wood species call be expected.
EC5: Part 1-1: Table 4.1
CIBep The increase in deformation of plywood with time, due to rlle combined effect of creep and moisture, is talcen into account by the factor k,,,/.Plywood panels are slightly more prone to creep than solid timber due to the glue lines.
Durability The natural durability of wood based panels depends less on the species of wood than solid timber. Additional factors which may affect the durability of plywood are
-
-
thickness of veneers composition (use of different materials within the board) properties and quantity of adhesives.
Ilnproved durability can be obtained by using selected wood species for the veneers, special lay-ups or by chemical protection. For the choice of specific wood species of suitable durability see EN 350-2 "Durability of wood and wood products. Natural durability of wood - Part 2: Guide to the natural durability and treatability of selected wood species of irnpofiance in Europe". The application of hazard classes of biological attack to wood based panels is given in EN 335-3 "Durability of wood and wood-based products. Definition of hazard classes of biological attack - Part 3: Application to wood-based panels".
Structural properties The structural properties of plywood are affected by the folIowing parameters
-
geometrical factors (number and thickness of veneers; composition) material factors (wood species; moisture content) load factors (type of stresses; direction of stress related to grain direction of face veneer; duration of load). JI
In the case of bending, it is important to differentiate between
-
-
1
bending perpendicular to the plane of the panel (see Figure 3) in-plane bending (see Figure 3).
It is also intportant to note the difference in properties related to the orientation of the board. The stress distribution in all cases is based on a linear stress-strain reIation for the lay ups of the veneers and will be explained using an example for a 5-layered plywood panel.
Betldirzg perpendicular to the picrite Bending perpendicular to the plane causes deflection of the panel perpendicular to the plane. The theoretical bending stiffness of a plywood panel with five veneers of thickness d is given by
El = C $ I,
Figrrre 3
(1)
Retrdit~gperpetiriicrclar to the plane. (n) pnrullel to the grab1 yf fnce rrer~ecr, (6) pcrpettrlictclnr to the grairl of fme Ijeneer.
STEPfEUROFORTECH - iln initinlive under the EU Comclt Programme
A 1013
In an approximate calculation for the bending stiffness El may be assumed as E90,,l,n,,, = 0 for the layers, i. e. ignoring the contribution of veneers stressed perpendicular to their grain.
-
With E(,,,,,,,, = E,, and b = 1 gives for (Figure 3a)
-
and for cr,
o,, parallel to grain of face veneer
-
perpendicular to grain of face veneer (Figure 3b)
The resuiting equations for the moduli of elasticity of the panel are as follows:
If, however Eq(,,,,,,,,, is taker1 as 1 /30 E,,,,,,, , as wou Id be typical for softwood veneers, the i~nprovemenisin ~nocluliare: EfI = 0,80 E,, EL = 0,24 E,,
for o;,, 11 grain of face veneer for ci,,, I grain of face veneer.
For calculation of deflections the bending stiffness El of plywood panels is needed where E means the inodulus of elasticity, defined as above and I tlie second tnolnent of total cross section. The weighting for different stiffness of the veneers is then attained. When bending perpendicular to the plane is carried out, then planar shear ("rolling shear") occurs in the plane of the plies of a plywood pnnel (see Figure 5b).
In-pla~tebending As a cainmon case of in-plane bending the load carrying bel~aviourof I- and boxbeam webs is well known. Usually the piywood panel of the web has the grain of: face veneer running parallel Lo the beam axis. For the plywood panel in the above example, in-piane bending results in the following. Firstly, ignoring the contribution of' veneers stressed perpendicular to heir grain, gives dl,
for o,,, 11 grain of face veneer
Ell = 3-Et, 12 1
= 2
"
dh El 12
for a,,, Igrain of face veneer
STBPIEUROFORTECI-I- an initiative under the EU Comctt Programme
(8)
A
-
-
Irr-plarre bcrrdirrg (nj p~~,ullel nrrd ( b ) pelpel~rlicrllarto the grain of face Irctleer.
Figrim 4
The resulting equations for the moduli of elasticity of the panel are as follows: d h 3 E,, 13E = = 0,GO E(,
"
4 5 5 1 h 3
IF E,),,,,,,,,,,, = E,,,, j30 is introduced, Illen it leads to
E,
= 0,Gl E(,
E,
= 0,41 E,,,
( a ) potlei s h w r strrss (b) pln~rat.s\lenr tress shorvrr).
In the case of in-plane bending, panel shear occurs perpendicular to the plane of the panel (see Figure 5a). The panel shear strength is much higher khan planar shear strengtl~.
-
STEP/EUROFORTECI+I an initiative undcr the EU Comett Programme
A1015
Tensiorz aizd cot~ipr-essioiz For tension and compression in plane of pIywood panels (see Figure 6) the elastic deformation may be calculated by using the summation of the IongitudinaI stiffnesses
Figure 6
Itr-plat~eterisiuri atid cortrpressior~(a)pcwalhl ( b ) perpeiidr'c~~~lnr to tl~egrc~itr of face veneer.
The application in the above exarnple gives
Ef
=
EL =
-(31 5 d
d E,,
1 ( 2 d E, 5d
.t
2d
+
. 0)
3 (d
=
. 0)
0,60 E,,
=
0,40 E ,
for o,.<11 grain of face veneer (15)
for or,
Tension stresses perpendic~llarto the plane of plywood panels are to be avoided. Compression stresses perpendicular to the plane of plywood panels induce srnaller deformation than in timber of the same species of wood, from which the veneers are made, because the transverse deformation is reduced by LIE lay up of the veneers.
Characteristic values EN TC 112.406
E N 1058 EN 789
For plywood panels which have a long history of st[-uctural use in the EC and EFTA countries, the characteristic values of mechanical properties and density values are given in EN TC 1 12.406 "Wood-based panels - Characteristic values for established products". For types of plywood not listed in EN TC 112.406, characteristic values shall be determined using the sarnpiing techniques set out in EN 1058 - "Wood-based materials - Determination of cltaracteristic values of mechanical properties and density" and testing procedures given in EN 789 "Timber structures - Testing of wood-based panels for tlie determination of mechanical properties for structural purposes".
Charcrcter-isficdensity The characteristic densities in EN TC 112.406 range from 350 kg.lrn"or softwood species up to 550 kgittt3 for beech plywood. Some characteristic density values are given in Table 2, STEPIEUROFORTECI3 - an initiative under the
EU Comctt Programrnc
-
4y7e oJ
chcirncrcristic srrertgth Fig.
Table 2
S-
,t:yrvood' 1
fk7
FINply~jood' f
r~ltrrN/IIIIH-111r11
USCANDPly~vood3 p/Jt,voori4 plyvood 5
1 fk fk N ~fk., I I I I"tlrnr It- ~hrtltl' trvn ~hiii11~ N / I ~ I , ~ z ~
Clrar~cfer-istic srrerrgrli 1rn11ie.sill ffharn' nitd clramcterisfic der~,sif)f r~diresill kS/rir" nccorciirrg to EN TC 112.30h for- estoblisl~edpr-odrccts.
5.
S\vedislr plyrt~oodP30, spurce, ic?r.sm~ded Firlrrislr birch pI~*rrrood,1,1 r?rnr Ireileer, sanded US pljotlood C-D, e~posrrreI , g w ~ c pI, rt~tsur~ded Cutmdiorr plyrt~ood,llouglas $fir; regrilar or r-egillar select shcntirilrg, rorscrnded Ger-rr~arrbeeci~plylvood (far k,, k2, k-q see Eqidafiorrs (171, (IS) orrd
6.
2 5-1aye~..r
I. 2. 3. 4.
f 19))
Cltnrncteristic n~ecltmticc~l properties
EN 635
- 2 and 3
Tables 2 and 3 give a selection of the established products froin EN TC 112.406. Characteristic values for French and Gerinan plywood panels consisting of uniform wood species can be derived using the composition factors of equations (17) - (19), see Figure 7. The required equations listed in Tables 2 and 3 are valid for E, I and 11 veneer grades in accordance with EN 635 "Plywood. Classification by surface appearance", part 2 for hardwood and part 3 For softwood.
Spfy~vood'
FINp(~voorl-
USC.4 NUplv~c~onr&3p l Y ~ ~ ~ o o dplylcloorl 4
Fig.
Table 3
Meall' valties of tttodtclus of elasticity irt N/tiun2 occorditrg to EN TC 112.306 for esrablishcd producrs. Footr~otcsI to 6 sce Tabie 2. 7. Cl~amcterisricvalue E,,, = 0,8 Eiqf ,,<,,,,
STEP/EUROFORTECI?- an initiative under the EU Comctt Prograrnmc
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For plywood of' mixed wood species, EN TC 1 12.406 gives extended composition factors in order to take into consideration layers consisting of different wood species in one plywood cross section.
The factors k, and 15 can be used for the calculation of characteristics of in-plane bending st!-ength f':,,,, on the basis of bending strength perpendicular to plane.f;,,+,:
The tnean value of the panel shear rnodulus G,,~,,,,,.,,,, Ibr the products in Table 2 ranges from 500 N/ti~m'for sofiwood species up to -700 Nlt~rm' for German beech plywood.
Concluding summary
-
Plywood, a classic wood-based panel is produced on the basis of a wellestablished teclinology and used for Inany structural components.
- For the application of characteristic vtlIues it is important to clifferentiale between - bending perpendicular to the plane of the panel - in-plane bending.
-
Characteristic values of mechanical properlies for established pIywood products can be taken from EN TC I 12.406.
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STEP/EUROPORTECI-l nn initiative undcr thc EU Comcll Progmmmc
Wood-based panels - Fibreboard, particleboard and OSB. STEP lecture AI I D.R.Griffiths University of Surrey
0bjectives To introduce the manufacture, properties and uses of fibreboards, particleboards and OSB.To identify how design data is derived for use with EC5.
Summary The various types of fibreboards, particleboards and OSBs are noted and their manufacturing processes detailed. An overview is given of board properties and this is linked to the methods adopted by CEN for the specification of boards and the derivation of design values. The range of uses in constmction for the board types described is tabufared.
Introduction Wood has been designed in nature to ~neet very specific engineering and environmental needs, but man seeks to adapt it to a very much wider range of uses. In order to overcome the shortcomings of timber in size and anisotropy, new man made forms of wood have had to be introduced. Gluiain and plywood developed with the advent of structural glues and the rotary peeling process. More recently, developments have concentrated on reconstituted forrns of wood such as particleboards, OSB, fibreboards and parallel strand lumber. These developments contribute much to i~nprovingthe efficiency of the forest resource. More energy is consumed in the conversion process but this is far outweighed by the benefits of using either waste or fast growing s~nalltimbers and in fabrication costs. The main use of this reconstituted or conlposjte wood is in wood-based panels. Table 1 shows the five main groups of wood-based panels and details tile three which fonn the subject of this lecture. Production and consunlption data show a marked increase in the use of wood-based panels in the last decade. 30 rllillion cubic metres were consumed in the 12 EC countries in 1989 and of this more than two thirds was particleboard. Furthermore, Europe is self sufficienl in particleboards and fibreboards but imports nearly two thirds of the plywood used. Wood based panels are very versatiIe and are used in many different industries including furniture, wall panelling, packaging and do-ityourself; 50% of the product is used structurally, principally in the constniction industry, and is covered by the Construction Products Directive (CPD) of the EU. Structural uses include flooring and roofing, wall sheathing, forniwork and specialist structural uses such as web members in 1 and box beams. The CPD also includes internal fitments such as doors and stair units which represent a further major market for wood based panels. Many types of wood based panels are relatively new materials and not all the boards suited to structural use have had their chnracteristic strength and moduli evaluated so that they can be used in conjunction with lfre k,,,, and k,,, factors a ~ ~ d joint information contained in EC5. Where panel products have a history of stnlcturai use and this experience has been incorporated in rlarional standards then this information has been used in the derivation of characteristic values. Otlier materials are put through extensive test programmes, using tests specially
formulated by CEN cornmittees to meet tlie varying requirements of different panel products, in order to produce design data. At the same time materials' specifications and performance requirements are being produced so that manufacturers can achieve conformity and use the CE mark which indicates compliance with the essential requirements of the CPD. Product standards are likely to remain the most common means of assessing the structural suitability of fibseboards, particleboards and OSB for many years to come.
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WOOD-BASED PANELS I
I
1
Plywood (STEP lecturc A10)
Boards Detailed in This Lecture
Spccial Bomd Products
I
I
I
Pnrticleboard
OSB
Fibrcboard
Bot~declivith
Mit~emlBotrcled
Bo~rderl1c1itlt Orgutric Bitldcr:~
1 Cement-Bonded Particlcbonrds
I Hardboards, Mediunzboards, Softboards,
Orgarlic Bin& I'.P
I Chipboards
Mitrernl Botldcd
I Gypsutn Fi brcboa~xki
MDF
Board types and manufacture
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Pnrticleborrt~cls A particleboard may be defined as a panel ~naterialmanufactured under pressure and heat from particles of wood (wood Flakes, chips, shavings) with the addition of an adhesive. The main types are named in Table 1. In the past, boards made using larger particles such as wafers and stlxnds have been included under the generic term particleboards. However, the major differences between OSB and chipboard and the continued growth in use of OSB has resulted in it being awarded a separate status in CEN codes.
A
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Clt ipbocr rcl Chipboard dates from the 1940s and was originalfy developed to utilise waste timber; it was generally of [ow quality. After a slow start, growtli has been tremendous and quality and tlnish have been improved and can be designed to suit end use by varying the materials, the lay up of the board and tlic pressing cycle. The wood chips form 85% of the board and are norn~ally from coniCerous softwoods such as spruce and pine although hardwoods such as birch may be used for heavy duty boards. Tlze chips ilre cut by a series of rotating knives to produce thin flakesfchips which are screened, dried and then sprayed with adhesive. The chips are next blown on to a forming platten and, by using different sized chips stored in separate hoppers, a multi-layered matt can be built up. Fine chips at the lop and bottom of the tnatt provide a smooth surface suitable for painting; long (30 t11in) thin chips provide a strong dense layer just under the surface and larger chips fonn a more econon~ic,lower strength and lower density core. The chips are randomly oriented such that the board performance will be sirnilar in all directions in the plane of the board. The common binders are synthetic resins, either urea fonnaldehyde (UF) for boards intended for use only in dry conditions or the more expensive rnelatnine urea forinaldehyde (MUF) for boards with enhanced moishlre STEPIEUROFORTECH - an iniliativc under lllc EU Comeit Programlnc
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The two processes start in a similar manner. Raw material, normally softwood forestry thinnings, but varying from sawdust to hardwood wastes and always exctuding bark, is chipped and rnechanically reduced to basic wood fibre. The chips are steamed under high pressure to soften the lignin, the natural gluing agent in the wood, which is thermoplastic and will provide all or part of the bond in the formed board. Alternatively, for wet process boards only, the Masonite (or explosion) process is employed where tile sudden ejection of the chips from a steam healed pressure vessel causes them to disintegrate. Manufacturing process Wet
Board density Low < 400 ~ ~ / I I I '
Tublt 2
High
> 900 kg/r11~
Softboard (SB)
Low Density Mediumboard (MBL)
Hardboard (HB)
Imprcgnatcd Softboard (SB.1)
High Density Mediunlboard (MBH)
Ternpered Hardboard (HB .I)
Dry Note:
Medium 2 400 kg/111~,< 900 kS/Ir?
Medium Density Fibreboard (MDF)
Board symbols shown in brackets; I means "with additional properties". Twes offibrebonrcl.
Wet process nza~irrfnctltre This is the older method of forming boards. The fibrous mass is mixed with hot water to form a pulp and additives are mixed in, as required by the final use of the board, such as flame-retardant chemicals and bitumen emulsion or other water repellent treatments. The pulp is then drained of water by suction pumps acting through the forming mesh and by the action of the thicknessing rollers. Softboard is formed at this stage by coolir~gand drying the board. The density will be between 200 and 400 k8/tn3 and thiclcnesses of 9 to 25 n ~ r rare common. For more dense boards, the material must first be pressed at a temperature of 160 to 180°C. The need to remove further water at this stage results in the typical board finish of one smooth face formed against a polished plate and one rough 'screen' face fonned against a wire mesh. Mediurn boards are in the density range 400 to thicknesses from G to 13 ,nm, Hardboards are 900 to 1100 kg/itl" in 900 kg/itr"ith density with thicknesses between 3 and 8 mnl. Tempered hardboard is a special quality structural hardboard of higher density, with added water repellency which is obtained by passage of the material through a hot oil bath, and possibly of higher strength achieved through the use of additives such as phenol formaldehyde.
Dty process n r n n ~ ~ o c t ~ u . ~ In this more modem process the fibrous mass is conveyed in an air stream to the matt forming station. The fibres must be coated with resin, either UF, MUF or MDI (isocyanate) and up to 10% by weight, to achieve good bonding. The matt may be up to 500 rilnl thick and is then pre-pressed between steel belts to remove air. Cut lengths are hot pressed into slteets giving two very finely finished surfaces. Medium Density Fibreboard (MDF) is available in thicknesses up to 40 mm and in densities in the range 600 to 1000 kg/tn3. Board edges may readily be profited for specialist use.
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Board properties Wood-based panels overcome some of the deficiencies of natural timber in that they have a lower degree of variability, lower anisotropy and higher dimensional stability in the plane of the board; they are available in very much larger sizes and provide a wide range of finishes. The variability is reduced by the random distribution ofthe components into a more even consistency. The reduction in variability increases as the size of the components decreases. This improves the characteristic value of a structural property in comparison with the mean perfonuance determined from tests. However, in comparing bending strength and stiffness for boards of a similar density, performance in general will reduce with component size. Unless the boards are very heaviiy densified, performance will be much lower than for solid timber; this is in part due to the reduction in anisotropy. A11 particleboards and f i b r e b o d s except OSB are nominally isotropic in the plane of the board. Timber, in both strength and movement, has a value of anisotropy of up to 40:l. Plywood can reduce this value to 5:l in simple 3 ply lay ups and to 1,5:1 in inore expensive multi lay ups, whereas OSB is normally about 2 to 2,5:1. Figure 1 compares strength ranges for typical timber and wood based materials.
Key:
(a) So(twood (c) Tcmlxred l-iardbonrd (e) (g) if
Figrirc I
MDF Chipboard Parallel to grain or strong direction
(b) Softwood Plywood (d) I-lardboard (0 OSB (h) Ccment Bonded Particleboard I Perpendicular lo gwin or weak direction
Con~pnrisonof bmclflirrg ,sfrer~grits f, of satvtt firltbet-nrrd urood-based paneis.
Isotropy considerations also affect the dimensional stability of wood based panels as shown in Table 3. Dimensional stability in the plane of the board is relatively constant for single board types and even between board types. It is much better than for timber across the grain. As a consequence sheet materials are ideal where large widths are required such as in flooring and wall sheathing but even so must be laid with 2 to 3 rl71ll gaps to allow for the small moisture movements.
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Stability across the thickness of the board is less good but depends very much on board type and can be reduced by additives or by conditioning the board prior to use. This process brings the moisture content of the board much closer to its end use condition col~~pared with the as-manufactured state and effectively reduces the problem of thickness changes and differential movements which could lead to bowing of the boards once they are fixed in position. Timher or wood-based pancl type
Percentage change in dimension Parallel to grain or board length
Perpendicular to board length
Through Ihickness
c0,10
c0,10
030 (R) 1,20 (R)
2,00 (T)
020
0,20
10,OO
0,15
0,15 0,15 0,20
3,50 3,50
Solid Timber
Douglas Fir Beccl~
I ,oo (T)
Plytt~ood
Douglas Fir Clripbonrd
Loadbearing dry Loadhearing humid
OSB
Filn-cbunrds
I-Iardhoard Tenlpered Hardboard MDF Notes:
0,15 0,20
3,50
R is radial direction. T is tangentit11direction. --
Table 3
Di~irertsionulsmbility of rirnber arrcl ~vood-based~~atrels: perccrrtcigc clrmrge it1 clintetrsiorr fiotti 65% to 85% relative Iruirtidity.
Particleboards and fibreboards comprising mainly timber are visco-elastic and susceptible to creep. However, due to the smaller component size, the rate of creep is substantially higher than for timber and plywood. In design this affects the k, and k,,,factors quoted in EC5 (see Table 4). Creep effectively results in very low stresses and moduli being used for permanent and long term loads, although the effect diminishes for medium and short term conditions. In addition to the standard effects of moisture, load intensity and duration, the effect of creep in wood based panels increases as the quality of the board decreases, usually related to density and glue quality, and as the size of particle decreases.
One of the most important factors affecting the end use of a panelboard is moisture. Ilumid conditions encountered in kitchens, bati~roomsand roof spaces reduce the perfonnance of boards, as is the case with all tirnber materials. Lower quality boards show very little recovery on subsequent drying. However, higher quality boards, usually denoted by the use of moisture resistant glues such as MUF, PF and MDI or by specialist processing such as oil tempering, are capable of very considerable recovery and are therefore able to be used in service class 2 conditions. Cement bonded particleboard is very stable under humid conditions and is the only wood based panel that can be fully recommended for exposed external cladding use (service class 3). STEPIEUROFORTECH - an initiative under tllc EU Come11 Programme
Material
Solid lirnbcr Glulnm Plywood
Particleboards (heavy duly) OSB grades 3 and 4
Load duration class
k,l,adI
kt,,'
k,l,,,,f
b,;
Pcrnmanent
0,60
0,803
0,40
Medium tcrm
0,80
025
Short term
0,90
0,OO
Instantaneous
I , 10
Fibreboards
knwri;
k,1,;
k,lu,~
k,jrl
1,50
0,30
2,25
0,20
3,00
0,70
0,50
065
0,75
0,GO
1,OO
0,90
0,OO
0,85
0,OO
0,80
0,35
1,fO
Notes:
Pnrticlcbortrds
(loadbearing) (loadbearing dry) OSB grade 2 Hardboitrds (load bearing humid)
r,lO
1,lO
'Values also given in EC5 for service classes 2 and 3. 'Values also given in EC5 for scrvicc class 2. v a l u e for plywood, use 0,G for solid Limber and glularn.
Tnble 4
Co~aparisonof kJJU,,, ancl k,,,,ficlor:r. for service clcrss I (dt-y cortditiotts) otrly for cI$trent titltbcr atid ~cloodbmed ~ ~ u n11mteria1.s. el
Moisture content also affects the durability of the board with respect to fungal attack. In general, this will ]lot be a. problem as the board should not be used in conditions which will support fungal growth. However, most particIeboards arid standard fibreboards (i.e. those without specially improved properties) will be less durable than the wood species from which they are made. The incorporation of fungicides will increase the resistance of the board and give more confidence when boards have been exposed lo accidental wetting. Wood based panels will not normally be attacked by the rodents and wood boring insects common to most of Europe; specialist treatments would be necessary where abnornlal conditions prevail. Certain types of board offer specialist properties, for instance the thermal insulation of softboards, but in general where the board density is in the normal range for timber, then tl~ermal,acoustic and fire properties will not be significantly different from those of solid timber,
Specification and design values In order that wood based panels [nay be safely used, it is necessary to set standards for board quality. Minimum specifications are defined which relate to the type of board and the general properties important to its end use. Test methods are detailed which allow lnanufacturers to control the quality of their board and demonstrate its performance relative to the minimurn 1eveI. Initially CEN standards categorise wood based panels illto the board types defjrled earlier. These types are then graded into their potential for end use, including both structural and non-structural applications. Table 5 identifies the grades of board. General recjuirements are detailed fbr each board type, covering dimensional accuracy, density variation and moisture content, together with others specific to a type of board, such as surface soundness and formaideliyde contertt. Further specifications are then set for strength properties which are used for factory quality control tests covering:
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bending strength and ~iiodulusof elasticity related to n small specimen three
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point bending test,
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transverse tensile strength which measures the internal bond for a small 50 irtrpt square specimen,
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thiclcness swelling measured over 24 hours in cold water,
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bending strength, modulus of elasticity and transverse tensile strength tests after accelerated ageing; restricted to boards specified for use in ltumid conditions.
Supplementary properties may be supplied by the maufacturer based on CEN tests to cover properties such as iinpact andlor static point loading on the board surface, creep and axial screw withdrawal. Other information important to specification could cover thermal movement, thermal conductivity and vapour transmission. The strength properties of chipboards and OSB are very dependent on thickness and require thickness classes to be introduced in their specification. Fibreboards are more consistent through thickness, requiring fewer classes, but their specification is made more complex by the range of densities of board and types of manufacture. (see Tables 2 and 5). The strength properties covered by the specification of wood-based panels must not be used directly in structural design. Two approaches are then available to the engineer. Either to use characteristic values for the structural properties together with the k,,,,,,k,,, factors given in EC5 or to use performance specification standards for particular components such as floors, walls and roofs. The latter standards will relate grades of board to an end use based on their material specification and their performance in the relevant special prototype tests which are in preparation by CEN. These tests will enable the performance of all materials to be evaluated in relation to the problems defined by their end use. Of particular relevance to floors and walls is impact damage and it is clear that this cannot be directly related to the properties covered in the material specifications. In the former design approach, characteristic values for boards will have been derived by one of two means. Firstly, where boards have a history of safe use and have in the past been subjected to rigorous test programmes, then the available information has been adjusted to calculate the required characteristic values. Secondly, where there is no history of previous stnrctunl use, the values are based on a new set of structural tests which have been introduced by CEN to enable all wood-based panels to be assessed in terms of bending, tension, compression, panel shear and planar shear properties. These tests have been developed for a "medium size of sample" which has reduced the effect of the variability in cross-section of the larger component type boards sucli as OSB and plywood but without requiring expensive full sheet testing. The tests determine a five minute strength and a stiffness modulus in the range between 10% and 40% of the strength values. These tests are detaiied in prEN789 "Testing of wood-based panels for the determination of mechanical properties for structural purposes". Environmental conditions are defined to determine the performance at the boundaries between climate classes. Additional creep information may then be required to determine ,k and kc,,, factors appropriate to the board and thus derive long, medium and short term strengths from the test data if these factors are not included in EC5.
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CEN Code Tor specification
Notation of boards in CEN code
Chipboard - General purpose, dry - Interior filrnenls, dry - Loadbearing, d ~ y - Loadbearing, humid - Heavy duty, loadbearing, dry - Heavy duty, foadbearing, humid
EN312-1 EN312-2 EN312-3 EN3 12-4 EN3 12-5 EN312-6 EN312-7
P2 P3 P4 P5 PG P7
Cement bondcd - Single grade only
EN634- I EN634-2
CB
Board type and description by use
Characteristic values for design available
Yes Yes Yes Yes
EN300
OSR
- General purpose and ii~teriorfitments, dry
- Loadbearing, dry - Loadbearing, humid
- Heavy duty, loadbearing, humid
EN622-2
Hardbowds
- General purpose, dry - Genernl purpose, humid
HB HB.H HB.E HB.LA HB .HLA I HB .HLA2
- General purpose, cxlerior - Loadbearing, dry - Loadbearing, humid
- Heavy duty, loadbearing, burnid Mediuinboards - General purpose, dry - General purpose, humid - General purpose, exterior - Loadbearing, dry - Loadbearing, humid - Heavy duly, loadbearing, dry - Heavy duty, londbearing, humid
EN622-3
Dry process boards
EN622-4
MBL, MBH MBL,H, MBH.H MBL.E, MBH.E MBL.LS, MBH.LA1 MBH.HLS 1 MBH.LA2 MBH.HLS2
MDF
- General purpose, dry - General purpose, hunlid - Loadbearing, dry
MDF.H MDF.LA MDF.HLS
- Loadbearing, humid
S oftboards - General purpose, dry - Genernl purpose, humid - General purpose, exterior - Loadbearing, dry - Loadbearing, humid Table 5
EN622-5 SB SB.H SB.E SB.LS SB.HLS
CEN code grurlitlg of rtrood-based patlels.
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Yes
Yes
The assessment of existing structurally used boards tias been restricted to chipboard and types HB.HLA2, and MBH.LA2 fibreboards (see Table 5). Their characteristic values are included in CEN document EN1 12.406 "Wood-based panels: Characteristic values for established products", and design factors are given in EC5. OSB has been the first material to go through the CEN test procedures and is also included in EC5. Other boards, sucl~as cement bonded particteboard, have the durability qualities to be used st~ucturallyand may well be included in revisions to EN I 12.406 and EC5 when characteristic values become available, but at present their structural use is restricted to the perfonnance specification route. Table 6 compares cliaracteristic values for typical wood based panels for a datum thickness as close to an 18mm datum as possible, and notes the appropriate thickness class. Propcrties
Board type Particlchoards P4 landbearing, dry
Particleboards P7 l~cavyduty, loudbcuring, l~umid
Fibreboards MBH.LA2 loadbcaring, dry
Fihrehoards HB.HLA2 heavy duty, loadbcaring, hun~icl
13 - 20
13 - 20
> 10
>5,5
Density kC:/~rt3
GOO
600
600
800
Bending f,,
12,5
16,7
15
32
Tension f;
7,9
10,6
8
23
11,l
14,7
8
24
Panel shear f;.
61
8,1
4s
IG
Planar shearf,
1,6
2,2
0,25
2.5
Thickness range lltltl
Cornpression f,
Men~rA.Iod~tiirof Eiasticity (Nhrrtli')
Bending E,,,
2900
4230
3900
4600
Tension E,
I700
2485
2900
4600
Compression E,
1700
2385
2900
4600
Pancl shear G,
830
1195
1200 --
Tnble 6
f 900 -
CEN clraracteristic ~~ctlrres .for establislred bvuod-bused pur~els.
Joitlts For nailed, screwed and bolted panel to timber joints, the rules for timber to timber joints apply. However there are very few characteristic values available for embedment strength and head pull through strength for fibreboards, particleboards and OSB. Hence, it may often be necessary to undertake CEN perfonnance tests on fasteners and panels to determine the resistance of joints in panels to lateral and axial loads. In many end uses of wood-based panels, such as timber frame walls, the fixing performance is not individually assessed but is covered by tests on a typical full scde structural member which may incorporate many fixings. STEP/EUROFORTECH - an inilialive undcr thc EU Comctt Progr:ln~mc
Use The use of wood-based panels is wide ranging and dependent on the nature and properties of the different board types. Being a composite material, it is often possible to build a specification for a board based on a projected end use; an example of this would be the development of MDF for the furniture and semistructural fittings industries. For structural use, many types of board will be eliminated based on tlteir quality and durability. Boards may then be limited to a narrow range of uses due to their special properties and to negative influences such as cost; for instance, the density of tempered hardboard makes it difficult to nail as a sheathing but ideal as a web material in I beams. However, the majority of boards which are of a similar density to timber will compete with one another and with plywood in a rmge of markets. The grading of the board in terms of strength and moisture resistance will then deternine its specific use in the various domestic, commercial and industrial construction situations. Table 7 delails typical end uses and the types of wood-based panel that might be most appropriate. Use
Board type Particleboards
OSB
CBPB'
Fibreboards
Sarking
P5
OSBl3
CB
SB.H, MB.H. HB.H
Flat roof decking
P5
OSBl3
CB
Cladding Fascias Soffits
OSB13, OSBl4
CB
HB.E
CB
HBH.HLA1, HB.E
Ceilings and partilions
All boards !nay be sui(nb1e but will be limited by special requirements Tor impact, fire, moisture and sound.
Domestic
P4, P5
OSBl2, OSBl3
Commercial
P5
OSBl3, OSB/4
Industrial
P7
OSB13, OSBl4
Webs or stressed skins
P7
OSB/4
Notes: T ~ b l e7
CB
HB .HLA 1/2
' Single grade ol board, notation dcfincd in Table 5 no1 used by CEN. Use of ~c~ood-bnscd porrels.
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Concluding summary Fibreboards, particleboards and OSB are refatively new structural materials. They are efficient in their use of waste or low quality timber and small diameter logs. As composites their properties may be developed to suit their end use and they are now able to replace solid timber and pIywood, in many situations. Board development is on going and not all boards have had their characteristic structural properties defined. Thus alternative methods of specification are sometimes necessary to enable thern to be used in structural situations, typically in Rooring, roofing and waf 1 sheatliing.
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Adhesives STEP Iect~rreA I2 E. Rnknes The Nonvegian lnstiiutc of Wood Technology
Ob,jectives To give an overview of the different structural wood adhesives and to show how they are used in timber products and timber structures.
Prerequisite A4
Wood as a building material.
Summary The theory of adhesive bonding is briefly described, and reference is made to the present situation concerning EC5 and adhesive approval. A brief description of current and potential structural wood adhesives is given relating to composition, durability, application, classification. Types of joints (parallel, end-to-end, crosswise) and the process of bonding are described in principle, and bonding of pressure-treated wood is briefly mentioned.
Introduction Structural wood adhesives are used to bind two or more wooden parts together in such a way that the product behaves as a static unit. The task of the adhesive is to fill the voids between the wooden members, and to produce adhesive bonds to each member which are equally strong and durable as the cohesive forces within the members. In addition, the adhesive layer itself must have sufficient strength and durability to retain its integrity in the assigned service class throughout the expected life of the structure. The attraction forces between adhesive and wood are of the same type as the cohesion forces in the wood, i.e. electric attraction forces between molecules. The resulting bonds are mostly of the secondary bond type, i.e. hydrogen and van der Waals bonds. Some primary bonds, for instance covalent, are also likely to be produced with some adhesives. In order to provide the intimate contact necessary LO produce bonds of this type, the adhesive must, at some stage in the bonding process, be in the liquid fonn. T l ~ ebonding process consists of two steps:
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application of a liquid adhesive which wets the surface of both adherents so that attraction forces between adhesive molecules and wood molecules are created across the borderlines,
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transformation of the liquid adhesive, which fills the voids between the members, into a solid of sufficient strength and durability to retain its integrity throughout the service life of the construction.
The latter process is called hardening. It may be brought about in three ways:
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by a physical process, like the removal of solvents, or the solidifying of a melt as in thermoplastic adhesives like Polyvinylacetate (PVAc) and hot melts,
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by a chemical process, in which the adhesive ~noIeculesreact with each other, forming primary bonds and creating a polymeric network such as in epoxies and polyurethanes,
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by combination of solvent removal and chemical reaction (urea-, melamine-, phenol- and resorcinol-formaldel~yde).
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With structural adhesives there is afways a chemical reaction involved. Adhesives relying purely on physical curing such as them~optasticshave, generally, too much creep to be used for structural purposes.
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EC5 classification of adhesives At present there is only one established EN-standard for classification of structurai wood adhesives, namely EN 30 1 , "Adhesives, phenolic and aminoplastic, for load bearing timber structures: Classification and perforn~ance requirements". The corresponding test standard is EN 302, "Adhesives for load-bearing timber structures - Test methods, part 1-4". The standards apply to phenolic and aminoplastic adhesives only. These adhesives are classified as:
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type I-adhesives, which will stand full outdoor exposure, and temperatures above 50 "C,
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type 11-adhesives, which may be used in heated and ventilated buildings, and exterior protected from the weather. They will stand short exposure to the weather, but not prolonged exposure to weather or to temperatures above SO "C.
According to ECS only adhesives complying with EN 301 may be approved at the moment. Plywood and particle board are used as elements in some timber stnrctures. TI~ere is, at present, no EN-standard for the classification of the adhesives used in these products, and hence they have to be evaluated using national standards. (e.g. BS 1203, "Specification for synthetic resin adhesives for plywood", BS 1455, "Specification for plywood manufactured from tropical hardwoods", DM 53255, "Bestirnmung der Bindefestigheit von Spemholzleimun,oen im Zugversuch und im Aufstechverfahren" and DIN 68705, "Sperrhoiz, Begriffe, aligemeine Anforderungen, Priifung".
Current types of structural wood adhesives Reso~i~tol~bl~t~lctIcIeI~~~cle ( R F ) nrrd Pltetrol-1-~sorci~t~1-for~~~zald~'i~~~cle (PRF) nc/lzesives
The pure resorcinols are made by reacting resorcinol (a phenolic compound) with fo~lnaldehyde.The process is carried out with a deficit of formaldehyde, and the reaction stops when this is consunled. The adhesive, which is a liquid, is used with a "I~ardener"containing formaldehyde. This co~npletesthe cure of the resin to an infusible state. In addition, the hardener usually contains inert fiIlers of various kinds, in order to make the glue "gapfitling". As resorcinol is an expensive ctlemical, some of it is now usirally replaced with other, cheaper phenols. For both types, curing may take place at room-temperature (15-20 "C) or at elevated temperature. These adhesives are suitable for radio-frequency curing. The bonds formed in the reaction between resorcinol and other phenols with formaldehyde are of the -C-C- (Carbon to Carbon) type. These bonds are very strong and durable, and not susceptible to hydrolysis. The RF's and PRF's therefore give very durable bonds: they are fully water-, boil- and weather-resistant, and will also withstand salt-water exposure (Selbo 1965).
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Members glued with these adhesives will not delaminate in a fire. Permissible glueline thicknesses are up to approximately 1 rrrrn with ordinary adhesives and up to 2 I I ~ ~ with II special, gnp-filling types. The gluelines are neutral, i.e. neither acid nor alkaline, and hence they will not damage the wood or corrode metals. They are very dark in colour. Tlie cured adhesive will not emit formaldet~ydeor other hannful chemicals. RF's and PRF's are type I adhesives according to EN 301, They are used in laminated beams and arches, Rngerjointing of structural members, Ibeams, box beams, gusset joints, nail-gluing etc., both indoors and outdoors.
PIteiioi-for7r1n1rlel~j~c~e adl~esises(PF), hor-settirtg These are made by reacting phenol with formaldehyde under alkaline condition, at elevated temperature. The reaction is stopped by cooling. The adhesive may be supplied as liquid, powder or film and is alkaline. I1 is cured by the appljcation of heat (1 10-140 "C), and, for some types containing more reactive phenols, by a combination of lieat and the addition of a formaldehyde-containing hardener. Tlie gluelines are very dark. They have the same durability properlies as the RF- and PRF-adhesives. Hot-setting PF's are typically hot-press adhesives, and they are used in structural and mwine plywood, in fibreboard, etc. Radio frequency-curing is not possible because of "burning", but microwave curing is used for some products, like laminated veneer lumber (LVL) beams. Hobsetting PF's cannot be classified according to EN 301. When tested to BS 1203 or BS 1455, they will meet the most severe requirements (WBP, "Weather and boil proof').
Pl~enol~fbrr~tsil~Ze/~~~rIe ocl/~esives(PF), cold-settir~g In order to make a PF cure at room-temperature it must be made acidic. This is not possible in an aqueous solution, as the acid would precipitate the resin. The adhesive is, therefore, dissolved in alcohol, and made to cure by the addition of a strong acid. The gfueline itself has the same strength and durability properties as the other phenolic-type adhesives, i.e. fully water-, boil- and weather-resistant. The hardener, however, is so strongly acidic that it is liable to damage the wood surfaces. Cold-setting PF's are classified according to EN 301, but the current types are likely to be eliminated by the "acid damage test" given in EN 302-3. These adhesives were used lo some extent in the fifties and sixties in glulrun production. Some of these buildings actually collapsed many years later, and there is reason to believe that acid damage from the adhesive is the cause. Cold-setting (acid-curing) PF's of current type, therefore, should not be used for structural purposes.
Urenlfor7nnlcfel~jtrle orl/~esiijes(UF) UF's are made by I-eactingurea with formaldehyde. The reaction is speeded up by acid and heat. At a suitable stage the reaction is stopped by cooling and neutralising. It is started again by adding an acid-releasing hardener and, for some types, by heating in addition. UF's are a very versatile adhesive family. They may be supplied as liquids or powders (sonletimes with hardener added), and they may be cured at illly telnperature from 10 "C upwards. Speed of curing may be adapted to the process. They are also suitable for radio frequency-curing. The gluelines are light in colour. Tile hot-press types are used for non-structural plywood and chipboard etc. They are classified by for instance BS 1203 tuld BS 1455 where they meet the two lowest r*equirementsonly (INT, "Interior", or MR, "Moisture resistant"). Only special cold-
setting UF's are suitable for structural purposes. They must not be too acidic, and they must have filler added to make them gap-filling (up to 1 nrm), otherwise the gluelines will crack on their own if thicker than 0,1 t r l t ~ Even . these adhesives have limited heat- and water-resistance, and they are broken down fairly quiclcly by combined heat and high relative humidity. In a fire they will tend to delaminate. UF's for structural purposes are classified according to EN 301 as type 11-adhesives. They are used in glularn production and fingerjointing for interiot construction.
Melnrrrirre-iirea .forr~~alcieliyde nclitesives ( M U F ) These adhesives are closely related to UF adhesives, but some of the urea is replaced with melamine in order to increase the water- and weather-resistasice. Some of thein even contain resorcinol for the same purpose. MUF-adhesives are supplied as hot-press adhesives, for pIywood etc., with intermediate waterresistance, and as cold set where together with hot set adhesives they are used for glularn and fingerjointing. Tlze cold set ones are classified according to EN 301. Some of them will be type 11-adhesives, with properties comparable with UF's. The best will meet the type Irequirements, and thus be classified as "weather-resista~lt".They are, however, less resistant than the resorcinols, and not suitable for marine purposes (Selbo 1965). However, MUF's are often preferred for economic reasons, and because of their lighter colour. Casein adItesi\~es The main constituent of these adhesives is the milk protein, casein. The adl~esive is delivered as a powder, consisting of casein and various inorganic salts. When the powder is mixed with water a series of clle~nical reactions occur. Aftcr approxin~ately 15 minutes these have resulted in the casein being dissolved as Sodium Caseinate. After 4-8 hours this has been transformed to Calcium Caseinate, which is fairly insoluble in water ("Curing-reaction"). The gluelines are fairly light in colour. They are less water resistant than UF gluelines, but more resistant to combined heat and high relative humidity. Caseins are probably the oldest type of structural adhesive and have been used for industrial glularn production since before 1920. They have proved suitable for indoor and protected outdoorsconstntction, but have to be protected against mould attack with a suitable fungicide. Caseins do not meet the requirements of EN 301. Environment
RF/PRF PF(hot)
MUF
UF
Casein
x
x
x
C
+ +
+
-b
+
GIueIirre colour
Dark
Dark
Light
Light
Light
EN-class
301-1
301 - 1/11
301 - 11
+
Marine
-< 50 "C,;85 5%
r.11.
+ Suitable x Not suitable (+) Sorne brands suitable - Not covered by existing EN-standards Tc~bleI
Stritabili~of air-rcnr str~rctitrulwoad ucNle~*ives.
STEPIEUROFORTECH - an initiative under the EU Comett Programrnc
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Potential new structural wood adhesives Test methods developed for one or more types of adhesives, like those in EN 302, are not necessarily suitable for other types. Approval of a new adhesive type, therefore, wilI involve two steps:
-
establish with adequate confidence that the long-tenn durability of the new type is satisfactory,
-
devise shorl-term tests which are able lo distinguish between the good and the bad brands of the new type.
A generd methodology for this is given in the CIB-publication 96 (1987). The following four adhesive types are at present considered as potential structural wood adhesives.
Epo.~y ctcllr esivcs These are two part adhesives:
-
pat-t I is an epoxy resin whose lnolecules are terminated with epoxy groups, part 11usually consists of bifunctional amine(s).
None of them contain solvents. When mixed together epoxy and amine react to make up an infusible resin. Epoxy adhesives may be "tailored" to the area of application, and some of them are definitely suitable for wood gluing, They have very good gapfilling properties. I-lowever, due to their high price and their application properties they have only been used in special cases for wood bonding, for instance:
-
building of wooden boars,
-
bonding of nietal, plastics, rubber etc. to wood,
-
repairing wood with decay or other damage ("casting"),
-
glued-in bolts.
repairing delaminated glulaln beams,
Epoxies have very good strength and durability properties, and the weather resistance for the best ones ties between MUF's and PRF's.
Two-par-tpoZylrr-et/~nnw Part I consists OF bi- or trifunctional isocyanate and part I1 of bi- or trifunctional alcohols. Both are solvent-free. When mixed together they react to form a polyuretlime resin, These adhesives have good strength and durability, but experience seems ro indicate tliat they are not weather-resistant, at least not all of them (Hedlund 1987). As for wood bonding they have mostly been used for special purposes, for instance:
-
aIu~niniuinto plywood in sandwicl~constructions, corrugated steel plates to plywood for load-bearing roof elements (used in Scandinavia for more than 10 years), glued-in bolls.
SEPIEUROFORTECH
- an ir~iliaiiveirnder tllc EU Cornelt Programme
A 1 2/5
Orre-pcrr.!pol?llrrethcnlc.s The reactive component is an isocyanate. When applied to wood, part of it will react with ~noistureand be converted to amine. This reacts with the remaining isocyanate to form il poly-urea resin. Carbon dioxide is formed duiing the curing, and this will make the adhesive foam if the glueline is thick. Strength and durability properties are muct~the same as for two-part PU's, or slightly inferior. They are not gap-filling.
In Gertnany two brands of one-part PU's have been approved for use as a structural wood adhesive, both indoors and outdoors. They are limited to G 117 spans and 0,3 tltrrr
glueline thickness.
El~ruisioitpo1~~1tzc.r isocj~nrtcrtes(EPI) These are also two-pall: adhesives:
-
par1 I: Emulsified polytner, e.g, poiyvinylacetate (PVAc), part 11: "Blocked", e~nulsifiedisocyanate.
Working properties and initial curing is much the same as for PVAc-adhesives, but when the glueline dries, the isocyanate is released and acts as a crosslinker. Strength and durability are reported to be very good for these adhesives, and soilie brands are approved by the American Institute of Timber Construction as exterior grade adhesives for sln~cturalwood bonding. Others have been found to be less durable (Yoshida 1986). Within each of these four adhesive types there are brands of very difFerent properties, Some of [hem may be suitable its structural wood adhesives, and some are definitely not. The problem is that at present there are no short-term approval tests to identify the suitnble brimds. Property
Epoxy
Two-part PU
One-part PU
EPI
Weather rcsistnncc
?
'I
?
'I
Heal rcsistilncc
7
);
I?
'I
Water rcsistancc
'?
'1
?
'?
Creep
'I
'I
,4
?
Toughness
i
i-
f
+
Gapfilling
+
i-
x
x
i-
f
o
-+ +
Adhesion Easy to
usc
x
x
x
Curing time
o
o
o
+ Good, probably bctter than currcnt adhcsivcs. o Co~nparablcto currcnt adhesives. x Inferior to currcnt adhesives. ? Uncerlain, large variations between brands.
The use of structural wood adhesives Three ways of bonding wood !nay be distinguished. STEPfEUROFORTECI-I -
iW
initiative undcr the EU Comctt Prograrrlmc
Prr~-~lllel (sirkw~ys) joiitts Here the glue must match the shear strength parallel and the tensile strength perpe~ldicularto the grain direction of the timber. Approved adhesives will nialcli these requirements without problems. Swelling and shrinking stresses wilI be small, since all the members are in line with each other.
End-to-ertc?joiitts 111this casc the adhesive should match the tensile strength of the tirnber in the grain direction. Structural butt end jointing of timber, which irnplies that the adhesive must lnatcfl the tensile strength of the timber, is not possible wit11 current techniques. Instead, the jointing is carried out in such a way that tensile stresses in the litember are transformed to sliear stresses in tile gluelines. This may be done in various ways, but the method used irtdustrially is fingerjointing. In this joint the combined shear strength of' all the finger areas should ideally match the tensile s~rengthof the cross-section of' the member. Since the shear strength is only 1/10 of the tensile strength, the glueline area should be approxi~nately10 tirnes the crosssectiori area. Again members are in line with each other, minimising swelling and shrinking problems.
CI-ossv-i~ise joirltiilg In this case the adhesive must match the shear strength parallel and the transverse tensile strength of the wood, which is not a problem. The jointed members will, however, be at (more or less) right angles to each other, and this can cause great stresses in the gluelines due to rnoisture movement of the wood. Such gluing is, therefore, lnostly limited to two cases:
-
the ~nembersto be jointed are so thin that they will restrain tlie movement of each other (fairly) effectively e.g. in plywood, OSB, particle board, fibreboard,
-
restrained members like plywood and particle board are glued to solid wood ~nemberswhich are fairly narrow e.g. in I-beilrrrs, box beams, gusset joints.
In such products the sniail lengthwise movement of the solid wood members will match approximately with the restrained movement of the woodbased panel. Stresses along the glueline are therefore rattler small, but they [nay be high across the glueline if the ruernbers are wide, or the moisture fluctuations great. This may produce fatigue failure in the joint with time.
The boltdiitg pr-occss This consists of the following steps: -
conditioning the timber to a moisture content corresponding to the average ~noisturecontent which is likely to apply in service,
-
machining of the surfaces to be bonded, preferably just before bonding, because freshly cut dust free surfices give the best giuelines. This must be done with sharp tools, to prevent darnaging the surfaces,
-
mixing and application of adhesive,
-
application of sufficient pressure to Itold tlie members in contact with each other until the adhesive I~asgot sufficient handling strength,
-
in some cases: application of heat during the pressing period in order lo
STEPEUROFORTECI-1- an initiative under ~ h cEU Cornell Progriimme
A 12/7
speed up curing,
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conditioning of the bonded members to obtain postcuring and temperatureand moisture-equilibrium.
BoncIi~tgo j chet~ticcrflj~ treated wood Clle~nicaltreatment may be used to protect wood against decay, or to make it fireresistant or water-repellarlt. If the members are used in glulam production afterwards, they will have to be planed before gluing. This requires a certain penetration of the chemical, or n~ostof it will be removed by the planing.
Such treatment of tiiaber may affect the gluing properties, dependant on the type of treatment. As a nlle the treat~nent/adliesive-combination should be tried out beforehand. The following guidelines may be applied:
-
creosote and other oilbased treatments. Gluing is difficult but possible with PRF and polyurethane-adhesives. Gluing firs1 and impregnating afterwards is recornmended.
-
waler-soluble salts. The copper-chroine-arscrlic salts usually give no difficulties. Salts containing free acid (e.g. boric ilcid) or compounds able to react with formaldehyde (e.g. ammonium salts) may give problems. Some of the decay protecting and most of the fire protecting salts are of this type.
-
-
-
References CIB WSOIRILEM 71-PSL (1987). Prcdiction of service life of building matcrinls and components. CIB-publication 96. Ilcdlund, B. (1987). Weelhcr-cxposure of glued laminated blanks for windows (in Swedish). SPrapport 1987:40. Stateris Provninpsnnstall, Borb, Sweden.
-
-
Selbo, M.L.(1965). Pcrfor~nanccof melamine adhesives in various exposures. Forest Prod. J. 15 (12). 1965, p.475. Yoshidn, H. (1986). Bond durability of water-based polymer-isocyanate adhesives (API-resins) for wood. (Japanese with English summary), J. Jap. Wood Res. Soc. 37-(6) 1986, p.432.
STEPIEUROFORTECH - an initiative under thc EU Comctr Progrnmmc
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Behaviour of timber and wood-based materials in fire STEP icciure A 13
Objective
14. Hart1
To present information about the beliaviour of timber and wood-based malerials under the influence of fire.
ZiviIingenieur riir Bauwesen
Prerequisite A4
Wood as a building material
Summary Information is provided based on the lmowledge of the essential colnponents and natural properties of timber affecting its behaviour when exposed to fire, that is the cl~elnicaland physical changes under the influence of fire, are explained.
Introduction There is no simple way of expressing the behaviour of a matet-ial with respect to fire. There are two distinct phases to a fire, the developing phase and the fully developed phase and a materials performance has to be categorised in respect of those two conditions. The developing phase incorporates a number of separate phenomena, the combustibility of the material, the ease of ignition, the speed of the spread of firefflame across its surface and the rate at which heat is released. The fully developed phase represents the post ilasll over conditions where all combustible materials become involved in the fire. The desirable properties are the ability to continue to carry load to contain the fire within the zone of' origin without the escape of flames or hot gases and without conducting excessive heat to the unexposed face that ]nay lead indirectly to fire being transmitted to adjacent areas. The ability to resist the fully developed fire is known universally as the fire resistance but in general terms this can only relate to an element of construction rather than to a material. The performance of even a simple eiernent such as a column or a beam is dependent upon such Faclors as the end conditions and the magnitude and distribution of any loading. Considering the behaviour of wood-based materials and solid timber when subjected to the developing fire, wood-based malerials will burn and are rherefore rated as combustible. Whilst the coznbustible nat~iremay be rnodified by the use of coatings or impregnation with flamelfire retarding salts, none of these can render timber, or its related products, non-combus~ible,albeit higher levels of energy may be needed to cause it to bum. Solid timber is not readily ignited and there are very few recorded cases where timber will have been the first material to be ignited. Solid limber will require surface temperatures well in excess of 400 "C if the material is to ignile in the medium to short term without the pressure of a pilot flame. Even when a pilot flame is present the surface temperature will have to be in excess of 300 T for significant time before ignition occurs. Timber tends to be used as the basis against which other materials are adjudged as timber is not considered Lo represent an unacceptable ignition risk in most environments. The actual values are related to the density, species, moisture content and shapefsection factor. Timber, being combustible will spread fire across its surface, the phenomena being a number of ignitions each triggering an adjacent ignition. As timber is not readily STEP/BUROFORTECI~I- an initiative under tile EU Comctk Progrumtne
A1311
ignitable the speed at which fame will spread across its suri'ilce is also reasonable for a combustible material. Nearly all countries will permit the use of untreated timber for low risk applications. The raie at which timber releases heat is obviotisly very dependent upon the nature of the initial heating regime, the availabililiy of oxygen and the density, shape and size the timber member being located. As wit11 all of the above properties, European countries each developed their own bencti scale tests for establishing the fundalnenlal performance of materials against these categories and as such there is no pan-European way of expressing the performance of timber against tliesc developing fire conditions. All coi~ntriesallow the use of timber in inany applications, indicating that its bchaviour is not considered to be particularly hazardous. When timber or wood-based materials are exposed to a fi~llydeveloped Sire they exhibit tiiany desirable characterislics. Whilst the exposed surfaces will ignite when the heat flux becomes great enough, and initially bum fairly vigorously it soon builds up a layer of insulating charcoal, see Figure 1. As wood is a poor conductor of Ileal there is very little transmission of heat into ren~ainingunburnt material. This has rnany benefits.
i r e I
Tlie charlges itr tirrll~errtrrdcr- tile it!flrtatce qj'jirz.: ( a ) chnrrecl tirrzher, (b) [~yralisislayel; (c) rbiher u~~affectecl I I fire. ~
in tile case of solid timber the core section remains cool only a short distance behind the burning zone. As a consequence the temperature or the residual section is cool and the construction does not have to accommodate darnnging thermal expansions. Also, because the core retilains cool, all of the cold slate physical properties of the timber are retained and any loss of loadbearing capacity is as a result of reduced cross-section, rather than a change in thc physicaI poperties. When wood-based slieet tilaterials are used in the construction of seperating elemnetits, both as structural riie~ubersand linings, the low thennal conductivity prevents the heat from being easily transmitted from the hot lo the cold face of the construction. The fully developed fire is chari~cterisedin tests by tile standard temperature-time curve given in IS0 834 (see Figure 2 ) or the equiilalent nalional standard. The relevant criteria are given as:
-
loadbearing capacity (separating and non-separating elements) integrity (separating eletnents) insulation (separating elements)
Critical deflection and rates of deflection are norrnally given as criteria for loadbearing capacity. The integrity is generally evaluated by means OF the development of gaps of excessive size (set nationaily) or the ignition of a cotton fibre pad. Insulation is deemed to be compromised if a mean temperature rise of I40 "C is experienced or a rnaxirnum rise of I80 "C is exceeded. STEPIELJROFORTECII - an initiative under tllc EU Cornell Progrdmmc
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-
-
ROD
Timber. will only lose loadbearing capacity when the cross-section of the non-fire damaged/residual section is reduced to the size wllere the stress in the section as a result of' the applied load is in excess of the strength of the limber. Timber-based materials will not fissure or shrink such that gaps Inay develop until the timber is so thin that burn-through is close and the rise in temperature will only exceed the criteria when tile thin, heat affected zone reacl~esthe outer face and again burn-through will soon follow. Timber is highly predictable when exposed to the rully developed fire conditions.
Fundamentals Timber and wood-based materials consist ~nainlyof cellulose and lignin, which the~nselvesare formed from carbon, hydrogen and oxygen. They are therefore combustible and it is alnlost inipossibie to make the112 incombustible. But complete incombustibility is only necessary in very rare specific cases.
Ii!j7ueitccs on the fire be1tnviou1The form, surface, dlape and the size of the cross-section of timber and wood-bused elen7ents are of great influence upon tl~eirfire behaviour. Combus~ibilityis dependent on the surface/volume-ratio. The grealer this is the inore easily ignition starts and the raster the flames spread. Many sharp corners and coarse surfaces enlarge this ratio and result in a less favourable fire bchaviour. Cracks and shdies also increase the effects of fire. Tllus thc charring rate of glued laminated timber, which is rnostly free of shltkes and cracks, is lower than for solid timbcr. The iiine taken for wood to ignite and for con~bustionto spread is dependent on the (oven dry) density. Thus different lcinds of wood behave differently under the influence of fire. The relationship between density and the rate of combt~stionis shown in Figure 3.
i r e3
Relcirions/ril~benvceri clcr~siryp atld rure rd' corrlbrr.stiott RC (Kollrrlorr~~ and Cord 1968).
The relationship between density and ignition is similar: the higher the density the longer it will talcc for the wood to ignite. The moisture content ol' timber is another i~iiporlantfactor inri~~ericing the bchaviour of timber wlien exposed to llre, 111 timber structures the rtloisture content is mostly between 8% and 15%. This inearis that for each tonne of wood about 50 to 150 kg of water have to evaporate before the wood will burn. The innucnce of the moisture content upon the charring rate need not be taken into account because of the low variation in tlie equilibturn moisture content.
Cltenzical artd pltysicni processes cii~ringtt~eco~rll>rr,stiorl qj' rvood When wood and wood-based materials burn, chemical decomposition starts with the resultant formation of charcoal and combristiblc gases. Spontaneous ignition of a thin strip of wood may occur within a range of temperature from 340 to 430 "C. But ignition is also possible at a much lower te111perature(e.g. 150 "C) if the piece of wood has been subjected to heat for a long time. Tcrnperrtt~iresunder I0O1'C but well above room temperature !leal up the timber and bring about a drying process. A decrease of strength and modulus of elasticity takes place. When tlie temperature of 100 "C is reached water begins to evaporate and steam takes the path of lowest resistance to escape through corners, arrises, joints, open pores and shakes. fn these places the timber dries more quickly. The temperature does not increase until all of the water has evaporated. Figure 4 shows the temperature below the pyrolisis layer, when the timber is heated according to the IS0 temperature-time curve and in relation to time. The figure shows that the temperature increases after the water has evaporated (100°C). The pyrolisis layer is the zone between the charred and natural timber where the wood has been aFfected che~nicallyby the fire but has not fully decomposed. Between 150 and 200 "C gases are generated which consist 70% incombustible carbon dioxide (CO?) and 30% combustible carbonmonoxide (CO). Once the temperature reaches 200 "C, more and more combustible gases form and the proportion of CO, decreases. As soon as the gases ignite the temperature on the surface increases rapidly. Carbonization of the wood then continues. The decomposition occurs in a the pyrolisis layer which is about 5 17rr)l thick. At temperatures above 500 "C the production of gas is very much reduced and tile
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STEPJEUROFORTECH an illitiativc lindcr the EU Comclt Programme
production of charcoal increases. This explains the appearance of timber after exposure to fire.
loo -
r
e4
Tetl~peratrttz,ill rlle Ileafed rirtrbcr i~elontlte pyrolisis lager (see Figitre 1 ) accor~i'irrgto !Ire I S 0 tcnrperartcre-tim cline (Figrrre 2).
The thermal conductivity of charcoal is only about one sixth that of pure solid timber. The layer of charcoal tlterefore acts as an insulant and tile decomposition of the deeper internal zones of tile remaining cross-section is tlius greatly retarded. Due to this effect and because of the low hear conductivity of tinlber tlle temperature in the iniddle of the cross-section is much lower tllnn on the surface. For this reason the fire resistance of timber is mucl~higher than genenliy supposed. The following Figure 5 shows beams and columns exposed to fire from 3 and 4 sides.
Figure 5
Benms a11d colruntir btifore mid crfier tile exposure lo,fire. ( a ) rerrrflinirrg crosssecfio~l, (12) clmrrecl titnbe,; fc) jire barriers.
Clt ar-ring rates Many lest resuIts for wood and wood-based materials hove shown a linear relationship between charring depth and time. A consrant charring rate can therefore be assumed for calculation of tlte fire resistance of' a section. TIte following charring rates p,, in Table 1 can be used for simple methods of struclural fire design (see STEP lecture B 17) without the need to take special consideration of the rounding of edges. Thus the residual cross-section is considered to be rectangular in fire design calculntions. The more acctrrale assesslnent of residual cross-section covering rounding of arrises allows n slower charring rate, in Table 2.
P,
STEP~UROFORTEC1-I- an initintivc under dm EU Comet1 Progmmnic
A 1 315
Material Solid softwood Glired laa~inatedsof'twood Wood panels Solid hardwood Glued laminated hardwoctd Oak Solid hardwood Gli~ecllatninated hardwoocl Plywood Wood-based panels EC5: Part 1-7,: 3.1
Tc/l?lc I
with with with with with
p, 2 290 kg/r1r3and min a 2 35 rtrm p, 1 290 kg/tri3 p, = 450 kSht13 anti t,, = 20 rnru p, 2 450 kghtl" pk 2 450 kS/trta
with p, with pI with p, wit11 p,
2 290
F;~~II'
2 290 k.g/tr$ = 450 kg/rrr\~~ld ti, = 20 rrrrrr = 450 kSht13i d ti, = 20 U I I I I
Desi,q~iclrar-ii~rgrores P,,. t,: tlrickrress f!"\tooorl utirl wood-bcrsec.1parreis, n: ~~~idtfl/dLptir of C I ' ( I . S S - S ~ C I ~ O I I .
For other densities and thicknesses of wood aticl wood-based panels the charring rate sliot~ldbe calculated as Po.p,r
= Po,ds,.o
kp
4
(1)
where
For closely packed inultiple layers the charring rate may be calculaled hased on tlic total thickness. in trtttdttrhr
Material SolirI softwood Glued latninated softwood Solicl harclwood Glued laminated hardwood
with pi 2 290 kg/tn3 with p, 1 290 kght? with p ,,,,,,,, 1 3 5 0 kg/trr3 with p,,,, 2 350 kg/rt~'
0.67 0.63 0,54 0,54
Tile shape of' the char-line at nrrises should be assumed as circular with a timcdependant radius according to Figure 6. For more coinplicated neth hods of structural lire design applicable for parametric fire exposure should be used the charring rate PI,,,, according Annex D in EC4: Part 1-7,.
STEPIEUROFORTECI-I
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Example Calculation ol' residual section rind second moment of area after 60 minute fire for a glulant beam (softwood, p, 2 290 k,S/rl13, b x h = 200 x 600 I I I I I I ) .
I
C I V S S - S C Cqf ~ ~SIUICIIII O I I bcanr.
7
Cnse I
p,,= 0,7 mndtnin 4,,,,,= 60 0,7 = 42 ~nrn Charring depth Residual cross-section area A, = (200 - 84) (600 - 42) = 64723 I I I I ~ " Second nlornent of area I, =
'
5583
12
= 1,68
. 10'
rm4
cnse 2 p = 0,64 /anr/rrlirr [I,.,,,,, = 60 . 0,64 = 38,4 nrnr Charring depth radius at arrises r = 30,O nmt (see Figure 6) Residual cross-section area A, = (200 - 76.8) (600 - 38.4) - 0,5 . 30' (4 - n) = 68803 nrtrl' Second moment of area
Reference ICollmann. F.F.Pand Calk. W.A. (1968), Principles of wood science and ~cchnoiogy.Volume 1, Solid Wood. Springer Bcrlin, I-lcidclbcrg, Gcrmnny, 502 pp. ISBN 0387042070.
STEPIEUROFORTECN
- :In inilioti\fc under lllc EU Cornctt Programme
A 1317
Detailing for durability STEP ICCLII~CA 14 G.Sagot Consuiting Stmclurai Enb'Tincer
Objectives To set out guidelines relating to the use of timber slructural members in a range of climatic conditions and limiting the need for preservative treatment withoul compromising the load-bearing integrity and durability of the timber or wood-based product.
Prerequisite A 15 Durability - Preservative treatment
Summary This lecture begins with an examination of the various conditions which Rvour biological attack by fungi or wood-boring insects (including termites). Particular attention is given to the influence of the geographical zone and its corresponding climate. Practical examples are provided which identify building details to avoid, and forms of construction which are recommended.
Introduction Timber is susceptible to biological attaclc whereas metal components may corrode. Biological attack is of two main types:
F~cngalntrnck This occurs in timber which has a high moisture content, generally between 20% and 30%. Fungi need the presence of water and oxygen to develop and the optimum moisture content varies according to the particular fungal species. The presence of fungal attack can seriously reduce the load-bearing capacity of timber structures. The loss of strength may be variable, depending on type of fungus and the extent of attack. Significant strength loss may be present, even in cases where the appearance of the timber remains largely unchanged. Where possible, the design of the building should minimise the situations in which structurnl timbers are sub-jected to 11jg11 rnojslure levels which allow fungal decay, Some fungi, such as Lenzites sepiaria, can survive through dry periods and continue their attack in timbers which are subject to intermittent wetting. Therefore, design should provide conditions which:
-
-
prevent wetting of the timber wherever possible; ensure rapid drainage and ventilation of the timber where it is i~npossibleto avoid periods of wetting; use timber with sufficient natural durability, or timber treated with an appropriate wood preservative, where it is not possible to avoid exposure to persistent wetting.
Irlsect nffrrck This is encouraged by warm conditions which favour their development and reproduction. Termites are particularly aggressive to timber, and are only active in the warmer parts of Europe. Their presence and activity decreases towards the STEP/EUROFORTECH - an ini~iativcundcr Ihc EU Comcll Propramnic
A1411
Northern parts of Europe. The presence of central heating within buildings may encourage the activity and development of insects by maintaining moderate teniperatnres during the coldcr parts of the year. Insect larvae may die if subjected to low temperatures. The development of cracks or splits in preservative treated timber which penetrate through the outer treated layer may provide sites for egg laying or the initiation of attack, significantly reducing the value of the treatment. The natural durability of different limber species in relation Lo insect attack is variable. In most timbers, the heartwood is normally durable, but the heartwood OF different timber species shows various levels of resistance to termite attack. The sapwood region may or may not be durable depending upon the timber species and the insect type. The sapwood of all timbers is considered susceptible to termite attack. EN 350-2 "Natilral durability of solid wood - Part 2: Guide to natural durability and treatability of selected wood species of importance in Europe" gives an indication of the durability to insect attack for comrnon timber species (Table I). In plywood construction, the natural durability may be enl-ranced by the presence of chemicals associated with modein synthetic resin aclhesives. Cornmerci:~l name Fir, Norway Spruce Larch. Douglas Fir, Maritirno Pine Scots Pine, Redwood Oalc, Sweet Chestnut European Beech, Popl:ir Tcrble I
Hvlotrunes SH S S nla n/a
Anobiurn SH S S
S S
Termite S
S S M S
Nut rtrcr 1 ~ilirclhiligrof tvood species ( S : .srrsce[>riblc,SN: hccr t.rrr~oorlolso .susceptible, h4: ttiode,n~clydtrrnble, rr/cl: rrnr~ap~~licc~ble).
Cost-osiotl oJ' lrreral cunrponettts In r~ormalservice conditions, timber is nor attacked by acids and bases. Metal cornponents should be protected against cor~osion,where necessaiy if the service conditions can affect their long term performance. Painted or coated metal cotnponents rnay be required to prevent staining of timber elements where appearance is a factor. Ci~issij'icatiottqf setvice conclirio~ts Tlte levels of exposure to moisture are defined differently in EC5 and EN 335-1 "Durability of wood and wood-based products - Definition of hazard classes of biological attack - Part I : General". EC5 provides for three service classes relating to the variation of timber performance with moisture content: Senlice c l ~ s sI is characterised by a moisture content in components corresponding to a te~nperatureof 20 OC and a relative humidity of the surrounding air only exceeding 65% for a few weeks per year (maximum 12% in the timber).
Service class 2 is characterised by a moisture content in components correspondi~~g to a temperature of 20 "C and a relative humidity of the surrounding air. only exceeding 85% for a few weeks per year (maximum 20% in the timber). Sen~iceCIISS 3 involves clirllatic conditions leading to higher t~ioisturecontents than
in service class 2. In EN 335-1, five hazard classes are defined with respect lo the risk of biological attacks: STEP/EUROFORTECI.I - an initiative under [lie EU Cornet1 Programme
Haznrd class I , situation in which timber or wood-based product is under cover, Tully protecied from the weather and not exposed to wetting; Nazc~rdclcrss 2, situation in which timber or wood-based product is under cover and fully protected fro111the weather but where high environmental htrmidity can lead to occasional but not persistent wetting;
Hcrznrd c1rrs.s 3, situation in which tiniber or wood-based product is not covered and not iu contact witli the ground. It is either continually exposed to the weather or is protected from (lie weather but subject to Srequent wetting; Ncrznrd clc1.u 4, situation in which timber or wood-based procluc~is in contact witli the groutid or- fresh water ai~dlhus is pennanentfy exposed to wetring; Nuznrfi cl~iss5, situation in which timber or wood-based product is permanently exposed to salt water. to The examination of these classes shows that service and hazard classes I ~~clate siniilar conditions as service and hazard classes 2. The service class 3, however, ellibraces hazard classes 3, 4 and 5, It is in these hazard classes that tlie risk of biological attack is tnost severe and requires greatest attenriorl to detail in the building design in order to reduce the conditions of timber exposure to those of the lowest hazard class. Timber in classes I and 2 may only require tnoderate or low levels of natural durability, or reli~ti~ely light preservative treatments to ensure satisfactory long-term performance. The risk of attack in hazard classes 4 or 5 excludes the use of glulam where this relies on preservative treatment to tile laminations before gluing and assembly, as tile subsequent planing necessary to produce a fiat surracc would remove part of the most effectively treated outer zones. 111 heartwood regions, where penetration is Iirnited, this may expose portions of untreated core. Suitable supplementary treatnient is necessary.
Designing for durability Many factors come into play concerning the durability of timber. Timber should be moisture content, appropriate to the installed close to the estimated equilibri~~rn building, so tl~otis only necessary to limit ~noisturevariation during tlie year. Timber which is installed at too high iI nloisture content or is directly exposed to weathering or where the climate conditions produce wide variations in air humidity is likely to show cracks or splits caused by shrinkage. These can expose unprotected timber in preservative treated material, allowing water and fungal spores to enteror- insect eggs to be laid beyond the protecled zone. Tlie designer has to consider moisture variation induced by: -
water i n its liquid state,
-
high hurnidily which in turn is affected by temperature.
In the liquid stale, water progression in timber is primarily parallel to the grain. This rnust be taken I I I ~ Oaccount by protecting the ends, either by keeping the timber out of situations wliere water can rise by capillary action or by treating the end grain in such a way as to limit further rnoistirre intake, for exan~pleby applying rcsins or epoxides.
STEPIEUROFORTECI-1- nn
initi:~tiveu~lclcrthc
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Comctl Programme
Examples of some situations which may result in high moisture contents in timber include:
-
Moisture will easily penetrate timber placed in warm, damp air, for example in poorly ventilated attics where ventilation shafts emerge.
-
Joints between timber elements or between timber and masonry constitute an area wltere end grain may be exposed to air if shrinkage occurs after drying.
-
Condensation can result in timber becoming cot. Condensation can be controlled by insulation combined with a vapour barrier. Drainage should be provided where condensation is likely to occur, e.g. at the base of glass walls.
-
Direct wetting will occur in titnber in ground contact, in door and window fiarties and in areas, where wind driven snow may collect. Consideration should be given to the risk of direct wetting in rooms where water is laid on, such as showers, bathroom, kitcl~ensetc. where there may be an overflow or splashing.
-
-
Water may become trapped bettind waterproof barriers in walls, in the ground or in mechanical joints, preventing its natural elimination by evaporation. Arrangements sliould be made to avoid the accumulation of water close to metal plates. Wetting risks are increased during storage on site and building erection prior to rooting. Timber stocks should be covered arid only be left on the site for the 111inirnum tiit~e necessary for erection, and one weelc at the most, especially in bad weather.
Prevention of fungal attack In the Decision Making Sequence (see STEP lecture AIS), it is possible to limit the preservation treatment 10 be applied. This decision making sequence applies not to tile overall building, but to each individuai structural member. If the insect risk exists in all classes in so far as their presence is reported in the region, the risk of cryptogarnic attack increases considerably, together with the hazard class. It is possible to reduce the risk through careful construction details, especially to reduce timber moisture content. It is, on the contrary, impossible to influence the extremes of temperature which depend upon [lie geographical siluatiotl and the rislc increases with the raising of mean temperature.
If it is impossible to stop water penetration, is usually possible to provide for a system of rapid water evacuation in order to avoid exceeding d ~ 20% e inoisture content litnit, or to limit the humidified zone. Solutions to this could be provided using a ciecompression space, a water pipe or a ventilation space.
The moisture content of timber is consequent upon a balance between water absorbed and water evacuated, and can be reduced where arrangements are made to retard uptake and promote evacuation. A good example is metal shoes at bases of colunins which wise the timber at least 100 /tit11 above the ground level and the cut foot is then Ieft in contact with air. In case of trickling, water does not collect, and if slight absorption of water occurs by capillary, it is evacuated by evaporation at the cut, as soon as the source of ~noisturedisappears.
Qnra
1
14t(t11joirlt prirzciple it1 titrlber c-otrstrnctior ( 0 ) air-~ighrjoinr. ( b ) rtleclrcrtlicnl os.senzbl~crlld ( c ) de~0111pre.~.siO11 SpCICe.
In horizontal or oblique members, the existe~~ce of longitudinal surface cracks increases the risk of penetration by conducting the water directly towards the inside of' llle piece, just where it is most difficrllt to evacuate. As far as possible, timber rmernbers ~ilustbe placed so as to avoid this phenomenon. It is advisable to set the Inn~inationsof glularn members with the heart upward as recommended by EN 386 "Glued laminaled timber - Perfornlance requirements and ~ninimumproduction requirements" (see Figure 2). Such oriented laminations reduce the penetration of water into surface cracks and facile drninage when the surface is subject to wetting. For the same reasons, glularn members which curve downwards concentrate water in the lower part withoiit any possibility of' evitcuation, and fungal attack is Inore likely to occur.
liigrrre 2
Dispnsiriott qf larrrirlariorrs irr exterior glrrlnnr; leff: rarldotr~orier~tatioirof ic~n~inarion.~: 1i~flrel.petietrafe.r i n ~ owood; right: nric~rtatecll~rtriinario~ts: itrater cntr escape (N'1imbleor. t~~'atecI tirrtbei.coi~eritigloitit ~~etltif~tiurl space orr top).
