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My/Muy

Fig. 5.12. Axial force-moment interaction curve for bi-axial bending when either Xrel,y or •^rei,z > 0.3, and with factor km applied to the ratio of moments about the z-z axis.

member cannot occur or is prevented (e.g. members whose cross-section is square or circular, or the relative slenderness ratio for bending is <0.75). If lateral torsional instability can occur, the equations are valid when the member can only be subjected to bending about the weak axis.

Under this condition, because axial load buckling effects have to be taken into account, no benefit is taken of any plastic behaviour in the member and the ultimate load is achieved when the material reaches its failure strength in the extreme fibre. This is in line with the elastic theory interaction approach shown in Figure 5.10a.

With this approach, the EC5 procedure for the design of members subjected to combined bending and axial compression when Xrel y and/or Xrel z exceed 0.3 is as shown in Figure 5.12 and requires:

kc,z/c,0,d /m,y,d /m,z,d where the functions remain as previously defined and, as with equations (5.19) and (5.20), where size factors are relevant, the bending strengths about the y-y and z-z axes can differ.

As in 5.4.1(a), equations (5.21) and (5.22) are only valid for situations where lateral torsional buckling of the member will not or cannot occur, otherwise the member can only be subjected to bending about the weak axis.

In the case where there is axial loading and bending only about the major y-y axis, the strength validation equations will reduce to equation (5.23):

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