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Bulletin of the Seismological Society of America; April 1962; v. 52; no. 2; p. 405-416
© 1962 Seismological Society of America
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Mode superposition in multi-degree of freedom systems using earthquake response spectrum data

H. C. MERCHANT and D. E. HUDSON

DEPARTMENT OF MECHANICAL ENGINEERING UNIVERSITY OF WASHINGTON, SEATTLE, WASHINGTON
DIVISION OF ENGINEERING CALIFORNIA INSTITUTE OF TECHNOLOGY, PASADENA, CALIFORNIA

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.




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