A theoretical study of the inelastic stability of nonproportionally loaded steel beam-columns and flexibly-connected frames is conducted. Specifically, solution techniques are formulated to predict the nonlinear behavior of cross sections, spatial beam-columns, and nonsway plane frames under the combined influence of imperfections, flexible connections, and nonproportional loads. A set of new inelastic slope-deflection equations for imperfect members are derived and their use illustrated through in-depth studies of flexibly-connected portal and two-bay two-story frames. These equations are derived from a system of nonlinear ordinary differential equations. The member studies are carried out using a second-order finite-difference solution to a set of nonlinear equilibrium equations, and coupled to a tangent stiffness procedure for cross sections. The majority of the theoretical studies are carried out on a conventional sequential computer. Efficient concurrent computational algorithms are also presented for biaxial bending and column stability problems. Results are obtained using a multiprocessor computer known as the Finite Element Machine. A critical appraisal of the conventional tangent modulus approach is presented in light of the analysis which includes elastic unloading of the material. It is found that the tangent modulus approach results in a fictitious ductile behavior. Furthermore, is is also realized that there is a dramatic difference in the nonlinear behavior between the proportionally and nonproportionally loaded structures. It is also observed that the proportionally loaded structures lead to rather unconservative peak loads. Additionally, members as integral parts of a frame may exhibit significantly different load-deformation behavior as compared to that of isolated members. The study on members and frames shows that nonproportional loads have a significant effect on their behavior and strength.
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