Lateral Torsional Buckling of Wooden Beams with Mid-Span Lateral Bracing

Abstract

An analytical and numerical investigation is conducted for the lateral torsional buckling analysis of wooden beam with a mid-span lateral brace subjected to symmetrically distributed loading. Two models are developed; one for the case of a rigid brace and another one for the case of a flexible brace. The analytical solutions are based on the principle of stationary potential energy and a Fourier expansion of the buckling displacement fields and bending moments. The validity of both models are verified against 3D finite element analyses in ABAQUS. Where applicable, verifications were also conducted against available solutions from previous studies. Parametric studies were conducted to investigate the effect of geometric and material parameters on the critical moments. The results indicate the presence of two separate groups of potential buckling modes, symmetric and anti-symmetric, with fundamentally different behavioural characteristics. The governing buckling mode is shown to depend on the bracing height, load height and lateral brace stiffness. The study shows that beyond a certain threshold bracing height, the critical moment is governed by the antisymmetric mode of buckling. Also, above a certain optimum bracing stiffness, no increase is observed in the critical moments. The models developed are used to construct a comprehensive database of parametric investigations which are then employed for developing simplified equations for determining the threshold heights, associated critical moments, and optimum stiffness.