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Unformatted text preview: Introduction to Design in Timber
Wood is a very versatile raw material and is widely used in construction. Timber can be
used in a range of structural applications including marine works: construction of wharves (e.g.
fenders), piers, cofferdams; heavy civil works: bridges, piles, shoring, pylons; domestic
housing: roofs, floors, partitions; shuttering for precast and in situ concrete; falsework for brick
or stone construction.
Timber is naturally occurring. This makes it a very difficult material to characterize and
partly accounts for the wide variation in the strength of timber. However, this problem has
now been largely overcome by specifying stress graded timber. The suitability of a particular
timber type for any given purpose will depend upon various factors such as performance, cost,
appearance and availability. The task of the structural engineer has been simplified, however,
by grouping timber species into nine strength classes for which typical design parameters, e.g.
grade stresses and moduli of elasticity, have been produced.
Design of timber elements is normally carried out in accordance with BS 5268: Structural
Use of Timber. The design principles which will be outlined here are based on the contents of
Part 2 of the code (i.e. Part 2: Code of Practice for Permissible Stress Design, Materials and
Workmanship). It should therefore be assumed that all future references to BS 5268 refer
exclusively to Part 2. BS 5268 is based on permissible stress design rather than limit state
design. This means in practice that a partial safety factor is applied only to material properties,
i.e. the permissible stress and not the loading.
Before discussing the design process in detail, the following sections will expand on the
more general aspects mentioned above, namely:
1. stress grading 3. permissible stress 2. grade stress and strength class
The strength of timber is a function of several parameters including the moisture content,
density, size of specimen and the presence of various strength-reducing characteristics such as
knots, slope of grain, fissures and wane.
The first step for assessing the strength of timber involves grading structural size timber.
Grading may be carried out visually or mechanically. The latter approach offers the advantage
of greater economy in the use of timber since it takes into account the density of timber which
significantly influences its strength. Mechanical stress grading is based on the fact that there is
a direct relationship between the modulus of elasticity measured over a relatively short span,
i.e. stiffness, and bending strength. The stiffness is assessed non-destructively by feeding
individual pieces of timber through a series of rollers on a machine which automatically
applies small transverse loads over short successive lengths and measures the deflections.
These are compared with permitted deflections appropriate to given stress grades and the
machine automatically assesses the grade of the timber over its entire length.
The grading system consists of two visual grades: General Structural (GS) and Special
Structural (SS), and four machine grades: MGS, MSS, M75 and M50. The MGS and MSS
grades correspond directly with the visual GS and SS grades respectively. The structural
strength of the four machine grades occur in the order: M75 > MSS > M50 > MGS. The
(visually or mechanically) graded timber is then subject to short-term load tests. The results are
used to determine the characteristic stress, which is taken to be the value below which not
1 more than 5% of test results fall. Finally, the grade stress is obtained by dividing the
characteristic stress by a reduction factor which includes adjustments for a standard depth of
specimen of 300 mm, duration of load and a factor of safety.
Grade stress and strength class
There are nine strength classes, SC1-SC9, with SC1 having the lowest strength
characteristics. The grade stresses and moduli of elasticity associated with each strength class
can be read from tables. Structural timber design is normally based on strength classes SC3 to
SC5. These classes display good structural properties and are both plentiful and cheap.
The grade stresses were derived assuming particular conditions of service and loading. In
order to take account of the actual conditions that individual members will be subject to during
their design life, the grade stresses are multiplied by modification factors known as K-factors.
The modified stresses are termed permissible stresses.
BS 5268 lists over 70 K-factors. The commonly encountered K-factors are namely:
K1: Wet exposure geometrical properties factor K5: Notched end factor K2: Wet exposure strength characteristics factor K7: Depth factor K3: Duration of loading factor K8: Load-sharing system factor Geometrical Properties, K1
Variations in the moisture content of timber will
cause it to shrink or swell (Figure 1). The geometrical
properties of timber sections are normally quoted for the
dry exposure condition. This is assumed to be when the
moisture content of timber is 18% or below. The
geometrical properties for use in designing for the wet
exposure conditions are obtained by multiplying the dry
exposure value by a suitable modification factor K1. Dry
Wet Figure 1. Effect of
wet exposure Strength Characteristics, K2
The strength characteristics of timber also vary with the moisture content. Where wet
conditions exist, the grade stresses and moduli of elasticity for timber exposed to dry
conditions are multiplied by a modification factor K2.
