Qr Method And Program Designs For Nonlinear Dynamic Analysis Of Plane Steel Frames With Semi-Rigid Connections

Because of its high strength and ductility, steel frames have wide application in the building structure. Tests showed that all of the beam-column connections have certainly semi-rigid. Because of the thin of the bar section and its low lateral stiffness, under the action of strong wind or earthquake, it appears obvious non-linear dynamic response, and brings great difficulties to precise calculation of the structure, and the efficiency is very low by using the finite element analysis software.This paper considers the influence of the semi-rigid of beam-column connections and geometric nonlinearity and material nonlinearity, to deal with the nonlinear dynamic analysis of the plane steel frames with semi-rigid connections based on the QR method. Main work is as follows:(1) To derive the general beam element stiffness matrix and mass matrix;(2) The free vibration of steel frame are analyzed, and the impact on the free vibration characteristics of rotation stiffness of steel frame with beam-to-column semi-rigid connections is studied;(3) To establish the calculation format of QR method for the elastic dynamic analysis of plane steel frames with semi-rigid connections, and the elastic dynamic response of steel frame is analyzed;(4) Considering only the influence of geometric nonlinearity, the calculate format of QR method for the second-order elastic analysis of plane steel frames with semi-rigid connections is established.(5) On the basis of considering the geometric nonlinearity, using a model which called Kishi-Chen, to describe the nonlinear of semi-rigid connections, using the plastic hinge model to simulate material nonlinear of the bar section, and establishing the calculation format of QR method for the elastic-plastic dynamic analysis of steel frame, and nonlinear dynamic response of steel frame are analyzed;(6) Using the dynamic calculation programs to analysis some typical examples, checking the reliability of the algorithm, and the seismic response of the steel frames with semi-rigid connections are analyzed.The results show that: The semi-rigid of connections can increases the sidesway of the structure. When considering the influence of the structural geometric nonlinearity, the semi-rigid of connections will further strengthen the second order effect of the structure, and increase the structure lateral response. When considering the influence by the geometric nonlinearity and semi-rigid of beam-column connections and material nonlinear of the structure at the same time, structure is complicated, both of the development order of plastic hinge and internal force have changed, it has a great influence on the structural dynamic response. QR-method for the nonlinear dynamic analysis of steel frames with semi rigid connections, using generalized displacement parameters of spline node as the basic unknown quantity, the Rigidity of each spline node contains a number of unit nodes rigidity contribution which in its domain.The discrete grid can be made only for one-time. In nonlinear dynamic analysis based on the plastic hinge model, unknown quantity of the structure is constant, the local failure of the structure will not change its freedom degrees, in terms of time and the overall structural failure as the end of the control, and the difficulties and drawbacks of the nonlinear solving which existing in the finite element method can be avoided. So the method has great superiority.