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These relationships are given in equations (6.21) and (6.22) of 6.3.2 in EC5.

When the member is short and stocky, buckling will not occur and failure will be due to the timber failing under stress and in EC5 this applies when both Xrei y and AreljZ are <0.3. Inserting the characteristic values for /c 0,kand E0.05 given in BS EN 338:2003 [3] for softwood species into equation (5.3), when Xrel = 0.3, the maximum slenderness ratio of the member will be between 16.2 and 18.1, the range being slightly greater for hardwood species. For a member having a rectangular cross-section with a least lateral dimension, b, the effective length will be obtained from LE = b|\/12A.rel resulting in column lengths of 4.66b and 5.23b respectively. It is clear from these results that for most practical situations the design condition is likely to be based on a buckling failure rather than a stress failure.

When Xrel y and/or A.rel,z exceed 0.3, the effect of member buckling has to be taken into account. From equation (5.3), at Xrel = 0.3, the factor of safety between failure by buckling under the Euler buckling load and failure by direct compression is approximately 11. This is based on a theoretically idealised condition assuming no defects or out of alignment imperfections, and pure elastic behaviour applies.

According to Blass [4], under axial load the stress-strain curve for timber will be as indicated in Figure 5.5 and using these relationships, taking into account the effects of increase in slenderness ratio and member imperfections, the buckling strength of compression members has been modelled [4]. The evaluation was based on a second-order plastic iterative analysis that incorporated the yield behaviour of timber and the consequent change in member stiffness, and the design guidance in EC5 on members subjected to axial compression has been developed from this work.

From the analyses, for different strengths of timber a plot of the characteristic buckling strength against slenderness ratio was obtained, and a typical plot showing the strength reduction as the slenderness ratio increased is shown in Figure 5.6.

By covering the range of timber strength class properties and associated geometric imperfections, the buckling strengths at varying slenderness ratios were obtained for timber (and glued-laminated members). From these results, an approximate curve has been derived in terms of Xrel (or Xrel z) from which a buckling strength reduction factor, kc y (or kc,z), called the instability factor in EC5, is obtained for solid timber,

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