Duration of Loading, K3
The normal grade stresses apply to long-term loading. Where the applied loads will act for
shorter durations, e.g. snow and wind, the grade stresses can be increased by the modification
factor K3 that takes into account various load combinations. 2 Notched Ends, K5 Notches at the ends of flexural members (Figure 2) will result in high shear concentrations
which may cause structural failure and must therefore be taken into account during design. In
notched members the grade shear stresses parallel to the grain are multiplied by a modification
he he h h Figure 2. Notched beams Depth Factor, K7 The normal grade bending stresses only apply to timber sections having a depth h of 300
mm. For other depths of beams, the grade bending stresses are multiplied by the depth factor
Load-Sharing Systems, K8 The normal grade stresses apply to individual members, e.g. isolated beams and columns,
rather than assemblies. When four or more members such as rafters, joists or wall studs,
spaced a maximum of 610 mm centre to centre act together to resist a common load, the grade
stress should be multiplied by a load-sharing factor K8 which has a value of 1.1.
Symbols (BS 5268)
b breadth of beam i radius of gyration h depth of beam I second moment of area A total cross-sectional area Z section modulus Bending
L effective span σm,a,|| applied bending stress parallel to grain M design moment σm,g,|| grade bending stress parallel to grain MR moment of resistance σm,adm,|| permissible bending stress parallel to grain Deflection
δt total deflection δm bending deflection δv shear deflection δp permissible deflection E
G 3 modulus of elasticity
mean modulus of elasticity
minimum modulus of elasticity
shear modulus Shear
τadm Fv design shear force τa applied shear stress parallel to grain τg grade shear stress parallel to grain permissible shear stress parallel to
F bearing force σc,a,⊥ applied compression stress perpendicular to grain σc,g,⊥ grade compression stress perpendicular to grain lb length of bearing σc,adm,⊥ permissible bending stress perpendicular to grain
Design of Flexural members Beams, rafters and joists are examples of flexural members. All calculations relating to their
design are based on the effective span and principally involve consideration of the following
1. bending 4. shear 2. deflection 5. bearing 3. lateral torsional buckling
However deflection is usually critical for long-span beams and shear for heavily loaded shortspan beams. For simply supported beams, the effective span is normally taken as the distance
between the centres of bearings.
Bending If flexural members are not to fail in bending, the design moment (M) must not exceed the
moment of resistance (MR):
M ≤ MR = σm,adm,|| Zxx where σm,adm,|| is the permissible bending stress parallel to the grain and Zxx the section
modulus. For rectangular sections with breadth of section b and depth of section d
Zxx = bd 2 / 6 where. The permissible bending stress is calculated by multiplying the grade bending stress,
σm,g,||, by any relevant K-factors:
σm,adm,|| = σm,g,|| K1 K2 K3 K7 K8 (as appropriate) Deflection Excessive deflection of flexural members may result in damage to surfacing materials,
ceilings, partitions and finishes, and to the functional needs as well as aesthetic requirements. 4 Such damage can be avoided if the total deflection, δt, of the member when fully loaded does
not exceed the permissible deflection, δp:
δt ≤ δp = 0.003 × span
≤ 14 mm (for spans over 4.67 m) The total deflection, δt, is the summation of the bending deflection, δm, plus the shear
δt = δm + δv
Lateral Buckling If flexural members are not effectively laterally restrained, it is possible for the member to
twist sideways before developing its full flexural strength, thereby causing it to fail in bending,
shear or deflection. This phenomenon is called lateral buckling and can be avoided by ensuring
that the depth to breadth ratio (d/b) is not excessive.
Shear stress parallel to the grain If flexural members are not to fail in shear, the applied shear stress parallel to the grain, τa,
should not exceed the permissible shear stress, τadm:
τa ≤ τadm = τg K1 K2 K3 K5 K8 (as appropriate) where τg is the grade shear parallel to grain. For a beam with a rectangular cross-section,
the maximum applied shear stress occurs at the neutral axis and is given by
τa = 1.5 Fv / A where Fv is the applied maximum vertical shear force and A the cross-sectional area.
Bearing Perpendicular to Grain Bearing failure may arise in flexural members which are supported at their ends on narrow
beams or wall plates. Such failures can be avoided by ensuring that the applied bearing stress,
σc,a,⊥ never exceeds the permissible compression stress perpendicular to the grain, σc,adm,⊥:
σc,a,⊥ ≤ σc,adm,⊥ = σc,g,⊥ K3 K8 (as appropriate) where σc,g,⊥ is the grade compression stress
perpendicular to the grain. The applied bearing stress
(Figure 3) is given by h σc,a,⊥ = F / (b lb ) where F is the bearing force, b the breadth of section
and lb the bearing length. Figure 3. Bearing stress Further details on timber design are available in "Design of Structural Elements, concrete,
steelwork, masonry and timber design to British Standards and Eurocodes, C. Arya, 1994". 5 ...
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This note was uploaded on 12/01/2010 for the course CIVL 2007 taught by Professor Profchai during the Spring '10 term at HKU.
- Spring '10