Computation of shear buckling stress of thin-walled sections using constrained spline finite strip method

Abstract

The direct strength method (DSM) design for shear incorporates the elastic shear buckling stress of the cross-section to evaluate the ultimate shear capacity of thin-walled members. To calculate the shear buckling stress using the finite strip method (FSM), the shape functions for longitudinal interpolation are an issue, while capturing the phase change of displacements along the plate strip. This paper presents a novel constrained spline finite strip method (cSFSM) that eliminates the phase change of displacements. Although constrained buckling analysis for shear stresses is reported in the literature based on FSM, the present study is unique in determining pure buckling stresses for simply supported members subjected to shear edge stress. The formulation also provides an accurate representation of the variation of shear stress along the longitudinal and transverse directions of the plate. Hence, coarse discretization of cross-section is sufficient to obtain the accurate shear buckling stress. The formulation is demonstrated on channel sections with lips subjected to shear edge stresses, and elastic buckling stresses are compared with results available in the literature and also with the finite element method (FEM). Illustrative examples are presented on lipped channel members with different end conditions and longitudinal stiffeners on flanges and webs, to calculate the pure elastic buckling stresses under shear edge stresses. The calculation of buckling stresses for members subjected to longitudinal variation of shear and flexural stresses is also presented to calculate coupled and uncoupled buckling stresses.