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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Relative slendemess ratio

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Relative slendemess ratio

Fig. 4.6. The value of £crit for different values of Xrei>1

The effect of deviation from straightness is also relevant within this range of relative slenderness however the adoption of linear behaviour as defined in equation (4.12) is a conservative approach and will offset the strength reduction effect arising from this imperfection.

A graphical representation of kcrit plotted against the relative slenderness ratio for bending, Xrel m, is shown in Figure 4.6.

To demonstrate that lateral buckling of the beam will not occur, the bending stress in the beam must be less than or equal to the reduced bending strength, i.e.

where am>d is the design bending stress (i.e. the moment on the section divided by the section modulus), fm,d is the design bending strength, kcrit is a factor taking account of the reduced bending strength due to lateral torsional buckling.

The bending strength is derived from the characteristic bending strength in accordance with equation (4.5), i.e.

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