| Conventional analysis and the design of steel frameworks are performed using the assumption that the connections are either fully rigid or ideally pinned. However, as is evident from experimental observations, all beam-to-column connections used in current practice possess some stiffness that falls between the two extreme cases of fully rigid and ideally pinned. In order to estimate or predict the behavior of steel frame correctly, it is necessary to take the nonlinear characteristics of beam-to-column connections into account. Based on the current nonlinear analysis and calculation methods and beam-column element model of frame as well as the principle of functional minimum potential energy, the nonlinear element stiffness matrixes, which incorporate the effects of geometric nonlinear and end connection flexibility, are derived. As application, a general program of nonlinear analysis for semi-rigid steel frame is drawn up.According to comparison between rigid steel frame and semi-rigid steel frame, lateral displacements and rotations of joints of semi-rigid frame are more than that of rigid frame. The connection flexibility influences not only displacements but also distribution of moments of frame.Moments of joints of semi-rigid frame are more than that of semi-rigid frame that include more flexible connections. By contraries, lateral displacements are more in frame that include more flexible connections.Finally, the formulas of moment of semi-rigid beam are derived. And some practical-approximate methods for elastic analysis of semi-rigid steel frame are presented.
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