Bowing Effect on Elastic Stability of Frames under Primary Bending Moments

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Abstract
A refined method of analysis for the elastic stability of rigid frames considering the prebuckling deformations due to primary bending moment is proposed. It differs from the method presented originally by Chwalla, and later by Mansur et al. and Lu, in that the proposed method considers precisely the bowing effect in the determination of axial displacements and leads to a symmetric tangent stiffness matrix. The Chwalla method ignores this effect, leading to an asymmetric matrix. Based on the results of our numerical studies, the nonlinear behavior of portal frames is classified into three types (i.e. bifurcation, limit‐load instability, and monotonic increasing) according to the values of structural parameters. Further, it is found that the primary bending moment does not always reduce the buckling load of portal frames. These results are quite different from those obtained previously by the Chwalla method.

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