[Ozioko, 3(11): November, 2014] ISSN: 2277-9655 Scientific Journal Impact Factor: 3.449 (ISRA), Impact Factor: 2.114 http: // www.ijesrt.com © International Journal of Engineering Sciences & Research Technology [665] IJESRT INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY Dynamics Analysis of Two Storey Plane Rectangular Rigid Frame Subjected to Ground Motion Ezeh J.C., Ibearugbulem O.M., Ezeokpube G.C. and Ozioko H.O. Head of Department, Civil Engineering, Federal University of Technology Owerri, Imo State, Nigeria Senior Lecturer, Civil Engineering, Federal University of Technology Owerri, Imo State, Nigeria Head of Department, Civil Engineering, Michael Okpara University of Agriculture Umudike, Abia State, Nigeria Lecturer, Civil Engineering, Michael Okpara University of Agriculture Umudike, Abia State, Nigeria Abstract 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, t he 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 eigenvectorϕ_1. Keywords: Identical, eigenvalues, overturning, eigenvectors and frames. Introduction Structural dynamics is a type of structural analysis which covers the behaviour of structures subjected to dynamic loading. Dynamic loads include earthquake loads, people, windstorm, waves, vibration of the ground due to a blast nearby, hurricanes, flooding, tornadoes, vibration effect from compound disc player, vibrations effect from moving vehicles, vibration effect from heavy construction equipment etc. Any structure can be subjected to dynamic loading. Dynamic analysis can be used to find dynamic displacements, eigenvalue, eigenvector, shear force and bending moment. It has been observed that most of the buildings designed, and constructed in Nigeria by contractors were designed and constructed without considering the effects of these loads. This negligence may have resulted in the cracks or collapse of buildings in our vicinity. Cases of building cracks or collapses at the neighboring town of an area defected by earthquake have been observed. For example, the 2011 Virginia earthquake that cracked and collapsed structures in the neighbouring towns, Ottawa Canada and West Cleveland Ohio (Raghunandan and Liel, 2013). Nigeria has recorded earth movements in some of the above mentioned areas. In 2012, some parts of Nigeria experienced flooding which may have resulted to the crack or collapse of buildings located at the area. Areas like Aguleri in Anambra State, Ohaji /Egbema in Imo State, Lokoja in Kogi State etc were affected. Some of the buildings at those areas may have collapsed due to the effect of dynamic load caused by the flood. At Borno State there have been several blasts from the terrorist group called Boko Haram. The vibration effects from these blasts have contributed to the cracks and collapse of buildings around these areas. Some of those structures may have been saved if there dynamic loads were considered at the design stage. There are cases where man induces this ground motion on the purpose of