Cross-sectional deformations of rectangular hollow sections in bending: Part II — analytical models

Abstract

In this part, analytical models to predict the deflection of cross-sectional members such as flanges and webs are developed. The models are based on the deformation theory of plasticity along with the energy method, using appropriate shape functions capable of including the restraining effect of adjacent members. The present method provides explicit solutions of cross-sectional deformations prior to buckling, onset of buckling, as well as post-buckling deformations at different stages of bending. The predictions show that the suck-in of the tensile flange is closely related to geometry parameters, particularly the flange width. Plastic anisotropy appears to be the most significant material parameter. The width-to-thickness ratio tends to be the governing parameter with respect to buckling of the inner (compressive) flange. Also, the strain hardening of the material has a major effect on onset of buckling as well as post buckling deformations. Upon continued bending after buckling, the wavy deformation of the inner flange develops more rapidly than the more uniform deformation of the outer (tensile) flange. For relatively compact sections, however, the deformation mode of the compressive flange resembles that of the tensile flange without any typical buckling waves. There are also obvious interactions between deformations of different members. Comparing the theoretical predictions with the experimental results presented in Part I, a reasonably good agreement was found.