Nonlinear Analysis Of A Column Failure Steel Frame Based On The Force Analogy Method

Nonlinear analysis is a significant aspect in structural analysis, particularly to structures undergoing excessive loadings, such as severe earthquakes. The nonlinear analysis based on force analogy method (FAM) is proposed by varying displacement instead of stiffness. It greatly reduces computational efforts in dynamic nonlinear analysis because the state transition matrix in the state space method is only needs to be calculated once. And it can be used to analyze structures with various properties, not only elastic-plastic but also strain-hardening and strain-softening properties.The FAM is used in the nonlinear analysis of a steel frame structure in this paper. The basic concept and theory of the FAM is firstly introduced. Then a new algorithm based on the FAM for studying the static structural behaviors under vertical loads is proposed and the general equation is deduced. Moreover, application of the proposed algorithm based on MATLAB to a six-story building under vertical loads is presented. Comparison of the static nonlinear structural behaviors before and after the failure of key-column is performed to demonstrate the influences on the plastic hinges.Based on the combination of the FAM and state space method, the inelastic dynamic state space response with state space reduction is demonstrated. And the applcation of the proposed algorithm is carried out based on a procedure written by MATLAB. Firstly the dynamic nonlinear analysis of the basic structure with different plastic hinge properties subjected to a modified El-Centro earthquake is presented. Then the dynamic nonlinear analysis of the basic steel structure due to the failure of key columns is presented. Comparisons of the dynamic behaviors due to the failure of key-columns are performed to demonstrate the influences of the failure of key-columns.At last, the basic steel structure model is taken into SAP2000for a nonlinear time history analysis calculation. Compared with the results achieved by the numerical algorithm based on the FAM, the analysis results of SAP2000are used to verify the accuracy and efficiency of the FAM.