Accuracy of Modal Combination Methods in Seismic Design of Barrel Vault Cylindrical Roof Shells

Abstract eng:
The design of a structure using modal analysis is usually based on finding the maximum responses using one of the two combination methods of square-root-of -sum-of-squares (SRSS) and complete quadratic combination (CQC). It is generally accepted that the predicted approximate responses would be conservative and accurate enough for practical structural design analysis. However, in this paper it is shown that for barrel vault cylindrical roof shells the modal combination methods may not result in conservative results. In this paper a semianalytical method, which has been previously verified using a finite element modelling, is used to find the time history response when barrel vault cylindrical shells are subject to synchronous vertical motions from typical earthquake records. The analytical method adopts an explicit solution based upon the Love-Timoshenko straindisplacement relationships and employs a Lagrangian approach to the derivation of the equations of motion. The investigation on the accuracy of modal combination methods using the two methods of square-root-of-sumof-squares (SRSS) and complete quadratic combination (CQC) shows that both methods estimate the maximum displacement and axial membrane stresses within the practically acceptable percentage of error. However, the stress resultants other than the axial membrane stress cannot be accurately estimated using these modal combination methods and they do not always provide conservative results. It is concluded that performing a modal combination methods could lead to serious underestimation of responses for large roof shells subjected to earthquake loading.

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