A Signature Curve for Cold-Formed Channel Sections in Pure Shear (No. R919)

Abstract

Thin-walled sections in compression and/or bending may undergo one of the three modes of local, distortional or overall (Euler) buckling, or combinations of these. The Semi-Analytical Finite Strip Method (SAFSM) developed by YK Cheung has been widely used in computer software (THIN-WALL, CUFSM) to develop the signature curve of the buckling stress versus buckling half-wavelength for a thin-walled section under compression or bending to allow identification of these modes. The minimum points on the signature curve are now used in the Direct Strength Method (DSM) of design of cold-formed sections in the American Specification and Australian/New Zealand Standard for cold-formed steel structures. Plank and Wittrick (1974) included shear in the SAFSM theory for calculating the stiffness and stability matrices by using complex mathematics. The complex mathematics is needed to allow for the phase shifts in the buckling modes (eigenvectors) for sections under shear. This paper summarises the theory then applies it to the buckling of channel sections in pure shear. Signature curves for shear are developed for channel sections and compared with classical solutions, and those produced by the Spline Finite Strip Method (SFSM) previously published by the authors. The effect of including a web stiffener on the signature curve and buckling modes is demonstrated.