Time History Analysis of Frame Structure Systems by State-space Representation Method

Abstract

This paper develops the state-space representation (SSR) in the field of seismic analysis of the building structures. Dynamic analysis of multi-degree-of-freedom structures involves the solution of second-order linear differential equations which they represent the equation of motion of the structure. In this paper, a SSR was formulated to replace differential equation with two coupled first-order linear differential equations. The objectives of this study are as follows: (i) To implement the SSR as a powerful tool in dynamic analysis of frame structures and (ii) to conduct a linear time history analysis for large structures subjected to ground acceleration and the seismic responses of the building were studied as well. The analysis was based on the assumption that the system is elastic linear time-invariant system and material nonlinearity is not considered. The 1940 El-Centro earthquake time history record has been used in the study. There are many effective traditional methods which can be used for carrying out linear dynamic analysis of the structures, however, this paper introduces a state-space model as an alternative approach to perform this analysis. The advantage of this method, it works properly with MATLAB software, gives explicit result for time-invariant systems, applied to multi-input and multi-output control systems, solve the equation of motion for complicated dynamic problems.