Simplified expressions for elastic lateral torsional buckling of wooden beams

A beam finite element formulation is developed for the elastic lateral torsional buckling analysis of wood beams with rectangular cross-sections. The formulation accounts for moment gradient, load height, and pre-buckling deformation effects. The validity of the finite element and underlying variational principle is established through comparisons with critical moments obtained by 3D FEA simulations and experimental results. The validated variational expression is then adopted to develop approximate analytical expressions that separately characterize the effects of moment gradient, partial twist restraints that may exist at beam-ends, load height, and pre-buckling deformation effects. Dimensionless coefficients were formulated to characterize each effect for simple beams and cantilevers under common loading scenarios. The derived coefficients are then consolidated into a unified framework that accounts for all effects combined to predict the elastic lateral torsional buckling capacity of wooden beams.