timber lesson 2

8/10/2019 Timber Lesson 2

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DESIGN IN TIMBERTO MS 544 PART2


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COURSE OUTCOME

At the end of the lecture student will be able to;

Understand design philosophy of permissiblestress design

Design flexural member


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INTRODUCTION

Timber can be used in a range ofstructural application (like piers),

heavy civil work (like bridge and piles)

or domestic housing (like roofs andfloors)

Timber structures are loaded with

different type of loadings ie flexural,compression, tension shear etc.

So it is important to know the

allowable and permissible stress of


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Different materials have differentstrength properties.

Permissible stress are the properties

of material under bending,compression, tension etc.

These stresses together with the

loading criteria will form the basis ofdesign for the various timber

components.


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Design of timber members

In accordance with

BS5268: The structural use of timber

or

MS544 Part2: Code of Practice for

Structural use of Timbers: Permissible

stress design of solid timber


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Design philosophy

Permissible stress design derived on a statistical basis and

deformations are limited.

Design based on the allowable and

permissible stress of the materials Elastic theory is used to analyse structures

under various loading conditions to give the

worst design case. Then timber sections are chosen so that

permissible stresses are not exceeded atany point of the structure.


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MS544 Part 2 and BS5268 is based on

permissible stress design (or elastic

design) rather than limit state design (as

in BS5950).

This means that in practice that a partial

safety factor is applied only to materialproperties not to the loading.


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Working stress design

Permissible stress design

Allowable stress design

Elastic method design

Has been used by designers and

engineers in timber construction and

this MS544 and BS5268 adopted this

design


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Working stress design

The adequacy of a structure ischecked by calculating the working

stress to maximum expected loads

and comparing them with thepermissible stresses.

The permissible stress is equal to the

failure stress design methods tosuccessful structures at that time


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The safety factors for the newmaterials were estimated in

comparison with those for traditional

materials by taking into account thenature for the new material and its

uncertainty or variability

Elastic method of design has formedthe basis of structural codes and

standards for most of the century.


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Structural timber design may be

based on either The grade stress for the individual

species for dry exposure or wet

condition given in Table 1 and 2 pg 5

16. The grade stresses for the strength

group SG for dry exposure condition

given in Table 4 pg 18


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Timber grade stresses

1. Since timber which is naturally occurringand has varying range of properties, its

grade has to be classified accordingly. Its

properties are affected by conditions of

growth(temperature, wet or dry season,

wind etc) and therefore its strength varies

2. Strength is also determined by the

process of various strength reducing

characteristics such as knots, slope of

grain, fissures and wane


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3. Strength Group, SG is defined as the

classification of timber based on

particular value of grade stresses Timber having similar strength and

stiffness properties have been group

together for simplicity in design procedure(Table 4 pg 18)


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Definition of stresses

a) Basic stress

The stress which can safely be

permanently sustained by timber

containing no strength reducing

characteristic

Includeduration of loading

- size and shape of actual

member

- factors of safety

- variabilit of stren th


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b) Grade stress

The stress which can safely be

permanently sustained by timber of aparticular grade.

c)Green stress

A stress applicable to timber having amoisture content exceeding 19%

d) Dry stress

A stress applicable to timber having amoisture content not exceeding 19%


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Derivation of Permissible

Stresses

Strength

properties ofsmall clear

specimens

Grade stress(individual species)

Characteristic stress

Basic stress

Permissible stress

Grade stress

(strength group)


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Derivation of Basic Stresses

Test results (for at least 30 samples)for each species were tabulated andthe average strength value (stress) is

calculated using the followingequation:

X =

X= strength value

N = number of samples

n

X

n

33.2X X


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Basic stress

Basic stress: = X2.33

F.S

Where F.S is factor of safety

k


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Safety factor

A safety factor is applied and it is usually assumed thatthis factor will cover such items as accidentaloverloading, assumptions made during design anddesign accuracies together with errors in workmanship,etc.

Property Reduction factor Formula

Bending and shear 2.5 X2.33

2.5

Compression

parallel to grain

1.5 X2.33

1.5

Compression

perpendicular tograin

1.3 X2.33

1.3

Mean modulus of

elasticity

1.0 X

Minimum modulus

of elasticity

1.0 X2.33


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Grade stress

The stress can be safely permanentlysustained by timber at a particular grade

They are derived from individual species

and are governed by the effect of visiblegross features of defect such as knots,

sloping of grains, fissures, etc.

Reduction strength expressed in terms of

strength ratio i.e of strength of piece oftimber with defects to the strength of the

same piece without defect.


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Grade stress

Grade stress = Basic stress x reductionfactor

Reduction factor for grade stress taking into account of varying

amounts of defects based on basic stress and this gives three stress

grades of timbers namely Select, Standard and Common

Property Select

%

Standard

%

Common

%

Bending, tension and

compression parallel tograin

80 63 50

Compression

perpendicular to grain

85 80 75

Shear 72 56 45

Modulus of elasticity Same as the basic value for all grades

Table 2.0 Strength ratio


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Permissible stress

The stress which can be safely besustained by a structural component

under the particular condition of service

and loading Permissible stress is the final stage at

which all allowances are made for the

particular condition of services and

loadingPermissible stress = grade stress x modification factor

= grade stress x K1xK2xK3xK4xK5xK6


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Modification factors


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DURATION OF LOADING

Modification factor K1Table 5 MS 544:2001 Part 1

Duration of loading Value of K1

Long term (dead + permanent imposed)

Medium term (dead + temporary imposed)

Short term (dead + imposed + wind)

Very short term (dead + imposed + wind)

1.00

1.25

1.50

1.75


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LOAD SHARING FACTOR (Clause 10 of the MS544:2001 Part 2)

Load sharing means a system whereby a number of members act together tosupport a common load.

