A study of the significant number of modes in moment frames

The computation of the fundamental mode in structural moment frames provides valuable insight into the physical response of the frame to dynamic or time-varying loads. In standard practice, it is not necessary to solve for all n mode shapes in a structural system; it is therefore practical to limit the system to some determined number of r significant mode shapes. Current building codes, such as the American Society of Civil Engineers (ASCE), require certain class of structures to obtain 90% effective mass participation as a way to estimate the accuracy of a solution for base shear motion. A parametric study was performed from the collected data obtained by the analysis of a large number of framed structures. The purpose of this study was the development of rules for the required number of r significant modes to meet the ASCE code requirements. The study was based on the implementation of an algorithm and a computer program developed in the past. The algorithm is based on Householders Transformations, QR Factorization, and Inverse Iteration and it extracts a requested s (s<< n) number of predominate mode shapes and periods. Only the first r (r < s) of these modes are accurate. To verify the accuracy of the algorithm a variety of building frames have been analyzed using the commercially available structural software (RISA 3D) as a benchmark. The salient features of the algorithm are presented briefly in this study.