Prevention of insect attack I~~itiolly, the natural durability of the selected timber species should be established with respect to the particular irisecl species to which it may be exposed. It is also necessary to establish whether the particular insect is present in the region in which the timber to be used (see STEP lecture A15). Where a risk of insect attack to the timber exists, the timber must be treated with an insecticidal wood preservative. The application must be carried out before the timber is installed but as far as possible, after any machining or working of the surfaces. If re-worlring of the timber surfaces on site is needed, preservative treaiiiienl sl.~ouldbe re-applied to these areas. STEP/EUROFORTECI*I-
:in
initiative trnder ihc EU Cornet1 Rugramme
A 1 415
For stirfaces which can develop significant cracks or splits, and exposed untreated core surfaces, pcriodic maintenance treatment is required. Consideration [nust be given to the provision of free access to the timber surfaces. If this is not possible, a more intense preservative treatment should be specified, which penetrates to a depth greatcr than that to which subsequent cracks are likely to develop. This reduces the risk of the exposure of an unprotected timber core to insect atlack. Where a specific risk of attack by subterranean termiles is present, in addition to noimal protection by natural durability of wood or preservative treatment, the use of mechanical barriers between thc ground and thc timber may provide useful protection. This type OF termite produces a mud-covered gallery between the termite colony in the ground and the lirnber conlponents which it attacks. This protection may consists of a preservative treatment of the ground or a mecllanicat barrier. Thc use of iueclianical barrier- or caps enhances the visibility of the gallery if it is developed to a sufficient size to bridge tile barrier, Routine maintenance inspections to detect and remove the presence of the galleries is necessary and corisideration should be given to the access ability and visibility of surfaces linking the timber component to ground level,
Resistance to corrosion for metal fasteners and connections EC5 give exatnples of miniinusn corrosion protection or material specific9t' r ions necessary for different service classes. Sorne inore strict corrosion protection measures niay be required, for example in a chernical prod~~cts store, for salt and fertiliser storage, or in special plants sucti as phosphoric acid kictories where ir is esseiltial to use bolts, dowels and steel plates of the appropsiate grade of' stainless steel. Service Class Fastener I
2
3
Nails, Doweis, Screws.
None
None
Fe/Zn 25c"
Dolts
Norle
FefZn 12c
FclZn 25c"
Staples
Fe/Zn IZc
FeEn12c
Stainlesssteel
Punclled rnetal plate I'asteners and steel plittes up to 3 nlnl thick
FelZ11 12c
Fe/Zn l2c
Stainless steel
None
Fe/Zn 12c
FelZn 25c"
None
None
Fe/Zn 25c"
Steel plates over 3 t ~ t t t r in thickness
tjittt
Steel plates over 5
~nrtt
up to 5
'I For especially corrosive conditions consideration sliould bc given to Fe/Zn 40, hot dip coating or stainIess steel.
EC5: Pan 1
Examination of individual cases Clcrddirzg rlsecl for blncirzg Claddings are generally considered to be in hazard class 3. Boards are often piaced at 45" to provide racking resistance. Surface water is then conveyed preferably towards a "V" cut. A drain pipe must put in place at this spot so as io allow the water to evacuale quickly by gravity or by evaporation at the cut end of the board. STEPIEUROFORTECH
- ;in initiative under the EU Comet1 Rogrammc
Figtur 3
Detnililtg csa~ltplefor- cladclitrg joint wirh "V" crtr.
Exfer-tml colll~nits These columns are considered to be in either hazard class 2 or in hazard class 3 according to the measures required. The moisture risk is, in fact, very limited if the column is far from the ground. If no precautions are taken, the columns must be considered in liazard class 4, The base of columns of sheltered but. unenclosed structures must be set in place in such a inanner as to ensure efficient ventilation and to avoid any entry of water by capillary. The height of the timber above the ground varies with the climate and the risk of accumulated debris at that spot (see Figure 4). The post can be placed on a low wall but, in this case, the boitom end of the post must be treated to avoid the entry of water by capillarity; for example using epoxidc resin, r-ubber paint or asphalt.
Figtrre 4
E.~orl1pleof bnse
fflexterior colrcntrrs.
Edge beauts These lnelnbers are usually considered to be in hazard class 4. They are exposed outdoors to rain and sun and indoors to an atmosphere whicl~is often hot and damp. The classification can be improved by providing a ventilated surface covering, e.g. by a protruding roof, and by ensuring that the external coating is more permeable to water vapour tl~nnthe inner coating (see Figure 5). STEI:I)/EUROFORTECH - an initiative undcr the EU Comcll Programme
A 1417
r
e5
Edge beans detailing for limiter1 pcnetmtiorr of ulater; left: eaves, right: ( a ) itapour pernleai~lrand water-figltffi1t11, (b) vapoltr-tight filnl.
Special case of switnniitzg pools These constructions are subjected to moisture hazards from several sources: water splashes, from the pool or floor-washing, condensation on the glass partitions with dripping on the inside, rainwater on the outside, and with water accuiliulation on a level with the lintels. Great attention must be paid to leading this water towards contact for example, by placing, the the outer face of the timber, or to limiting base of the timber posts sufficiently above the ground. When ail precautions are taken, timber, in swimming pools, can be considered in hazard class 2, otherwise they must be treated according to hazard class 3 or 4.
Briclg.es mzd gnitgways These can be bare or covered. In the case of uncovered bridges and gangways, their classification in llazard class 3 or 4 is essential. In the case of covered bridges and gangways, the classification may be lowered to hazard class 2, especially if precautions ~ u taken e to coat horizontal beams open to driving rain or sun. Special attention must be paid to the protection of cantilever joints where these exisl. In all cases care must be taken to educe water accumulation due to rain and other causes.
Figure 6
Profecriort of bricIgc tinrber:
STEPlEUROFORTECH - an initintivc under [he EU ComeU Programme
Concluding summary If it is not possible to use durable naturally heartwood , the most important point for preservation against insect attack is to assure a continuous barrier with a preservative treatment. -
In order to limit use of preservative treatment against fungi attacks, it is necessary to prevent water ingress.
-
It is essential to provide a suitable outlet for water and waler-vapour in the event of accidental penetration of water.
-
If it is impossible to ensure that moisture content is below 20% the treatment prescribed for hazard class 3, 4, or 5 should be applied. In this case it must not be forgotten that machining takes off the nlost important part of treatment, e.g. by planing.
STEMEUROFORTECI~I- an initiative unclcr the EU Comclt Progmmmc
Durability - Preservative treatment STEP lecture A 15 L.M.R. Nuncs, P.P. dc Sous:\ Laborat6rio Nacional de Engcnhoria Civil (LNEC)
Objectives To explain the need for preservative treatment and to introduce the different types of treatment. To outline the specification of a preservative treatment for timber and wood-based panels.
Prerequisite A4
Wood as a building material
Summary Fungi and insects are tlie two main biological agents responsible for till~ber degradation it1 service. Tllerefore, their life cycles and types of action are summarized. The concept of natural durability is explained and tile factors influencing this timber properly are outlined. Different wood species have different natural durability, thus the concept o i durability classes emerges and is explained. Preservative treatments can be used to avoid timber degradation and the types of preservatives and methods of treatment are described. The specification of a preservative treatment for timber and wood-based panels is outlined. Future perspectives in timber preservation are also discussed.
Introduction Under ideal conditions timber can be in use for centuries without significant biological deterioration. However, if conditions are not ideal, many widely used species need a preservative treatment to be protected froin the biological agencies responsible for timber degradation, mainly fungi and insects. Prese~vativetreatments are cllernical treatments where specially formulated products containing biocides (fungicides andtor insecticides) are incorporated into Lhe timber in order to upgrade its durability against the biological attacks. These preservative treatments are normally applied to the timber before use; however they can also be applied to timber in service. Timber preservation is indeed a major issue. For example, this was demonstrated by the results of a survey carried out in 1980 involving Inore than two hundred Swiss architects (Sell et al., 1982), where, in opposition to the high rating of timber when compared with other building materials in terms of aesthetics, durability was clearly the major shortcoming of this material. I1 is obvious that it is very difficult to increase the use of structural timber witllout taking care that the durability of lhe material is assured during its intended life. When a designer proposes a timber structure, a doubt occurs frequently on whether 11e should specify for a preservative treatment for the timber and, iF so, what type of treatment and preservative should he reqirest. The answers to these questions are not always simple, as a certain number of inter-related factors should be taken into itccount. EC5 states these factors in a general way and also states that "the environmental conditions slzall be esti~natedat the design stage to assess their significance in relation lo durability and to enable adequate provisions lo be made Tor protection of the products". Moreover, with respect to tlie resistance to STEP/EUROFORTECI-I- on inilialive under the EU Comclt Progrnm~rle
A1511
biological organisms, it requests that "timber and wood-based materials shall either have adequate natural durability in accordance with EN 350-2 for the particular hazard class (defined in EN 335-1 to 3), or be given a preservative treatment selected in accordance with EN 351-1 and EN 460". 111 this lecture a background summary of durability and preservation of timber is given. The information will be linked to the package of European Sti~ndards(EN Standards) about this subject, already published by the European Committee for Starldardization (CEN) or in final phase of elaboration by the Tectinicai Co~nmiftee CENtTC 38 - "Durability of wood and wood-based products". These documents will apply in Europe in the near future and will help designers to answer tlie questions formulated above.
-
-
Biological agencies of timber degradation The two main biological agencies responsible for timber degradation are fungi and insects although in specific situations, timber can also be attacked by marine borers. Some notes about these agencies are given below.
Flr~zgi Taking into account the effect of their action, two types of fungi can be distinguished: wood-destroying fungi and wood-disfiguring fungi. The attack of the latter have nor~naHyno significant effect on the mec11anic;il resistance of timber as they only depreciate the aestlietic appearance of the material, without destruction of the cell wall. I-Iowever, este~isivedegradation of decorative coatings can occur due to the action of these fungi that include mould and blue stain fungi.
-
--.
On the other hand, wood-destroying fungi affect tlie mechanical resistance of timber and are of greater interest within the scope of this lecture. These fungi auaclr timber by rtieans of an enzymatic action that results in rot and they include the Basidiomycete wood-rotting fungi responsible for brown or white rot - so called due to the coiouration given to the timber attacked - and the soft rot fungi, which are grouped together on the basis of their ability to f o ~ mcavities in the wood cell wall, that leads to a surface softening of the timber and eventually to rot in depth. For the growth of wood-rotting fungi a moisture content higher than 20% is needed.
I~lsects Insects attack timber by opening tunnels which sometimes arc packed with bore dust. The two main types of insects causing tlie deterioration of timber are beetles (Coleoptem) and termites (1.soptem). Beetles are insects with a larvae cycle. The flying insects lay their eggs in cracks, splits, rough surfaces of timber or wood pores and, the resulting larvae penetrate the tiinber by boring tunnels as they develop. This is the dest~uctivestage of the life cycle; the adult insect will complete it after metamorphosis and the opening of tfle exit I~ole,which will probably be the only visible sign of the attack on the tirnber surface. There are several species of wood-boring beetles throughout Europe; the most colninon are the House Longhorn beetle (Hylotrupes I~ujirlrrs),the Common Furniture beetle (Alrobiiurl pl~ncintiwi), the Death Watch beetle (Xestobirrttt nfofovillosu~~) and the Powder Post beetle (Lycins brr/~~tieus). Although only attacking softwood, the House Longhorn beetle is by far the most damaging and it can cause Failure in structural timber, particularly when the sapwood content is high. Normally, beetles attack dry timber but they can tolerate higher values or moisture content. STEPIEUROFORTECI.1-
at1
initintivc i~ntlcrtlje EU Comet1 Programme
--
-
T e r ~ n i ~ eare s social insects tl~atbuild their nests in contact with the ground and forage over a distance for their food, building tunnels between their nests and the source of: timber, which should have moisture content conditions similar to those referred to for wood-destroying fungi (greater than 20%). This description applies only to the most important species found in Europe, the subterranean termites, namely Reticulitennes lucifugus and Reticulitermes santonensis.
Mnrine borcra In European rnarine waters the most common borers are the shjpworn~(Teredo spp.) and the gribble (Limnoria spp.). The stlipworm is a bivalve mollusc with larvae that settle on tilnber where they lodge by boring an extensive network of holes. The gribble is a small shrimp-like crustacean that bores into the timber surface, where it lives, making numerous side burrows and causing erosion on marine tirnber structures.
Presertce of bioiogicnl crger~ciesirt Errrope The biological agencies referred to previously are not present all over Europe. In fi~ct,a survey carried out by CEN/TC 38 in the different CEN Members (no data from Iceland and Luxembourg) sllows that there is a generalized rislc of fungi attack in all countries (with an insignificanr risk of' attack by some species in Austria and Italy) but the risk of attaclc by insects varies significantly from country to country linked to the average air temperature - as it is reflected in Table 1, resulting from that survey.
Ilousc Longhorn bccllc
R
R
R
1IL
R
R
R
R
0
L
R
L
0
Common Furnilurc bcctlc
R
R
R
I
R
R
R
R
R
R
R
R
R
Dcath Warch beetle
R
1
R
I
1
R
1
I R 1 1 0 O
I
I
Powder Post bectlc
R
R
R
O
R
R
R
R
I
O
Tcrmitcs
0
O
I
O
R
L
I
O
O
-
R Risk; I
TnDIe I
L
R O
O O
R R
- Insigtiiticnnt risk; 0 - Na risk; L - Locally prcscnt in khc counlry Nc~tiono/CIL'C~II'C~I~OIZS C O I I C ~ ~ Ithe ~ I t,isk ~ S of ffttcick by insects.
Timber properties related to preservation N(I[~{I-01 clur~lbili~y Natural durabilily of timber, understood as the ability to resist the attack of a biological agency without any preservative treatment, varies significantly fro111 timber species to timber species and, within the same species, it is greater in the heartwood than in the sapwood. In order to assess tlte natural durability of a timber species, a series of tests can be performed, and the results obtained usually lead to the attribution of a certain durability class to the different tilnber species. EN 350-1 "Durability of wood and wood-based products. Naturitl durability of soiid wood - Part I : Guide to the principles of testing and classification of the natural durability of wood" establishes those tests (field tests andlor laboratory tesls) and the criteria for the evaluation of the results, and defines a certain number of durability classes regarding the resistance to the nttilck of fungi, beetles, ternlites and marine borers. STEP/EUROFORTECH - :ln initiative under the EU Cornctt Progrnrnmc
A 15/3
However, natural durabiIity tests have been performed for a long tirne on different tiri~berspecies all over the world. The infonnation resulting from those Lests was gathered in EN 350-2 "Durability of wood and wood-based products. Natural durability of solid wood - Part 2: Guide to natural durability and treatability of selected wood species of importance in Europe", where, whenever possible, the durability classes defined in EN 350-1 are assigned to around 100 rilnber species, including softwoods and hardwoods. The use of this infortnation should be made, however with care, taking into account the criteria set in EN 350-2. For instance, the natural durability class assigned for resistance to Lirr~galattack, refers only to the heartwood, as sapwood is considered not durable for all tiniiber species (note that ~ t hardwoods is lower than in softwoods). sapwood c o n t e ~ in
Trentcibili~ The effectiveness of a preservalive treatment depends mainly on the amount of preservative that is absorbed by the timber and the depth to which it penetrates, although factors like distribution of preservative iiiay also pIay an impostant role in tllc effectiveness. The ease of titnber impregnation is naturally related to the type of product used and to the tiiethod of treatment adopted but it depends luainly on the degree of permeability and the moisture corltent of the timber. EN 350-2 also includes, for the tirnber species listed, an indicatior~ of the corresponding treatability, based on a four classes system (treatability classes). From this infonnation, it becornes clear that sapwood is much easier to impregnate than heartwood; in the end, it is quite possible that the durability of the sapwood of a certain tilnber species sub.jected to a proper preservative treatlilent becomes higher than the natural durability of the heartwood OF that same species.
Timber preservatives Timber preservatives are chemical products intended to increase tiriiber's resistance to the attack of biological agencies. They have usually been classified into three major types: tar oil preservatives, organic solvent preservatives and water borne preservatives. However, aqueous emulsion systerns are also now well established in timber preservation. Tar oil preservatives were the first to be used to treat timber industrially and include a set of different products obtained by distillation of coal tar; the most important products of this group are creosote and the anthracene oils. Due to its odour, difficulty to over-painting and general eco-toxicological ch~?racteristics,rnost countries have now restricted the use of this type of preservative to exterior works (e.g. transmission poles, railway sleepers) and immersed timbers. Orgarlic solvent preservatives are solutions of biocides (fungicides and/or insecticides) on a non-polar organic solvent that can be volatile or non-volatile. Products using a volatile solvent (e.g. white spirit) are the i~lostcornmon and can be described generally as light organic solvent preservatives (LOSP) or paintable preservatives; additives like water repellents and colouring agents rnay also be included. The lcey features of these products are the ready penetration on timber even when applied by superficial methods (edgebrushing, dipping) and the absence of dimensional changes of the timber. These products are widely used in joinery and cladding. Water borne preservatives are basically constituted by miner111 salts dissolved in water. The most common products belong to the group of preservatives known generally as "chromated copper". Amongst this group are chromated copper arsenate (CCA), chroitlated copper borate (CCB) and chrornated copper silicafluoride (CFK). STEPIEUROFORTECI-I- on inilioiivc undcr thc EU Comcit Programrile
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These products are nonnafly forced deep into timber, using pressure and the treatment requires tIie drying of the timber after treatment. Other water borne products like disodium octaborate tetrahydrate and sodiu~nfluoride are also used but their application is mainly by diffusion in green timber. Water borne preservative products are probably the most widely used in timber structures. Timber adequately treated with CCA is suitable for internal or external use and in situations where the risk of attack is high. Corrosion of inetal devices in contact with CCA treated timber car1 occur - especially if the moisture content of timber is high - and adequate protection should be provided. Lastly, it is important to point out that there are several European Standards (EN Standards) already published concerning the test methods for the evaluation of the effectiveness of preservative products. Actually, two EN Standards about preservative products with special interest for this lecture are in preparation: EN 351-1 "Durability of wood and wood-based products, Preservative-treated solid wood - Part I : Classification of preservative penetration and retention", prEN 599 "Durability of wood and wood-based products. Performance of preventive wood preservatives as determined by biological tests - Part 1 : Specification according lo hazard classes" and prEN 599-2 "Id. - Part 2: Classification and labelling".
Methods of preservative treatment Methods of preservative treatment of timber norlnally coinprise a set of techniques used to force a preservative product to penetrate into tlie timber iii order to get an adequate retention and penetration. There are several methods of treatment with different degrees of effectiveness. The right choice depends on the timber species and the retention and penetration values relevant to the hazard class. The following methods of timber treatn-lent are widely used: brushing, spraying, dipping, diffusion, double vacuum and vacuum pressure. The first four are nonpressure inetliods but, in the last two, pressure is needed and the necessary equipment includes a closed cylinder (autoclave). A brief description of these methods is included in Annex A (infonnative) of prEN 599-1, where the product penetration inlo the timber (defined according to EN 351-1) normalIy attained in those treatments is also given. Based on that infomiation, rt brief description of pressure methods probably the most appropriate for timber used in stiuchlres - is made. In the vacuum pressure method, timber is introduced into a closed cylinder and subjected lo a vacuum to remove air from the cells. The preservative liquid is then introduced and a pressure usually between 0,8 and 1,5 N ~ I I J Uis? applied. A final vacuum removes excess liquid from the timber surface before nonnal atmospheric air pressure is restored and the timber removed. This process, called "Bethel1 process" or "full-cell process" can be slightly changed on the "Rueping process" or "empty-cell process", in which the initial vacuunl is replaced by an air pressure, in order to increase the recovery of preservative during the finai vacuum.
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The double vacuum method is similar to rhe vacuum pressure ~netl~od ("Bett~elI" process) but the pressure applied is lower (less than 0,2 Nhnnr2)and the period of final vacuum is bigger. Furthermore, it is important to notice illat the vacuum pressure and diffusion methods rely heavily on water borne preservatives and can be used to treat timber even in the pole form. The use of organic solvent preservatives is usually restricted to the double vacuum rnetliod and superficial applications. With these treatments the tiinber sliould be at the finai dimensions and any areas exposed by subsequent cutting or drilling sl~ouldbe further protected. STENEUROFORTECI-I - nn initialivc u ~ ~ d cthc r EU Comclk Prognrnimc
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Specification of a preservative treatment for timber Previously in this lecture, a brief background concerning the biological agencies responsible for timber degradation, the timber properties related to preservation and the methods of preservative treatment was given, and relates closely to the standardisation work ongoing in Europe. This information will be useful now to answer the questions that designers are often facing with, as fortnulated in the beginning of this lecture. They concern the need of a preservative treatment for timber in a specific situation and the choice of the type of treatment and preservative product to be used. The answers to these questions will be also based on the EN Standards already published or in final phase of elaboration.
In orcier to deal with this problem, some basic data is still missing. They concern the assessment of the risk of attack by biological agencies of il certain timber piece in a specific situation and From this emerges the concept of hazard classes. EN 3351 "Durability of wood and wood-based products. Definition of hazard classes of biological attack - Part 1: General" establishes five hazard classes for timber and wood-based products and indicates the biological agencies relevant to each situation. EN 335-2 "Id. Part 2: Application to solid wood" defines those classes for timber and includes, in an informative Annex, a decision-making sequence to help designers to select a suitable titnber species for a specific use.
not he ;~cliicvcd by prcscrvi~tivc tr~atment
I I
be nchievcd by prescrvnlivc ~rentntvnc
I
prcsewalivc (5)i~nd
/ trcatmcnt
2) Scc EN 350-2 I ) Scc EN 335-1 tmd figure A.2 of EN 335-2 5) Scc prEN 599.1 3) Scc EN 460 4) See EN 35 1-1
Figure I
Gertelal cleci.sion-r~~nkilzirtg seqrtertcc for selectio~to f tit~thcrnppt.opriate to the Irazard cluss of use Urotri EN 335-2).
Figure 1 shows this decision sequence adapted from EN 335-1; it should be noted that all standards listed in this figure have already been referred to previously in STEPIEUROFORTECI-I- an initintivc t~nderthc EU Comctt Progrnrnme
this lecture, with exception of EN 460 "Durability of wood and wood-based products. Natural durability of solid wood. Guide to the durability requirements for wood to be used in hazard classes" that gives guidance on the selection of a timber species according to its natural durability for use in a particular biological hazard class. This decision sequence shows that a coherent system of EN Standards is in its final pllase of preparation to help designers in making decisions about this subject. The infonnation included in this lecture gives a general overview of this standardisation system but it is obviously not complete; therefore, the only way for a designer to take the right decisions when specifying a preservative treatment for timber is by careful consultation of tlie appropriate EN Standards that soon wiIl be in force in several countries of Europe and that will be probably adopted later on to a larger extent.
Specification of a preservative treatment for wood-based panels Wood-based panels are also extensively used in timber structures, namely, plywood, particleboards, fibreboards and oriented strand boards, and durability of these products should obviously be discussed.
It is important to emphasize that the majority of the infonliotion given so far also applies to wood-based panels. The main difference is related to the natural durability of these products, wliich depends less on the species than in the case of timber; in fact some additional factors Iilce thickness of particles and plies, fibre preparation, binder characteristics and quantity can also contribute to durability. Additionally, the equilibrium moisture content of a wood-based panel in a given environment, usually differs from that attained by timber of the same species from tvhicli they are ~nade. Taking this into account, prEN 335-3 "Durability of wood and wood-based products. Definition of hazard classes of biological attaclc - Part 3: Application to wood-based pal-rels" defines, siil~ilarlyto Part 2 for timber, different hazard classes for plywood, particleboards, fibreboards, and cement-bonded particleboards, the latter being considered to have an insignificant risk of attack in all hazard classes. Furtliern~ore,prEN 335-3 includes art informative Annex giving guidance on the suitability of different types of wood-based panels (characterized by appropriate EN Standards relating to tlie products) for use in tlie hazard classes. It is important to note that prEN 335-3 applies to non-coated panels, though, in timber structures, this will be the common situation. The natural durability of woad-based panels can also be increased by a preservative treat~nent.In this case, the preservative products used are normally organic solvents and the treatment is usually rnaclc, or by brushing, or incorporating a preservative product in the binder or in the plies during the fabrication. This latter method assures a greater protection than tlie first. Some innovative metllods of treatment like vapour boron treatment have, in recent years, shown promising features for the treatment of wood-based panels.
Future perspectives in timber preservation In recent years, two principal factors have provoked changes in treatment teclir~ologyand preservative products: the increasing cost of some solvents, and the even more iinportant concern over environ~nentalaspects of timber preservation, including air and water quality standards, and the effect of treated timber on man arid oti non-targeted organisms. STEP/EUROFORTECII - nn initiative urrdcr the EU Cornctl Programmf
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Most countries now have regulations regarding timber preservatives and Enany of tbern do not allow the use of certain active ingredients such as dieldrin. TraditionaI organic biocides, like creosote, pentachlorophenol or lindane are partially rest icted as well as the inost comrnonly used water-borne copper-chrome-arsenic forrnulntions. Nowadays, several products, either new or rediscovered, are already being introduced into the market and these include: borates and copper naphthenates or organic and organometailic systems like isothiazoles, chlorotalonil, thiazoles and r triazoles. Environmental health and safety requirements point lo the use OF preservatives that cornpty with the following characteristics: the preservative should be non-toxic lo hurnans and to the environment or at least be rendered non-toxic rviten fixed in the limber; the treatment should be carried out when the timber is in its Final shape in order to minimize treated timber waste; plant operations should exclude e~tlission of toxicants and there should be no soil, air or waterway contamination; and redundant preservative treated timber should be recycled or disposed of with minimal environr~lentaldisruption.
Reference Sell J. et al. (1982). I-folz in1 Bauwescn. Report No. 210, Swiss Federal h h o r a ~ o r yfor Maierials 'Testing and Research (EMPA), Dllhendorf, Switzerland.
S'l'EP/EUROFORTECM
- an initiative under the EU Cornctt
Programme
Environmental aspects of timber STEP lccturc A 16 T.Viitavnincn 'I'echnicnl Research Ccntrc of I=inland (VT[T)
Objectives To give a global overview of the major potential environmental i~npactsof timber, in all stages of the life cycle (from "cradle to grave"). To discuss the method for assessment of environmental impact.
Summary The environmental aspects of building materials, and thus of timber, are gaining more weight ns selection criteria for application in constructions. As this is a relatively new research area, methods for assessment of the environmental impact of wood are under develop~nenr(e.g. Life cycle assessment). The environmental aspects of timber in general are regarded as positive, as conipared to otlter buildirlg materials, the main reasons being that
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wood is a renewable material,
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the European forest is a sustainable source of timber,
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the positive effect on the Global Warming or Greenliouse Effect of the earth, by reducing the CO, level during production in forests and by replacement of fossil fuel by wood in the waste stage,
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the general low energy requirements for production,
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the potential for reuse, recycling or energy production, thus producing a ~l~inilnum of waste.
The areas that need more environmentally friendly alternatives are gluing, wood preservation and coating. Emission of organic voIatile compounds (e.g. forinaldehyde, hydrocarbons) froni glues and paints and emission of components fi-orn preservatively treated tirnber are the major potential environmental risk factors.
Introduction Environmenlal aspects have become, along with tecflnical and econornic aspects, increasingly important in the evaluation of products. Environmenlal aspects have gained inore and more attention in legislation, product approvals, standardization, and in the consumers' choices and preferences. Environmental labelling systems are increasing and different steering measures are being introduced in order to reduce the overexploitation of nntural resources and to avoid pollution and environtnental risks.
Environmental assessments of materids and products Environmental consequences of the use of a certain material or a product must be evaluated from "cradle to grave", that means over the whole life cycle of the product. In the assessment, the consumption of inaterials and energy and the effluents to the environment over the life span are considered. The methodology of the life cycle assessrlient (LCA) of materials and products is still in the developing phase. A number of LCA methods have been proposed, some of thein mainly concentrating on the inventory of environmental data over the life cycle, some also STEP/EUROFORTECI.I - an initintivc under thc EU Corneit Programme
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proposing steps for the evaluation of environmental consequences. It is, however, vely difficult to estabIish uniform criteria for the assessment of different types of environmental impacts. The need for guidelines for LCA has been identified and among others, the Society of Environmental Toxicology and Cf~emistryas well as standardization organisations IS0 and CEN are working in order to produce a code of practice.
In this paper, environmental aspects of timber and wood products are discussed excluding pulp and paper. Wood products are mainly used for building and construction, for packaging and for furniture. Previously few LCA studies have been made for wood products. The environmenial assessment of wood products should include harvesting and transport of wood raw inaterial, industrial m a ~ ~ u h c l u rofe the product, transport to the site of use, building process or installation, period of use including maintenance, demoiirion and management of wastes. For each stage, an input-output calculation shall be made and the total environmental effect evaluated on the basis of the calculations. In order to evaluate the environmental impacts of the use of timber one should also be able to compare those itnpacts with the use of other, alternative ~naterials.The most important alternatives for timber and wood products are concrete and other ininerai materials, steel, aluminium and other metallic materials as well as plastic materials and different co~npositematerials. It is generally accepted, that wood has environmentally fiivourable properties in comparison with many substitutes. Tlle most important Fact is that wood is a renewable raw material. Wood products require relatively little energy and cause little pollution to the environn~ent.It is 110 longer, however, adequate to refer to these qualitative statements; the environmer~tal itnpacts IIILIS~ be corlfirined quantitatively. In the future all producers will have to demonstrate the consumption of energy and resources as well as the emissions to the environment caused by their products. Iir~paclslo be :tsscssed
Structural liPc span Felling, trilnspon of logs
Industrial processing
Use of wood producks
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to soil 10 watcr
Demolikion, waste tnanagernelli - -
Timber resources and harvesting The world's forested area is estimated to be about 5 billion hectares, of which just under 3 billion hectares are closed tkrests. Over half of the forests are in temperate STEPIEUROFORTECI-1- iln initiative trnclcr the EU Comett Programme
and cold areas. Historically, lnan has destroyed and reduced forests on enormous areas by clearing land for agriculture and other uses and by forest felling. It has been estimated that only about one third of the world's original forests still exist. The rate of deforestation during the last decade has been about 17 million hectares per year. Deforestation is mainly taking place in tropical forests which disappear by 1,8% per year (Dudley 1992). Also Europe has seen large scale forest losses in the past, particularly in tlie south and in the Mediterranean area. Currently, the forest cover is estimated to be around 160 nill lion t~ectares(the European part of the former USSR is not included). Contrary to the historical generalisation above, the last 100 years have been a period of net gain due to positive afforestation and conservation legislation. Also the annual growth of forests per unit area has been increasing thanks to effective silviculture and forest improvement. The estimated ainount of timber in the European forests in 1990 was 18,s billion n13. The annual net increment in 1990 was estimated at 584 n13, which is 20% bigger thim the estiniate in 1980. The annual production of roundwood in Europe in 1990 was nearly 400 rnillion 111" which is about 1 1 % of the total world production. The annual harvesting in Europe is 25-30% s~nallerthan tlie annual net increment (FA0 1992). Deforestation and forestry practices have become items of serious concern in the international environmental debate. The disappearance of forests is a most serious ecological threat to the earth and most countries have now bound themselves to sustainable forestry. Also, the member countries of the International Tropical Timber Organization (I'lTO) have decided that the international tropical timber trade should be brought to a basis of sustainable production by tlie year 2000. Earlier, tlie maintenance of the productive capacity of forests has been emphasized as the main measure of sustainability. In the future it will be necessary to pay attention to more complex enviroillnentaI goals such as protection of the forest ecosystem as a whole, conservation of biodiversity (abundance of species) and protection of' culrural, recreational and aesthetic values. The United Nations Conference on Environment and Development (UNCED) in Rio in 1992 produced a number of decisions for the protection of forests. Also, the users of timber have started to dern;uld guarantees for that the Limber originates from ct sustainable forest. Logging changes the ecology and e~ivironnienlalconditions of the forest in many ways. Nulnerous forest plant and animal species require specific habitats in order to flourish. In today's Europe there is very little native or old growth forest left. Native forest areas and special biotopes are, as a rule, excfuded from commercial exploitation or placed under regulated timber production. The issue of the sufficiency of conservation areas and natural parks has, however, been a subject of constmt debate. In Europe, commercial forests are normaily well tended. Confrontations ]lave ellierged, however, between the forestry practices used, clear cutting in particular, forest values. The forestry sector has taken heed of the and noncor~~~mercial criticism and management practices have been modified Lo be Inore compatible with natural phenomena. It continues to be a challenge to European forestry to develop and improve utilization methods that are both efficient and based on tlie principles of sustained yield accompanied by a keen awareness of environmental issues. To ensure this, European countries have increased international efforts in research (e.g. European Forestry Institute establisl~ed in 1992) and created n~onitoringmechanisms (e.g. Minislerial Conference on the Protection of Forests
in Europe in 1992). An existing threat to the European forests is the decline in tree health caused by the inlpact of atmospheric pollution and acid deposition. In particular, northern conifer forests are sensitive to air pollution. International cooperation is absolutely necessary in order to reduce pollution.
Forestry and greenhouse effect Wood material is Formed by the assimilation by trees of carbon dioxide, water and solar energy. Wood is an important part of the short-term civbon cycling on Earth. Atmospheric carbon dioxide fixed by trees is fiteststored in living trees and later in wood products for tlundrecb of years. By deterioration or combustion the carbon is released back in to the atmosphere and fixed again by trees. Carbon dioxide is the tnosl important ol' so called "greenhouse gases" in the atmosphere. Its concentration in the atmosphere i s constantly increasing because of the irtcreased use of fossil fuels. The increase of greenhouse gases causes warming of cliinate which is considered to be one of the most important environmental problems ahead us. There are also indications that the increase of carbon dioxide !nay play a role in the depletion of tile ozone layer particularly in the northern hemisphere. In order to act against the greenhouse phenomenon an international agreement (entering into force in 1994) has been made to oblige countries to reduce emissions from fossil Cueis. The greenhouse phenomenon can also be reduced by increasing the binding of carbon dioxide in forests and in other. biomass. This has actually happened in Europe as the surplus of annual increment over annual felling in forests has increased. However, the net fixation of carbon dioxide cannot be increased simply by reducing the felling. An old forest will reilch a saturation point where the fixation is balanced by the release of carbon dioxide by decay.
Solar energy
Fonniltion of wood
I
l++
-l Wood prwducls
In the combustion of wood solar-derived energy is released to be used for the production of heat or electricity in order to substitute for fossil fuels. Tile carbon dioxide released by cotnbustion does not increase the net carbon dioxide level of the atmosphere because only the same carbon dioxide is released back that was originally bound from the air into the wood material. This carbon dioxide would, in any case find its way into the atmosphere even if wood were not used for energy production but left to decay. On the other hand, the increase in the amount of
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carbon dioxide in the air will be restrained, if ~.enewablewood lnaterial is used to substitute for fossil fuels or as an alternative for products which require more fossil fuels in production.
Environmental impacts of forest industry From the environmental point of view, every industry should mdce the most of its raw materials while minimizing the harmful effects on the environment. Wood maierial is utilized fairly coinpleteIy by the forest industries even if large amounts of by-products and waste wood are produced in single processes. The yield of sawn tirnber for instance is only about 50% of the round wood volume, but the byproducts are used for the production of pilIp and paper, reconstituted boards etc. Bark and other wastes unsuitable for raw material are utilized for energy production. The manufacture of wood products requires in general less energy than the manufacture of alternative products of other materials. It is very difficult to give exact figures of energy consumption because the production systems may vary widely. The figures presented in the literalure often lack information on the lneans of calc~ilationand on the system boundaries. Regarding the pollution resulting from the energy production, the source of energy used is very decisive. A considerable proportion of the energy in the wood industry is produced by burning bark and wood wastes, about 80% in the sawmilling industry. Even if the energy demand in the wood industry is low, there still is a continuous need to strive for energy economies in order to keep the advantage. The pl-oduction phases that require most energy are drying of wood and heat pressing (panel products). Malerial timber Glulnm Pnrliclc board Fibreboard Plywood Cement Concrelc Bricks gyp sun^ board Steel PVC pl:~stic PU plastic Aluminium Sawn
Primary cncrgy content kI.YII/kg
kWlAtr3
0,7
350 1200 2210
2,4
3,4 3,4 5,4 1,4
0,3 03 2,4 5,9
1 S,O
40,O 52,O
3400
3240 1750 700 1360 1820 46000 24700 1800 141500
Among the different industrial branches, forest product industries itre considered fairly harmless to the environment. In the sawmifling industry, environmental impacts are caused by water storage of logs because of dissolving bark and wood substances. Environn~entalproblems are also caused by noise, smell and handling of wastes. The most serious environnlental problems have been connected with the use of toxic blue-stain preservatives (chIorinated phenols in particular), which may have polluted soil and watercourses. These have nowadays been replaced in most STEPIEUROFORTECH - nn initiative undcr thc EU Cornctl Progrnillme
A 1615
countries in Europe by less harmful chemicals and the need for their use has diminished due to efficient kiln drying practices. Even if the qualitative environmental problems are fairly well known in the sawmilling industry, much more research is needed in order to find out quantitative emissions into soil, water and air. Research needs regarding the effects of floating, water storage of logs and barking, impacts of blue-stain preservatives, emissions From drying kilns and from energy production, dust, mould spores and volatile organic emissions from wood should be considered. In the joinery and furniture industries, problems to the environment are caused by different additive materials, by hydrocarbon emissions to the air, noise, dust and waste treatment. The most acute problem is surface finishing. Ciirrenlly used finishes and lacquers are mainly based on organic solvents. The new European directives will presume sigriificant reduction of organic solvent emissions, which will require installation of cleaning eqi~iplnentor change of finishing systems. Today the general trend is towards water-based and bio-based finishing systems. In the panel products industry, problems are caused by adhesives that may create harmful emissions and problem wastes. Problems may also emerge from coatings and various additive materials. From the environmental point of' view, one of the problem areas of the forest industry is tirnber impregnation plants. The most used chemicals have been CCAsalts and creosote oil. These give good durability to timber but are more and more considered questionable from the environmental point of view. In rnany old plants soil and sometimes even ground waters havc been contaminated by toxic preservatives. Due to more advanced technology, better environmental protection and waste management, the conditions are usually satisfactorily controlled in modern plants. A new European standard for treated timber is under preparation. It will include a whole range of impregnation classes so that the level of protection is better adjusted to the need of protection for the particular end-use. Development work is under way in order to find new, environmentaIly more friendly concepts for preservation.
Transport Logging and transport of logs require sorne energy (oil, diesel fuel) and cause disturbance and destruction to the forest nature. Nowadays, vegetable oils may be used instead of diesel oil in harvesters. The transport of logs and of finished products accounts for only a s~liallshare, usually only a few percent, of the total energy consumption and emissions over the life cycle of forest products. For environmentat calculation, data on the means of transportation, the average distances and types of Fuels used are needed.
Wood in use Timber and wood products are generally safe in use and cause very little effect on the environment during utilization. In recent years there has been growing interest in the health and safety aspects of the indoor climate and building materials. Many building materials emit different volatile organic compounds (VOC) that may cause health problems. The knowledge of the emissions from different materials is still very poor. Regarding wood-based STEPIEUROFORTECII - an initiative i~ndcrl l l e EU Comcu Programme
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products, formaldehyde emissions from certain adhesives and finishing materials 11ave created most concern. The problem was most acute in the case of ureaformaldehyde glued particleboards. Nowadays, very strict regulations have been set upon the formaldehyde emissions from products and the problem has been overcome by changes in the glue composition and in the manufacturing processes. Wood contains slnall amounts of different extractive compounds, e.g. terpene compounds, that are volalile and rnay be perceived as the typical smell of fresh wood, Tile amounts emitted are very small and depend upon the age of tile wood surface. No connections have been proven between these emissions and health problems but some of the terpene compounds are considered to produce allergic effects. Durability of a product is also an environmental aspect because it may dictate the service life of the product. Timber constructions when properIy designed have good durability. If the moisture stresses are too high, unprotected wood is susceptible to biological deterioration like growth of mouId and decay fungi. As well as reducing durability, growing fungi produce bad smells and their spores may give rise to health problems.
Demolition and waste management Increasingly strict requirements for the management and reduction of wastes are expected to affect aI1 producers more and inore in the future. Nowadays, the building sector produces large amounts of waste both at the building site and on demolition. There is a growing demand for increased reuse and recycling of building materials. After the first period of use, timber or wood products can be reused in other constructions, recycled (manufactured into new products like reconstituted boards) or used for energy production. From the point of view of waste managenlent, wood has an advantage over many materials in that it is easily degraded biologically in nature. However, reuse or recycling or utilization for energy production should, as il rule, be preferred to disposal by dumping. Considerable environmental advantages can be gained by increased utilization of wood products for energy production after the period of use as a construction material. The theoretical energy content of wood varies with ntoisture content and density. The effective thermal value of dry wood fuel is 5,3 - 5,5 kWlr/kg. Combustion of wood produces, in general, similar emissions to combustion of other fuels. The main difference is thal wood cornbustion does not produce notable sufpl~uremissions. The quality and amount of en~issionsdepend upon the burning conditions. High temperatures are required for complete combustion of organic compounds. Wood ash con be used for soil fertilization. Burning of moist wood or improper combustion conditions can result in high einissions of carbon monoxide and hydrocarbons. Special requiren~entsare set on the burning of wood products including citemica1 preservatives, certain adhesives or additives, which may produce toxic emissions or in the case of inorganic compounds, concentrate in the ash. Wooden products and constructions are seldom made of pure wood but combined with several other ~naterials,which may ~nakereuse or recycling more difticult. STEP/EUROFORI"ECH - an initintivc undcr [he EU Comctl Programme
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There is a need to pay more attention to the aspects of reuse and waste managernenr already in product development, planning and design phases.
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Concluding summary
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Wood is a renewable raw material when it originates froin a sustainable forest. Wood material is fortued in living trees from carbon dioxide and water by means of solar energy.
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European forestry is based on susrai~lableyield. However, there is a need to develop the forestry practices further so that felling will cause as little destruction to the natural environment as possible.
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The use of: renewable wood inaterial will help to reduce reliance on the remaining resources of nonrenewable materials.
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It is ei~vironmentallysound to use tilnber fro111European forests efficiently. If the forests are underexploited, tilnber has to be substituted by other materials which are likely to produce Inore impact on the environment than the use of timber.
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Forest industries cause r.elatively little pollution to the environment and the irnpact is further diminishing with the n~odemizatioi~ of d ~ eproduction processes. The industry should, however, monitor the a~nounlsof effluents and other impacts more closely and colltinue to minimize these impacts.
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Regarding forest products, environmental concerns are often caused by materials other than wood: preservatives, adhesives, finishes etc. Development work is needed to introduce environmentally Inore friendly alternatives to many of the present materials.
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Wood is easily degraded in nature, which is an advantage concerning waste management. Wooden wastes should, however, in rlle first place be reused, recycled or utilized for energy production. As wood material forms a part of the short-term carbon cycling, the co~nbustionof wood does not increase the net level of carbon dioxide in the air. The increase in the level of carbon dioxide can be counteracted by using wood to substitute for Fossil fuels or for products that require Inore fossile fuels in production.
References Dudley. N.(1942). Forests in uoublc. A rcview ofthe sraius of [emperate forests worldwidc. WWF. London, England. 260 p. F A 0 yearbook 1490 (1992). Forest Products. F A 0 krcstry Series NO. 25. Rome, Italy. 332 p
STEMEUROFORTECI-I - an initilitivc nndcr tl~cEU Comctt Programme
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Serviceability limit states Deformations STEP lecture A 17 S. Thelnndcrsson Lund University
Objectives To explain the motives for the control of deformations and to describe liow deformations in timber structures can be estimated during the building lifetime within the context of EC5.
Prerequisites A2 Limit state design and safety format A19 Creep
Summary Short- and long-term deformation behaviour of timber as influenced by climatic conditions and load variations is briefly described. Various reasons for the control of deformations in timber structures ilre discussed and criteria for serviceability design are suggested. The formal calculation method proposed in EC5 is presented and a design example for the serviceability limit slate concludes the lecture.
Introduction The overall performance of structures sl~ouldsatisfy two basic requirements. The first is safety, usually expressed in terms of load bearing capacity, and the second is serviceability, which refers to the ability of the st~ucturalsystem and its elements to perform satisfactorily in normal use. It is generally understood that violation of the safety criteria may cause risk to human life and substantial damage, whereas violation of serviceability requirements rarely leads to risks for humans and usually involves lower economical losses. On the other hand, the overwhelming majority of structural defects actually observed in practice are related to serviceability. For this reason, the question of serviceability is very important in stn~ctrrraldesign.
In the case of horizontal tin~berelements, serviceability requirements with regard ro deflections and vibrations are very often decisive for the structural dimensions. This lecture deals with ser?iliceabilily related to deformations in timber structures.
Deformations in timber structures during the building lifetime The fact that variable loads (such as imposed loads on floors and snow loads) often dominate in timber structures means that the deflection will vary considerably during the lifetime of' the structure. This llas to be considered in a rational serviceability design. Figure 1 illustrates the deflection history of a beam loaded with per~nanentload and snow load (see Mktensson, 1992; Theiandersson and Mbrtensson, 1992). The total deflection can be subdivided into one part 6, due to permanent loads immediately i~fterloading and one part 6, which is variable during the lifetime of the structure. The variable part 6, consisrs of a reversible portion 6,,,, which is present only during limited periods when the variable Ioad is high, and n continuously increasing poltion 6,,,,,,, which for all practical purposes Inay be considered us irreversible (Mktensson, 1992). Sllort duration load peaks, such as those illustraied in Figure STEPIEUROFORTECI-i - nn initinlive under tl~cEU Cornctt Programme
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1, occur both for snow loads and imposed loads in most common types of buildings.
IMk,
'2, irrsr
I
Figlire 1
x
6.
Tin~rvariation iri principlefor clejlccriori of n bean1 ivit11pcrtrratlertt (G) atlrl varialrle (Q)lorrds. Cfrnle A shows the deflectioil if the Dcatir is loaded with the c11aracteri.sticloclrls G, + Q,d~rrirrgtlie ,t~lioleperiod F is t t ~ rload S the deflrctioiz and t tile tirite iri jrec1r.s.
Hence, for design purposes, the following deflection components lnay be defined with reference to Figure 2':
6;
is the precamber of the beam in the unloaded state (0).
6,
is the beam deflection due to permanent loads immediately after loading (state 1).
&2
is the deflection of the beam due to variable loads plus any time dependent deflection due to permanent loads (state 2).
6,,,
is the sagging of the beam relative to the straight line joining the supports.
'
The llotation 6 for deflection is used hcrc in n conceptual sense. In EC5, wllere lt~enotation u is used. the definitions of deflection components arc siigtiily different from those in Figure 2.
STEPIEUROFORTECH - :In inilit~tiveundcr the ELI Conlett Programme
Figlrr-c 2
Deflectiot~co~lrponeatsfor a siltrply srrppor-fed ileanl.
Normally both 6, and 6, are fixed wher~the construction work is completed and do not change during rite lifetime of the structure (unless the permanent load is changed). The components 6, and ti,,,,however, will vary during the lifetime of the structure.
Load combinations for the serviceability limit state ECI:Part 1: 9.5
The basis of design common to all Eurocodes, specifies different types of load combinations which may be used for verification in the serviceability limit state. Two of these, the characteristic (rare) combination and the frequent combination are of interest in connection with timber structures. The cltaracrerisric coi~ibir?atiorlis intended for use mainly in those cases where exceeding the limit state causes significant damage or unacceptable irreversible deformation. The symbolic definition of this combination is:
~ h e p e ~ u e tcont~irmtion lt is intended For use mainly in those cases when exceeding the limit state is associated with minor damage or ~xversibledeformations. The symbolic definition of tlie frequent combination is:
In the above expressions Gkjand Q,,{are characteristic values of permanent and ~ ,!11~,, ~ Qti and ' L I ~ Qkei ~ represent .~ the variable loads, respectively. The ternis ~ y Q,,, combination, the frequent and the quasi-permanent values of variable load Q,, respectively.
Limitation of deformations The most common reasons for the limitation of defor~nationsin structures are: -
general utility and appearance (e.g. to limit annoying visual effects and to avoid sloping floors),
-
structural requirements (e.g. to avoid damage to non-structural elements such as partitions, doors, windows and claddings and lo guarantee smooth assembly, water tightness, drainage of roofs),
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equipment requirements (e.g. to guarantee proper f~~nctioning of machinery, pipes, cables, ducts and their supports).
Modern codes like EC5 onIy give functional requirements in general terms stating that structures sl~ouldbe designed in such a wny that serviceability aspects such as those listed above are considered. Specific numerical limits of deflection or slope should in principle be decided by the structural engineer from case to case, depending on the actual situation and the demands of the client. STEP/EUROFORTECH- iln initintivc under ihc EU Comclt Programn~e
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Deflection criterion to avoid significant damage A typical case is when excessive deforn~ationsmay cause significant damage to partitions, instaIlations, fixtures arid finishes. In this case the risk of exceeding the deflection limit should be kept at a low level. Therefore, the deflection should be calculated using the characteristic load combination defined by Equatiotl (1). The damage is ~iormallycaused by deformations occurring after the constnlction work is completed and a deflection criterion for sit.trations where significant darnage can be expected can be written as:
where ti1 is defined in Figure 2 and 6,,,,, is the critical value of the deflection generally depends on the nature and detailing of causing damage. The limit 6,. the elements which could suffer damage. In the absence of more precise information 6,,<,, could be taken as a fixed value, say 30 111111, or a certain fraction of the span Q, say U300 for a simply supported beam and U150 for a cantilevered beam. These values are often recommended for beams in floors arid roofs which are in contact with partitions and non-structural elements.
Deflection criterion related to appearance and general utility From the point of view of' appearance and general utility it may often be desiritbie to avoid excessive deflections which are permanent or occur over long periods. Occasionnlly exceeding the detlcction limit may, however, be acceptable if the deflections are reversible and limited to short periods of time. In this casc a somewhat higher risk of passage of the Iimit can be accepted and the deflection may be calculated on the basis of the frequent load combinatio~tdefined in Equation (2). An appropriate criterion for this case is:
-
-
where 6 , , , is defined in Figure 2 and S,,,, is the acceptable deflection limit with respect to appearance and general utility. The value of 6,,,., depends on a number of factors such as type of building, type of structure, whether the beam is visible or not, tile attitudes of the building users, etc. For instance, the requirements are normally ii~uchhigher in residential buildings than in industrial buildings. As a general recommendation the value 6,,j,,., = U250 may be given.
EC5:Part 1-1: 4.3
Deflection limits recommended in EC5 EC5 gives some recotninendations for limits ofdetlection which may be used in the absence of more precise information. All limits given in EC5 are related to the chai-acteristic load combination, Equation (1). with ipo in the last term replaced by yf,. In cases where it is appropriate to limit the instantaneous deflection 112,i,tsc due to variable actions the criterion II,,~,,.,~ IU300 is recoml-~iendedfor a beam on two supports with length Q.This criterion can be relevant for example when excessive deformation rnny cause darnage to non-stnrctural elements. In cases where it is appropriate to limit the final net deflection it,,,,p,, the criterion rt,,,, < U200 is recommended. This criterion can be relevant when the deflection control is motivated by requirements of appearance and general utility. This limit is more liberal tllan that given above, since in this case the criterion is related to a more severe load combination.
STENEUROFORTECI-I- an iniliativc under tile EU Co~neltProgrnmmc
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Calculation of load induced deflections based on ECS principles The instantaneo~isbending deflection it,, can usually be calculated from elementary beam theory using formulas given in standard textboolcs and manuals. Since the shear stiffness for wood is comparatively low, shear induced deflections may sometimes be significant. The detlection u,, due to shear can be calculated by the well established theory for shear deformations of beams. The total instantaneous deflection liinr, is the sum of it,, and u,,. To get an idea of the significance of shear deformations, consider a simply supported rectangular timber beam with uniformly distributed load. For this case, the ratio between shear deflection 14,. and bending deflection ir,, at the mid span is approximately given by:
The ratio E/G is approxirnateIy 15 for timber and glulam. Tllus ~ r , / l c , , , is roughly 0,15 for Plh = 10 and less than 0.05 for elh = 20. For a concentrated load at the mid span the correspondi~~g ratio is about 20% higher. The long term deflection or creep under sustained loads in timber depends to a great extent on the climatic conditions, even if the rate of creep in wood at a constant high moisture content is only siightly I~igherthan jn wood at constant low moisture content. The most important factor is the intensity of variation of moisture content in the material. This means that the long term deflection is higher for timber in outdoor conditions, with rapid and frequent flucluations in relative humidity, than for timber indoors, where the climate is controlled. For the same reason, timber with large cross sections exhibits lower creep than timber in small sizes, since the material in a heavy timber beam has a much slower response to fluctuations in the surrounding relative humidity. Su~facetreatment leading to increased moisture resistance at the surfaces has the same effect (Martensson, 1992, Taylor et al 1991). In addition to Ioad induced deformations, the serviceability of structural systems in timber is very much influenced by shrinkage and swelling in the material. The deformations imposed by moisture variations arid moisture gradients can often be of the same order of magnitude or larger than tl~oseinduced by mechanical loads. Suc1-1effects have to be controlled by appropriate structural design and detailing and by adequate moisture control of the timber before it is built into the structural system. Pure moisture induced deformations will not be considered further in this lecture. EC5: Part 1-1: 4.1
Principles for the calculation of deformations are given in the form of application ~ , an ~ rules in EC5. According to these rules, the instantaneous defom~ation~ t under action should be calculated on the basis of mean values of the appropriate stiffness moduli, which are specified in standards associated with EC5 for timber and glulam as well as for those wood based materials which are classified for structural use. The final deformation ulin including long term deformation is calculated as: il/in
= f ~ i , ~ rI( +
(6)
where $,/is a creep factor which describes the increase in deformation with time depending on climatic conditions and the duration of the load considered. Values of k,,,, are given in EC5 (Table 4.1) for different materials and for different service classes and load-duration classes. STEPIEUROFORTECH - an initinlive under the EU Comclt Progri~nim~
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~
When the deforrnation is to be calculated for a load combination with actions belonging to different load duration classes, the contribution of each action to the total deflection should be calculated separately and then added.
Design example Figure 3 shows a flat roof supported by straight glulam beams with cross section 165 x 990 iitrti, spacing 6 111 and a span of 20 H I . Strength class GL36 with E,,,,n,,,, = 14500 N/ltlnz2. Service class 1. The dimensions of the beam have been determined on the basis of design in the ultimate limit state. The second moment of area is I = bh3/12 = 1 3,3 1 0' m~nr".
Figure 3
Roof strucrraz. corrsiderr.d itz dcsigtl e,~onrple.
Characteristic load values: permanent load: G,= 0,5 kNAtr2 Qk= 0,8 ~ N A ~ Iyr,,? ,= O,6, yr, = 0,2, yrz = 0 snow load: Uniformly distributed loads q, on the beams (spacing 6 t n ) and corresponding creep factors k,,/are given in the following table (snow load taken as medium term load): Lond
q, (N/~!vtr)
41,
Permanent
3,O
0,6
Snow
48
0,25
First, the instantaneous mid-span bending deflection 1,O N/lnm is calculated.
it,
for a reference load q,:, =
-
The shear component of the deflection can be estimated from Equation (5). With HG15 and Pllr 20 the additional deflection due to shear is about 33% of the bending deflection. Thus, the total deflection due to q,, becomes rf,,,, = 1 1 2 i,mt.
Deflectiorz control for the case wlzen sign$cnrzt dartrage can be expected In this case the additional deflection occurring after the building has been erected is assumed to be of interest (8: in Figure 2). The criterion given by Equation (3) is used with the characteristic load combination, Equation (1).
STEPIBUROFORTECf-I - an initintivc under tl~cEU Cornett Programme
Creep deflection from permanent load
=
[3,0 . 0,6
+ 4,8 (1+0,25)]u,
+ final deflection
= 7,8
it,,
from snow load
= 84 tnr?r (or 11240).
If the deflection at the mid-span needs to be limiled due to structural requirements this value is usually too large. If a non-structural element connected to the beam needs to be protected against excessive deformations, the deflection at the point where the partition is placed should be checked. The criterion I ! ? , . , ~ ,2~ U300 recommended in EC5 could possibly also be applied ~ ~U300 = 67 rnnr. here. In this case rt,,;,,, = 4,8 i(,/ 54 I I I < Thus, the beam performance is considered acceptable according to this criterion. It is quite clear that any suggestion of a general deflection limit can be questioned. The only way to assure a rational serviceability design is to evduate the design situation based on the relevant circumstances in each specific case.
Def7ecfion control n~irltrespect to appenmrzce at~clgenerctl utilit)~ From the point of view of appearance the final net deflection is usually of interest. The criterion given in Equation (4), with the frequent load combination, Equation (2), is relevant in this case. Final deflection due to permanent load + final deflection due to yf, Qk(frequent value of snow load) = [3,0 . (1+0,6) + 4,8 . 0,2 (1+0,25)] ir,,/ = 6,0 urd = G5 nrm. This value corresponds to QJ300 and can usually be considered acceptable for a beam of this size. The corresponding criterion recommended in EC5 is in principle the same, but with the characteristic load combination, Equation (I). This gives:
This value is higher than the recommended limit in EC5, which is U200 = 100 rtlrtr. Again, different criteria intended to check the same functional requirement give different results. In this particular case, quite large deflections may occur on very rare occasions with extreme snow loads. These large detlections are only temporary and reversible and might be accepted in many cases. A way to avoid them without increasing the beam diinensions is to apply a precamber 1 1 , lo the beam. The precamber could be chosen equal to the deflection due to permanent load + half the deflection due to the frequent value of the variable load. This gives a precamber of 4 ll,,, = 43 mrw.
ConcIuding summary Serviceability criteria related to deflections often govern the dimensions of horizontal timber elements.
-
The deformation of timber stnictures changes during their lifetime, due to variable loads, moisture variations and creep.
-
The reasons for limitation of deformations should be clearly defined by the designer in each specific case.
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The choice of load combination for calculation of deflections should depend on the expected consequences of excessive deformations.
STEPEUROFORTECH - an initiative undcr
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References Mirtcnsson, A. (1992). Mcchrtnical bchaviour of wood exposed to humidity variations. Dep. of Str. Eng., Lund Univ. Report TVBK-1006, Lund 1992. Mlrtensson, A.. Tiiclandcrsson, S . (1992). Control of deflections in timbcr s~ructurcswith reference to Eurocode 5. In: Proc. of thc CIB W18 Mccting, Ahus, Sweden, Papcr 7-5-102-2. Ti~ylor,G.D., West, D.J., Hilson. B.O. (1991). Crccp of glued leminntcd timbcr undcr conditions of varying Itumidity. In: Proc, of the 1991 Int. Timber Eng. Conf:, London, UK.
STEPlEUROFORECH - an initiative undcr thc EU Cornet( Progrnmntc
Serviceability limit states Vibration of wooden floors STEP iecrure A I S
Objectives
S. Ohlsson
To explain the n~echanismsof serviceability reduction due to the disturbing vibrarion of wood floors and to explain the background and application of the dynamic methods specified in section 4.4 of EC5.
~ h a ~ r n e rUniversity s of Technology
Prerequisite B3
Bending
Summary Servjce requirements based on tluman tolerance of vibration are described. Service loads from human footfall and from rotating machinery are surveyed. The design loads according lo EC5 (unit impulse and static concentrated force) are described and the way in which they are believed to represent real dynamic loads is explained. Static stiff~~ess properties of timber floors related to concentrated vel-tical forces are described. Models and calculation methods are introduced. Dynamic properties of plate-like stmctures are introduced. Dynamic properties of timber floors are explained in some detail, especially for one-span simply supported floors. In particular, eigel~frequencies,mode shapes, modal masses and modal damping itre essential concepts. The design method based on iimitation of the impuIse velocity response is explained. The background assu~nptionsare surveyed, effects of various possible re-designs are illustrated, and limitations of the method are outlined. Effects from the general strucrural properties of the whole building and its mechanical system on the transfer of vibration are briefly explained.
Serviceability requirements A buiIding is generally rated as serviceable as long as it fblfils all its intended functions in an appropriate fasl~ion.A11 serviceability aspects which are strongly dependent on the slruclural system or on the structural co~nponentsof a buiIding are included in the terrn "structulmalserviceability". These aspects should be considered by the struclural engineer during the design process. Structural serviceability requirements are usually formulated in relation to a building or in relation to a fairly large portion of a building. Most serviceability criteria originate from the following objectives: -
-
Acceptable llurllan comfort. Ensured functionality of building and insmllations. Acceptable visual building appearance.
These design objectives are referred to in EC5. Damage to surfacing materials or partitions may for instance represent a loss of building hnctionality (loss of water tightness of a bathroom floor) or an unacceptable appearance (cracked STEPEUROFORTECII - ;in initiative under tlic EU Comctt Programme
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Serviceability requirements are to some extent different in nature when compared to classicaI requirements on safety. Some states of violated serviceability are reversible. This is for instance true for human discomfort caused by vibration. Another specific case can be illustrated by the visual appearance and the functionali~yof a floor. Both qualities are related to the deviation from a flat and horizontal condition. Consequently, the total deviation composed of initial deviation, deviations due to static load and deviations caused by climate factors, is relevant. In such cases it is possible to use pre-cambered components in order to limit the deviation. Consideration of such initial deviation (pre-camber) is permitted in ECS, where limiting values of deflection are given. This is not applicable in conjunction with dynamic problems. I11 order to facilitate engineering design of timber stluctures, the rnost essential ECS serviceability requirements have been transformed to design limiting values for deflections and vibrations respectively. The remaining part of this paper is focused on criteria for vibrations.
Vibrational serviceability In general there are many load-response cases where structural vibrations rnay constitute a state of reduced serviceability. The main concern, however, is with regard to human discomfort. People are in most cases the critical sensor of vibration. Among different dynamic actions, htrinian activity and installed machinery are regarded as the two most important internal sources of vibration in timber-framed buildings. Human activity not only includes footfall from normal walking, but also childrens' jumping, etc. Two critical load response cases are finally identified:
-
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Human discomfort from footfall-induced vibrations. Human discomfort from machine-induced vibrations.
Human susceptibility to vibration is a compiex matter. Griffin (1990) provides an extensive monograph on the subject, and I S 0 2631-2 (1989) rnay be co~isideredas a summarising document. The following basic statements are valid in most situations: The hunian sensitivity to vibration is:
-
-
related to vibration acceleration for frequerlcies < 8 Hz; related to vibration velocity for frequencies > 8 H i ; increased by the duration of vibration; decreased by proximity io and awareness about the source; decreased by physical activity.
In the light of these conclusions, two different design aims emerge. Firstly, the vibration levels in the vicinity of the dynamic action should be limited and secondly, the transfer of structural vibrations to adjacent building units (e.g. another apartment) should be avoided. The first aim may be achieved as described in the following suitabte structural system must incorporating both vertical and
by proper design of the local load-bearing floor, sections. In order to attain the second aim, a be chosen. The use of moment resisting frames liorizontal members can enable vertical vibration
STEP/EUROFORTECH - an inilialive undcr thc EU Cornell Programme
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transfer to adjacent storeys and may not be the best choice in this context. Continuous floor construction between different apartments should be avoided. Partitions should preferably be located above each other and be vertically supported by the foundation. Location of a partition at floor inidspan in just a single storey may stlucturally couple the two adjoining floors and they will experience almost the same vibration. This vibration may be acceptable on the floor where the dynalnic load acts, but it may be intolerable on an adjacent floor where the neighbour is unaware of the source.
Human-induced vibration EC5 is concerned with the design of residential wood-based floors with respect to vibrational serviceability. Dynamic influence from ordinary human activity, i.e. footstep forces, is considered. More severe dynamic loads, which can be anticipated from dancing and rhythmic exercises call for other design methods, Allen (1 99O), T11e design criteria presented here apply to floors with a fundamental frequency f, higher than 8 Hz. Floors having a lower fundainental frequency will experience more severe dynamic resonanl response from people in motion. Such floors must be designed due to principles not covered by this lecture. Eriksson (1994) discusses design principles for such floors, which usually have larger spans than are common for wooden floors. The different eigenfrequeticies of a rectangular floor simply supported along all four edges may be calculated according to the approximate Equation (1).
where f, is approxiinately equal to the fundamental frequency for a corresponding beam inember of unit width, f,, which is given by Equation (2):
-
The palameters used are as follows:
n
1r1
I El
is the mode number (only first order inodes are considered, that is only modes with a mode shape corresponding to a half sine wave in the direction parallel to the span direction are incorpornted). is the rnass per unit area (kg/nt2). is the floor span (In), O is tf~efloor width (111). is the equivalent plate bending rigidity per unit width (N~w'lnt), index I and b refer to perpendicular directio~~s and I represents bending in the stiffer direction.
It lnay be observed Ronl Equation ( I ) that the difference between consecutive resonances is dependent on the ratio between rhe bending rigidity in two perpendicular directions. Most wood floors will have a high degree of anisotropy, that is the quotient between such bending rigidities will be low. As a consequence, typical wooden floors will have a high number of closely spaced resonance frequencies within the frequency band of interest with respect to serviceability. The criteria and corresponding methods for calculation are based on the proposal STEPIEUROFORTECN - nn initiative undcr thc EU Cornell Pmgarnmc
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presented by Ohlsson (1988). The scientific background is documented by Ol1lsso11(1982). A sulnrnary of the background is presented here. The dynamic footfall contact force from ordinary tvalking has been experimentally verified. A case representing a person treading in place will cl-eate a forcing function like the one in Figure I . In residential prelnises the transient short-time response will be governing. The force is composed of two different component types:
-
Low-frequency components (0 frequency and its harmonics.
-
High-frequency components (8 40 Hz) whicli mainly originate from impacts when the heel contacts the floor surface.
-
S Hz) which originate from the step
-
Since the fundamental frequency of the Floor is supposed to be higher ~ h a n8 Hz, the lo~v-frequencycomponents will generate vibrations which are semi-static in the sense that their alnplitudes are governed by the structural stiffness, while the rnass of the floor is rather insignificant. Since this assumption is important, EC5 requires that the filndalnental frequency is cniculated and shown to be at least 8 Hz, or higher.
I
1
Sr~coessivcfovrstep cotiiact forces F fiottt ordirtcoy )!!alkittg PL'I.SQII ( { I ) ftitd cor-rz.sporrclirtg aggrrgrrrcd 1-e.sltltarlt force F,,,, acting otr the f i o r (b). 0ltl.ssor1 (1988).
As a consequence, the corresponding design action is taken as a static concentrated vertical force oT 1,O k N , see Figure 2. The resulting vertical deflection rl is limited to 1,5 nint. It should be pointed out that the calculation may be based or1 a model reflecting the reat two-wny action of a floor. The high-frecluency impulsive force compolients are represented by a unit impulse of 1,O Ns as the design action. The resulting vibration velocity v caused by such an idea! impulse is a property of the structure.
STEPIEUROFORTECI-I - an initio~ivet~ndcrihc EU Cotnctt Programme
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-
Figrou 2
Typical r.estiltc?trr.force-titirc iiistoty front 0 r ~ ~ i l l ~~polkitlg, 1 3 ~ iIli(strntiot?of correspottclitig iiieciliscd rlcsigt~iictiotrs corwisting of GI sturic force F, crarrcf u r~rlit irrtprtlse 1 (top), ~.csrrltittg deflcctior~ rt (bottoili left) orti1 vihl.ation ~~eiocity v ( t ) (bottonr riglrt) arrd iirriirirtg cl-iteria.for. riesigir ctrlcrciatiorls !I,,, illlii L1,.
It may be recalled thal if the floor had been a free rigid body with a concentrated mass 121, a unit impulse would have resulted in a velocity of the mass equal to 11h4. For a practical floor with distributed stiffness and inass, the initial maximum velocity may be calculated using Equation (3):
where the summation is taken over all different modes of vibration 11. @,, is the lnode shape function for mode r t , which is normalized for unit maximum modal displacement and ,?I,, is the nlodal mass (sometimes referred to as the gerleralized mass) for mode 11. Two modifications of Equation (3) are now undertaken. The first one concerns the sunlmation of contributions from different modes of vibration it. Experimental work has shown (Ohlsson, 1982) that the frequency content of imp~llsiveforces induced by footfall is essentially confined to the frequency range below 40 H i . Consequenlly, the summation may be restricted to all modes with eigenfrequencies lower than 40 Hz. The second modification concerns the mass wl~iclishould be included in the calculations. It is difficult to state assumprio~lsRere, wl~ichare on the safe side. With regard to many timber floors, however, it will be co~~sentative to assume a Iow value for the distributed mass. It is thus stated that calculations sIlal1 be carried out based on the distributed Inass of the floor only. The second modification is that the modal for properties (eigenfrequencies, mode shapes, m d modal masses) are calc~~lated this "bare" floor, but a standard addilion of 50 lcg to each modal mass rn, is allowed when calculating the velocity response. This addition represents a notional vibrating portion of the body of the person which is supposed to be disturbed by the vibration.
It has been found that Equation (3) can be significantly simplified for the ordinary case of a rectangular floor which is simply supported along all four edges, Ohlsson (198s). Assuming floor dimensions b x I n12 and a mass of a unit are:i floor nt k,g/~tr" Equation (3) may be approxilnated by Equation (4), which STENEUROFORTECH - an initiative under
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EU Cometl Programme
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corresponds lo the formula given in EC5.
The parameter n,,, represents the number of eigenlnodes with eigenfrequencies lower than 40 Hz and mbf is the floor mass. The additional 50 kg of modal mass in the denominator is represented by the quotient 41200 in Equation (4). The number a,, can be calculated from Equation (51, which is an approximate expression.
An effective way is established of calculating the maximum vibration velocity due to an ideal unit impulse. The favourable effect of a short vibration duration must also be taken into account. This is achieved by making the limiting value dependent on the damping of the floor. The most relevant damping parameter in this context is the damping coefficient a,. This parameter represents the decay rate expressed with respect to time rather than with respect to the number of oscillations. The damping coefficient is defined as: Go = f C (6) where f may be rakcn as equal l o the fundamental frequency 'f, and the modal damping ratio 6, !nay be taken as 0,Ol (1%) for ordinary wood-based floors. Darnping is a parameter which shows large scatter and an expected value may be around 1,5% to 2%, Chui (1988) and Ohlsson (1982). If a value higher than 1% is to be used for calculations, duration ought to be verified. In fact, it sllould be shown that such a bigher damping value will be valid for the entire expected service life of the structure. The limiting value is expressed as a h~nctionof the damping coefficient in accordance with the procedure suggested by Ohlsson (1988):
where f is taken as equal to the fundamental frequency .f, divided by I ,0 Hz in order to achieve a dimensionless exponent.
Example A floor in a private dwellinghouse with the following properties is to be checked. The dimensions in plan I x b are equal to 3,9 x 4,8 supported. The floor is constructed with:
-
-
t11"
All four sides are simply
22 /nm chipboard flooring in accordance with prEN 312-4 supported by 45 x 220 mrrt' wood joists of grade C22 according to prEN 338 and spaced at 600 urtrr centres (span = 3,9 171). 70 x 45 111111' spaced boarding of grade C16 according to prEN 338 which is fixed at 300 tnrn centres (length = 4,8 i n ) . II
rrzrlz
plasterboard.
Cliaracteristic values For the different materials according to EN 112.406 and prEN 338: I991 are as follows: STEP/EUROFORTECFI - an initiative ulidcr tlic EU Comctt Ptopralnmc
Floor chipboard E,:,,,,,,, = 2650 Nhm11'. Wood joists E,,, ,,,,, = 10000 Nhn111'. Spaced boarding E,,,,,, = 8000 Nhntnt'.
The Inass per unit area
m equals 35 kg/rr12. Equivalent bending rigidities are calculated:
The static deflection I / from a static concentrated force F of 1,O kN is calculated using a grillage model and the computer program BLAG (1991). The resulting vertical deflection rr is found to be 1,3 nrnt. This value is lower than the limiting value of 1,5 ~ n n t .A diagram based method like the one illustrated by Pharn Sr Gianarakis (1980) may be used instead. The fundamental frequency f , should be larger than 8 Hz. Since f, is approximately equal to.f,, Equation (2) can be used:
The fundamental frequency is found Lo be higher than 8 Hz and the design methods are thus applicable. The number of contributing modes is calculated according to Equation (5):
The value of the impulse velocity response is calculated according to Equation (4):
The limiting value is calculated according to Equation (7): - 100(~*'"~')= 0,019 (I JsY(Ns) 'nlar,~irnir The floor is thus found to comply with the criteria for human-induced floor vibration in EC5.
Machine-induced vibration Slructural vibrations caused by installed machinery should be limited. The human sensitivity to steady vibration from such sources is estimated according to Griffin (1990). Accepti~blelevels of vibration may be taken from Table 2 and Figure Sa in annex A to IS0 2631-2 (1989). Calculation of steady vibration should be based on expected unfavourable co~nbinationsof pennanent load and variable load as stated in clause 4.4.2 of EC5. The variation of ihe corresponding effective mass will consequently be rather high. Since many wood-based STEPIEUROFORTECH - an initiative under the EU Cornet1 Programme
A1817
sttuctural components have closely spaced eigenfrequencies, the frequency bands where an eigenfrequet~cy must be expected to occur will be rather wide. Vibration isolation or separate stn~cturilsupports for installed machinery may be the best solution in many cases.
-
Concluding summary
-
Serviceability is a lnatler of quality and performance in relation to cost. The limiting values corresponding to criteria for human-induced floor vibrations presented here should be regarded as minimum requirements. It is essentiai to stimulate active customer decisions about desired levels of' functional quality at the design stage of a constn~ctionproject.
-
References
-
Allen, D.E. (1990). Floor vibration from ilcrobics. Canadian Journ of Civil Eng, Vol 17, No. 5, pp. 77 1-779. Blag (1991). Manual for PC progtatn fbr skalic and dynamic noor calculations, Aby-konsult, Gothenburg. Clu~i,Y.H. (1988). E\uluation of vibritional pcrfortnance of' liglit-weight wooden floors. Proc. ol' the 1988 Int. Conl: on Timber Eng., Vol. I, pp. 707-715, Forcst Prod. Rcscarch Soc., Madison,
-
Wi.
Eriksson, P-E. (1994). Vibration of' low-frequency floors - Dynamic forces i~nd response precliction, Doclorat thcsis, Ctialn~crsUniversity 01' Tect~nology,Gotlicnburp. Griffin, fv1.J. (1990). I-landbouk of Iiurnan vibration. Ac;rdcmic Prcss, London.
IS0 1631-2 (1989), Evaliiation of human cxposurc to wl~olc-body vibralion, Pall 2: Cuntinuous and shock-induced vibration in buildings (1- 80 Hz). [SO, first edition, k b . Ohlssun, S. (1983). Floor v i h r ~ t i o ~ond ~ s humiln discomfort. Doctoral thesis, Clialn~essUniversily of Technology, Gotl~enhurg.
-
Ohlsson, S. (1988). Springiness and human-indttccd floor vibrations. Documer~t012: 1988, Swedish Council Ibr Building Research. Slocktlolrn.
-
Phi~m.L,& Gianankis, C.M. (1980). toad distribution i r ~tirnbcr beam grid systcnrs. Techn. papcr, 2nd scricsl Div. of Building Rcscarcll; No. 36, Cornmonwceltlr Scientific and lndusttial Rcscarch Org., Australin.
-
STEP/EUROFORTECH - an initinlivc under tile EU Coinett Progr;~mn~e
Creep STEP I
~ C I A U 19 ~ ~ I,.D, Andriomitantsoo CEBTP
Objective To describe the basic concepts for understanding the phenomenon of creep in wood and timber.
