Energy‐based Equations for Local and Anti‐symmetric Distortional Modes of Lipped Channel Columns

Abstract

AbstractThis paper presents an energy‐based approach to obtain the critical length and stress of local (L) and anti‐symmetric distortional (D2) modes of simply supported lipped channel columns. For each mode, deformed shapes are assumed and the Rayleigh Quotient Method is applied to obtain analytical expressions for the buckling stress. The shape functions adopted for local buckling ensure compatibility of rotation and bending moments at wall junctions and at the stiffener's free end. For the D2 mode, equilibrium of bending and twisting moments are considered leading to an analytical derivation of the mode's warping stress distribution. While for L mode it is not feasible to obtain a closed expression for the critical length (but a simple length testing procedure is sufficient), for D2 mode an expression dependent on geometrical properties is derived. The developed equations for L and D2 modes are validated against CUFSM's pure local modes and GBTul's pure D2 mode (mode 6 in GBTul convention) respectively. For sections with flange‐to‐web width ratio, bf/bw, ranging from 0.2 to 1.0 and lip‐to‐web width ratio, bs/bw, from 0.1 to 0.4 the average ratios obtained for critical stresses (σcr,reference/σcr,proposed) are 1.014±0.019 and 1.011 ± 0.014 for L and D2 modes respectively.