Chapter 7 Timber Part 1

1Structural Timber Design

Steel and Timber DesignSteel and Timber Design

BFC43003 BFC43003

Department of Structural and Materials Engineering Department of Structural and Materials Engineering

Faculty of Civil and Environmental EngineeringFaculty of Civil and Environmental Engineering

University University TunTun Hussein Hussein OnnOnn MalaysiaMalaysia

Introduction

Timber is unique in its structure and mode of growth, results in characteristics and properties which are distinct and more complex than those of other common structural materials such as concrete, steel and brickwork.

Some of characteristic which influence design and are specific to timber are:

a) the moisture content.

b) the difference in strength when loads are applied parallel and

perpendicular to grain direction.

c) the duration of application of the load.

d) the method adopted for strength grading of the timber.

As a live growing material, every identified tree has a name based on botanical distinction (MS 544: Part 2: 2001:Table A1).

The design codes, however, adopt a classification based on stress grading.

2Applications

The Stadthaus, Hoxton, London: Tallest

timber building (9-story).

The University of British Columbia Earth

Sciences Building: A five-story wood

structure.

Applications

3Nelson Marlborough

Institute of Technology, New

Zealand: Stand even during

earthquake 4th September

2010.

Applications

Physical Properties

Physical properties affecting strength of wood:

Moisture content

It is essential that wood is dried or seasoned under a controlled condition before being used. With controlled

seasoning, moisture is expelled from the cell walls and the

timber shrinks.

This process enables gain of strength.

In MS 544: Part 1:2001, the strength properties or stresses are given as wet stresses and dry stresses based on moisture

content.

a) Moisture content > 19% wet stresses

b) Moisture content < 19% dry stresses

4Physical Properties

Specific gravity

A nominal specific gravity can be determined based on the volume of wood at the time of test and its weigh when ovendried.

Specific gravity is a good indicator of the strength of wood. It also shows that amount of wood substance a piece of wood contains.

Defects in timber

Seasoning defects twisting, cupping, bowing and cracking caused by uneven exposure to drying agents.

Nature defects the presence of knots are often accompanied by decrease in the physical properties of timber such as the tensile and compressive strength.

Slope of grain stress parallel and perpendicular to grain

Modulus of elasticity this give stiffness and deflection factor of wood.

Timber Design Procedure

Permissible stress design

When using permissible stress design, the margin of safety is introduce by considering structural behaviour under

working/service load conditions and comparing the stresses

thereby induced with the permissible value :

safety offactor

stress failure loads by working induced Stress

5Timber Design Procedure

Stresses:

= applied bending stress perpendicular to the grain

= permissible bending stress perpendicular to the

grain

= applied compressive stress parallel to the grain

= permissible compressive stress parallel to the grain

= applied shear stress

Whilst not given in the clause, the grade stress, is often used. Grade stress is defined as the stress which can safely be

permanently sustained by material of a specific section size

and of a particular strength class, or species and grade.

The grade stress is divided into four grades in MS 544, i.e. Select-80%, Standard-63%, Common-50% and Basic.

||,,ac

,,am

,,admm

||,,admc

a

g


Modification factor

Modification factors are multiplied with grade stresses to obtain

the design permissible stresses. Modification factor for solid

timber are K1 K9.

K1 Duration of loading

K2 Load sharing

K3 Length and position of bearing

K4 Notched ends

K5 Form factor

K6 Depth factor

K7 Minimum MOE for trimmer joist and lintels

K8 Compression members

K9 Effective length of spaced column

ngadm K=


Duration of loading, K1 (Cl 9)

The strength of a member is dependent upon the time of loading.

Wood has a unique structural property in that it can support

higher stresses if the loads are applied for a short period of time.

Group of load duration:

a) Long term no increase in the stress (DL + LLpermanent, ie. for

design floor) : K1=1.0

b) Medium term increment of 25% in stresses is allowed (DL+PL

for floor or DL+LL for roof design) : K1=1.25

c) Short term increment of 50% wind load of 15sec Class C

Building : K1=1.50

d) Very short increment of 75% wind load 35 sec Class A and B

: K1=1.75



Loading Sharing System, K2 (Cl.10)

1) 4 or more elements in a system acting together

2) Spacing no more 610 mm c/c

3) Lateral load distribution

When all criteria are fullfilled, therefore K2=1.1

Emean is used for K2=1.1, and Emin for K2=1.0 (no load sharing)



Bearing Stress, K3 (Table 6)

At any bearing on the side of timber, permissible stress in compression perpendicular to the grain is depended on the

length and position of the bearing.

For a bearing length less than 150m long located 75mm or more from end of a member as shown, K3 should be

determined according Table 6.



Shear at Notched End, K4 (Cl. 11.4)

Square corner notches at the ends of flexural member cause a stress concentration which should be allowed for as follow:


Form factor, K5 (Cl. 11.5)

Grade bending stresses apply to solid timber members of rectangular section, K5 = 1.0 and for other shapes of cross

section, as folllow:

K5=1.18 for solid circular sections

K5=1.41 for solid square section loaded on diagonal

Depth factor, K6 (Cl. 11.6)

The grade bending stress is applied to timber having a depth of h>300mm. The grade bending stress should be multiplied by the depth modification factor, K6 where:

for solid and glued laminated beams.

