A case study to report the advantage of using signed response quantities in response spectrum analysis

Abstract

Static method of seismic analysis is based on the assumption that fundamental mode of vibration is predominant and there are no mass and stiffness irregularities in the structure. These assumptions of static analysis do not hold good for the irregular and/or tall structures. In such structures, Response Spectrum analysis is preferred as it provides an easy solution compared to Time History analysis. The results of Response Spectrum analysis are computed from modal responses obtained by performing modal analysis. Individual modal responses are combined using modal combination methods (SRSS, CQC etc.) to get maximum absolute responses. Modal combination process generates absolute response quantities. Unsigned member forces at the both ends of the members do not satisfy static equilibrium for the Response Spectrum load cases. Support Reaction of the supported nodes in Response Spectrum load case is also unsigned quantity. It does not allow understanding whether the supported node is subjected to uplift or not.Hence load combinations with these unsigned response quantities may lead to untenable and unrealistic support reaction. It may be observed that footing designed with such load combination is being subjected to huge uplift and requires unrealistic thickness. This problem can be easily eliminated if the sign of the responses of the dominant mode of vibration is considered. This has been clearly demonstrated in the present case study of a watch-tower constructed in seismic zone four in West Bengal where unsigned response quantities resulted in a huge uplift force in support reaction which resulted in unrealistic thickness of the foundation. It was observed that on using sign of the dominant mode, the supported nodes were not actually subjected to such huge uplift. It can be inferred from the present case study that the responses obtained from modal combinations should be used for load combinations only with proper sign which is often not considered by the designers.