Dynamics Analysis of Two Storey Plane Rectangular Rigid Frame Subjected to Ground Motion

The dynamic analysis of plane rectangular rigid frame subjected to ground motion is presented. The matrix stiffness method, static condensation method, Szilard household characteristic equation method, Newton-Raphson’s method and Gaussian elimination method were used in the analysis. The plane rectangular rigid frame was fixed at both support and the masses were concentrated at the floors level (lump masses). Matrix stiffness method was applied to generate the element stiffness matrix. Various element stiffness matrices were combined to form the global stiffness matrix. Due to large size of global stiffness matrix, the method of static condensation was applied to reduce the size. By substituting the condensed stiffness matrix in the free vibration equation and applying Szilard household characteristic equation method, Newton-Raphson’s method and Gaussian elimination method, the eigenvalues and eigenvectors were obtained. From eigenvectors we obtain the base shear forces and base overturning moments. A comprehensive visual basic excel program was developed from this method to obtain eigenvalue, eigenvector, base shear force and base overturning moment as follows: 0.0464, 0.33, 4.526KN and 9.051KNm respectively. Comparing the present study and the direct stiffness method for two storey frame, gave a percentage different of - 0.0273 for eigenvalue w_1 and -17.303 for eigenvector?_1.