Two Stage SEREP Method for Condensation of Space Frame Structure for Dynamic Analysis

Abstract

Analysis of frame structure can be done by the computer analysis, but there is requirement of simple and easy model which can give accurate result or with tolerable accuracy. The process of reducing the size of matrix is called condensation. It needs to be converted into system or model having less number of degrees of freedom as huge computational effort is required to analyze big models. Also, the models which requires analysis multiple times, for example, optimization of structural system, condensation is very useful. The single stiffness value can represent the stiffness of the whole story (elastic, rectangular frame with evenly distributed load), which give the responses accurately or tolerable accuracy. With this we can create a single lumped mass system of the frame structure which come very handy in further analysis of structure. For finding the single stiffness value, there are various approach like by using Approximate Story Stiffness Formulas, Static condensation, System Equivalent Reduction Expansion Process (SEREP) etc. Approximate Story Stiffness formulae don’t give very accurate result. To overcome its shortcoming Static Condensation and SEREP methods are used. Static Condensation gives better result but there is significant difference in the responses. Especially for space frame structures it is difficult to directly condense in to single degrees of freedom at each floor level. Hence, the present study proposes two stage SEREP method for condensation of spaceframe structure. Firstly, space frame is reduced to single degrees of freedom at each node, then it is further reduced to single degree of freedom at each floor. The proposed method gives very less (acceptable) error in comparison of natural frequencies.