Mode superposition in multi-degree of freedom systems using earthquake response spectrum data

Abstract

Dynamic responses of a series of typical three-degree of freedom structures to strong-motion earthquake excitation were calculated by analog computer techniques and were compared with approximate responses obtained by a superposition of individual modes derived from response spectrum curves. The results indicate that a suitably weighted average of the sum of the absolute values of the individual modes and the square root of the sum of the squares of the modes will give a practical design criterion for the base shear forces in multi-story buildings. For critical designs, this weighted average reduces to the absolute sum of the modes, which is found to be close to the true value for a significantly high proportion of typical earthquake-structure combinations.