Effect of shear restraint of the lateral torsional buckling resistance

It is known that the lateral torsional buckling resistance of a simple supported beam can be significantly increased if its compressed flange is connected adequately to a trapezoidal decking.

Eurocode allows to consider the compressed flange as fully restrained laterally, if the following condition is met (EN 1993-1-1 BB2.):

If the condition is not met, Eurocode doesn’t provide too much guidance how the contribution of a less rigid sheeting can be considered.

The following graph shows the effect of shear stiffness on the ultimate load capacity of a 10 m long simple supported IPE purlin loaded at the level of the top flange. It is assumed that several of these purlins are uses with 3 meters of distance between their centers.

The blue line in the graph shows the ultimate load carried by this purlin, in function of the actual shear stiffness. Shear stiffness of the sheeting measured by “S” is shown on the horizonal axis and a reduction factor applied on the plastic moment resistances is shown on the vertical axis.

The graph has been built with the help of Consteel software, using 7DOF beam finite elements. Such beam elements are adequate to consider the presence of any shear restraint.

In case of S=0, the value is calculated without any contribution. By increasing the shear stiffness the line approaches the maximum value of 1, when no reduction of the plastic moment resistance due to lateral torsional buckling is required. In other words when lateral buckling checks can be disregarded.