The behaviour of pin-ended flange elements in compression

• An “exact” solution is presented for the post-buckling behaviour of pin-ended flange elements.
• Expressions are derived for the post-buckling axial stiffness including the change in stiffness under load and asymptotic values of axial stiffness.
• The ability of elliptic functions to concentrate curvatures and twistatures near the centre of the element is elucidated.
• Strength curves based on first-yield are derived and compared with solutions based on simplified assumptions that ignore secondary warping.

Stowell's solution [1] for the buckling behaviour of flange elements in compression was premised on the assumption that the element was fixed against flexural rotations at the ends, a condition representing relatively thick elements for which the thickness dimension is adequate to prevent rotations. This paper presents a solution similar to Stowell's which is applicable to pin-ended flange elements. Aspects not considered in Stowell's work, such as the use of elliptic functions to describe the gradual change of mode shape from sinusoidal to essentially linear, and the gradual and asymptotic changes in axial rigidity in the post-buckling range are described in the paper. The paper also presents comparisons between the behaviour of pin-ended and fixed-ended flange elements. Finally, simple strength equations for flange elements in uniform compression based on the first yield criterion are derived.