Prerequisite A4
Wood as a building material
Summary The lecture explairls the basic phenomenon of creep, before emphasising the effects of the main parameters and their relative importance. Typical experimental curves are presented as illustrat'ion.
Fundamental aspects Creep represents the increase of the defo~~nation with time, under a constant applied action. It is a particular aspect of ~nechmicalbehnviour of a material. Wood is generally considered to be a viscoelastic material. As sliown in Figure 1, the creep pad of the deformation begins after. the insrantaneous deforlnatio~l u,,,. Experimentally, r r , , , is obtained by progressively applying the load within n well defined time and under defined conditions, up lo a fixed value.
Fiig~oaI
A schcriratic rcpr~.seitratio~~ of ~~iscucii~sric /.eltatjiotrrof (1 rrrcrtcric~l.14 i s flte rlcfo,atnrio~i,F tire locrrl c11d r rlic rit~ie.Creep a; tirne tji,, is ilji,,- llbtSr R is [Ire I%Col~el-y.
In this representation, creep exhibits two principal cl~aracteristics:
-
a r.elatively rapid increase part at the beginning, as shown by the steep rtnd variable slope of the curve. The slope of the creep part of the curve u(r) is the creep rate.
-
n range rtpproilchillg stabilisation wit11 a constant creep rale.
On unloading, a progressive recovery, total or partial, to the initial state occurs. Total recovery corresponds to pure viscoelasticity. Partial recovery means that plastic darnage, even microscopic, has occured. In a stabIe environment and for stresses less than about 35% of the instantaneous strengll~of wood, the deformations under two different stresses have a constant ratio, independent of time and equal to tile stress ratio. The co~npliance (deformation/stress ratio) is independent of the stress. Viscoelastic behaviour is then considered linear.
In the design ~nethods,all conditions, and particularly the load (or stress) are such that this assumption of linearity is always appropriate.
Principal parameters of creep The parameters influencing creep in wood are:
-
-
-
load duration, i~ioisturecontent, temperature, and stress level.
Generally, interactions occur between all of them but only the combined effects of load duration and moisture content are taken into account in the design rules. Some brief comments on the temperature and the stress level effects are presented for information.
Irz~z~errce of load ciziruriolr Under steady-state environmental conditions, creep deformation increases with load duration. Its amplitude strongly depends on load level, which must be maintained lower when the duration of load is extended in order to ensure an acceptable deformation limit of the structure with time. For instance, under a given load, creep of solid timber may increase from two to four times for load duration ranging from six months to twenty years. EC5: Par1 1 - 1 : 3.1.6
In the calculation rules, five load duration classes are defined. Tile value of creep, for a given class, is talien as constant.
Itlfltietzce of nloistrrre content Solid limber, glulam, and board materials are all, to different degrees, sensitive to humidity, with a very ~narkedeffect on creep beyond certain limits. Creep increases with tnoisture content. Generally, under the same conditions, it is considered that creep of wood based panels is higher and, of these materials, plywood has the least creep. Creep amplitudes, from once to twice the instantaneous deformation, are current values for indoor use under permanent load. Thcy can rcach three to four times the instantaneous deformation when the moisture content is close to 20%. Research results on structural sized solid timber and glulam (Rouger et al., 1990) show elsewhere that creep is practically equivalent for these two materials when the average moisture content does not exceed the value of 20%. The experimentally observed differences between the two materials are mainly caused by the differences of the instantaneous deformation. These differences are directly related to the modulus of elasticity andlor to the moisture content. STEMEUROFORTECI-I - an initiative under illc EU Cornelt Prograrnmc
-
ECj: Pna 1-1: 3.1.5
The design rules clearly distinguish three service classes, corresponding to three different ~noisturecontents of the wood. An additional situation must be underlined for solid timber, whose moisture content, near to the fibre saturation point at t11e time of' erection on site (25 to 30%), will greatly decrease to reach the equilibriuln state in service. Where there is variable moislure content under stress, there is an acceleration of creep and the final deformation is even greater. Experimental rcsults on solid timber and glulam, under protected external conditions, show creep values ranging from once to twice the instantaneous deformation, after more than one year under stresses of 2 N / I , T ~ I5T ~ ,h n r n h n d15 Nhlmt' (Andriamitantsoa, 1992). Different curves, illustrating four moisture content effects on creep are preserzted in Figure 2.
Figror 2
Rclc~tivrdefori~ratiatr-fimcrrrvrs for beattrs at difleret~~ ~ltoistrrrecotrditior~s. A, grwe,~tirrtber k q ~ glrerr; t B, green rini/~erdrying to 12% moisrlar catl~er?t; C,tinrbo kcyt (11 12% trroislirre rorltcrrt; D, iirrrbo. irririai1.y ot 12% ~nroistr~re cotrtetil crllo~vucito rtbsorh irtoisrltrc. r(d) is titw itt days. All.~itreusli. 24% of creemge $hart tcrttr ,srre~rgrlr.T=25"C. (Artturtwrg atrd Kftrgstorl, 1962).
I~flirertceqf terertlpei~crtr~l-e The polymeric nature of' wood cornponerlts makes it also sensitive to temperature. For practical purposes, the higher the temperature, the greater the anlpiitude of rile creep. Further, variable telnperarures result in an acceleration of the creep (Dinwoodie et al., 1991).
In fact, in normal use, when the telnperature does not exceed about 50 "C, its influence on creep is negligible and masked by the effects of moisture content variations, even when these variations are low. Nevertheless, it must be kept in mind that the notions of temperature and nloisture content movelnents, in situ, have to be related to two parameters:
-
the thickness of wooden elements added to that, for instance of encasements,
STEP/EUROFORTECl4 -
:in
iniiiiltivc under Ihc
EU Comctt Programme
A 1 9/3
finishes, or similar means which decrease the exchanges with the environment.
-
the speed and the frequency of the ambient atmospheric variations.
Unsteady gradients occur ncross the section and one consequence is a reduced creep amplitude co~nparedwith a coinplete humidification or drying, where a steady state !vould be reached. i~tjlilrrenceqf Stl'ESS
Provided that the rpplicd stress and the duration of the measurement are sufficient, the creep curves for wood (deforn~ationversus tin~e),generally terminate, just as with nlost collstn~ctionn~arerials,in an acceler;tted stage preceding ruphlre, which can be explained by progressive damage of the wood. The higher the stress, the higher the rate of creep and the shorter is the time before fracture (see Figure 3).
Figlrr-c 3
iitflrrcr~ceof stress (evel.~nrr c*rzcpa, < t i is 111rc/~fur.rtirrtiu~~, t tlrc tinle.
(3,
< a, < G, < CTv
In the design metliods, the stress levels are calculated so that creep remains within the stable phase, where the rate of deFormation is low and stable during the lifetime of the cor~sttuction.Experi~nentalresults, show11 in Figure 4, present this applzrent stability, for stress levels less than 35% of the instantatleous resistance.
STEPfEUROFORTECI1 - an initiative ur~dcrihc EU Conicti Prograrumc
Influence of load duration anti moisture content according to EC5 The combined effect of load duration and moisture content is quantified by the factor k,,+ in the general expression of the final deformation:
Writing,
it can be seen that the value of creep is equal to k,,p, itia,,. In timber structures tllese effects must be calculated for eaclli component such as joints or members and then sunlimed to obtain the total deformation (see e,g. STEP lecture 39).
Mechanical joints Similar behaviour. exists in mechnnical limber joints, because of the local deformation of wood, in colnpression under the fastener. The magnitude of tlliis creep may also be at least as important as that in wood. Maximum creep is obtained when one of the jointed pieces of wood is loaded perpendicular to the grain.
Concluding summary
-
Load duration, moisture content, particularly moisture content variations, temperature and stress level influence the extent of creep deformation. Even if rl~ereare complex interactions among these variables and even if these inler.acLions change from one material to another, the combined effect of the two first parameter-s can be considered as tile most significant in normal use of timber and wood based panels.
-
Creep deformation is calculaled by n~ultipIyingtlie factor- k,,ty by the initial deformation. The factor k,,,,depends on the load duration and service classes of the structure.
References Andriamilantson 'L.D. (1992). klcchnnosorptivc bcl~aviourof struclural sizcd solid timber and glula~n (in French). Proc. IUFRO, Vol 1 : 317-8, Nnncy, France. Ar~nsirong,L.D. and Kingston. R.S.T. 11962). T l ~ ccffccl of riroisttlrc contcnt changes on lhc dcfi)rnmtion of wood undcr strcss. Aus~rali:in Inrrn~:~l of Applied Scicncc, 13(4):257-7-76. Dinwooclie J.M., Iiiggins J.A., Pnxton i3.i-I. ilnd Robsori D.S. (1991). Qt~;lntifying,prcdic~ingand understanding 111c rncchnnism of crccp in ba;~rdmnterinls. Proc. COST 508. Fnndamcnlnl sspccts on crccp in wood, 99-118. Lund, Sweden. hluct, Ch.. Guitard. D. nnd Morlicr, P. (1988). Lc bois cn slructurc. Son cornportemcnt diff6rC. Annalcs dc I'ITBTP, N" 469 dbccmbre 1988. 33-83. Frnncc. Rougcr F., 1-c Govic C., Crubilf P.,Sot~hrclR. and l'aquei J. (1990). Crccp lxlchitviour of lrencil jvood. Proc. Inter. Timbcr Eng.. Vol 2 : 330-36, Tokyo. Japan.
STEPlEUROFOR'l'EC1.1
-
;111 initiative
undcr the EU Comcit Progran~mc
Volume and stress distribution effects STEP lecture B 1 F. Rougcr Cenlrc Technique du Bois et dc I'Amcublemcnt
Ob,jectives To explain volume and stress distribution effects as a consequence of the weakest finlc theory for brittle materials. To describe the options of Eurocode 5 and CEN supporting standards for deriving characteristic values and evaluating design stresses.
Prerequisites
Solid timber - Strength classes Glued laminated timber - Production and strength classes Tension and compression Bending Members Shear and torsion
A7 A8
B2 33 B4
Summary The lecture begins with a presentation of the weakest link theory, for tension in brittle materials, and explains volume effects. This theory is expanded to other stress fields, with attention to bending, tension, shear and tension perpendicular to grain. Research results are summarised. The options of EC5 for bending and tension perpendicular to grain are explained. Some examples of calcularions are given.
Theory The weakest link theory has been developed by Pierce (1926), T~lcker(1927) and Weibull (1939) who studied brittle materials, including concrete. This theory says that "when subjected to tension, a chain is as strong as its weakest Ijnk". To explain this theory, consider a reference volume subjected to tension. The probability of failure P, of this volume is defined by:
PJ
=
F(a) = Probability (Strengthso)
(1)
where F is the cumulative distribution of the strength, ns illustrated in Figure 1
Figilrc I
Cmarflnfir1eprohabilitjl of failr~refor a refel-ettce rrohitite.
Now consider a series assembly of N reference volumes. This system survives if eacl~of the members survives, i.e.:
STEP/EUROPORTECCI - an initiative undcr the EU Comctt Programme
Bffl
where P, is the probability of survival of the system and P,s(i)is the probability of survival of an individual element i. Roin Equation (2) and assirrrzirzg llrnt r
F(a)
=
a ( a -a,)"
(4)
-
-
The probability of failure is then expressed by:
This inode1 is known as the 3 parameters Weibull rnodel. It is also well known as the 2 parameters Weibull rnodel when a,,= 0. The paraarneters111 and k can be estitnaled from the mean of 0 (E('(o))and the coefficient of variation of a (CV(a}} by solving the following equations:
-
where T(s) is the Gamma funclion. -
The theory can be used to explain the size effect in tension. Consider a volume V, which has a given probability of failure P,(a,) at level 0,and a volulne V? which tias a given probability of failure P,(o,) at level 02. IF the characteristic strengths of these two volumes are compared, the following is obtained:
This equation is the basic expial~ationof size effect. In the case of stress fields otller than lension, these equations are modifiecl to take into account the stress variations: o(~,YJ)= ww(x,y,z) (9)
=
where o is tlie rnaxin~urnstress in volume V ~tr(x,~;z)is a spatial distribution function (dir-nension-free). Ttte Weibull model is then written:
P, (a)
=
1-e
-v.$P
where I/:': is defined by:
-
STENEUROFORTECI-I an ir~iliativeunclcr i l ~ eEll Corncit Progranlmc
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For example, a si~nplysupported beam with rectangular cross-section and loaded at the rnidpoir~tby a cot~centratedforce gives the following value for Vk:
This method of calculating the stress distribution effect has been used by Larsen ( 1 986) and Colling (1986) to evaluate the volume and stress distribution effects on the shear strength nr~dtension perpendicular to grain for- curved, tapered and calnbered beams. In Larsen's paper, the term "distribution factor" (ktIiJ is used, where:
Tile kt, factor is used to cillculate the design tension pe~pendicularto grain strength for different load configurations:
wherej",,,),,,, refers to a reference volurtle V,, under uniforin stress.
In Colling (1986), the following notation is used:
where h, and h, are called "fuI1ness parameters".
Research results A vast amount of dnra has been published to explain size effect for srructural size timber. These results are sornetirnes conflicting (Barrett and Lam, 1992; Madsen, 1992), and might be due to the following reasons:
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The sizc effect is jtlslified by a brittle failure theory, whicl~is applicable to tension parallel and perpcndicuIar to grain (Barrett, 1974; Colling, 1986), and to shear (Foschi and Barrett, 1976; Foschi, 1985; Colling, 1986). But in the case of compression, and particularly in bending which is a mixed 111odeof failure between tension and coll~pression,the use of this theory is debatable.
-
The size effect is based on an equal probability of failure of the "reference volumes". This assumption is nor dways verified for all the species, especially for pines in which knots are not randomly located.
-
For visunlly graded lumber, defect sizes increase with the sizc of the member. This means that the material changes with the size, which can mask a pure size effect. In particular, when size effect is investigated in a mixture of grades, the effect of grading will have an influence on the size effect.
-
When tests are conduc~edfor constant span to depth ratios in bending, the size effect is a combination of n depth effect and a length effect (Barrett and Fewell, 1990). These effects cannot be identified separately.
The following tables surn~narizethese I-esults.They show some discrepancies, which have been explained by Bnrrett and Lam (1 992). STEP/EUROFORTECH - an il~ilintiveundcr the EU Contell Programinc
B 113
In Table 1, different factors for bending size effects are recorded:
-
a length factor S, (for beams tested at constant depths) which is calculated from:
a depth factor S, (for beams tested at constant spans) which is calculated from:
-
a "size factor" S, (for beams tested at constant span to depth ratio, i.e. Li = k Iti), which, according to the combination of equations (16) and (17), is calculated from:
Author
3,-
8,
s,t
Barrett and Larsen, 1992
0,17
0,23
0,40
Madsen, 1992
0,20
0,o
0,20
Ehlbeck and Coiling, 1990
0,15
0,15
0,30
Table I
Size fc~ctorsfor henditrg.
Additional results are reported for glulam (Ehlbeck and Colling, 1990), but are based on a sample size which was much s~lialler.The size effects for glulam are Iower than for solid timber, probably due to a lamination effect which increases the strength. In Table 3, load configuration factors for different bending cases are reported according to Johnson (1953). These load configuration factors are derived according to Equations (9), (10) and (1 I ) , and normalized to the reference four points bending case. Tension results are slightly different from those for bending. This might be due to a pure brittle failure mechanism (see Table 2).
s,,
Barrett and Larsen, 1 992
SL 0,17
023
0,40
Madsen, 1992
0,20
0,lO
0,30
Author
Table 2
Size f i i c t o r ~for rensioir.
STEPIEUROFORTECH - nn initintivc undcr thc EU Comctt Progralnrne
sz,
ToDle 3
Load cor~figrtmtiorr.fnctor-~o.
For compression,
results of the different studies are in general agreement:
For tension perpendicular to grain and for shear, a volume factor (S,,)llas been derived by Colling (1986), who also derived fond configuration factors for tension perpendicular to grain
These I-esults are subject to different opinions but show m evidence of size effects for imny stresses, together with a stress distribution effect which can be as significant as the size effect itself. For code purposes, the approach has been siinplified, especially in the case of stress distribution effects.
Size and stress distribution effecfs related to EC5 prEN 338: 1991
TIE first application of' size e f t c t s concerns the modification ol' characteristic strengllts given in prEN338 "Structural Timber - Strength classes". Tile chariicteristic strengths in bending and in tension are. given for a reference depth of 150 111rrr for solid limber nnci GO0 n!m for glulaln. For depths less tllan these reference vnlues, Il~esestrengths are multiplied by a size factor, which has a fixed upper limit. This means tllat size effect is only applied in one direction, as shown in Figure 2.
STEPIEUROFORTECI-1- an irlilintivc undcr tllc EU Corncri Prognmmc
ECS: Par1 1-1: 3.2.2
For- solid tintlev
.
where It is the beam depth in ECECS: Part 1 - 1 : 3.3.2
For girtlrrltt :
k,,
=
lisr
min.
Figrcr-e 2
EC5: Part 1-1: 5.1.3
ECS size *fcilutu?-jorsuliri tirlrber iir be~~ditlg or- fension (solid litre), relaled to ~ltenly(rlalaslted line),
For tension perpendicular to grain and for shear, characteristic strengths are also given for a reference volume. But, for simplicity, a size factor is only proposed for tension perpendicular in glulam. The designer is then required to verify the following equation:
where EC5: Part 1 - 1 : 5.2.4
111rrr.
\I,,
is a reference volume of 0,01 m3.
For dorrble tapered, curved and pitched cambered beams, an additional requirement is included to account of the stress distribution effects. The designer must verify the following equation in the apex zone:
kc,,, is a stress distribution factor which has been fixed for special cases: /Q, = i,4 for double tapered and curved beams kJfi,= 1.7 for pitched cambered beams.
For simplicity, other aspects of size and stress distribution effects like compression size elfect and load configuration factors Iiave not been taken into account.
STEPIEUROI'ORTECI1 - nn initiiltivc undcr thc EU Comctt Prograinmc
Calculation examples Exarnple 1: Bending Strength of a solid timber beam of cross-section 40x100 n7m, strength class C24. C24 strength class provides .A,,,, = 24 1V11nm' k,, = (150 1 100)"82= 1,08 < 1,3 j;,,,,(modified) = 26 Nlrl?~n~
Example 2: Design of a double tapered beam. Verification of tensile sll-esses perpendicular lo grain.
prEN+1 194 : 1993
EC5: Part 1- 1: 5.2.4
b = 150 mrt~ h,,, = 1,20 1r1 Span: L = 20 111 It = 1 nt Glulatn Strength Class: GL 36 GL 36 strength class provides A,%,,= 0,45 Nlrnnl' To calculate n design strength, take k,,,,, = 0,sancl y,, = I ,3 This implies = 0,277 ~ l ~ i m t ' The volu~neof the apex zone is equal to: I/ = 0,2097 1 1 1 ~ Tlius (V,,l\I)"" = 0,544 For a double tapered beam, k,,,= 1,4
The maximum design stress perpendicular to the grain is equal to :
Concluding sunmary
-
Size and stress clisiribution effects are explained by WeibuII theory.
-
liesearch results show discrepancy, especially Tor depth effect in bending.
-
EC5 provides n sin~plisticapproach to size and stress distribution effects to aid the designer.
References Bnrrclt, J.D.. and Fcwcll, A.R. (1090). Size Ctctors Tor the bending 2nd tcnsion s(rcng(h of structural lumber. Proc, ol' the C1B W18 Mccling, Lisbon, Portug;il, Paper 23-10-3. Barrctt. J.D.,and L:im. F. (1992). Size crfcc~sin visually grarlcd soltwoad structural lunibcr. Proc. of (tie CIB WIS Mecling, Ahus. Swcdcn. Papcr 25-6-5. R;~rrett,J.D. (1974). Efrect of size on tension pcrpendiculnr lo gririn strcngtfr 04' Douglas Fir. Wood and Fibcr G(2): 126-143.
Colling, F. (1986). lnflucnce of' vofumc ilnd stress dis~ributionon thc sllcar strcngtll i~ndtcnsilc strcnglh perpendiculiir 10 groin. Proc, ol'thc CIB W18 Mccting, Florence, Italy, Pi~pcr19-12-3. STENEUROFORTECH - an initiative under Ihc EU Comctt Progmmnic
B 117
Ehlbcck, J., and Colling. 1;. (1090). Rending strcngth of glula~nbeams, n dcsign proposal. Proc. ol' the CIB W18 Meeting, Lisbon. Portugal, Paper 3-3-12-1. Foschi, R.O.(1385). Longit~~dirinl sllcar dcsign of glued Inminclted hcarns. Proc. of tl~cCIB WI8 Meeting. Beit Orcn, israel, Paper i8-10-2. Fosclti, R.O., and Barrett, J.D. (1975). Longitudinal shcar strcngtll o l Douglas Fir. Canadian Journal or Civil Engincering, 3(2): 198-208. Johnson, A.I. (1953). Strcngtlt, safety iirid cconolnical dimensions of structures. Swcdisii State Committee for Building Rescarcll, Bulletin n. 22, p. 159. Larsen, H.J. (1986). Eiirocode 5 and C1B structurnl Limbcr design code. PFOC.of the CIB W18 Meciing, Florence, Italy. Pnpcr 10- 102-2. Madsen, B. (1902). Slruclurnl Bellnviour oCTimber. Timbcr Engineering Ltd., Nortl~Vancouver, B.C., Canada. Pierce, F.T. (1926). Tension tests for cotton yarn. Journal of the TcxLilc Institute, pp, T155-T368. Tucker, 1. (1927). A study of conlprcssive strenglll dispersion of material with applicirtions. Journal of the Franklin Iostitute, 304: 751-781. Weibull, W. (1939). A statistical theory of the strength of rnatcrisls. Roy:il Swcdish lnsiitutc for Engineering Research, Proceedings, N. 141, p:45. Weibull, W, (1939). 'rhc phenomenon or rupture in solids. In: Royal Swedish Instiultc for Engineering Research, Proceeding, N. 153, p:55.
STEP/EUROFORTECH - an initiative itndcr the EU Comctt Progri~mtllc
Tension and com~ression STEP I C C ~ U ~I32 C R. Edlund ChaImcrs University of Technology
Objective To describe the strength and stiffness of timber loaded in tension and compression a1 different angles to the grain.
Prerequisites A4
Wood as a building material
Summary This lectrire deals with tension and compression actions when parallel to the grain, perpendicular to the grain and at an angle to the grain and considers both clear wood and structural timber. Each of the four basic cases: tension parallel and perpendicular to the grain and compression parallel and perpendicular to the grain are first discussed for clear wood. The influence of different parameters on the strength and stiffness properties on it small-scale and at macroscopic level is presented together with examples of failure modes. The more general case of loading at an angle to the grain is described, noting wood as an orthotropic material, with the application of different failure theories such as I-Iankinson's formula. The final section considers tension and compression actions in structural timber.
Introduction Wood is an anisotropic material, i.e. it has different properties when loaded in different directions, e.g, parallel or perpendicular to the grain. A tree trunk may as an idealisation be regarded as being cylindrically orthotropic ( i s , orthogonally anisotropic), Figure la. In Figure Ib the directions L, R and T denote the longitudinal, radial and tangential directions, respectively. The properties in the R- and T-directions are often treated together as one group, i.e. regarded as properties perpenciicular to the grain.
Figicre I
Prir~cipafases and prirrcipnl plaries in ,r~ood. For a st~tall rectarrgular block taken out froill the orrfer part of tfie tree trrrltk fire rectalrgtrfar coor(iiriafesystetn L,R,T, (b), car! be deJtrad.
The following sections deal primarily with both the strength and the stiffness i loading. Unless otherwise stated the values properties of wood under s h o ~ term STEPIEUROFORTECI-1 - nn i~litiativcunclcr the EU Comctt Prograrnmc
BY1
are selected for n typical European softwood with a moisture content of 10 to 15%. Structural timber, i.e. ~imberwith normal defects prepared in structural sizes Sor structural purposes, is inhomogeneous. There is n large variation in the raw illaterial propeflies (density, strength, rnodulus of elasticity etc.), i.e, over the cross section of a log and along the log. Further, there is also a variation in tile properties between different trees of the same species ilnd, of' course, between different species. Also within one annual ring tlie properties vary, namely belween eaclywood and latewood. These variations ;Ire, however, not furti~er discussed in this lecture. First, the properties of clear* wood (small specimens) will be treated, then sawn timber in structural sizes with defects.
Clear wood in tension and compression
Figure 2
Str.c.ss-sf~'rritt rtrrves for clear wooil lactded parnuel to the S I ~ ~ I(.rolid I iirlc) attd perpenrlir~rlc~rro the grcrin (cla.sAc~llirte) crt a cairs~ctttrstritin mtc. m i c a [ \allresfor sofi,tmooci:J,, = SO to /OO N / V I I.[,,, ~ I= ~ ,10 to 50 N / I ~ I I ~ , E,, = 11000 to 15000 ~ h ~ r t t t ? .
Tctlsion pnrcrllel ro file grclirt When testing sniall wood specimens, selected to be as homogeneous as possible, and loaded parallel to the grairi, a stress-strain diagram of the type sliown in Figure 2 (fiiliy drawn curves) is obtained. It sl~ouldbe noted that the tensile strength .I;,,, i s larger than the compressive strength A;,,. The stress-strain curve in tension is linear almost up to failure and the fracture 117ode is sudden and brittle. In compression a more ductile failure is obtained.
EC5: Part 1-1: 5.1.3
Teltsiort pet-peizdicirlnl. to tlze grclirt The lowest strength for wood is in tension perpendicular to the grain .f;:x,. It is roughly of the order of magnitude of I to 2 ~/tturr?,but there is an important dependence on the stressed voiume, see Table 1 and STEP lecture E l . The volume effect for the other strength properties is less pronounced. The tensile strength .I;,, is considerably reduced by defects like fibre disturbances and initial cracks, especially in the earlywood. STEP/EUROFORTECII-
;in
initiative urlclcr tllc EU Comctt Programme
-
9
Also the niodulus of elasticity is tnucli lower perpendicular to tile grain, E9,, = 400 to 500 Nh~rttr" than parallel to the grain. In the design of timber slructures tensiIe stresses perpendicular to the grain should be avoided or kept as low as possible. It is iniportant to identify areas of a structure, where tensile stresses perpendicular to the grain occur and to male design improvements to reduce their magnitude. Exa~nplesare ~iiemberslike curved beams and fraine corners in glula~astructures, notched beams at the support or beams with holes, certain connections, see STEP lectures B5 and C2.
Coi~tpt-cssionpal-ciflel to the groin The compression test specimens have Lo be short enough to avoid overall (column) buckling. As can be seen from the curve in Figure 2, the fibres will s~~ccessively yield unlil a maximum load is reached. The failure mode is by buckling of n row of fibres, see Figure 3. It is a kind of local instability due to shear along a sloping plane.
(0) Figrrt-e 3
fb)
Cot?~prz..ssio~i fnilrire nt A,, Br~cklitrg of jiblzts. (Hoflt?teycr, 1990). LW Ia~eiclood,EU' earlj~~r~ood, il R at11trial rings, CC cot~iprrs~siott crc~u.ses.
The modulus of elasticity is E,.,, = 11000 to 15000 Nhrn~' as in tension, but the stress-strain-curve levels off earlier, so the limit of proportionality is also of interest.
Con~pressionperl3etldiclclnt- to tlze grain It1 the case where the whole specin~enis loaded (case ( ( I ) in Figure 4), the fibres are just squeezed together like a bundle of tubes until a kind of squash load is reached, where the tangent modulus beconles very low. At the maximum load the strairi is very large. W1.1en just a portion of the upper wood surface is loaded, the stiffness is higher and the change in stiffness will occur aL a higher stress than for case (a), and this stiffness change will be less pronounced than for case ( a )and corresponds to a bend in the stress-strain-curve, see Figure 4. The reason for this is that the concentrated load will be carried over by the fibres to the neighbouring unloaded parts. In case (b) these unloaded parts are too short so ;I maximum load is reached just above tlie bend. For cases (c), ((1). and ( e ) tlie loading lest can be continued to a higher strain than that in Figure 4 without any pronounced failure. However, tlie deformations will be considerable. Therefore, it is practical to limit tile strains to a certain value, say I%, and to use tlie corresponding stress as a kind of strength (or "proof stress") value. In this case A,,,, = 2 to 4 ~h1ttn'. However, the values will STEP/EUROFORTECI.I - MI initiotivc undcr ihc EU Con~cttProgramme
B2/3
atso depend on the orientation of the annual rings in the cross sections of the loaded bar, see Figure 5.
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Applied stress pcrporclilicrrlar to [Ire graiti IT. rfer~icnlcnt~rptr,s.sirtesrrairr .frottl tesls or1 tirtlbet. 15 s 15 crti'. Srreriso~~ (1938).
--. 4 0,8 T+,,
--
-
p&
$
0
--
-
-1-
-2.E: \
',
-
2 -3
\
.....
Figrrre 5
Woad ill cbotrij)ressionpcrpendicttlar in the groitr. Moti~tl~rs q/' elcisficity mrd srrrss lirrrir. Here i;, = /it,,,, is 11re liniif of propat.tionolitj: Vulrres fi.orti Siirrles cltld Liil-i (1952) nricl G ~ b e (1940). r
Lociding ot an ntrgle to tile gr~zin Let
-
a be the angle between the load direction and the grain direction.
Hankinson (1921) proposed the following equation for the failure stress .f;.<, in compression.
which gives good agreetnent with test results. For the strength under te~lsiIeload at an angle to ltle grain an analogous expression can be used, i.e. with .A. being replaced by .f;, coinpnrc Figure 6a and Gb. STBP1EUROFORTECI.I - an initiative uridcr ~ h cEU Cornctt Progr;lmnie
--.
9
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It is seen in Figu~e6, that for small angles a the strength is very sensitive to changes in a, i.e. srnall deviations in slope of grain will cause a significant strength ~.eduction,especially for tensile load. On the other hand, for a = 90". i.e. near j;,,, and f;:,,, there is praciically no cllange in tensile and co~npressive strength when the angle is changed by 10 to 12 degrees. It may be sl~own (Edlund, 1982) that, for the case of a symmetric orlhotropic material, Equation ( I ) is (1 real linear approxinlaiion Lo the more general Tsai-Wu failure criterion for orthotropic materials.
Figtrrr 6
hilitre drtr to load nr otr arlgie to tire grniri. (CL) t,ctl.sio~z;(bj corrtpres+siorz. Tlrc jid!). drnlrltr crtt-ves are nccorciing ro Hatlkirrson, Eqiialiotr ( I ) ; rile daslzd atn1e.s fire ~vlrefr rlre .fo'nil~ita c~ot~dirion of otie ptrre srrc?ssA:,, ./;,,,or f,,is nrmiticd.
For uniaxial lension or co~npressionwith an angle a to lfte 1-axis (the natural axes of ortl~orropic materials are I and 2), Figure Gc, 6d, ihe equilibrium equations are: (T,
o2 f,z
=
--
CT,COS'~
0;, s i n k CT,, sina cosa
For coinparison, the limit curves for the 1111-eeseparate failure conditions o, 5 -
.frsl, CT.
Structural timber under tension and compression Gerterczl For timber in strucrural sizes used in load-carrying structures the effect of different inherent defects such as knots and slope of grain must be considered. A knot of "ordinary" size reduces the effective cross-section of a board and is associated with local fibre disturbances. This ofien results in load eccentricities and high local stresses. Further, where the fibres change direction around a knot in a tiniaxially loaded board slresses perpendicular to the grain will be induced. This is especially imporrant l'or titi-iber loaded in retlsion parallel lo the grain. Although the tensile strength for cleat. wood loaded pari~llelto the grain is mucli Iligher ihan in compression, the reverse is true for sti-uct~~ral Limber. This is STEP/EUROFORTBCI.I - an
iniliotivc t~ndcrllic EU Comelt
Progrilmmc
B2/5
partly due to the sensitivity to slope of grain mentioned above in colinection lecture B l ) , which comprises all other types of defect as well.
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With regard to important inl'luences of load duration (creep) and ~noistilresee STEP lectures A4 and A19.
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with Figure 6, partly to the brittle type of failure and the size effect (see STEP
Tensioil The inhornogeneities and other deviations from an ideal orfhot~~opicmaterial, which arc typical for structural timber, are often called defects. As just mentioned, these defects will cause a fairly large strength reduction in tension parallel to the grain. For nordic softwood (spruce, fir) typical average values are in the range of J;,, = 10 to 35 N/tnn12. In several investigations the luean off;,, was fbund to decrease proportionally with the increase in size of the largest knot diameter. However, the scatter is large and the correlation poor. The values obtained also depend on t!ie test method, since failure [nay be induced by the stress concentrations at the end grip devices. EC5: Part 1-1: 3 2 . 2
EC5: Part 1-1: 3.3.2
In EC5 the ~Ilaracteristicstrength values of solid timber are related to a width in tension parallel to the grain of I50 ttzm and to a volume of 45 x I80 x 70 rtznz" 5,67 . 10.'' t ~ ? f o r the . tensile strength perpendici~larto the grain. For- widrlls in tension of solid timber less 1ha1.r 150 nzni the characteristic villues !nay be increased by a factor k,, which is the smallest of (150//1)",' and 1,3. For plulc~$rlthe reference width is 600 IIIIII and, a~~alogously, for widths s111aller than 600 r~rlna factor I<,, should be applied wiiicli is given as tlie s~nallestof (GOO/h)"-?and 1 , I 5. Tests by Johansson (1976) on 296 spruce (Picen cii~ics)laminations 33,3 x 155 irnn stlow that there is also poor correlation, jrl = 0,5 to 0,6, between the tensile strength on one hand and density and ring width on the other. But, if knot data and density are cotnbined into one parameter a considerably better prediction of the tensile strength may be actiicved (coefficient of correfatioit r = O,SO). The modulus of elitsticity measured near the location of failure (called ESF) is tlie single parameter, measured by Johansson (1976), that gives the best correlation with the tensile strength ( r = 0,86). Some improvernent was obtained if the parameters ESF and knot data were combined (rA = U,S9). Similar conclusious are drawn in an investigatiori by Glos (1982).
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For long boards under uniaxial lension due consideration should be laken both of the size effect (Iengtlt effect) and of the lengthwise variation of the tensile strength, see, for example Barrett (1974) and Larn and Varoglu (1991).
-
For tension perpendicular to the grain the size effect is especially iinportant, see Table I .
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STEMEUROFORTECI.1 - an initialivc under the EU Cornc~tPro_~r:~rnrnc
Conipl-c.ssio12 T l ~ estrength in compression par-nllcl to the grain will be somewhat reduced by the growth defects to f;.,, = 25 to 40 iV/rrnlr2. Vie reduction in strength depends on the testing method. If the specimen is cotnpressed between two stiFf end plates, which are restrained from rotation, a local failure of some fibres will lead to stress redistribution over the rest of the cross section. This will result in a higl~eraverage stress than if the specinien had been loaded via n hinged endplate. The influence of growth defects on the strength perpendicular to t l ~ cgrain is s~nal I.
Concc.i7iratecl loarli~tgpet-pendiculm to [he grni17 As mentioned above and demonstrated in Figure 4 the stress o,, a1 the bend of tlie stress-strain curve is much higher when the distribution length of o (co~~~pressive) load becotnes smaller, provided that there is enough unloaded length n from the load to the end of the loaded mernbel-, see Fig~u-e7.
0 15
Figwe 7
100
2tH) I I I I I I
Conipressive "yield" stirsses for pcrtclr loadirirlg wiflr ietgtlr I or1 n ttxwdx?rnippo~ierlalnrrg its .vi~lioleler~gth(botiorrr Ike) cotlrpared 1vit11str-engtlr llafites fizr cI$et-er~t strctzgrh cirrsses occortlirig to EC5 (cz 2 100 nz~ir). k"lrrcs fro111Barttrrnnrt attd Larrg f 1927) arrd Bnckscll (1966).
In stri~cturaicodes tlris effect is usually taken into account by tlie coefficient k,.jm in a condition of the type EC5: Part 1 - 1 : 5.1.5
GV!II~,~,5 kt.!~o
.L>>oJ,
(5)
In EC5 there will be no increase it1 bearing strength for I 2 150 ntnl, see Figure 7 . If n 2 I00 tam a linear increase may be assunxed for the coefficient kc,,,,, in the . smaller interval 15 5 I I150 r l i r t ~ up to a value A,:,,, = 1,S for i I 15 n ~ a t For edge distances, i.e. a c I00 mni, the increase will be smaller, see Table 2.
Tcrble 2
\f(rlnes of kt:,, irr Eqircifinn (5) gil~c~trIJJ EC5 ,for rlte case si~oir~rri l l Figure 7.
References Backsell, G. (1966). Expcrirncnt;~l investigations into deformations resulting from strcsscs pcrpcndiculnr to grain in Swcdish whitewood arld rcdwood in rcspcct of thc dimensioning of concrctc forn~work.Stetcns rid fijr hyggnndsforskning. Rapport 12: 1966, Stockholm. Swcdcri. Barrctt, J.D. (1974). El'l'cct of size on tcnsion pcrpcndicular-to-grain strength ol' Douglas-fir. Wood and fibcr G(2): 126-143. Baumann, R. and Lang, (1927). Das tlolz als UaustoSf. Munchcn, Ccrmany. 13odig. I. and Jaync, B. (1981). Mcch:inics of Wood nnd Wood Compositcs. Van Nostr;md, Ncw York, N.Y.. USA. Edlund, B. (1982). Bruchhypothcscn fiir orthotropcs Mntcrial. In: Ingcnieurholzbau in Forschung ~indPraxis. (Bundcsvcring K. MBl~icr).Karisruhc, Gcrmay. p. 17-21. ather, E. (1940). Druckvcrsuchc qucr zur Fascr an Nadcl- ur~dLaubh6I'rcrn, Holz als Roh- und Wcrkstoff 3: 222-226. Glos, P. (1982). Fcstigkcitsvcrhaltcn \!on Urcttscliicl~tliolz hci Zughca~rspruchurrg unri scinc Abhlngigkcit von Wcrkstoff- und Einwirkungskcnngrijsscn. Bcrichtc zur Zuvcrl~ssigkcitstl~corie dcr Bouwcrkc, 1163, Tcchn. Univ. Miinchen, Gcrmany. varying anglcs of grain. of crtislling strcngth of sprucc Hankinson, R.L. (1921). lnvcstig~~tion Air Scrvicc Inform. Circular III, No. 259. US Air Scrvicc. Washington DC, USA. I-lofincyer, P. (1990). Failure of wood as influcnccd by rnoisturc and duration of load. Ph.D. Thesis, S\r\\c Univ. of Ncw York. Syracuse. N.Y., USA. Scction 4.2.1. Johonsson, C-J, (1976). Dmgl~AllSastl~cthos lirntriilamcllcr. (Tcnsilc strcngth of laminations for glu1;im. In Swcdisl~), Chalmcrs Tckniskn I-logskola. St& och triibyggl~nd, Int.slir. S76:18. GBtchorg, Swcdcn. Kollmnnn, F, and CBtf, A. (1968). Principles of Wood Scicncc ;~ndTechnology. f)arl 1. Solid Wood. Springcr-Vcrlag, Bcrlin, Gcrmany. Lam. F. and Varoglu, E. (1991). V;iriatian of tcnsilc strcngth along the length of lumhcr. Part 1. Expcrimcntnl. Wood Sci. Tcchnol. 25(5): 35 1-359. Larscn. 14. and Ribcrhalt. H. (1981). Strength of glued lamit~atcdbcams. Part 4. Tensilc strcngth perpcndiculnr to grain. Aiilhorg Univcrsitctsccntcr. Inst. for Bygningstcknik. Rcport 81 10, Aalborg, Dcnmark. Siimcs, F. and Liiri, 0.(1952). lnvcstigatioris of tlic strcngtti properties ol' wood I. Tcsts on small clcar spccimcns ol' Finnish Pinc (Pit~~csSy1~~c.sfr'i.s).(In Finnish). Valtion Tcknillincn Tutkimuslailos, Ticdotus 103, I-lclsinki, Finland. Sucnson, E. (1938). Zuliissigcr Druck auf Querholz. Hoiz als Roh- und Wcrksrolf l(6): 213-216.
STEP/EUROFOR'TECi-1-
initiatiuc under the EU Comctt Progammc
Bending
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STEP lecture B3 B.S. Choo University of Nottinghnm
Objectives To develop an understanding of the behaviour of tiinber beams, including lateral torsional buckling and to illustrate the procedures for the design of simple beams to EC5 by way of examples.
Summary This lecture begins with an introduction to the bel~aviourand design of simple, solid timber or glularn beams in accordance with the requirements of EC5. It goes on to describe the factors whicl~influence the lateral torsional bucklinglinstability behaviour of beams. The principles described are illustrated by a design example.
Introduction Beams, in general, are horizontal structural elements whicli span at least two supports and transmit loads principally by bending action. The bending moments on the beam are due to loads which act in the plane of bending of the beam. The standard design procedure for timber beams, where the direction of grain in the wood is parallel lo the span, is to ensure tllal:
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the design bending strength is not reached or exceeded and that the bending stresses do not cause lateral torsional bucl
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the design shear strength, (see STEP lecture B4), is not reached or exceeded the design compression strength perpendicular to Lhe grain (bearing strength) is not reached or exceeded at supports and at concentrated load points
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the beam's deflection ineets the serviceability deflection criteria (see STEP lecture A I 7)
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vibration (see STEP lecture A18) would not be a problem.
This lecture is concerned primarily with sirnple beams, i.e, beains without notches, tapers or curves. The effects of notches in beams and strength reduction in curved and tapered glularn beams are covered in STEP lectures B5 and B8, respectively. In so far as bending stresses are concerned, it is necessary to check tirat there is adequate capacity at the critical cross section (whicli may e.g. be rectangular, T or L shaped) which for a simple beam will be at the point of rnaximum bending moment in the beam. EC5 also requires that the influence of initial curvature, eccentricities and induced deflections are taken into account.
Simple beams If t;lte dimensions and support conditions of the beam are adequate to prevent instability i.e. deflections occur only in the loading plane, then it can be shown according to the theory of eiasticity that the bending stresses in the beam are given by
where
n/l
is the bending moment acting on the beam,
STEP/EUROliORTEClf
- an initintive undcr the EU Comett Propr;lmmc
I3311
I
o
is the second moment of area of the beam cross-section, is a distance from the neutral axis, and is the stress at distance y.
In general, this equation may be used to describe tlie behaviour of beams if
EC5: Part
1 - 1 : 3.1.4
ECS:Pnrt 1 1: 2.2.3.7
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the section is bent only about its minor*principal axis or,
-
when bent about its major principal axis, where closely spaced, discrete bracing is provided so that the slenderness is low.
-
Since EC5 allows the design of timber structures to be carried out on the assumption that they behave elastically, the above expression [nay be used lor design purposes. The design bending strength , of a beam is defined as
-
x,,,,,,
wliele
,
is the characteristic bending strer~gth, is tlie partial safety factor for inaterial properties, and k,,,,,,, is a ~nodificationfactor which takes into account the influence of load duration, service class arid material type.
,
In addition to the k,,, factor, it is necessary to consider other factors which affect beam strength. For example, the influence ot'bearu size on ihe bending strength is taken account of by the size factor k,(see STEP lecture B I ) and, if the beam is part of's load sharing system, its bending strength may be increased by the Factor k,, (see STEP lecture B 16).
Combined stresses The most common use of a beam is to resist loads by bending about its major principal axis. I-Towever, tlie introduction of forces, which are not in the plane of bending, on the bean1 results in bi-axial bending ( i t . bending about both the rnajor and rninor principal axes). Additionally, tile introduction of axial loads in tension or cotnpression results in a further combined stress effect. For beams which are subjected to bi-axial bending, the following conditions bot11 need to be satisfied:
JnrJ,d
Jm,z,d
where the symbols are defined as follows:
om,.ZI
.L8.,.‘1 (3,r,.L11 fnl,;,, km
is the bending stress due to ~noritentsabout tlie y axis, is the bending strength due to moments about the y axis, is the bending stress due to moments about the z axis, is the bending strengtli due to moments about the z axis, and is the combined bending strength Factor, which allows for the effects of biaxial hending stresses and the fact that the load-carrying capacity of the beam is not exhausted just because the stresses (obtained from tile theory of elasticity) have reached the respective bending strengths at orie corner of the beam's cross-section.
-
-
Similar equalions are given in EC5 for combined bending with axial tension or compression. For a more detailed description of the design of columns i.e. structural elements subjected to both bending and axial compression see STEP lecture BG.
Beam instability When designing bearns, tlic prime concern is to provide adequate load carrying capacity and stiffness against bending about its major principal axis, usually in the verlical plane. This leads to a cross-sectional shape in which the stiffness in the vertical plane is often much greater than that in the horizontal plane. IL is shown in STEP lecture B6 on columns that whenever a slender structural element is loaded in its stiff plane (axially in the case of the column) there is a tendency for it to fail by buckling in a more flexible plane (by deflecting sideways in the case of the cotumn). Figure I illustrates the response of a slender simply supported beam, is terrned subjected to bending moments in the vertical plane; the pl~eno~nenon lateral-torsional buckling as it involves both lateral deflection and twisting. This type of instability is sir~iilarto the si~nplerflexural buckling of axially loaded colurnns in that loading the bean1 in its stiffer vertical plane has induced a failure by buckling in a less stiff direction. The bending lnornent 31 which such instability takes place is tenned the critical moment. The fornlulae for critical moments for beams are given in standard text boolcs such as that by Ti~nosiienkoand &re (1961). It is usually assumed that the beam inaterial has ideal elastic isotropic properties. Nevertlteless, it was shown by Hooley and Madsen (1964) that tiie theory is also applicable to timber beams where tile material is not isotropic. The critical lnornent For the bent11 shown in Figure I which is sinipty srrpported at both ends in both the )I and z axes, and is torsionally restmined about the x axis at the supports is given by
where
I,, and 1, are thc second moments of area about the respective axes, E is [lie ~nodulusof elasticity of the material, G is tiie shear modulus of the material, I,,,, is the torsional second rnoment of arca for the beam cross-section, and I, is the unrestrained length.
simplified CI-iticd For a beam OF rectangular cross-section b s / I , the correspo~~ding bending stress is given by
It should be noted that the right hand square root tenn varies from 0,94 to 1.05 for l~/'ll ratios of O,I and 0,7, respectively, which represent the realistic range of rAectanguIartimber beams. It is therefore conservative to replace the square root with 0,94.
Figure I
Latoal-fur.sior~uiI~ccklirigo f a sitt111iy.sup~~otled becrni sllnlvitrg cIi.\-~~lncettteti~ at cerrtre of beam ~rrlc/crr t t ~ i f o l mrnorticnr. ([I) sinlply s~rpparfedbeatrr, (I)) btrcklecl bemr~.
For a liomogeneo~~s material there is only one value for E and G. In wood, the values of E and G depend on the angle between the direction of stress and the grain. In general, tlie E value (parallel to the grain) should be used and G is conservatively taken as EIl6. This results in a critical stress of
Similar expressions for the critical stress niay be obtained for a variety of load cases, load positions and support conditions. The expression Sor Ad,,, given in Equation (5) is for the basic case wlierc a simply supported beam is subjected to constant in-planc moments. If the beam is subjected to a central load acting at the level of the centroidal axis of the beam, a similar expression is obtained in which thc terrn n is replaced by a constant 424. The ratio of 7d4,24 is often referred to as the "equivalent uniform moment or m factor" and is a measure of the severity of a particular pattern of moments relative to the basic case. The values of' the In factor for a number of load cases are given in Table I . In general, lateral stability improves as the molnent pattern becomes less uniform.
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The location of the load is important loads localed at the top of a slender bea13-r have a destabilising effect on its behaviour whilsr loads located at the bottom of a beam have il stabilising effect. Clearly, support conditions are also i~nportant,in that lateral support conditions which inhibit tlie developn~entOF buckling deformations, i.e. against twisting of tlle bean? at the supports in both the s and y axes, will improve a beam's lateral slability. The irnprovernent in stability due to si~pport conditions is generally reflected i n smaller values of effective lengths. Lateral torsional buckling of beams is a cotnplex subject outside the scope of this lecture and reference should be made to standard textbooks such as Timoshenko and Gere (1961). Summarising the above details the main factoras which influence lateral stability include: -
the ~tnbracedspan of' tile compressive portion of the beam (i.e. the distance between points at which lateral deflection is prevented,
-
tlie beam's lateral bending stiffness (El7), ..
-
the beam's torsional stiffness (GI1,,.), and
-
the restraints at the beam ends.
STBP/EUROFORTECI-I- an
initiative undcr [hc
EU Colnctt Progrannie
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-
-
Tobit I
Eqrrivc~lct~t rttiifon~it~~oliletlt factors (rake11f i t 1 1 Kirl~yc~tidNethercot, 1979)
The load carrying capacily of a beam which is liable to lateral-torsional instabiIity nlay be improved by the provision of' bracing members. The milin requirenients are that the bracing members are sufficiently stiff to fiold tile beam effectively against lateral ~novementand that they are sufficiently strong La witl~stand the forces transmitted by the beam (see STEP lectures B15 and R7).
EC5 requires thar a chcck is cat-ried out for the instability condition and timi t11e bending capacity is rnodif?ed by the factor K,.,, sucli that
'
Lr,z,d
(8)
' ~ I I J . ~kcri~
k,,,,
= 1
(for. A
2
0,751
and ~vl~el-e the relative slenderness ratio h , . , , , for- bending is given by:
The critical bending stress q,,,,for Equation (12) is obtained using the 5-percentile stiffness value E,+,. Variation of k,,,, with A,,,,,,, is shown in Figure 2. The similarity to the buckling strength-slendec~iessratio curves for columns as described in STEP lecture BG should be noted.
I
0
2
3
4
5 -
hr,l. ,I,
Figitre 2
\fctriatiorr qf kc,, (or k,,,,,) ivith reicttive .sle~rder~ievs ratio
A,,.,.
-
Design example A simply supported rectangular solid timber floor beam of cross section 50 x 200 r l t t ~ t ,with a clear unsuppol-led span of 3500 rrrtll is required Lo support a design medium-term load of 2 k N / r ~uniformly distributed, in service class I conditions. Check that the bending strength of the beam satisfies the requirements of EC5. prEN 338: 199 1
-
Assume the following characteristic values for bending strength and rnodtil~~s of elasticity taken from prEN 338 "Structural tin~ber- Strength classest'.
-
Mociijicarion jbctors
-
For service class I (medium-term), k,,,,,,=0,8. If the floor beam may be assumed to be laterally restrained throughout the length of its compression edge (e.g. by floor boards) with torsional restraints at its supports (e.g. by suitable hangers) then k,,, = 1,O. Since the floor beams do not span inore than 6m, and assuming the attached declcirig is continuous over at least two spans and the joints are staggered, they may be treated as a load-sharing system, hence k,., nmay be taken as 1,1 Finally, since the beam depth is greater than 150 mm, the size factor, k,, is 1.0. EC5: Pnrt 1 - 1 : 2.2.3.2
-
Hence, the design value of the bending strength is:
The design bending stress is:
STENEUROFOR'I'ECtl
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-
EC5: ]'art 1-1: 2.3.2.Ib
Thus tlie beam satisfies the bending req~iire~nents of EC5 as the calculated bending stress is less than the corresponding design value. It would also be necessary io check tl~atthe beam's shear stress and bearing stresses at the supports, as well as the mid-span deflection, are witl.~inEC5 limits.
-
It should be noted that EC5 liniits the deviation from straightness measured midway between supports to 11300 and 11500 of the length of structural tinlber and glued laminated beams and columns, respectively. Deviations of cross-sections from target sizes we limited by tolerance class I in prEN 336 for struclural timber and by prEN 390 for glued Iaininaled timber.
ECS: Par1 1 1: 7.2
If tlle floor boards cannot be relied upon to provide tlte necessary lateral restraints to the colnpression region of the beam, the bending design strength would have to be cliecked for possible reduction due to lateral instability.
Fro111Equation (7), o,,,.,., is
A I I ~from Table I , the unifoim ttloment factor for a unifor~nly loaded silnply supported beam is 0,88. Thus using Equation ( 1 2), the relative slenderness ratio is
And frorn Figure 2, or using Equation (10) the instability factor kc,, is 0,52. Thus
fn,,'!
= kcrir 10,s
= 0,82
*
10,8 = 8,86 ~ l l n ~ t z ' .
Since the actual bending stress is 9,2 ~/l,rnr', the beam would have to be enlarged or lateral restraints would Ilave to be provided.
Concluding summary The "siinpIe" beam, i.e. that which deflects only in the plane of bending, represents die great majority of bealns which the engineer has to design. -
Tile rnain design requirement for simple beams is to ensure that the values of the design strengths exceed the applied stress levels as obtained using the elastic theory and that the actual deflections are wilhin EC5 limits.
-
Tlte design strength values are obtained by applying various modification nnd partial safety factors on tlie appropriate characteristic strengths.
References Tinloshcnko, S. and Gere, J.M. (1961). Theory or' Elas~icStnhility, McGr;~w-MillBook Co. Inc. New York, NY., 2nd Edition. Noolcy, R.P., ;ind Madscn, 8. (1964). kltcral Stability or' Clue Ltminntcd Bmms. Journal of' thc Slrucluri~lDivision. ASCE, ST3: 201 - 218. Kirby, P.A. and Netllercot, D.A. (1979). Design for Structural Stnhility, Constrado Monogr;ipi~s. Crosby Lockwood Stoplcs. Gran:idn Pubtisi~ing.
-
STEP/EUROFORTECl-I nn inirintive under Lllc EU Comcll Progrnmmc
Shear and torsion STEP lecture B4
Objectives
P. Aunc Uaiversity ol'T~.ondtlcim
To explain the two pheno~nenashear and torsion on b e a m with rectangular or circular cross-sections. To present the design methods given in EC5 and the governing conditions.
Summary The presence of vertical and horizontal shear in a horizontal beam subjected to verticaI loading is stated. The shear stress distribution over the cross-section is presented and also the governing shear strength (shear paralIeI to the grain). An introduction to torsional stresses caused by torsional loading is given. Tile governing criteria and the EC5 design method are presented. Shear stresses and torsional stresses may well occur si~nultaneously.The combined action which is nor covered in the EC5 is, nevertheless, briefly commented upon. Design methods are illustrated by examples.
Introduction When bending is produced by transverse loading, shear stresses will be present according to the theory of elasticity. Shear stresses transverse to the beam axis will always be accompanied by equal shear stresses parallel to the beatn axis. In glued thin-webbed I-beams and box beams there will be shear stresses in the web (panel shear) and in the contact surface between the web and the flanges (planar shear). The planar shear strength is normally less than the panel shear strength, but either one may be critical and have to be considered. Similar considerations have to be made in the case of glued thin-flanged beams. Shear also has an effect on the bucicling of the web or panel (see STEP lecture B9). For timber (and glulam) the shear strength parallel to the grain is considerabiy lower than the shear strength across the grain (cutting off the fibres), thus the fornler is critical and has to be considered in the design of solid timber and glularn beams. Research has indicated that the shear strength depends on the stressed volu~ne (Barrett and Foscl.~i,1980), but so far a possible volume effect concerning sliear has not been introduced in EC5 (see aIso STEP lecture BI). This lecture only deals with solid timber and glulam beams with regard to shear. Torsional stresses are introduced when the applied loild tends to lwist a member. This will occur when a beam supports a load which is applied eccentric to the principal cross sectional axis. A transmission mast may be subjected to an eccentric horizontal Ioad, resulting in il combination of shear and torsion.
Shear From elastic beam theory it might be recalled that the shear stress at any point in STEPlEUROFORTECI4 - a11initiative undcr thc EU Cotnctt Progrnm~ne
B4/ 1
the cross section of a beam can be written, in general, as:
vs
TI.=-
I b
where 2, is the shear stress, V is the shear force, 1 is the second tno!nerit of the area about the neutral axis, 6 is the width of the shear plane at tile level of consideration and S is tile first moment of the area above the sllear plane taken about the neutral axis.
-
-
For a rectangular section the rnaxin~umvalue is:
The shear stress distribution is parabolic as shown in Figure 1 for a rectangular section with the rnaximurn value at the neutral axis. For a circular section tile maxiinu~nvalue is:
where A is the area of the cross-section.
It has been found by several researchers (e.g. Keenan, 1978) that the shear stresses due to point loads near the supports are less than those calcuiated according to elastic beain theory. This has led to the introduction of the so called reduced shear force.
The contribution to the total shear force of a point Ioad F within a distance 211 of' the support car1 be reduced according to the influence line given in Figure 2.
Figr~~.e 2
Redrrced ir!flrrcrlce lir~c.fir. poi~itlocrrls.
STEPJEUROF0RTECI.I- an initiative
under t t ~ cEU Comelt Programmr:
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The shear stress should satisfy the following condition: EC5: Part 1- 1: 5.1.7.1
'1:d
'
85d
.f;',,,, is the design value of the shear strength.
Design example Glulam beam will1 span 1 = 16 n r and cross-section b x 11 = 190 x 655 rz111t with solid timber decking nailed to top suface of the beam. Strength class GL32 according to prEN 1194 "Timber stnlctures - Glued laminated timber - Strength classes and determination of charncteristic values", with loading as shown in Figure 3. Design values for the governing toad case: g, = 3 kN/ijt (permanent) Dead load: 1;,= 20 kN (short term) Variable lond: EC5: Part 1-1: 3.1.7
Service class 3: k,,,,,, = 0,7 (short term) 21~=2.655=1310nznt=1,31rtz say1,3,n Maxin~u~n V, by using the so called reduced influence line, when the one point lond is placed 1,3 to the right of the support (see Figure 3).
Figlire 3
C~.iticallond ~rrangenre~zw.
Left support:
Maximum M at the point wl~ereV = 0, i.e. at a distance 7,s support A,. Maximum h1,:
3 .7,s2 -20 .(7,5 -7,4) =232fdVIrz Md =42,5 - 7 3- 2 Area: A = 124 lo3trtltl'
-
STEPlEUROFORTECI4 -
tin
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itr
from the left
Section modulus:
W =13,6 10%r1rrt3
Characteristic material properties: The characteristic values are taken from prEN I 194:
The design strength values are:
Vet-if'ication of failure condition: G,,,.,t
I3CS: P~III1 - 1 : 5.1.2
2 k,T,I
./;,,,,I
k,.,,, = 1 .O since the beatn is psevenled from bucltling laterally by the decking. 17,l c 17,2 N/ltwi2
Verificalion of hilure condition: ECS:Park 1 - 1 : 5.1.7.1
'i:,,
.Ls.r/
0,70 < 1,88 Nhnm'
Torsion According to commonly accepted elastic theory ttie maximum torsional slress for solid members can be written: Circular cross-section: - 2T ',or - TT r 3 where T,,, is tlle maximum torsional stress, T is the torsional monienl and r is the radius of the section.
where 11 2 b and a are numerical factors depending on the ratio /I//>.Tirnoshenko (1955) gives the following table:
STEP/EUROFORTECI-1- nn initiil~ivcunder the EU Comclk Programrnc
The iorsional stress distribution alo~lgthe principal axis for a rectangular section is shown in Figure 4. The maximum stress value occurs at mid point of each longer side.
EC5: part I-!: 5.1.8
The torsional slress shall satisfy the following condition: tf0r.d
According to Mohler and Hemmer (1977) the above mentioned criterion is on tile safe side.
Shear and torsion in combination A combined action may occur in some cases. Little research Iias been carried out, and limited information is available. EC5 provides no guidence for this situation. Mohier and Hemrner (1977). however, have suggested the following governing condition:
is the design torsional strength, which is considered to be different where fro111(and higher than) the design sliear strength, .L,,,,.
Design example GIulam colun~n(pole) with cross-section b s h = 140 x 300 n r t ~ r .Strength class GL32 according to prEN 1 194. Design values for the governing load case: \I,, = 18 kN (shoit term) Shear force: T,, = 2,4 kNt11 (short: tertn) Torsional moment: ECS: Ptlri 1 - 1: 3.1.7
Service class 3:
krrrrd= 0,7 (short term)
Area: A =42.10~mar'
-"--- 300 = 2,14 b 140
and u = 0,249 (Table 1)
STEP/EUROFORTECI-I - an initialivc under lilt EU Comett Progrilmmc
Characteristic material properties: The characteristic value is taken from prEN 1194:
The design strength value is:
EC5: Pi\rL I-!: 5.1.7.1
Verification of failure condition:
E C ~ h: r t 1-1: 5.1 .S
Verit'ication of failure condition:
According to Mohler and Hemmer (1977) the governing condition for the combined action is:
There is no design (or characteristic) value, A,,, given, and so the.f,,-value is used, which is on the safe side (Mohler and Hen~mer,1977).
Concluding summary -
Shear is rarely a governing condition in beam design.
-
For beams of sinall span-depth ratios, or subjected to concentrated loads close to the supports, the shear co~ltrolmight still be critical.
-
It is permissible to reduce the shear force due to point loads which are
located close to supports.
-
For poles or masts embedded in the ground (and thus cantilevered) the shear force may be high and therefore critical.
-
Coilcerr~ing torsion tnase research is needed to confirm the torsional strength value.
STEPIEUROFORTECi-1- an initinrive under thc EU Colt~ctlProgramme
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Further investigation Ilas to be carried out in order to establish a reliable basis for design criteria in the case of co~nbinedshear and torsion.
References Barreit, S.D. and Foschi, R.O. (1980). Consider:lrion or size cfrccts in iongi!udinel shear strength. In: Proc. of thc Cll3 W18 Meeting Otanicmi, Rnlnrtd Pnper 13-6-7. Kecnan, F.J. (1978). 'Il~cdis~ributionol' shear stresses in timber benms. In: Proc, of the C1B WIX Meelins Perth, Scotland Paper 9-10-1. MBhler, I(, and Hemmer, K. (1977). Vcrrormungs- und FestigkeitsvcrhnIten von Nadclvoll- und Rre~tschichtholzbci Torsionsbeanspructiung. Holz 81s Roh- und Wcrkstoff (35): 473-478. Tirnoslrcnko, S. (1955). Srrength of materials - Par1 I, D,Ven Nostrand Company, Inc. Princeton, Ncw Jersey, Third Edition.
Notched beams and holes in glulam beams STEP iecturc BS P.J. Guslnfsson Lund University
Objectives To develop an understanding of strength and fracture of' notched beams, and beams wit11 a hole, and to review concepts of fracture mechanics, forming the theoretical basis for the notched beam strength equation in EC 5.
Prerequisite A4
Wood as a building Inalerial
Summary The lecture begins with a general introduction to the performance of beams with a notch or a hole. Then, a brief review of the concepts of frachlre mechanics is given. For end-notched beams a strength equation from EC 5 is included and for glularn beams with a hole an equation from literature is included. Some typical test results are indicated. Methods for reillforcement are mentioned.
Introduction In Figure 1 beatns with various types of notches or holes are shown. A notch or a hole may very significantly reduce the load bearing capacity of a beam and should preferably be avoided in design. Thougll not to be desired, a notch may be needed in order to bring floors to desired levels, to give clearance or to enable fit between structural members. In particular in very old timber construction, various types of notches can be observed to have been e~uployedin the detailing of sti-ucturai joints. Large holes in glulam beams can be required, for instance, for accommodating of ventilation pipes.
Fignrc I
Norclled bearirs utrd beartis 119i1h0 Itole. Brokol li~icir~rlicatesprobable crack pi.ol~ngaiionpntlr.
Fracture may develop from a notch or a hole as indicated by the broken lines in Figure 1. The fracture is often of a very sudden and brittle nature, taking place without being preceded by any large deformation or after visible warning. Depending on the geometry of the beam, the rapid crack propagation along the beam may or may not lead to a complete collapse of the beam. The initiation of crack growth is due to perpendicular to grain tensiIe stress or shear stress or a combination of the two. At the tip of a notch these stresses may become v e ~ yhigh. According to linear elastic stress analysis the stress at the tip of a sharp STEPIEUROFORTECCI- an initiative undcr tlie EU
Cor~lcttProgrnrnrnc
notch even approacl~esinfinity, Figure 2. In suck cases the magnitude of stress cannot be defined and the stress is then denoted as singular. Due to the limited strength of the material the stress at the tip of the notch does, in reality, not approach infinity. Instead, due to local damage of the material the stress distribution at the instant the crack starts to propagate may be as indicated by the broken curve in Figure 2.
Figtrre 2
Stress ar rlrc lip cfcr ~rotchcrccordir~gro litleur elcisric rlicory citrcl CIS cstir~tcited it! prc'ctice, ~u.specrii~ely.
Drying of the wood can give a very significant addition to the local high stress and also itself cause the development of a crack at a notch or a hole. The effect of drying is twofold. As end-grain is exposed bare at a notch or hole, the rate of drying may locally become high. Moreover, the non-uniform cfiaracter of' the geometry at a hole or a notch adds to the magnitude of the moisture gradients and to tile prevention of free shrinkage of the material. To reduce the risk of fracture caused by drying it is stated in design recorn~nendationsthat end-grain surfaces at a notch or hole must be painted, or finished in some other way, so that moisture transfer is prevented. The general recommendation to avoid notches and holes is of particular relevance if the climate and relative humidity may vary.
Concepts of fracture mechanics Bcickground As the very high stress is often concentrated in a very srnatl region it is difficult, stress even meaningless, to try to determine and in the case of theoretically i~~finite by any conventional stress criterion the load bearing capacity of a beam with n hole or a notch. According to a conventional failure criterion the magnitude of stress in the [nost highly stressed point is compared to the fracture stress, i.e. the strength of the material. To determine load carrying capacity one has instead to rely either soIely on tests or else, in addition to tests, on concepts of fracture mechanics other than conventional stress criteria.
Frcictc~~-e rlzecha~rics- geneml Fracture mechanics is a part of the science of the strength of materials. A solid body responds to extreme loading by undergoing large deformation or fracture. The phenomenon of fracture, i.e. separation, loss of contact, between parts of the body, is the topic of primary interest in fracture mechanics. From an engineering point of view, the calculation of the magnitude of load that causes fracture is of the lnost interest. In cases when there is no or only minor stress concentration, e.g. in the case of a structural member in homogeneous tension or bending, the calculation of the fracture load can be carried out by a conventional stress criterion. On the other hand in the case of a very high stress concentration, e.g. at the tip OF a sharp notch or crack, some other approach is needed. Then, within the framework of linear elastic STEP/EUROFORTECM - an initiative undcr the EU Cornctt Programme
theory, a rational calculatior~of fracture load can be based on either analysis of the .stress i~ite~tsit), at the tip of the notch or else on analysis of the energy relense rate when a crack is propagating. Although these two alternatives are fonnally different, they are basically quite analogous. Here only the latter approach will be furtl~er discussed. Analysis of cracks within the framework of linear elastic theory is often called lirreor elcrstic .fincrrrre rneclianics. B y other lnodels attelnpts are inade to consider explicitly the non-linear performance of the material in the vicinity of the tip of the crack. This refers in particular to the fracture softening and damage that talces place in the .fr.rrcirire process regi011 in front of the open crack. In linear elastic fracture mechanics this energy dissipating fracture process region is assulned to be very small when colnpared with the size of the actual structural detail and is lnathe~~iatica~ly regarded as a point, i.e. a region of zero size.
A beam with a considerable longitudinal crack and loaded according to Figure 3 is considered. It is assumed that stress and strain within the bealn are zero when the external load, F, is zero. According to linear eiastic theory the potential energy of the actual system, consisting of the beam and the load, is
where rr is the displacement of the point OF loading. By elementary theory of bending of beams
where E is the tnodulus of elasticity and I = b(i1/2)~/12the second lnoment of area of the cross-section of each cantilever part. Wiih 11 from Equation (3, Equation (1) gives
The change of the potential energy, dW, during a srnail propagation, dci, of the crack is then obtained by dcriv~t' lon:
This decrease of the potential energy corresponds to a positive energy release, - (IIV, and to a simullnneous increase of the fractured area by b cl a. The energy release, -dW, pel- frncture area, b d o, is usually denoted C (after A.A. Griffith, who in the 1920s presented pioneering works on fracture mechanics) STEP/EUROFORTECH
- at1 initiiuivc unclcr ~ h EU c Comctt Progmmrnc
B 513
G = =-dW - F"~ bda bEl When the load F is so large that the crack starts to propagate, G has reached its critical value, G,. This value corresponds to the energy dissipating ability of the material and is regarded as a matcrial property. For European softwoods, depending on the de~isityof d ~ ewood, G,. is roughly in the order of 150 - 600 .1/Itr2 for perpendicular to grain tensile fracture (Larsen and Gustafsson, 1990). Thus, the fracture criterion is G = Gc (6) wl~iclltogether with the expression for G, Equation (S),gives the fracture load PC:
In this equation two general and importatlt principles should be noted: a)
The material properties that are decisive for resistance to crack propagation are stiffness, here denoted by E, and fracture energy, here denoted by C,..The perpendicular to grain terlsile strength of the material is not predicted to i~ifluencePC,at least not directly.
b)
The load bearing capacity, is strorlgly size-dependent in the sense that the magnitude of some forn~alstress at failure, e.g. I;;. /(bh), decreases if the absolute size of the specimen is increased.
the above exarliple it has tacitly bcen assumed, by using Equation (2), that the speciruen is sle~ider,i.e. that nicio I~/ciis small. The above method of calculntion can be applied to other cracked geometries. Then Equation (2) lnust of course be replaced by an equation relevant to the co~nplianceof the actual geometry. I11
End-notched beams; theoretical and experimental results
By the above method of tlleoretical analysis, for a beam loaded and with an endcrack according to Figure 4a) (Guslafsson, 1988) the load at crack propagation is
a and p are geometric ratios as defined in the figure. G,, and E,, are the n~odulus of shear stiffness and the ~nodulusof elasticity parallel to grain, respectively. The STEPtEUROFORTECI-I- nn initintivc under tile EU Cornett Progrnrn~rlc
same equation is valid for a square shaped end-notch, Figure 4b), and also for the various types of notch indicated in Figures I g), 11) and i). For small notch depth, i.e. for a close to 1,0,the resistance to notch failure is high. In that case also the risks for ordinary shear failure and bending failure of the net cross-section, altb, must be considered.
In Table 1 a few examples of various experimental results regarding short term load bearing capacity are given. (From compilation of literature and tests: (Guslafsson, 1988) and (Riberholt et al., 1991).) The values indicated are mean values and they were obtained for dried timber with a homogeneous moisture content. The coefficient of variation for a test series is typically in the order of 20 %. Table 1 aims to illustrate the achral and low strength of notched beams even at the current favourable conditions and how various parnmeters infiuence. It is interesting that the mean value as well as the 5-percentile value of V, has been found to be higher for specimens with a knot in the vicinity of the notch than for those without any ltnot (Larsen and Riber-holt, 1972) and (Mtjhler and Mistler, 1978).
Pine
50 200
44
0,75
0.5
0
4,04 1,9L
Clulam
300 567
90 160
0,50
0,1S
0
2,16
120
32
0,83 0,75 0,50 0,33
0,25
0,92
0,42
0
380 I ,32 [,I3
Spruce
Gldnm
600
100
1.41
0
2,90 2,52 2,39
122
0,75 0,50 Spruce
95
45
0,75
0.33 O,G6
0
3,33 2,94
GIuinm
305
79
0,70
2,5 5,5
0
0,69 0,36
Spruce
95
45
0,75
0,33
0 I 3
3,44 4,7 1
0
2,16
GIulnnl
Tablc I
300
90
0,50
0,15
3,33
2
2,76
8
4.16
Test rcsrilrs. Strerigrll (rltea~tvnl~rcjof va~.ionsetrcl-t~otchsdbeorlrs.
EC5 equation for end-notched beams and its background Before the development of the EC5 equation, n few simplifying modifications of Equation (8) were made (Larsen, 1992). The ratio E,IG,, was throughout set equal 10 16. Secondly, the introduction of the "new" material parameter G, was avoided is proportional to the shear strength of the material, .fir. by assuming that The constant of proportionality was found fro111test results. Solid wood and gIulam were assigned somewhat different constants. Moreover, from test results (Riberholt et al., 199 1) a factor that considers the effect of a taper, Figure 4c), was developed. STEPEUROFORTECi-I - an initi;ltive under ~ h EU c Co~ncriProgramme
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ECj: part
1.7.2
From the above the risk of crack propagation from a notch is taken into account in EC5 through a formal reduction by a factor k,,of the design shear strength,j;.,,,, of the net cross-section ball:
where the reduction factor k,.(6 1,O ) is
For solid Limber k,, is set equal to 5,O and for glulam k,,is set equal to 6 5 . Note that of another the beam depth, h, 111ustbe in urn?.To avoid the risk of the deveiop~~~ent mode of failure, shear failure in the net cross-section, a value of k,,greater rhan I ,O may not be used in Equation (9). If the notch is located on the compression side of the beam, Figure lc), k,. Inay be set equal to 1,O. Figure 5 illustrates how li,, is affected by a, P, i and 11. The EC5 equation refers to beams of stnlctural size. For very s~nnllrnembcrs the non-zero size of thc fracture process region can be of importance, To consider this ill an iipproxi~nateInanner the distance P h may in the calculations be assigned i1 somewhat increased value, e.g. increased by 10 I ~ I ~ Such I . a consideration is of particular significance if parameters a, P iuld It are all small.
Figrrre 5
Factor I;,. versits
.fur solid finlber-beants with variorr.s 11,
artd
i.
Glulanl beams with a hole In EC5 no strength equation is incIuded for beams with a llole. Therefore, the design of such a beail1 will involve specific consideration in each case. In the following some guidance for i? preliminary estimate of the effect of a hole is given. In design recommendations the risk of crack development as shown in Figure 1, d) and e) is often considered by a reduction analogous to Equation (9) of the design shear strength: STEP/EUROFORTECl-I- nn initiative under the EU Co~nettProgranlme
Various proposals for the calculation of the reduction factor lih,,J,can be found. Based on test results, according to a Swedish glulam design manual (Carling and Johannesson, 1958): ( I 2a) For Dllr 5 0,1 : k,*,,= 1 - 5 5 5 ( ~ / k ) ~
For
D / h > 0,l : k,,, = 1,62/(1,8+ ~ l h ) ~
(12b)
For circular holes D represents the diameter of the hole and for square and rectangular holes D is the length of the diagonal. The hole is assumed to be placed symmetricaily wit11 respect to the depth of the beam. Comers of the hole must be rounded with a radius of curvature 2 25 ~ m l i ,the side lengtit ratio of rectangular holes rnay not be greater than 3,O and a, see Figure 6, rnay not be less than 0,5. Moreover, measures to reduce moisture variations in the timber are required.
Figlire 6
Nnri~irtalslrcar stress at o-ncking. T, ~crstrsltolr size ratio D/Ii. For tlte square arrcl rec~mrgrrlarIro1e.v D is tlre dictgorial.
Equation (12) is based on several sets of lests,of glulaln beams of one size: Iz = 90 Intti and h = 500 1 2 1 ~ 1 (Johannesson, 1983). According to the actual design recommendation, if 6 > 90 nrmt k,,,,,shall be multiplied by the furlher reduction factor (90/b)"' before inserted in Equation (1 1). In Equntion (12) there is no explicit consideration of bending. In the case of pure bending, cracks have been found to develop as shown in Figure I I'). According to the actual reconimendation, if less than 8 lamination boards remain in the net crosssection, the design bending strength shall be reduced by 25 %.
