Timber - Introduction to Design in Timber Wood is a very...

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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 Stress grading 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. Permissible stresses 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 factor K5. 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 K7. 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) Geometrical Properties 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 Emean Emin 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 grain Bearing 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 aspects: 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 deflection, δv: 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 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.

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