Seismic response of structures by the response spectrum method

Abstract

The problems of the acceleration profile at the lower elevations of cantilever structures and the response of relatively rigid structures are explored. It is shown that the use of the conventional methods for the above problems provide very approximate results. An alternate combination of the modal responses is proposed that not only resolves the above problems but also provides better estimates of response for the complete range of structure frequencies. The procedure treats the relative and rigid body responses separately and then appropriately combines the two results. For the rigid range of frequencies (fundamental frequencies greater than about 2 Hz), the proposed procedure does not encounter any numerical difficulties because of the additive nature of the component responses; however, the application of the proposed procedure for very flexible structures causes accuracy problems since the rigid body effects tend to be subtractive from the flexural response of about equal magnitude. For this latter class of problems, the conventional approach of modal combination provides adequate results and avoids the above mentioned numerical difficulties.