+

+=

56800

9230081.0

2

2

6h

hK

10


Lateral stability (Cl. 11.8)

The depth to breadth ratio of solid and laminated beams of rectangular section should be checked to ensure that there is

no risk of buckling under design load. Alternatively the

recommendation of Table 7 should be followed:

Solid Timber Beam Design

Beams are the most commonly used structural elements, for

example as floor joists, and as trimmer joists around opening,

rafters, etc.

The crosssection of a timber beam may be one of a number of

frequently used sections as those indicated in figure below.

11


The principal considerations in the design of all beams are:

i) Bending

ii) Shear

iii) Bearing

iv) Deflection

v) Lateral stability

The size of timber beams may be governed by the requirements:

The elastic section modulus (Z), to limit the bending stresses and ensure that neither lateral torsional buckling of the compression flange nor fracture of the tension flange induce failure

The cross section, to ensure that the vertical and/or horizontal shear stresses do not induce failure

The second moment of area, to limit the deflection induced by bending and/or shear action to acceptable limits.


Generally, the bearing area actually provided at the ends of a

beam is much larger than is necessary to satisfy the permissible

bearing stress requirement.

Lateral stability should be checked, it is frequently provided to

the compression flange of a beam by nailing of floor boards, roof

decking.

Most timber beams are designed as simply supported with

effective span.

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i) Bending

The applied bending stress is determined using simple elastic

bending theory:

where:

= maximum applied bending stress parallel to the grain

= maximum applied bending moment

= elastic section modulus about the axis of bending (xx)

The permissible bending stress is given by:

where:

= grade bending stress parallel to the grain

Z

M a||,, =am

||,,am

aM

Z

6521||,,||,, KKKKgmadmm =

||,, gm

||,,||,, admmam

Solid Timber Beam Design ii) Shear

The grade and hence permissible stresses given in the MS relate to the max. shear stress parallel to the grain for a particular species or strength class.

In solid beams of rectangular crosssection the maximum horizontal shear stress occurs at the level of the neutral axis, and is equal to 1.5 times the average value.

where:

= maximum applied horizontal shear stress

= maximum applied vertical shear stress

= crosssectional area

The magnitude of must not exceed given by:

where: = grade stress parallel to the grain

A

Va

5.1||, =

421||,||, KKKgadm =

||,g

||,a

V

A

||,a ||,adm

||,||, adma

13

Solid Timber Beam Design For other type of cross sections:

where:

= the shear parallel to gain stress at level being considered

= the vertical external shear

= the area of beam above the level at which is being cal.

= the distance from the neutral axis of the beam to the centre of the area Au

= the complete second moment of area of the beam at crosssection being considered

= the breadth of the beam at the level at which is being cal.

If is evaluated, this gives the total shear force parallel to

grain above the level being considered per unit length of beam.

x

uv

bI

yAF=

xuv IyAF /

uAvF

xI

b

y


iii) Bearing

The behaviour of timber under the action of concentrated loads,

e.g at positions of support, is complex and influenced by both the

length and location of the bearings, as shown in Figures (a) and (b).

The grade stress for compression perpendicular to the grain is used

to determine the permissible bearing stress.

14


The actual bearing stress is determined from :

where:

= applied concentrated load

= actual bearing area provided

bac

A

P=,, ,,,, admcac

P

bA

Solid Timber Beam Design The actual bearing area is the net area of the contact surface and

allowance must be made for any reduction in the width of bearing due to wane.

In timber engineering, pieces of wood with wane are frequently not used and consequently this can often be ignored.

15


iv) Deflection

In the absence of any special requirements for deflection in

building, it is customary to adopt an arbitrary limiting value

based on experience and good practice.

The combined deflection due to m (bending) and s (shear)

should not exceed (0.003x span) or 14mm whichever is the

lesser (Cl.11.7).

These limitation are intended to minimize the risk of

cracking/damage to brittle finishes (plaster ceilings), unsightly

sagging or undesirable vibration under dynamic loads.

The calculated deflection for solid beams is usually based on

the bending action of the beam ignoring the effects of shear

deflection (this is considered when designing plyweb beams).

( ) mmLsmtotal 14;003.0+


To determine m:

16


To determine m:


To determine s:

The maximum shear deflection induced in single span simply

supported beam of either rectangular or square crosssection

may be determined from following equation:

where:

= the cross section area of the beam

= the maximum bending moment in the beam

AE

Ms

max2.19=

A

maxM

17


iv) Lateral Stability

A beam in which the depth and length are large in comparison

to the width (i.e. a slender crosssection) may fail at a lower

bending stress value due to lateral torsional buckling.

Unbraced length

Buckling shape


The critical value of bending moment which induces this type of failure s dependent on several parameters, such as :

i) the relative crosssection dimensions

ii) shape of beam

iii) modulus of elasticity

iv) shear modulus

v) span

vi) degree of lateral restraint to the compression flange

vii) type of loading

This problem is accommodated in BS 5628Part 2: 2001 by using a simplified approach based on practical experience, in which limiting ratios of maximum depth to maximum breadth area given relating differing restraint conditions. In Table 7 MS 544: Part 2, values of limiting ratios are given varying from 2 when no restraint is provided to maximum 7 for beams in which the top and bottom edges are fully laterally restrained.

18

Example 7.1 : Timber beam design

e actual bearing area is the net area of the contact surface and allowance must be made for any reduction in the width of bearing due to wane.


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Chapter 7 Timber Part 1

Documents

strength of wood

stress grading

induced stress

timber shrinks

structural timber designsteel

physical properties

strength properties

slope of grain stress