Authors: Ahmed S. Brwa1 & Twana Ahmed Hussein2 & Barham Haydar3 & Siva Kumar4
1Department of Civil Engineering, Faculty of Engineering, Tishk International University, Erbil, Iraq
2Department of Civil Engineering, Faculty of Engineering, Tishk International University, Erbil, Iraq
3Department of Civil Engineering, Faculty of Engineering, Tishk International University, Erbil, Iraq
4Department of Civil Engineering, Faculty of Engineering, Tishk International University, Erbil, Iraq
Abstract: This paper compares the time history analysis results for state space representation (SSR) method using MATLAB with the result conducted using ETABS. The equation of motion of the structure subjected to seismic excitation represented by second-order linear non-homogeneous differential equation. This equation reduced to two coupled first order differential equations and state space representation was formulated to represent the system in matrix form and MATLAB Simulink was used to determine response of the structure. The objectives of this study are i) to conduct a comparative study between the state space representation which is a powerful tool with results of ETABS. ii) to investigate the accuracy of SSR method. iii) to conduct a performance based dynamic analysis for shear frame structures and study outcome responses of the structure. This analysis was based on the assumptions, i) the total story mass is lumped at the center of story diaphragm. ii) No deflection occurs in beams; story beams are infinitely rigid in comparison to story columns. iii) no changes in the nature of the boundary conditions during and after the analysis iv) the system is elastic linear time-invariant (ELTI) and material nonlinearity is not considered. So that that structural degree of freedom decreased to be equivalent to the number of storys. The results showed a significant similarity in comparison with ETABS software. The maximum absolute difference of displacement and story drift ratio was 3.35mm and 0.0016 was obtained at the roof of third and fifth story respectively.
keyword: State Space Representative, Time History Analysis, Shear Frame, Dynamic Analysis, Linear Time-Invariant Systems, MATLAB, ETABS
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