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* The ratio between the effective length lef and the design span I is valid for a beam loaded at its centre of gravity. If the load is applied at the compression face of the beam, lef should be increased by 2h (where h is the depth of the beam) and, for a load at the tension face of the beam, may be decreased by 0.5h.

t For this case, at the fixed end the cantilever is restrained laterally in position, restrained torsionally and prevented from rotating in plan while free to move laterally and rotate at the other end.

* The ratio between the effective length lef and the design span I is valid for a beam loaded at its centre of gravity. If the load is applied at the compression face of the beam, lef should be increased by 2h (where h is the depth of the beam) and, for a load at the tension face of the beam, may be decreased by 0.5h.

t For this case, at the fixed end the cantilever is restrained laterally in position, restrained torsionally and prevented from rotating in plan while free to move laterally and rotate at the other end.

To link the buckling strength of a beam, am>crit, to its bending strength, /m k, the following relationship is used in EC5:

(^rel,m) am,crit fm,k and is defined in EC5, equation (6.30), as follows:

V am, crit where Areljm is defined as the relative slenderness for bending.

Equation (4.10) is only valid when the critical bending stress is less than or equal to the elastic limit of the material. Beyond this limit, the relationship has to be modified to take account of the effect of inelastic behaviour of the material and to set a minimum value for the relative slenderness below which lateral torsional buckling will not arise.

In EC5 a value of Xrel m = 0.75 has been adopted as the limit below which the beam will be stiff enough not to buckle laterally and for all values less than 0.75 the design condition to be met is that the maximum bending stress in the section will not exceed

Table 4.3 Value of kcrit for beams with an initial deviation from straightness no greater than the limits set in EC5,10.2

Value of kcrit

Value of relative slenderness Xrel m

0 0

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