Abstract
An efficient nonlinear approach is presented in this paper in matrix form for the analysis of the static and dynamic response of steel frames subjected to horizontal loads arising from wind or earthquakes. This approach is particularly suitable for developing a computer program for evaluating ultimate capacities of buildings in steel frames. The stiffness matrix equations for basic elements of steel frames are first outlined in the paper. The effects of geometric nonlinearity, material nonlinearity and shear deformation are considered in the proposed stiffness matrices for beam and column elements. Next, the stiffness equations of the extended column elements with panels attached and extended hybrid beam elements attached to both connections and panels are established to consider the effects of shear deformation of panels and flexibility of beam-to-column connections. Then the nonlinear behaviour of an arbitrary steel frame with flexible connections and deformable panels can be analysed by simply assembling all the stiffness matrix equations of the panel elements, extended column elements and extended hybrid beam elements of the frame to form the overall stiffness equation of the entire frame. Finally, the robustness, accuracy and efficiency of the proposed approach are demonstrated through several numerical examples.
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