Inelastic torsional-flexural behavior and the three-dimensional analysis of steel frames

A method is developed for the three-dimensional analysis of frames. The objective is to establish an efficient and straightforward method for treating the inelastic out-of-plane behavior of steel members and frames, i.e., the common problems of lateral buckling of beams, the torsional-flexural buckling of beam-columns, and the stability of the systems of which they are components. Spread of plasticity in members under axial load, biaxial bending, and non-uniform torsion is considered. The method is called a "quasi-plastic hinge" approach since it provides the accuracy of distributed plasticity methods with the computational efficiency of the conventional plastic hinge methods.; The formulation involves a three-dimensional beam-column element with consideration of non-uniform torsion. Gradual plastification of the cross section is modeled in terms of stress resultant-strain relationships using nonlinear functions that describe moment-curvature and axial force-strain behavior. These functions are calibrated to numerical data of a representative wide-flange steel section, obtained by a detailed cross section analysis. Flexibility coefficients of the element are developed by integrating the nonlinear stress resultant-strain functions along the length. Effects of torsion on yielding of the cross section are included by considering the longitudinal stresses caused by bimoments arising from warping restraint. Geometric nonlinearities are taken into account by using a geometric stiffness matrix that has provisions for both finite rotation effects and warping. Residual stresses and geometric imperfections are also considered.; The quasi-plastic hinge model has been incorporated in CU-STAND, a static analysis and design interactive computer graphics program developed at Cornell University. Features of CU-STAND have been extended to accommodate this model and to improve the nonlinear solution techniques. Verification of the model has been carried out through comparisons with the results of detailed analytical and experimental tests on small frames and isolated members subjected to out-of-plane and spreading plasticity effects. The ability of the model to analyze frames susceptible to out-of-plane instabilities is demonstrated.