An algorithm for the detection of collapse in steel frame structures subjected to earthquakes and identification of causative factors

Current code provisions for aseismic design rely on the capacity of the structure to resist deformations beyond its elastic limit. As a result, a severe ground motion may induce large lateral displacements and, hence, partial or total collapse by lateral instability. An analytical tool is needed to check a structure's safety margin against collapse, and to identify the structural components that may be reinforced. This work presents an algorithm to perform this analysis for three-dimensional steel frame structures with tests performed to assess its effectiveness and illustrate its application. The algorithm is formulated on the basis of a step-by-step finite element analysis and utilizes nonlinear large-deformation three-dimensional shell elements to account for material and geometric nonlinearities and spread of plasticity. It detects a partial or total collapse when a zero or negative eigenvalue is found, and operates on the updated stiffness matrix at the time the zero or negative eigenvalue is found to identify the buckled regions that lead to collapse. The structures considered in the tests are a cantilever beam for which experimental results have been reported in the literature, a portal frame and a two-story frame designed to meet the 1991 AISC specifications. The first two are subjected to pushover loads and the third under the horizontal and vertical components of one of the ground motions recorded during the 1994 Northridge earthquake. The test with the cantilever beam examines the adequacy of the algorithm against experimental results, the portal frame to verify its ability to detect different collapse modes, and the two-story frame to investigate its capability to identify regions of local instability that initiate the collapse. The results from these tests show that the algorithm is able to predict the spread of plasticity and regions of local instability in a structure. The results of the two-story frame also demonstrate how the algorithm can be conveniently used to identify the section in need of reinforcement and how this reinforcement may raise the safety margin against collapse.