Plastic Torsional Buckling of Cruciform Compression Members

In this paper the plastic torsional buckling of a cruciform column is revisited. The interest in this classical problem resurfaced from a practical application in the area of seismic protection of structures. The theoretical challenges associated with this problem emerge from the "paradoxial" differences between the plastic buckling strength that results from the total deformation and the incremental theories of plasticity. The paper shows that when the flanges of the column are not perfectly straight, the incremental theory of plasticity predicts that at the onset of plastic torsional buckling, the shear stress and the shear strain are related with the tangent shear modulus. The analysis presented herein involves a small-strain theory, examines the column at its slightly deformed configuration, and results are obtained with hand calculations. Experimental evidence supporting the theoretical findings is presented.