First- and Second-Order Stiffness Matrices and Load Vector of Beam-Columns with Semirigid Connections

Abstract

The firstand second-order stiffness matrices and load vector of a prismatic beam-column of double symmetrical cross section with semirigid end connections including the effects of end axial loads (tension or compression) and shear deformations are derived in a classical manner. The derived matrices can be used in the stability, firstand second-order elastic analyses of framed structures with rigid, semirigid, and simple connections. The classical stability functions are utilized in the stiffness matrix and in the load vector. The proposed stiffness matrices can also be utilized in the inelastic analysis of frames whose members suffer from flexural degradation or, on the contrary, stiffening at their end connections. The validity of both matrices is verified against available solutions of stability analysis and nonlinear geometric elastic analysis of framed structures. Three examples are included that demonstrate the effectiveness of the proposed matrices.