Explicit Tangent Stiffness Matrix for Nonlinear Analysis of Planar Frames Considering the Effects of Spread of Inelasticity

This paper is concerned with nonlinear analysis of planar frames emphasizing how to model the effects of spread of inelasticity accurately and efficiently. A flexibility formulation is used first to derive the incremental flexibility matrix on the basis of the sectional moment-curvature-axial load relationship. The derived flexibility coefficients are explicit and have very simple expressions; therefore computer implementations are easy to perform. Then, the incremental inelastic stiffness matrix is determined from the incremental flexibility matrix using the congruent transformation. If the effects of geometric nonlinearity are important, the conventional geometric stiffness matrix needs to be added to the incremental inelastic stiffness matrix to result in the tangent stiffness matrix. The use of the tangent stiffness matrix in nonlinear analysis of structures follows the standard procedures. Since the presented formulation is based solely on the sectional moment-curvature-axial load relationship, the proposed stiffness and flexibility matrices are applicable to framed structures of various materials. Due to space limitation, only one numerical example on steel frames is provided.