Timber Engineering Step-1

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

Contents

Preface

AcknowIedgements

AII~/ZOI'S

National Representative Organisations

. .

Contract im~zpleinentat~

. . . , . . . . . . .

A

Basis of design and material properties

A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A1

l

A 12 A13 A14 A 15 AXG 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

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

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

T M D A

-

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.

Eurocode

5 is the result of tremendous cooperative efforts involving people from industry

and

most timber researchers in Europe (with substantia1 contributions 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~rgen

Larsen,

Chairman, Eurocode 5 Drafting Committee

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~armonisation of 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

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~nenral du 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, D-

80335 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-76 128 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, D- 80797 Miinchen, Germany

R,

G~rlacher,

Universitiit Karlsruhe, Lel~rstuhl Er Ingenieurholzbau und

Baukonstruktionen, Postfach 6980, D-76 128 Karlsruhe, Gemany

D.R. Griffiths, University of Surrey, Dept. of Civil Engineering, Guifd ford, Surrey GU2 SXN, United

Kingdom

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

. . . -.

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

Nerh

erlcznds

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

Porfi

4

gal

NliO: Laborat6rio Nacional de Engenl~aria Civil, 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

:

TRAD

A, High Wyconlbe , Buckinghanlsl~ire

Supporting organisations: Timber Research and Development Association; Gang- Nail Systems Ltd.; Brighton University; University of Nottingham; University

of

Surrey; Meyer International; SCOTFI; institute of Wood Science; MiTek Industries Ltd

.

; Sin~pson Strongtie International Incorporated; James Donaldson & Son; Donaldson Timber Engineering

Contract implementation

Centrum

Hout,

STEP/Euroforiech Secretariat, 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, Be1 field, Dub1 in 4, f reland

The following loadslload combinations are possible, see Figure 4:

-

_{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 ~nornent it1 the columns.

Communication 94lC 62/01

-

each of them referring to one of the essential requirements listed.

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;

-

European technical approvals;

-

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~ational standard(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

-

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 Duration' Exarnples A,,,,, for

Class of loading Service Classcs

1 & 2 3 Permanent more than 10 years self weight 0,60 0,50 Long-term 6 months

-

10 years storage 0,70 0.55 Medium-term 1 week

-

6 months irnposcd load 0,80 O,G5 Short-tcnn less than one week snow" and wind 0,90 0,70

Instantaneous accidental load I , 10 0,90

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~s und k,,,,,! for solid rinrbcr attrl glr~lcim.

"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, cernent- bonded 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

E N V

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.

Action \lf~ '\'I K!

Imposed load in buildings 0.7- 1 ,O 0,5-0,9 0,3-0,8

Snow loads 0,6 0 2 0,O

Wind loads 096 0,s 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-oss- sections, deviations from straigl~tness, usually correspond to the values specified in the design or to nominal values.

Actions

Design

values

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.

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-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 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.

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~miulative probability 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~nated by statistical ntctlrods, attd in the future srtclt rt~etlrods rrtay 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.

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.

Safety verification

-

The

partial coefficient method

In the Eurocodes the safety verification is based on the partial coefficient method described below.

Fig~trc 2 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 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 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.

.' Tffc prubalrility of faillrrc carr be esti~tiated by 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~r sysren~s used in practice.

Action \I'o \If, 'lfz

Imposed load i n buildings 0.7- 1 ,O 0,s-0,9 0,3-0,8

Snow loads 0,6 0 2 0,O

Wind loads 0 6 0,s 0,o

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~nctrical data

Actions

The ctlaracteristic geo~netrical values, such as spans, ditnellsions of cross- sections, deviations from straightness, usually correspond to the values specified in the design or to no~ninal values.

Design values

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~itude and direction of an actiot~.

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

~h

Q,.

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 combinationsJ

.

'' Thc sin~plificd cxpressioris are on tlie i~nsnfc side for Q, icss than 30-50%1 of Q,.

"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 A 15).

-

CENfrC

1

12 currently has a worlc programme that includes around 80 itenis covering particleboards, oriented strand boards, fibreboards, plywood, cetnent-

bonded 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~rocode 5.