In Figure G a set of the shear loading test. results is sltown. The centre of each mark represents the mean value of 4 tests. Maximum and minimum of the individual values are indicated by the vertical bars. The quality of glulam tested was for D/lr = 0 estimated to have mean shear srrength.f;, = 5,2 N/rnm2. The corners of square and rectangular holes were rounded to r = 25 mnt, the beam size was 88 x 495 mm', the distance from supporl to centre of the hole was 1250 nrrrr and the side length ratio of the rectangular holes was 3,0.To be perfect the curve in Figure 6, representing Equation (12), should coincide with tlte mean value marks. Current deviations are on tlte safe side, STEP/EUROFORTECH - an initiative undcr thc EU Comet( Programme
B517
Methods of reinforcement
Some conceivable methods of reinforcement at an end-notch are shown in Figure 7 (Mtihler a ~ i dMistler, 1978). Principles of reinforcement to prevent failure at a hole are similar. Depending on the stiffness of the reinforcanlent and its attachment to the gfulam, the reinforcement may act together with the wood and significantly increase the load at cracking, or else the reinforcement inay become active only when the wood has cracked.
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Using a bolt as indicated in Figure 7a) it is normally required that the screw nut must be re-tightened to avoid loss of stress due to creep and shrinkage. The method according to Figure 7a) should in general be avoided. With a rod, bolt or screw glued into a drilled hofe, Figure 7b), a reinforcement with high stiffness is achieved. It must be noted that this arrangement prevents shrinkage of the wood and may therefore cause cracking if the wood is dried. A steel plate nailed to the wood, Figure 7c), may not be expected to have any very significant effect until tile wood has cracked. Gluing and nailing plywood to the sides of the beam, Figure 7d) and e), is from the technical point of view probably one of the best ways to reinforce glulam at a hole or a notch. The giue is normally designed to be the active part, the main purpose of the nails is to give pressure during hardening of the glue. Glassfibre reinforcement, Figure 7e) and f), acts in a similar way (Larsen et a]., 1994). An advantage of glass-fibre reinforcement is its appearance: it is transparent and looks like a thick lacquer. A disadvantage is that practical experience is as yet very limited.
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Other strength and safety improving measures are by tapering, Figure 4c), and rounding off. To achieve a proper effect by rounding off a notch, the radius of curvature must be large, say at least 25 tntn.
Concluding summary
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Notches and holes should preferably be avoided. They often give locally very high perpendicular to grain tensile and shear stress that may cause crack propagation. The fracture can be very sudcien and rapid. Moisture change increases the risk of fracture.
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In the case of very local and concentrated stressing conventional stress criteria are not applicable. Rational analysis can instead be carried out by fracture mechanics. Such an analysis based on energy release considerations shows that there is a size-effect in the strength. Moreover, the stiffness and fracture energy, together forming the fracture toughness, are found to be the decisive material properties.
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For end-notched beams a strength equation is included in EC5. For simplicity it assumes that the fracture toughness of the material is proportional to its shear strength.
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Beams with a hoIe or a notch can be reinforced by a bolt tightened by a nut, by a rod or a screw glued into the beam, or by nailing or gluing a steel plate, plywood or a layer of glass-fibre to the sides of the beam.
References Carling, 0. and Johanncsson, B. (1988). Limtfihandboken (Glulnm manual). Svenskt limtrY, Siockholm. Gustaf'sson, P.J. (1988). A study of slrcngtti of notched beams. In: Proc. of CIB-W18A Meeting 21, Parksville, Canada, Paper 2 1- 10-1. Johanncsson, R. (1983). Design problems for glulam beams with holes, Thesis, Clialmers University oTTecRnology, Swcden, 73 pp.. ISBN 91-7032-2. Larsen, H.1, and Riberl~olt,H. (1972). Tests with not classified stmc(ttral timbcr. Rapport nr R 31 (in Danish), Technical University of Denmark. Larscn. N.1. and Gustnfsson. P.J. (1990). The fracture energy o l wood in lension perpenlficulnr to thc grain - results from a joint tating project. In: Proc. of CIB-WISA Meeling 23. Lisbon, Portugal, Paper 23- 19-7. Larsen, 1-1.3. (1 992). Latest development of Eurocode 5. In: Proc. or CIB W l8A Meeting 2.5, AIIUS, Sweden, Paper 25-102-1. Guslafsson, P.J. and Traberg, S.(1994). Glass fibre rciniorcernenl pcrpcndicular to grain. Larscn, H.J., In: Proc. of t l ~ cPacific Timber Eng. ConT. 1994, Surfers Paradisc, Austnlia. MBhtcr, K. and Mistlcr, ILL. (1978). Untersuchungcn uber den Einilui3 von Ausklinkungen im Auflagcrbereich von Hofzbiegctdgern auf' die Tragi'estigkeit. Report, Lehrstuhl for Ingcnieurholzbau und Baukonstruktionen, Univcrsitiit Karlsruhe, Germany. Ribcrholt, I-I., Enquist, 9.. Guslnfsson. P.J. and fcnsen, R.B. (1991). Timber beams notched at the supporl. Rcpoti TVSM-707 I , Lund University, Sweden.
STEPIEUROFORTECH - nn initiative undcr the EU Come(( Progralnmc
Columns STEP ~ccturcBG
Objectives
I-I.J. Blass Delli University
To develop an understanding of the ptlenolnenon of in-plane buckling, to identify the governing parameters and to present the procedures of EC5 as a design method.
o l Technology
Prerequisites A7 A8
Solid timber - Strength classes GIued laminated tinlber - Production and strength classes
Summary The lecture begins with a non-mathematical introduction of flexural buckling. It presents the principal factors influencing the stability of colunins and shows how the buckling curves in ECS Ilave been derived. A practical example of the design of an eccentrically loaded column cornplclne~ttsthe lecture.
Introduction When a slender colun~nis loaded axially, there exists a tendency for it to clef-lect sideways. This type of instability is called flexurai buckling. The strength of slender mernbcrs depends not onIy 011 the strength of the material but also on the stiffness, in the case of timber colurnns rnainly on the bending stiffness. Therefore, apart from the colnpression and bending strength, the modulus of elasticity is an important inaterial property influencing the load-bearing capacity of slender columns. The additional bending stresses caused by lateral deflections are taken into account in a stability desigrt.
There are two principal ways to design a con~pressioninember: tile first involves n second order analysis whereby the equilibrium of' monxnts and forces is calculitted by considering tile deformed sl~apeof the respective member or stixcture. The secorld approacl~uses buckling clrrves to account for the decrease in strength of n real column compared to a compression member which is inlinitely stiff in bending. Here, the stability design is ci~rriedout as a compression design with ~nodifiedco~npressionstrength. The decrease in load-bearing capacity depends on the slenderness ratio of [he Inember in question and is based on the behnviour of a two-hinged colu~nn(see Figure 1). For single metnbers or compression rnembers STEP/BUROFORTECl-I- an initintivc u~ldcrthe EU Conlctt Programme
13611
forn~ingpart of a framework, this method can be used by First determining the respective buckling (effective) length (see STEP lecture B7) and subsequently treating the structure as a two-hinged column of the same length. This lecture only deals with column design based on btickling curves.
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Factors influencing column strength
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The Fdctors influencing the ioad-bearing capacity of a timber column may be divided into two groups. The first group involves the nominal geometry of the compressiot~member such as its cross-section and length, its support conditions and the material properties which are dete~minedby the choice of the strength class, the surrounding climate and the load duration class of the governing load case. The factors belonging to this first group are either determined by or known to the design engineer. The engineer is able to influence the Ioad-bearing capacity and hence meet the design requirements by adjusting these factors.
A second group of factors also influencing column strength involves geometric and material imperfections and variations. Since real structures are never perfect, these factors have to be considered during the design of columns. However, because the design engineer in general has no information regarding these factors, their influence has to be taken into account implicitly. The influence of these factors on the Ioad-bearing capacity of timber columr~sis included in the design rules in EC5.
Figrire 2
ECS: Part 1-1: 7.1
Stress-s~rrrit~ clrwc. of tittlber accorclittg to Glos (1978). A,, is t11ea.sy~t~ptotic value of contpressiorl s~rettgtltcind E , , , i~ the con~prcsssivestrair~at fiiil~crc.
The most important geometric i~nperfectionsof timber compression members are initiaI curvature, inclination of the member axis and deviations of cross-sectional dimensions from the nominal values. Deviation from straightness is limited to 11500 of the length for glued laminated members and to 1/300 of the length for structural timber. Deviations in cross-sectional dimensions from target sizes are limited by values for tolerance class 1 in prEN 336 "Structunl timber. Coniferous and poplar timber sizes - permissible deviations" for structural timber and by prEN 390 "Glued laminated timber. Sizes. Permissible deviations" for glued laminated timber. Material imperFections include growth characteristics and other factors which influence the stress-strain behaviour of timber. GeneraIly, the stress-strain curve is Iinear elastic until failure, for timber subjected to tensile stresses, and non-linear with considerable plastic deformations, under compression stresses (see Figure 2). The shape of the stress-strain curve of European softwoods depends mainly on the fotlowing properties (GIos, 1978): density, knot size (knot area ratio), content of compression wood and moisture content. GIos (1978) derived reIationships between STEPIEUROFORTECH - an irlitiativc uridcr the EU Comctt Programme
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these properties and the shape of the stress-strain curve for both sawn timber and laminations for glued laminated timber. From a knowledge of the density, the knot size, the content of compressio~lwood and the moisture content it is possible to calculate the stress-strain curve for a piece of timber.
Baclcground to the buckling curves of Eurocode 5
EC5:Pan 1.1: 7.2.3.2
Buclcling curves generally describe the influence of slenderness on the characteristic load-bearing capacity of two-hinged columns. Each value on a buckling curve consequently represents the characteristic load-bearing capacity of columns with the corresponding slenderness ratio. The slenderness ratio is defined as the largest ratio of the unbraced length to the radius of gyration. There are several possibilities for deriving characteristic colun~nstrength values. One possibility is to determine ctlaracteristic values 13, from tests. However, because of the vast amount of necessary tests, this procedure is too expensive to be justified. To derive the buckling curves for ECS a different method was chosen (Blass, 1986; Blass, 1987 and Blass, 1988). This method is based on the simulation of tests by computer. Here, columns are nod el led by assigning them material properties and geometric imperfections based on observations of real columns. This means that strength and stiffness values as well as initial curvature or deviations from target sizes are cl~osenrandomly for a certain column. Of course, the assigned properties have to be realistic and the correlation between the different properties llas to be talcen into account during the simulation process. Like a real column, a simulated column is then characterised by a set of properties determining its load-canying capacity.
0
40
80
120
I GO
h Figitre 3
200
Disrr-ibrrtiatrof bitckiirtg sfr-crtg~f~ nrtd c/rorc~c~er-istic irrrlriesfor hilo sletrdertres.r mrios.
Si~nulatillga Iarge number of columns of the same slenderness ratio and strength class, and subsequently calculating their ultimate loads, results in a distribution of ultimate load values. The variation in the resulting column strength values is determined by the variation in strength and stiffness properties as well as the geometric imperfections. Frorn the distribution of ultimate load values, the 5percentile as the characteristic value is determined. This characteristic value then represents one point on the buckling curve (see Figure 3). Such simulations and ultirnate load calculations may be performed for a range of slenderness ratios, resulting in a series of characteristic load-carrying capacities, or buckling strengths. Characteristic buckling strengths for a range of slenderness STEPIEUROFORTECH - an inili:~tive~inder11tc EU Comctl Programme
R6/3
ratios, obtained by such simulations, are shown in Figure 4. Since a diagrnm is inore difficult to manipulate mathematically than an equation, approximate curves have been fitted to a series OF buckling simulations like those shown in Figure 4. The form of the equations corresponds to tl~oseused in Eurocode 3 for the design of steel coiurnns. Figure 5 shows an example of a series of characteristic buckling strengths determined by sirnulation, together with the corresponding fitted curve.
0
figure 4
40
80
120
160
h
200
Clroracteristic bccdlitig .strcrrgtl~vn1rce.s for rl#ireirf slerrc1crtre.s.s rutins.
The calculation of the ultinlatc loads of the sitrtulated columns is based on a second order plastic analysis, using the plastic defonuation potential of timber subjected to compressive stresses. This method - although requiring a comprualiveiy long calculation time, caused by the necessary iteration procedures - leads to higher i~ltimateloads coltlpared with results based on an elastic solution, where the ultimate load is defined as reaching the material strength in the most stressed fibre in the critical cross-section. The plastic approach results in an increase in the perforn~anceunder combined axial compression forces and bending moments.
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Figurn 6
E C ~Part : 1-1: 5.1.10
Baidittg raonrent-osic~lforce irrte,nctio~lcrin~cs.
Figure 6 shows a bending moment-axial force interaction diagram of a rectangular cross-section, where the linear interaction represents elastic behaviour and the solid curve the characteristic strength of the cross-section when the plastic behaviour of the timber is considered. The dashed line shows the EC5 design rule for combined uni-axiai bending and axial colnpression when no instability condition is to be considered or when the internal forces and moments Ilave been determined using a second order analysis. For members under combined coinpression and bending, which are able to deflect sideways, the interaction curve changes from the shape sliown in Figure 6 for very stocky members into a nearly linear interaction for niembers with a high slenderness ratio. For the design of stocky members, the dashed line is valid for slenderness ratios h up to about 30 (correspondi~~g to A,",= 0,5)and a si~nplelinear interaction was chosen for all members with a slenderness ratio exceeding this thresl~oldvalue.
Buckling curves ECS: port 1-1: 5.2.1
In the following, the buckling curves of EC5 are presented. The relative slenderness ratios are defined by:
and
where
A, and h,,,, correspond lo bending about the y-axis (deflection in the z-direction), hZand A,.,,, correspond to bending about the z-axis (deflection in the y-direction).
For both h,,,., 5 0,5 and conditions:
5 0,5 the stresses should satisfy the following
where oc,osd is the design compressive stress and Lf;,,is the design coinpressive strength. on,,:,,and or are the respective design bending stresses andf,+?, , and-f,,,,,, the design bending strengths. k,,, is 0,7 for rectangular sections (see STEP lecture B3) and 1,O for other cross-sections.
,
In all other cases the stresses should satisfy the following conditions:
where the symbols are defined as follows: cs,,, bending stress due to any lateral loads
(similarly for k,;:) (9)
(similarly for k:) (10)
p, is a factor for members within the straightness limits mentioned above:
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for solid timber: for glued laminated timber:
P,
= O,:! = 0,l
PC
The difference between solid timber and glued laminated timber is mainly caused by the smaller initial curvature of glued laminated timber members and their smaller deviations from target sizes. Moreover, the mean value, as well as the variation of the moisture content, is lower in glued laminated timber columns compared with solid timber columns. A higher moisture content causes a decrease in compression strength of the timber and consequently a decrease in coIumn strength for low and medium slenderness ratios whereas the modulus of elasticity, which mainly determines the load-bearing capacity of slender columns, is hardly affected by a change in moisture content.
Design example Timber column with square cross-section 200 x 200 ~ ~ I Nbuclcling Z, length I s 4,O m. Strength class C24 according to prEN 338 "Structural timber. Strength classes".
STEPIEUROFORTECH - an initiative undcr the EU Comett Progran~me
Design values of permanent and variable load for the governing load case: permanent load: Gd = 162 kN (axial ioad, permanent) variable load: Q,, = 5 2 5 kNhr (line load, short-term)
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EC5: Pert 1-1: 3.1.7
Service class I :
k ,,, = 0,9
Design compressive stress:
Design bending stress:
Characteristic material properties: The characteristic vaiues of bending and compression strength as well as the modulus of elasticity are taken from prEN 338 "Structural timber - Strength classes". For the modulus of elasticity, tile 5-percentile value is used in tlte design since an ultimate limit state is considered.
EC5: Pert 1-1 : 2.2.3.2
The design values of the bending and con~pressionstrength are:
8, = 0.2
The design value of the member buckling resistance is calculated using the buckling curves for solid timber:
A
(soIid limber)
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EC5: Part 1-1: 2.3.2.1b
Verification of faiiure condition:
Concluding summary
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Timber columns that are not adequately restrained along their length are subject to flexural buckling.
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Buckling length, slenderness ratio, cornpression strength and rnodulus of elasticity as well as geometric and stluctural i~nperfectionsare the primary influences on buckling resistance.
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The buckling curves of ECS are based on a second order analysis where tile plastic behaviour of timber under co~npressionstress was tilken into account.
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The design of columns with A > 30 and subjected to bending stresses due to lateral loads and eccentric axial load is based on a linear interaction of buckling strengtll and bending strength.
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References
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Blass, I.I.J. (1986). Strcngtl~modcl for giularn colunms. In: Proc. ol' thc Joint Meeting CIB W18IIUFRO S 5.02, Florence, [taly, Papcr 19-12-2.
Blass, 1I.J. (1987). Dcsign of timbcr colurnns. In: Proc, of [tic CIB W18 Mcaing, Dublin. Ireland,
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Paper 20-2-2.
Blass, N.J. (1988). Tlic influence of creep and duration of load on thc design of timber colunms. In; Proc, of tl~c1988 In[. ConC on Tirnbcr Eng. Scnttlc, U.S.A. Glos. P. (1978). Zur Bcs[irnmung dcs Festigkcitsucrhaltcns von Rrcttschichtholz hi Druckbcanspr~~chung aus Wcrkstoff- und Eit~wirkunyslrcnngriiucn. Dissertation, Tcchniscllc UnivcrsitYt Mlinchcn, Germany.
STEPtEUROFORTECH - an initiative under tl~cEU Comctt Prograrnmc
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Buclding lengths STEP lecture R7 11.1. Blnss
Dclft Universily of Technology
Objective To describe the concept: of buckling (effective) length and its application in design to practical colun?ns and frames.
Prerequisite B6
Columns
Summary The concept of the effective or buckling length is described. The principal factors influencing the buckling lengtl~sof columns and frames as well as simple approximations for practical cases are given. An example of n three-hinged frame with semi-rigid comer connections complen~enfsthe lecture.
Introduction Buckling curves for the design of timber colulnns are generally based on the load bearing capacity of columns where both ends are simply supported (see Figure 1). The support conditions of cornpression members in actual timber struchxres often differ from those shown in Figure 1 . In order to be able to employ the buckling curves in EC5 for these more practical cases, tile concept of an effective length is used.
One example of the difference between real length and buckling length can be found in the internal member of a truss. In practice, t l ~ eexternal members (chords) are often braced at the outer edges of the top and bottom chord, respectively. In this case, the buckling lengths of the internal members car1 be assumed to correspond to tile distance between the braces and hence are larger than the distance between the ~nembernodes. The effective or buckling length of a con~pressionmember is defined as the length of a hypothetical two-hinged column with the same elastic critical buckling load as the member in question. Thc effective length can be visualised as the distance STEPIEUROFORECH
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B7/1
between two cor~secutivepoints of contraflexure of the actual cotnpression member (see Figure 2). In practice, an effective length factor P is used which denotes the ratio of the effective length to the real length of the member. Figure 3 shows the four EuIer cases where the buckling length is given for different idealised support conditions of the column.
&tire
2
Effective lerlgth qf ci clcrn~pcdcohrn~rt1vitl1rr ser~ri-r'igiclbase corr~reciiorr.
In this lecture, approximate solutions for the buckling lengths of different systems are given. Where the approximate solutions do not apply, a second order analysis shouid be carried out, calculating the equilibrium of moments and forces and considering the deformed shape of the respective member or structure.
Figure 3
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6.1
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Btlcklirrg lcrrgrhs for iilealisecl sttpport co~rdiriolls( E ~ ~ lcases e r I to IV).
Influence of rotations in semi-rigid connections
133: Part
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Since completely rigid connections are almost impossible in timber structures, the rotations in semi-rigid joints should be taken into account when determining buckling lengths. The rotational stiffness K, of a semi-rigid connection is defined as the moment necessary to cause an angle of rotation of one radian. With tile slip modulus K,,of the fastener, the rotational stiffness of a setni-rigid connection is calculated as:
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where I ; denotes the distance between the single fastener and [he centre of the conr~ection.As an example, the buckling length of the column in Figure 2 is derived considering the influence of the rotation in the semi-rigid joint at tbe base of the colurnn. The approximate solutions for buckling lengths, ldcing into account the influence of the rotation in semi-rigid joints, are valid in those cases wltere this influence decreases the critical elastic buckling load by not more than about 20%.
Using the notation of Figure 4, the bending moment M is:
M(x)
=
N yCy)
(2)
This results in the follotving differential equation
with the solution y = A sin(p .v) where p = { m i
Using the condition
M(x=l)
=
N y(x=I)
=
K, yl(x=l)
yields
An nnalytic~tlsotution of equation (8) does not exist. However, for
STEP/EUROT;ORTECf.i - an initiative under Ll~cEU Comctt Praprammc
Substituting for tan (p 1) using the approximation in equa~ion(lo), the critical elastic buckling load becomes:
Compared to the critical elastic buckling load of a two-hinged coiulnn (Euler case 11)
lCJ
the effective length factor
is giveti by
Interconnected colrrrnns
IF LWO-hingedcolumns are braced by a coIulnn clamped at its base (see Figure 5), the critical buckling load of the cla~npedcolurnn decreases due to the additional forces Ni which cause r\ horizontal force in the deformed system. Considering the effect of the rotation in the serni-rigid joint at the columli base, the effective length factor for the systein shown in Figure 5 (buckling in tlie systein plane) i s approximately:
witti a as defined as in Figure 5. The two-hinged columns braced by the clarnped column are of course to be designed with a buckling length corresponding to their real length, STEPIEUROFORTECH - an initiative under tlrc EU Coinett Programme
Arches For three- and two-hinged arches (see Figure 6) with a ratio IT/[ between 0,15 and 0,5and essentially uniform cross-section the effective length for buckling in the arch plane may be assumed to be Lg = 1,25 s (15) where s equals half the arch length. The normal h r c e at the quarter point should be used in the buckling design.
Two- and three-hinged frames For two- and three-hinged frames with an angle of inclination of the columns of Iess than about 15" (see Figure 7), the following equation for the buckling length of the colunln applies:
Figat-e 7
The-lrirrgeclf1'ff111~.
The respective buckling length of the rafter is:
where N and No denote the axial forces in the column and the rafter, respectively. For tapered rafters or columns equations (16) and (17) may be used provided the second ~nomentsof area of the nfter and the colulnn are taken at 0,65sand 0,6511, respectively (see Figure 7). These second moments of area are also used to determine the slenderness ratios. STEPIEUROFORTECH - an initiative under thc EU Comelt Progmmlnc
B 7/5
Columns or rafters with knee bracing The buckling lengths of the colulnns of portal frames as shown in Figure 8 (left) and the buckling lengths of the rafters in Figure 8 (right) for buckling in the frame plane can be estimated as: (18) lef = 2 s, + 0,7 so
Figwe 8
Bor-tul frorile (left)
N I I fltrec-hingedficltt~c ~ bclitll
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V-slrriped colitn~trs(right).
Torsional buckling of spatial frames
For axi-symmetrical structures two types of buckling may occur: the first is the buckling within the plane of the half-frame, the second is the rotational buckling of the spatial structure (see Figure 9). The latter is characterised by rotation OF the compression ring about the verticaI axis of symmetry. For 1 < P < 2 and ~ l / s< 0,2 the following approximate solution for the effective length factor for tile rdfter of the half-frame exists:
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P
Here, El is the bending stiffness of the rafter for bending about the vertical axis and K, is the rotational stiffness of the connection between the rafter and the compression ring, also for bending about the vertical axis. For tapered rafters, the bending stiffrtess is taken at a distance of 0,65 s from the semi-rigid rafter-compression-ring cor~nectionsimilar to the procedure for two- and three-hinged fratnes.
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Example In the following example, the buckling lengths of the column and rafter of the tbree-hinged frame shown iri Figure 10 are calculated. The influence of the semirigid conrlections in the frame corners is taken into account. STEPIEUROFORTECN - an initiative under ;lie EU Comelt Programnle
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Fig1tr.e 10
prEN I 193: 1993
Tltree-hitiger1 fratttc rclitit semi-rigid frart~c corners. I?: Rafter, C: Collln~rt. Oarer- circle: 20 cfoio,c~els p> 24 rnn~,inlzcrr circle: 16 clowels 0 24 nufz.
Glued laminated timber strength class Gt28.
E,,
=
p,
=
EC5: Part 1- 1: 4.2 EC5: Part 1-1: 6.1 Equation (1 )
K,,, = K,, = K, =
Equation ( 1 6 )
Column:
9600 N/IIII~' 410 kghi3 pkl" d / 20 = 410'" ' 24 1 20 2 KT,,/ 3 2 - 6640 . (20 . 550% 16 . 330')
STEPlEUROFORTECI-1:-
tin
= 9960 N/n~nz = 6640 N/mut = 76,9 . 10' Nntnr
initiative under ~ h EU c Cornctt Progmmmc
Equation (17)
Rafter:
Concluding summary
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The concept of effective length enables buckling curves for two-hinged colutnns to be used for the practical desig1.r of con~pressionn~emberswith different support conditions.
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Rotations in semi-rigid connections generally decrease the elastic critical buckling load of timber coinpression members.
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Where the approxitnate solutior~sgiven here do not apply, a second order analysis should be carried out, calculating the equilibrium of momelzts and forces considering the deformed shape of the respective meit~beror structure.
References
Briininghofl, H. ct 81. (1989). I-lolzbauwcrke - cine ousfilhrlicl~cErliutcrung zu DIN 1052 Tcil 1 bis Teil 3. Beutii. Berlin Kiiln, Germany, 238 pp. tleimesf~ori',R. (1979). Be~ncssungvon l-iolzstiir~cnmit nachgicbigcm FuOanschluU. Holzbau Statik Aktuell No. 3, Arbeitsgerneinsci~aitFlolz, Diisscidori, Germany.
Additional Notation K, Rotational stiffness of a semi-rigid connection r,
p
Distance between a single fastener and the centre of a connection Effective length factor
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Tapered, curved and pitched cambered beams STEP lccture 88 J. Elilbccl~J. Iciirth Univcrsit%tICi~rIsruI~c
Objectives To describe tile special aspects of tapered, curved and pitched calnbered beams a i d to present tlte design methods of EC5.
Prerequisites A8 B1
Glued laminated timber - Production and strength classes Volutne and stress distribution effects
Summary Tile lecture starts with basic information relatecl lo stress calculations for tapered, curved and pitched cambered beams and explains the parameters influencing the bending strength. EC5 equations for cnlc~~lalion and design are given. Two practical examples, one for a curved beam and the other for a pilched cambered beam, complete the lecture.
Introduction Glued laminated beams are often tapered andlor curved in order to m e t architectural requirements, to provide pitched roofs, lo obtain niaxi~tiurninterior cleara~ice,and to reduce wall height require~nentsat the end supports. Tile most commonly used types are the single tapered beem, the curved beam with constant cross-section, the double tapered beam and the pitched cambered beam (see Figure I).
Fig~~1 re
(0)Sil~gle tapered bec~~zr, ( b ) crtnled benrli ivirh corrsirritt cross-sectiotf. ( c ) clo~ible~crperedbeanr, (cf)pitclred caarberrd beatlr.
As a result of their shape and the ~nanufacturingprocedure, tliese beams usually have parts with sawn taper cuts and apex zones with or withoilt curved la~i~inations, It is reco~nrnendedillat the laminations should be parallel to the tension edge of the beam wit11 the tapered edges located on the compression edge. The distribution of' bending stresses in tapered beams is non-linear and therefore should be calculated using the theory of thin anisotropic plates, taking into account the ratios of E,:,/Ew',, and E,JGand Poisson's ratio. For clesign purposes the maximum bending stresses at the topered edge can be calculated approximaleiy (Riberllolt, 1979) according to simple bending theory modified by ri factor depending on the slope of the top face (see Equation (4)).
In tlie apex zone of' curved and tapered beams the distribution of the bending stresses is also non-linear. In the apex zone of curved and tapered beams the distribution of the bending stresses is also nonlinear. Additionally, radial stresses perpendicular to the grain are caused by bending moments. Figure 2 shows an incremental section of a curved beam to illustrate the distribution of the bending stresses. The fibres on the inner side of the beam are shorter than those on the outer side. Based on Navier's theory and assun?illg the neutral axis at mid-depth the strains at the edges are as follows: E
'
.
Adl. = I dl,
i r e2
>
Ad1 O dl,
=
E0
Distribrttiorr qj'bendi~rgst~.esse.sin a cut~~ecl i~ealt~.
Thus, in accordance with Hooke's law, the nlaximum bending stress 1 cr, I is greaterthan 1 o,,. Equilibri~~~n of the internal rorces over the cross-section is only possible if the neutral axis is closer towards the inner edge. The distribution of the bending stresses is therefore non-lincar and hyperbolic with the maximum stress at the inner Fibre. For design purposes the maximum bending stresses can be calculated approximately (Blumer, 1975, 1979) by 111odifyingkf/lV with a shape factor k, (k, > 1, see Figure 7) which depends on the ratio of the cross-section depth a1 tlie apex, Iz,,,,, to the radius of curvature of the centerline of the member, 1; as well as for tapered beams on the slope of the top face, a. For cur-ved beams of constant depth, a = 0.
I
Bending rnornents in curved members cause radial stresses perpendicular to the grain. Figure 3 sl~owsthe apex section of a curved beam under a constant moment. Assuming, for simplification, a linear stress distribution, it can easily be shown that the resulting tensile and compressive forces, & and F,., lead to the force U in tlte radial direction. If the rnornenl increases the radius of curvature, the radial stresses at the apex can bc calculated are in tension. The maximum tcnsior~stress, max a,,,,, <,1 , see Figure 7). approximately by rnodifying M/W with a shape I'accor I,, (li, In addition to the bending stresses in glued laminated curved beams, consideration must be given to the bending of the laminations during glulam production, especially in beams with a sinall radius of curvature. The bending stress in a curved lamination with thickness r, ratio of curvature r, / I = 240 ancl E,, = 10 000 Nhnnt', is theoretically:
These stresses are reduced due to plastic deformations and relaxation, but they have STENEUROFORTECH - an initi;~tivcundcr the EU Comeu Progrumn~e
to be taken into account in cases of large curvature. Thei-efore, the design bending strength of the beam has to be modified by a curvature factor li,.
Figure 3
S~ressesperpericlicrrlar to grai11 utider C O I I S ~ ~ Irtiot~iet~t. ~I
Figlrre 4
St~.essesparnllel arid perpo~dicrrlurto grai~lrrrld slzear s~lzs~scs c ~ at raper.ed ecige tn~der;( a ) cbot~rpres.si,~e henriirrg sfress, (b) fetlsile be11~1itzg stress.
At the edges of' tapered beams with sawn tapered cuts, stresses perpendicular-tograin arid shear stresses coexist with bending stresses (see Figure 4). The perpendicuiar-to-grain stresses are in co~npressionor in tension, depending on coinpressive 01- tensile bending stresses, respectively.
This stress cornbination can be lalten into account in the design procedt~resby using 3 reduced design bending strength, J;;,.,,,as de~nonstratedin Equation (7).
Design Procedures Sir~gletopel-ed ben~~ts
WItere the grain is parallel to one of tlte surfaces, and the slope a < lo", the design bending stress in the outernlost fibre, where llte grain is parallel lo the surface, sllould be calculated as (see Figure 5):
and on t11e tapered side as STEPJEUROFORTECI-I-
;in irlitii~livcilndcr
thc EU Comctt Prograrnmc
B 8/3
o,,,,,,d
=
(1
-
4 tan'ol)
6Md -
bk'
The rnaxil~lunlstress condition occurs at the paint s,where 30/3,~= 0. In the case of uniformly distributed load s ~'esultsin: x = 1 1 (1 -1. /lop 1 /is)
In the oulertnost fibre at the tapered edge the stresses should satisfy the following condition: u,,a,d
'
-
(6)
L,a,d
-
where P
in tile case of con~pressivestresses parallel to the tapered edge (in the case of tensile stresses, f,,,,,,, in Equation (7) is replaced by A,,).
-
Dolrble tapered, crlrvecl nild pitclted cantbered bentits The apex design bending stress should be calculated as follows:
-
where Ir,, is defined in Figure G and
The slope angle a is defined in Figure 6. For curved beams wit11 constant crosssections, the slope angle a sliould be assumed as a: = 0".
Fiigrtre 6
Elel~atiarzalrd s~rc!ss di.\*tribrrtiolz nt npcx ,far ( a ) iionble tuperccl bemrl, (b) pitclted cur~rberaclDenr~r.
The design tensile stress perpendicular to the grain due to the bending ~noment should be calculated as follows:
where
with 1c5= 0,2 tana
k,
= 0,25
-
1,s tana
+
2,6 t d c t
(17)
Mi,,,,,, is the design bending snoment at the apex. In the apex zone, the design bending stresses sllall satisfy the following condition: 'm,d
'
(1 9)
krf;n,d
where
I
k r =
\
0,76 + 0,001 r,, It
for
r , , It
for
q,,It. < 240
2 240
In tile apex zone the design tensile stress perpendicular to llie grain should satisfy tile following condition: 'r,eo,d
'
k d ~(0'
lv)O'z-6.9o.d
(21)
where k,,is a Pictor which takes into account the stress distribution. The ratio of the reference volume I/,,= 0,OI 1 1 1 ~to the stressed volume V considers the influence of the volume on the perpendicular-to-grain tensile strength (see STEP lecture B1). I/ should as a rnaxirnum be taken as 2/3 of tile whole beam volume Y,, (see Table 1).
STEPEUROPORTECFI - an iniiiillivc undcr thc EU Comctt Programme
1.0
0,oo
0
0,l
0
0,3
0.4 l'cl,P
Figtire 7
Curved beam wit11 k,, crosssection Double tapered beam
= 1,4
= 1,4
k,,
=
Pitched cambered
Table I
I,7
V=
crrt-rlatlim, r;
P b ( /to,,2 180
+
=
0,5
b sinacosa ( r ,
+
/r
atrd slope angles, a.
2 Zri,,hOp)s ?V6
tana
V = bltop ( 1 - -)
V
0.4
0,3
I1'IP
2
k,
0,2
0,l
fr
I;crctoia k, nrld k, ,for-d@e~.errtt-uc1itt.s of
constant
beam
0
0,s
4
/r,,J2
2
5
- V6 3
- ria 180
s
3
Fclctor k , , arrd vollrtrre I/ for d[ffercfrttype.s of Beatils.
Design examples Curved i~enuzptritl~ constci~~t CI.OSS-S~C~~~~Z Material:
Glued laminated timber made of spruce. Strength class GL28 according lo prEN 1194 "Glued laminated timber - Strength classes and determination of characteristic values"
Figure 8
Elc~~atiorr c111dS~I.E.SSdtstribtttior~ut ~ e - ~ jcrrrved u r fienrtl of cotlstarlt crosssecriorl trr~cler~itlifOrt?t load qtP
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Design bending stress and design tensile stress at apex:
v=1,40m3
kd,=1,4
k,=1,0
Characteristic material properties (CL28, prEN 1194): .f;n,A,I.= 28 N/tntrrz = 0,45 ~ h t m " The design bending and tension perpendicular to the grain strengths are:
Verification of failure condition:
Pitched canlbei-ed benit1 System and loading as before; apex with glued haunch (see Figure Gb). Depth at apex: Radius: I- = 19,50 +. 1,32/2 = 20, I G tn A,,, = 1,32 nl Design stress perpendicular to the grain at apex ( a = p = 10'): wit11: V = 1.55 1n3, k,,,= 1,7, k, = 1,0
k,,
=
0,2 tanlo' c
+
( 0,25 - 1,5 tan 10'
+
2,6 tan210' )
( 2,l tanlo' - 4 tati210' ) . 0,065"
Verification of failure condition: or,,,,, = 0,249 N / I ? I I ? J ~ > k,,/ I<,,&
, = 0,36
. 0,065
0,041
*
1,7 . 0,277 = 0,172
~ / ~ i t l l t ~
The failure condition of the perpendicular-to-grain tensile stress is not satisfied. This compared to the curved beam. One reason is the fact that in Equations is s~~sprising
-
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(14)-(18) a constant Inornent is assumed to act in the curved part of' the beam. A more accurate calculation shows that the stresses in a pitched cambered beam under uniformly distributed loads are 20 % less, whereas the stresses in the curved beam remain aln~ostunchanged (Ehlbeck, ICutth, 1990). Nevertheless, differences exist between the results from tile design methods of' EC5 and test results showi~igthat both beam types have similar failure loads.
Concluding summary
-
-
-
[n single tapered, curved, double tapered and pitched cambered beams the tensile bending stresses at the inner edge are greater than in straight beams.
-
-
In curved zones with a bending moment increasing the radius of curvature, tension stresses perpendicular to the grain occur.
-
-
Tapered edges reduce the bending strength because of' the combined effects of bending, compression, tension and shear parallel and perpendicular to the grain.
-
-
Bending of the laminates in curved beains reduces the bending strength when the radius of curvature is small.
-
References
-
Blumcr, 14. (1975). Spannungshcrcchnung an Brcttschichtholz ]nit gckriimn~ter Lingsachse und ver9ndcrlichcr TriigcrhBhc. In: I~loizbau(Ziirich) (6): 158-1 6 1; (7): I9 1- 194: (8): 235-737. Blumcr. 14. (1979). Spannurtgsbcrcchnung :In anisotropcn Krcishogcnschcibcr~und Sattcldachtriigern kons~anterDickc. Vcriifie~~tlichung dcs Lchrstuhls fur Ingcnicurholzhau und Baukonsin~ktionct~, Univcrsillil Karlsruhc (Tfl), Dcutschland. Ehlbcck, J. and Kilnh, J. (1990). EinlluO dcs qucnugheimspruchtcn Volumcns ouf dic TragMhigkcit gckriimmtcr 'f'riigcr konst;~ntcr EIBhe tlnd gckriimmtcr S;~ttcldachir;igcraus Brcttscl~ichtholz. Forschungsbcricht dcr Vcrsuchsnnstalt for Stahl, I-lolz und Stcine. Abt. Ingcnicurholzbau, Uni\fcrsitPt Kadsrutlc (TIJ). Dcutschland. Ribcrholt, 1-1. (1979). T:~pcrcdtirnbcr beams. In: Proc. ol' the CLB W18 Mecling, Wicn, Ostcrrcich, Paper I 1-10-2.
STEP/EUROFORTECI.I - an initiative undcr the EU Comett Programme
-
Glued thin-webbed beams STEP Iccturc 139 f<.H. Sotfi -.
-
-
Norwegian lnsliiutc of Wood Tcchnoiogy
Ohjectives To introduce glued thin-webbed I-beams and box beains and to explain the background to the design method given in EC5.
Prerequisites Wood as a building material A10 Wood-based panels - Plywood A1 1 Wood-based panels - Fibre board, particle board and OSB A17 Serviceability limit states - Deformations A4
Summary The lecture starts with a general description of a thin-webbed beam. It then covers the necessary design controls based on E C ~and provides n brief lieo ore tical background. A design example is given.
Introduction A glued thin-webbed bean1 conlprises three main parts as follows:
-
flanges,
-
and glued joints between flanges and web.
web,
The flanges are often tnade of finger jointed structur~nltilt~ber,but they can also be made of otller materials such as glued laminated timber or laminated veneer lurnber (LVL). The main purpose of the flanges is to carry the stresses caused by bending moments and axial forces. Since tlre flanges normally have slnait dimensions it is important that the material has few and smalf defects.
Tile web (or webs) are made of different wood-based panel materials such as plywood, particleboard, fibreboard etc. Tile main purpose is to carry the stresses from shear forces. For long beams it may be necessary to have joints in the web. If the web joints are put in regions with low shear force they can be made as butt joints. If not it will be necessary to reinforce tile web joint. It may also be necessary to reinforce the web at the supports. The reinforcement can be made with gusset plates of wood-based panels which are nailed or glued to the web. The reinforced web at joints and supports must be designed to accom~nodatethe actual shear forces.
Production Glued thin-webbed beams are normally produced in an industrial process. To achieve an adequate glued connection between the web and the flanges it is important that the temperature is correct (see STEP lecture Al2). It is illso important that the faces of tile Ranges have been planed and cleared just before gluing and that the moisture content in both the flange and web materials is under control.
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Use of glued thin-webbed beams Glued thin-webbed beams have a high load capacity and stiffness compared with their weight. This make them easy to handle. They can also be easily rt~odiried by hand tools. Such beams cart be used principally in the saine places as solid timber. For floor and roof constructions where it is diSf'ictrlt to obtain large enough sections of solid timber and where glued laminated timber [night be too expensive (i.e. for a span of 5 - S m ) glued thin-webbed bearns often are used.
-
When the glued thin-webbed beams are used as ~uernbersin lloor, roof and wall constructions the depth of the beam ~niglitbecome quite big (300 - 500 17zr11). This makes it easy to accommodate different types of technical equipment. The depth will also give roonl for enough insulation material where this is required. In countries with cold wintcrs the di~nertsionof' the studs are defined by the demand of insulation thickness. By using a glued thin-webbed profile it is possible to optimize the material consun~ed.
-
The use in seiavice class 3 might be Iiniited because of the web material's restrictions for use in this class.
-
-
-
Special aspects of production and transport The stiffness about the z-axis is vely low compared with the y-axis. This must bc considered during the production and all transportation phases from factory to the building she. The web materials are in addition very sensitive to clamage caitsed by trarlsportation and handling. The beams ~niistbe kept under dry conditions during the building period. IL' the moisture content in the web becomes too high, the risk of getting non-eiastic deforn~ationsin the final construction is high.
-
-
Lateral stability Flanges which carry compression stresses rnust be supported to prevent lateral deflection and buckling. When the beams are used in floor cotistn~ctionas sirnply supported beal~lsthe connection between the compression flange and the floor oficn will be sufficient to avoid lateral instability. Care must be taken where the cottipression stress changes from one flange to the other, as for example at the il.ltermediate support of' a continuous beam.
EfFective values toor the cross-section It is a presumption in the calculations shown later that llte web and flanges are glued together to form a stt-uctural unit. It is also assumed that the variation of strain over the deplh of tile beam is linear. Based on Hooke's law t11e stress at a certain point can be expressed by the product of the strain and the modulus of elasticity. A bean1 may be built up with materials which have different rnoduli of elasticity leading to different stresses at the same depth. Figure I shows an example ol' how the stresses might vary for such a beat11 profile sub-jected to a bending moment. Since the rnoditli of' elasticity are different over the cross-section, it is cotnmon practice to calculate so-called effective values for the cross-section. This can be done by regarding the whole profile as one homogeneous material with the same properties as the flange material. The contribution from the web ~llustthen be reduced in proportion to the ratio of the moduli of elasticity.
STEP/EUROFORTECbI - :in iniiiativc under rl~cEU Colnclt Progrclmrne
--
-
-
--
-
Figrrra I
Exantpie of .srrcsse.s i?;igirted I - a~idBus beams.
Effective area:
Effective second moment of aren:
Because the distribution of the stresses within a co~npositecross-section changes over time due to the different creep behaviour of the components, the stresses have to be calculated at instantaneous and at final deformation.
Control. of the stresses in the flanges In a beam profile canying a bending moment most of the stresses in the flanges are caused by axial compressive or tensile stresses. The portion of pure bending will be quite small. For a symmetrical profile carrying only bending inolnent the stresses in the compression and tensile flanges will have the same absolute values. If the beam in addition to the bending moment also carries axial compression or tensile actions, the fiange stresses shall be calculated as the sum of stresses from the ~nomentand from the axial Forces.
Flirirgw The n~aximun~ stress in the extreme fibres of the compression flange is given by the following equation:
The axial stress at the centre of: gravity of the compression flange is given by the following equation:
where STEPIEUROPORTECI-I- an initiative undcr the EU Cometi Progrnrnmc
0913
kid
is the design value of the bending moment,
yo
is the distance between the neutral axis of the beam and the ultilnate fibres of tile flange. For sy~nmetricalcross-sections y,, = hl2 when h is the depth of the beam, is the axial load (in addition to the bending moment), can be compressive or tensile, and
y,
EC5: Pnrt 1-1: 5.3.1
is the distance between the neutral axis of the bearm and the centre of gravity in the compression flange.
When the actual stresses are calcu1aled they must be compared with the design strength values of the Flange: '~c.rrmr,d'fm,d
(5)
Where k,, is a factor which takes into account lateral instability. The factor 14. may be determined (conservatively, especially for box beams) according to EC5, 5.2.1 with EC5:Part 1 - I : 5.3.i(3)
A
rnb
= ----...-1,
(7)
I, is the distance between the sections where lateral deflection of tlie compression flange is prevented, and O is the thickness of the flange. The stresses in the tensile flanges are calculated accordingly.
Control of axial stresses in the web The main purpose of tlie web is to carry the stresses From shear forces but the web will also have to t,&e some of the stresses caused by the bending moment and axial loads. Therefore the web capacity must also be controlled in accordance with these stresses. Since the strain variation is assumed to be linear over the depth, the web stresses can be expressed by the following general equation:
When the equation is corrected in accordance to the actual load duration and service class, it can be expressed as:
As shown earlier the stresses in the flange are given by:
where y , is the distance between the neutral axis of the beam and the point where he stress value is calculated.
Co~~rpression side of tlie web Thc maximum stress in the compression zone of the web can be calculated ns:
where g,,,,,, is the distance between the neutral axis of the beam and the compression edge of the web. This stress shall satisfy the following condition: EC5: Part 1-1; 5 . 3 . 1 ~
(12)
CI,~:c,max,dsfc,tcgd
Tensile side of flze web The maximum stress in the tensile zone of the web can be calculated as:
where )I,,,., is the distance between the neutral axis of the beam and the tensile edge of the web. This stress shall satisfy the following condition: EC5: part 1-1: 5.3.lf
'tv,f,mn,d
(14)
'fi,,v,d
and .f;,,,,., are the compressive and tensile bending strengths of the web. Unless other values are given, tile design compressive and tensile strength of the web should be taken as the in-plane design compressive and tensile strengths.
J;.,,l,,rr
Shear stresses in the web EC5: Part 1-1: 5.3.1
Unless a detailed buckling analysis is made it should be verified that:
h,,, 70 b,,
Vds 5
(15)
,n 1
+
(
)
for 35 b,,,r itv r 70 blv
where V,,
is the design value of the shear force in the actual section,
ti
is the number of webs.
x,,f;,,,,,,is the design panel shear strength,
Shear stresses irz tlie gIlted joiizt befiveen the flnizges mtd the web As previously mentioned it is advantageous that the capacity of the glue-line is higher than the corresponding capacities of the flange and web material. Normally the weakest link in this joint will be the rolling shear strength of the web, f;,,,,,. It is assumed that the *design shear stress (T,,,,,,,,,)at the actual section is uniformly distributed. T,,,,,, can be expressed by the following equation:
where
5'' is
the first moment of plane area for a flange, calculated from the
STEP/EUROFORTECH - an initislive under the EU CornetL Progrnmme
B 915
neutral axis of the beam cross-section and I, is the total length of the glue-line in the same flange. ECS: Pert 1-1: 5.3.1
The calculated shear stress shaI1 satisfy the followil~gcondition: t ~ c o n , dsJ;:95,~,d
ir
for 19s 4 b,,
4 b,,l
r,,lm,d
., ! ,I.
,I.
d
(19)
for. l y 4 b,,,
Example
Figure 2 shows the actual cross-section. Service class 2 M, = 5,O kvtn
F ,
= 18kN
V,
= 4,8 kN
The actions are assumed to consist of 25% permanent load and 75% mediumterm load. Flanges:
strength class C30 according to prEN 338, . = 14,2 Nht~nz' k, .~sl,, = 1 1 I El = 12000 N/IIIIII'?
Lrsd= 1 8,5 Nhttttz2
z
0,95
Web: particleboard according to EN 312-6, r = 10 ~rini. .f; = 5.97 ~/nlrrl' , = 4,44 ~/,rlin' , = 3,30 N ~ I z ~ ' .f;,,q,l,il= 0,804 N/nttn2 E ",,.,, = 2475 N/iilm3 #.,+ ,.
Medium-term: Permanent:
k , k,,
= 0,75 = 2,25
kt,,,,, = 0.55
Since the particleboard web shows larger creep deflections than the solid timber flanges, the norrnal stresses in the flanges will increase and in the web decrease in time. Consequently, the normal stresses in rlte web are calculaled at inshnlaneous and in the flanges at final deformalion.
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For contt-01 nr btstnl~tnlzeousdeforiantiun
For- cuntr-01 at .fiizni!dcfor-incr fion
Cotttror! of' coiltpressi~~e flange at firtnl defor-rnation
Co~ztrolof con~plasskestrass in the web at insta~~tnneorts defoi.~?l~tio~i
STEP/EUROPORTECH - an initiative under [he EU Comctt Prograrnmc
Control oj'tensile stress in tile web at irzstailtnrzeorts defor~~iation
Corttrol of tile shear stress in the web h,,,= 100 m m <70 b,, = 700m1n h,,< 35 b,, = 350~21~
[
(50iF)]
V d = 4 , 8 W ~ 1 0 . 1 010+0,5 --- 3,30 = 4,95 W
Corzrrol of the shear stress in the glued joint befivee~rj7cirzges and Web nt filzal defom~atiorr Since the normal stresses in the flanges will increase in time, the shear stresses in the glueline between web and flanges will also increase. ConseqtientIy, the shear stresses in the glueline are calculated at find deformation.
Calculation of deflections Deflections of glued thin-webbed beams are calculated according to the same principles as given for solid timber. NevertheIess it is important to remember that the shear deflection in this case also has to be considered. The deflection from a given load is then expressed by:
where A and B denote factors given by the type of load and the structural system. Unless a more detailed analysis is made, the shear deflection can be based on the real area of the web (A,,,),
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Stressed skin panels STEP lecture B 10
Objectives
J.G.M.Raadschcldcrs,
To present a procedure for calculating stresses rrnd deflections of stressed skin panels and to introduce the concept of effective flange widtl~.
M.J. Blnss Delft University or Technology
Prerequisites B4 Shear and torsion B I I Mecllanically jointed beams and colu~nns
Summary The lecture begins with a general description of the layout of stressed skill panels. Tlte concept of the effective flange width is introduced and the composite action between webs and panels, depending on the type of connection, is explained. Finally the calculation method is demonstrated. Another fonn of stressed skin pnnel is the sandwich panel where wood-based panel flanges are separated by an intermediate core such as foam or honeycomb. The principles of the design method of this panel are outlined at the end of the lecrure.
Introduction Stressed skin panels consist of webs in the direction of the span connected with wood-based sheets forming tlle skins on one or both sides. In most cases the webs are made frotn solid timber whereas the sheets may consist of plywood, OSB, particleboard or fibreboard. The connection can either be glued or made with mechanicaf fasteners such as nails, staples or screws. Stressed skin panels are mostly used in prefabricated timber frame construction as bending members for floors and roofs or as walls loaded in compression, bending and racking. Due to the connection between webs and flanges the stressed skin panel acts as a composite rnelnber and consequently the bending stiffness and bending capacity will exceed the values of the webs alone.
Figtrc I
Co~~,s~rrrcriott of a slrcs.~cdskirt punel. (a) ~wb.r,(f3) Blocks nnrIf7angc splices, ( c ) jlu~lges,(cl) .srres.sed skiri pariel.
Structural layout of stressed skin panels The dimensions of stressed skin panels x e primarily limited by transpork and erection. Stressed skin panels used as walls are about 2,50 m in height and up to I0 IPI in length, and the web units span vertically. The width of floor or roof panels lies norinally between 1,25 111 and 2,50 nt and should correspond to the dimension of the sheets for 111aximumeconomy. With sawn tirnber webs the usual spans are between 5 and 6 11). STEP/EUROFORTECH - an initi:ttivc undcr the EU Comctl Progmrnmc
B 10/1
Flanges
-
The thickness of wood-based panels used as flanges is usually between 10 nzm and 19 tttrrt. If plywood is used the grain-direction of the ,face veneer can either be oriented perpendicular or parallel to the webs. The choice of the direction is influenced by the web spacing (bending of flooring) and the method of production. If the orientation is perpendicular to the webs, the bending capacity of the flanges between the webs is higher allowing larger web spacings. In this case, however, the strength and stiffness of the wood-based panel acting as part of the composite member is smaller compared with an orientation parallel to the webs. If large panels are prefabricated, tile wood-based panel sheets have to be connected by splice joints. These joints can be made as glued scarf or finger joints or as lap joints using blocks on the inside of the panel. Fewer joints will be necessary if the longer direction is parallel to the webs. In designing stressed skin panels care needs to be taken to check the direction of the face grain in ~*eiationto the longest side of the panel.
Figure 2
-
Gl~rcdjoirtrs for-tfie cotr~recriotiofJatlge ycrrtols. ( a ) splice joitr f, (6) fitrgcr joitlt, (c) S C N I joitzt. ~
Webs Apart from sawn timber, glued laminated timber, wood-based panels or prefabricated I-beams can be used for the webs. The thickness of sawn timber webs for wall panels is usually between 38 ~ n r t tand 80 ~rrazand the depth between 80 I ~ I and 200 tttm. For floor or roof panels the corresponding dimensions are between 38 rnttt and 63 nzm for the thickness and 150 ~nnrto 300 mnz for the depth. The depth of the webs is not only influenced by the necessary stiffness and load-carrying capacity of the stressed skin panel but also by the thickness of insulation layers. If mechanical fasteners are used in the joints, the minimurn edge distances of the fasteners have to be considered when detennining the web thickness. In glued stressed skin panels the narrow edges of sawn timber webs have to be planed (regularised) before gluing. The web spacing usually lies between 300 ~nnrand 625 rurrt and for efficiency should be related to the sheeting size.
~ I
Co~~?zections In the case of glued panels, the connection between flange and web is assumed to be infinitely stiff. Consequently, a linear strain distribution over the depth of the composite cross-section may be assumed. In the case of mechanically jointed panels, however, the slip between flange and web has to be taken into account (see STEP lecture B 1 1).
Effective flange width Due to shear deformations, the normal stresses in the centre plane of the ut-isupported area of the flanges are not uniformly distributed (see Figure 3). The contributions of the flanges to the bending stiffness and bending capacity of the composite cross-section consequently decrease with increasing distance from the nearest web. The extent of the stress decrease rnainly depends on the ratios bI/l and E/G. Here, b, is the web spacing, I is the span, E is the modulus of elasticity of the flange in the direction of the span of the stressed skin panel and G its shear STEPIEUROFORTECH - an initiative undcr the EU Comctt Programrnc
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modulus. The effective flange width decreases with increasing ratios E/G and b,/I. A mathematical derivation of the effective flange width, taking into account the shear defomation in the flange can be found in Mohler et a!. (1963). The resulting ratio between the effective and actual flange width brJlhJ for uniforn~lyloaded beams on two supports is:
where a1 =
A, * bf 2 2
and where pv is Poisson's ratio. In order to be able to use the elementary beam theory in the calculation of stressed skin panels, the concept of the effective flange width is used. The effective flange width be, is defined as the width of an idealised flange cross-section where the normal stress in the centre of the flange resulting from elementary bean theory equals the maximum stress according to the correct theory, taking into account the shear deformations in the flanges. The total flange force thus remains the same and gives the same moment of resistance.
EC5: Part 1-1: 5.3.2
EC5 gives the following approximation for the effective flange width b,,. for Ibeams (or internal beams), respectively:
b, =
4 , + 4, for b
(8)
~ +,b , 1 3
and for C-beams (or edge beams), respectively: bd = 03 bCsd b,, (or 0,5 b,,cJ bb,) +
+
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B 1013
The values of b,, and bLefshould not be greater thail the maxirnutn value calculated for the shear lag. In addition the value of b,,, should not be greater than the maximum value caiculated for plate buckling. The values according lo EC5 are given in Table 1. Flange material
Platc buckling
Shear lag
Plywood, with grain direction in tlie outer plies: parallel to the webs 0,I 1 perpendicular to the webs 0,I 1 Oriented strand board
0,15 1
25 11,
Particleboard or fibreboard with random tibrc orientation
0,2 1
30 11,
Tuble I
-
kIc~~irtucrn effcctille flrl~lgert~idthsrl~reto shenr Irlg atrcl p1c1te biickli~~g.
Figure 4 shows the effective flange width according ro equation (1) and the corresponding approximation of EC5 for shear lag. Most stressed sicin panels in practice show ratios b,/l slnaller that1 0,3.
0,o
-1
I
I
II
0,O
0,3
o,4
o,G
II
0,8 b,./l
l,0
Eflective flange ~ v i d t luccordir~g ~ to eqrrutio~l( 1 ) and EC5. (n) pc~r~iclebocrrd erj~cltiorr( I ) , (b) purticlebo~~rd EC5, ( c ) plyltmod eqllatiotl ( I ) , ((1)ply~~oacl
EC5.
Flanges loaded in compression are prone to buckling. A detailed buckling analysis can be carried out for example according to von Halhsz and Csiesielslci (1966). If a detailed buckling investigation is not made, the clear flange width b, should not be greater than twice the effective width to avoid plate buckling. For nailed or stapled stressed skin panels the withdrawal capacity of the nails has to be sufficient to anchor the sheets against buckling. 4.
b,f
4,- 4%
,I.
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25 11, 20 lrf
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Glued stressed skin panels The equations needed to calculate the bending stiffness and the stresses in the different components of a stressed skin panel with a flange on the top are given below. Glued stressed skin panels are calculated assuming rigid joints between flange and web.
Cross secfioti of n g h e d ,strcrsscci ski11pa~rcl.I u'errores t11cJa)ige. 2 rhe wreb.
Figrtre 6
The effective bending stiffness is: 2
The compression stress acting at the centre OF the flange is:
The compression stress at the top of the flange is:
The tension stress at the centre of the web is:
The bending stress at the bottom of the web is:
The shear stress at the joint between the web m d the flange is:
For stressed skin panels with flanges at both top and bottom and for mechanically jointed stressed skin panels reference is made to EC5 Appendix B and STEP lecture
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B 1015
Design example A stressed skin panel used as a flat roof bending member on two supports, span I = 4.7 nr, web spacing bf + b,, = 625 nun, nailed connection between flanges and web. The design example only covers the stresses at the instantaneous deformation. A tnethod for determining the stresses at the final deformation, using the appropriate values of k,,,, is s11ow1.1in STEP lecture B9.
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Characteristic and design values of permanent and variable load per web for the governing load case: permanent load: g, = 0,31 kN/t,i g , = 0,42 kN/r)z (permanent) q, = 1,25 kNha q, = 1,88 kN/t~r (medium-term) variable load:
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Top flange:
EC5: Part 1-1: 3.1.7
prEN 338: 1991 E C ~ Part : 1-1: B2(1)
US Plywood C-C, Exterior, Group 1, unsanded according to EN 112.406 "Wood-based panels. Characteristic values for established products." d = 16 111111, three layers, orientation of the face veneer perpendicular to the webs.
Webs:
Strength class C22 according to prEN 338 "Structural timber. Strength classes". O x h = 40 x I80 NINI.
Bottorn flange:
US Plywood C-C, Exterior, Group 1, unsanded according to EN 112.406. d = 11,5 t?tuz, 5 Iayers, orientation of the face veneer perpendicular to the webs.
Service class I :
k,,,,, = 0.8 (solid timber and plywood)
Characteristic material properties: The characteristic strength values as well as the modulus of ehsticity are talcen from prEN 338 and EN 112.406, respectively. For the modulus of elasticity and the slip modulus of the nails, the mean value is used in the design although an ultimate limit state is considered. Top flange:
.fnt.vo.k
Ec,.~.nrmtt
GK,,~,.,
h,9u,k E
, , , , ,o,c
p,
= 22,O N/III~H' E O ~ , ~ ~ , ~= 10000 N / I ~ I ~ I $p,
Webs:
fn1.k
Bottom flange:
f,,,,, Er.o.tr*ean Glj.nlrl,n
Nails:
= 12,l N/tt1ni2 = 5600 Nhnm' = 500 Nhat~t'
d &'Yak
= 8,4 N/tnin2 = 4400 N / n ? t ; ~ ~ = 41 0 kg/ni3 = 2,4 N . t t ? ~ n ~ = 340 kg/,,i3
= 12,9 N/tnrn2 &,,,o,k = 7000 N h ~ l i l i ~ ,,,, = 500 N/I~ZIII' p,
= 7,2 Nhnni2 = 4700 N/t?tm2 = 4 10 kg/ni3
= 4,O rnrn = 6620 Ntnnt
= 40 tntlt
s
EC5: Part 1-1: 6.2.1
The design load-carrying capacity per shear plane per fastener of the nailed panelto-timber joints is: Top flange - web: R,t = 903 N Bottom flange - web: R,, = 842 N
EC5: Part 1-1: 5.3.3
The instantaneous slip modulus per shear plane per fastener of the nailed panel-totimber joints results as: K,, = 583 Nhtznt
B 1016
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EC5: Part 1-1: 5.3.2
Effective flange width: = 20 . 16 = 320 I ~ ? I ? I I = O,l I = 0,l -4700 = 470 b,, top flange: bottom flange:
II1177
b,, = b , , + b , = 320 + 40 = 360 nirn < 625 171111 b,,/= b,,, -t b,,.= 470 + 40 = 510 rrrmr < 625 lnrn
According to Mohler er al. (1963), an effective flange width for the top and the bottom flange of b,/ = 567 ~ m nand b,, = 564 I I I I ~ I ,respectively, results.
The effective bending stiffness of the cross-section is calculaled according to EC5 Annex 3. Table 2 shows the results of the calculation including the corresponding equation numbers taking into account the effective flange width according to EC5 as well as according to Mohler et al. (1963). Equation No. I i , (nirn)
11,
(tl1111)
Table 2
EC5
Mijhler et al. (1963)
16
16
180
180
Calcltlatioti of cflecrii~ebetdbig srifjiress accordi~rgto EC5 A1tt1e.r B.
Design shear force:
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Design bending moment:
Md =
(gd
+
4d)
8
l 2 - (0242
*
1,881 4700' = 6,35 . 106 N~~~~ 8
For the calculation of the design stresses, the effective bending stiffness based on the effective flange width according to EC5 is used. EC5: Part 1-1: B3a
Design compression stress in the top flange:
EC5: Pnrt 1-1: B3a, B3b
Design bending stress in EIle web:
EC5: Pnri 1-1: B3a
Design tension stress in the bottom flange:
EC5: Part 1-1: B4
Design shear stress in the web:
With k = 0,5 11,
ECS: Part 1-1: 65
-t-
a? = 89 ~ ? l r ~the z design sliear stress results in:
Design fastener toad in the top flange:
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EC5: Part I - t : I35
EC5: Part 1-1: 5.3.2(5)
Design fastener load in the bottom flange:
A detailed buckling analysis is not necessary since the clear flange width h, = 585 is smaller than twice the effective width due to plate buckling:
I ~ I I ~
Instantaneous deflection: "imr
-
5
kk
+
qx-1 "1
384 ( E l ) ,
5 (0,31 + 1,25) . 47005 384 . 469 . lo9
=
1
21,2 rnrn = 222
Sandwich panels Sandwich panels with faces consisting of wood-based panels and a core of expanded foam are increasingly used as walls or roofs in timber frame buildings and as roof eIemenis for industrial buildings. The faces often consist of particleboard, the core of polyuretl~aneor polystyrene foams.
EC5: Part 1-1: Annex I3
Using the following assumptions, three layer sandwich panels can be calculated as mechanically jointed components:
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the norinal stresses in the foam core in the direction of the member axis are disregarded,
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the shear deformations in the foam core are taken into account by replacing the joint stiffness K/sin a mechanicaIly jointed component by G,,,,,llt for the sandwich panel. Here, K is the slip modulus and s the fastener spacing, G,,,,, is the shear modulus and A the thickness of the foam.
A detailed description of the calculation of sandwich panels is given in Aicher and von Rot11 (1987) and in Aicher (1987).
Concluding summary
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Stressed skin panels are primarily used as bending members in floors and roofs and as compression members in walls.
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Due to shear deformations in the wood-based panel sheeting the flanges contribute only partly to the composite cross-section. In stressed skin panels where the conneclions between web and flange are made with mechanical fasteners, the slip in the connections has also to be talcen into account.
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For maximum economy, the size of stressed skin panels as well as the web spacing should col-respond to the di~nensionsof the wood-based panels.
References Aicher, S. and von Roll), W. (1987). Ein modjfizierles 7-Vcrf~hrcnfur das mechnnische Analogon: dreiscl~icl~tiger Sandwictlvcrbund - zwciteiiiger verschieblicher Vcrbund. Bautechnik 64 (1): 21-29.
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13 10/9
Aicher, S. (1987). Bcrncssung biegcbeanspmchtcr Sandwichbalken rnit dcrn modifiziertcn Verfahren. Bautcchnik 64 (3): 79-86.
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Mbhlcr, K., Abdct-Saycd, G. and Eltlbeck, J. (1963). Zur Bcrcchnu~igdoppelsci~aiiger.gclcimtcr Talelelernente. 1-Iolz als Roll- und Werkstoff 21: 328-333. VOIIt-Ialdsz, R. and Csiesielski, E. (1966). Berecilnung und IConstruktion gclcimter Trlgcr rnit Stcgen nus Furnierplatten. Bcrichtc aus dcr Bauforschung, Heft 47, W. Ernst und Sohn, Berlin, Germany.
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Mechanically jointed beams and columns STEP lecture I3 1 1
Objectives
14. Krcuzingcr
To explain the computation and design of mechanically jointed beams and columns, to provide analytical solutions, and to illustrate the use of computer programs.
Tcchnische Univcrsit8i Miincheri
Prerequisites B2 Tension and colnpression B3
B6 C1
Bending Colunu~s Joints
Summary An exn~npleof a beam made of two parts is illustrated, for wl~ichnnalytical solutions for computing stresses and deformations are derived, The possibjlity of using a computer program for the design of such beams is indicated. A design example is provided.
Introduction Cross-sections of beams or columns may be composed of several components, connected by mecllanical joints. Longitudinally h e cross-sections are not jointed. In the junction between the individual composites, the mechanical joints mairlly carry shear forces. Thus a wide variety of cross-sections (see Figures 1 and 2) ]nay be built. The dowelled beam is known from ancient timber constructiorrs. Adding additional cross-section parts is a suitable way of strengthening an existing profile. These parts may be of solid timber, glued laminated timber or wood-based materials.
For coiumns, cross-sectional parts are often separated by gussets at a given distance. Especially for beams the cross-section with two flanges connected by a web, which carries tile shear, is very common. The flanges may be of solid timber or glued lalninated timber, the web may be of planks, wood-based panels or lately steel. It is also possible to build a co~npositestructure from a concrete piate and a timber tension flange.
Figtire 2
Ctoss-secfiorrs~vitlrt i t a firlgcs orid rfiscrerc or- rotr~irtrtarcscorrnccriorr.
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BII/I
Semi-rigid joint The connection of a number of cross-sections is made by mechanical fasteners such as nails, boIts, dowels or nail plates (glued joints are regarded as rigid connections). Each joint is stressed by shear forces causing a displacement. The relation between the displacement of the cross-section parts 11 and the force is specified by the slip modulus K. Figure 3 shows some corninon patterns of joints, the dispfacernent u and the shear force v .
Figrrre 3
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Displncelr~entaiicf slrear j?)rcr bettoeerr the paus.
For the computation, and in order to develop application equations, it is necessary to distribute the joints continuously along the beam. The effect of this is a continuously acting shear force v, such that:
If the distance between the fasteners is considerable or if the joints are concentrated at very few points, the computational model of a continuous joint: is no Ionger valid, and a different mechanical model is required, for instance a frame model.
Computation methods Beants For beam design the following parameters are required: stresses a and t in all parts, forces in the joints and deflections. For mechanically jointed beams, the bending-theory for beams is no longer applicable because of the slip in the joints. However, the theory is applicable to individual components. Analytical solutions are developed by use of differential equations of equilibrium (Mohler, 1956; Heimeshoff, 1987) or energy considerations and specially developed design programs are available, see for example Icneidi (1991). The development of the differentia1 equations is conveniently shown in a T-cross-section rnade of two parts (Figtlre 4). The solutions require that for every part simple bending-theory is valid and shear displacelnent is omitted. The connection is regarded as continuous and the profile and the joint stiffness are constant in the direction of the beam's axis.
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---
..
The deformations are (see Figure 5): rr,, fr2 are the longitudinal displacelnent of the axis of cross-section I and 2, rv is the co~nmonbending deflection and ti is the relative displacement of the cross-section parts at the location of the joints. II =
;)
15 - I',+ w ,(I;- + 2
= u2 - ul + w ' a
ir is independent of the position of the joints. The critical di~nensionis the distance a of the axes of the cross-sectional parts. The derived equations are not only valid for cross-sectional parts located one upon another, as shown in the T-profile, they also apply to cross-sectional parts located side by side. This is only true if shear deformation is neglected.
Elasticity principles matching the simple bending theory:
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Equilibrium of the two elements iri x and z direction: [I'I= 0, ( N , + N,)' = 01
N,' + \'
=0
(7)
M~' = v l - v -"11 2
(gal
The sum of ( 9 4 and (9b) is differentiated once with respect to s and V' is replaced by the tenn -I>: hii'' t M,"
+ s' a + p = 0
-
(1 0)
If the internal forces and moments are repiaced using elasticity principles, the following system or differential equations results:
E, A, u," + k ( I / ? - El, 4- HI' (1) = 0 E, A, clZ" - k (11,- - 1 1 + ~ I V ' a) = 0 (ELI , + E2 I?) M!' " - k - 11' + \v' ' 0) = p
-
-
(11) (13) (1 3)
In this way three equations of equilibriuin (7), (8) and (10) are formulated for the three defontii\tions i f , , it, and III.
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The variation of the elastic energy is also determined from these equations: ~ = 2~ ~ [ E , A ~ ~ ' ~ ' ~ E ~ A , ~ ~ ~ ' + ( E ~ I , + E , I ~ )(14) W " ~
-
+k($ - u l + w i n ) ' - ~ ~ w ] d x -
Elastic foundation effect k,,,, and the influence of second order- theory effects could be taken into account by adding the term li,,.\I> - No n ~ "to Equation (13). For single span beams with a sinusoidal load distribution, a simple, analytical solution can be given because the shape of the deformations in the direction of the axes corresponds to cos- or sin-functions. Altl~oughthe derivation is based on the synusoidal load distribution, the solution is also applicable to most other load distributions.
p = p o "(;x)
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(15)
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These terms, when placed in Equations (111, (12) and (13), give a system of equations for the constants rr,,, I f ? , and IV,:
x k- a 1
n"
n k- a I
- ( E l Il + E2 I,)
iJ
2
kn -a2 = 1
-1
The solution is:
1 k I =--n2 EiAt and y 1 = "1 i l +k,) With these deformations and applying elastic principles, the stresses can be computed. The stress in the axis of part 1 of the cross-section is (Figure 6):
o1= El lt { (.v
= 112) =
-El
n
l t I O ~
( 1 9)
Using the following terms
Y I E I A I ~. Y tElA, 44-42 ' the stress is
a2 =
+
This type of the equation is equivalent to the equation For the stress in a simple beam. In EC5, Annex B, further equations are given. EC5: Part 1-1: 5.1.9, 5.1.10
The bending stresses and [he stresses in the axes of the ~nembersmust verify the condition of combined bending with axial tension or axial compression. If necessary the stability condition must also be satisfied such that: STEP/EUROFORTECH - an initiative under tile EU CorneH Prograrnlne
B1 I15
EC5: Pan 1-1: 5.2.2
'
or,tt~i k
(22)
i t xtt.t,
kc, takes account of the bending stress according to the lateral deformation resulting from 2nd order tlleory effects. For this purpose the critical bending stress is necessary. The bending stiffness of tlie beam about the wealc axis and the torsion stiffness are required.
Co/in~zn.s The computation of mecllanically jointed columns has to allow for buckling, and the influence of 2nd order theory. It is clear that the effective bending stiffness (El),. is the dominant factor for buckling. If the expression N,, . 1v" is included in tlie Equation of equilibrium (13) and if the determinant of the equilibrium equations is set to zero, the buclcling load is also obtained.
The axial stiffness of a colnposite colulnn is ( E A ) , f = (EA),,, = C EiA, since the joints are not considered to be stressed by the axial forces. The slenderness of a mechanically jointed column can be computed in a similar manner Lo a simple column.
Each member of a coiiiposile colurnu coi-responds to the simple column, and for each unernber of the cross-section the relative slenderness arid the buckling factor can be computed.
If, at tlie same time the column is stressed by bending, the bending stress nii~stbe superimposed. Normally the design will be governed by colnpression in a single member such that
The compression force and its corresponding def'ormation results in a transverse force If,, which is dependent on the slenderness. To this, any transverse force due to direct loading must be added.
In EC5, Annex C, equations are given to cornpute the effective slenderness of columns with different cross-sections. For spaced coluinns with packs or gussets, and for lattice columns, the effective bending stiffness can be co~nputedusing frame programs. Here, the deflection \vo in relation to a sinusoidal transverse load p,, and taking into account the yielding of the connection, results in an effective bending-stiffness given by:
PO l4 ( E l ) =ef
MIO
n4
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Design example Figure 7 shows a beam made up of a single plywood flange and a timber web jointed by nails. The desigii stresses and moduli are also given.
k=gOO Nhiun; s=40 n1r11 System, cross-sec~ia~t, design values.
Design values
1 2
'0,rrtner
fc.,~,k
x.+o,d
.f;.o.d
./;II,~/
4500 11000
19,5 21,O
I2,O
8,0 8,6
12,O
12,9
(N/1121112
14,7
For both ultimate and serviceability limit states E,,f,,,f,,l values are to be used. For calculation of deflections the sIip rnodulus K;,, will be used, for ultimate limit state K,, = 213 K
Computation EC5:Part 1- 1: A~lncxI3
Values of cross-section:
Stresses in LIE middle of the span caused by a bending moment h/l, = 6,4S kNr~r
Stresses caused by a compression force F,,= 30 RN a, = 30000 4500 / (4500 * 13000 + 1 1000 . 19200) = 30000 . 1 1000 / (4500 12000 + I 1000 .I 9200) 0 2
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= 0,5 1 N/1711ti2 = 1,25 N ~ J I I ~ I '
B 1 117
Maximum force li, in the joints for a shear force V,, = 4 . 3,613- = 7,2 k N .
F,
=
-
0,33 -4500 . 17,000 .S7,7 40 7200 / 601,s
10' = 741 N
Concluding summary
-
Tile basis for the computation of mechanically joir~tedbeams and columns is shown and the analytical solutions given in EC5, Annex B and C, are show11for simply supported beams and colulnns with a span length 1.
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For more co~nplicatedsystems such as Frames or beams and columns with varying cross-sections, along the main axis, it is necessary to use numerical solutions offered by computer programs. The members rnust then be modelled as bars and the joints as either bars or springs.
References MBhler, K. (1956). fjber das Trngvcrhaltcn von Dicgctdgcrn und Druckstiiben mit zusnmmengestezten Qucrschnitten und nacllgiebigcn Vcrbindungsn~ittcl~~. I-iabilitation, Technischc Universitlit Karlsruhe. Gcrmany. I-Icirncshoff; B. (1987): Zttr Bcrccllriurig von BicgctriBgcrn nus nocligicbig mitcinandcr vcrbundenen Quersclinittstci[cnin1 Ingcnicuri~olzbau.ln: Holz Roh-WcrkstofF45:237-247. Kneidl, R. (1991). Bin Bcitrag zur linearcn und nicbtlincaren Rerechnung von Schichtbnlkensystemen. Dissertation, Tectlnischc Univctsitlt Miinchen, Germany, Bcrichtc aus deli1 Konstruktivcn Ingenieurbau, 619 1.
