Second-Order Analysis of Plane Frames with One Element Per Member

摘要

A corotational element is developed directly from the governing second-order differential equations of beam theory. The corota-tional element includes not only the effect of axial force on the bending moment (P-delta effect) but also the additional axial strain caused by end rotations. Hinged and semirigid end conditions are also included so that plastic hinges could be considered. The resulting local element tangent stiffness matrix is compared to traditional local element elastic and geometric stiffness matrices. The method is implemented and executed on two example problems in which only one element per member is used. Results compare favorably to those from a nonlinear commercial program in which several elements per member are used. A third example problem includes both geometric and material nonlinearity to develop a pushover curve.