Fig. 5.9. Eccentric loading.

The behaviour of a member under pure axial compression is discussed in 5.3.1 and, where lateral torsional instability cannot occur, two failure modes can arise:

(a) When both Xrel y and Xrel z are <0.3, buckling behaviour is not relevant and failure will be based on the compressive strength of the member.

(b) If either Xrei y or Xreljz is >0.3, buckling can arise and failure will be based on the compression strength of the member multiplied by the associated instability factor, i.e. kcy (or kc>z).

The design requirements in EC5 for the above conditions are as follows:

As there is no strength reduction due to buckling under this condition, EC5 takes advantage of the strength benefits associated with the plastic behaviour of timber when subjected to compression stresses.

Figure 5.10 shows interaction diagrams for a member subjected to combined bending moment and axial compression based on the application of elastic and plastic theory. Under elastic theory, the failure condition will occur when the combined compression stress in the member reaches the compressive strength of the material. When plastic theory applies, the material yields when it reaches the compressive strength allowing the stress in the section to extend over the surface and enhance its strength.

With the elastic theory approach, the sum of the combined axial and bending stress to strength ratios cannot exceed unity. With the plastic theory solution however, the axial stress to axial strength ratio becomes a squared function enabling the member to take a higher value of bending stress to bending strength ratio for the same value of axial stress to strength ratio. For example, with an axial stress to strength ratio of 0.51, the strength increase when using plastic theory rather than elastic theory is approximately 50%.

Because of the plastic behaviour of timber under compression, EC5 adopts the plastic theory approach when both Xrel y and A.rel,z are <0.3, and the interaction diagram for the design of members subjected to combined bending and axial compression with factor

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