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Trusses STEP tccture 13 1 2
Objectives
To understand plane trusses as part of three dimensional stnlctures, to show the M.EI. Kesscl Labor fur I-iolzlechnik LIIT different types of trusses and to present the general and silnplified analysis and I-lildcshcirn the strength verification of members and joints of EC5.
Prerequisites A17 Serviceability limit states - Deformations BZ Tension and compression B3 Bending 3 6 Columns B7 Buckling lengths
Summary Proceeding from three dimensional trussed structures the shape and the appropriate load-bearing bel~aviourof plane trusses is discussed. Tile lay-out of various types of trusses is shown and indications of the selection of the web system are given. T11e principles and rules of EC5 for a general and simplified analysis are described. Strength verification rules and limits of deflection complete the lecture. Exrtmples are included at various stages.
General Trusses are built to cover spaces (living rooms, In general, the members are statically represented by three diinensional straight rods which have six degrees of freedom (three displacements and three rotations) at each end. For static and fabrication reasons, very often, the three dimensional truss struct~treis built up of two dimensional vertical trusses (truss A) which are erected parallel or concentrically and joined together by two dimensionally inclined trusses (trusses B1 -B4) between them (see Figure I).
F i r 1
ECS: Part 1-1: 5.4.1.1
T1trz.c di11it.nsioncr1!nr.sscrl ~'1ntc11irc: pal-altrl (left), cotrcc~itrical(riglit).
Truss A is intended to cany only the loads which act in the plane of the rmss and hence it follows that statically truss A is a plane problem and consists of lnernbers (plane rod elements) which have three degrees of freedoln only (two displacements and one rotation) at each end, In EC5 these elements are called beam elements.
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B 1211
EC5:Par1 1-1: 5.4.1.3
E C ~ P,W : 1- 1: 5.4.1.1
Under certain circumstances members of two degrees of freed0111 (two displacements) at each end (pin-jointed elements) can be used. The rnernbers of two din~ensional trusses are designated in two categories: external members (top chord, bottom chord) and intefnnl or web members (a11 interior vertical or diagonal members between the top (upper) and bottom (lower) chord). Joints at which ~nernbersintersect connect are called nodes or panel points. The following statements may be used to describe two cli~nensionaitrusses:
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Unless a more general inodel is used, trusses shall be represented for the purpose of analysis by bean1 elements set out along system lines and connected together at nodes (e.g. as sfiown in Figure 2).
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The system lines for all members shall lie within the member profile, and for external members shall coincide with the member centre line.
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A more general load-bearing ~ ~ l o dcould el be to present 1~x1s~ members by shell elemel~tswhicli could be very costly, however..
Figutz -3
Two rlirtrerwiortcil trrtss: ( a ) sy.yter/r litle, (11) Day, ( c f irrterrrul mertiber; ((1) .viippot.t, ( c ) ~ ' ~ t c ntt~et/lbel; t ~ l Ifi fictitior~~ Oeatti elernet~t,(.g) ~iocle.
For fabrication reasons in most trusses do not consist of members which articulate perfectly along the centreline. Firstly, chords are fabricated from one timber itnd therefore are contirluous over several bays. Secondly, rectangular or circular sl~aped plate connectors always cause a certain rotational stiffness. Member forces and architectural considerations deter~nine the type of connections to be used and can result in rotationally fixed, seinifixed or pinned joints. Thirdly, the depll~sof ruembers and the dimensions o l connectors lead to eccentricities in the joints between adjacent ~~tembers. This last case determines a general application rule: Fictitious beam elenlents (see Figure 2) may be used to model eccentric connections or supports. The orientalion of fictitious beam elements should coincide as closely as possible with the direction of the force in tile member. This rule which gives an esti~nation of the cornplex stress distrib~~tiollat eccentric connections is to allow an economic analysis. Corresponding to the general design requirements it shall be verified that no EC5: relevant limit state is exceeded. 1 1 verifying assernbiies like trusses, distinction has to be made between necessary global awl local limit states. In both states second-order effects due to initial global and IocaI curvatures, eccentricities and induced deflections shall be taken into account, in addition to those due to lateral STEPIEUROFORTECH - an initiative under
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loads. A very close approximation of the global geometric non-linear behaviour of trusses is intended by [he application rule: In tile analysis the geometric non-linear bel~aviourof a member in conlpression (buckling instability) may be disregarded if it is taken inlo account in the strength verification of the individual member. This means that only the influence of global imperfections on the displacements and rotations of truss nodes has to be taken into account. This is done by using the node coordinates of the irnperiect (initially deformed) truss. The influence of local imperfections of each tn~ssmember between its nodes can be neglected in the analysis, i.e. by assuming that members remain straight between nodes, if it is taken into account in the strength verification. This procedure simplifies the analysis significantly and ofrers an econotnic use of finite element programs. Concerning global limit states it has to be emphasized that, in general, tnrsses are three di~neilsionalstructures as mentioned earlier. Nevertheless, frequently trusses A and B in Figure 1 and Figure 3 are treated as two dimensional systems loaded in tl~eirplane without any nlrttual intluence.
Figrite 3
Tlrrcc dir~tctrsiotlirl luc~cl-6errrillgbelruviortr. (a) trrrss A ~rrrstressed 1?\1 lufernl louris, (0, c) trrtss A srrasserf,
However, this is valid only for system (a) in Figure 3, where truss A carries the vertical Ioads independently and tnlsses B1 and B2 the ialeral loads (external loads, i.e. wind, seismic loads, internal loads due to buckling of compression and bending members), B2 supporting BI. In the case of systems (b) and (c) in Figure 3 truss A agnin carries tl~evertical loads independently but trusses B IiB2 and B need the cooperation of lnlsses A lo fonll a three dinlensional loi~d-bearingsysteni lo providc sufficient lateral resislnnce (Kessel 1986). Due lo STEP/EUROFORTECH - an initiative undcr t t ~ cEU Co~ncttPrograinnic
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that fact i t becomes evident that bracing leads to stresses in trusses A resulting from loads F which do not even have a component in the plane of truss A.
Truss Types The type of timber ti-uss most commonly built is triangular, i s . double pitched (see Figure 4). The web system should be selected For convenience of connection and resulting member stresses. For instance, in some cases space for ventilation tubes is required. Web locations and node sp-acings 111ay be dedicated by selection of secondary purlin framing so as to minimize cllord bending stresses and buckling lengths of chord inembers in compression. Web directions may be chosen in a way that short internal members are in compression and long members in tension to avoid additional web bracing.
Figurn 4
Types of rrttsscs. ( [ { I , a2) tt-icrngtrlar (b) corr1~7otrr1cl( c ) parcrllal (d) scissors (c) bo~vstritrg(fl $dz-bellied
By varying geometric paranleters a large variety of trusses can be developed for nearly a11 kinds of application. Although the dimensions of trusses are restricted by prefabrication procedure and transport, the height of triangular trusses can be very large. In such cases it may be necessary to use a trapezoidal load-bearing truss completed by n slnall triangle (see Figure 4b) to produce the desired triangular roof shape. Sometimes the bottom chord shape is dictated by architectural considerations concerning interior decoration. Instead of a straight chord its centre point with correspondence to the supports is raised up (see Figure 4)or layered down (see Figure 40. While the first case is of no particularity the special feature of tile load-bearing behaviour of the second one should be mentioned. If the top chord is fiat, i.e. the top chord approaches a straight line (see Figure 5a and Sb), a stability problem arises due to the fact that the centre point of the bottom chord can deflect laterally (Kessel 1988).
F i r5
Kirtp
II.IISSCS (a,
6) nr~dartic rrirss (c).
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A further important variant of the triangular truss is the attic truss of domestic roofs (see Figure 5c) whicli however, is no longer a truss in the original sense. Due to the lack of webs [he external loads cause, in addition to the axial forces, important bending nloments in tile chords. Particular attention must be paid to the joints in the lower chord, These joints are stressed axially with respect to roof loads, transversaliy with respect to ceiling and floor loads and rotationally with respect to unavoidable eccentricities of connection members.
In order to lninirnise deflection, the span-to-depth ratios of trusses should decrease with increasing span. Large deflections not only may cause serviceability problems, they can also create substantial secondary stresses i1.i cor~tinuouscliords. According to Ozelton and Baird (1976) truss deflections can be mininxised by
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using timber of lower strength classes and consequently larger ~ n e ~ n b e r sizes,
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keeping the number of joints and meclianically jointed splices to a tninimum, and
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using fastenings with stiff slip characreristics.
The use of lower strength classes may appear uneconomical, since the necessary cross-sectional dimensions increase. However, since the fastener spacings and distances often determine the size of the cross-sections, the choice of a high strength class frequently does not lead to material savings. Because the ioadcarrying capacity of connections using mechanical fasteners depends on the density of the timber, and the ratio of density over strength increases with lower strength classes, it is usually more economic to use timber of lower strength classes when the necessary lnechanical cor~nectionsdetermine the cross-sectional dimensions.
Preliminary design Generally arcliitectural considerations determine the shape and pitch of roofs. But for econo~nicreasons the following rules concerning the depth-span ratio of trusses should be fo'oilowed: triangular or pitched bowstring flat or parallel chord
116 or deeper, 118 to 116, 1/10 ro 1/8.
Once the truss geometry has been fixed, the centrelines of the members are dependent on their size. Therefore, it is usually necessary to conduct a preliminary design to determine approximate member sizes and connection types. For this purpose a simplified analysis is used with all loads placed at nodes and all joints assumed pinned. Member forces can then be determined graphically or analytically. Based on these axial forces, preliminary web and chord sizes can be selected taking into account approximate moments due to any distributed loads or concentrated loads that will not in practice be applied at nodes.
General analysis EC5: Part I- I: 5.4 I 2
Trusses shall be analysed as framed structures, where the deformations of the inembers and joints, the influence of support eccentricities and the stiffness of the supporting structure are taken into account in the determination of the niember forces and moments. If the system lines for internal members do not
coincide with the centre lines, the influence of the eccentricity sliall be taken into account in the strength verification of these members. The analysis should be carried out using the appropriate values of menlber stiffness and joint slip. Fictitious beam elelnents should be assumed to be as stiff as the adjacent element. Care should be taken if the fictitious beams have to be very short, i.e, shorter than about 100 nrm. This could lead to a nearly singular stiffness rzlatrix and to unreasonable liumerical results which could be missed. Sometimes, it is advisable to use an adapted analysis, e.g. finite element analysis which makes available rod elements with built in end eccentrici~ies.
E,~an~ple: it can be assumed that a colnputer program is available for analysing trusses. For the input the merrtber4stiffness of the bottom chord and joint slip of the dowel connection is given here: Bottom chord with a rectangular cross-section O x 11 = 50 x 180 rtrm'. Strength class C24 according to prEN338. Meruber stiffness: E<:,, = E(,,,,, = I 1000 N/I~WI' Timber-to-tirnber connection with dowels cl = 8 trim K,,t,,,,= 380"" 8/20 = 3000 N/,tlttr is the instantaneous slip modulus per shear plane under service load I;,,.,. If ri geometric tion-linear analysis is carried out, the Inember stiffness should be divided by the partial factor yln(given in EC5 table 2.3.3.2). Verifying serviceabiiity EC5: Pari 1-1: 4.1 (4)
E,, = E(,5,,/ y, = I I000 / i ,O = 1 1000 ~/,tzm' K.wr,/i,t = K.wr ( 1 +
ECS: Part 1-1: 6.1 ( 9 )
and verifying strength of rnembers and joints El, = k,,,,, El,, / y, = 0.9 . 7400 / 1,3 = 5 100 ~ / r r ~ r n ' KtrSpn = 2K.v.r / (3 ( 1 + k , ~ ~ : ~ ) )
kt,tf)
Joints may be generally assumed to be rotationally pinned. Translational slip at the joints may be disregarded for the strength verification unless it would significantly affect the distribution of internal forces and moments. Joints may be assumed to be rotarionaliy stiR if their deformation would have no significant effect upon the distribution of member forces and moments.
Simplified analysis EC5: Piat 1-1: 5.4.1.3
As an alternative to a general analysis, a simplified analysis is permitted for fully triangulated trusses whicfi cotnpiy with the following conditions:
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there are no re-entrant angies in the external profile, some part of the bearing width lies vertically below the support node (see Figure 2), the truss height exceeds 0,15 times the span and 10 times the maximum chord depth.
The axial forces in the members should be determined assunling that every node is pin-jointed. The bending moments in single-bay members should also be
determined on the basis that the end nodes are pin-jointed. Bending moments in a member which is continuous over several bays should be determined as if the member was a beam with a simple support at each node. Tile effect of defection at the nodes and partial fixity at the joints should be taken into account by a reduction of 10% in the node bending moment. The reduced node moments sllould be used to calculate the span bending moments.
Strength verification of members and joints ECS: Part 1-1: 5.4.1.4
For elernerits in compression, the effective column length for in-plane strength verification should generally be taken ils the distance between two adjacent points of contraflexure. For fully triar~gulatedtnlsses, the effeclive colunln length for members which are only one bay long without especially rigid end connections, and for continuous members withour lateral load, sfiould be taken as the bay length. When a simplified analysis has been carried out, the following effective colu~nn lengths may be assumed (see Figure 6 ) .
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for continuous members -svith a lareral load but without significant end moments
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in an outer bay: in an inner bay: at a node:
0,8 times the bay length, 0,6 the bay length, 0,6 times the largest adjacent bay length.
for continuous members wit11 a lateral load and with significant end molnents
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at the beam end with moment: in the penultimate bay: remaining bays and nodes:
0 ( i s . no column effect),
1,O times bay length, as described above.
For the strength verification of ~nenlbersin compression and connections, the calculated axial forces sllould be increased by 10%.
A check shall also be made that tile lateral (out-of-plane) stability of the inembers is adequate.
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Limiting values of deflection EC5: Part 1- I : 4.3.2
EC5: Part 1-1: 5.3.5.3
EC5: Part 1-1: 4.1
For trusses the limiting values of deflection for beams apply both to the colnplete span, and to the individual deflection of members between nodes. Referring to the tmss span I , the limits are
These limits are recommended unless special conditions call for other requirements, e.g. for the deflection of bracing systems (see trusses B of Figure 1). Furthermore it should be noticed that the horizontal bracing load of trusses increases with their vertical deflection. The final deforrnatioli of a truss fabricated from members which ltave different creep properties should be ciifculated using modified stiffness moduli, which are determined by dividing the instantaneous values of the modulus for each member by the appropriate value of ( I + IG,,~). The deflection 11 of a truss may be determined by computer program, e.g, based on finite elements, or analytically by the rnethod of virtual work, using the relationship lr
= C FiF,, li / A i Ei
where
Fi F,i /ti
i2 7, Fi
F,, I ni Ki
axial force of ttr~ssmember i, force of truss member i caused by unit load, number of fasteners at one joint of truss member i.
Trusses with punched metal plate fasteners EC5: Part 1-1: 5.4.1.5
Additio~~al ~rtlesfor trusses with punched metal plate fasteners are given in Annex D and for joints in STEP lectures CI I and D3.
Concluding summary
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Trusses form part of three dimensional structures.
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By varying geometric pwalneters a large variety of trusses can be developed for nearly all kinds of application.
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In general, trusses shall be analysed as framed structure (rod elements), where deforn~ationsof nlelnbers and joints and eccentricities are taken into account.
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Certain conditions allow a simplified analysis assuming pin-jointed n1ember.s.
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Lateral global and local stability of trusses ltas to be verified.
References Kcssel, M.H. (1986). The Bracing of Trussed Beams. In: Prac. of tltc Joint Mecting CIB Wf SIiUFRO S 5.02, Florcncc, Italy, Paper 19-15-2. I
1st
edn. Crosby Lockwood Slapies
Diaphragms and shear walls STEP lccturc B I 3
Objectives
T.Atsmarker Lund University
To explain in principle, the behaviour of structural diaphragms, such as floors and walls, in timber framed buildings and to present appropriate design methods.
Summary Walls, floors and roofs in timber framed buildings are often sheathed using different types of sheathing materials and may be used as structural diaphragms in order to transfer laterai forces to the foundation. This lecture describes the structural behaviour of horizontal floor diaphragms as well as the behaviour of shear walls. Simplified design methods to be used in ultimate limit state are suggested.
Introduction A building is subjected not only to vertical loadings, such as self weights and i~nposedloads, but also to horizontal loadings caused by wind or earthquakes. This lecture relates to structural behaviour under wind action. Wind has a number of effects on a building. Its direct action is to cause pressure on one or more of the faces and suction on the others. Figure 1 shows the principal distribution of wind loads on a building for wind direction perpendicular to the long side wall, see STEP lecture A3.
r
e1
.Exten~al~crirtdloads for ivirrd dilrclior~pcrpeitdicrriar to tire lorrg side itu~ll. The arrortr sho~i!srlre roirtd (iirecrioi~.
The wind direction sl~ownin Figure 1 results in pressure on the windward wall and the windward side of tile roof and suction on the corresponding faces of the leeward side. A low pilch may result in suction on the windward side of the roof as well. Note, that the side walls are subjected to suction perpendicular to tlie wind direction. In addition to these principal wind Ioads, the wind may also cause suctiorl or pressure on the inner faces of the building,
In order- to transfer wind loads to the foundation, some form of wind resistant system is needed. Quite often the use of diaphragms and shear walls can provide STEP/EUROFORTECH - an initiative under the EU Comett Programme
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an effective and econornic design. The principal structural behaviour is illustrated in Figure 2 for a simple single storey box like buiIding, exposed to wind perpendicular to the long side wall. The walls are assumed to be simply supported between the roof and the foundation. Hence, half of the total wind load acting on the long side walls is distributed into the horizontal roof diaphragm, which is assumed to act as a deep bearn. The roof diaphragm is srlpported by the end walls, which transfer the forces to the fooundation by their in plane shear action.
J Figlire 2
Pri~tcipcrlforce disrribution irr a sirrrple sirigle storey box like l~uilditlg, whew tlic roof acts ns N I~oriio~lrc~I dic~phrag~~i nitd the errd ,vnll.s ns shear walls.
The srabilising system in timber framed buildings consists of several components which [nust be properly fastened together to ensure that there is a complete load path for the shear transfer.
Horizontal diaphragms Floors, ceilings and roofs may be used to transfer horizontal forces to the supporting walls. In timber framed buildings these structures are basically built up from timber joists sheathed with different types of wood based sheathing materials for floors and most commonly fastened to the joists by screws. The ceilings typically consist nf one or two layers of gypsum plasterboard, either nailed directly to the roof trusses or joists or screwed to secondary spaced timbers, which in turn are nailed to the joists. These types of ceiling may also be used as structural diaphragms, see Aismarker (1992). However, in this lecture only floor diaphragms will be discussed, see Figure 3. This type of floor diaphragm may be assumed to behave in a similar way to a deep I-beam, supported through the struts by the walls running parallel to the wind direction. According to EC5 this [nay be assumed so long as the span is less than six times the width of the diaphragm. The sheathing acts as the web, resisting sllear forces, while the chord members act as the flanges, resisting the applied bending motnent. Figure 4 illustrates the principal behaviour.
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For timber framed buildings, the double top plate of the walls is used as the chord member of the diaphragm. The plate members are lapped with staggered end joints and connected together by nailing or bolting. Alternatively, a continuous header or trimmer joist may be used as the chord, It is assumed that all of the bending moment is resisted through the chords. Hence, the chord members must be designed for tension or compression forces of F,,J = Fr.d = Mnl,lx,J17
(1
where M,,,,,is the maximum moment and O is the width of the diaphragm. The shear flow qJc,between the sheathing and the chord may be calculated as q ~ =d P t f , , f ' ~ ~ C
(2)
where F,,.,, is tile total shear force and b,. is the centre-to-centre distance between chords. The sheathing must be designed to resist a shear flow of v,, = FI5Jb
where F,,,, is the total shear force and b is the width of the diaphrrtgn~.
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(3)
Finally the spacing of the Fasteners connecting the sheathing to the joists is calculated as
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where R,, is the design capacity of an individual fastener, and shear flow.
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11,~
the calculated
For simply supported diaphragms, as shown in Figure 4, the shear force is transmitted from the diaphragm to the shear walls by the perin~eter members, known as struts, at the end or the diaphragm. The shear force is assurncd lo be uniformly distributed along the diaphragm edge. The struts as well as the chords must be properly fastened to the top plate in order to transfer actual shear fo~~ces to the shear wall below. Where the sheathing is not directly fastened to these members, it is necessary to ensure that another load path exists. For a wind direction perpendicular to the end wall the struts become chords and vice versa. Therefore, these members tnust be designed, including the nailed or bolted lap splices, to carry the strut forces as well as the chord f ~ r c e s Where . the chord and the strut also f~inctionas a header, they must be designed for a con~binationof vertical and axial loadings. When using the suggested model it is assun~ed that the sheathing boards essentitllly act as one and hence the individual sheets should be blocked. The stiffness or the diaphmgni will depend on tlie orientation of the sheets relative to the joists or blockings. I-Ience, the best performance is obtained froin a floor with the sheets staggered rather than in a stacked configuration. However, the diaphragm is often used for wind bracing in two opposite clirections. Staggering should therefore be oriented for the worst loading direction. The sheets are well restrained fsom buckling by the joists and their thickness is normally determined by gravity loads. In the case of large holes in floor diaphragms, it is viral to ensure a path for the transfer of forces around the hole. Compression and tension forces can be transmitted by using blockings and steel straps respectively. To ensure the shear t~~ilnsfer it is essential that the sheets are properly nailed or screwed to tlie blackings and joists around the hole. The detailing of the different connections details is critical.
Shear walls In general the walls in a timber Framed building consist of vertical studs, spaced at a regular interval, forming a ladder type frame together with the top and bottorn plates. The framework is usually sheathed on one or both sides with different types of sheathing material, nailed or screwed to the frame. Slructurally the wall can be regarded as a cantilevered diaphragm loaded by a concentrated force applied at the top plate. Using the sheathing as a bracing this force may be transferred to the foundation in a vety effective manner. Figure 5 illustrates the stn~cturalbehaviour.
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The studs are fastened lo the bottom and top plate by nails or other types of metal fasteners, From a structural point of view the frame joints can be regarded as being pinned. Hence, the displaccrnent of the timber frame must be resisted by the sheathing a11d the fasteners connecting it Lo the frame. The most henvily loaded fasteners are located where the largest displacements occur between the frame and the sheathing, that is in the corners. In the upper corner lo the left and the lower comer to the right fasteners will have force directions towards the free edge. The other two corners will have opposite Force directions. In Figure 5 the studs are assumed to be fixed to the foundation. Whether the studs can be prevented from lifting from the foundation or not is often the nlost i~npotlant factor influencing the shear capacity of wall diaphragms in timber framed buildings. 111addition to appropriate Fastening, vertical loads can be used to resist uplift and stiffen the panel. Apart from uplift, the studs must be designed for a concentrated compression force. The strength of tlie fasteners as well as the shear strength of the sheathing are other important factors that influence LIie ioad-bearing capacity of wall diaphragms. These factors would have further significance if it is necessary to consider the stiffness of the diaphragm and ils horizontal in-plane deflection under load.
The total maximu~nload for a wall that is built up of several wall units, can be calculated in a simplified rnanner as the sum of the rnaxitnutn loads for each unit, even where the wall units are built up from different co~nbinationsof sheathing materials and fasteners. Noweser, where there are different combinations of sheathing materials and fasteners on the two sides of the framework, according to EC5, only half the load carrying capacity of the weaker side should be used. When there are window or door sections in a wall, these sections should be disregarded in calculating the load-bearing capacity of the entire wall. A rather simple madel may be used to calculate the internal force distribution between Fasteners connecting the sheathing to the framework. This model assumes linear elastic behaviour of the fasteners, hinged connections between individual beam elements and that uplift is prevented. Furthermore, the beam elements as well as the sheathing are considered to be completely stiff against bending and elongation in the loading plane. Taking these assulaplio~lsinto consideration, the internal force distribution [nay be calculated as
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Hky, cri and c Y,! =
H It xi Fsi= -
c4
where FJiand F,, are the force components in x- arid y-directions respectively for a fastener in position (.ri,jli). The total force is simply given by
where xi,yi H
11
Cs',Cy'i
are the co-ordinates for the aclual fastener. is the total shear force on the wall unit. is the height of wall unit. are the sum of the squared distances for a11 fasteners.
The ulti~natedesign condition is failure in the most I~eavily loaded fastener, which is located at the corners of the panel. ECj:Part 1 - 1 : 5.4.3a
According lo EC5 the racking load carrying capacity of the panel is calculated as
I;r..d = hd I!?/$
(7)
where FJ, is the design capacity per fastener and s is the spacing of the fasteners. In this model :be applied force is uniformly distributed over the fasteners connecting tlie sheathing to the top plate and does not account for concentrated forces at the corners of tile panel. EC5: Park I -I: 5.4.3d
The tensile studs and the anchorage should be designed for a force F,,,,, where F,,,,= FBSsd 11/b
(8)
and the compression studs should be designed for a force: EC5: Part 1 - 1 : 5.4.3b
Fc,', =
ECS: par^ I -i: 5 . 4 3
FC,(,= 0,75 F,,,/
-
for shearhing on both sides, or
F,.,,
for sheathing on one side
The end studs of the shear wall as well as the bottom plate must be adequately anchored to the foundation in order to resist uplift forces and shear forces respectively. In multi-storey buildings the shear walls 111ust be connected to each other in a manner that allows tliese forces to be transmitted through the different levels of the building.
Design example Calculate the horizontal design capacity H,, for the wall unit in Figure 5, where b = I200 nun and It = 2400 i t r m ~ . The spacir~g of' the fasteners are as follows: s = 150 ttzm, t = 150 rnnl and r = 150 mm. The design capacity, T%,,, for a single fastener is 0,2 kN.
The force in x- and y-direction for fasteners located in the cot-ners are
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F,, = 0,s - N,, .2400~/44,82. I 0" = 0,0643 . H , F,,,, = 0,s . H, . I200 2400/13,5
. lo6 = 0,107
H,,
which gives the total force as
F, = 0,125 . H,, and
Hd= 1 ,b IiN For the actual wail unit, the same result is obtained if using the EC5 melhod.
Internal walls The distribution of horizontal loading to the internal waIls is governed by the of the walls. Assuming a rigid stiffness of the diaphragm relative to the stiff~~ess diaphragm supported by flexible walls is one extreme of the solution, and a flexible diaphragm supported by stiN' walls another. In tile first case the horizontal loading is distributed to the shear walls according to the relative stiffness of the walls. For a diaphragm supported by three walls of equal stiffness, each wall wit1 resist one third of the total load. Note, that if tile internal wall is not placed in the centre of t l ~ e diaphragm, the torsional component must be accounted for as well. Assuming a flexible diaphragm supported by stiff walls the question is whether the diaphragm may be regarded as a horizontal beam spanning continuously over intermediate supports or as separate beams being simply supported. The conservative approach is to design the end walls assuming the simply supported condition and the interior wall based on continuity. The case of timber diaphragms on timber shenr walls is in between the two extremes and the assumption of a rigid floor diaphragm should be used with caution. The assumption of a rigid diapl~ragnishould only be used for a plan aspect ratio near unity, related to the diaphragm depth, h, divided by the span between internal walls, I.
Concluding summary -
All of the colnponents of the shenr wall and diaphragm system niust be adequately fastened together so that the struclure acts as a n effective unit.
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Floor diaphragms !nay be assumed to behave similarly Lo a deep I-beam.
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The assumption of rigid floor diaphragms should be used with caution.
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Wood shear walls can be regarded as ca~ltilevereddiaphragms loaded by a concentrated force applied at the cop plate.
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Shear walls must be prevented from lifting from the founda~ion by adequate anchorage at the end studs lo comply wit11 EC5 design rules.
Reference Alsmarkcr, T. (1991). Gypsum Plnstcrboards ilS Wind Bracing Elcmcnts in T i n ~ l x r Priimed Buildings. Lund Inslifutc of TcchnoIogy, Dcpl. of S~ructurillEngineering.
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I3 1317
Portal frames and arches STEP lecture B 14 Objectives To develop an understanding of the limit state design verification of portal M.N. Kessel Labor fGr Iiolz\echnik LI-IT frames and arches including lateral buckling and to illustrate the design proceHildcslieirn dure of EC5 by showing an example.
Prerequisites A4 A1 7 B2 B3 Bb
B7
Wood as a building material Serviceability limit states - Deformations Tension and co~npression Bending Columns Buckling lengths
Summary After introducing different types of portal frames and arches, the ultimate limit state design is demonstrated in two ways. First, a simplified analysis is shown considering in plane and lateral buckling. Secondly the application of a second order linear analysis is explained using a curved frame as example.
Introduction Frames and arches often f o n ~ lthe main structural elements in three dimensional structures covering halls of rectangular or circular ground surface, typically used in gymnasia, swimming pools or stores of bulk goods. Span dimensions vary between 20 and 100 m and in rectangular buildings the length is usually two to three times the spm. Constn~ctionheight is normally between 10 and 30 m. For fabrication and transportation reasons frames are normally three-hinged with one hinge at each support and one hinge at the top ridge. The width of the glued laminated timber cross-sections can be up to 240 tnrn and the depth up to 2 177. Larger arches can use built-up sections of glulam. In Figure I six different construction types of frames are shown. Figure l a details a system consisting of a two-piece column to resolve the corner moment into tension and compression elements. In Figure l b the shape of the frame is achieved by means of a finger jointed haunch linking the rafter and column units. In Figure l c the single rafter units are enclosed by two glulam columns which are linked along their length and designed as spaced columns. The haunch connection is effected by circular groups of dowels. The curved frame in Figure Id takes advantage of the ability to curve glulam and leads to arches which are shown as a three-hinged variant in Figure le. The two-hinged arch in Figure If is necessary for flatter roofs but is greatly restricted in overall height and span by transportation requirements. EC5: POII 1-1: 2.3.1
In general it has to be verified for all roof members that no relevant limit state is exceeded taking into account load actions in three dimensions. This lecture, however, is restricted to the verification of frames and arches due lo loads acting in their plane. Hence it follows that members forming frames and STEPIEUROFORTECII - an initiative under Ihc EU Come!! Programme
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ECS: Part 1-1; 5.4.4
arches are stressed mainly in compression and in-plane bending. In addition, lateral bending due to buckling effects has to be considered. The stresses caused by geometrical and structural imperfections, i.e. deviations between the geometrical axis and the elastic centre of the cross-section due, for example to material inhomogenities, and induced deflections shail be talcen into account.
Figurr I
Sonle rypicnf frames: (n) V - .slrapeO, (b) crl~vedhn~rr~clr,(c) clo~velled haanch, ((1) j51rger-joitrtcd Iru~rtlclr.Sonic typical arches: ( e ) tfzree-hi11,pcd (fi flat two-hitrgecl.
Simplified analysis
EC5: Purl 1-1: 7.2 P ( I )
Frames and arches can be verified by a simplified analysis in the same rnaimer as columns and beams. The calculation of stresses due to external design loads is based on a Iiilear theory considering equilibrium of tile undeformed static system. Stresses caused by geotnetrical and structural in-plane and lateral imperfections and induced in plane deflections are laken into account by rnultiplying the cornpression and bending strength values by reduction factors such as kc and .,k These factors have to be determined from the appropriate critical compression and bending stresses of in plane and lateral buckling. The deviation from straightness measured midway between the supports shall be limited for frame members to 1/500 of the length for glued laminated members.
Design example
Figure 2
Estlnrple: Cllr~~eclflun~e of a ricli~tg-lruil.
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Tile design values of the vertical (V) and horizontal (H) support reactions and the internal axial forces (N) and moments (M) at cross-sections I , 2 and 3 and the ridge deflections rt,,,, and u,,,, are given in Table 1 corresponding to the appropiate combination of actions 1,35 g t I ,5 s.
s,, V
units kN
H
kN
N,
kN
4 MI M: M3 '(ttsr
111111
JOYrr
~tilll
1,35 g
s 54
23 -44 -4 I -30 -73
kN kN kN11i kNt11 MIII
N3
Tnble 1
6
48 31 -50 -56
-42 -104
-9 1 -61 O
-133
21
32
-92
+ I,5 s 145 78 -134 -139 - 104 -255
-322 -220
O
Design vnlrtcs of rracrialrs, irltcrrial mi01 forces arrd rl1arftetrts nrid ridge deji'ections.
Tlte frames are fabricated of glued laminated timber GL 28 with the following appropriate material design properties (see prEN 1194): 0,9 -28 = 1 9 , 4 ~ h m ~ fm,ad= design bending strength 123
-
design compression strength moduli of eIasticity
Eo.scnn,r: Eo.05.1
= 12000 N/lnrrt2 = 9600 N/lnm2
Verification of ultimate limit shtes In cross-section (2) E C ~ ~arl : 1 - 1 : 5.2.1
Co??zpressio~? brrcFclbrg It is assumed that cross-sections ( 1 ) and (3) are laterally supported. kc = 1ni11(kc,>,krt:)
In the case of in plane buckling the curved frame can be interpreted as an arch with sufficient accuracy. One half of the arc length is estimated as the sum of length of rafter (1 1 n ~ and ) coIurnn (6 1 1 1 ) .
A,= 1,25 (11 + 6 ) / i y = 7 5 STEP lecturc B7
In the case of lateral buckling, the buckling length is estimated as arc length between cross-sections ( I ) and (3).
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ECS: Part I - 1; 5.1.2
Lateral torsio~talbticklil~g In addition it is assumed that cross-sections (1) and (3) are torsionally fixed.
(See Timoschenko and Gere 1961 or Pfliiger 1975.)
EC5;Part 1-1: 5.2.4
Reduction in strength due to bending of laminations during production
5r
2
240
i.
k, = 1,O
Design bending stress
Design compression stress
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Verification with respect to compression buckling
Verification with respect to lateral torsional buckling
ECS: Part I - 1: 4
Verification of serviceability limit states In this design no precamber is included. I-Iowever, precamber could be necessary in other cases especially where deflections in curved members are caused by changes in moisture content. Vertical ridge deflection,
tc,,,,l,
due to permanent load, 8,(see Table 1).
Vertical ridge deflection rr,,,,,, due to variable load s (see Table 1). 32 l ~ r t t i = (1 + 0 , X ) 32 = 40 rltltr
I ~ , . , , , ~ ~ ~= ~.~~
ti,,, ,,,?,I,
For frames and arches, EC5 gives no recom~nendations on deflection limits, because such limits are related to the intended use of the construction. In the absence of special conditions that call for other requirements, EC5 recommends the final net ridge deflection to be
ECS: Pan 1-1: 5.4.4(2)
Second order linear analysis The calculation of stresses is based on geometric nonlinear theory considering equilibrium of the defonned ilnperfect static system. The contribution of any joint slip to the induced deflections should be taken into account. Besides the limit states of rupture or excessive deformatioil of a section, member or connection, the nonlinear calculation must be able to detect a possible limit stale due to the transformation of the structure into a lnechanisln or due to instability. For example, firstly a Icing post truss with a precambered upper chord transforms into a lateral n~ecl~anismwhen the vertical deflection reaches tire value of the precamber and secondly a flat three-hinged roof loses its stability by snap tbrougl~buckling. Nowadays, these calcuIations are carried out by finite element computer programs. Normally two di~nensionalfjnite rod elements (two displacements and one rotation at each node) are used. These elements are able to tdte into account imperfections and induced deformations in the plane of the frame. All stresses due to lateral effects have ro be calculated using the simplified analysis. Otherwise, a more co~nplexdescription of the frame by three dimensional finite elements is necessary (Kessel, et al. 1984 and Young 'and Kuo 1991). Cornpared to the simplified metl~od,the advantages of a second order linear analysis are: STEP/EUROFORTECH - ;in initiative under the EU Comet1 Programme
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no need lo estimate critical stresses in determining the factors kc and
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no need to estimate bracing forces if a tltree dimensional simulation of a set of frames or arches is carried out (Kessel 1984).
Design example The second order linear analysis is shown for the previous example in Figure 2. A two dimensional nonlinear finite rod element is used. The initial deflections are shown in Figure 3 assuming an anglef of inclination
which leads to a corresponding initial vertical ridge deflection
as sl- own in Figure 3a and a corresponding initiat horizontal ridge deflection
as sl~ownin Figure 3b.
Figrcr-e 3
Itrrpstfect slnibrlre: (a) corrcspotlrlitrg to syr~lt~ietricalnctiotls. (b) correspotlditrg to rnor~-syarrrteiricnlncrio~rs.Dashed lirie: initial franrc; solicl line: irrclinecl fra~~ze; cf~aitt-dottedlirte: irrcfirwdfr-anre itlcludirlg cnrvatlire.
The combination of actions remains unchanged, but the stresses and deflections are calculated using a value of E of
E = E,,,, f ;,,,,,1f, = 9600 . 19,4 / 28 = 6650 ~ h t t t t i ~ The resulting design values are given in Table 2.
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s,
units
1,35g+ 1,5s
symmelric 144 79
- 135
146 79 - 1 35
-140
-140
-105
- 106
V
kN
H
N1 Nz
kN kN kN
N3
kN
Ad, M,
kNr11 kNt11
-269 -343
4
Writ
-238
Table 2
non-symmetric
-260 -327 -227
Nor~lirreararmlysis. Desigrl vnlrtes of laactions, i~rler-rrcrlarid farces and ntarrr el7 ts.
Verification of ultimate limit state in cross-section (2) Since, lateral buckling is not part of the applied nonlinear analysis the factors k, = k,,: and k,,, remain valid therefore: the design bending stress is
the design compression stress is
and the interaction equation is
References Kessel, M.11.(1984). Geornetrisclt nichtlinean: FE-Anrvendungcn im Ingcnjcur~iolzbnu.In: Finite ElemenLe - Anwendungen in der Baupraxis. Verlag Emst Jlr Sohn Berlin, 237-245. Kessel, M.l-I., Hinkes, F.J., Schclling, W. (1984). Zur Sichcrung des Drcigetenkral~mcns aus Bre!tschichtholz gegcn Kippcn. Bauingenieur 59 (1984) 189- 194. PflUgcr. A.. (1975). Stabilit3tsprobIeme der Elaslostatik. Springer Verlag Berlin Heidelberg, New York, 3rd Edition. Tirnoshenko, S. and Gere. J.M. (1961). Theory of' elastic stability. McGraw-Hiif Book Co. Inc. New Yorli, 2nd Edition. Young, Y.B, and Kuo, S.R. (1991). Consistent Frame Buckling Analysis by Finite Efcment Metlmi. J. Struct. Eng. 117 (1991) 1053-1069.
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Bracing - Design STEP iccturc B 15 Objectives tf. Bruninghoft' To develop an understanding of how con~pressionor bending members need to Gcsamtl~ochschulcWuppcrtnl be braced in order to avoid instability, to identify the governing parameters and to present the procedure of ECS as a worltable design rnetl~od. Bcrgischc Univcrsitai
Prerequisites A4 B2 B3 B6 B7
Wood as a building nlaterial Tension and co~npression Bending Columns Buckling lengths
Summary The lecture starts wit11 a non-mathematical introduciion to the ~nechanismsof bracing structures. It presents the principal factors influencing the actions on bracing members and shows how the equations offered in EC5 have been derived. A practical example showing how the actions on bracing structures are evaluated comple~nentsthe lecture.
Introduction Coluinns require a stability calculation to check against failure or unacceptable defor~nations.Often it is advisable lo restrain one or more points (between the main supports) from lateral deflection by bracing. This is done in an analogous way to that used for slender bearns to prevent lateral buckling. Colu~nnsor beams could be part 01a combined structure, for example an upper chord of a truss. The actions on the bracing structure may be derived by using a second order analysis whereby the equilibrium of moments and forces is analysed by considering the deformed shape or the respective structure. The stiffness of all ~nernbersconcerned and the slip of built- in joints is tdien into account. However, EC5 presents a simplified method based on the above approach.
Factors influencing actions on bracing members It is necessary to differentiate between compression and bending melnbers lo be braced. Furthermore either a single higilly loaded support or several supports which form pa11 of a bracing structure, e.g. a buss, could be analysed. The actions on supporting structures depend on the general geometry of the structure to be braced, such as cross-seclional and Io~tgiludinnldimensions, support conditions and marerial prope11ies determined by the cl~oiceof the strengtl~class, the climate and the load duration class of' tile governing load case. The stiffness of rnenibers and the rigidity of existing joints are very imporlant factors, not only as attributes of the st~vclure to be braced but especially for the bracing structrlre itself. To perfon11 a second order analysis, geometrical and stn~cturalimperfections sl~ouldbe incl~ided.
EC5: Pad I - I: 7.2
In EC5 the initial curvature of the rneniber axis is limited by deviation from straightness to 11500 of the length for glued laminated timber and to 1t-300 of the length for structural timber.
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1111
initi:~tive unclcr tlic
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Comet1 Prognmnic
B15/1
Baclcground of the design methods of ECS Single szrpports of conzpression nrembers
N,,-p ,-1.-
C)
F1r
0
Figure I
'r :
d)
+N 11
I
-(I
Sj~.stemnrrd cli$'ectioris of'bruce~lr11erliber.s.
Compression members of the length I regularly braced by elastic supports to avoid buckling produce big spring Forces if the deflected shapes shown in Figure 1 b and c are assumed. Mohler and Schelling (1960) showed that the niinimum spring stiffness should be
-
where ks
X
= 2 ( 1 +cos - ) 111
and a the length, I I Z the number of waves, so that I = it1 n to guarantee a deformed line of member axis with two hinged ends and with k, = 2 for one wave shape or I;, = 4 for an infinite number of waves. The spring force F, (see Figure 2).
Figrtre 2
-
Sltupe uttd forr~lsof utt elastically sicppor-ied member.
can be calculated conservatively by a second order analysis to be:
where e is the maximum devia~ionof' straightness. Figure 3 shows that spring forces of I;;, = N, 158 and i;,, = N, 196 could be included, if deviations of straightness in an unloaded sittiation of 11300 or 11500 are assumed for solid timber, or glued laminated timber, respectively. The results have been approximated in EC5 to N , 150 or N, 180. STEPIEUROFORTECH - an inilielivc undcr the EU Cornelt Programme
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Figitre 3
Coeficiettt of bmcitrg force as u fnnction of deviatiori of strrrigfitrress.
Single nipports of bendilzg nieinbem Burgess (1989) proposed the substitution N,,in equations 5.4.5.2 d and e of EC5 with
-
Nd = M,,Ncric Mcr,
where Nc,i, and M,,i, are the critical forces calculated according to tile classical theory of stability. EC5 proposes an alternative approxi~nation
where k,, is calculated from equations 5.2.2 c to e of EC5 for the unbraced length of the member. Here the torsional rigidity of a beam is taken into account. No bracing is required if I,, = 1 . Tlie procedure only works if the beam is braced dong the compression edge.
Bracing of beam or truss systems To achieve maximum actions on a bracing structure the iluperfections of the compression or bending members to be horizontally supported by a bracing structure of the stiffness (El),/ is assumed to be a single wave sine curve as shown in Figure Id. Con~pressionforces, N,, produce a moment (see Figure 4) Md = n N d y
Figrm 4
Braced con~prc~siotl ttrenzbers utld deflections; (a) slrrright lirre, (6)it~zpetfect is rhe stQj$res.s of the bracing str-rtctrrre.
axis, ( c ) deflected axis.
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The resistance component, negIecting the stiffness EI: of the slender members to be stiffened, is given by the differential equation of elastic line with regard to the predeflection
which equation may be combined such that
where the predeflection is a y, = e sin (-XI l
and
M,
=
nN, y
The solution of the preceding differential equation leads to
see also Briininghoff (1983). The evaluation of this equation requires knowledge of the bracing stiffness (EI),:,lo be calculated, taking into account not only the elastic behaviour of all members, e.g. chords and diagonals of a truss, but also the contribution related to any joint slip. To provide a simplification for comrnon design situations, EC5 limits the maximum deformations of the bracing structure caused by q, to N700.
Then the elimination of (EQfout Equations (10) and ( I 1) above and the conversion of a sine shaped load qd into a constant form give
where k, = 1 . For spans of more than 15 i n a particular accuracy of workinanship [nay be expected to limit deflections so that i t is reasonable to reduce tfle span-related imperfection by the factor I
where I is given in
171.
The design engineer st~ouldcheck the deforn~ationsof the system if the deflection limitations are likely to be exeeded. Using beams (instead of compression members) in structures the co~npressionedge should be supported so that the equations in EC5 may be taken for bracing analysis. SI'EPIEUROFORTECN - an initiative undcr tile EU Comet1 Proprainmc
To take into consideration the torsional capacity of beams as described above, the compression force can be reduced to
where h is the depth of the beam
Design example A hangar 60 m lengtll, 20 rn wide and 8 height is to be constructed, using glulam beams of strength class GL 28 according to prEN 1194, "Timber structures - Glued laminated timber - Strength classes and determination of characteristic values". The beams span 20 nr, are 1200 inm deep and 160 r71tn wide and are spaced at 6 m centres. Design values of permanent and varable load for the governing load case: permanent load: g , = 5,4kN/ln (line load, permanent) q , = 6,O kNAn (line load, short term) variable load: EC5: Part 1- 1: 3.1.7
Service class I :
k,,,,,,= 0,9
Cllni-acterisric innrerial properties prEN 1 194: 1993
The characteristic valua of strength as well as modulus of elasticity for bending and torsion are taken from prEN 1194 "Timber structures, Glued laminated timber, strength classes and determination of cl~aracteristicvalues". The 5-percenlile values are used in the designwork since an ultimate limit state is considered.
cross-section values: h 2 b = 38,4 . lo6 rrrnr3 Wy= 6
I,, = q3 h b3 = 1500
. lo6 r11ni4
Tlie critical moment is
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and the critical stress is a"l,c"~
Mcril = 7,44 iV,7,17,z2 = -
WY
The relative stress slender~iesscan be calculated
and the buckling coefficient
The compression rorce of the glularn beam is to be determined
where
M,, = (g,, + q,,)
= 570 kNvt
The bracing load is then given with
where the imperfection factor is: I
11
N,,
=I0 = 349 ItN
for 9 ft~llyloaded beams and two 50% loaded gable walls as shown above.
The limitation for horizontal deflection is if700 for bracing actions, N500 for the combination of wind and bracing loads. These are normally fulfilled if the bracing strilcture is properly designed connected and the relationship of span I and spacing e, is less than 6, here
-
-
Concluding summary -
-
-
Bracing structures ate needed to restrain slender compression or bending members from lateral buckling.
-
The major factors influencing the bracing actions are ditnensions of the system and the beams, geolnetric and structural imperfections and material properties such as strength and modulus of elasticity for bending and torsion.
-
The procedure offered in EC5 is based on a simplified second order analysis, such that an additional check of Iateral deflections is generally required.
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References Mohler. K. and Schelling, W. (1968). Zur Bemcssung von langcsin Code Bracing Rccommendations Lbr Beams and Calumns. In: Proc. ol' thc CIB-W 18 Meeting, Bcrlin, Germany, Paper 22-15-1. Brilninghorr, H. (1983). Dclcrrnination of' Bracing Structures for Coinpression Members and Benins. In: Proc. of the CIB-W 18 Mecling, Lillehammcr, Norway, Papcr 16-15-1
Notation n c,
length between elastic supports spacing of beairis
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Load sharing STEP leclure B I G I-I.J. Btass ~eifiUniversity of Tecl\nology
Objectives To develop an understanding of the phenomenon of probabilistic load sharing in parallel stnrclural systems and to quantify the effect on the load-carrying capacity of systems.
Prerequisite A4
Wood as a building material
Summary The lecture presents examples of parallel structural systems, where the positive correlation between the strength and the stiffness of timber members increases the load-bearing capacity of systems compared with that of single members. The influence of the material behaviour and the variation of timber strength and stiffness on the load sharing effect is discussed. For common structural systems the load sharing effect is quantified.
Introduction EC5: Part 1-1:5.4.6
EC5, like other design codes, includes a load sharing factor for assemblies consisting of several similar members connected by a load distribution system. An example of such an assembly is a timber joist floor, where the joists are linked by panel sheathing. Tile load sharing factor increases the member design strength by taking into account two effects: first the reduced chance that a weaker member or pare will be placed at a position where the stresses are particularly high, and second the positive correlation between strength and stiffness of timber members. This positive correlation enables a stiffer member to carry a higher proportion of the applied load. On the other hand, less stiff members, which in most cases are also weaker cany less of the load. Load sharing counteracts the materiill variability effects lo a certain extent.
Figitre
I
Hoor Ioyorit rmder tile action of rr cotrcerttintcd load.
The load sharing or load distribution effect improves the member 'behaviour in systems for both concentrated and distributed loads. For concentrated Icrads, the load distl-ibution system transfers part of the load to the adjacent members, relieving the most stressed member under the concentrated Ioad. Figure I shows a[ floor crosssection under the action of a concentrated toad. In uilifonnly loaded systems, the load-sharing effect is less evident. If the stiffness of a11 members is the same, the deformation of all members would be identical even without a load distribution system. Since in reality the inember stiffness varies, STEPtBUROFORTECH - an initiative under ihc EU Comctt Propnmmc
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softer members tend to deform more than stirfer members. Line (b) in Figure 2 shows the different joist deformations in a floor if no load distribution system is effective. If a load distribution system connects the joists, the deformations become more uniform (see line (a) in Figure 2). In this case, the load distribution system decreases the load on flexible members and increases the Ioad on stiffer members.
Figlire 2
E'ect of the load di.striDutiorr systerri on the joist dcfornicitions. ( a ) rvitli crrrcl ( b ) witliorrt load clistribirtiori systctrt. 1V: 101v d~;tjctres,s aember; S: high .stiflress rtiettiber; A: average strfiress trrer?rber.
The same situation is true where the member behaviour is no longer linear. If the stiffness of a single member under loads close to the ultimate load decreases due to ~nicrocracksor plastic deformations, the load is redistributed within the assembly and the partly damaged member is able to contribute to the load carrying capacity of the system, the total assembly load can still be increased.
A
-
-
Load sharing in different structural systems Flool;r and . f i t roofs Foschi, Folz and Yao (1989) performed a numerical study of the design of floors and flat roofs in order to derive system factors for modifying single member design ec~uations.The structural analysis carried out in this study was restricted to linear behaviour. The loads considered were uniformly distributed dead and live loads. The load sharing factor was derived by a reliability assessment of a single beam within the floor, i.e. the way in which the performance of a single member was affected by its i~lsertioninto the structural system was considered. Sensitivity analyses were carried out to determine the influence of different parameters. Tlie load sharing factor k,, was found to be quite insensitive to variations in the support conditions, the size, number and spacing of the joists and the ratio between dead and live load. The following factors increase the effect of load sharing:
-
increasing the ratio of the stiffness of the Load distribution systetn to the average member stiffness,
-
increasing the variation of the member modulus of elasticity and
-
raising the correlation between lnodulus of elasticity and bending strength.
-
-
-
-
The bending strength variation of the beams also significantly influences the load sharing factor. For very small and very large values of the coefficient of variation (COV), the load sharing factor is small with a maximum for COV values between 0,20 and 0,30. For a typical floor or flat roof, the load sharing factor determined was k , = 1,15. This corresponds quite we11 to the value of 1,10 in EC5.
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-
Roof Trlrsses Load distribution in roof truss asselnblies has been studied by Wolfe and McCarthy (1989) and Wolfe and LaBissoniere (1991). Tests were performed on individual trusses and full-scale roof assemblies using three different truss configurations. The Ioad distribution system was I:! n m ~plywood sheathing across the tnlss rafters. By measuring the load-deflection response of individual trusses independently and as part of the roof assembly, the effects of assembly interaction under uniformly distributed loads as well as line loads on individual trusses were evaluated. Roof load carrying capacity was increased and apparent truss stiffness variability was decreased by load sharing mechanisms within the assembly. When partial damage occurred to individual trusses, a redistribution of loads away from these trusses enabled them to continue to contribute to the assembly load carrying capacity at a lower Ioad level. If a single truss in a system was loaded along its top cllord with the design load, 40% to 70% of that load was transferred to adjacent trusses by the sheathing. The load sharing effect on the load canying capacity of the trusses resulted in ratios of measured roof assembly strength to minimum truss strength from 1,09 to 1,47. These values depend on tile effectiveness of the load distribution system and on the position of the truss in the assembly. They indicate that the design load carrying capacity of the entire truss, i.e. members and connections, can be increased by at least 10% due to the load sharing effect. For most systems, a factor of 1,10 can be considered as a safe minimum value.
Slzect piling Load sharing effects also increase the bending capacity of planks in sheet piling or retaining walls, if they are interconnected, for example by tongue and groove joints. In this case, the load distribution system is the connection between the single planks. This connection causes a nearly uniform deflection of the individual planks under uniformly distributed loads although their stiffness values may vary considerably.
A theoretical analysis (Van der Linden et a]., 1994) was carried out, based on the following properties of ekki planks (Lophirn alata) in wet condition: J;,
= f 03 Nhrur1'
and
E ,,,,.,,,,= 17600 Nhlrnr'.
The coefficient of cor~elationbetween bending strength and modulus of elasticity was 0,73 and the coefficient of variation for both bending strength and rnodulus of elasticity 15%. The bending stress distribution over the depth of the planks included a plastic behaviour in the cornpression zone, leading to n decrease in stiffness at higher stress levels. The analysis included the generation of sheet piling systems based on varying properties between the planks and constant properties within the planks and the subsequent calculation of their Ioad carrying capacity using a nonlinear finite element model. Comparing the characteristic load carrying capacity per plank for systelns with ten planks to the capacity of individual planlts leads to a load sharing factor of about I,I5. This factor is applicable only to the bending strength values for the planks, since the load distribution system is not effective for axial forces.
Design example Timber floor with beams b x It = 60 x 200 Ilttrr spaced at n = 0,60 rr1 interval with tongued and grooved floor boards acting as ioad distribution system, span STEPtEUROFOR~CH- an initiative under Il~eEU Cornett Programme
B 1613
1 = 4,60 !ti. Strength class C24 according to prEN 338 "Structural timber. Strength classes". Design values of permanent and variable load for the governing Ioad case: distributed ly load, permanent) permanent load: g, = 1.0 k N / r ~ ~ ~ u n i f o r m q,, = 3,O IcN/ti? (unifonnly distributed load, medium-term) variable load: EC5: Part 1-1: 3.1.7
Service class 1:
k,,,,, = 0,8
Design bending stress:
prEN 338: I99 I
Characteristic material property: The characteristic value of the bending strength is taken from prEN 338 "Stmctural timber - Strength classes": j;,,,,= 24 N/nun2.
EC5: Part 1- 1: 2.2.3.2
Design value of bending strength:
E C ~Part : 1-1: 2.3,z.ib
Verification of failure condition:
Concluding summary
-
Load sl~aringincreases the characteristic load carrying capacity of members in parallel structural systems compared to single members, based on the positive correlation between strength and stiffness of timber members.
-
A stiff load distribution system, a close correlation between strength and stiffness and pIastic behaviour of the members are all beneficial to the load sharing effect.
-
Typical assemblies where the Ioad sharing effect increases load carrying capacity are flat roofs, floors, trusses, rafters, wall studs and sheet piling with effective load distribution systems connecting the individual members.
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-
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References Foschi, R.O.. Folz, B.R. and Yao, F.Z. (1989). Reliability-Basecl Dcsign of Wood Slructurcs. Structural Rcscarch Sci-ics, Rcpon No. 34, Department of Civil Etlginccring. University of Britisli Columbia, Vancouver, Canada, ISBN 0-88865-356-5. Vikn dcr Linden, M.L.R., Van dc Kuilcn, J-W. G. and Blass, H.J.(1994). Application of' the Holln~an yield criterion for Load sharing in timber sheet piling. In: Proc. of the 1994 Pnc. Timber Eng. Conl. Gold Coast, Australia.
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Wolfe, R.W.and LaBissonicre, T. (1991). Structural Performancc of Light-Ramc Roof Assemblics. 11. Conventional Truss Assemblics. Research Paper FPL-RP-499, Forest Producls Laboratory. Forest Service, US Department ol' Agriculture, Madison, Wisconsin, USA. Wolfc, R.W. and McCarthy, M. (1989). Structural Pcrformmcc of Lighr-Fmmc Roof Assemblics. I. Truss Asscrnblies With High Truss Stiffness Variability. Research Paper FPL-RP-492, Forest Products Laboratory. Forest Servitc, US Dcpartmcnt o l Agriculture, Madison, Wisconsin, USA. STEPIEUROFORTECH - an initiative uridcr the EU Comctt Prograrnnle
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Fire resistance of timber members
1-1. EIarll
Objective To present calculation lnethods for slructural fire design.
Zivilingcnieur fijr Bauwcsen
Prerequisites
STEP lcclurc B 17
A4 Wood as a building material A 13 Behaviour of timber and wood-based materials in fire
Summary The calculation methods for structural fire design according
to EC5: Part 1-2 "General rules Supplementary rules for structural fire design" are discussed and a comparison between these methods is shown with the help of an example.
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Introduction Generally the same principles are followed to calculate fire resistance as in standard design. Thus for actions and for material properties characteristic values are applied. However most fire testing is based on deterministic methods using mean values for strength. In order to ensure the same safety level EC5:Part 1-2, gives approximate calcuIation methods that satisfy both requirements, see Figure 1.
For .rr(itrrk~rd/iree.tpo.rttrc: - Cltiirrit~gcic/~rii~ f ~ l l =l l rPo I or P r
Rcclrtccd .vrer~xtlteirld str#ie.r rrrctlrad
firfwrctinerricjirc c.~/~~isrtre: C/rnrrirr# rfc~>lbdc.ll,, rti:cmr.dirig EC5:pctrr I -2:A1tttc-r1) - hind corryinx crrf,ercir)t~~/'rtrcr~il~crs ~virlrtr rcsidtrcrl crossscclion: 1 ', = f h -1 (b 2 ele,rrr,J f i r4 ~iflc.~,/irc c.f~~ris~rrc 11, = (h -2 %,l,l,j (b - c/ch,,J jirr 3 .~ide$flrc?erpo.rrorr
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C
- GloItc11smrcfrtntl rtrrrr!~~.~i.r c~t;cort.lirgEC5:Part 1-22.5.1 ~wcrirlchorring rnc~tfels
- Terfr]~errrlarc prc1jT1c.r iit rkc rc*sidrtcrlcrr~sr-scctio~; - Strcnjir/r ccirrl srifJrc!s.c f~rmpcrrie.rrIc~~ciidcrrr on tcrrrl>ercrtrtrc rttrd nroisltrre rarrfcrrt
fig tire I
Sfnictttml fire
clcsigt1 accurcii~igEC5: Parr 1-2
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Verification EC5: Part 1-2: 2.5
The effect of actions E(t) and the resistance of timber members R(t) during fire exposure is in principle shown in Figure 2 . The fire resistance is reached at the time t, when R(t) becomes less than E(t). Thus the verification on the design level is
0
10
20
30
40
50
GO
f (ulirt.)
Figrcrs 2
Effect of aciiorrs E(t) ar~drasistarrce of timber rrlenll~er:~ R(f) rlrrririg Jre e.YposlI re.
El,,, is the design effect of actions in the event of fire R,., is the design resistance in the event of fire
Design values for material properties
Material pr-operties for- tltet-ilmi analysis EC5: Part 1-2: 2.3
X,(O) is the characteristic value for material properties at a temperature 0, depending on whether property increase is favourable for safety or not.
Tllernzo t~iecitntricalproperties of strengrll arid ttlod~rl~ls of elasticity For load-carrying verification the design strcngth and stiffness values shall be determined from EC5: Part 1-2: 2.3
For deform;ition verification the stiffness values sl~ailbe taken from
is the design value of material property (strength or modulus of elasticity) is the characteristic value of material property kmMIJis a reduction factor taking account of the influence of temperature and moisture content on strength and stiffness in case of fire is a coefficient which alters the characteristic property LO a mean value I/ = 1.15 for glued laminated timber and wood based panels kr = 1,25 for solid timber kr = I ,O is a partial safety factor for material properties Y,,~
XJ,,
X,
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Char-ring depths Charring depths for members exposed to fire can be calculated by means of the cllarring rate (linear relation between charring and time) and the Lime of exposure to the fire (see STEP lecture A13).
Design values for actions and effect of actions According to EC5: Parl 1-1, the accidental cornbination rule is used in fire design. EC5: Parl 1-1: 2.3.2.2b
C YG,,,~
Gk,j
+
A,,
+
V ~ ,Q k If
+
C'I~,,Q~~ i >I
Where G, are the permanent loads and Q, the variable loads. y is a partial safety factor and ~y is a combination value. (A, is normally equal to zero, but has to be justified in the fire situation). can be derived from the norrnal design For fire design tlie forces and mo~nenls(SL,) value (St,) by the following equation:
S' = 11
(6)
S,l
7 can be calculated by division of the fundamental and the accidental cornbination rule (case of fire) or 11 is sinlplified to a value of [0,6]. In this case conservative results are possible.
Esort7ple System:
1 is the span and e the distance between the beams; I = 5,O Loading: G, = 2,l kN/tn" Q = 1,2 kN/t?t2 Q = 0,5 ~ N / N I '
112;
e = 1.20 m
Permanent action Variable action (snow) Variable action
Normal design (fundamental coinbination): y is tile partial safety factor for actions; y, = 1,35 for permanent actions and ye = 1,5 for variable actions
Bending moment:
EC5:Parli-l:2.3.2.2b
Fire design (accidental cornbination): y, is the partial safety factor in the event of i'lre; y,
= 1,O
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\ifi is a coinbination value; \if,,, = 0,2 combination value for the first variable action in the event of fire, yr,, = 0,3 combination value for olher variable actions in the event of fire.
y,
= 2,49
.
1,30 = 2,99 kNlttz
Bending moment: J 4,/= 8
2.99
. 5.0'
=
9,34 kN,,,
8
Calculation methods
Te1r1perlc1frir.eprofiles The temperature for the actual charline is of n 111agniiudeof about 300 "C. The charline derived froin P,, (Q) can be piit at 200 "C. For a fire exposure of 111orethan 70 minutes ambient temperatures are reaclied at a distance below the clinrline which remain constant for the remaining exposure time. This distance is about 30 t m t i from tile charline and for the charline related to PI, (P) about 25 tilitz. The shape of the iemperature profile is given in Figure 3.
Figwe 3
Tettipemtlire profife for b, > a,,,, see Hnrtl (1990).
If the width of the residual cross-section b, is stnalle~.than n,,for exposure from one side or smaller than 2nl, for exposure froin two sides, the gradient llns to be modified to account for a temperature increase beyond ambient in Lhe middle of the section (see Figure 4).
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Figure 4
Temnperature profile for b,< 2 a , , see Hartl (1990).
Tenzperat~cradepetzdent strengtfi alzd stifitess properties The dependency of the strength and stiffness properties is sl~ownin Figure 5 , where E is the modulus of elasticity, f,, f, and f, are the strength values for tension, bending and compression strength of solid timber. From these fundamental findings the following calculation methods are derived.
Figure 5
Tenrperati~redepe~rderrtstrerrgtll and s t t ~ ~ z e properties, ss see Glos (1990).
Effective cross sectiorz l?tctlzod For the effective cross section method the time of tire resistance depends on the load bearing capacity of the uncharred remaining cross section. This effective cross section is shown in Figure 6, with ECS: Part 1-2: 4.1
',
=
'tlurr
+
'0
where 4, = 7 fn11z.
EC5: Pnrti-2: Figure 4.1
Figrcre 6
EJfcctive cross seclion.
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(8)
The factor rl,, is calculated in the following way: Integration of the temperature profile according to Figtire 3 gives an average temperature of about 80 "C. Adopting an average temperature-dependent strength at 80 "Cof about 70 % (between bending and compression in Figure 5 ) implies that 70 % of a,, may be regarded as unaffected and 30 % as ineffective. 30 % of a, = 25 rllrtt gives about 7 rltrlr (rl,,). Faclor k,, according to the required time of' fire resistance is given in Table I . Unprotected surfaces
Surfaces protected by wood based panels
tf,rcq
< 20 min.
if,,c,,
2 20 min.
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I
~
'
-
tr
-
1,rccl
Surfaces protected by gypsum plasterboards (inner layer)
,
<~ 20~min. ~
20 rnin. t p r < 10 min. tpr 2
k,, =
,k k(, =
tf.rctl -tpr
----20
=
I ,O
tf,rrq
-'
pr
,
10
t,,,,, is the required time OF f'lrc resistance and t,,, tile failure time of protective claddings. EC5: Part 1-2: 4.1
Tuble I
Drterrrrirmtion oJ k,,.
Reclrtccd stmrtgtlr arld sriJfiess r~rcthod This tnethod is also derived from the afore mentioned temperature profiles (by integration average temperature). Tile load carrying capacity is calculated for the residual cross-section. Due to an allnost linear relationship between temperature and strength and stiffness properties an equation was found where the reduction factor can be calculated in dependence on the perimeter of the fire exposed cross section (p) and the area of the residual cross section (A,), see Figure 7.
E.g. k,,,,,,,
for standard fire exposure, coniferous timber and for bending strength
where is the perimeter of the fire exposed residual cross-section in metres 11 is the area of the residual cross-section in ni" A,
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EC5: Part 1-2: Annex A
Figure 7
k,,r,,,,Jfor letl.siotr ( I ) , betiditrg (,ti), cort?pre.ssio~t ( c ) crrrd ~ttohllesof elnsficily
t.0 General c n l c ~ r l a t i o imct/?ods ~ For general calcuIation methods the telnperature and moisture conlent in any point of the cross section is considered. Also the relationship between strength and stiffness properties and temperature and moisture content has to be taken into account. Therefore an increase in the amount of design work is inevitable, but these more complex methods would lead to more economical constnrctions.
Example:
EC5: Part 1-2: 3.1 . l a EC5: Part 1-2: 1.3: PO)
The following calculation is based on the example given on page 3 for fire exposure from 3 sides and for a fire resistance of R30 and RGO (30 and 60 minutes): b x h : 180x220 ntm cross-section strength class C27 = 27 N/tltt~t' Po = 0 i r solid timber (see STEP lecture A13) k, = 1,25 solid timber M I = 4,77 k N ~ a see example page 4
EC5: Pnrt 1-2: 4.1(2)
EJffective cl-oss section ~rictltod ~,,I,,~IJ = I $0
EC5: Part 1-2: 4.2a
(I,,
R30:
= p, t,,,, + k, d effective cilarring deplh = 7 ltlI71 = 1,O according to Table 1 k,, C I , ~ ; , ~ = 0,8- 30 i- 1 , O m 7 = 31,O rnrrr
(4
y, =
EC5: Part 1-2: 2.3il.b
I, f.30 h' J30 = I18 6
.
design bending strength
design bending stress
189'16
=
703
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lO"nu11"
section modulus
Utilization factor 13,3 / 33,7 = 0,394
R60: Utilization factor 29.4 / 33.7 = 0,871
Redrrcecl strength and stiffrzess nzettzod ECS: Part 1-2: 4.1a
R30: charring depth
- p,,
llc,ulr-
1
section modulus
ECS: Part 1-2: Anncx A(4)
--
k m o ~ ~
1 P -200 Ar
design bending strength EC5: Part 1-2: 2.3a.b -
.f mJ,d -
ke%wif k/
'",' = 0.899 -
1 ,25
. 27
= 30,3
N/,r~tn
'
Ynrs
design bending stress
Utilization factor 1 1, 1 / 30,3 = 0,364 R60:
Utilization factor 22,5 1 28,8 = 0,784
Canclusion It depends on the amount of design work how econamical the results of calculaiing the fire resistance will be. It should also be pointed out that not all the problems related to fire resistance are calculable. The results from fire testing especially for floor and wall design are useful.
The effective cross section method and the reduced strength and stiffnes method are very useful For approximate results for the fire resis~nce,which might be enough in most cases. They are not adequate if the fire resistance time needs to be very precise or if 2.-order effects are not negligible. If timber members are covered by panels and if they are be included in the calculation, other design procedures shouid be applied. In this case testing or more detailed calculation is unavoidable (see e.g. STEP lecture E12).
References Hart!.
H.(1995). Brandvcrhaltcn von Holtkonstruktionen. Inforrnationsheft.
Glos.
P (1990). Fcstigkcit von Bauholz bei hohen Temperaturen. ForschungsberichL.
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Mechanical timber joints - General STEP lecture Cl P. Raciier CUST Civil Engineering Blaisc Pascal University
Objectives To give an overview of the types of mechanical fasteners used in timber structures. To define the geometry and the basic properties of these fasteners. To give general guidance and specific guidance on factors governing the design of the joints.
Prerequisites A4
B2 B4
Wood as a building material Tension and compression Shear and torsion
Summary This lecture describes the various types ,of mechanical fastener used in timber structures. The geometry and the application of the most cornrnonly used fasteners are presented. Further, the behaviour of mechanical fasteners is examined to aliow a proper selection depending on the aims of the designer. Then, general recommendations relating to the layout and the design of timber connections are given. They cotnplement the EC5 rules for assessing reliable designs (see STEP lectures C2 to C16).
Introduction The basis of design relates to the layout of the structure, the choice of the framing system, the proper design of the components and the ease of const~uction.For timber structures, the serviceability and the durability of the structure depend mainly on the design of the joints between the elements. For commonly used connections, a distinction is made between carpentry joints (see STEP lecture C12) and mechanical joints that can be made from several types of fastener. For a given structure, the seleclion of iasteners is not only controlled by the loading and the load-carrying capacity conditions. It includes some construction considerations such as aesthetics, the cost-efficiency of the structure and the fabrication process. The erection method and the preference of the designer or the architect are also involved (Natterer el al., 1991). It is impossible to specify a set of rules from which the best connection can be designed for any structure. The main idea is that the simpler the joint and the fewer the fasteners, the better is the structural result. In the first part, this lecture presents the different types of fastener. Obviously, it is not possible to present all types of fastener or connection devices in a single lecture. Therefore, only the most important and common fasteners are presented. The general geometry and structural applications are given. The second part deals with the classification of the fasteners according to their behaviour and their loadcarrying capacity. Then, the final part mentions some calculaCions and details to be considered in the design of the joints.
Types of fastener The traditional mechanical fasteners are divided into two groups depending on how they transfer the forces between the connected members.
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cI/l
The main group c o r ~ ~ s p o n dtos the dowel type fasteners. Here, the load transfer involves both the bending behaviour of the dowel and the bearing and shear stresses in the timber along the shank of tile dowel. Staples, nails, screws, bolts and dowels belong to this group. The second type includes fasteners sitcli as split-rings, shear-plates, and punched metal plates in which the load transmission is primarily achieved by a large bearing area at the surface of the members. The load transmissiori is primarily achieved by a large bearing area at the surface of the members. When dealing with larger structures, fasteners could be used with special steel hardware especially for the connection to the foundation or at tile apex of the structure. Apart from mechanical fasteners, a mention should be made of a new group relating to glued joints. They require specific quality control (Ozelton and Baird, 1976).
This technique is mainly carried out using glued-in bolts for beam connections or large finger joints for frame corners (see STEP lectures C14 and D8).
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Nails Nails are the most commonly used fasteners mainly for structural components such as diaphragms, shear- walls and trusses. They are manufactured in many sizes, shapes and materials (see Figure 1). Round wire nails are the most comrnonly used fasteners for timber. Improved nails with square cross-section or deformed shanks are also available. The sizes of nails are related to diFferent standardised gauges in the European countries. The common sizes rangc from 2,75 to 8 rtrrtl in diameter and 40 lo 200 ntnr in length. For* nailed joints, the main development results from the use of power-driving equiptner~tusing coriipressed air. For nail lengths up to 100 mrrr, it allows fast installation reducing the cost of the execution. The equipment should be set carefully to avoid over driving the nails especially in wood-based sheet material.
Figure I
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Slrapes of rlnils: ( { I ) rolrrrd \iiire nrri1.s. (6) l~elically tlrreadcd rlnils, (c) ~11r11lr1nr ritrged sl~ailknails, ((1) ~tlraclrirtedri~)cnnnils.
For the installation of nailed joints, predrilled holes may be necessary Lo avoid splitting or to enable nails to be driven into dense hardwood. For softwood species, tliis operation should be carried out For Douglas-fir and larch mernbers. Then, the hole diameter has to be no greater than 80% of the nail diameter. In timber structures, the nails have to be used primarily in single shear for connecting timber, steel or wood-based panels as side members. The designer has several possibilities for enhancing the load-carrying capacity of nailed joints. For a lateral load, larger lateral load-carrying capacily can be obtained using square nails. The other possibility is to insert steel sheets into the members. The nl'lr s are driven without predrilling for sheets up to 2 ttlr?! in thickness. To increase both STEPIEUROFORTECIJ - an initintivc under the EU
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lateral and withdrawal load-carrying capacity, the common clloice is to use special nails (helically threaded or annular ringed shank nails). They provide greater witlidrawal strength and reduce the hazard of timber splitting.
Plir~cl~ed rile fa1 plcites As nailed plates, punched metal plates allow joints to be ~nadebetween members in-plane. They are manufactured from galvanized steel plates of thickness ranging . installation of the punched metal plates requires special between 0,9 to 2,s I I I I ~ The equipment in a factory. Tiley are mainly used for light-framed timber trusses for wliicll the member thickness should be ar least 35 rnlrt. Because of the out-of-plane flexibility of such trusses, care should be taken in handling to avoid darnage to the joints during erection as recomn~endedin prEN 1059 "Timber structures - Production requiretnents for fabricated trusses using punched nlcttal plates". There exist inany proprietary plates. The designer should refer lo Lhe manufacturer's specification which should be approved by a certification organisation.
Bolts nltd d o ~ ~ e i s Boils are commonly made from ordinary rnilcl steel with hexagonal or square heads and nuts. The diameters range between 12 and 30 m111.For ease of installation, EC5 requires holes to be driven 1 tr71lr larger than the boft diameter although in practice larger tolerances may be required. This bolt hole clearance reduces the capacity of the bolted joints. For this reason and for appearance, dowels are taking tile place of bolls. They are pieces of round steel rod fitting lightly into drilled holes. As specified by the EC5 rules, both steel and timber properties affect the loadcarrying capacity of bolted or dowelled joints. Using ordinary bolts as standardised for steel structures in EN 20898 "Mecl-lanical properties of fasteners-part 1: bolts, screws and dowels", Table I defines the relevant properties. In addition, Table 2 ' gives the properties of the steel bar to be used in the design of dowels. Depending on the size of the connection or the method of erection, some dowels may be replaced by fitted bolts or end-threaded rods to hold the niembel-s together. Bolt grade
(N/t>lmz)
f;.
T~tbleI
4.8
5.6
5.8
6.8
240
320
300
400
480
)'icltl .v~re.ssS, aird tensile .stref~gthA,,, for ordirru~:yDoits.
Steel grade f,.
4.6
(NhrttrJ)
Fe360
Fe430
Fe5 I0
235
275
355
- --
T ~ l l ~2l e
\fo/l~esof f,. c~nd,f;,., for coirol~ottsteel burs.