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, i s . , 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~nplement these 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 Duration" Bxatnples k,,,,, for Class of loading Service Classes

1 & 2 3

Permnncnt more than 10 years self weight 0,60 0,50 Long-term 6 months

-

10 ycars storage 0,70 0,55

Mediurn-term 1 week

-

6 months irnposcd load 0,80 0,65

S hort-tenn less than one week snow" and wind 0,90 0,70

Instantaneous accidental load 1.10 0,90

a The Load-duration Classcs are charac~eriscd by 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,,,tfbr solid tittrber ar~d gltllnnr.

Communication 94/C 62/01

-

each of them referring to one of the essential requirements listed.

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;

-

European technical approvals;

-

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~lal standard(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~ations are 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~ation gives 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.

Actions

on structures

STEP lcciurc A3

objectives

P. Racllcr To give an overview of the classification of the actions applied to structures. To

CUST Civil Engineering define the cl~aracteristic value for the n~osl colnrnon actions applied to buildings. Blnisc Pascal University TO 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~ents the lecture.

Introduction

For

the intended col~slruction work, 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~nption may 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} wile11 subjected 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~nic amplification 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.

General concepts

-

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

I 1 to 5 Temporary structures

2 25 Replaccablc structul-al elements

3 50 Buildings and common structurcs

4 100 Bridges or other engineering works

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:

-

-

_{persistet~t ,sitiratio~r.s} related 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

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:

-

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

-

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*i4 and upper value G,,,,. Assuming a Gaussian distribution for G, these vaIues are given by:

G,,,

=

G,,,,, ( 1

-

1,64

COV

) ; G,, =

G,,,,,,

( 1 + 1,64 COV ) (1)

The characteristic variable actions Q, are related to a given return period of

N

years, corresponding to a probability of exceedance p =

1/N

in 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

X

QN

= 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 frequenl value (yf,Q&, which is exceeded for 5 percent of the time,}

-

_{the quasi-permanent value (I~I~Q,), which is related to the time average value.} In practice, the values Gk, Qh (I@,) and

(\yrQk)

are usually considered when 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 deformations) are assessed considering the values G, and

(y2Qk)

on the loading side, 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

ECI: Part 2-1

A 314

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~nplify tlie 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~ate may 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~Jfloor a~.eas in 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.

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 QL is related to the sl~ort-tern1 duration class.

Category Type of area q I ) (2, (IcN)

General 2 2

Floors, accessil~le roufis: A stairs

3 2

Balconies 4 2

General 3 2

Stairs,balconies 4 3

C General 5 4

areas with tables 3 4

areas with fixed seats 4 4

possibility ol' co~~centralions 5 7

D Shops 5 4

Department store 5 7

E General 5 7

slope: < 20'

Norr-accessible roofY: 13 _{z 40"}

Table 3 I~rlposed loods on floors arrd r-oo/i it; 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 ~ e hand rails (0,S to 1,2 111). Table 4 defines the characteristic

values of the line action q,.

Category A B C,D Public events in C or D

Tablc 4 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.}

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 15 30 GO

a ("1

Figrire 2 Strorv shcri~c coeflcients 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-mngettterrts orr 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 short- term load duratiori class. The structural response could be considered as the

-

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:

" r c j = CDIR CTEM CALT " r c h ~ 1111s (4)

where 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.

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.

I.

B

1.

4,

1

1.

4,.

1.

b,,, A< l Ic/>,,, //1<2

(4 (11) (4

Figure LC De$tzitioa oJ rlra rcfcrance lreiglrf ,;,, .for btrildi/rgs: p1m1 ntrd cross\t7irtd

dir~re~r.siol~ (a) rrlalls ( b f .flat ( c ) pirched ((d) c~trcl vnril~ed ( e ) roojk.

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 , ) =

K,

In

f

max( 2,"

zmin)

1

zol

( 6 )

where z,, is the roughness length,

z,,,,,

is

the height of' the ground layer where the wind velocity is