A modified member stiffness procedure for dynamic progressive collapse analysis of planar frames

A computer program for progressive collapse analysis of planar frames is under development. The software has a capability to analyze structures after failures of members in which failure can occur at one or both ends of a member. When an end of a member fails, the failed end separates from the main structure and becomes discontinuous. In this paper, a modified member stiffness procedure with releases of end forces to track the response of a failed end is discussed. The procedure utilizes a condensation process of the element stiffness matrix of the failed member. An example in applying the modified member stiffness procedure is given to show that the assembly process for the stiffness matrix and the applied force vector of the main structure does not change. In addition, the Equation solver still determines the same number of unknown degrees of freedom. Accordingly, this approach provides a convenient, simple, yet efficient means of keeping track of all failed members for progressive collapse analysis of frame structures.