Generally, bolts or dowels are iised in double or muliiple shear joints. To ensure the performa~~ce of the joints, a minimum thickness is required for timber elements: 30 1nm for side inembers and 40 rtzrrt for internal members. All the tigtltened fasteners should be instalfed with a washer under any I~eadsor nuts in contact with the limber. STEMEUROFORTECI-I- nn initiative undcr the EU Comctt Progrilmnlc
C113
Scre~vs
The main type of screw used for structural applications is the coach screw. The common sizes range from 6 to 30 imti in diameter and 25 to 300 mrn in length. As for bolts, the use of a washer is required. In large connections, they conveniently hold timber connectors in place or replace bolts when they are not suitable. Another use is to fix joist hangers or framing anchors in combination with nails. A limitation to their use results froin the predrilling needed to install the coach screws.
Co!ttzectors The use of timber connectors alIows the transfer of heavy loads by increasing the bearing area in the timber. For truss connections, a nearly perfect pinned joint can easily be achieved using a single connector unit instead several dowel-type fasteners. Figure 2 shows the typical shapes of split-ring, shear-plate and toothedplate connectors.
Figrrre 2
Uslml tirtrber connectors; ( a ) split-ritrgs, (b) shear-plates, (cJ sirigle and dotrblc sided too(lzed-plates.
Split-rings and shear-plates are formed from aluminium cast alloy, cast iron or steel with diameters varying from 60 to 260 nrm. Precision in grooving and boring is essential for the installation and performance of these types of connector. The second type is the toothed-plate connector which is made from cast iron or hotdipped galvanized steel. Their diameters range from 38 to 165 mm. Larger connectors are available for connection of glued-laminated members. In structural t installed. To limit the effects of timber, connectors with diameters up to 75 ~ t r r are the transverse moment, the joints are held together by fasteners installed with round or square washers of a size about half the diameter of the connectors used. Split-rings and double sided toothed-plates are used in a similar way for timber to timber joints. They transfer the load directly between the surfaces of the members that are in contact. The assembly is generatly done on site. On the other hand, shear-plates and single sided toothed-plates are suitable for steel to timber joints as well as timber to timber joints. They allow the prefabrication OF the joints and only the bolts are instalted on site. For these connectors, the load transfer is achieved by the bolt stressed in shear by the bearing area of the connector centre plates.
Behaviour of fasteners and structural joint modelling The design procedure has to combine the global analysis of the structural timberwork and the local analysis of the connections. The key problem lies in joint behaviour that affects the distribution of the forces and the deformations of the structure. It can be determined from test results for the chosen joints according to
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EN26891 "Joints made with mechanical fasteners - General principles for the determination of strength and deformation characteristics". Otherwise, the joint properties are assigned from the behaviour of a single fastener. Figure 3 shows the experimental behaviour of different fasteners where the load is defined per shear plane.
Figure 3
Esperi~nentalland-slip crtrves for joitib irr tetuion parnllel to tlte grain: ( a ) glried joints (12,5 Id nrnt2), (b) split-rittg (100 tnni), (c) dotrbh sided toothed-pfare (62 ~ z m ){Hiru~fzir~m, 1990), (d) do~vcl(I4 nu~r),(c) bolr (I# nmz), Ifl purrcl~edplote (10'
tr1171'),
(g) nail (4,4 1t7tn).
In contrast with rigid glued joints, mechanical fasteners exhibit large deformations that must be considered by the designer. Apart from the stiffness of the joints, the overall behaviour depends on the stress concentrations in shear and in tension perpendicuIar to the grain. These induce a brittle behaviour for the split-ring connector and for shear-plates. The other fasteners exhibit an elasto-plastic behaviour resulting from the deformation of the fasteners as well as the crushing deformation of the timber. Two important features should be mentioned from these curves:
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the initial slip for the bolted joints due to the oversized holes. This leads to brittle behavjour and a reduced load-carrying capacity for multiple fastener connections (see STEP lecture C15). An initial slip can also arise for shearplate and single-sided toothed-plate connectors;
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the punched plates show a small plastic deformation capacity. It can induce a brittle failure depending on the geometric imperfections of the joints, within the fabrication tolerance.
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Furthermore, the yielding of dowelIed joints depends on the slenderness of the fastener as sliown in Figure 4. Roughly, the slenderness can be defined for a doitble shear joint as the ratio between the thickness 1, of the central timber member to the diameter d of the dowel (see STEP lecture C3).
Figare 4
Influerice of tile slendernes.~of the cloltlcl on fke load-slip behnviour of a tirrrbcr to timber sirrgle joirrt irr tetrsiori parcrllel m /he grcritt.
The direction of the transferred forces nrfects the behaviour of the joint. For a single fastener, this influence depends on the size of the fasteners co~nparedwith the thiciiness of the growth rings or the timber. Froin test results (Sinith and Whale, 1986), the load-carrying capacity of fasteners with a diameter up to 8 r l z r l ~ is independent of the direction of load to grain. In the case of loads acting at an angle to the grain, tension stresses perpendicular to the grain reduce tfle ductility and the capacity of the joint. To prevent brittle failure and splitting, the ductility of the joint can be enhanced by reinforcirlg tile members in the joint area. Efficient reinforcement can be made with steel or wood-based panels glued on the internal sides of the connected members. Such designs couid be suitable for resisting accidental actions such as seismic actions (see STEP lecture C 17). In order to rnodel the joint for structuraf calculations, a joint classification can be conveniently based on tile static ductility Ds= ic,/rr, of the joint (Figure 5a).
fc)
9"11
Figure 5
Hd'li;,
a~
Joitrr mrodellitig: (o) defltritiorrs of trite parameters, (b) modei,for senriceability lirrrit smtes, ( c ) atrd ( d ) 11ro~1el.s for ~iltir~znte lit~litStntes.
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- an initiative undcr thc EU Comctt Pragrammc
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Following this ciassification (Table 3), design calculations can be achieved using the join1 models defined for the serviceability and ultimate limit stales. Joint type and loading conditions
D,
model at ultimate limit states
D, 1 3
5c
3
5c
G < D,
5d
- axially loaded nails and screws,
- glued-in bolts, - split-rings, shear-plates, - dowel-type fasteners with failure mode 1 * or loaded at a grain direction greater than 60", -
toothed-plates,
- punched ~netalplates, - dowel-type fasteners with failure mode 2:@, - nail plates, - dowel-type fasteners wit11 failure mode 3* Table 3
Cln.ss(ficntior~ofjoirirs based oft file srntic dtrcrility (:? see STEP Iecrrtre C3).
Considering the choice of joint shape, mechanical fasteners provide the designer with a wide range of possibilities. The proper selection should include strength and stiffness criteria. As an example, a tension splice joint between glued laminated members (GL7-4) is considered. Following the design rules given in the STEP lectures C3 to C9, Table 4 presents some joints able to transfer the design load equal to 51. 1 0 9 N . Number A, (10 ' r t ~ i ~ t ~ )R, ( I @ N)
Fasteners split-rings d,=100 nrrrr dowel d = 24 nttrt dowel ti = 14 r/rrrt dowel d = 9 r ~ z r l r nails d = 3,4 nlaz, I = 80 ntnl Tnbie 4
2
266
52,6
2
242 165 136
51,2
52,4 53,7
240
52.9
4 8 2 x 38
KJt,r(lo3N/trtnz)
45,G 35,6 41.5 53,3 59,9
E.mtrrple of joitrts wit11 sirttiinr load-cortyir~gcapacity (service c1as.s I ) .
The proper selection depends on the stnstural system and the loading conditions as well as the assumptions considered for the slructural analysis. In this example, the first three joints correspond to pinned joints. For die two others, attention should be given to their rotational stiffness since it can induce overloading of the fasteners. Depending on the bending efficiency of these joints (see STEP lecture Cf G), it should be considered in the structural analysis in order to clleck the design of the joint itself and the design of the members. This example exhibits also large variations in timber joint size and stiffness for the same strength level. With many smaller fasteners, the translational stiffness is increased.
Genera1 Joint design To ensure the design performance of the joints as given in EC5, the correct location of the Fasteners with respect to the end and the edge of the members is of utmost importance (Wilkinson and Rowlands, 1981). Despite this requirement, the design is not always controlIed by the load-carrying capacity of the fasteners. It may depend on the joint shape that can induce supplementary stresses in the members. The main factors are now examined. STBP/EUROFORTECI-I - itn initialivc under lhc EU Comclt Programme
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Swelling nrzd slzritzkage Emphasis has to be put on the dimensional changes of the timber cross-section that can occur with variation of moisture content. In the area restrained by the fasteners, the moisture changes cause stresses perpendicular to the grain that can induce spiitting (Figure 6a). To avoid or limit splitting, the restrained area has to be limited, When possible, the fasteners should be put together in the appropriate part of the connected members (Figure 6b). The fasteners used to hold the joint components are installed in ovalshaped holes. In other cases such as moment-resisting joints in frames, the larger restrained dimension should be Limited to one metre.
Figitre 6
.loirlt details: ( a ) splitting drce to shrirrkage, (6) correct joirtt tiritlr oval shaped iioles.
Eccerttricities In structural work, the joints and the members should be symmetrical and concentric wherever possible, especially in heavily loaded members, Nevertheless, eccentricities can result from several causes (Figure 7): -
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the type of fasteners used, the installation of the designed joint, the layout of the stn~cturalsystem.
Figlire7
Eccerr~ricities in ttle strtlctittas dire to rite fasteners ( a ) or the trzenrbers ( c ) arrd r~lodificdinstallations to ni~oideccentricities (b),(4.
For eccentric timber fasteners such as connectors, the influence of the secondary transverse moment is included in the calibration of the design strength. The installation of the required washers counteracts this type of eccentricity. STEPfEUROFORTECH - an initiative under the EU Comett Programme
Often, the eccentricities can be avoided by providing a proper layout of the fasteners and members as shown in Figure 7b and 7d. Otherwise, the design has to consider the secondary forces (moment, shear and tension) jnduced on the fasteners and the members.
Group nctiolz When using a closely packed fastener pattern or many fasteners in line, the loadcarrying capacity of the joint may be controlled by the tearing strength of the member (Figure 8). This block shear failure for a group of fasteners involves shear along one plane and tension on a perpendjcular plane.
Figrire 8
Block sitear failure itr joitrt: ( a ) rnisiot~faillire of flre fret area S , , (6) sltenr failnre of tile net area S,
The failure mode is sequential with a fracture on one of the resisting areas, S, Followed by yielding and failure on the area perpendicular to the fracture plane. For a brittle lnateriai such as timber, the strengths on both planes must not be added. Tf~en,the strength of the member is checked considering the net section S, in tension or S, in shear and the design strength of the material. The design biock shear strength corresponds to the larger value.
Coinbilzatiort of fasteners For the transfer of a given force, the design of joint with a combination of various fasteners can sometimes be achieved especially in trussed structures. To avoid overloading caused by large stiffness differences or by oversized holes, gluing or bolts shall not be combined with other mechanical fasteners.
Figrcre 9
.Ioi~rfntncle utitli a cot~r6irratior1 of fasterzers:
IT,,
do~r~els arld
11,
nails.
Conservativeiy, the design 01.' a joint is made with the assulnption of an elastic behaviour of the fasteners. The distribution of the design load F,, is based on the slip ~nodulusof ihe fasteners, For lateral load on two types of fastener (see Figure 9), equilibrium condition and compatibility of deformation are expressed as follows:
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Clf9
with K,,,, and K,,*,, the slip modulus at ultimate limit state for fasteners A and B. The ultimate design load f;,, and F,,, on a fastener is :
Otllet-j;?cto,s Another chatlenge for the designer is to fulfill the fire resistance specifications. At present, the trend is lo hide the joints in the members. At the same tin~e,this gives aesthetic solutions. With the design of the joints, the aim of the designer must be the limitation of stresses pe~.pendicular to the grain. This is interesting work as it requires the examination of the path of the forces i n the timber structure and the joint area. When the force acts at an angle to the grain, the joint [nust be located so as to reduce tension perpendicular to the grain. Lastly, some consideration is given to corrosion when designing connections in aggressive or exposed conditions. As a starting point, the design should avoid water being trapped in the joint area. For exposed connections, a covering provides an efficient protection from tile sun and water (see STEP lecture Al4). In severe conditions, corrosion is resisted by rustproofing of stecl coinponents or using corrosive-resistant metals. The designer should also consider the compatibility of the ~netalwith timber treatment. As example, caution should be taken for the installation of coniponents made from aluminium or steel into timber treated with preservatives containing copper.
References I-Iirashima, Y. (1990). Latcrtll resistance of timber connector joints parnllcl to grain direction. Proceeding of thc Inlcrnalional Engineering Conference, Vol. 1: 254-261, Tokyo, Jnpnn. Hilson, B.O., Whale, L.R.J. Popc, D.J. and Smith, I. (1987). Charnctcristic properties of nailecl and boltcd joints under sltort-term lnlcral load. Part 3: analysis and interpretation of cmbcdmcnt icst data in tcrms of dcnsity relatcd trends. J. institute of Wood Science 2 (1 1): 65-71. Naucrcr, J., 1-lcrzog, T, and Volz, M. (1991). Holzb;s atlas xwci. Edition franqaisc, Presses poly[cctlniqucs ct univcrsitaires romandcs, LC Mont-sur-Lausannc, S\vitzerland. Olzcton, E.C. and Baird, J.A. (1976). Timber dcsigncrs' manual. Cmn;icla publishing limited, London, United Kingdom. Smith, I , and Whale, L.R.J. (1986). Mechanical timbcr joints. TRADA, Research Rcport 18/86, I-lugllcndcn Vi~llcy,England. Witkinson, T.L. and Rowinnds, R.E. (1981). Analysis of mechanical joinls in wood. 1, of Experimental Mccl~anics 2 1 (1 1): 408-314.
STEPIEUROFORTECH
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Tension perpendicular to the grain in joints
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STEP Icc(ure c2 J. ~hlbcck,R. GBrlachier UnivcdtBt Knrlsruhe
Objectives To describe the special problem of tension stresses perpendicular to the grain in joints when the force in the joint acts at an angle to the grain and to present different design methods.
Prerequisites B2 B4 B5 C1
Tension and compression Shear and torsion Notched beams and holes in glulam beams Meclianical timber joints - General
Summary Illustrated exalnples are given of joints which tend to fail due to perpendicular-tograin tensile stresses. The failure modes are explained. EC5 provides a simple application rule for designing against these failures, but some more sophisticated design procedures based on fracture mechanics as well as on purely empirical equations are presented. Practical applications following such procedures are demonstrated by design examples.
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Introduction The load-carrying capacities of timber joints with mechanical fasteners loaded at an angle to the grain direction are normally determined by taking into account the bending resistance of the fasteners and the embedding strength of the timber. However, local stresses perpendicular to the grain may under certain conditions lead to failure at a lower load level. Some typical examples (Figure I) where tension perpendicular to the grain in joints occurs are: (a) joist hangers (steel-to-wood joints) (b) punched metal plate fastener joints (c) joints with dowels or ring and shear-plate connectors (giulam beams) (d) glued-in bolts
Figntz. I
E.tn11rples of tension perpe~tdicitlnrto the grain irz joirit.~rvifh probable c m c k propctgntio~zpath.
Tension perpendicular-to-grain stresses combined with shear and bending stresses can be estimated by means of the finite element methods. However, such calculated STEPfEUROFORTECH - an initintivc under the EU Cornet1 Programme
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stresses do not directly compare with the characteristic tensile strength determined from standard test specimens. Since the stresses in joints loaded perpendicular to grain are similar to the stresses in notched beams, similar calculation methods, for example based on fracture mechanics as adopted in EC5 for notched beams, could be used. Other methods for taking into account these stresses use empirical solutions. The perpendicular to grain design is replaced by a shear design procedure with certain Fictitious strength reductions or by assigning the load component acting perpendicuiar to the grain to an assumed effective area and comparing the resulting stresses with certain design stresses perpendicular to grain.
Reducing the risk of a tension perpendicular to the grain failure First, the factors influencing the load carrying capacity of joints loaded perpendicular to the grain are described. From these factors structural rules for reducing the risk of a tension perpendicular to the grain failure are derived. Figure 2 shows a mechanical timber joint loaded perpendicular to the grain. The force F, is acting perpendicular to the grain and is transferred to the beam by dowel-type fasteners. The fasteners are spread over a certain area.
Figlire 2
Joi~lt~ i l i t l tI; acting perpettdiarlar
to
tlte graitt (riotation).
The load-carrying capacity of this connection is influenced by the following parameters:
-
The ratio between the distance b, of the Furthest row of fasteners from the loaded beam edge and the beam depth h. Therefore, fasteners should be placed as near as possible to the unloaded beam edge to avoid tension perpendicular to the grain failures.
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Several fasteners in a row spaced along the grain direction distribute the acting force over a larger stressed area in such a way that the stresses perpendicular to the grain are considerably reduced. This advantageous influence increases with the number of rows and with large spacings.
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Increasing the depth h or the width t of the beam leads to increasing loadcarrying capacities. Attention must be paid to the fact that only a part of the width is stressed with tension perpendicular to the grain.
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Spreading the fasteners over many rows reduces the tension perpendicular to the grain stresses.
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The tension perpendicular to the grain strength of the timber depends on the actual stressed volume and consequently influences the load-carrying capacity of joints in beains with different sizes.
Design of tension perpendicular to the grain in joints Design nccol.cii~zgto EC.5 Unless a more detailed cafculation is made, for the arrangement shown in Figure 3 il shouId be shown that the following condition is satisfied:
provided that bc > 0,Sh. The symbols are defined as follows: V,
b,.
cr
is the design shear force (max(V,,,V,,,)) produced in the inember of thiclcness r by the fasteners ( V , + \rz = F sina), is the distance from the loaded edge to the furthest fastener or connector and is the angle between force I; and grain direction.
This design procedure substitutes the design perpendicular to the grain with a fictitious shear design over the residual cross section. Some important factors influencing the load-carrying capacities are, however, not taken into consideration. In the case of b, c 0,511a Inore detailed calculation is required in any case.
Desigrz based ort. frnctrir-e rttechanics The design of notched beams accordi~~g lo EC5 is based on the theory of fracture mechanics. Although tension stresses perpendicular to the grain in joints are similar to those in notched beams the design methods according to fracture mechanics have not been adopted in EC5. Nevertheless there is a proposal (Van der Put, 1990) based on fracture mechanics and supported by test results.
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for
5
3
Md
for
l (Vd 11)
Md = - > , I Vd ll
Md < 2,l Vd h
and
for
b, > 0,712
where symbols are defined as foltows: t
12, 12
M, V,
is is is is is
the thickness of the member, the distance from the loaded edge to the furthest fastener, the beam depth (in mnr), the maximum design bending moment nearest to the joint and the design shear force introduced in the member by the fasteners.
This design proposal modifies the EC5 design rules by taking into account the influence of the beam depth / I . By this means, the restriction b, > 0,5 h is omitted. Note that this design proposal based on fracture mechanics leads for deep beams (11 >> 130 ~tim)and with 0,7 h > b, > 0,5 h to substantially lower design values than EC5. On the other hand there is a discontinuous point at b,. = 0,7 11. For infinitesimally small changes of / I , there is a "design jump".
Design based on rxperiitzetztnl and flleol.etical irtvesrigarion.s Based on test results and their concl~rsions(Ehlbeck el al., 1989), design for tension perpendicular to the grain in joints can be carried out by checking that the Following condition is satisfied:
This equation was derived for. a characteristic perpendicular-to-grain strength related to a voiume of 0,071 m! Since EC5 now relates to a reference volume of 0,01 I?? Equation (5) should be tnodiFied by a factor (0,Ol nt3/0,02 rrr"0a3 = 0,87. Thus, Equation ( 5 ) should read:
The factor q makes allowance for the fact that only part of the load F,,,,, causes tensile stresses, some of it also causing compressive stresses perpendicular to the grain.
The factor k, allows for the fact that the load F,,,, is distributed over several rows of fasteners so that only a reduced portion of tensile stresses is acting in the Line of the furthest row of fasteners:
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The effective area A,,represents a fictitious area, because the perpendicular-to-grain stresses are unevenly distributed along the length, 1, of the row of fasteners and, in addition, also stresses the timber for a certain distance beyond both ends of the row. It can be roughly assumed that
with
The effective thickness, t,/,can approximately be assumed as the sum of the depths of penetration, 1, of the fasteners (Figure 2). (1 1) ttj = El r: t For nails and screws I should not be assumed to be greater than 12 d If two groups of fasteners are positioned near to each other with a centroidal distance of 1, the effective area increases by the factor
In cases where the joint is near to the beam end, it should be realized that the load or the stresses cannot distribule unchecked. If the distance of the joint from the beam end is less than the beam depth itself, only half the effective length should be taken into account.
Examples Design of a joint with force acting perpendicular to the grain. Joint with dowels acting perpendicular to the grain of a glulam beam with a cross section of r x h, 100 x 600 r?t17r (Figure 4) Service class 1: k,,, = 0,8 Strength class GL 28 according to prEN I 194 "Timber structures - Glued laminated timber - Strength classes and determination of characteristic values." fi~,~,k = 3.0 N/lnm2 A:jox,k = 0,45 N/1?1t7? Design values: .f;,,.d
= 1,85 N / r n m y f , , , , , d
= 0,28 Nhnnt'
Design load-carrying capacity per shear plane per dowel: R,! = 8,15 kN Design load-carrying capacity of the joint. R,,,oi, = 2 . 12 . 8,15 = 196 k N
Design of tension pet~endicrrlarto grain in joirtts accol-ding to EC5:
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Figlire 4
Joirrt witlr dowels.
Desiglz based on fractlrre niechalzics: Assumption:
Design based on experinzetztal invesfigatio~w:
t4 = El
2 t =
AU = l,,ej teI
=
100 rttm 28300 ?tznzZ
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Discussion of the design results In Ehlbeck, Gorlacher and Werner (1989) some test results wit11 dowelled joints in glulaln beams under heavy loads perpendicular to the grain are presented. One of these test specimens corresponds to the design example shown in Figure 4. The short term load-carrying capacity of this joint was 110 kN. Assuming the same k,,:,a, value and safety factor as used in the design example the comparable test value is 1 10 . 0,8 1 1,3 = 67,7 W .Assuming a 5-percentile of 0,6 to 0,8 times the single test value the design values is about 41 to 54 kN. The EC5 design method in many cases seems to be on the unsafe side, whereas the two other design metl~odslead to more realistic values. In a future version of EC5 one of the more precise methods is likeley to be included.
Concluding summary
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Joints may fail under certain conditions due to perpendicular to the grain stresses.
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In order to reduce this risk of failure the fasteners should be placed as near as possible to the unloaded edge.
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Spreading the fasteners over a certain area reduces the tension perpendicular to the grain stresses and increase the safety.
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The EC5 design of joints with Ioads acting perpendicular to grain is very simple but does not take into consideration some important factors influencing the load-carrying capacities. Tesl results indicate that the design according to EC5 may lead to unsafe design situations.
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Some more sophisticated design rules do exist and should be used in cases where 0,7 h > be > 0,511.
References Ehlbeck, J., GGrlacller, R., Werner, H. (1989). Delerminnlion of perpendicular-to-grain tensile siresses in joinls wich dowel-type-fasteners. Proc. of the CIB W I8 Meeting. Berlin, Germany, Paper 22-7-2. Van dcr Put, T. A. C. M. (1990). Tension perpendicular lo rhc grain dlc ClB W 18 Meeting, Lisbon, Portugal, Paper 23- 10-1.
;II
norches snd joints. Proc. of
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Joints with dowel-type fasteners Theory STEP lecture C3
Objectives
B.O. Hilson University of Brigklon
To define embedding strength and to demonstrate how it is measured. To develop the ultimate load equations for laterally loaded joints with dowel-type fasteners and to show how they may be represented graphically.
Prerequisite C1
Mechanical timber joints
- General
Summary Embedding strength is defined and the parameters to be controlled in the design of embedment test apparatus are described. Johansen's equations for the ultimate strength of timber-to-timber joints, and steel-to-limber joints, are developed. Graphical representations of the timber-to-timber equations based on Moller are shown.
Introduction Laterally loaded joints with dowel-type fasteners are illustrated in Figure I . Typical dowels that might be used include nails, staples, screws and bolts.
Figtire I
Laterally loarfcd joirlts rcjith do,vcl-type fasfertars. ( a ) Dowels irr si~rglc sirem (i.e. orrc sirear plorte per c/olvel), (17) Dorclels ill cio~lblesllcnr (i.c. trvo slrear. plotres per rlo~vel).
In the past the working load design values for these types of joint have been determined from the results of short-duration tests on relatively small numbers of replicate joints. One approact? made estimates of lower percentile values, eg lower first percentile, assuming a normal distribution, and these were then divided by a Factor to account for safety and workmansi~ipand to reduce the strength to an equivalent long-duration load value. The data available from the above tests are generally insufficient to enable reliable estimates to be made of the characteristic strengths required for EC5. To obtain the data by mass testing would have been prohibitive because of the inany combinations that are possible in practice. Conseqtrently, techniques have been developed which enable characteristic values to be predicted froin material properties and joint geometry. STEPfEUROFORTECI-I- an initiative under the EU Comctt Programme
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The equations used in EC5: Part I-! are based upon a theory first developed by Johailsen (1949). The equations predict the ultimate strength of a dowel-type joint due to either a bearing failure of the joint members or the simultaneous development of a bearing failure of the joint members and plastic hinge formation in the fastener. The precise mode of failure is determined by the joint geometry and the material properties namely the fastener yield molnent and the embedding strengths of the timber or wood-based materials. Many researchers have carried out tests to validate Johansen's equations including MolIer (1951), Aune and Patton-Mallory (1986), Hilson et al. (1990) and in every case, provided the effects of friction between inembers and axial force development have been minimised, good agreement has been found between experiment and theory.
Material properties The embedding strength of tirnber, or of a wood-based material, is defined as the ultimate stress obtained from a special type of joint test called an embedment test. A typical test arrangement is illustrated in Figure 2.
,*...,, . l L " , , * O i i r ~ . P *.. Ciiif
tF Figure 2
T~picalem6edrrieni rest c~rrat~go~re~ri, A - s1~ecirtler1,B rigidly clattlpi~~g favtener.
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steel side plates
Bending deformation of the dowel must be minimised and this can be achieved by clamping the ends of the dowel in the steel side plates and by limiting the thickness of the test specimen typically to twice the dowel diameter.
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A typical load-embedment characteristic is shown in Figure 3 and the embedding strength is defined as the maximum load, or the load at a specified limiting deformation, divided by the projected area of the dowel in the specimen i.e C
where t is the thickness of the test specimen and d is the dowel diameter.
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The embedment, r r , is the movement of the dowel relative to the specimen, i.e. of BB relative to A in Figure 2. Further guidance on the determination of embedding strength is given in EN 383 "Determination of embedding strength and foundation values for dowel type fasteners" and suitable apparatuses for measuring embedding strength are described by Rodd et al. (1 987). Even in the most carefully designed apparatus some slight movements, in addition to the embedment of the dowel in the specimen, will occur. The characteristics of the apparatus should be measured, therefore, by carrying out a test with a rigid, (e.g. steel), central member and a tightly fitting dowet of the same diameter and surface condition as those under investigation. This characteristic should then be deducted from the normal test characteristics to obtain the true load-embedment characteristics. Procedures for measuring the yield moment of nails are set out in EN 409 "Determination of the yield moment for dowel-type fasteners - nails". E C ~ Part : 1-1: 6.2
Johansen's equations. Fasteners In single shear In deriving Johansens's ultimate load equations it is assumed that both the fastener and the timber are ideal rigid-plastic materials, e.g. the load-embedment characteristic for the timber is as shown in Figure 4. This approximation simplifies the analysis and makes little difference to the final result.
The following notation is used: t , and t2 are the timber thicknesses or fastener penetrations,
is the characteristic embedding strength corresponding to t,. .f,,,, is the characteristic embedding strength corresponding to tz, j'j,*,,
p =fh ad where 9
* k f Y
is the design value of embedding strength, nr rl is the diameter of fastener, M,,, is the characteristic yield moment for fastener, fh,l,d
- M YF
=
is the design value of fastener yield moment and
R,, is the design resistance per shear plane. The numbering of the failure modes used in the following derivations follows that used by Johansen. STEPIEUROFORTECH - an initiative under the EU Comett Programme
C313
R,, = fit.1,$ 11f' R, = fil;?,l~ f2 d R,, = 13 fh.I,
From Figure 5 From Figure 6 Rd
I
I
Rd
Rd
Figure 5
Mode l b failure it1
Figure 7
Mode la failitre.
Figure 6
tl.
Mode l b failure irt
Rd
b1 Equating and putting b, = P gives :
STEPIEUROFORTECH -
~ J Iinitiative
under the
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tz.
Substitution gives:
Solving for b, gives:
,f!flk61.;
,I. I ,,, 62 f2f2,.
b ~ , ~
t
t
R'I
Figure 8
R,l
Mode 2cr failure.
Figlire 9
Mode Zbfailiirc.
At kin,, shear = 0
Substituting f;,,,,d = Pfh,l,d and
t1 - bl gives: =-
2
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and K,,= A,,),tr
Failure rnode 2b As before b , =
{fiortl
Figure 9)
P b2
- b2 gives : 2
Substituting b1= P 4 and a2 =
*z
Fclilure Mocfe 3 worn Figrtre 10)
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Figirre 10
Mode 3 failitre.
Johansen's equations may also be derived using the Virtual Work approach (Aune and Patton-Mailory, 1986).
Additional resistance As the fastener deforms under load axial forces can develop for failure modes 2 and 3. These are caused by friction between the fastener and the timber and also by the constraints produced by the heads of nails and the washer assemblies in bolts. The force in the inclined part of the fastener will have a component parallel to the applied load and wilt, therefore, enhance the resistance. EC5 talces this effect into account by enhancing the resistance for inodes 2 and 3 failures by I0 per cent. In an actual joint the load carrying capacity will correspond ro the lowest value obtained for Rd by substituting into the full set of equations. The equation giving the lowest capacity will also identify the failure mode.
Moller charts Moller (1951) represented tile Johansen equations for single shear, in cases for which f3 = 1, by a graphical representation. In this lecture the Moller chart has been modified to incorporate the 10% enhancement for modes 2 and 3 failures and is shown in Figure 11. It should be noted that in this chart t, is the larger thickness or embedded length. Similar charts may be produced for other values
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t2
of
p. By calculating the two dimensionless parameters t1 and
a point
may be found on the chart, the appropriate failure mode identified'and hence the
appropriate equation chosen.
J",t,d
fir, d Fklrm 11
M ~ d g e dMLiller c l r ~ r t-
Moci#ed Muller ~ / t a r-l double sltear (P = I).
Figiirg 12
sitzglc slrear {P = I).
Johansens's equations. Fasteners in double shear Using the same basic approach, Johansen equations for fasteners in double shear may be developed. The resulting equations are as follow^: Rd = .haI ,d f t ~1
Mode I b (Figure 5)
R,, = 0,s j;,,r,,, 12, d p
Mode I b (Figure 6)
(8)
(9) i
R ~ .2 + @
[ ~ l Mode 2l (Figure ( 8 or 9) (10) l &,f,ddtl
Mode 3 (Figure 10)
( 1 1)
The Figure number refers to the diagram showing half of the corresponding symmetrical double shear joint. In these equations t, is the central member thickness and t, the thickness of an outer timber or the penetration in an outer timber whichever is the smaller. In each case R, represents the resistance of one shear plane so the resistance of the whole joint is normally 2R,. The equations apply to symmetrical double shear joints - other geometries may be analysed using the same principles. Again to allow for axial force effects the modes 2 and 3 values may be enhanced by 10%. A modified Moller chart incorporating the enhancement is shown in Figure 12. STEP/EUROFORTECH - an initintivc under the EU Comelt Programme
Johansen's equations for steel-to-timber joints In steel-to-timber joints, provided the steel plate is thick enough, then for modes 2 and 3 failures the plastic hinges will move to the interface between she steel and the timber and different lohansen equations may be developed. A steel plate thickness at. least equal to the fastener diameter is normally assumed sufficient for this approach to apply. Using the above assumption, the following equations {nay be derived:
Figrcre 13
Mode 2 failtire steel plate.
- tlrick
Figure 14
Mode 3 Failrfrc - thick steel plate.
Thick steel plates - Mocie 2 From Figure 13
t1 - bl gives : substituting a, = 2
Tizick sreel plates - Mode 3 From Figure 14
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Tlzick steel plates
- Mode ib
Again for modes 2 and 3 a 10% increase is suggested in EC5 to allow for axial force effects.
Tlzi~asteel plates For thin steel plates the plate will be unable to provide the rotational resistance to develop a plastic hinge in the fastener and so the EC5 equations have been developed assuming no moment of resistance at the interface.
EC5 defines a thin steel plate as one having a thickness equal to, or less than, haif the dowel diameter. Using the above assumption the following equations may be derived:
Figurr I5
kIode / a failure sreel plate.
I~I~II
Thitz steel plates - Mode l a Froill Figure 15 moment at interface = 0
Figtire 16
Mode 2 .faillire - tilitr steel plarc.
l l z i r z steel plates - Mocle 2 From Figure 16 moment at interface = 0
Allowing 10% increase for axial force effects gives
Note: Double shenr joint
-
Centre nrembet. of t?~i?tsteel The same equations apply as for thick steel plates since the symrnelry of the joint enables a plastic hinge to form in the steel plate, provided the plate is strong enough to resist the applied forces. For steeI plate thicknesses between 0,Sd and d EC5 suggests that resistances should be determined by linear interpolation between thick and thin plate values.
Referellces Aunc, P. and Patton-Mallory, M. (f986). Lateral lond-bearing capacity of nailed joinls based on [lie yield tllcory - Theoretical development and experimental vcrification. US Department of Agriculture, Forest Products Laboratory, Rescnrcli Papers WL 469 cP: 470. Hilson, B.O.. Whnlc, L.R.J. and Smith, 1. (1990). Cl~aractcristicpropcrties of nailed and bolted joints under shori-term lateral load. Part 5 - Appraisal oT current design data in BS5268:Paa 2:1984 Structural Use of Timber. J. Inst. Wood Sci. 1 i(6) 208-212. Johansen, K.W.(1949). Theory of Limber connections. lnlemational Association of Bridgc and Structural Engineering. Publication No. 9:249-262. Bern Mijlier, T. (1951). En ny metod fijr berlkning av spiki'ijrband. Report No 117, Chalmers University of Technology, Sweden Rodd, P.D.,Anderson, C., Whale, L.R.J. and Smith, I. (1987). Characleristic propcrties or nailed and boltcd joints under short term lateral load. Pan 2 - Embedment test apparatus for \\rood and wood-based sheet materials. 3. Inst. Wood Sci. I I(?): 60-64,
-
STEP/EUROFORTECII an initiative under the EU Comctt Programnne
Nailed joints I STEP ~ecturcCJ B.O. I-li~son University of Briglrton
Objectives To describe the different types of nail arid present typical exa~iiplesof their use. To present empirical equations for the predictio1-1 of etnbedding strength in e n t nails. To introduce nail spacing requirements and timber and yield ~ i i o ~ r ~ for to give an example of a timber-to-timber nailed joint design. To dernonstrale the effects of pre-drilfing and slip.
Prerequisites C3
Joints witli dowel-type fasteners - Theo~y
Summary Val-ious types of nail are described includirig sn-looth wire (round asid square sections), annular ringed shanli, helically threaded ant1 square twisted nails. The advantages of the different forms are discussed. The etnpirical equations for embedding strength and yield moments are quoted and a brief description of their origins and limitations presented. The need to control spacing is described and EC5 recommendations are given. The advantages and disadvantages of pre-dl-illing are discussed. The i~nportance of slip is stressed and an example of the design of a nailed tiruber-to-timber joint is presented.
Types of nail Nails are the most commonly used fasteners in timber construction and are available in a variety of lengths, cross-sectional areas and s~rrfacetreatments. The most conlmon type of nail is the s~noothsteel wire nail which has a circi~lar cross-section i d is cut from wire coil having a ~ninilnu~n tensile strength of 600 N / I ~ I IIt~ is I ~ available . in rt standard range of diameters up to a maximum of S rllrlt and can be plain or treated against corrosion, for example, by gnlvanising. The head of the nail is most com~nonlyforged into n flat circle of approximalely twice the dia~neterof the shaft but sonie nails are available with s~uallerheads to enable these to be driven flush witli the timber surface. 'In some cou~itriesnails are produced with a square cross-section and t11ese are
used in the same applications as the smooth round nails described above. The performance of a nail, both when under lateral load and under withdrawal loading, may be enhanced by modifying the surface of the nail. One approacli is to deform the s~rrfaceof a smooth round nail by cutting annular threading or helical threading onto tlie shank of the nail. Another Lakes nails with a square cross-section and twists them into a helical pattern. This process not only modifics the nail surface but also work hardens the steel thus raising the yield strength. Galvanising, chemical etching, coating with cernent and coating with plastic are other ways in which tlie performance of a nail [nay be enhanced.
Nails may be driven by hand or by pneumatically operated portable machities. In the latter case cartridges of special nails, such as T-nails and nails with a segment of the head cut off, are used to enable them to be assembled in groups.
-
Pre-drilling
-
When nails are driven into dense timbers there is a danger that excessive splitting will occur. This can be combatted by blunting the pointed end of the nail so that it cuts through the timber fibres rather than separating them but a more reliable approach is to pre-drill the timber. In this latter case the nails are driven into pre-drilled holes normally having a diameter not greater than 80% of the nail diarneier.
-
Pre-drilling produces three main advantages:
-
-
-
the laterai load-carrying capacity of the nail is increased; the spacings between nails and the distances between the nails and the end and edge of the timber may be reduced tlius producing more cornpact joints and less slip occurs in the joints.
On the other hand, pre-driiling is labo~uintensive and, therefore, expensive and
the net cross-sectional area of the member is reduced. Consequently, it is normally only used wlien the characteristic density of the timber is 500 kghz3 or Itlore.
Embedding strength EC5 recommends the following values for the characteristic embedding strength for nails up to 8 N ~ I I Iin diarneter driven into timber and they apply for all angles of load to grain direction. Without predrilled holes
&,,
= 0,082 p,
d
iV/mrtt2
With predrilled holes
A,, = 0,082 ( 1 - 0,O1d )p, Nl ntm where p, is the characteristic density in k g h i 3 and d the nail diameter in
irir?i.
No increase in embedding strengtil is currently recommended far annular ringed shank nails, helically threaded nails and other nails with modified surfaces. This is due to a lack of einbedment test data For these types of nails. The equations for characteristic embedding strength have been determined by carrying out a large number of embedment tests covering a range of timber densities, timber species and nail diameters. An illustration of the type of analysis that was used to produce Equations (1) and (2) is presented by Whale et a!. (1989).
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STEPIEUROFORTECI-I an initintivc undcr thc EU Comcu Prograrnmc
Yield moment EC5 only presents guidance for the characteristic yield moment for cosnmon smooth steel wire nails made from a wire having a minimum tensile strength of 600 N/lmn2. For round nails it proposes,
and for square nails,
For round nails d is the diameter in tnrlt and for square nails the side dimension in ITlUl. Other types of nail would have to be tested in accordance with EN 409 "Determination of the yield inonlent for dowel type fasteners - Nails" to determine suitable values for M,,.
Nail spacing Nails must be spaced at suitable distances from each other, and fron-i the ends and e d g s of pieces of timber, in order to avoid ~lnduesplitting. The var-jous distances involved are shown in Figure I .
I I
r
e I
Nail spacirrgs arrd dislnrzces. a, GI,
n, a,
spncbtg palallel to the gmitt spaci~~g perper~rlic~rlalto the gmilr et~cidistnricc ecige dis~ance
Tlie end distance is said to be loaded when the load on the nail has a component towards the end of the Limber. Otherwise it is referred lo as an unloaded end distance. Loaded end distances need to be greater than unloaded ones. In a similar way the edge distance may be loaded or unloaded. The i~lostsuitable vnlues for spacings and distances will vary from species to species depending principally upon the cleavage and shearing strength of the tiinber, the timber density and the nail diameter. Pre-drilling reduces the splitting tendency considerably and hence allows much closer spacing of the nails as described earlier. The spacings and distances recoin~nencfed by EC5, and based on years of experience are presented in Table 1.
STEPIEUROFORTECI-I- i ~ iniliativc n uncicr thc EU Conlett Progr:lmmc
c4/3
Distrunce
Spacing parallel Spncirig perpendicular Loadecl end
Unloaded end Loaded edge Urlloaded edge TctOle I
No Pre-drilling 420 < p, < 500 kghzr' p, 2 420 kg/rrri d < 5 tnrrr: l(kl 15d rl 2 5 nlnl: 1L)d
Pre-drilled
(4+3 1 cosa ( jd
5cl ( I O-t-5co.~a)d
5d
(3+ 1 sirla ( )d
(15+5co.sa)cl
(7-1-5cosot)d
1Ocl (5+5.sir10()cI
lSd (7+5silra)d
7d (3+4siila)c/
7d
3d
5d
Sjmcirrg.~nrrd clistances J I rrcril.s, ~ d = r~ailclicrnreter ir~irrnl, jorrc to grcritr directiorl.
a = arrglc c!J
Naif slip Nailed joints, in comnlon with joints nlade with rill other types of nicchanical fi~stener,slip under loacl. This is illusrrnted in Figure 2 which shows a typical load-slip characteristic fos a cornpression test on a three member nailed joint.
Fiigllr~2
Lnotl-slip chamcteri.stic for n ~lniledjoirit. /;I,,,!,i.s rl~ertln.rirtrrrrrt loa~l,F,,, is 111eservice load crrtcl t~,,,,,11lc irt.srar~~crrreorrs slip.
An estir~~atc of the instantaneous slip tililt will occur whet1 the service Ioad is applied may be ob~ainedfroin n knowledge of tile instantaneous slip modulus K.,,., determined from tests carried out in accordance with EN26891 "Timber structures. Joints made with mechanical fasteners. General principles for determination OF strength and clefonnation characteristics," or frotn the following reco~nme~idations in EC5. For pre - drilled situations : K,,, = For no pre - &itling :
pyd N/mrn 20
Kser= p,
do'' Nlmm 25
1,5
where p, is the characteristic timber density in kg/ir~%a~idd the nail diameter in 1)11?1.
Final slip measurements in nailed joints will be greater than the instantaneous \falues due to creep and may be estimated frorn:
-
It is essential to allow for the slip in the joints when calculating the displacement of a nailed timber structure under service load. Normal elastic theories predict the displacement of struclures from the elastic shortening or lengthening of the members in the case of trusses and from the assumption of no slip between the component parts in beams. Joint slip will add considerably to these effects and, therefore, produce much larger displacements.
The deflection of a nailed timber truss due to slip in the joints can often exceed that due to the elastic axial lnovements in the members. In nailed composite beam construction the simple theoly of bending will not apply and stresses and deflections must be calculated allowing for [he slip that will occur between, for example, the flanges and the web of a nailed I-beam. This incomplete interaction niay be assessed using a procedure described in Annex 3 EC5: 1-1. Slip also affects the momenl-rotation characteristics of joints such as nailed plywood gusset joints in some portal frame construction.
Design example. Nailed tension splice joint Specificatioil
Fig~tre3
Te~rsiotlsplice joirrt.
Timber not pre-drilled Design load (ultin~atelimit state) = 3600 N Strength class C1G S~nootkround nails 3,35 111117 diameter, 65 r,ttn long Service class I , load duration class medium tern?: k,,,,,,= 0 3 G,=lOOON Q,=l500N = 0,082 p,d-'g3 N/mrn2 For strength class C 16 p, = 310 kS/m3
Assur~~ing the same strength class for each component,
P= 1
STEPIEUROFORTECI-I- an initiative i~ndcrtllc EU Comeu Programme
Nails in sirzgle shear (a)
Man iral ap~~ronch
Clleclc all equations for ~ninimumvalue of R,,
Mode 1 b
R,
=& ,,, t,d = 10,9-35-3,35 =
1278 N
= pointside penetration
I2
= nail length - headside timber thiclcness = 65 - 35 = 30
minimum
R,
mtn
= 8cl = 26,8 tlznl
< 30 r w r l
=fir,l,dt2d p = 10y9*30*3,35.1,0= 1095 N
Mode l a
Mode 2a
Mode 2b
STEP/EUROFORTECIi - an initiative undcr tile EU Comctt Programme
Mode 3
Minimum value = 494 N Mode l a failure
( b ) Completer- approach The set of design equations can be written into a computer program with j;,,,,,,, I,, t,, d, p and M,,,,as input parameters. (cJ Moiler- char-t ~ppronclr If MoIler cllarts are available, in tIiis case for = I , then the mode of failure may be identified quickly and only one equation needs to be used.
P
In this exan~pler, = 35 rtil?~and t , = 30 dimension for the Mtiller chart.
mln
since
r, has to be the larger
From Figure 1 1 in STEP Lecture C3 the failure mode is identified as mode la. Number of nails =
Design load
Design resistance per nail
- -3600
= 7,3 each side
494
Adopt eight nails each side for symmetry as shown in Figure 4. The nails will overlap in the centre member and this is perntitted by EC5 provided that the thickness of' tile central member less tile pointside penetration is greater than 4cl. In this exarnple 47 30 = 17 itrrtr and 4d = 4 3,35 = 13,4 t11t11 17 tu11t > 13,4 tlirli acceptable
-
-
Spacii7gs p, = 310 kg/,n! No pre-drilling. a = 0" From Table 1 : Spacing parallel Spacing perpendicular Loaded end distance Unloaded edge distance
= 10d
= 5d = 15d = 5d
= 3 3 3 171111 = 16,s ~nnz = 50,3 t i ~ i i z = 16,8 rnn~
An acceptable arrangement is shown in Figure 4.
STENEUROFORTECI'I - ;in initiative under r l ~ eEU Comett Programme
F i r4
Acccprobie nailing patfern.
Total length of each splice plate
= 2 (60+35+60)= 3 10 rnrn
No reduction in the cross-sectional area of each member is assumed since the nail diameter is not greater than 6 nrrti and the nails are driven without predrilling.
Slip For no pre-drilling
Design load (serviceability limit state) = 3-500 N load per nail 312 5 instanteous slip per nail = 2 = 0,54 mm 574
All nails are assus~~ed to slip by the same artlount and so each central member
will move 0,54 nrru relative to the cover plates so that the abutting faces of the central inembers will draw spat by 2 - 054 r?tr?t = 1,08 nun.
Final joint opening = 2
*
0,76 = 1,52 rurtl
Reference Whnlc, L.R.J., Smith, 1. and Hilson, 8.0. (1989). Characteristic propertics of nnilcd and bollcd joints under sliort term lareral loiicl. Part 4 - Thc influence of resling mode and filslcncr diameter ilpon embcdrncnr tcsr data. J. Insc. Wood Sci. 1l(5): 156-161.
STEP/EUROFORTECI-I - an initiative iincier tlic EU Comctt Programme
Nailed joints I1 STEP I C C ~ U ~cs C B.O. I-lilson University of Brighton
Objectives To present an example of a laterally loaded, nailed panes-lo-timber joint design. To discuss the use of axially loaded nails.
Prerequisite C4
Nailed joints I
Summary The empirical equation for the embedding strength for plywood is given and the scope for the introduction of new panel products wit11 the adoption of Joha~~sen's theory is emphasised. An example of the design of a laterally loaded, nailed, panel-to-timber joint is presented. The use of axially loaded nails is discussed and the factors to be considered are presented together with a design example.
Nailed panel-to-timber joints I~zfroc~ztction Joliansen's equations are generally applicable for m y combination of woodbased materials provided the appropriate material properties are known. Equations for the cf~aracteristicembedding strengtlls for some panels have been developed experimetltally by carrying out a large number of embedment tests. For example, for plywood:
where p, is the cl~aracteristicdensity in kg/i7r3and 6 tile nail diameter in ntm. One of the main reasons for adopting Johmsen's equations for joints in EC5 is that new materials, in particular panel products and new dowel-type fasteners, may easily be accolnmodated by developing tlle appropriale empirical equalions for cl~aracteristicembedding strength and characteristic yield momer~t. Also Johrtnsen rype equations may be developed for any combination of materials using the approach described in STEP lecture C3.
Nuil spncii~g For panel-to-timber joints and for steel-to-timber joints closer spacings may be adopted than those recoinmended for timber-to-timber joints (see S'IEP lecture C4). This is because there is generully less tendency for the panel product to split on nailing and the nails are normally used in single shear so that they do not fully penetrate the solid timber member thus reducing tile splitting tendency in that member. These effects have been confirmed by nailing tests.
EC5 recommends, for plywood-to-timber joints, that the nail spacings recommer.~dedfor timber-to-timber joints tnay be reduced by snultiplying the tabulated values by 0,85 but the minimum values in the plywood for an unloaded end or edge distance should be 36 and for a loaded end or edge distance (314sin a) (1. STEREUROFORTECIi - an initiative under l l i c EU C o m c t l Progntmrnc
C5/ 1
Similar moditications are suggested recommended multiplier is U,7.
for steel-to-timber joints but
Design example. Plywood-to-timber tension splice joint Spec$icatiotl
Characteristic density of plywood = 640 kg/rn3 Minimum thickness of 18 nzt11 nominal plywood = 17,l t r i ~ i Timber not pre-drilled Timber strength class C22, p, = 340 kS/ui3 Smooth round nails 3,35 rnm diameter 50 t t t t ? ~long Design load (ultimate limit state) = 7200 N Service class 2, load duration class medium term: k,,,,, = 0,80 G, = 2000 N = 3000 N
k"I0d
&,k
h,d = ---Y hi
Plywood Timber
=
=
0,80 1,3
'4970
= 30,2 N / ~ ~ , ~ "
0y80.19,4 = l l , g ~ / r r t s l ~ 1,3
A,, pointside -- A,, timber =
headside
f,,, plywood
l1Y9 = 0,39 -302
Nails in single shear Check all equations for minitnuln value of R,,
the
Mode I b Rd = A,,,,,,1 , (1 I?
= 30,2
-
17,1
- 3,35
= 1730 N
= pointside penetration = nail length - headside ~hickness = 50 - 17,1 = 32,9 IIIIII > ~ninirnu~n = 8d = 26,8 rnr?t
Mode l a
Mode 2a
Mode 2b
Mode 3
Minin~uinvalue = 597 N
Number of nails
=
Mode I n failure
7200 - 12,06 each side, 597
say 12 each side
Check nail overlap in cenlrnl ~nen~ber: 47 - 32,9 = 14,l
irtrlt
STEPIEUROFORTEC1-1- an initiative under ~ h cEU Cornell Programme
> 40 = 13,4 1711ll
C5/3
Spcicii~gs
p, = 340
k,S/r,lf,
no pre-drilling, a = 0"
Spacing parallel Spacing perpendicular Loaded end distance Unloaded edge distance
= 0,85 - IOcl = 0,85 - Sd = 0 3 5 - 15cl = 0 3 5 - Scf
In plywood, unloaded edge not less than 3d loaded end not less than 7cl
= 28,5 11rrll = 14,2 ~ I Z I T I
= 42,7 rlittr = 14,2 I I I I I Z = I0,l
I~~IIJ
= 23,5 ttlru
No reduction in cross-sectional area is assumed
5000 Design load per nail (serviceability limit state) = 12 417 Instantaneous slip per nail = - = 0,4 nirrt 1058
=
417 N
Opening of joint = 3 - 0,4 = 0,s rnnt
Final joint opening = 1,20 nu~r
Axially-loaded nails Smooth steel wire nails are relatively weak when loaded axially and, therefore, EC5 recom~nendsthat they should not be used for permanent and long-term axial loads. The best resistance is obtained when tile nails are driven into side STEPIEUROFORTECH - an initiative under lhe EU Comctt P r a g r i ~ m n ~ c
grain. Nails driven into end grain are norn-ially assumed to Iiave negligible axial load capacity. Changes in the ]noislure content of the timber will also reduce the axial load capacity of smooth nails. Other fdctors which affect the resistance that nails can offer to axial withdrawal loads include the density of the timber into which the nail is driven and the surface condition of the nail. Consequently, cement-coated nails, annular and helically threaded nails and square twisted nails all perform better under axial loads than smooth nails. Another advantage of annular and helically threaded naiis is tllat their resistance to withdrawal is little affected by changes in the moisture content of the timber (see EC5: 1-1 For further guidance).
Figitre 3
Perpendicrrlai. trailing.
There are two ways in which the nailed joint shown in Figure 3 is likely to fail (ignoring tensile failure of the nail itself): (a) (b)
withdrawal of the nail froin the member receiving the point, and the nail head being pulled through the sheet material.
Empirical equations for resistance have been developed for a number of combinations. For smooth nails the resistance is given by the lower of the following values: For pointside withdrawal For head pull-through Wirere
R , = A,, (1 l R,, = i,,,, G! 11 + f2,d
d is the nail diameter, nrtn h is the thickness of headside timber, rltrlz 4 is the pointside penetration, mni f,,, is the design strength for member receiving point A,, is the design strength for lieadside inember
EC5 suggests the following equations for cl~aracteristicstrengths: f,*,= (18
-
10'" pp,'-Nhnrti" and A,, = (300 - 10'" pp,"N/lnat2 where p, is in li6hn3. When the head diameter of a smooth nail is at least twice the diameter of he nail shank then it may be assumed that the head pull-through mode of failure cannot occur. STEPIEUROFORTECI-i- an initialivc under lhc EU Cornell Programme
c5/5
The pointside penetration, 4, should not be less than 12d.
Design example. Axially loaded naiis Specification
Figure 4 shows 12 ~ t i r l lthick plywood cladding nailed to timber studs acted upon by a wind generated suction force Q,,
Q,,= 750 N per metre of height Charncteris6c density of plywood = 550 kghti" Timber strength class C16, not pre-drilled Smooth round nails 3,00 fnm diameter, 50 rl~rrrlong Service class 3 Find the necessary spacing For the nails. For strength class C16, p, = 3 10 lig/rrt3 =I8 -310' =1,73Nh7zt?12 S?, = 300 - LO'' - 550' = 90,75 N/tr1tn2 For service class 3 and short-term load duration
f,, = 0,7*&73 = 0,93N/rntn2
43
Pointside withdrawal resistance f,.J@ = 0,93 - 3,00 - (SO - 12) = f 06 N For head pull-through (assutning liead diameter < 2d) 12,OO + 48,8 = .f,,, d h + j;,, d' = 0,93 - 3,00 A,
-
- 3,00' = 473 N
Pointside withdrawal critical
Nail spacing required
=
106
- .I000 750
=
141 m m
Provide 3,00 x 50 mni nails at 140 mm centres. STEP/EUROFORTECl-I- an initi~aivcundcr thc EU Cornctt Programrnc
Bolted and dowelled joints I STEP lccturc C6
Objectives
J. Ehlbeck, 1-1. Werner
To describe ultimate limit state design procedures for bolted and dowelled joints including rules for spacings. To present empirical equations for the prediction of embedding strengths and fastener yield moments. To show briefly some possibilities for improving the performance of these joints.
Univcrsit%t Karlsruhc
Prerequisites C2 Tension perpendicular to the grain in joints C15 Multiple fastener joints
Summary Design rules for ultimate limit stare design for various types of bolted and dowelled joints are evaluated. The rules for spacings, end and edge distances are explairled and the influence of load-to-grain angle is commented upon. Empirical equations for the embedding strengths of' the members and the fastener yield moments are given. The effect of system properties (e.g. fastener surface friction) on the chatacre~.isticload-carrying capacity of the joints is described and possibilities to improve the joints' performance are presented. The load distribution between fasteners in fine is discussed.
Introduction Dowels (Figure I) are slender cylindrical rods made of steel, mainly with a smooth surface. The minimum diameter is G n t m . The tolerances on the dowel are -0,O1 +O,f ~ t l i t t and the pre-drilled holes in the timber member should have a diameter not greater than the dowel itself. The holes in steel members may be predrilled 1 ntar larger than the dowel diameter and due allowsu~cemay be made for any extra slip that may occur. Bolls (Figure I ) are dowel-type fasteners with heads and nuts. They should be tightened so that the members fit closely, and they should be re-tightened if necessary when the timber has reached equilibrium ~noisturecontent. Bolt I~oles may have a diameter not more than I 111111 larger than the bolt. If a bolt is fitted in a hole which is not greater than its shank, the design method for dowelled joints can be applied. Washers with a side lengttl or a diameter of at feast 3 d and a thickness of at leust 0,3 cl (d is t l ~ ebolt diameter) should be used under the head and nut. Washers shou1d have a full bearing area. Joints with dowels are used in timber construction to transmit high forces. This economic type of joint is easy to produce. In large dowelled connections it may be necessary to replace some dowels wilh fitted bolts in order to maintain the fonn of the joint. Dowelfed joints are stiff, compared with bolted joints. Therefore, bolted joints should not be used in construction where large deformations impair the serviceability.
Figitre I
BOO with ~r1nslrerarid (Iolo,vel.
Bolts and dowels can be used For liinber-to-timber joints, panel-to-timber joints or steel-to-timber joints.
Ultimate limit states design The doininant properties influencing the load-carlying capacities of dowel-type fasteners are
-
the embedding strength of the timber or panel members, the geometry of the joint and yield moment of the fasteners.
The embedding strength itself depends on
-
-
-
the density of the member, the diameter of the fastener, the angle between force and grain direction and the friction between fastener and timber.
The embedding strength can be assumed to increase linearly with increasing wood density. Small spacings as well as small end distances of the fasteners can cause premature failures. Therefore, splitting in timber joints should be avoided by appropriate spacings and distances. When the force acts at an angle to the grain the influence of the tensile stresses perpendicular-to-grain shall be taken into account. Design methods for this are given in STEP lecture C2.
E~nDetIdingstrmlgrlr of titnber n~zdwood-based pnrlels Tile embedding strength should generally be determined in accordance with prEN 383 "Timber structures - Test rnethods - Determination of embedding strength and foundation values For dowel type fasteners" with the evaluation of the test results following the procedures given in EC5 Annex A. This strength is defined as the average compressive stress at maximum load in a specimen of timber or woodbased panel under the action of a stiff linear fastener with the fastener's axis perpendicular to the surface of the specimen. The embedding strength depends on STEPEUROF0RTECf-I - an initiiltive under thc EU Comcll Progrnmmc
EC5:Part 1-1: 6.5.1.2 ( 1 )
the type of fastener, the manufacture of the joint and tlle wood density or the cluality of ttie wood-based materials. Tflus, the embedding strengtll is not a special material property, but a systems property. For bolts and dowels up to 30 ntrtr diameter the following characteristic embedding strength values for timber should be used:
0,082(1- 0,014 Pk witlt p, in lig/rn3 and d in nutt.
&,oak
=
fh,cr,k
=
N/IIIIII
(1
A4,o.k
kgOsin'
for softwood: for hardwood:
ct +
cos' a
lcw
=
k,
=
1,35+ 0,015d 0,90+ 0,015d
a is the angle between load and grain direction. The influence of the angle a between load and grain direction is illustrated in Figure 2.
Figrrre 2
~c5:Parri-1:6.5.1.3(2)
A,,
/ f,,,plotted agai~isfutrgle cx bet~veetl loud orld gruirr riirectiotr; ( a ) Irald~voud;( b ) sofr~i~oorl.
For wood-based products characteristic embedding strength values to be used for bolted or dowelled joints are not yet available, except for plywood. EC5 recommends for plywood the following value: fh,k = O,I l(1- 0,014 pk N / I ? Z I ? ~ ~ (5) wit11 p, in Icg/tn3 and d in 177nl. These values are applicable independent of the angle between load and Face grain direction.
Yield il?or~lerltof.fitstc?ner's The yield moment of dowel-type fasteners should generally be determined in accordance wit13 prEN 409 "Tinlber structures Test metl~ods- Determination of the yield tnoment ordo~veltype fasteners - Nails". Althougl~prEN 409 is developed for nails only, it hns been verified (Elifbeck and Werner, 1992) that rile test ~neihods given in prEN 409 can in principle also be used for bolts and dowels. For round steel bolts it11d dowels the characteristic value for the yield moment should be. calcu lated approxitnately ns
-
EC5:
klrt
1 - 1: 6.5.1.2 (2)
STEPJEUROFORTEC1.I -
i ~ ninitiative
undcr the
EU Cometi Progranlmc
C6/3
where J, is the tensile strength of the fasteners.
EC5: Rtrt 1-1: 6.5.1.2 ( 3 )
M~~lfiple - fasfet~ei'joii~t The loads in bolted and dowelled joints are non-uniformly distributed between the individual fasteners in a n~ultiplefastener joint. For more than six fasteners in line with the load direction, the load-carrying capacity of the extra fasteners should be reduced by 113, i.e. for rz fasteners the effective number rzcf is 1iCl
=6
+
2 -
3
(tl
- 6)
(7)
If the failure of the joint is not governed by splitting and if plastic deformations are possible, then the loads can be redistributed in the joint. For further information see STEP lecture CIS.
Fcrstener sl>acirtgs at id clistatices The minimum spacings as we11 as the end and edge distances for bolts and dowels are different because of the size of the washers. The minimum spaci~igsand distances for bolts are given in Table 1, those for dowels in Table 2. The spacings parallel ( a , )and perpendicular (cr,) to the grain, the end (a,) and edge (a,) distances are defined in Figure 3-5.
Figure 3
Fastetre,-q~acirlgsporullcl mrd perper~cliclrlarto grain - cief71lifiotl~.
-90.5a < 90'
Figrtra 4
Fostelrer ertd distctltlces - defini~iorrs(iefi: loacled crrd; right: ~rrrionclelecierrd).
0'5 a < 180'
Figtire 5
90"5 a c 270'
180'.1'_ a < 360'
F~rsfcrleredge c1ilistcri1ce.s- definitions (lefi: laaclcd edge; rigizt: rinloodecl edge).
STEP/EUROFORTECH - an iniliativc under thc EU Comctt Programme
a,
Parallel to the grain
(4+3 icosa ( ) d
a2
Perpendicular to llle grain
4d
a,,
- 90" 5 a < 90"
7(1 (2 SO ttml) 4rl
150' < a 2 210' 90" < a < 150' 210' c a < 270"
1
(j.i,,
1
,
0's a 2 180" all ollier values or a
(1
+- 6 1 sin a 1 ) (1
(2 -1. 2 sin a ) d 3rl
(24 4 (2 3d )
a is (lie onglc between load and grain direction ECS: Part 1- f :6.5.1.2(4)
TcibIe I
A4i1~inrtrt>l spacirrgs nrtd riistorrres for Dolls.
n,
Parallel to the grain
( 3 + 4 1 c o s ~ Ir ) d
cl2
Perpendiculnr to the grain
3rl
a,,
- 90' I a 5 90'
7d (2 80 tnni) 3d
150'5 aI210" 90' < a < 150" 2 l 0 " < crc270"
ox,
fl4.1
a,,
0'5 a 5 180" all other values ol' a
CI~.~
1 sin a 1
(2 3d)
(2 + 2 sin a ) d 3d
(2 3 d )
cx is the angle bet\veen load and grain direction ECS: Part I - I: 6.6 (2)
Mini~jjicaispncittgs N I Idisturlces ~ for-
Tubit.2
ciolor~!els.
The spacings a, may be redt~cedto a minimum of 4d. In this case the load-carrying capacity decreases due to the danger of splitting. Tl~esefore,the characterislic embedding strength J,,o.k should be reduced by tile spacing factor k,,: for bolted joints I
For dowelled joints
For plywood the spacing factor k, can be disregarded.
Lnterally looded bolts nrtd clovvels EC5: Pact 1-1: 6.2
The design load-carrying capacities for bolted and dowelled joints can be calculated using tile modified Johansen theory. This theory is described in STEP lecture C3.
EC5: Part 1-1: 2.3.3.2 and 3 The design values of the relevant lnaterial properties are calculated with the
modification factor k,,,,,,, and the values of y,, according to EC5. Because of friction between the fastener and the timber and the constraints produced by the washer assernbiy in bolted joints, the load-carrying capacities, especially for fasteners with a profiled surface, are higher. This phenomenon is called the "chain effect". After significant fastener deformation the component of the axial load in the STEPEUROFORTECH - an inikiative under the EU Corneli Programme
C615
fastener parallel to the interface of the joint tnelnbers can be added to the lateral shear load. Ttte component perpendicular to the surfaces of ihe members forces these members into tight contact and may cause additional resistance in the direction of the joint load due to the friction between the members. This clamping effect diminishes gradually because of wood relaxation and shrinltage. The increase of strength in joinls made with resin injected bolts (Rodd et a1.,1989) has the same reason. The embedment characteristics are also superior to those of plain bolts in terms of both strength and stiffness. The load-carrying capacities of a joint can substantially be increased by gluing a wood-based panel onto the members. (BlaR and Werner, 1988). In ttiat case the spacings arid distances af the fi~stenersmay be reduced. Tlie reinforcing material is able to spread highly concentrated loads uniforlnly while tile glueline transfers the load into the timber member by shear stresses. Splitting in timber joints can be avoided. Design proposals are given by Werner (1993).
Asially lurrderl bolts EC~: P~II: i-1: 6.5.2
The ter~silestrength of axially loaded bolts shall be checked in accordance wit11 EC3: Part 1.1 "Design of steel structures - general rules and r ~ ~ l for e s buildings". The wasl~ersshall have a surficient thiclcness in order to guilrantee uniform colnpression stresses perpendicular to the grain. The design cornpressive stresses under the wasl~ershould not exceed
strength can be increased because the loaclecl area is small. The co~t~lpressive
Concluding summary The design load-carrying capacities of bolted and dowelled joints should be calculated using the general design equations for dowel-type fasteners
-
The decisive properties influencing the load-carrying capacities are the enibedding strengths of the jointed members, the geometry of ~Iiejoint, the yield inornent and tile dinn-reier of the fastener.
-
Bolted joints are, because of larger holes, not as stiff as dowelied joints and the mini1nu111spacings required are greater.
-
For riiore than six fasteners in lirle with the load direction the load-carrying capacity sliould be calculated with an effective, i.e. a reduced number of fasteners.
References Blall, i-I.J. and Wcmcr, 11. (1988). Stabdiiklverhindungenmil versiirkten AnschluRbcreichcn. Uauctl mil Holz 90: 601-607,
Eltlbcck, J, and Werner, H. (1992). 'l'ragfiihigkcil von Laubholzvcrbindungcn mit stnbfCirmigen Vcrbindurlgsmittelrl. Resenrch Report. Versuchsimslall fiir Stnhl, f4olz und Steinc. Abt. Ingcnicurl~olzbau,Univcrsitiit K:lrlsnlhc, Gcrmany. Rodd, P.D., I4ilson. 13.0.and Spriggs, R.A. (1989). Rcsin injcctcd mechanically fi~srencdtirnhcr joints. In: Proceedings o f the 2nd Pacific Timher Engirlccring Confercrlcc. Vol. 2, 13 1 - 136. Wcmcr, H. { 1993).TragWhigkcit von
i-lola-Vcthindunge~ mil stif\fiirmigcil Verbir~dungsr~~itteln unrer Bcriicksichtigung van strei~endcnEinfluUgiilJen. Dissertation. Univcrsit:il Karlsruhe, Gcrmilny. S'~P/EUROFORTECI.I- an iniiiativc under the EU Colnctt Programme
Bolted and dowelled joints I1 S ~ lecture P C7 J. Ehlbeck, H. Wcrncr Universitdt Karlsruhe
Ob,jectives To describe serviceability limit stare design procedures for bolted and dowelled joints and to demonstrate the effect of slip. To present examples for designing laterally loaded, timber-to-timber, panel-to-timber and steel-to-timber jojnts.
Prerequisites A1 7 Serviceability limit states - Deformations C6 Bolted and dowelled joints I
Summary Design rules for serviceability limit stare design are presented for bolted and dowelled joints. The design procedure and the importance of fasteners' slip are deinonstrated by examples.
Serviceability limit state design The load-carrying capacity and the defonnation behaviour of'joil-ris will1 dowel-type fasteners can be described by load-deformation curves. Figure 1 shows idealised load-deformation curves of bolted and dowelled joints with approximately Lhe same load-carryirrg capacity. I;,,,,,,.,, is Lhe estimated maxin~umload.
Figrrre I
EC5: Pnrl 1-1: 4.2 ( 1 )
The instantaneous slip modulus I<,., is determined from such curves as a characteristic value of the joint. Based on many test data EC5 recornnlends an instantaneous slip modulus K,,,per shear plane per fastener under service load for dowelled joints
with p, in ECS: Part I-!: 4.2 (2)
Irfraliseci load-cfefoi.~~~nrion crtr.ves of c/ort~rl/ecl (0)arid bolte0 (b)jni11f.c
lig/rn3
and d in nnrr.
If the characteristic densities of the two jointed inembers are different then p, STEPIEUROFORTECH - an iniii:itivc under the EU Comctt Programme
c7/1
should be taken as
This procedure is, of course, not applicable for steel-to-timber joints. The instantaneous slip u,,,,, shouId be calculated as
F
=-
Vi,@
Ks, EC5: Part 1-1: 4.2 (4)
F is the load per shear plane per dowel under service load. The final joint slip is given by 1%"
-
kd&l>(l+kdcj?)
L$,st
1%"
(4)
with k,,,.l. from EC5 Table 4.1 . Because of the bolt hole tolerances, bolted joints have an initial slip of about 1 mtn. Therefore, the instantaneous slip EC5: Part 1-1: 4.1 ( 5 )
ititGt
EC5: Part 1- 1: 4.2 (6)
rr,,,
iii,,
and the final joint slip
rtfi,,
are given by:
F
= -+ 1 ltlftl Ksc*
with
-- (u,-
1 mm) /(I+ kdd,)(l+ kdd2)+ 1 frt111
KvFrfor dowels of
the same diameter.
Esmnple I: Dowellecl tinher-to-tirwbcr joi~zr Dowel d = 12 ~ ~ f r j ~ Structural timber-strength class C24 according to prEN 338 Service class 3; load duration class: short-term Load for the governing load case: permanent load variable load
A,, = 360 N/rwlz2 p, = 350 kg/rn3 k,,,,,, = (49 G,= 12 kN Q, = 14 kN
Ultil~~rrte lirrzit state design Fd = 1,35 12+ 1,5 14 = 37,2 kN
-
Design values of material properties: ECS: Pan 1 - 1 : 6.2.1 ( 2 )
Embedding strength (y,
EC5: P:lrt 1-1: 6.6 (3)
centre member:
ECj: Part 1-1: 6.5.1.2 ( I )
= &,,2,d = 0,87
= I ,3):
a1 = *
6o d = 5,3d 12 cos20'
0,082 (1
k,
- 0,01 . 12) - 350 . -019-
= = 15,21
1,3 outer members: a , = 4.43 d > (3+4 cos70") = 4,37 d
STEP/EUROFORTECkI - an initiative under thc EU Co~ncitProgramme
= 0,87
~/ntm'
EC5: Part 1-1: 6.2.1 (3)
Yield moment (y,
DoilBle shear rlu~c~rllerl joint. Dimc~rsiorwin
i r e2
EC5: Pat( 1-1: 6.2.1 ( I )
= 1,l):
(rlirll).
Design load-carrying capacities per shear plane per dowel
R,, = ~ n i n
16779m75403
(2+1,28).10
-1 $8 11,91 .12.802
design load-carrying capacity of the joint
Sc.t-nicenbility litnit state desigrt
F,, per shear plane per dowel: FSCr=
26,O = 3,25 kN 2 . 4 -
EC5: Part 1-1: 4.2 ( 1 )
Instantaneous slip modulus per shear plane per dowel: 1 KSCI = - 350i15 - 12 = 3929 N]mm 20 STEPIEUROFORTECI-I - an initiative undcr the EU Comett Program~nc
Values for permanent short-term
k,,,in service class 2 kcdej = 0,80 kdd = 0,Oo
instantaneous slip
fiitst
=
3250 = 0,83 1nnr -
3929 0,46 . 0,83 (I
E C ~ Part : 1- i : 4.2 (4)
final slip
EC5:Part 1- 1: 6.6 (2)
Do;,t/el spacillgs clllcl clistatlces
=
ccnuc member
+
0,8) + 0,54 . 0,83 = 1,14
outer
ltlitt
mcmbers
The same joint configuration as for example I , except centre member made of plywood of 20 nrrrr thickness.
Ulti~nateiinrit state desigtl Embedding strength of plywood (y,,=1,3; k,,,,,,, = 0,9):
ECS: Part 1-1: 6.2.1 (1)
0
=
- 0,01
O,11(1
=
EC5: Pan 1-1: 0.5.1.3 (2)
43 56 11,91
=
12) . 650
. 9 = 43,6 IV/,ti,rr2 1,3
3,66
design load-carrying capacity of the joint
E C ~ Part : 1 - 1 : 4.2 (2) EC5: Port I - I : 4.2 (1)
Sel-viceability liltlit state clesigrr pk = J m = 477 kglm3 Ksw =
1 . 477'~~ - 12 = 6251 20
N/mm
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Vnfues for lid,./ in service class 2 EC5: Pnrt 1-1 : 4. I ( 6 )
EC5: Part 1-1: 4.2 (4)
timber
plywood
permanent
030
1 ,00
short-term
0,OO
0,OO
r$,,
=
0,46
0,52
. \/(I
+
0,8)(1
+
1,O)
+
0,54
0,52
Dowel ii = 24 11tnt Glued laminated timber according to prEN 1194: GL 24 Steel plate Service class 1 ; load duration class: short-term permanent load Load Tor the governing load case: variable load
=
llzrn
= 360 Nhmt~" p, = 380 kghn3 t = 15 trr1i7 k,,,, = 0 ~ 9 G, = 130 liN Q,= I95 kN
Dowe! spctcings ctrid distances
-
0,74
EC5: Port I 1 : 6.6 (2)
c1,=1201il111(5(1)1 ) c d < o , < 7 d a, = I00 ~ t t r t t(4,2 d) > 3 d n,,,= 170 ?7117? (7,l c/} f)> 7 d and > 80 117r1r a, = 100 111ri1 (4,2 rl) > 3 cl
E C ~Part : 1-1: 6.2.1(2)
Einbedding strength (y,, = 1,3):
EC5: Par1 1 - 1: 6.2.1(3)
Yield momenl (y, = I , I ):
E C ~ Pnrt : 1-1: 6.2.1, (2)
Design load-cnrrying capacities per shear plane per dowel
STEP/EUROFORTECH - :In initiative unrlcr the EU Comcll Progranlmc
design load-carrying capacity of the joint: RdJoi,,, = 2 . 10 * 23,8 = 476 id\r > 468 idV
A check should also be made on the strength of the steel plate (see EC3: Part 1.1 "Design of steel structures - general rules and rules for buildings" (ENV 1993-1-1)).
Servicenbilihl lirtrir store desigtl F,,,per shear plane per dowel
values for k,,. in service class 1 permanent: k,,, = 0,60
EC5: Part 1-1: 4.2 (4)
I%"
- 325 13'
-
1,83 {(I
short-term: kfleJ= 0,000
i
O,60)
195 . 1,83 1 + 325
= 2,02
11tm
Excin~ple4: Bolted steel-to-timber joint The same joint configuration as for example 3, except bolts instead of dowels
Balr spacirigs nrld distnrlces EC5:P;utI-1:6.5.1.2(4) a , = 1 2 0 n t 1 1 ! ( 5 d ) 4 c / 5 a l C 7 c 1 n2 = 100 mm (4,2 cl) > 4 cl a,,,= 170 m1n (7,l cl) > 7 cl and > 80 frrrri cr, = 100 m ~ t i(4,2 d) > 3 d
Ultil~lcrteliinit state desigii Design procedure see example 3 Setviceability li~lritstctte clesigrl
I;,,, =
16,3 kN K,,, = 8890 N/~ttnz
EC5: Pan 1-1: 4.2 ( 5 )
rri,
=
1 mm
+
16300 = 8890
2,83 rnnt
STEPEUROFORTECH - an initit~tivcunder thc EU Comelt Programme
Screwed joints STEP lecture C8 J. Ehlbeck, W. Ehrhsrdt Universilat lCarlsruhe
Objective T O describe the load carrying behaviour and the load-carrying capacity of screws.
