Buckling Studies of Cold-Formed Channels in Shear using the Semi-Analytical Finite Strip and Spline Finite Strip Methods (No. R932)

Abstract

The finite strip method is computationally efficient for the static, stability, post-buckling and vibration analyses of thin-walled structures. The finite strip employs simple polynomial functions to describe the transverse variations of the displacements and continuous harmonic series functions or discontinuous spline functions to describe the longitudinal variation of the strip displacements. While the Semi-Analytical Finite Strip Method (SAFSM) generally uses the longitudinal harmonic series to satisfy the boundary conditions at the longitudinal ends and to give compatibility between strips, the Spline Finite Strip Method (SFSM) employs local spline functions in the longitudinal direction to account for different boundary conditions. The Semi-Analytical Finite Strip Method (SAFSM) has been widely used in computer software (THIN-WALL, CUFSM) to develop the signature curves of the buckling stress versus buckling half-wavelength for a thinwalled section under compression or bending to allow identification of buckling modes. Recently, a complex mathematical technique has been applied in the SAFSM theory to allow for the case of shear. The shear buckling modes produced include local, distortional and overall with phase shifts along the member. This report provides the analysis and comparison between the new SAFSM development for shear and the SFSM for whole plain channel sections including flanges and lips where the sections are loaded in pure shear parallel to the web. The main variables are the flange widths and lip sizes. For the longitudinal direction, the SAFSM determines the shear signature curves versus buckling half-wavelength and the SFSM determines the elastic shear buckling stresses versus the member lengths of the whole channel section. The SAFSM is limited to a single half-wavelength whereas the SFSM can include multiple buckles as seen in the wellknown garland curve. The report demonstrates the potential for coupling between multiple short halfwavelength modes in shear and longer single half-wavelength as may occur in distortional buckling.