Some issues regarding the models of the mass and damping matrices in nonlinear seismic analysis of moment resisting steel frames

Abstract

Software users concerning seismic analysis of buildings usually use the concentrated mass (ML) matrix and the Rayleigh damping matrix (C). Similarly, the initial stiffness matrix (KO) and the first two modes are commonly used to calculate C. In addition, it is commonly believed that damping forces are small so there are no significant errors if the Rayleigh model is used. The evaluation of the accuracy of these practices for the case of steel buildings constitutes the main objective of this research. To this aim the seismic responses of three models, representing steel buildings of low-, mid- and high-rise are considered. If ML is used, shears and bending moments in columns are underestimated by up to 31% and 65%, respectively. If the first two modes are used, shears, drifts, and bending moments in beams are underestimated by up to 27%, 50%, and 55%, respectively, while for axial loads and bending moments in columns the underestimation can be up to 78%. Similarly, damping forces and damping moments are underestimated by up to 350% and 325%, respectively. Damping moments represent a considerable fraction (0.47) of plastic moments in beams. If KO is used in C, axial loads in columns are underestimated by up to 80%. The results of this study give rise to state that the consistent mass matrix should be used in the structural modelling of the structural system under consideration. Similarly, first mode and one superior, and the tangent stiffness matrix should be used to formulate the Rayleigh damping matrix.