Prerequisite C3
Joints with dowel-type fasteners - Theory
Summary The lecture describes the load-canying behaviour of screwed joints and presents the design rules given in EC5.
Introduction Wood screws are especially suitable for steel-to-Limber and panel-to-limber joints, but they also can be used for timber-to-timber joints. Suck screwed joints are mainly designed as single shear joints. Screws with a diameter greater than 5 ntm should be turned into pre-drilled holes to prevent splitting of the wood. The holes should be pre-drilled over the length of the unthreaded shank with the diameter of the smooth shank and over the threaded portion with a diameter of about 70 per cent of the shanlc diameter. Screws should be inserted by turning and not by driving with a hammer, otherwise tile load carrying capacity, mainly the withdrawal capacity, will decrease significantly. Requirements referring to design and material of the screws will be fixed in a European product standard. In the design equalions d should be taken as the diameter of the screw measured on the smooth shank. Tile diameter d of coach screws varies from 8 to 20 nml, the diameter of countersunk head or round head screws varies from 4 to 8 m m z . The root diameter of the screw in the threaded portion cl, is about 70 per cent of the diameter measured on the smooth shank. The depth of the thread Ill varies from 0,125 d to 0,14 d, the threadpitch h, from 0,4 d to 0,5 ci. The length of the threaded portion is about 60 per cent of the total length of the shank.
I
Figtire I
I
I
Typical \i~ooclscrews: (a) conclr scre\v (6) cortnfersrolki~ead(c) ralrrtd earl.
At present the relevant national product standards do not specify any values regarding fastener properties with respect to the load carrying capacity. It is STEPRUROFORTECH - an initinlive undcr [he EU Cornell Programrnc
C8ll
assumed that the design rules for screwed joints in EC5 are applicable for screws according with the British Standard BS 1210 "Wood screws" and the German Standards DIN 96 "Halbrund-Holzschrauben rnit Schlitz", DIN 97 "Senk-Holzschcauben mit Schlitz" and DIN 571 "Sechskant-Holzscl~rauben".
Load carrying hehaviour Laterally loaded screws have nominally a srnaller load-carrying capacity than nails or round steel bolts with, because the yield moment in the threaded portio11 is smaller than the yield moment of the smooth shank. For srnail diameters the angle between the force and the grain direction has no significant influence on the load-carrying capacity. For larger diameters there is an increasing influence on the embedding str.engtti of the members. Therefore, joints with screws having a diameter less than 8 vim can be designed principally as nailed joints, whereas for diameters greater than or equal to S nlnr the decreasing embedding strength for increasing angle between force and grain must be taken into account. It should also be taken into consideration, that screws taper to tlie point, so that there is almost IIO contact in the region of the point. For applying the lules in EC5 it is assumed that:
-
-
the screws are turned into pre-drilled holes and the length of the sn~oothshank is at least equal to the thickr~essof the member under the screw head
LateralIy Ioaded screws For screws with a diameter less than 8 mnr the rules for nails apply, for screws with a diameter equal to or greater than 8 nrtn the rules for bolts apply. In designing spacings and endledge distances the diameter of the smooth shank is decisive. The penetration of' the screw should be at least 4d. The design load-carrying capacity should be taken as the smallest value found from the formulae given in STEP lecture C3. To calculate the value of the yield moment an effective diameter of cl,,.= 0,9cl should be i~sed,provided that the root diameter of the screw is not less than 0,7cI. This effective diameter assurnes that the thread itself also contributes to the yield moment. If the length of the ~11100thsllank in the pointside tnernber is not less than 4 4 the shank diameter may be used to calculate the value of the yield moment. For calculating the Ioad-carrying capacity tlie depth of penetration t , or t, should be reduced to an effective depth of penetration, to take account of the influence of the tapering point of the screw. It is recornti~endedthat the depth of penetration be reduced by about 1,5d. Tile following value for the characteristic yield moment should be used:
EC5: Part 1-1: 6.5.1.2~
Or
where A,+k is the characteristic tensile strength of the screw material and d is the diameter tneasured on the smooth shank (nominal screw diameter). STEPIEUROFORTECI~I- an iniriativc under the EU Comcu Programme
Axially loaded screws Screws ilre especially suitable for carrying withdrawal loads. To determine the design value the effective depth of penetration is assumed to be tile lengtl.1 of the threaded portion of the screw in the member receiving the point. The influence of the point is taken into account by deducting one diameter from the effective length. The design withdrawal capaciry of scl-ews driven at right angles to the grain should be taken as Rd =
hd UeJ.- 4
N
(3)
The design value of tile withdrawal parameter should be calculated from the characteristic withdrawal parameter taking into account the load duration class, the service class and the partial safety coefficienr .y,,
ECS: Part 1-1: 6.7.2b
cl lfl p,
is the screw diameter in tmn ineasured on the smooth shank is the threaded length in rltr?? in the member receiving the screw is the characteristic density in kghn3
IF a depth of penetration of more than 10d is taken into account, the stresses should be checked against the design tensile strength of the screw material in the root area. The head pull through effect for axially loaded screws with sheet material should be checked using the equations for annular ringed shank and threaded nails. For timber to timber joints it may be necessary to use washers to avoid high pressure perpendicular Lo the grain.
Combined faterally and axially loaded screws For screwed joints with a combination of axial load F,, and lateral load Ft,, the following condition should be satisfied: EC5: Pan 1-1:6.3.3b
where R,,, and R , , , are the design load-carrying capacities of the joint loaded with axial load or lateral load alone.
Design example Screwed joint of a wind bracing. It is assumed that the spacings are in line with the relevant design rules.
I;,, = 222 kN (short-term), Service class 2, k,,,c,L) = 0,9, p,= 350 lig/)n3 4 screws I$ f 2 x 120, it= 400 ~ h n m '(producer's specification) d > 8 nltn; the rules for bolts apply Lateral load: t = 6 nznz (thin steel plate) t , = 1 - t - 1,5 d = 120 - 6 - 1,5 12 = 96 nzln 0,4 1 - t = 0,4 . 120 - 6 = 42 m m s 4 d = 48 tnitz +
STEPIEUROFORTECH - an initiative under thc EU Co~nertProgramme
The yield moment shouid be calcr~latedwith an effective diameter d,/ dd = 0,9 d = 10,8 mrtt EC5: Part 1-1: 6.5.1.2~
EC5: Part 1 - 1 : 6.5.1.2b
4 -1
M,,,, = 0,8
400 2 10 g3 . 1 = 61100 6 1,l
0'8
pk ktt,od -f;lC = 0,082 (1 - 0,01 6)-----YM
EC5: Part 1 - 1 : 6.2.211 EC5: Part 1 - 1: 6.2.2b
=
c5 y ,
Rd
(@-1)
A,,, t , d
1,I J
w
=
=
0,082 (1
0,41
d = 1,1 42
O,I2) 350 ' Oy9 = 17,5 ~/t!tttt' 1,3
96
17,5
= mill
-
N~llnt
12
.
lom3= 8,26 kN
. 61100 . 17,5 . 12 .
10') =5,57 kN
Axial load: I,/ = 0,6 120 = 72 nrnr < 10 d = 120 mrn No need to check against tensile strength of screw rnateriat EC5: h r t 1- 1: 6.7.2b
&,,
EC5: Pan 1-1: 6.7.2a
= (1,s + 0,6 d)
=&,,
R a ~ ~
($ -
4
6Y
AI
= 113
. (72
Od
(1,5
+
0,6
12)
9 = 113 N , I ~ Z I ~ Z 1,3
- 12)
- loe3 = 6,76 kN
Interac tion: EC5: Part 1-1: 6.3.3b
0,707 22 4 5 ,
(
+
(
2
Oy707 22 4 . 6,76
)
=
0,49
+
0,33 = 0,82 r 1
Conciuding summary -
Screws are remarkably suitable for withdrawal loads.
-
Screws with a diameter > 5 mnt shall always be turned into pre-drilled holes.
-
The length of the smooth shank s110uId be greater or equal to the thickness of the member under the screw head.
-
Under lateral loading for screws with a diameter less than 8 nlrti the rules for nails apply, for screws with a larger diameter the rules for bolts apply.
STEP/EUROFORTECH - an initiative under the EU Con~cltPrograrnmc
Ring and shear-plate connector joints STEP lecture C9
Objectives
I-I.J. UInss Dclfi Ulliversity
To show the different types of timber connectors placed in precut grooves and the fabrication of respective joints. To explain the background of the models used to calculate the characteristic strength values of ring and shear-plate connector joints.
of Tedlnolagy
Prerequisite C15 Mulliple fastener joints
Summary Various fomx of ring and shear-plate timber connectors are identified. The loadcarrying behnviour of connections with ring, or shear-plate connectors, and bolts is described. The possibie failure rnodes for different load-grain angles and their effect on the design values of the connection strength are discussed. Special attenti011 is given to the required spacing, end and edge distances of the connectors in a joint.
Introduction Ring and shear-plate connectors are used in later-ally loaded timber-to-timber and steel-to-timber joints, generally in conlbinatio~lwith bolts. While ring connectors nre exclusively applied in timber-to-limber joints, shear-plate connectors may be used for steel-to-timber joints as well as for timber-to-timber joints. Shear-plate connectors are nonnally installed before the osselnbly of tile structure and the joints are demountable (see Figure 1).
Ring and shear-plate connectors are itvailable in a variety of sl~apesand sizes, with diameters ranging from 60 to 260 m n ~ They . are always circular because they are placed into precut grooves produced by rotary cutters and ore made from aluminum cast alloy, steel or cast iron. Those connectors comn~onlyused in Europe are specified in prEN 912 "Timber fasteners - Specifications for connectors for timber". In prEN 912 ring connectors are denoted as Type A wilereas sltcar-plate connectors are listed as Type 3.
The production of ring and shear-plate connector joillts comprises severaI sreps. First, the bolt hole and the connector groove are drilled into the wood (see Figure 2 left). For the connector grooves proper cutters are necessary, corresponding to the shape of the ring cross-section. Then, the connectors are placed into the grooves and the titnber members to be connected are put together. Finally, the bolts are inserted into the holes and tightened (see Figurc 2 right). As an alternative to bolts, coach screws ruay be used to hold the connection together.
Fi~rii-c2
Driliiitg o f !lie bolt llole orld c u t t i i ~rlrc , ~ grooite ,for ;lie coarrectnl. (Icfif rrrrrf a.sse1111)ly of CI rir~gcottrlecror joirtt (ri,qhrJ.
Load-carrying behaviour and calculation model The load in a ring connector joint is transferred Frorn one timber rt~embertl~rough embedding stresses into the ring connector and f'ur-ther through the shear resistance of tile ring into the other timber member. In shear-plate connections, the load transfer is slighriy differerrt: after the transfer of the load into the connector, the bolt is loaded through embedding stresses between shear-plate and bolt, and the load is transferred ~hroitghthe shcur resistance of the bolt. Then, either the steel metnber or the second shear-plate is loaded by the bolt. In shear-plate connections the hole diatnerer in t l ~ eshear plate consequerltly corresponds to the bolt diameter plus n srnall tolerance. Due to this tolerance, an initial slip can be expected in shear-plate connections. Based on observations during tests, the Failure of ring and shear-plate connections in lension is described by a inodel assuming a shear block failure of the wood in front of the connector. This rnodel is to be included in a future version OF EC5 or in National Application Documents. The ernbed~nentstresses which in reality are unevenly distributed over the half diameter of the ring ore assumed to be uniformly distributed and acting parallel to the load direction. The embedment stresses are then transferred through shear stresses into the tension member (see Figure 3). The capacity of the bolt is ignored, since the bolt is usually placed in oversized holes and only just starts bearing when ihe connection fails. Figure 4 shows a failed tension test connection wit11 shear failure both in the middle and one side me~nber. Assurning the shear block failure as the governing failure mode for tension joints the capacity of the connection consequently depends on the shear area in front of the connector and oil the shear strength of the wood. The shear area within the connector is disregarded since in most tests the wood core within the connector shears off before the ultimate load of tl~econnection is reached. STEP/EffROFoRTEC1-I -
;In
iniliativc undcr the EU Conlclt Pragrammc
However, the shear block failure occurs only if the embedding strength of the wood in front of the connector is sufficiently large. Otherwise embedding failure will govern the load-carrying capacity of the connection, as it will with larger end distances, a,.
I;igtirc 4
Slteur failrrre of rttidd/a atid side r~rnrlber-iil a ring cortrrector tcr tsiott.
lortclcd iir
The load-carrying capacity of a ring or shear-plate connector loaded in tension parallel to the grain can consequently be written as:
where R, , A,
f;, dc It,
is the load-canying capacity of one connector, is the apparent or average shear strength, is the shear area per connector, is d ~ eembedding strength, is the connector diameter and is the depth of the connector embedment.
The apparent shear strength decreases with increasing shear aren. Based on tests with ring connector joints by ICuipers and Verrneyden (1964), he following relationship between the apparent shear strength and the shear area is assumed:
fi, =
K A;"~'
(2)
where K is a parameter describing the shear strength of the wood. Hence, the load-bearing capacity of a ring or shear-plate connector results as: STEPIEUROFORTECH - an i n i ~ i i ~ i vundcr e thc EU Comctt Programlnc
C9/3
For a joint with one connector per shear plane the shear area is (see Figure 3):
where a , , is the distance to the loaded end. For joints with several connectors arranged in a line, the shear area for the second and each further connector is: (5) = (dc + 2 I ~ Ja, - n d: 1 4 where a, is the connector spacing parallel to the grain.
Ring or shear-plate connector joints loaded at an angle of more than 30" to the grain or in co~l~pression, respectively, show different failure modes. Connections with load-grain angles between about 30" and 150" show a splitting failure mode, where in most cases the member with a loading co~nponentperpendicular to the grain shows a tensile failure perpendicular to the grain (see Figure 5).
Cornpression joints mostly fail in a combined embedding-splitting failure mode (see Figure 6). Here, the splitting occurs only after considerable embedding deformations under both the connector and the bolt. For ring or shear-plate joints loaded in coinpression, the bolt therefore contributes to the load-bearing capacity of the connection. This load sharing between bolt and connector can be observed only for joints loaded in compression showing larger defonnations at failure ar~da distinct plastic behaviour when compared with joints loaded in tension or at an angle to the grain which generally fail in a brittle failure mode. Because also in compression joints the wood core within the connector shears off before the ultimate load of the connection is reached, the embedding area of the bolt is reduced by the area within the connector.
STEPIEUROFORTECH - an iriitiativc ttndcr tilt EU Comctt Progrnmme
Strength and stiffness values from tests The results reported Itere ore based on tests performed in the Stevin-Laboratory of Delft University of Technology and in the Danish Building Research Institute between 1957 and 1991. One shear-plate diameter, 67 1?11n,and two ring diameters, 72 1?1r?t and 112 rttrtt, were used. A total number of 948 lcsts were evaluated. A detailed description of these tests and their results is reported in Blass ec al, (1994). The tests to establish the embedding strengtli of tlie wood under the connectors were performed at Brighton College of Technology (Iiilson, 1969).
E~~~belicli~rg str-e~igih Based on 139 tests with varying timber density, Hilson ( 1 9692) gives the following relationship between the embedding strength under a ring or shear-plate connector and lhe timber density at 13% moisture content: with p in k ~ / r t t ' (6) f, = 82 ( p / 1 0 0 0 ) ' ~IV/?rz1n2 ~~~ Eq~~ation (6) can be replaced by a more simple linear relationship: with p in kghn"7) f;, = 0,078 p ~tnzrtt"
If the bolt contribution is ignored, iln approximate value of the joint strength may be obtained by using an artificial value for.6 ~nultipliedby the projected area of tlie connector. Frotn Hilson (1969b) the mtio of the tl~eoreticalconnector contribution to dleoretical joint strength including the bolt, based on 30 tests, averaged 0,804. The resulting value of .f, with p in kg/~/ln"8) fh = 0,078 / 0,804 p = 0,097 p N/nt1n2 agrees well with the results of the cornpression Lests reported in Blass el: al. (1994) which result in the folollowing characteristic value of the embedding strength: with p, in kgh? (9) = 0,095 pk ~ / n z m ' In the following, a value of 0,09 p, is used for the embedding strength A,,.
Co1ntection sb.engflr From the ultimate load and the timber dimensions, the parameter K in equation (2) was determined for each tensile tesr specimen. From all the values of the parameter K, a characteristic value was tlien determined as the 5-percentile value. Based on service classes 1 & 2, a specified minimum timber member thickness and a characteristic density of the timber of 350 kg/rn3, the characteristic value of the parameter K was found to be: STEPIEUROFORTECH - nn initiative undcr the EU Comctt Progrrlntme
Cw.5
Based on this value for K, and a characteristic embedding strength.6,. = O,09 PI, the characteristic load-carrying capacity of a ring or shear-plate connector loaded in tension parallel to the grain is:
where A , is the shear area per connector according to Figure 3 and equation (4) or (5) in ~ i t r n ' . Limiting values for the member thickness have been introduced since, with small member thicknesses, a splitting instead of a shear block failure mode, or embedding failure, is more likely to occur and consequently the cotlnection strength decreases (Scholten, 1944). The evaluation of the test results is based on a rninimuln side member thickness of 3 fi,, and a minimum middle metnber thickness of 5 h,, with 11, as defined above. Although the calculation rnodet which assurnes a shear block failure of the wood in front of the connector describes only the behaviour of tension specimens loaded at an angle of up to about 30", it has been applied to all connector joints with loadgrain angles up to 150". This means that joints loaded at an angle to the grain with a splitting fiiilure mode have also bee11 evaluated on the basis of the assurr~edshear block failure. The model nevertheless gives fairly uniform results wiilt respect to the 5-percentile value OF the parameter K. This can be explained by the fact that the end distance and the connector spacing similarly influerlce tlie ultimate load if splitting is the governing failure mode. Irt this case an increased end distance obviousiy increases tlle ared Ioaded in tension perpendicular to the grain. Only if the end distance becomes very large and the failure inode does not include splitting, can a further increase of connection strength with increasing end distance not be expected. The results of the tension test evaluation show no indication of an influence of number of conllectors for up to three connector units per joint. The same applies to the compression joints where a clear relation between the 5-percentile value of the parameter K and the number of connector units per joint cannot be established. This does not mean, however, that there exists no influence of number of fasteners per joint on the characteristic load-carrying capacity of ring and shear-plate connections. Until further research can clarify the influence of number of connectors, the effective number rrCl of more than two connectors in line with the load direction should be assunled as: 11, = 2 + (1 - rt / 20) (rr - 2) (12) where
11
is the number of connectors in line with the load.
Corrrrectioti ~'fi,!firess
EC5: Part 1-1: 5.3.3
For serviceability calculations, as well as for mechanically jointed components, slip are necessary. For moduli of the different types of mechanical timber co~~nections serviceability limit states calculations, the slip modulus K,,,corresponds to the slip modulus k, according to EN 2G89Z. For tile design of mechanicaily jointed components in ultimate limit states, the instantaneous slip modulus K,, is talcen as two thirds of the corresponding value of the slip rnodulr~sK,,.,.
C9/6
STEP/EUROFORTECI-I - ;m iniliativc undcr rllc EU Cornett Programme
Since the stiffness \~aluesof the tested connections vary considerably, the influence of different parameters on the conneclion stiffness is difficult to estimate. Consequently, a si~ilplerelation was chosen to represent connection stiffness as a function of the connector diameter and the characteristic density of the timber. The influence of load-grain angle, timber rnoislure content, member thickness and tile number of' connector units per joint was neglected. Based on a value of 350 kS/r?r3 for the characteristic density, the followir~gaverage v a l ~ ~ofethe slip modulus k , according to EN 2689 1 was deterri~ined: (13) Ic, = 0,6 d, pk (Nlant) where rI,. is the connector diameter in nim and p, is the characteristic density of the respective strength class in kg/m3.
Design equations If equation ( I 1 ) is applied to a ring or shear-plate connector joint loaded in tension parallel to the grain with a distance to the loaded end n,, of' 2 cl,., a side niember thickness of' 3 It,., a middle meluber thickness of' 5 h,, and a characleristic density of the tirnber of 350 k8h:/,n" the characteristic Ioad-carrying capacity per shear plane for those connectors listed in prEN 912 is given by:
Disreoarding the contribution of the bolt, the characteristic load-carlying capacity ?' of a r ~ n gor shear-plate connector joint can be written as:
EC5: Part 1-1: Fig. 6.3.1 .?;I
where
R~,o.k
a is the angle
belween load and grain direction,
35 di5 k p k, k, (N) 31,s d, he kp k, (N)
with (I,. and I:,, in
t1tm
(16)
For joints with one axis of connectors loaded in co~npression(I 50" S ol < ?lo"), only [he embedding strength criterion is applicable: with rl,. and It,. in it1111(18) Rc,og = 3 1 3 dc h, kp k, IN) For compression joints will] more than one axis shear failure between tlte rings is possible and both conditions of equation (16) have to be verified in this case. The lnodification faclors for timber density, distancc to the loacled end (only for tension joints) and inember thickness are defined as follows:
where p, is the chriracteristic density of' rlle timber strength class in kg/rit3 For joints lor~dedin tension only (-30" distance may be applied:
< cr, S
30") rr modification hctoi- for end
k,t3 = tnin
I
1,25
5
(20)
2 (Ir
where a,, is the distance to the loaded end with a minimum value of 1,5 d,.
k,=min
I
I I, -
311~.
(21)
'2
5
Itc
where t , and rZ are the side and middle member thicknesses, respectively, and h, is the depth OF the connector embedment. Equation (21) is applicable only, if t , and t? are larger than 2,25 11, und 3,75 h , , respectively.
Concluding summary
-
Ring connector joints are used in luterally loaded timber-to-timber connections while shear-plate connector joints can also be applied in steel-totimber connections.
-
Timber and connector dimensioits, spacing, end distances and density are the pri~naryinfluences on the connectioil strength.
-
Connection stiffness depends mainly on connector diameter and timber density.
-
Tile L'dilure mode of joints loaded in tension is a shear block failure of tlte wood in front of the connector unless large end distances lead to an embedinent failure mode. Joints with Load-grain angles between about 30" and 150" show a splitting failure mode of the inember loaded perpendicular to the grain. Because of the brittle failure mode and the initial slip of the bolt in its oversized hole, load sharing between bolt and connector is not taken into account.
-
Ring and shear-plate connector joints loaded in compression show a combined embedding-splitting failure mode.
References Blass, H.J., Ehlbcck. 1. and Schlagcr. M. (1'194). Strength and stiffness of' ring and shear-plate connections. Molz :11s Roh- und Werksloff 52: 71-76. Hiison, 0.0.(196911).The bchaviour of sofiwoods loaded in compression parailcl to the grain arid supported against lateral rnovemenr. Journal of thc Ins!. of Woad Scicncc 4 (4): 11-23. Hilson. B.O.(1'169b). Tile ultimate strcngltl of timber joints will1 split-ring connectors whcn loadcd parallcl to (he grain. Journal of the Inst. of Wood Scicncc 4 ( 1 I): 6-26.
Kuipers, J. nrid Vcrmcydcn, P. (1964). Rcscarch on timberjoints in ltle Netherlands. Rapport 4-64-15, Ondcrzock v-7, Stcvin-Luborntoriurn. Tcchnischc Hogcschool Delft, Neihcrlands. Scholtcn, J.A. (1944). Timbcr-Connector Joints - Thcir SLrcngth and Design. Tt'cbnici~iBullclir~No. 865,USDA Fnresl Service, Washington, D.C., USA.
STEPEUROF0RTECt.l
- itn initiativc undcr thc EU Comctt Programme
Toothed-plate connector joints STEP lecture c 1 0 14.1. Uloss Dclfi University o i l'cci~nolopy
Objectives To show the different types of toothed timber connectors and the fabrication of respective joints. To explain the background to the characteristic strenglh values of toothed-plate connector joints.
Prerequisite C3
Joints with dowel-type fasteners
- Theory
Summary Various fonns of toothed timber connectors are identified. The load-bearing behaviour of connections with toothed-plate connectors and bolts is described. The failure modes and their impact on the design values of the connection strength are discussed. Special attention is given to tile required spacing, end and edge distances of the connectors in a joint.
Introduction Like ring or sl~ear-plateconnectors, toothed-plate connectors are used in laterally loaded timber-lo-timber and steel-to-timber joints, generally in combination with bolts. While ring and shear-plate connectors are placed into precut grooves (see STEP lecture C9), toothed-plate connectors are pressed into the timber members to be connected. Double-sided toothed-plate connectors are used in timber-to-timber joints; single-sided connectors may also be used if the connectors are installed before the assembly of the structure or if the joints sl~ouldbe demountable (see Figure 1). Single-sided con~lectorsare also used for steel-to-limber joints. Because of the need to press the teeth into the timber, toothed-plate connectors can only be used in timber with a characteristic density of not more than about 500 kghn3.
Toothed-plate connectors are available in a variety of shapes and sizes, with diameters ranging from 38 Lo 165 mm. They are mostly circular, but square and oval shapes are also available. The connectors are made either from cold rolled band steel, hot dipped galvanised mild steel or malleable cast iron. Those STEP/EUROFORTECI4 - arr initii~tivcunder rhe EU Comet1 Programme
clo/f
connectors colnrnonly ~ ~ s in e dEurope are specified in prEN 912 "Timber Fdsteners Specifications for connectors for timber". I11 prEN 912 toothed-plate connectors are denoted as Type C, Toothed-plate connector joints are manufactured in a similar way to bolted joints. First, the bolt hole is drilled into the wood. Then, the connectors are placed between the timber members and the connection is pressed together. Because the pressing of the connector teeth into the timber requires considerable force, either a hydraulic press or a high strengtii bolt is used. Only for small connector diameters, up to about 65 mni, can the usual 111iId steel bolt be used. If bolts are used to press the connector teeth into the wood. large washers have to be used because of the otherwise high stresses perpendicular. to the grain and the consequent csushing of the wood. After pressing, the mild steel bolt is inscrted into the tirnber members and tightened. Coach screws may be used in connection with toothed-plates as an alternative to bolts.
-
-
-
Load-bearing behaviour and calculation model The load in a double-sided toothed-plate connector joint is transferred from one timber member through embedding stresses into tile teeth of the connector and Further through the plate into the teetl~on the opposite side and the other timber member. In single-sided toothed-plate connections, the load transfer is slightly different: after the trr~nsl'erof'the load into the connector, tile bolt is loaded lhrongh einbedding stresses between connector and bolt and the load transferred by shear in the bolt. Then, either the steel member or the second toothed-plate is loaded by the bolt. In singIc-sided colinections tile hole diameter in the toothed-plate consequently corresponds to the bolt diarneter plus a sinall tolerance. Due to this tolerance, an initial slip can be expected in single-sided connections.
The failure of toothed-plate corinectioris nor~nallyis caused by an e~nbedinent klilure of the wood under both he connector tceth and the bolt, eventually conibined with tooth bending. In tension joints with small end distances, however, splitting and shear out oS the wood in front of the bolt is the governing fairure mode. Generally since toottled-plate connector joints show a plastic failure mode, both bolt and connector contribute to the load-carrying capacity of' the joint. Figure 2 shows a Sailed coltipressiori specimen with embedment failure under the connector teeth and the bolt and plastic deforniations of connector teeth and bolt.
Figure 2
E~t~berltrrer~t fnilrrre of tire ~rjoodutrcler tire corlrrcctor tcetJ1 N ~ I C I111e001t. Tfic bolt crtrd !Ire corrrlectnr tectlr c11.c d e f ~ r t ~ l pl~~sticull)~. ed
-
The model used to describe the load-carrying capacity of toothed-plate connections is based on the assuinption of a load-sharing between toothed-plate connector and bolt. The co~lnectionstrength is consequently written as:
5,k = 4 , k
+
(1 )
&,k
where
R, R,, R,,
is the characteristic load-carrying capacity of the toothed-plate connection containing both toothed-plate and bolt, is the characteristic load-carrying capacity of the tootiled-plate connector and is the load-carrying capacity of the bolt according lo EC5 based on the characteristic values of the embedment strength and the fastener yield moment.
The characteristic load-carrying capacity of a circular toothed-plate co~~nector can be described by the following empirical relationship:
where A
(I,
is n factor depending on the connector type and determined through tests and is the connector diameter.
Strength and stiffness values from, tests The test results I-eportedhere ore based on tests performed in the Stevin-Laboratory of Delft University of Technology and in the Danish Building Research Institute between 1957 nnd 1991. Only tests with one type of toothed-plrtce connector, the Bulldog connector, were evaluated. Circular connectors with diameters between 50 rlrrn and 1 17 m.tni, two square shaped connectors wit11 100 m111and 130 lrrr?i side length and an oval connector 70 rrti11 by 130 mt11 were tested in spruce (Picea nbies) specimens. A total of' 486 tests have been evaluated. A detailed description of the test results and their evaluation is reported in Blass et al. (1993).
Carri~ectiorlstrengtil From the timber di~nensionsand using a characterislic density of 350 1kgh11~the characteristic load carrying capacity of the boll was detern~inedfor each tested specirnen according to EC5. Tile load-carrying capacity of' tile bolt was then deducted from the ultiniate load of the connection before calculaling the parameter A for each test specimen. Bnsed on service classes I & 2 and a specified minin~um timber member thickness, the characteristic value of the parameter A was found LO be: (3) A, = 18 N/nrm
'*'
Limiting values for the member thickness have been introduced, since snlall member thicknesses result in a splitting instead of an embedment failure mode ilnd consequently the connection strength decreases. Tlie evaluation of the test resulls is based on tile same n~ini~num timber ~~lelnber tl~icknessesas for ring and shearplate connector joints, namely a minimum side member thickness of I ,5 ti,. and a minimum middle member thickt~essof 2,5 h,.. 11,. is the connector height for doublesided toothed-plate conneclors and twice the connector heigl~tfor single-sided toothed-plate connectors. The results of t l ~ etest evaluation show il slight decreilse in the clirrr.c~ctcriuticloacicarrying capacity per conneclor will1 increasing number of connectors for up to STEPIEUROFORTECI.1 - an inifinlivc under thc EU Cornclt Progrnmmc
C 1013
tllree connector units per joint. The decrease in the civerage load-carrying capacity per connector with increasing number of connectors is more distinct. Until further research can clarify the influence of the number of connectors, the effective number ti,, of more than two connectors in line with the load direction should be assumed as: (4) r t , = 2 + (1 tz 1 20) ( a - 2)
-
where
11
is the number of connectors in tine wilh the load.
es 30' and 180" is quite Although the number of tests with load-grain ~ u ~ g l between small, the 5-percentile value of the parameter A seems to be independent of the load-grain angle.
Co~lrzectio~z stijji1es.s
EC5:Part 1-1: 5.3.3
For serviceability calculations, as well as for mechanically jointed coliiponents, slip lnoduli of the different types of mechanical tilt~berconnections are necessary. For serviceability limit states calculations, the slip modulus K,,,, corresponds to the slip modulus k, according to EN 26891. For the design of mechanically jointed coniponents in ultimate limit states, the instantaneous slip modulus K,,is taken as two thirds of the tor-responding value of the slip modulus K,,. Since the stiffness values of the tested connections vary considerably, a simple relationship was chosen to represent conllection stiffness as a function of the connector diameter arid tile timber density. Load-grain angle, timber moisture content, member thickness and the number of connector units per joint were ignored. The following average value of' the slip modulus k, according to EN 26891 was determined for connector types C1 to C9 according to prEN 912: (5) k, = 0,3 d, p, (Nlam) Based on a comparison of stiffness values for different toothed-plate connectors in DIN 1052 ( 1988) the slip modulus k , for connector types C I O and C I I according to prEN 912 may be assumed as: (6) ks = 0,445 d, pk (Eu'l~rmr) where clc is the connector diameter in rtrnl and p, is the cllaracteristic density of the respective strength class in kghn3.
Design equations The following equations to determine the characteristic strength of a toothed-plate connector joint per shear plane apply: (7) Rj,cr,k= 'c,li Rb,a,k +
EC5: Port 1-1: Fig. 6.3.1.h
a R R,,
is the angle between load and grain direction, is the characteristic ioad-carrying capacity of the connector joint and is the chancteristic load-carrying capacity of the connector:
ReTk= 18 k, k,, k, d:'l (N) for connector types C1 to C9 according to prEN 912 and
-
STEPIEUROFORTECH an initiative under thc EU Con~ettProgti~mn~c
(8)
for connector types C10 and CI 1 according to prEN 91 2 with d, in tmn. EC5: Part 1-1: 6.5.1
R,,,,, is the load-carrying capacity of the bolt according to EC5 based on the characteristic values of the embedment strength and the fastener yield moment.
EC5: Pad 1-1: 6.5.1.2
Minimum spacings and distances for connector types C1 to C9 according to prEN 912 are given in Table I , those for types C10 and C11 in Table 2. Additionally, minimum spacings and distances for the bolts have lo be colnplied with.
+ 0,3 I cosa 1) d,
a,
Parallel to !he grain
(1,2
a?
Pcipendicular to the grain
1,2 d,
03.r
-90" S a 5 90"
1,s clr *)
a,,
150°1a1210" 90" c a < 150" 210" < a < 270"
1 2 (Ic (0,9 + 0,G I sina 1 ) 4 ( 0 3 i0,6 f sinrw 1 ) ciC
a,,
0°
(0,G + 0,2 sina) (1'.
a ,
all oUler values of a
0.6 rf,
)
For tension joints (-30' I a < 30') the end distance a , , may he further reduced 10 I , I d,, if thc characteristic load-carrying capacity is reduced proportionally. -
Taliie 1
-
Mirtir~rrmrspacit~gsnt~ddismmtcc.~ for coi~neoortype CI lo C9.
+ 0,8 1 cosa 1 ) 4
a,
Parallel to the grnin
(1,2
a2
Perpendicular to ~ilegrain
1,2 clc
a,,
-90" 5 a 5 90'
2 (i, *)
150'5 a I2 10" 90" < a < 150" 210" < a c 270"
l,2 d'. (0,4 + I ,G I sina I ) cl, (0,4 + 1 G , Isina I ) (lc
o,~,
0" 1 a I180"
(0.6 + 0,2 sina) (I,
(I,,
all other valucs of a
0,6 d,
)
For tension joints (-30' 6 a I 30") {he cnd distancc a , , rnay be further reduced to 1,s (1, if tile cllaracteristic load-calrying capacity is reduced proportionally.
I
The lnodification factors for timber density, Ioaded end distance and member thiclcness are defined as follows:
kP = min where p, is the characteristic density in class.
kg/lt13
of the respective timber strength
STEPIEUROFORTECI-1 - an initiative under thc EU Comeu Propmmmc
C1015
For tension joints (-30" 5 a < 30") a modification hctor for the distance to the loaded end may be applied. For connector types CI to C9 according to prEN 912 this factor is given as:
ke3 = rnin
(1 1 )
'3.r
Mere ( I , , is the distance to the loaded end with a minimum value of
where (1, is the bolt diameter in
IIUIZ.
For connector types CIO and C1 1 according to prEN 912, the modification factor for tension joints (-30" 5 cx 4 30") is:
r
k,, = min
i
I rL3,f
[IL. 2
with a minimurn value for the distance to the loaded end, a,,!:
where dl, is the bolt diameter in n ~ m .
k,
=
tnin
I
where t , and tI are the side and rniddle member thickness, respectively, and h, is the connector height for double-sided toothed-plate connectors and twice the connector height for single-sided toothed-plate connectors. Equation (7) is applicable only, if t , and t2 are larger than 1 , l 11, and 1,9 It,, respectively.
.-
-
Concluding summary
-
Double-sided toothed-plate connector joints are used in IateralIy loaded timber-to-timber connections while single-sided toothed-plate connector joinls can be used in steel-to-timber connections and in demountable timber-totirnber joints.
-
-
Connector and timber dimensions as wet1 as the load-carrying capacity of the bolt are the primary influences on the connection strength.
-
Connection stiffness depends mainly on connector diameter and timber density.
STEPIEUROFORTECI-I - an initiative under thc ELI Cornclt Programrnc
--
-
Toothed-plate connector joints can be used for timber with a characteristic density of not Inore tlian aboilt 500 I c ~ ~ T I ~ .
-
The failure mode of toothed-plate connector joints is an einbed~nentfailure of the wood under the connector tee111 and the bolt. Tension joints with small end distances, however, sllow o splitting or shear out failure mode of the wood in front of the bolt. Appropriate values of loaded end distances are therel'ore essential.
References Blass, I-I.]., Ehlbeck, J. and Schla~cr,hcl. (1993). Characteristic strengl11 of ~ooll~ed-plnle connector joints. Hotz als Roll- ilnd Wcrkstofi 51: 395-399. Dctitsches Institr~t Sur Normling (1988). DIN 1052 Tcif 2 Ho1zb;luwcrkc fiihrung. 13cull~Berlin, Getmany, 27pp.
STEPIEUR0FORTECI-i - an initiative i~ntlerthe EU Co~llettProgramme
- Bcrcchnunp
kind Aus-
Punched metal plate fastener joints STEP lecturc CI 1
Objectives
L.R.J. Whnlc Gang Nail Systems UK
To develop an understanding of the design principles appropriate to joints made with punched metal plate fasteners, and to provide a working familiarity with the design method given in EC5.
Prerequisite C1
Mechanical timber joints - General
Summary The principal factors influencing tile strength of punched metal plate fastener joints are introduced. The test methods used to establish plate properties are described, along with the method used in EC5 to establish required plate sizes for joints based on botll their anchorage strength and their net cross-sectional steel strength. Finally, some general plate dimensioning rules are given, along with a description of the means by which the slip of puncl~ed metal plate fastener joints can be predicted under load.
f ntroduction A punched metal plate fastener is defined in prEN1075 "Timber Structures Joints made of punched metal plate fasteners" as a fastener made of metal plate having integral projections punclled out in one direction and bent perpendicular to the base of the plate, being used to join two or more pieces of timber of the same thickness in the same plane. They are generally manufactured from pre-galvanised mild steel or stainless steel strip with thicknesses varying from 0,9 rrlrrt to 3,5 nun (Figure 1). The innovation of using plates with pre-formed (integral) "trails" first took place in the USA in the late 1950's as a development of 111e conventional hand nailed steel or plywood gusset plate. Botl~systems brought about the ability to form in-plane timber connections, but punched metal plate fasteners were better suited to factory pre-fabrication of trusses and were able to transfer member forces with s~nallerconnection areas, with consequent cost savings in materials.
Figure I
'Ijlpicul pmlclted tltctal plate firsferret-.
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Nowadays, punched metal plate fasteners are widely used throughout the industrialised world to form tniss connections as well as joints in many other plane timber stnlchlres (Figure 2a). Many different forms of punched metal plate fastener- have been developed, involving a variety of nail patterns, nail lengths and nail shapes. The strength of a11 such plates is dictated by certain key influerlcing variables however, enabling a common design approach to be established in EC5 appropriate for all fasteners of this generic type.
Factors influencing the strength of punched metal plate fastener joints Load is transferred in a punched metal plate fastener joint first from the member into the plate teeth, then fioni these teeth up into the pIate steel and across the joint interface, then back down into the teeth in the member on the other side. The limiting strength of a punched metal plate fastener joint will therefore be detennined by one of two criteria; either its anchorage (gripping) capacity in any of the jointed members or its net sectional steel capacity at any of the interfaces between these members. The factors affecting each of these strength criteria (with reference to Figure 8) may be sum~narisedas follows:
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Aizchornge
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a is the angIe between the force and the lengthways direction of the plate (defined as being parallel to the direction of the plate slots) i.e. the angle at which the individual plate teeth are being loaded. This affects the area of timber being loaded by each plate tooth.
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p is the angle between the force and the grain direction i.e, the angle to grain at which the plate teeth are loading the timber.
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The individual species or the strength class of the timber being jointed i.e. its resistance to loads applied via punched metal plate teeth.
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A,, is the area of effective punched metal plate teeth in any member i.e. the plate contact area on any member, less any allowances for ineffective ~iaits on the edges or ends of the timber and for any misplacement tolerances when positioning the plate. The effective contact area is defined as the smallest area arrived at, after first assuming that the plate could be ~nisplaced from its correct position in any direction by a set tolerance (typically k 5 rtlttt), and that simultaneously any plate area which encroaches within a set distance (dependent upon the plate type) of tile member edges or ends tnust be disregarded (see Figure 2b).
r,,,, and I,, are respectively, the distance from the centroid of A,, to the furthest point of Ad, a n d t h e second moment of area of A,,. about its centroid i.e. the shape characteristics of A,./. Note: These particular properties only matter when moments are being transferred by the punched metal plate fastener.
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Steel cnpnciol y is the angle between the lengthways direction of the plate and the joint interface i.e, this dictates the net sectional steel area presented along the joint Iine.
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1, a,, b,,,, are respectively, the net projected plate length along the joint interface, and in directions parallel and perpendicular to the plate direction at the joint interface i.e. the length of plate available at the joint interface to sustain loads in the two orthogonal plate directions.
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The steel type used to manufacture the plate i s . the strength cl~aracteristics of the steel material itself.
Figlire 2
Typical joint - (a) picrorinl vieru arrrl (b) ai~clrol-age areas.
For the purposes of design, these variables are included in a number of fomulae which predict the strength of joints based on certain key characteristic plate strength properties. These characteristic plate properties and the way in which they are established from tests are described in the next section.
Establishment of characteristic plate strength properties from tests EC5: Partl-1: D6.3(1)
The following characteristic plate strength values are required in EC5 for the design of punched metal plate fastener joints: .frr.ap.r
is the characteristic teeth anchorage capacity per unit area at various angles a and P.
.A,o,k
is the characteristic plate tension capacity per unit width of plate in the lengthways direction (a = 0").
A.90,o.n
is the characteristic plate tension capacity per unit length of plate in the widthways direction (a = 90").
A.0.k
is the characteristic plate compression capacity per unit width of plate in the lengthways direction (a = 0").
fc,,o.k
is the characteristic plate compression capacity per unit length of plate in the widthways direction (a= 90").
L,o,k
is the characteristic plate shear capacity per unit width of plate in the lengthways direction (a = 0").
f;..~0.1:
is the characteristic plate shear capacity per unit length of plate in the widthways direction (a= 90").
Each of these plate properties should be established from standard tests, described in prEN 1075. These 5-percentile test values are later converted to design values by multiplyjng by the appropriate modification factor (A,,,,,) and dividing by the partial coefficient for materials (y,,,). For the anchorage strength these modification factors will relate lo the timber, but for the pIate strength they should be taken as 1,O and 1,l respectively. n~ust be established over a range of a and P The anchorage strength values. If sufficient values on the surface have been established then simple linear interpoiation can be used between them, however fewer tests are necessary if n presumption is made as to its form. EC5 contains suclr a
x,,4,k
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presumption which strictly requires the definition of just three constants from tests as follows: a)
f;,,,, is the characteristic anchorage strength for specimens loaded parallel to grain (p = 0'). It is obtained from straight joints (Figure 3), typically with plate angles a = 0°, 15", 30°, 45", GO", 75", 90". A lower bound bilinear relationship may then be fitted to these data (Figure 4) yielding fitted constants k,, and q,for use in the following predictive equations:
cxscX(,
where k,,
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Fig nrr 4 Dcrii~atiartof car~~~tattt.~ kl,k2,a,,
is the cliaracteristic anchorage strength for specimens loaded parallel to the plate direction (a = 0"). It is obtained from T-joints (Figure 5), typically with "T angles" j3 = 15", 30°, 4.5". 60°, 75", 90".A lower bound sinusoidal reiationship [nay then be fitted to these data (Figure 6) as foliows:
f,,op,t
Figure 5 Stattdarcl lest specitrletts (a = 0').
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&, q are fitted constants.
Figllrc 3 Statrdarrl test specirlrerts (P = 0").
b)
(1)
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Figtwe 6 Derivation of constattt C.
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Generally f,,@, is close
~OA~,~,,, and this being the case:
Having established fitted lines describing the lower bound relationship between j & , and f;,,9, (bi-linear) for straight joints, and the lower bound relationsl~ip between &, and f;,,o, or il,mo (siilusoidal) for T-joints, an interpolation between these extremes: procedure is provided in EC5 for arbitrary values
The characteristic shape of the fitted f;lqap,,,surface given by Equations (4) (5) and (6) compared with that given by the raw data for a typical plate is shown in Figure 7.
Figrcrc 7
Typical f,,&,,, sit$aces - iefi: tlreorctical and rigltt: e.~perirr~ozlal.
Punched metal plate design EC5: part-I: D ~ . s . I ( ~ )
Aizchol-age capacity Induced stresses from both direct forces and moments acting on punched metal plate areas may be calculated as follows:
FA M,
is the resultanr direct force acting at centroid of A,/; is the total moment acting at the centroid of A,
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Figure 8
Purict1ed riletot plare jhstoler juirrt - Geontetry and looclitrg.
Wit11 reference to Figure 8, the total nioment will comprise an intenla1 eccentricity induced moment, and may also extend to include an external moment as desired: MA
=Fe+M
(9)
The internal eccentricity motnent may sometimes counter the external moment of course. ECS: P ~ ~ L I D6.5.1(3) -I:
The following ultimate limit state anchorage conditions need then to be sa~isfied in each member at a joint before an acceptable plate size and position can be said to have been found:
Pfate steel capacity For the purposes of verifying the plate steel capacity at a joint interface, EC5 resolves all applied forces and plate resistances into each of l t ~ eorthogonat plate directions x and y (Figure 8): F,r= F cosa c 2 F,, siny
(13)
/;l, = F sina +. 2 F , cosy
(14)
where: the resultant direct force on the joint (compression = negative). Ft,, is the moment induced force in the joint where FA,=2M/I (Figure 8).
/; is
EC5:Parrl- l :D6.5.2(7,)
The design resistances in these directions are catcuiated as follows: (if tension)
R,,,, = tttas
or f,,,,,
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, R,:,, = ~ n n . ~
(if tension) or
f,:),,,,
(if compression)
Then, the following limit state condilion should be satisfied at each joint intel-face:
Plate dimensioning ruIes In addition to the above calcuIalion rules, the Eurocode includes certain ad-hoc rules for dimensioning punched metal plate fastener joints: EC5: Partl-1: DG.5.1(2)
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In joints subject to a net compressive force, only 50% of the force needs lo be lransferred through the plate, the remainder being transferred by direct timber bearing.
EC5: ~ a r i l - 1 :DG.5.3(t)
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,411 joints should be capable of resisting a short-term handling force in any direction, equal to:
F = 1,o + 0,1 L
kN
(18)
where:
L is span of the truss in metres. EC5: Pnrtl-I: DG.5.3(2)
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ECS: parti-I: ~ 6 . s . x ~ ) -
Irrespective of any other design requirements all punched metal plate fasteners should overlap llle timber members by a lninirn~irnof 40 r n l l r or by one-third of tile depth of the timber member, whichever is the greater. Splice joints on external (chord) members shouid cover at least two-thirds of the member deptli. Splice joints may be nod el led as rotationally stiff in the structul-a1 analysis if they occur in a zone where the bending stresses are no greater than 0,3 ti~uestile ~neinberbending strength and provided that the assembly would remain stable if the joints did act as pins, or if the splice joint is overdesigned by 50% under the combined action of the direct forces and moment present.
Joint slip ECS: Partl-1: D2
Axial slip in punched melal plate fastener joints may either bc allowed for in truss deflection calculntions by the use of prescribed dips, It,,., (in itttlt) 01. slip nioduli, K,,.,(in N/r~int)established from joint tests and determined in accordance with EN 26591 "Timber structures - Joints rnade with ~nechanicalfasteners General principles lor the deterinination of strength and det'ori~iation characteristics". These II,,,., or K.,c,,,values relate to the serviceability load level. Corresponding values may also be detenilined at the ultimate load level, for use in second-order (nonlinear) analysis, as follows:
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In addition to tile axial slip ~nodulidefined above, rotational slip moduli rnay also be determined for use in design, from tests described in prEN 1075.
Computer aided design In practice most design of punched rnetal plate fasteners is undertaken by specialist fabrication coinpal~ies using purpose written CAD packages. Many such programs exist, capable of dimensioning the members of timber tnlsses and deterniining the optimum size and position of plates in seconds. Access to this technology is easy to gain via specialist fabricators, making punched rnetal piate design convenient and easy to achieve in practice.
Concluding summary
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The design of punched metal plate fastener joints requires tile definition of a two-dimensional teeth anchorage strength surface, and 6 separate plate steel strength characteristics. Standard tests for each of these properties are given in prEN 1075. Plate areas on joints must satisfy three separate verification equations accounting for- direct forces applied to the plate, and ~llomentsinduced from both internal and external sources.
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The net plate steei resistance at each joint interface is verified by an interaction equation written in terms of the applied stresses and plate resistances in both orthogonal piale directions.
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The punched illeta1 plate design rules in EC5 are supported by many years of research in Scandinavia (Aasheim and Solli 1990, Kangas 1991, Kallsner and Karigas 1991, Kangas and Kevarinmarki 1992) and can be said to represent the state-of-the-art as far as European knowiedge is concerned.
References Aasheim, E. and Solli, K.1-I, (1990). Proposal far a design codc for nail plates, CIB-W18A meetins in Lisbon, paper 23-7-1. I
KYllsncr, R. and Kangas, J. (1991). Theoretical and cxpcrimental tension and shear capacity of nail platc connections. CIB-W I8A meeting in Oxford, paper 24-7- 1. Knngns, J , and Kevwinmlrki, A. (1992). Design values of anchorage strength of nail platc joints by ?-curve mcthod and interpolation, CIR-WI8A mceting in Ahus, Sweden, paper 25-14-2.
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Carpentry joints STEP teclure C I:!
Objective
J . Ehlbeck, M. Kromcr
To describe design procedures for carpentry joints.
UnivcrsitBt Kirisrullc
Prerequisites A6 A7 B2
Strength grading Solid timber Strength classes Tension and co~npression
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Summary Supported by drawings and figures, the most frequently used carpentry joints are presented. By explaining the defonnation and load-carrying behaviour of such joirlts, the possible field of application is described. Special execution rilles and reco~nmendationsare given. Design rules for ultimate limit state as well as serviceability limit state are evaluated, and their application is demonstrated by typical examples.
Introduction An ancient timber slructure usually consisling of single timber members is only efficient if the individual parts are formed into a reasonable construction. Joints transfer the inner forces caused by external actions from one member to another. Two or more members of tile constnlction are assembled at nodes. In many cases the forces will be passed on by contact of the joint areas or by friction. Some carpentry joints are completed by fasteners made of iron or wood in order to ensure a correct fit of the connection or to allow the transmission of additional forces. Althouglr there are a lot of forms of carpentry joints, it is possible to reduce the ~x~ultifude of joints to some basic types. Some typical basic carpentry joints, such as half-lap joints, framed joints, tenon joints and cogging joints are sl~ownin Figures 1 and 2. These joints are either used to lengthen singie members parallel to grain or to join elements that meet each other at an angle. In the following sections the defo~mationand load-carrying behaviour of framed and tenon joints is explai~ied.
F i g I
B N S ~fon11~ C of carlrettfry joints: (a) hay-fopjoi/rf, (b) coggi'rg jnitrf.
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Figrrre 2
Brrsic jbrtrls of carpolrty joints: ( c )frczrrled joit~t,(dl tteilot~joiwr.
Framed joints Framed joints are used to transrnit cornpression forces fro111one inember inclined to another at a given angle. The compression force of the strut is trans~niltedby contact using the frontal area of the joint. The chord is loaded in shear. In the past an additional tenon was used to keep the joint in the right position. Today this is rnostly brougllt about by nails, so~tletirnesalso by screws, bolts or laterally nailed cover plates. Framed joints can be formed with a notch in the front area or in the rear of the strut. Cornbinations of both approaches are also possible (see Figure 3).
Fiptre 3
I;t.uwed joitlfs ~ t ~ i trotcl~ th itt 111cfi.ottt cweu (lop leji), it1 the rear area (top right) E I I I it1 ~ co~t~bitrciliott (botto~t~).
When designing a framed joint it is necessaiy to prove the load-carrying capacity of the available areas of the joint. Thus, if' the strut has a slope between 30" and 60n,only the frontal area of the joint is taken into account. The size of the t'ro~ltal area can be calculated from the effective width b,,[and the cutting depth t,. in the chord. STBP/EUROFORTECH - an i~litiiitivcunder tile EU Comelt Programme
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The resulting compression stresses at an angle to the grain should satisfy the following condition:
For optimising the joint it is recommended that the angle of the frontal area is set to half of the angle between strut and chord. Thus, the angle a between force and grain is the lowest possible for both the chord and the strut (a= P/2). In this case the compression stress in the front area of the joint is:
If the notched area is at the rear of the strut the cut is made perpendicular to the longitudinal axis of the strut. In this case, the angle between force and grain is the same as between strut and chord. Then the compression stress is:
Fd cosp (Tc,a,d
=
bcl ft'
Using double famed joints, it is possible to transmit the sum of the two single framed joints as described before. In this case it is important that the frontal area as well as the rear area of the strut fit perfectly into the corresponding pxts of the chord. Assuming a ut~iforrnlydistributed colnpression stress in rile strut, the force is transmitted into the chord by shear stresses. The average shear stress in the chord is:
In double framed joints the shear areas should not coincide. Therefore, it is recornmended that the following condition is satisfied:
When delemining the required lengtl~ I,, in the chord, the total horizontal component of the compression force of the strut should be talten into account. When designing tire strut, any eccentricities from the joint co~lfigtlrationmay cause additional bending stresses in the strut. In the tension chord the reduced crosssectional area must be considered.
Design example Joint of a compression member with a rectangular cross section b x k = 140 x 140 tttm, slope P = 45", with n chord B x It = 140 x I80 nrnl. Cutting depth r,, = 45 n ~ m shear , length in the chord I,, = 250 ilrm. Timber of strength class C24 according lo prEN 338 "Structural limber. Strength classes" . STEP/EUROFORTECW - an initinlive under thc EU Comctl Progmmme
Figlire 4
Desigti e,,mnlple of a frnttrccl joint.
Governing design value of permanent and medium-term load: I;,,= 63 kN Y,\r = 173 Serviceclass 1: k,,,,,=0,8 Characteristic material properties: The characteristic values of compression and shear strengths are taken from prEN 338 "Structural timber. Strength classes". f ,= 21 N
.f;,YU,I.
= 5,7 N / u ~ n iArk ~ = 2,4
~/ttttn'
The design values of the compression and sbear strengths are:
With an angle a = PI2 = 22,5" between the direction of the force and the grain of chord and strut, the design compression strength shall satisfy the following condition:
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Verification of failure condition:
,z, =
Fd cos p 63000 ' 'Or 45 ' = 1,27 bq 140 - 250
4
N[UINI~ 4 1,48 ~ [ n s a ~
Tenon joints In carpentry tenon joints are used for joining members transmirting transverse forces in ceilings, walis and roof constructions. Today, due to economical reasons, tenon joints are only used if they are produced by machines. Basically there are joints with a central tenon or ones with a tenon at the bottom edge of a member. Joints with a central tenon are nor~nallyused for joining members of the same depth, whereas joints with a bottom tenon are used to connect members with different depths, e.g. girders. The depth h, of hand made tenons is usually one third of the beam depth A. In modern constructions the tenon depth depends on the size of the processing machines, The tenon lengths vary from 40 to 60 rnnr. If the tenon joint is additionally fastened by a peg, greater lengths can be realised. Mortises should only be arranged in the centre or in the compressive area of a beam. For designing the beam the reduced cross-sectional area shall be talcen into account. The design of tenon joints can be carried out in line with end-notched beams. Therefore, the following condition should be satisfied:
where 11, is the tenon depth. The factor k,, is a reducing factor taking into account the geometry of the tenon joint, such as the beam depth h, the tenon depth If,, and the distance s of the shear laad from the tenon corner. For joints with a tenon at the bottom edge of the member, k,.=l. For joints with a central tenon:
k,, = Inin
1 [jm fi
5
+
*,*
Furthermore it shall be proved that the design cotnpression stresses perpendicular to the grain do not exceed the design compression strength. 'c.90,d
'
(8)
kc,90 &,%,d
For the most common tenon joints it may be assumed that k , , , = I .
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Design example Joint of: a girder with a rectangular cross section b x 11 = 100 x 180 nrrtl, with central tenon (tenon depth / I , = 60 I , I ~ I I ) . Timber of' strength class C24 according to prEN 338.
Governing design value of permanent and medium-term load: V,= 3 kN Service class I :
k,!,,,= 0,8
Characteristic material properties: The characteristic values of compression and shear strengths are taken from prEN 338 "Structural timber - Strength classes".
A,,,= 2,4 ~ / t t t n ~ ' fl.,9,., = 5,7 N/t?r~n' The design values of the shear and compression strengths are:
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Verification of failure condition:
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Joist hangers and framing anchors STEP lecture C13 E. Gehri ETI-1 Zurich
Objectives To describe the form and load carrying behaviour of colnrnon cold-formed steel fasteners for the connection of timber members. To present a design method for joist hangers and framing anchors.
Prerequisites C5 Nailed joints II
Summary The application of corn~nonlyused cold-formed steel fasteners is shown. The loadcarrying behaviour and the capacity of joist hangers under vertical loading is demonstrated, depending on the different components of the connection. A method is given for the design of joist hangers loaded at an angle to the symmetry axis.
Introduction Joist hangers, framing ai~chorsand other fasteners made from cold-formed steel have widely replaced traditional carpentry joints due to their ease of use and to avoid the need for complex machining of the timber members. Figure 1 shows examples of timber connections using cold-formed steel fasteners. The steel is usually between 1 and 4 rlzrlt thick and is either hot dip galvanised mild steel or stainless steel.
Figllre I
E S C I I I of I ~cold-fot7t;ed ~C.~ stccf.fastcrrels.(a)frunzi~rgar~clrot:(b)joist hurrge~; ( c ) itltcgrol fa.~terte~; ( d ) shear force splices, (e) cleat # angle brncket.
The connection between timber and steel is generally nailed using for example annular ringed shank nails without pre-drilling the nail holes in the timber members. The nail holes in the steel Fasteners are pre-punched thus allowing simple assembly on the building site. STEPIEUROFORTECH - an initiative undcr the EU Comctt Programme
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Load-carrying behaviour The load-carrying capacity of timber joints with cold-formed steel fasteners not only depends on the nailed steel-to-titnber connection but also on the strengths of the timber members and the steel. In particular tensile stresses perpendicular to the grain are likely to cause failure in timber members before the capacity of the nailed connection is reached. Connections prone to such failures include the framing anchor and the joist hanger in Figure 1. Tensile stresses perpendicular to the grain can be taken into account using the design methods given in STEP lecture C2. In most practical cases mprure of the steel in the net cross-section is prevented by the layout of the fastener. Because the number of pre-punched nail holes limits the force transferred by the nails the steel net cross-section can normally be designed so as not to govern the load-carrying capacity. However, in many connections plastic deforinations in the steel fasteners will occur before the rnaxiinum load is reached. In most cold-formed steel fasteners there are at least two steel-to-timber interfaces located in different planes used in the load transfer. The consequent eccentricity causes a combined lateral and axial loading of the nails.
Loud carlying clipacity of the ~zaileclsteel-to-rinzbe~.cortirectiorz The design load-carrying capacity R,,,,, per nail for single shear joints with a thin steel plate ( i s . for r 10,5d where t is the thickness) should, according to EC5, be
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taken as the smaller value found from the following equations:
For a thick steel plate (i.e, for r 2 cl) the design value of the load-carrying capacity should be taken as the smaller value found from the following equations:
If the steel plate thickness lies between 0,5 d ruid d a linear interpolation is permitted. The difference between the load carrying capacity according to equation ( I ) and (2), respectively, is caused by the clamping effect of the fastener in the steel plate (see STEP leccure C3). Tests with nailed steel-to-timber joints (Ehlbeck and Gorlaclier, 1982) have shown, however, that clamping of nails in the steel plate can also occur for steel plates with a thickness of r = 2,O 111r11 and annular ringed shank nails with a diameter of d = 4,O t t t ~ if~ ,the nails are conically shaped close to the nail head (see Figure 2) and are driven in tight fitting holes. In such a case, the load carrying capacities for thick steel plates, according to EC5, are reached. ECS:Part 1-1: 6.3.1.2~
The characteristic embedding strength f;,,ld depends on the nail diameter d in nlnt and the characteristic density of the timber p, in kg/In3 and is for non pre-drilled nail holes: (31 fh,h = 0,082 pk d -Om3 ~ l t t t i ~ t
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Figrtre 2
A~~~zrrlar rbiged shmlk trail for steel-to-tirtrbercolrt~ecriotlsrvifli a cotle sltaped shnrlk close to rhe nail heacl,
Because of the variable cross section of the nail in the threaded portion and the work hardening during manufacture the characteristic yield moment of the nails has to be determined by bending tesls. Calculating the yield moment from the plastic moment of resistance and the tensile strength of the nail wire is not possibIe for threaded nails. Werner and Siebert (1991) have published test results with annular ringed shank nails produced by four different manufacturer~s.From the test results, the following characteristic values For the yield moment M y , of galvanised and stainless steel nails can be derived: My&= 6,37 Nnr for d = 4,O mln and (4)
My$= 20,O Nnt for d
=
6,O nvrz
(5)
Here, d is the nominal or shank diameter of the nail. EC5: Part 1-1: 6.3.1.4
The load-canying capacities of nailed joints according to EC5 have been determined based on minimum nail spacings and distances. Since the nail holes in cold-fornled steel fasteners are pre-punched, the nail spacings and some end or edge distances are fixed. In designing joist hangers and framing anchors, care needs to be taken to check the necessary nail spacings and distances. For the spacings cr, and (I,, it is generally sufficient to check that the area A, per nail is greater than the value given by the product of the minimum spacings a, and a, in EC5. It should be noted that for steel-to-timber joints the minimum spacings given for rirnber-totimber joints may be multiplied by a factor of 0,7. A, al a, (6) The design witltdrawal capacity R , , , per fastener for annular ringed shank nails according to EC5 is: (7) Rm,, = A,, d 1 where 1 is the pointside penetration or the length of the threaded part of the shank, whichever gives the smaller value. The withdrawal capacity according to equation (6) corresponds to a withdrawal of the nail in the rnember receiving the point. The failure mode related to head pull through does not govern the withdrawal strength in the case of common steel-to-timber joints with steel plate thicknesses of at leas1 2,O nltn. Werner and Siebert (1991) give the following relationship for the parameter.f,, for annular ringed shank nails: f,, = 65 p2 (8) where p is the timber density in
kS/l,i3.
Joist hangers Joist hangers are frequently used as support for sawn timber or glulani beams. Joist hangers are produced in many different shapes and sizes. Figure 3 shows an example of a joist hanger for a timber-to-timber connection. STEPlEUROFORTECH - an initiative under the EU Cornet1 Prograrnrnc
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Figur-c!3
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Joist Itutrger-s for- n .seco~~clary beut~r rtjuirr beattt cor~~rccriori.
The load acting in [he plane of symmetry of the joist hanger connection is transferred from the secondary beam through both the nailed connection and contact with the bottom plate into the joist hanger and then through the nailed connection into the main beam. For joist hangers with only a few nails in the secondary beam, the major part of the load is transferred through contact with the bottom plate. For the design of a joist hanger it can be conservatively assumed that the shear force acts along the line of nails in the secondary beam connection. IF the load is mainly transferred through contact, however, the resulting force will normally be closer to the main beam. The connection between the joist hanger and the main beam is consequently loaded by an eccentric force leading to combined lateral and axial loading of these nails. Joist hangers with straps passing over the main beam often have fewer nails in the main and secondary beatn connection. In this type of joist hanger, the loads are mainly transferred by contact into the main beam. Generally, the load carrying capacities OF this type of joist hanger have to be derived from tests. Since the secondary beam nail end distance does not normally satisfy the minimum value specified in EC5,a reduction in load-carrying capacity of the nailed steel-totimber connection is to be expected. If the nails start to deform, however, the bottom plate of the joist hanger will be loaded by an increasing contact force and take over a larger portion of the load. Riberholt (1975) presented a mechanical model for estimating the contribution of the contact force in the bottom plate. The capacity of the nailed connection and the contact Force in the bottom plate can be added since both components have a plastic characteristic.
-
--
-
As an example, the verticai design load-carrying capacity is determined for the joist hanger in Figure 3 with a steel plate thickness of 2 null in service class I and for short-term load-duration. The nails used are annular ringed shank nails of the type shown in Figure 2, d x I = 4,O x 50 rrlili with a characteristic yield moment II/ly,,= 6,37 NIILThere are 12 nails in the secondary bean1 and 24 nails in the main bearn connection. The timber of both the main and the secondary beam has a characteristic density of 380 kS/t~13.There is a gap of 3 1 7 1 ~ 1between the end grain of the secondary beam and the side surface of the main beam.
Nailed seconrlary bear~rco~znectiorz Since the shear force is assumed to act in the centre of the nailed seconda~ybeam connection, each nail is loaded by the same vertical force. STEPlEUROFORTEC1-I - an iniliaiivc under the EU Comctl Progra~nrne
-
Nail spacing perpendicular to the grain: End distance:
0,7 . 5 rl = 14 tltrtl < 10 d = 40 r f ~ r n
n2 = 20
1 ~ 7 1 ~> 1
a,,. = 32
t~irn
The load-carrying capacity of the nailed steel-to-timber connection is calculated on the basis of the required minimum nail distances and the assumption that the contribution of the bottom pfale may be disregarded. This approach, which has been adopted by German Technical approvals and proved to be conservative by numerous tests with joist hanger connections, is subsequently followed to calculate the load carrying capacity R,,,,, of the secondary bean? support. R5b.d = l1,b
(9)
R,ad
Here, It,,, is the number of nails in the secondary beam connection and R , , , the design load-carrying capacity per nail. Because of the clamping effect of the nails in the steel plate, equation (2) is used to determine the lateral load carrying capacity per nail. Following the ptacedilre presented in STEP Iecture C4 tile capacity of the as secondary beam connection for the joist hanger in Figure 3 results conseque~~tly R,,,, = 12 * 1,22 = 14,6 kN (1 0)
Nailed
rnnilt beall1
corr~tectiort
The eccentricity of the force causes a combined lateral and axial loading of the nails in the main beam connection. The moment is transferred through the axial forces in the nails and the contact force between the end grain surface of the secondary beam and the side surface of the main beam. Tests have shown that after the closing of the gap the bottom edge of the secondary beam bears against the side surface of the main beam. The consequent distribution of the nail withdrawal loads is shown in Figure 4.
Figrirc! 3
Distribrlliort of'~~itlldra\vnl forces irr the rrcliled nlnirt bear)?cortrtection. Fc is !lie cotlmct forre.
The horizontal contact force I;,acts at the bottom of the secondary beain, the exact position depending on the bearing area. It is assumed that this position, which is also the centre of rotation of the secondary beam end cross-section is located I0 ntnt above the bottom of the secondary beam, The withdrawal forces of the nails are assumed to increase linexly with increasing distance from the centre of rotation. The maximum withdrawal load for the uppermost nails can then be written as:
where
STEP/EUROFORTECH - an initialive under the EU Comett Programme
V e ~i,,,,
zi
z,~, EC5: Part 1-1: 6.33
is the force transferred by the joist hanger, is the eccentricity of V with respect to the main beam connection, is the number of nails in the main beam connection, is the distance of the nail i from the centre of rotation and is the distance between the uppermost nail in the main beam and the centre of rotation.
The condition for colnbined laterally and axially loaded nails is:
and the lateral load per nail becomes:
Replacing V by R,,,,,,,,rtnd substituting F,, and F,,, in equation (12) by the expressions in equations (1 1) and (13), respectively, the load carrying capacity of the main beam connection becomes: 1
Rt,,b,d =
(14) i=I
For the joist hanger in Figure 3, the capacity of the main beam connection co~~sequently results as 1 Rn,b,d = = 22,2 IdV (1 5) 35.133 1 24 . 1220 l(907' . 175326 The secondary beam connection consequently governs the design. The load carrying capacity of the joist hanger is I$,,,d = 14,6 IdV
+ (
r
Joist harrgers loaded at an angle In most cases, joist hangers used in floors or flat roofs are loaded by a vertical force acting in the direction of the symmetry plane. If joist hangers are used in pitched roofs, however, the load acts at an angle to the principal axes of the joist hanger (see Figure 5). In this case, the load carrying behaviour differs substantially from the case of uniaxial loading. For joist hangers similar to the one shown in Figure 3 Ehlbeck atid Gorlacher (1 984) have studied the behaviour of joist hangers loaded at an angle to the principal axis. The load carrying capacity of a joist hanger loaded at an angle of 90" is according to Ehlbeck and Gorlacher (1984):
where
Rj,,,, is the load-carrying capacity of the joist hanger loaded at an angle of 90°, R , is the load-carrying capacity of the joist hanger loaded in the symmetry axis, IT,,, is the depth of the secondary beam with a maximum of 1,5 Ir,, and is the depth of tile joist hanger.
,
-
STEPIEUROFORTECH an i~litiativcunder thc EU Comcll Programme
i I
I
Figrtrc 5
Joisr l~nrigerloa~feclcis arr atrgle.
For joist hangers loaded at an angle a between 0" and 9O0,the load carrying capacity corresponds to the following interaction equation:
where F,,, and F,,,,, are the design values of the load components parallel and perpendicular to the symmetry axis of the joist hanger, respectively.
Framing anchors Friuning anchors are used to connect crossing timber members for example to transfer wind suction forces or as supports for timber beams. In most cases two diagonally positioned framing anchors are used in one connection. There are framing anchors with one and two rows of nail holes, respectively. The type with one row can only transfer tensile forces whereas the type with two parallel rows is able to transfer additional moments. When designing framing anchors, three different components have to be taken into account:
-
load-carrying capacity of tile nailed connection. Under the assumption of the load acting in the comer of the framing anchor, the nailed connection is loaded by a force and a moment (see Figure 61,
-
load-carrying capacity of the steel net cross-section and
-
load-carrying capacity of the timber members. The tensile stresses perpendicular to the grain can be taken into account following the design procedure demonstrated in STEP lecture C2.
STEPIEUROFORTECH - an initiative tinder the EU Comet1 Programme
For certain types of Framing anct~ors,Ramhiid (1986) has derived design rules for framing anchors based on an elastic distribution of the laterat nail loads. Based on this approach, the following simplified rides can be used to calculate the load carrying capacity R,,,, of one framing anchor under tensile load: (19) with one nail row Rb,, = 0,7 n RIa for il~lchor~
R/,,, = O,5
ti
R,,,
for anchors with two nail rows
(20)
where n is the number of nails per leg and R,,,,,, the lateral load carrying capacity per nail.
Concluding summary
-
Due to easy assembly on site, cold-formed steel fasteners in combination with threaded nails have replaced traditional carpentry joints.
-
Nailed connections in cold-formed steel fasteners are mostly loaded eccentrically. In the design of these connections, the steel cross-section as welt as the timber members, whicll are often loaded by tensile stresses perpendicular to the grain, have also to be checked.
References Ehlbeck. J. ilnd Gijrlachcr, R. 1982. Mindcstnitgclabstrndc bci Slahlblcc11-liolzn;~gel~~ng. Rcscafch Report, Vcrsucl~snnstaltfur Stahl, Holz und Stcinc, Univcrsitst Knrlsruhe, Gcrmnny. Ehlbeck. 1. and Giirl:~cher, R. 1984. Tragfiihigkcit von Ralkcnscl~uhen untcr zwcincllsigcr Beanspruchung. Rcscarch Rcporl, Vcrsuciisi~ns~alt Cur Stahl, Molz und Stcine. Univcrsitiit Ki~lsrullc, Gcrmnny. RibcrllolL, It. 1975. Bcrcct>nungvon Stahlblcch-HoizVcrbindungstcilcn in Dilncm;irk. Baucri rnil Hoiz 87534-536. Riimllild, K.T. 1986. Zum Tragkraftnachwcis von AnschlUsscn mit gcnrtgeltcn Sparrcnpfe~tcnankcrn. Baucn mit Holz 88:524-529. Werner, I-I, and Siebcrt, W. 1991. Ncue Untcrsuchut~geninit Niigcln fur den Holzbau. I-1017. ais Rohund Wcrkstolf 49:191-198.
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STEPlEUROFORTECH nn initiative under the EU Comctt Programme
Glued-in bolts STEP lecture C14 C.J. Jolinnsson Swedish Nniional Testing and Research Institute
Objective To describe the behaviour, design and manufacture of glued-in bolts primarily in glued la~ninatedtimber.
Prerequisites A4 A8 A 12 C2 C7
Wood as building material Glued laminated Limber - Production and strength classes Adhesives Tension perpendicular to the grain in joints Bolted and dowelled joints II
Summary An introduction to the major fields of application is presented together with the manufacturing procedure for glued-in bolts. The behaviour is described with emphasis on factors influencing the short-term strength of axially loaded bolts. The effect of changing moisture content in the wood is also mentioned. Finally the design of axially and laterally loaded bolts is shown.
Introduction Glued-in bolted connections have been used in the Scandinavian countries and in Germany for more than 20 years. The major area of application has been in glulam structures. Figures 1 and 2 shows some examples. The bolts are used to prevent cracks in tile apex zone of curved beams and in end notched beams or to transfer forces illto a structure or part of a structure as in a column-foundation joint and in a frame comer. The bolts can be loaded either axially or laterally or by a combination of both. Advantages obtained by using glued-in bolts include: -
High local force transfer.
-
Very stiff connection when loaded in the axial direction.
-
Good fire properties. The surrounding wood protects the steel.
Figure I
Girted-i~ibolts
(1.7
a rrreutis of pr-evortir~gcrack.
STEPfEUROFORTECI-i - an initiative under the EU Comett Programme
Fig~rrz.2
Gl~red-irrbolts Or ttiorrierrt siifl col~trrrr~-Juri~~~lu~ioti joirlr crrrd rtro~~le~it stif framrc cortrel: (a) Space filled rvitlr tnortar: (b)Stcel.fittirrg.
Materials and manufacture It is difficult to achieve sufficient adhesion between a smooth steel surface and glue. Therefore threaded bolts are preferred in order to obtain a mechanical bond between the bolt and the glue. Bolts with a diameter of between 12 and 24 tr1rn are common. The bolts are glued-in either by injection of the glue as is shown in Figure 3 or by screwing in the bolt. In the first case the holes are normally I rum larger than the diametcr of the threaded part of the bolt to givc sufficient clearance for the injection of' glue. In the other case the hole is smaller than the bolt diatneter, normally by an amount equal to the depth of the thread. Glue is poured into the hole and the bolt is screwed in. To allow for distribution of the glue the bolt has to have a channel cut along its length. The glue can also be applied along the depth of the hole arid the length of the bolt with a b ~ u s hand then it is not always necessary to use grooved bolts.
Figure 3
I~ljectio~r of gilrcd bolt corr~zecfiori. ( ( I ) sealirlg, (b) glrie ortt. (c) glire irr, ( d ) block ro preverri rlre bolt froin bcirrg forcer1 orrt bjj fhe gllie.