For load sharing , modification factor K2is 1.1 and the mean value of modulus ofelasticity may be used.

(For non-load sharing, there is no increase in the grade stress and the minimum Eis used).

For load sharing system to be applicable the following must be satisfied:

I. There must be at least four or more members

II. The spacing of members must not be more than 610 mm apart with adequate

provision of lateral distribution of loadIII. The stresses due to dead load or permanent load are not more than 60% of

stresses due to the total design load.

Members include rafters, joists, trusses or wall studs with adequate provision forlateral distribution of loads by means of purlins, binders, boarding etc.

Emeanshould be used to calculate deflections and displacements.


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LENGTH AND POSITION OF BEARING

For bearing < 150mm in length located 75mm or more from theend of member, grade stress should be multiplied by

modification factor K3.

75mm Bearing less than

or more 150mm or more

Length of bearing (mm) 10 15 25 40 50 75 100


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NOTCHING FACTOR

Beam with notch on the top edge Beam with notch on the underside

For a he

K4=

For a >he

K4= 1.0

K4= he/h

Beam with notch on the top edge Beam with notch in the underside

2

)(

e

e

h

ahahh e


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FORM FACTOR

K5= 1.8 for solid circular sectionK5= 1.41 for solid square sections loaded on a diagonal

DEPTH FACTOR

For depth of beams > 300mm, the grade bending stressesshould be multiplied by modification factor K6

For solid and glue laminated beams,

K6= 0.81


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Design of bending members

e.g, girders, stringers, bearers, purlinsand joist

In design, all follow the same design

principles as member subjected tobending forces

Beam may be supported as freely

supported, supported by intermediatesupports, fixed end with other end free

(cantilever) etc.


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Design considerations

The main design considerations for flexural members are:1. Bending stress and prevention of lateral buckling

2. Deflection

3. Shear stress

4. Bearing stress.

The cross-sectional properties of all flexural members have to satisfyelastic strength and service load requirements. In general, bendingis the most critical criterion for medium-span beams, deflection forlong span beams and shear for heavily loaded short-span beams. Inpractice, design checks are carried out for all criteria listed above.

The permissible stress value is calculated as the product of the

grade stress and the appropriate modification factors for particularservice and loading conditions, and is usually compared with theapplied stress in a member or part of a component in structuraldesign calculations. In general:

Permissible stress ( = grade stress K-factors ) appliedstress


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Bending stress and prevention of

lateral buckling

The design of timber beams in flexure requires the application of the elastictheory of bending as express by:

=My

I

The termI/yis referred to as section modulus and is denoted by

Z. The applied bending stress about the major (x-x) axis ofthe beam (say) (see Fig. 4.1), is calculated from:

My M

Ixx Zxx=

h

y

x x

y

b

Where:

m,adm,//=applied bending stress (in N/mm2)

M= maximum bending moment (in Nmm)

Zxx= section modulus about its major (x-x) axis

(in mm3). For rectangular sections


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Design considerations

Includes all as mention above

Additions:

Depth factor (Sec 11.6 pg 23)

Effective span Le

Clause 11.3 pg 22 recommends that the span of flexural

members should be taken as the distance between thecentres of bearing

Beam or joist

Clear span

Effective span

Span to centres of actual bearings


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Depth factor, K6

The grade bending stress given in Tables 1,2 and4 of MS544 : Part 2 apply to beams having adepth, h, of 300 mm (Clause 11.6). For otherdepths of beams, the grade bending stressshould be multiplied by the depth modification

factor, K6 where:

for h 72 mm, K6 = 1.17

for 72 < h< 300 mm, K6

= (300 )0.11

h

for h> 300 mm, K6 = 0.81h2+ 92

300 h2+ 56800


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Depth to breath ratio

I xx/ I yy 1 4 9 16 25 36 49

d/b 1 2 3 4 5 6 7

Note:forasimplerectangular beamtheIxx/Iyyratioissimplythesquareof

thed/bratio.

ateral Stability of built in beams

Beamswithlargedepthtothicknessratiosareatriskofbucklingunderbendingforces.BS5268uses

theratioofIxx(2ndmomentofareaofsectionaboutneutralaxis)toI yy(2ndmomentofareaofthesection

perpendiculartotheneutralaxis)toidentifythesupportrequirementssuchthatthereisnoriskofbucking


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Stiffness and deflection (Sec 11.7 pg 24)

Stiffness is related to deflection. When a member issaid to be stiff, it means that it is able to resist

deflection to a certain extend depending on the

degree of stiffness.

Deflection limits are decided through practical

experience and arbitrarily fixed.

For floors when fully loaded should not exceed

0.003 x span

In purlins, deflection should not exceed 0.005 x

span

Members may be pre-cambered to account for the

deflection under full dead or permanent load and in

this case the deflection under live or intermittent

load should not exceed 0.003 of the span


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In calculating the deflection, either the meanvalue or the minimum value of modulus ofelasticity (E) is used.

The mean value Emeanis used for roof joist, floorjoist and other systems where transversedistribution of load is achieved and where thestress induced by the dead load or permanentload is not more than 60% of the permissible

stress induced by the full design load.( the latterstatement is included because where thepermanent load is a large proportion of the totalload, will induce creep.

The minimum value of Emin is used for principals,

binders and other components which actsalone.


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Procedure in beam design

Design steps:

i. Calculate the loads to be applied

ii. Effective span, Le (Clause 11.3 pg 22)

iii. Find m,g,// = bending stress (grade

stresses) parallel to grain from table 1-4

M < MRWhere M: design moment

MR: moment resistance

MR = m,adm,// , // Zxx

Z = section modulus

m,adm,// = permissible bending stress // to grain

difi ti f t ( K1 K8)

timber lesson 2

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