Different types of adhesives, such as phenol-resorcinoi, two-component polyurethane and two-component epoxy, are being used. The choice of adhesive has to be related to the production rnethod and how the bolts are loaded. With the injection method, where the hole is larger than the bolt diameter, the withdrawal strength of the bolt to a very large extent depends on the strength and durability of the glue line. In bolts that are screwed in, the forces between wood and bolt are t12nsferred mechanically to a great extent in areas where glue is missing or if the properties of the glue are insufficient. The pi~enol-resorcinol adllesives have a long history of use in structural applications, for instance in glulam. Riberholt (1988). however, suggests that phenol-resorcinol should not be used in connection with the injection method STEPiEUROFORTECH
- an ir~itiarivcunder the EU Comet1 Programme
and oversized holes, due to the strength reducing effect of the initial hardening shrinkage of the glue. Two-component polyurethane adhesive is sensitive to elevated temperature (Aicher 1992) and should therefore be used with caution especially in bolts under high permanent loads if the injection method is used. In laterally loaded bolts the choice of adhesive is less important as the forces are mainly transferred via compression in the glue line.
Strength of axially loaded bolts Flrctors ir?fl~tertcitzgtlte slior't term strsl~gtlz Gcrold (1992) has analysed a large number of test results and his conclusions can be sumrnarised as follows:
-
The strength of bolts loaded in tension and co~npressionis the same.
-
Strain measurements along glued-in bolts confirm that the shear stress distribution corresponds with that obtained with the Volkersen (1953) theory (see Table I). The axial strength is influenced by the difference in stiffness between steel and wood, the glued length of the bolt and the stiffness of the bond between bolt and wood.
-
The axial bolt strength also to some extent depends on the wood density.
-
In geneml rhc axial strength is solnewhat higher for bolts glued-in perpendicular to the grain direction than parallel to the grain direction.
e C
---
- -- --
/ + -ig-d
Components wilh equal stiffness EA
!zziZzF Table I
F-F
I;
lbrce
lg
glued length of the bolt
d
bolt dinmetcr
Conlponents wit11 different
Components with equnl stiffness
stiffness Bond with Bond wit11 Shorl glued length high stiffness low stiffness
Long glued lcngth
Build stress ciisrribution irt tlre joirtt nssz~~ltirlgliaear elostic helrnvioirr- of all tnaterials nccorciirrg to the Voikerserl (1953) rheo~y (Gerolcl 1992). The clrrsl~edIbze represents the nvernge sl~earstress ( F / (lgcix)~.
According to Riberholt (1988) the axial strength can be estin~ated with the following equations which are based on regression analysis of test results from STEPIEUROFORTECH - an initiative undcr the EU Comet1 Programme
C14/3
bolts with diameters of 12 and 20 diameter of 15:
Far,,
=
rt11il
and with a ratio of: glued-in length to
0,784p d f i
(1
for two-component polyurethane and other ductile glues, and
for two-component epoxy, phenol-resorcinol and other brittle glues where F,,,, is obtained in N and the symbols are defined as fo\lows:
rl 1, p
is the bolt diameter in nun. is the glued-in length of the bolt in ~ t t n l . is the density of the surrounding wood in kghn3.
Equations ( I ) and (2) are valid for I, 2 200 am. For lower values the equations tend to overestimate the axial bolt strength.
Efjcecr of cha~zgiitgmoisture corztent Gerold (I992) indicates that shrinkage and swelling due to changing ~noisture content may cause considerable shear stresses in the bond between bolt and wood. Glued-in bolts should therefore be used with caution in service class 3 applications.
Laterally loaded bolts The load-carrying capacity of laterally Ioaded bolts n~ainly depends on the embedding strength. By gluing in the bolts an almost infinite coefficient of friction is obtained between the steel and the wood surfaces. For bolts perpendicular to the grain direction Rodd et ol. (1989) shows that this leads to a considerable increase of both the embedding strength and the stiffness (see Table 2). Bolt diameter in nlnl
Load parallel to the grain direction Strength increase fiictors
Table 2
Stiffness increase factors
-
Load perpendicular to the grain direction Strength increase factors
StiFfness increase factors
Stretrgtil a t ~ d stifft~ess increase factors (glitelf-it~bolt/pluiri bolt) for lorerally louded bolts glrrcd-irt perpetidicular ro rile nlentber irz sprclce tiniber (Rodd er al., 1969).
Design of glued-in bolts Axially loaded bolts The following design rules are suggested by Riberholt (1988). The characteristic axial capacity in tension and compression is given by:
STEPIEUROFORTECH - an initiative under thc EU Comctt Programme
-
for I, r 200 mnt Rar,k
= f;vl Pk
where R,,
for ig c 200 azml
Is
is in N and where
I " ~ brittle . glues, such f,,, is a strength parameter for Equation (4) in N / I ~ I ~ For as phenol-resorcinol and epoxy t l ~ evalue is 0,520 and for non-brittle glues, such as two-component polyurethane the value is 0,650. f,,,,
is a strength parameter for Equation (5) in Nhnrrr. For brittle glues, such as phenol-resorcinol and epoxy the value is 0,037 and for non-brittle glues, sue11 as 2-component polyurethane the value is 0,046.
p,
is the characteristic density in IrS/ln3. hole diameter in lnml
\
I,
bolt diameter is the glued in length in mrjt,
Equations (4) and (5) are valid provided that the minimum distances are according to Figure 4.
Minimum distance
"4
Figure 4
2d
Mitti~trntrrdi.m~jccsfor n-rjally loaded bolts.
In addition to this the following points should be considered:
-
For bolts parallel to the grain direction it should be shown that the total force in a group of bolts is less than the tensile strength of the effective area behind the bolts.
-
Due to stability failure in a compressed bolt the axial stress in it should not exceed 400 IVhntna.
STEPlEUROFORTECH - an initiative under the EU Comett Programme
C I 4/5
-
Experience from tested bolts shows that the withdmwal failure mode is rather brittle when the glued-in length is short. If the force distribution over a group of bolts is statically indeterminate, the glued-in length should be at least cf2, d in nlnr.
-
Lcrtcrally 10aclt.d bolts.
EC5: Part 1-1: 6.5.1
Gltiecl-~II bolts perpell~lic~lar tu the grairr: The design load-carrying capacity of bolts glued in pel-pendicular to the fibre direction tnay be calculated accordii~gto EC5. The effect of the glue may be co~lsideredby increasing the embedding strength by a factor I,2. Glued-it1 bolt^. parallel to the glaiit: Riberholt (1988) suggests the following design rules: The characteristic load-carrying capacity for a bolt carrying a force acting a distance s from the wood surface is
where
M,,,is the characteristic yield tnornent of the bolt in Nrilnl. hole diameter
cl=
rnax
\
in min
bolt diameter is the embedding strength parameter in Nhtzt?t2. f, fh = (0,0023 + 0,75d"sS)p,
Minimum distances should be according to Figure 5.
Minimum distance
Figlire 5
-
Il/li~zitr~lrm cfistnncesfor laterally lunrled bolt^..
STEPIEUROFORTECH - an initiative under the EU Comett Programme
Splitting can occur, see STEP lecture C2. Riberholt (1988) sltows how the loadcarrying capacity can be i~nprovedby bonding plywood sIeeves to the end grain.
Protection against corrosion For bolts loaded axially it is essential that corrosion is prevenred. Riberholt (1988) points to the risk of the bond between steel and wood being destroyed by expansion of rust. Glued-in bolts therefore have to be prolected against corrosion, for example with zinc coating. Riberholt (1986) found that some adhesives, for exa~npleepoxy, also give a good protection against corrosion.
Concluding summary
-
The connections are produced either by injecting the glue in an over-sized liole or by screwing in the bolt.
-
Adllesives with suFficient strength and durability properties should be used.
-
The axial strength is influenced by the difference in stiffness between the wood and tire bolt, the glued-in length, the stiffness and strength of the bond between boll and wood and the density.
-
Changing inoisture content may cause considerable shear stresses in the bond, especially for bolts placed perpendicular to the grain direction.
-
For Iateratly loaded bolts the glue causes an increase in the embedding strengtli of at least 20%.
-
Glued bolts normally have to be protected against corrosion by zinc coating.
References Aicher, S. (1992). Testing ol Adi~esivcsfor Bonded Wood-steel Joints. In: Proc. or the Meeting fUFRO S 5.02, Bordeaux, France. Gcrold, M. (1992). Verbund von Holz ond Gcwindcstnngcn aus Stahl. Bautechnik 69(4): 167-178. Ribcrholt, H. (1986). Glued Bolts in Glulam. Report No. R210, Technical U~liversityof Dcnmnrk, Dcpartrnent of Stmclural Engineering. Lyngby, Denmark. Riberholt, H. (1988). Glued Bol~siil GIulnn~- Proposal Ibr CIB Code. In: Proc. of tile CIR-WI8 Meeting. Pzrksvillc, Vancouver Island, Canada. Paper 71-7-2. Rodd, P.D.,Hilson, B.0. and Spriggs, R.A. (1989). Resin Injected Mechanically Fastened Timber Joints. In: Second Pacific Timber Engineering Conficrence. Auckland, New Zealand. Volkersen, 0. (1953). Die Schubkrartverteilung in Lcim-, Niet- und Bolzenverbindungen. Energic und Technik (1953). 68-71, 103-108, 150-154.
STEP/EUROFORTECH - an initiative under thc EU Comet1 Programme
Multiple fastener joints STEP
I C C L U ~ CC15
1I.J. Biass Delft University
Objective
To develop an understanding of the conlbined action of several fasteners in line within a timber joint and its effect on the connection srrengtll.
of Technology
Prerequisite C3
Joints with dowel-type fasteners - Theory
Summary An idealised elastic solution of the interaction of ~nultiplefasteners in timber joints is given. The main parameters influencing the load-bearing capacity of multiple fastener joints are plastic fastener behaviour, creep, rnwufacturing inaccuracies and variations in load-slip behaviour of single fasteners. The rules for multiple Fdstener joints for different types of fasteners according to EC5 are presented.
Introduction Mechanical timber joints generally contain more than one fastener. Even if the load on the joint is acting at the centroid of the connection, tile load distribution between the fasteners is non-uniform. The ultimate load of a multiple fastener joint equals the suln of the single fastener loads at failure. If tile single fastener loads at failure show large differences and some of tilose fasteners are loaded well below their own failure load, tile ultimate load of the multiple fastener joint is smaller than the sum of the ultimate loads of the single fasteners. This fact is the reason for reducing the load-carrying capacity per fastener in multiple fastener joints for certain fastener types. Principally, the different influences on the load distribution in multiple fastener joints apply both to joints with only one type of fastener as well as to joints containing different types of fasteners.
Elastic solution Lantos (1969) developed a model to calculate the load distribution in timber joints at an allowable load level assuming the same linear-elastic load-slip behaviour without initial slip for every single fastener and assuming that nonnal stresses are uniformly distributed over tile cross-sections of the connected membess. The validity of his analysis is Iinlited to Llle range within which the behaviour of the fasteners can be considered elastic and to loads acting parallel to the grain of the timber members. Crarner (1968) took n similar approacl~,taking into account the non-uniform distribution of the normal stresses over the cross-section and their influence on the extensional stiffness of the members. Because the elastic solution of Lantos forms the basis for the reduction of rile load-canying capacity of lnuIliple fastener joints in EC5, the solution for joints with constant fastener spacing is given. A more general solution can be found in Wilkirison (1986).
In Figure 1, a two-member joint is shown. The load transfer between member i
(M,) and member 2 (h.l,)occurs in discrete steps at the fastener locations. Each step represents the load transferred by the respective fastener. Considering the part of the joint between fastener i and i + I in the defonl~edposition, member 1 is loaded by the total joint load ininus the loads transferred by fasteners I to i, resulting in an extension r t I mof i the original length s. Accordingly, member 2 is elongated from s STEMEUROFORTECH - an initiative t~nderthe EU Comett Progliin~me
C1511
to s + 11,~~. In addition, the loads transferred by fasteners i and i cause fastener slip values of rcxi and L$;~,,.
F i r 1
-t
I , respectively,
-
V i e ~ of v irrtdefolnled corlrlectiort (top) arrd secriotr shorvitig cleforrtrecl positiarl (bottonr) M; Metnbcr I ; M,: kleniber 2.
-
Comparing the elongated meraber iengths plus the respective fastener slip values yields: f 1) UAi + S + 112,1 = S '+ lLt,i + llL1+l
-
Replacing the fastener slip by
\
where Ff is the load [ransferred by the fastener and K is the slip modulus, and replacing the elongation of the member between two fasteners by IL =
'n, E A
where Fn,represents the load transferred by the member between two fasteners, yields the load on the most stressed fastener at the end of the fastener row for connections where the connected members have the same axial stiffness EA:
with
STEPiEUROFORTEChI - an initintivc under the EU Cometr Programme
-
(3) --
The complete derivation of Equation (4) for different inember stiffnesses is also given by Lantos (1969). Figure 2 shows an example of the load distribution in a joint containing ten fasteners based on the Lantos solution. The toad concentration at the beginning and the end of the fastener row is clearly visible.
Fig lire 2
Load disrr-il~lrfiorl beticreet~sirrg lr.jhsterier.~accordir~gto Larrtn.~.F i . rhc ~ load and id is rlrc d~'fo~.rr~czrion.
The idea behind this elastic solution is that the 111oststressed single fastener should not be loaded above its allowable load level. Since the allowable load is reached first in tlie fasteners at the beginning or the end of the row, these then control tlte magnitude of the allotvable load for the joint. The factors influencing the difference in fastener loads according to the elastic solution are the longitudinal stiffnesses of the connected members, the rlu~nberof fasteners in a row, the fastener spacing and the slip modulus.
Main factors Apart from the effect of the difference in longitudinal deformation in tile connected members, there exist several other factors significantly influencing the load e in a timber connection. distribution between d ~ fasteners
Plctsric clefori~lntionscir?rl creep Isyumov (1967) took a snore general approach to calculate load distribution between fasteners arranged parallel to loading. He considered nonlinear load-slip behaviour of the fasteners resulting in a redistribution of loads between the fasteners at higher load levels. When the most stressed fastener at the end of the row begins to defonn plastically, its stiffness decreases co~nparedto the stiffness of the other fasteners in the joint. Since stiffer components attract more load in a parallel system, the fastener loads in the middle of the row consequently will increase. This effect counteracts the effect described by Lantos and Ieads to higher ulti~nateloads compared with connections behaving elastically until failure. The same is true for the influence of time dependent deformations in the connection. Creep reduces the initial stiffness of the fasteners thereby causing a fastener load redistribution. The magnitude of creep deformations generally iucreases with the load level. Therefore, the first and last fastener in the row are expected to show larger creep deformations leading to more balanced loads in the connection. STEP/EUROFORTECI.I - an inirialive undcr l l ~ cEU Come11 Programme
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The ultimate load of timber joints with dowel-type fasteners according to EC5 is based on the work of Johansen (1949). He assumed rigid-plastic behaviour for the fasteners as well as for the wood surrounding the fasteners (see STEP lecture C3). Consequently, the load-slip behaviour of dowel-type joints is assumed to be plastic at ultirnate load level. However, considerable plastic deformations can only be expected if the failure mode in the connectiorl corresponds to one of those described by Johansen and the spacing is sufficient for this purpose. If splitting of the tirnber along the fastener rows occurs at load Ievels well below the potential plastic capacity, a full redistribution of the load within the joint is prevented. Consequently, splitting especially decreases the load-bearing capacity of multiple fastener joints. Splitting in timber joints can be avoided by appropriate spacings and end distances. The larger the spacing, the smaller the tension stresses perpendicular to the grain caused by the wedge effect of the fasteners. Thus, large spacings contribute to a plastic connection behaviour and consequently increase the capacity of ~nultiplefastener joints although the elastic rnodel predicts the contrary. A further possibility to avoid splitting and to reach a plastic connection behaviour is to reinforce the tirnber in the joint area e.g. through glued-on plywood. Significant plastic deformations in mechanical limber connections can be expected for connections with nails and other dowel-type fasteners with a comparatively small diameter as well as for toothed-plate connections. The plastic deformation at railure in toothed-plate connections is the reason why the toothed-plate and the bolt are considered to share the load, whereas for split-ring connector joints, whicil generalIy fail in a brittle manner, a load sharing between split-ring and bolt is neglected in the design. Creep deformations, however, occur in all mechanical timber connections.
Figure 3
Locrcl clistriLirtiotr befrc!ee~r .frrsteners shobt~blgplastic bel~u~lio~ir: F is ttre loctd c~trdit is tlw defortrratiori.
Fabrication tole/-arlces If pre-drilled connections with for example bolts or split-ring connectors are used, fabrication tolerances like misalignment of the bolt holes, lack of straightness of the bolt holes and variations in the hoIe diameter and initiaI position of the bolts in the holes further increase the variability in load distribution between fasteners. Dannenberg and Sexsmith (1 976) as well as Isyumov (1967) ernphasised the importance of fabrication tolerances for the load distribution and the ultimate load of bolted joints and connections with split-rings or toothed-plates. According to
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Willtinson (1986), fabrication tolerances and different shapes of the load-slip curves within a jojnt cause most of the non-uniformity of the load distribution, while the influence of the different extensions of the connected members seems negligible.
In the elastic range, Cramer found fairly good agreement between his theory and tests with carefuily prepared specimens, avoiding misalignment of the bolts and the bolt holes. But, according to Crarner, even a small misalignment of bolt holes rnay cause large shifts in bolt loads and therefore the dist~.ibutionof bolt loads in fieldfabricated joints is difficult to predict. Fabrication tolerances, due for exa~nple10 misaligned bolt holes or split ring grooves, cause an initial slip for some of the fasteners in the joint. When the joint is loaded, those fasteners only start to carry load when the fastener slip exceeds the initial slip values (e.g. bolt No. 4 in Figure 4). If the failure mode is by splitting before significant plastic deformations occur, the fasteners with initial slip will not contribute to the load-bearing capacity of the joint at all. According to tests performed by Mass6 et aI. (19891, the ultimate mean load per bolt of joints made from glued laminated Douglas fir decreased by more than 50% when the number of bolts in a row parallel to the direction of loading was increased from one 10 four. Those test results emphasise the necessity of appropriate spacings and end distances securing plastic joi~ltbehaviour and a redistribution of loads especially for joints with fabrication tolerances. Fabrication tolerances can be avoided by precisely ~nanufacturingtimber joints using computer controlled equipment.
0
20
10 F,ot
Figure 4
Esnntple of u ioacl distriblitio~iin n bolrrri joitrt nccordirrg to IVilki~worl (1986). F, is die sitzgle fi~ste~rcr laod aud i;,,,,is tlte total joir~rlorrd.
Vnriatiort iit lorr(!-slil:,behnviorrl- befiveen sittgle fasteners Apart from fabrication tolerances which affect load distribution in pre-drilled connections to a large extent, variable material properties within the wood and between the fasteners cause variations in load-slip behaviour in a joint. ICnots, splits, pitch pockets, local slope of grain or density variations in the timber also cause variations of load-slip behaviour also in non-predrilled connections, for example with nails. Figure 5 shows an example of the load distribution in a nailed connection where the high density in knots causes particularly high fastener loads in fasteners No. 4 and 8. Although this variation of load-slip behaviour does not influence the mean value of the ultimate load of multiple fastener joints, the more important characteristic value STEPEUROFORTECH
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of the ultimate load depends on this variation. Considering the extreme case of identical load-slip curves within a inultiple fastener connection, a large variation in the ultimate load of the connection will result. This variation corresponds to ihe variation of single fastener joints, independent of the number of fasteners. A large value for the variation of ultimate loads means a low value of the 5-percentile as the characteristic ultimate load.
Considering the other extreme - the load-slip curves of the fasteners within a connection show the same variation as the load-slip curves of different single fastener connections - the variation i r i the ultimate loads of the multiple fastener connection would decrease with increasing number of fasteners. This is because with many fasteners in one connection the probability of having fasteners with both low and high ultimate loads increases. In this case the characteristic value of the ultimate load of the conrzectiotl would increase with increasing nuinber of fasteners. In reality, the load-slip curves of the single fasteners within a connection are neilher identical nor statistically independent. The correlillion between the load-slip curves consequently represents a parameter influencing the ultimate load of multiple fastener joints. However, these considerations are only correct, il the failure of the joint occurs after significant plastic deformations. If the joint fails in a brittle manner - e.g. by splitting of the wood - the equalisation of forces between tlte fasteners is prevented. In this case, the favourable effect of plastic deformations on the ultimate load cannot be used. Therefore, fastener spacing as well as end and edge distances should be sufficiently large. The potential load-bearing capacity of a connection can only be utilised, if splitting is avoided and plastic deformations are possible. The combined positive effects of plastic deformations and variations in load-slip behaviour are the reasons for the fact that the characteristic load-carrying capacity of nailed joints according to EC5 is independent of the number of nails in the joint.
Influence of number of fasteners The design procedures for different types of multiple fastener joints according to EC5 follow. The design procedure is based on the assumption of ideal pIasticity and a subsequent downgrading for the effect of number of fasteners.
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Nniled nrld stapled joiirts Any influence of the number of fasteners on the load-carrying capacity of nailed or stapled con~~ections may be ignored.
E C ~ Part : 1-1: 6.5.1.7- (3)
Bolted nrrcl ciowelled joints For more than six bolts or dowels in line with the load direction, the load-carrying cilpacity of the extra bolts oi- dowels, respectively, should be reduced by 113, i s . for 11 bolts the effective number IT,,, is:
Sclsrved joillts EC5: Purt I- 1: 6.7.1
For screws with a diameter less than 8 1771n the rules for nailed joints apply, that means any influence of the number of fasteners on the load-carrying capacity may be neglected. For larger diameter screws, the respective rule for bolted and dowelled connections applies.
E C ~ P;~rt : 1-1: 6.8
Tootl~ed-plateconnectar joirlfs In connector joints, the load sharing between fasteners of the same type as well as between different fasteners has to be considered. Since the failure mode of toothedplate connector joints in general is plastic, a complete load sharing between toothedplate and bolt is assumed. The capacity of the connection is the sum of the capacity of the toothed-plate and the bolt. If the connection contains several toothed-plates, a decrease in load-carrying capacity per toothed-platelbolt sil~lilarto the rule for bolted and dowelled connections will be inserted in EC5. Until a definitive rule is introduced, the effective number of connectors for inore than two connectors in a line can be assumed as (Briininghoff et al., 1989):
Xirzg aird shenr-plate conirectar joirrts The failure mode of ring and shear-plate connector joints in tension is often brittle, the failure being initiated by a silear failure of the wood in Front of the connector. Because the shear block failure often occurs at small displacements where the bolt carries hardly any load yet, the capacity of the .bolt is neglected when designing ring and shear-plate connector joints. For several connectors in a joint a decrease in load-carrying capacity per ring or shear-plate will be introduced in EC5. Until this rule is agreed upon, Equation (9) may also be used for ring and shear-plate connector joints.
Concluding summary
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The characteristic load-carrying capacity of a ~nultiple fastener joint is frequently less than the sum of the individual fastener capacities.
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The most important factors influencing the characteristic load-carrying capacity of multiple fastener joints are plastic deformations in the connection, creep, fabrication tolerances and variations in load-slip behaviour between single fasteners.
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Plastic defornlations and creep tend to equalise the loads between the single fasteners and are therefore beneficial for the load-carrying capacity of il multiple fastener joint.
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Fabrication tolerances in pre-drilled connections may severely decrease the
load-carrying capacity, untess significant plaslic defortnations take place before the failure load is reached. Cornputer controlled high precision marnufacturing largely reduces fabrication tolerances in pre-drilled connections.
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Variations in load-slip behaviour within the joint increase the ~~~~~~~~~~~istic load-carrying capacity of multipte fastener joints. The uneven Load distribution in the elastic range due to different longitudinal deformations of the connected members hardly influences the ultimate loads of tnultiple fastener joints.
EC5 includes a decrease in load-carrying capacity with increasing number of fasteners arranged in line with the load direction for bolts, dowels, large diameter screws and conllectoc joints. The design of conr~ectionswith slender dowel-type fasteners is not affected by the number of fasteners.
References Briininghoff, H.ct nl. (1989), tlolzbauwcrke - einc i~us~hrliclie Erllutcrung zu DIN 1052 Tcil 1 bis Teil 3. Beutli Berlin ICBln, Gcrmany, 238 pp. Cramcr, C.O. (1968). Load distribution in multiple-bolt tension joints. Journal of th Stnicturnl Divisio~i,ASCE 94(ST5):1101-1117. Danncnbcrg, L.J., R.G. Scxsmith. (1976). Sliear-plalc load distribution in laminated tirnhcr joints. Report No. 361, Dcpnrtrnent of Slnictural Enginccring, Cornell University, Ithrrca, Ncw York. Isyutnov, N. (1967). Load distribution in multiple shear-plate joints in tinlber. Forestry Braricl~ Dcpartmcnlal Publication No. 1203, Department of Forcstry and Rural Development, Ottawa, Ontilrio. Johanscn, K.W.(1949). Theory of timbcr connections. Internation:~lAssociation ol' Bridge and Structural Engineering, Pub1ic;ltion 9249-262. Lantos, G.(1969). Load distribution in a row of fasteners subjcctcd to lalerai load. Wood Scicncc l(3): 129- 136. Masst, D.1.. J.J. Salinns, J.E. Turnbull. (1989). L.~er;il strength and stilfness af single and rnultiple bolts in glued-lnminatcd timbcr londed parallel to grain. Contribulion No. C-029, Engineering and Stutisticai Rescarch Centre, Rescarch Branch, Agricullure Canada, Ottawa, Ontario. Wilkinson, T.L. (1986). Load distribution among bolts parallel lo load. jourmil of Strucluml Engineering 1 12(4):835-852.
Notation F,
F n
K s
E A
is is is is is
the load on the first or last fastener in the row the load acting on the joint the number of fasteners in a row parallel to the load F the slip inodulus the fastener spacing is the member modulus of elasticity is the cross-sectional area of the connected ntember
STEPIEUROFORTECH - an initiative under the EU Conictt Programme
Moment resisting connections STEP lecture C IG P. Rnchcr CUST Civil Engineering Blaisc PascnI University
Objectives
To present the main types of joints used to transfer moments and forces. To examine the influence of the stiffness of moment-resisting joints on strvctural beliaviour. To give the calculalion methods associated with force clistribution in the joint area.
Prerequisites A4
Wood as a building material
Summary Palterns of 'fasteners are described for several types of moment-resisting joints. Practical applications and general requirements are given for a .splice joint and frame corner connections. Tile influence of joint stiffness on structural behaviour is indicated. After an examination of the force and stress distributions in the joint area, the calculation methods are presented. These methods define the forces acting on the fasteners and the members, based on the assumption of elastic behaviour. The design of a frame corner with the fasteners located in two concentric circular patterns complements the lecture.
Introduction In timber stluctures, the joints are normally designed to transfer forces stressing the fasteners in the load direction. The analysis assumes the joints to be pinned because of the concentration of fasteners in a sindl area li~nitingthe moment aim. However, the development of glued-laminated timber and other wood-based materiaIs offers many stmctural possibilities. To fulfil the code requirements, or to optimise the construction work, designers increasingly use rotationally rigid joints. The type of joint and the jointing tecl~nologieswill depend to a great extent on the layout of the structure and how the connected members work. Moment-resisting joints can work according to three types of force diagram (Figure I). Depending on the rotation centre C of the joint, the resulting tnon~ent of the fastener withdrawal (F,,) or lateral (I;,)loads balances the applied moment.
Relating to the diagrams in Figure 1, Figure 2 presents some examples of mornentresisting joints sucl~as; (a) a joint of handrail support to deck beam in a pedestrian bridge, (b) a splice joint in a continuous beam or arch, and (c) a knee joint in a frame. The diagrams (a) to (c), respectively, are associated with these joints. STEPlEUROFORTECH - an initiative under the EU Comett Programme
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For tlie joint (2a), the action F arid the bending moment ( F a ) induce withdrawal forces on the fasteners. In the example (Zb), fastener forces balance the bending moment. Normal and shear forces are transferred to the foundation by steel hardware stressing the tiunber column in co~npressionparallel and perpendicular to the grain. As large stresses perpendicular to the grain can occur, this recilnique is used for tlie transfer of small bending moments. In the last joint (2c), fasteners are designed to carry forces and bending rnoinents given by thc structural analysis. The following sections deal with this kind of mon7ent-resisti~~g joint. The trend now is to instali joints working in accordance with diagram (c) as the traditional knee connection in frames. For this type OF connection, the designer must be aware of the possible additional stresses perpendicular to the grain. They are induced by swelling or shrinkage across the restrained cross-section. Either, these stresses have to be tsrken into account in the calculations, or the height of the restrained area should be limited. Apart from the possibility of spiitting, this type of joint offers many advantages. For long-span stnlctures, they are an effective way of overcoming transport limitations andlor of using economical timber sizes. AIthough curved frames or arches work more efficiently, timber frames are often designed with tapered members connected by rnornent-resisting joints. This design maxiinises internal space in the bttilding. For the joint calcuIations, the global analysis of the structure and the local analysis of the connection shouid both be considered. The stiffness of the joints can affect the structurnl distribution of forces and defonnations. The examination of the fastener forces and timber stresses allows tlie derivation of the design rilles.
Structural influence of moment-resisting joints Current design calculations assume the connections to be either pinned or fixed. As embedding defonnations in the timber produce large joint deformations, the modelling assu~nptions11ouId consider the joint stiffness. It affects the defom~ation of the structures and ihe distribution of the forces in the case of indeterminate structures (Leijten, 1988; Komatsu, 1992). To produce accurate designs, the joint can conveniently be classified by considering the coefficient P,:
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--
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where Kr is the rotational stiffness of the joint as defined in the following section and El is the bending stiffness of the connected member with a span L. The classification of the joinl as fixed, semi-rigid or pinned is examined in the example of a two-hinged frame (Figure 3a). Neglecting the deformations induced by normal and shear forces, the moment in the joint is given by:
where q is the unifo~mlydistributed load on the rafter. The joint efficiency is lneasured by the ratio R,,, which reIates the molnent Mj to the moment of a rigid joint corresponding to K, = m. For different layot~tsof the frame, Figures 3b and 3c present the influence of the joint stiffness on the ratio R,,,. (1
(El),
fm, =-
,-j
(El),
A substantial decrease in the moment in the joint occurs when the stiffness coefficient p, is lower than 6. Considering this variation, o joint may be considered as fixed when R,, t 0,85, which requires a p,-value from 8 to 12. In Lhe opposite extreme, a pinned joint is assumed if R,, I 0 , 2 0 relating lo a mean value P, = 0,5.In all other cases, the structure shall be designed as a structure with semi-rigid joints. Considering second order effects, this classification is related to braced structures, i.e, those prevented from swaying. For unbraced slructures, EC3 specifies a minimum value of 25 for when assuming fixed joints.
P,
Fi~rthennore,the assumption of semi-rigid joints gives the opporlunity for a moinent redistribution in the timber structures. Related to the aspect ratio L/H of the frame and the coefficient p,, tile relative values of tile moments in the joint and at midspan are given in Figure 4a. The upper curve is associated with the fully-rigid frame. Thus, the designer can choose a situation where the ~nomentsare equal in the joint and at mid-span. In tile example, the joint shalt be designed to give a stiffness coefficient respectively equal to 8 and 12 for the aspect ratio U H of 4 and 8. Figure STEPIEUROFORTECH - an initiative under the EU Conlett Programme
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4b shows that, simultaneously, the maximum deflection increases slightly. As the joints alone no longer dictate the sizes of the members, the use of the timber can be improved.
Figtire 4
Irlfiiierrces of'tlle jobr stifftress orr (cr) - tlre mtio between rile ~ ~ ~ o r nirie ~tile rt joittt urrd N I N I ~ C / - .(M,), ~ ~ C~I Il Il d(b) - IJIC 1.clfio( R , , ) i ~ ~ f w e edeflectiot~ tr at nlid-span in sertli-rigid ctrld rigicl.5-uttre.
(q)
Local behaviour of the joints To derive design equations, the mechanical behaviour of the joint is first examined when resisting a moment. To counteract Llle applied moment, the fasteners are loaded at a varying angle to the grain. Considering the orthotropic behaviour of Lhe timber, the load on the fasteners depends on the slip modulus in the direction of load (Ohashi and Sakamoto, 1989). In addition, the layout of the joint should be taken into account. Two main types of joints are dis~inguished:
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splice joints where the timber members are parallel (Figure Sa), cross-grained timber to timber joints (FigureSb).
To achieve an elastic analysis, the members are assumed to be rigid since they are stiffer and stronger than the joint. Therefore, the joint rotation results from the rotational displacement o of the fasteners (Figure 5c). Defining the rotation centre C as the geometrical centre of the joint, the equilibrium condition is given by:
where FhfJis the load on the fasaner j, and r ) its distance from the rotation centre.
Figure 5
Montettt-resisti~tg joirrts. (a) joirlt iviill~pamllel rller~iber~, (b) ~ro~.~-graittcci ~t~cmtrcrs, ( c ) ,g~orr~etr-ical cicfirritioru arid forces 011 fasterrcr:r..
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As the fasteners behave linearly, the folIowing relationships apply:
where K, is the slip modulus in the force direction
(a,+ nf2).
From Equations (3) and (41, the load on he fastener i is expressed as follows:
with the rotational stiffness K, :
II
j=I
For parallel members, the slip modulus is determined from the Ilankinson formula (Ecluation 7). For cross-grained members, the compatibility of the embedding deformations requires a modified slip modulus to be considered. If the members are u sindependent of the fastener position perpendicular to each olher, this slip ~ i i o d ~ l is (Equation 8).
In addition to Lhe load distribution on the fasteners, the timber stresses have to be considered in the jointed area. Figure 6 gives the stress distribution in shear and in tension perpendicular to the grain resulting from a linear orthotropic model.
liigrrrz. 6
Stresses in rtronrclrf r-esisti~rg joirrt, ( a )fastorer pcifterru, (h) sheclr sire.sses on tl~eltricldle plane of joilrts, nrrd ( c ) stresses itr rerisio~zpc)rpettrlicrrlcir lo [he grui~rf 05 ttitrr frorrr the e f ~ d(Racl~crarrcl Gallit~rurd,1991).
Figure 6 shows that a rectangular pattern leads to the most dangerous coinbination of shear and tension perpendicular to the grain. Locating the fasleners along tile edges of the members results in higher stresses perpendicular to the grain near to the end (Boult, 1988). For such patlerns, the risk of splitting can be reduced by not placing fasteners in the joinr corner, by using small diameter fasteners, or by gluing on some form of reinforcement. To calculate the maximum shear stress, the fastener forces are projected on ttre ydirection, considering half the joint. Using the previous notation (Figure 5), the shear force V,, due to the fasteners is given by:
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Design calculations The design has to refer to the value:
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K,,,.,,, for he calculatio~iof structural deformations, I(,,,,,, to check the load-carrying capacity of the joini and tile second-order effects (see STEP lecture B7).
Xotntiolzctl stijiress For dowel-type fasteners, the rotational stiffness is calculated using the slip tnoduIus K,,,specified in EC5. This low value can be assumed as an average for both the directions parallel and perpendicular to the grain. If tile joint is made with one type of fastener, Equation (6) gives the design rotational stiffnesses as:
Considering the connections shown in Figure 7, the rotational stiffness at the serviceability limit state is (KesseI, 1991): (11) = KSCI( t i I r I 2 + 1z2 r2' ) joi11i type A
where:
Figure 7
Gmtner~yof cott~r~rotr prrtterrts far- rtlotrierlt-rcsistitzgjoittfs. (a)jairrr rypc A, (bj B.
joirlt type
Load-ctrr-ryirtg crrpaci4, The moment induces a load F,, perpendicular to the polar radius of the fastener. The maximum value is calculated as: K a , 'i
F*, = -M ~ r , d Kr,
'-1
=
U, d
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STEPEUROFORTECH
ti,
ri2 +
ti2
2 Mu,d
r2
joirlt lype A
Jm
M,,, joirtt type B ( P.Te.T2+Pye>721
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( 1 4)
In addition, shear and normal forces ( V and N) are assu~nedto be uniformly distributed on the fasteners:
The total load is calcu1ated by [he vectorial suinmation of I;,,, FN and F,,. Depending on the ratio N/V, the maxinium load is obtained for:
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the fastener located at an mgte a where tan a = N/V in a circular pattern, the furthest Fastener in a rectangular pattern.
To checlc the load-carrying capacity of the joint, the variation of tlie embedding strength A,,,,, wit11 the angle a to the grain has to be considered (Heimeshoff, 1977). The joint must be clesigned for the largest value of the relative fastener load Sf defined as the ratio of load to strength for a fastener localed at an angle a. According to EC5 rules, Figures 8a and 8b show the variation of S, for dowel-type fasteners (d=24 11in1) in a circular pattern. This variation depends on the fastener slenderness h, = M,:,,lCf;,,,,,,t , Z GI). As illustrated by Figure 8, tlie critical fastener*in rt circular pattern is located close to the longitudinal axis of the connected members. In a rectangular or trapezoidal pattern, the critical one can be the same or the furthest fastener depending on the joint components and the geometrical ratio dl?.
Figttrr S
I~lflric~rcc o f the fusteiler localiorr on tlre relative capnciry SJ (6)fur cirrrrlar lIotterlr ~ r l dcfiflew~~t rario k = j;;y / = F,, /I;,,, . ((1) c(11111ec1ed ~ ~ ~ e t iC ~I ~b e ~ s olr n~tglcof 90' a i d (b) 1109
c,,
With forces defined by Equations (1 3) to (1 S ) , lnornent resisting joints are designed considering the load on the fastener located on the longitudi~lalaxis:
F,,,
=
/(F,,
+
FY)'
+
(16)
F;
and acting at an angle to the grrtin : a 1 =arEtYll
FA, F N Fv +
]
(17)
In the case of rectangular or trapezoidal pattern (type B), the furthest fastener should also be checked for the load:
at an angle:
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As previously shown, the shear strength of the members has to be checked in tile joint area. Considering Equation (9) and the equilibrium conditions, the design shear force is given by:
joittt type A
"Y
2 vye,
= M4r.d
(i -
2
p,e,
.+
Ct,e,
)
- 2
(20)
joint rype B
Sljecific rirles As load direction varies with fastener location, the load-canying capacities per fastener are not reduced with the number of fasteners used. Furthennore, placement of fasteners for type A and B joints should be in accordance with modified distances (Table 1). Bolt, Dowel
Ring, Shear-platc
Toothcd-platc
7 el
2 dc
1,s el<
Loaded end Edge distance Spacings: oil a circular or rectangular pattern between patterns
4 cl
clC
6 el 5 cl
1-5elc
2 el, I ,S el<
I ,S (1,
Design example A three-hinged frame (Figure 9) is designed with glued-laminated members of strength class GL24. The calculation of the knee joint of the frame is to be considered. Related to the short-term load duration class, the critical load combinatioil gives the forces in the column (see STEP lecture A3) to be used for the design: M,,,= 622 .lo3 Nln V,,d= 138 +lo3N Nfr,d= 166 .lo3 N
Figlire 9
Gen~i~eriy of the I,Pnle ( a ) arid layorit of the frattle cotvier (b).
The cilancteristic timber properties are:
f,,,k =
2,82
Nlrna2
p, = 380
kdr,l3
Loacls on tlie .fasteners rind tinzberConsidering the thickness of members (tz= 2 I , = 200 m~n),the designer chooses slender dowels with a diameter of 24 t l r t ~ iincreasing the joint ductility. With distances given in Table 1, the radii are:
= 0,5 h
- 4d - 5d
600 Nlrrl =480 m m
=
r r STEP/EUROFORTECH - an initiative under ttie EU Cornett Programme
2n r-,
2nr,
Maximum number of dowels per circle are:
I Z ~ S -
6d
=
26
nz<-
6d
= 20
The load induced by the moment has the value: FA, =
l- I 11
l P t 2 + 11, :'1
=
600 622 .lo6 = 26,7 .lo3 N 26 .6002 + 20.480~
Loads due Lo shear and norinal forces in the colunln are:
Considering the critical fastener located respectively on the longitudinal axis of column or rafter, the design load is:
The maximurn shear force stressing the timber in the joint area has the value:
with:
and gives:
F,,, = 288 .lo3 N
Fc~srt~ler. copncity In the direction parallel to the grain, the embedding strength has the following design value:
Tile coefficient A,, is equal to 1,71. Then, tile load-carrying capacity (see STEP lecture CG) is calculated considering for the fastener on column axis:
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angles between load and grain: a , =arctan[(F,, + Fv,c)/FN,c]=83,l
a , = a t + n/2 -13,5= 6,6" -
the embedding strengths:
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the ratio
p:
A,,,,, P
= 9,65
= [&.2,d
N/I I I I ~ ~ " , , ~ , ~
= 16,2
1& l , ~ , d ]=
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N/ntnr
Tlie calculations result in the minimum strength per shear plane defined by:
R, = min [23,1 ; 38,9 ; 15,6 ; 20,6].ld = 15,6.103 N For the fastener on the rafter axis, calculations result in: angles between load and grain:
a1=20,8"
a,=82,7"
-
embedding strengdis:
f,,,, , = 15,l N/mm2
-
ratio (3:
P
-
a n d design strength: Rd = ITLin [36,3 ; 23,l ;
= [fil,2,d
I fil,l,d]
=
f,,,2,d = 9,65 N/lntn2
0364
17,5; 20,3] - lo3 = 17,5 lo3N
For the chosen patterns, the load-carrying condition is clieclted: on cotumr~: = 2.15,6.10~= 31,l.lo3 N > Fd,c = 29,9+103N
5,
a11d on rafter:
%,, =
2 .17,5 .lo3 = 34,9-1c3N > F,,,
=
29,8.103 N
Tilnber shew In the joint area, the strength of the timber is checked for the calculuted force F,,,,,:
References Roult, B.F. (1988). Multi-nailed motnent resisting joinls. Procccditigs of [lie In~ernationalTimber Engineering Coni'ercnce, Vol. 2, p. 319-338, Seattle, USA. Heimeshoff, B. (1977). Bercchnung von Rahmenccken rnit Diibclanschlufl (Dubelkreis). A.G.H. flolzbau Stalik Actucll, Gcnnany,Folgc 2. I
STEPRUROFORTECH - an
initiative under the EU Comctt Programrnc
Timber connections under seismic actions STEP Lecture C 17 A . Cecco~ti Univcrsits degti swdi cii Fircnze
Objectives To provide an understanding of the behaviour of joints of timber structures in seismic zones and the method of evaluating the performance in accordance with the Eurocode 8 format.
Prerequisite C3
Joints with dowel-type fasteners
- Theory
Summary The behaviour of timber structures under earthquake actions is mainly determined by the behaviour of the connections under low cycle loadings. The different ~necllanismsfor dissipating energy such as plastic defoi~nationsin wood and steel, friction between different parts it11d viscous damping, are quoted and evaluated. Cyclic performances of different kinds of connections are considered, referring to rhe available test data. Finally the ~netlzod of evaluating test results is given according to Eurocode 8, Constructions in seismic zones, Part 1.3, chapter 5.
Introduction The mode1-n approach to the design of structures in seismic regions considers that buildings should resist the so-called "service" earthquake ("moderate" but "iiIcely", i.e. with a peak ground acceleration having an average return period of 50 years) witllout li~nitationsof use, serious deformations or significant damage. In addition buildings should resist the "ultimate" earthquake ("severe" but "accidental", i.e. wilh a return period of 250 years); in this case, there may be serious damage to the structural elements, but there must not be complete collapse. When subjected to a severe seismic motion, the structure "softens", increases its own period of oscillation, "dissipates" kinetic energy and, thanks also to the cyclic character of the input action, "has time" to invert its motion prior to develop deformations leading to collapse. The capacity of a structure to developing plastic deformations within its structural ele~nenesand to dissipate energy without breaking is an essential part of its capacity to resist a seismic input (Ceccotti, 1989). It is demonstrated that a structure with plastic and dissipative joints, if appropriately designed, can resist ltigher seismic motions than the same strucfure with rigid and non-dissipative joints. In principle this is true also for all kinds of structure. However especially referring here to the case of timber structures, it is necessary to take into account some f ~ ~ r t hconsiderations. er Under alternating load, timber elements exhibit a generally linear elastic behavionr. Failure is brittle, primarily because of natural defects like knots, and there is little dissipation of energy in the wood, except maybe in zones with compression perpendicular to the grain. Glued joints also behave linearly elastically, and therefore contribute neither to the plastic behaviour of the structure nor to the energy dissipation. T11is means that timber structures composed of glued joints and of inembers assembled with perfect hinges, for example, should be regarded as nondissipative, with no plastic performance whatsoever. However, plasticity and capacity to dissipale energy can be achieved in the STEP/EUROFORTECH - an initiative under (lie EU Cornell Programme
CI7/1
corlnections between the various structural elements if they are "semi-rigid" (as most mecl~anicalones are) instead of "rigid" (as glued ones are). Well designed joints with mechanical fasteners have, in general, a very pronounced plastic behaviour. Structures may be classified into categories taking into account their plastic behaviour and their ability to dissipate energy (see STEP lecture D l 0 for more detailed discussion). This is a fundamental aspect to consider when designing for seismic loads as it allows a much more economic design, than if every part of the structure had to be kept in the elastic range OF its behaviour. In terms of seismic design codes this is done by designing for the design earthquake Ioad actions divided by a beiiaviour coefficient q which reflects the above inelastic behaviour and the gIobal ductility of the structural system. The design earthquake to be considered is defined by taking into account the relevant seismic zone map (produced by the national authorities). In Eurocode 8, the coefficient q is called the "Action Reduction Factor" or "Beliaviour Factor", and each structurai category is characterised by a particular value of q. According to the type of timber structure, 4 ranges from I to 3. For perfectly elastic structures, obviously q = 1. But if a higher bel~aviourfactor is assumed, then sufficient plasticity and energy dissipating ability in the joints must be guaranteed. However, if design calculntions carried out for static loads anticipate forces on the sections that are already higher than the ones expected in the case of seismic loads (even when assuming q = l ) , then there is no advantage in requesting any particular ductility from the joints. This may be the situation with many large stnlctures with heavy snow loads. In these cases it is not necessary to make tests or foIlow particular detailing rules other than the usual ones for static situations. Apart from some particular cases, in general it is advantageous to consider an appropriate actioii reduction factor, but this implies the need to demonstrate that connections are sufficiently plastic and dissipative to match the foreseen q value. This can be achieved with dedicated tests or, in the case of very well known types of connection, by just following certain detailing mles as explained below.
Ductility Mechanical joints in general exhibit a very plastic behaviour, provided that tile usual requirements for end and edge distances are respected. This is due to the embedding behaviour of timber itself, coupled with the plasticity and the ability to dissipate energy of tile steel elements (see STEP lecture C3). The load-slip diagram under non no tonic static loading is characterised by an initially steep incline (see Figure la, I). Once the elastic limit of either the fastener material and/or the wood embedding stress has been passed, the slope of the load-slip curve decreases until a horizontal part of tlle diagram is reached, indicating the limiting resistance F,,,,, of the joint (see Figure la, fI). This is foHowed by a decreasing part (see Figure la, 111) which indicates that the joint has failed due to for example the splitting of the wood or the breaking of the steel. (Of course this part can only easily be recorded if the test is made under displacement control).
A definition of' ductility is given in Figure 1. A distinction is made between the case when the characteristics are approximately bi-linear and the case when they are completely non-linear.
STEPlEUROFORTECH - an initiative under the EU Comett Programme
I
I
Crilurin for evcrhrufiort of stalic d~rctiliry;e.~c~~~rplesfor difjirrcrrt possible lorrrlslip C ~ I Y I(61) J ~flvo . ~ ~Iqfere~rt . ~10pe.sare ctlsily iclei~ti'ecl(bj rlre cia-vc hns n cotrti~lriurtslyclrcr~~~itrg arn~cr~lrre. D , is tlrc ciircfilit)~,v, tlre ~ilfirrtateslip arzd v, tlte yield slip.
The idea in the second case is to take trtn P equal Il6 tan a. The factor 1/6 is a reasonable compro~nisebetween the different extreme curves. The uncertainties in the determination of I:, in order to determine the ratio v,/v,. may be disregarded, bearing in mind the other uncertainties present. The eventual descending part of the curve after the maximum load has been reached indicates that the joint is fractured but still resistant. Reference to a load 20% less than tlle maximum, if a larger ductility is to be considered, is usually permitted.
Cyclic behaviour and energy dissipation The cases in Figure I refer only to non no tonic loading, but some more complex phenomena will happen under seismic actions when cyclic loading with an inversion of the force is applied in a few seconds. Consider the case of simple regular cyclic loading applied, in a quasi-static manner, to a nailed joint as shown in Figure 2. On the first loading to a given level the wood fibres around tile nail are compressed and crushed, leaving a cavity, in which the nail is unsupported during subsequent loading cycles within the displacement range, The subsequent residual strength in this range arises solely from the strength of the fastener acting as a cantilever over the length of the cavity. As the previous displacement is exceeded, the nails once more take up bearing against the wood fibres, and loading proceeds approximateiy along the parent curve as it would during monotonic loading (slight differences may be due to the pull-out effect of the head of the nail, as shown in Figure 2b, and to strain I~ardeningof the steel during the alternating loading).
Figure 2
Cclvities in plyi~oodmrd fratrlitlg ndjace~rtto rlze trail irr IocicI c~rclirig.
Typical loops in the load-slip diagram, whether for low, inrem~ediateor high deformations, are quite narrow, or "pinched", as shown in Figure 3. They differ from the "fat" loops typical of miid steel, where the forces necessary to restore the plastic deformations to zero are similar to tilose causing the plastic deformations in the first place, (Figure 4c). The "pinching" of the nailed joint Ioops reflects the "cavityt' phase of the deformation.
STEPEUROFORTECH
- an initiative under the EU Comet1 Programme
C17/3
Figure 3
Tvpicnl loud-clrforri~ntiorrloops for- d~per-er~t loud 1esel.v for clolnli~elledjoitrts.
Figure 4a represents the shape of a well designed dowelled joint, where energy dissipation is due both to the embedding behaviour of the timber and the plastic behaviour of the steel. If the dowel is so rigid and resistant that it does not bend, and the dissipation of energy and ductility are those obtained from the embedding strength of the timber only, then the load-slip curve is as shown in Figure 4b.
-
g-u-M-@. [+-3. t't -
Cc4
t'f
4'4
.......
.......
It 11as been seen that the et~velopecurve for cyclic loading is assumed to coincide with that for monotonic loading, i.e. it is independent of the loading history. The difference between the two is norn~allyless than 10% unless there is so111e alteration in the configuration of the joint {e.g. a very pronounced pulI-out effect on the fasteners) or some fracture due exclusively to low cycle fatigue, even though mechanical timber joints are generally not vely sensitive to sttch effects.
-
There are exceptions to the above. An example is the many types of steel plates with integral punched nails (teeth). In these plates, failure under repetitive loading will often be caused by sudden tooth withdrawal or by brittle failure in the steel. Other examples are joints with light gauge steel straps and pre-perforated holes for nails. In these, the alternating load ]nay cause pull out of the naifs. Another case is that of timber framed walls with very brittle board materials where after cyclic loading, important pieces of material are damaged and the original strength is lost. Therefore in order to have a harrnonised basis for the evaluation of the cyclic behaviour of joints, a CEN Standard is under preparation, giving a simple neth hod for testing joints, in a quasi-static mode, performed under displacement control. Figure 5 represents the specified cyclic history, with triple cycles of amplitudes that STEPfEUROFORTECH - an initiative under ltle EU Conlctl Progra~nme
--
-
-
are multiples of the yield slip v,..
Figure 5
Rccor~trrtcr~derl pmcerlrlve for cyclic loadi~tgtests.
In Figure 6 AF represents the "impairment of the strength" at the same displacen~ent level, between the envelope curve of the first loading and that of the third loading.
Figrirr h
ltrt~~aintlerrt of sirsrrgth betlrlea~file cnvelope r r i t ~ ~cor7.esponditlg c to t h e w t cycle, crlrve N, N I I tlte ~ third c~lcle.
In the inelastic range, the amount of dissipated energy per half cycle due to plastic deformation (hysteresis) is rneasured by the slladed area E,, in Figure 7 . The ratio between the dissipated energy and the available potential energy El:,,is called the "hysteresis equivalent viscous damping ratio" v,,. Tlie Ilysteresis dissipated energy E,, increases with an increasing amplitude of the loops, whilst v,.,, remains more or less constant. Values of about 8-10% have been evaluated for well designed dowel type fastener joints and for plywood framed walls.
i r e7
Dissipatior~ofcttergy by ily.sfewsis.
STEP/EUROFORTECH - nn initialivc under thc EU Coniett Progmmme
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Of course, in the elastic range, the hysteresis damping is in principle zero (Figure 3a). However, in the elastic range, some energy can also be dissipated. In low amplitude dynan~icvibrations wilh no secondary structures in place, only a "viscous" damping ratio of less than 1% can be measured. But the damping ratio due to friction in the junctions between different elernents and through compression perpendicular to the grain can easily I-each values of 4% and more. This is especially the case with inany redundant ele~nentsand contact points, such as are found in dwellings. This explains why in the elastic range a value of 5 % for the damping ratio is usually assumed.
Betlaviour of different types of joint As seen above, the cyclic perrorrnance of mechanical joints is characterised by good ductility, lacli of sensitivity to repeated loads, and the ability to dissipate energy. In order to avoid brittle failure due to premature splitting, the rules given in EC5 concerning end and edge distances should be followed; these distances have been given in order to ensure ductile behaviour, otherwise the Johansen theory and the derivations of the verification formulae giver1 by EC5 would not be valid (see STEP lecture C3). At the present state of knowledge, there is no clear evidence that cyclic loadir~gper se worsens tlie risk of splitting. However, the adoption of greater spacings between rasteners, and larger edge and end distances would contribute to increasing the splitting resistance and consequently the ductility of the joint. Splitting can also be prevented by including in the connection area reinforcing materials with high tensile strength perpendicular to the grain, suci~as plywood or densified veneer wood. In this way not only is splitting better contlaolled, but also plasticisation of the steel fasteners is ensured, Illus improving tlie yield performance of $lie timber joinl in terms of ductility. Obviously the use of mild steel fasteners, which have a larger deformation capacity, will in general be more suitable for ductile and energy dissipating connections than hardened steel fasteners with Iow ductility. In order to improve the ability lo dissipate energy, it is possible to lalie advantage in design of the slenderness or dowel-type fasteners. Slenderness is defined as the ratio between the thickness of tile wood member and the diameter of the dowel-type fastener. Slender fasteners always tend to dissipate more energy, because plastic hinges will always appear in the steel whereas if stocky steel fasteners are used, they perform elastically without dissipation of energy in the steel. Moreover, splitting is better prevented if the thickness of tlle timber tnetnber is increased in relation to the diameter of the fasteners. To avoid irnacceptable loss of strength under cyclic loading, three general principles should be followed. These are to use details where elements cannot easily pull out, to avoid materials liable to brittle failure, and to try to use those inaterials which retain a consistent behaviour under repeated loading. Now the cyclic behaviour of the most common types of mechanical joint will be examined (for "detailing rules" see STEP lecture D10).
Nails, staples and screws Apart from those made from hardened steel, nails, staples and screws show a distinct plastic behaviour when loaded in mechanical timber joints. The length of the shank should be increased if risk of pull-out is foreseen. Smooth nails are not recommended, in order to prevent this. If the slenderness ratio of the nail is greater STEPIEUROFORTECH - an initiative under the EU Cometi Programme
than 8, good ductility will be ensured (Figure 8).
Figrirc 8
Tjy>iccllcyclic behnvioitr of a rlniierl joirrt (ircril slcrrrlerrless 8,s).
In corinections between plywood panels and timber elements, ductile behaviour can be obtained provided that the slenderness of the nails is higher than 4. Tests with nailed shear walls show large ductilities, and large energy dissipation capncities (Figure 9).
Dowels Connections wirh slender steel dowels are able to yield in both the steel and the wood, thus allowing a large amount of energy dissipalion. IF the slenderness of dowel fasteners is higher than 8, the behaviour will certainly be of good ductility. Irrespective of other parameters, such a slenderness will ensure mode three failure (see STEP lectures C3 and DIO). Will1 stocky dowels and standard spacings, plasticity will depend upon the ernbedding behaviour of the wood alone. With less capacity for energy dissipation, tests are recommended for assessing the ductile performance of such joints. Bolts In bolted connections, oversized holes due to fabrication tolerances cause nonuniform load distribution. The consequent overloading of particular bolrs may cause splitting of the wood under these bolts, preventing a redistribution of the load within tl~econnection. In seismic regions, therefore, only precisely manufactured bolted joints, and preferably those using slender fasteners, are recornrnended. Large bolts (d >16 ntnl) have difficulty in deforming and hence in dissipating energy. It is recommended that they shouId only be used in combination with tooilted ring connectors. STEPEUROFORTECH - an inilialive under the EU Cornctt Programme
C 1717
Split ring and shear plate connectors Because of the small plastic deformations which are possible, such types of fastener are less suitable for use in dissipative zones. Toothed plate connectors Tf well designed, toothed plate connector joints can exhibit good plastic behaviour. Attention must be paid to spacing mles, so that splitting does not occur. Punched metal plates Although load-displacement curves for joints with punched metal places show a certain amount of plastic deformation, the possibility of a brittle failure of the plate and the potential pull-out effect under cyclic loading indicate that prototype tests are advisable if dissipative design is intended.
Seisntic behaviour of mechanical joints Until now, consicferation has been given to the quasi-static evaluation of the cyclic behaviour of joints. But a different loading than that is imposed in a real earthquake. Obviously the influence of the loading rate cannot be taken into account by these types of' cyclic Lest. On the other hand, the frequency content of the seis~i~ic input is also unknown. It is emphasised, therefore, that cyclic tests seen1 actually to be st~fficient to estirnate with enough accitri\cy the seismic behnviour of joints. With tile present state of knowledge, it is felt that the actual behaviour of joints is likely to be inore stiff and resistant under "instantaneous" loading than under short-term loading of the sartie magnitude. It has not been shown that instaritiineous loading of the in reducing velocity ratio induced by earthquakes has any significant i~~fluence ductility. Cyclic tests are considered sufficient since they provide, with enough accuracy, all of the parameters necessary to predict the behaviour of a structure in a real earthquake. In fact i T the "shape" of the cyclic behaviour of the joint is lcnown (RILEM, 1994) a calculation prograinme for non-linear seismic analysis can be used and theoretical calculations performed in order to find the strength of the structure under a given earthquake i.e. tlie acceleration producing collapse (the problem of representing a parlicular earthquake is not considered here which, of course, presents the same difficulties for all materials and stluctures). Another point to be e~nphasisedis that under a real earthquake the cycles will be less "regular" than those in cyclic laboratory tests because the input will bc random and irregular: so tlle n~iinberof entire cycles at the maximum displacement will in general be very small, whilst the srr~allercycles will be more numerous. As an example, Figure 10 shows thc Moment - Rotation history of a dowelled corner joint of a portal St-a~ne,under the El Centro earthquake. This is based on a numerical sin~ulation,and the eartl~quakeeffect was amplified by a factor of 1,s.
Requirements of Eurocode 8 In EC8 "Constiuctions in seisnlic regions" structures are c~assifieciinto categories according to tile ability of their joints to be ductile and be capable of dissipating energy in the plastic field. It is, in any case, recommended that structures be designed to be sufficiently rigid to meet serviceability criteria. For structures designed to take profit from their ability to dissipate energy ( q > 1) it is also STEPfEUROFORTECH - an initiative undcr the EU Comctt Programrnc
.-
-
recolnmended that the strength of the timber members sI~ouldbe higher than the strength of the connecting joints. Tl1is implies that plasticity in the joints will be achieved.
The properties of dissipative joints under seismic actions are as a rule required to be de~nonstratedthrough testing, by ineans of agreed il~ternationaIsta~dards.By such tests, it must be shown that the ductility is sufficient and that rhe joint properties are stable under cyclic loading ut a reasonably high load/deformation level. To ensure sufficient ductility, il is required that the ductility obtained fi-OITI cyclic tests should be grealer than the assumed behaviour factor q multiplied a factor of 3. This value is reduced to 2 for panel structures, because of the highly positive effect in reducing inertia forces due to damping caused by friction, and due to compression perpendicular to the grain between parts. Such effects are believed to give a damping ratio more than the usual 5%. In addition, it is stated that cor~rlectionsbetween elements must be able to deform plastically for at least three fully reversed cycles at the above ductility ratio without an ilnpairment of their strength of worse than 20%. By complying wit11 these conditions, the designer is allowed to calculate the strengtll and stiffness ofthe joint following the nonnal design rules of EC5.
Concluding summary
-
For design purposes the seismic behaviour of mechanical timber joints can sirnply be related to quasi-static behaviour under cyclic loading.
-
Ductility of joints and dissipation of energy are the most important features for dissipative design of structures to resist eartliqtrakes.
-
If the cyclic behaviour of joints is srifficiently stable, seismic design can be performed using normal EC5 design values for the strength and stiffness of n~ecl~anical joints.
References Ceccotti, A,, cdilor, (1989). Slruclural Behnviour o f Timber Constructions in Scislnic Zones. Proc, of the rclcvnr~tCEC DG III - Univ, of Flor~cnccWorkshop. Fiorcncc, I ~ a l y . EUROCODE 8 (1993). Constructions irt sci~nlicregions. Ui~derpreparation by TC 250 of CBN,
STEPlEUROFORTECH - an initiative under the EU Comelt Progra~nine
C 1719
Brussels, Belgium.
RILEM TC 109 TSA (1994). Timber structures in scisrnic regions. RILEM Statc-of-tile-Art Report. Material and Structures 27: 157-184. Yasumura, M. el al. (1988). Experiment on a three-storied wooden framc building subjected to horizontal load, lo: International Timber Engineering Confcrcncc, Seattle, 1988: 262-275.
STEPIEUROFORTECH - an initiative under the EU Comctt Programme
Fire resistance of joints STEP lcclurc C i 9 kl. l-iar11 Zivilingcnicur liir Bauwcscn
Objective To present the methods used Tor calculating the fire resislance of timber connections.
Prerequisite A13 Beliaviour of timber and wood-based materials in fire
Summary Tile relevant cl~aptersfrom EC5: Part 1-2 "General rules - Supplementary rules For structural fire design" are described. Calculation methods are given relating to standard fire exposure (standard temperature-time curve) for unprotected joints with side members of wood and wilh external steel plates as well as for protected joints. Special attention is paid 10 connections for which an increase of the cross-section is necessary. In one example fire-test results and calculations are conlpared.
General The load-bearing capacity of fasteners made of fire-unprotected steel is considerably weal\-end by heat. All-round protection with wood or wood based materials offers resistance to heat, thereby protecting the steel members. The area of the non-protected surfaces of the steel-members is therefore relevant to the fire-behaviour of fasteners made of steel. Figure 1 describes the relevant yield point \.I'of steel dependent on tile temperature 6.
--0,ZO - -
_----
*-
4.
0,oo 0
i
260
'
I,
400
660
*-..I--L. 800
"C
1000
Relevar~tyield poi111'1' of steel itj c f e / ~ a ~ d e ~011t c the e
ECS: Part 1-2: 4.5. t
The following section relates to joints between members itt standard fire exposure situations Formed using nails, bolts, dowels, screws, connectors and steel plates. The EC5-rules are valid only for joints under lateral load and deal only with forces which are transmitted symmetrically (see EC5: Part I - 1: Figure 6.2.1, g-k). This restriction in EC5 has in practice often to be replaced by a logical, mathematical derivation of the fire resistance, e.g. in order to determine the fire resistance of limber structures with single connections (see Figure 2).
STEWEUROFORTECI-I - an initialivc undcr the EU Comctt Programme
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Unprotected joints with side members of wood EC5: Part 1-2: 4.5.2
Assuming that joints and their fasteners are designed according to EC5: Part 1 - I , tlley may be expected to display a fire resistance of I5 minutes (R15). Unless otherwise stated all joints sl~ouldbe designed for RI5. For a fire resistance of more than 15 minutes (more than R15) the end arid edge distances should be increased by a, (see EC5: Part 1-2: Figure 4.4) which should be taken as:
EC5: Part 1-2: Equation 4.2
ell =
Po &,,, -
15)
in
rrltll
(1)
where
%r.:, Po
is the required standard fire resistance in minutes. is the charring rate according EC5: Part 1-2: (see STEP lecture A 13, Table I).
A
+
-
-
The minimum end and edge distances a, and a, of fasteners should be increased by the extra distance equal to a/. No extra distance is required if the Following condition for n, and a, is satisfied: EC5: Part 1-2: Equation 4.7
Equation 4.8
Tlie total thickness r , of conditions:
he side members should satisfy tlie following
Equatiort 4.4
where Equation 4.6
The I7re resistance R30 is satisfied if
Ttie requirements of Equation (7) may be satisfied by increasing the number of fasteners in a joint, by cl~oosingfasteners with a higher- load-carrying capacity or. by using coverings.
.
For fire resistance between R30 and R60,il [nay be determined by: EC5: Part 1-2: Equation 4.9
, -
(8) -4
Deterrtlincttio~tof tire q30-~raIl~t'~ If the conditions in ECS: Part 1-2: Table 4.2, 4.3 are fulfilled, ?I,, could be taken as:
-
STEPIEUROFORTECM an iniliutivc undcr thc EU Comcit Programme
--
-
EC5: Part 1-2: Tabic 4.2
11,,, = 0,50 for unprotected wood-to-wood joints with nails, non-projecting dowels and connectors with nails.
EC5: Park 1-2: Tiiblc 4.3
1 1 ~=~ )I ,OO for unprotected steel-to-wood joints with nails or non-projecting dowels.
EC5: Part 1-2: Tnblc 4.2, ~ n b i c4.3
= 0,45 for unprotected wood-to-wood and steel-to-wood joints with bolts and connectors with bolls.
,,,TI
~ to be calculated according to EC5: Part 1-2: Annex 3. Otherwise 1 1 has
Unprotected joints with steel plates as middle members 30 or 60 niinutes fire resistance (R30 or RGO) of a joint with unprotected steel plates as middle members (tliicltness 2 2 lnnt) is achieved if the widths B,, of the steel plates given in Table 1 are observed.
unprotected edges in general
EC5: Part 1-2: Anncx 8 5
tinprotected edges on one or two sides
Table 1
bVidrh b,, q/ s1er.1plo1e.y :r.~jitlr rrrlpr-otecred er1gc.s.
Figrtrz. 2
S~eelplate joirrrs - defitritiort of b,,,
Sunimarising, the classification of unprotected joints with side members of wood under R30 or R60 calls for a new design of the joint with n ti~ilesthe number of actions (Table 2) than at normal tenlperature design.
11
=
N,l,n
--.
E,,
=
1 resp.
1 -
'1 3n
'1 .I
wood-to-wood joints nails, dowels
RGO
1
-= 0,20
steel-to-wood joints nails, clowels
bolts
5,OO
SI'EP/EUROFORTECI~I- iln initiiltivc under the EU Comctt Programme
C 1 913
Unprotected joints with external steel piates ECS: Part 1-2: 4.5.3
For unprotected external steel plates which are directly exposed only on one side, the Fire resistance R30 is satisfied for a plate thickness of: I,
26
for joints with
ttttll
11
I0,45
Otherwise calciilalion according to EC3, structural fire design, is required.
Example for an unprotected joint with side members of wood Test member, tensile joint with dowels:
I
t
Figiit'e 3
1,,,,,,
.
I
I
.
.
I
.
1 I
.
= 80 ttrttt t2 = 200 V I I I J (1 = 26 mln = 340 trrttr (10 tntn thick plrrg on encl~side) r ,,,,,,,,.= 70 nrtr~
dowel:
coniferous timber C 27: .h,o.k = 16 N / ~ I I I ~ I ' .f;,.a = 360 Nhltrn'
distances:
aI
strength class:
('3~
ECS: Pan 1-1:Tnhle h.6n
.
I
Tetrsile joitll 1vi1l1side ttrunbels of ~~,t,no~i nrrci rlo\r~cI.sitr doti61~'S I I ~ N I ; t,
prEN 338: Table I
.
I
= 140 mtn = I60 mnz
pk = 370 IiC:/t~l" N,,, =
85 rntlr
nlinimurn distances: =, , , = 7 d = 7 36 = 182 nzt?l '~.c.nnn = 3 d = 3 26 = 78 trun l I t l
Derernzirtarion o j clt.sig~~ loali-cclr-ryirrg c ~ c i p ~ c ioff y ttun?zctl tenll?et-cltr.4,z. a) design load-carrying capacity of dowels
Characteristic values:
(1
EC5: Part 1-1:6.5.1.2~
MYqk= 0 , 8 j ; , , k G
C 19/4
STEPIEUROFORTECII
=
26
O,8 -360 .-
G
"
=
844Ntt2
- an inilintivc under the EU Con~cllProgri~mrnc
Design values: EC5:Part 1 - I : 6.2.11
EC5: Pari 1-1:6.2.lj
-
.6,,1.11
-
I
I
0,8
=
Ynr
'
9*7
=
12,1 Nl,,lm
2
I ,3
Design load-carrying capacity per shear plane per dowel:
Design load-carrying capacity of dowels:
b) design load-carrying capacity of side members: = 2 e220 - 8 0 A,,,, = 2 26 8 0 A,,,,, = 35200 - 41 60
cross-section area area of dowel holes net area k~llfN!sl
EC5: Part 1- 1 : 6.2.11
f;..,k
A
=
OS8
'I6
=
9,85~/111m2
1-3
AI
Rdsrlr= An?,Jsr.ll = 31 000 . 9,85 = 306 kN
ECS: Part 1-2:4.5.2
= 35200 rni11~ = 41 60 tnm2 = 31000 nlttl'
...sin...side member
Veriji'cation of 60 nti~zntcs.fi~a resistarzce nccotdirlg to EC5: Port 1-2 1
= 60 ntirt = 1 ,o
-
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Determination OF qlo: EC5: Pirrt 1-2: Table 4.2
1,,,,,, = 2 tl,2.r,cr,r +. tl = 2 . 106 + 200
,', - -'z - - ~200 7 , d
==,
cl
26
4121tltt11 150 111111
6 9 2 6
condition not [net
Determination of qa in accordance with Annex B:
Determination of F
(7):
=
v(~,:
verification:
9 .
Vj,,2 5 7760 0,903 5 0,25
This condition is not FulfiIled, therefore a new joint has to be designed: ti?
t1,3
= 15 dowels in 3 rows t,,3,,lc,,c = 100 ~ 1 1 1 1 (without: plugs)
--
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New dimensions of the side members and ~niddlemember: brr,,,,= 6,,,,, = 2 (95 + 90) = 370 r r i r ? ~ l.,rrr,2 = 2 (1 60 + 4 - 140 + I GO) = 1760 rvm +
cross-section area area of dowel holes net area
verifications:
A2 A,, Aner,~
Ell - -------
.
= 74 000 mm' = I5 600 ianz' = 58 400 l?vn'
= 139
- = 0,246
Rd.Q~~~f.l
Fire-test result of the test member:
-
= 2 .370 100 = 6 .26 100 = 74 000 - 15 600
565
time of fire resistance: 62 minutes at 1; = 94600 N (test member 6)
Increased timber consumption of the side members only:
Based on the reduced strength and stiffness method for members (given in EC5: Part 1-2: 4.2 and Annex A) a logical, mathematical derivation of fire resistance could be applied to joints; the reduced cross-section must be checked. Care must be taken to maice sure that the steel temperature within the joint does not increase more than 600 "C. This is confirmed not only by tests on dowelled frame corners but also by calculation models. Hence it can be verified that the cross-section does not need to be increased more than the necessary dimensions for the load-carrying capacity for design at normal temperature.
EC5: Part 1-2: Equarion 2.7
Verification for R60 based on the red1l1tct.dstrer~gthnrtd stiJyi7ess rrrethocl Ei,,= Ik Ed = 0'6 ' 139 = 83,4 kN ...in most cases of civil engineering less than 0,G. where 5 = 0,6
EC5: Part 1-2: Tabfc 3.1
charring rate
p,, = 0,8 na?th/,nin
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remaining cross-section: b, = 220 - 2 .0,8 . GO = 124 r~un t, = 80 - 0,8 60 = 32 nlm cross-section area A = 2 . 124 32 = 7940 t?zrn2 area of dowel holes A,,,, = 2 .26 32 = 1660 nrm' net area A,,, = 7940 - 1660 = 6280 nzm' perimeter = 2 (2 3 2 + 124) = 376 rrlni p,
-
.
a) design load-carrying capacity of dowels: Cllaracteristic value of the embedding strength: = 19,7 N~IZ~IZ~
Xk=
Reduction factor: EC5: Par1 1-2: Equation A.5
knrod3,, -- 0
-
0 1 - p, 330 A
-- 1-10'..
1 376 =0,856 330 7940 a
kf = 1,25
Coefficient for solid timber: Partial safety factor:
I'M,
= 1to
Design values: EC5: Par1 1-2: Equation 2.1
4 = 0,856 -
19 7 .1,25 .-1-= 21,I Nlmm2 Ynrj I ,O MA,:,= k My,,= 0,3 . 767000 = 230 Ni~r assumption: k = 0,3 (Figure I: steel temperature: 600 "C) jj,l,l,= k !{,, k,
Design load-carrying capacity per shear plane per dowel: ECS: part 1-1: 6.2.1g
R,,,
r , d = 21,t . 32
.26 = 17500 N
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Design load-carrying capacity of dowels:
R L , ,,,,, , = 2 . 4 - 12,8 = 102 kN verification: E J ; ~ < RL~,,,,~,,,:~ 83,4 < 102
b) design toad-carrying capacity of side members: verification: = 83 400 A '~(i
,,
n
%I
< <
6280
krill,
&,o.~, L,o,k 16 kf - = 0,856 - I,25 .Yai,r 1 ,O
Protected joints EC5: Pnrt 1-2:
4.5.4
Joints are considered protected if the fasteners are covered with protective plugs or wood or wood-based panels with minimum af according to EC5: Pmt 1-2: Figure 4.5 ( a) and b) glued-in plugs c) protective panels). For fastening of protective boards the edge distance of fasteners should be at least equal to af according to Equation (I).
Concluding summary
-
The method given in EC5: Part 1-2, at its present stage is distinctly on the "safe side" and consequentely is an uneconomical design for fire resistances of R30 and even more so for R60.
-
One test member, a tensile joint wjth dowels and side members of timber, was checked according to EC5: Part 1-1. Subsequently this member was calculated using two different methods for a fire resisrance of 60 minutes (R6O). The tirst method reldes to calculation for joints (Part 1-2), the second to the structural fire design of members. The first method results in extremely oversized members because of the q-value applied. 1 for RGO is only a quarter of that for R30, which is equal to 1 in the example. Therefore the load-carrying capacity in nomlal temperature design has to be four times that necessary - four times the number of dowels and tripling of the timber dimensions.
-
A comparison of the resuIts show that the second method is in very good agreement with the fire-test results.
-
Classification of timber members into fire resistance classes requires that not only the single components they are built from, but also the connections should satisfy the requirements for fire resistance. It is often necessary to direct attention to joints and their fasteners, because the dimensions of the members depend in most of cases, under normal temperature-conditions, on tile design of their connections.
Notation $WO
required standard fire resistance in minutes as contrast to thickness t .
Subscripts <,tlr,l,*
dowel. side member, middle member.
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