Seismic Response of Structures with Flexible Floor Slabs by a Dynamic Condensation Approach
Rivera, Mario A.
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The flexibility of the floor slabs is quite often ignored in the seismic analysis of structures. In general, the rigid behavior assumption is appropriate to describe the in-plane response of floors. For seismic excitations with vertical components, however, the flexibility of the floor slabs in the out-of-plane direction may play a significant role and it can result in an increase in the seismic response. The simplified procedures used in the current practice to include the floor flexibility can lead to highly conservative estimates of the slab and supported equipment response. To include floor flexibility, a detailed finite element model of the structure can be constructed, but this procedure leads to a system with large degrees of freedom the solution of which can be time consuming and impractical. In this study, a new dynamic condensation approach is developed and proposed to reduce the size of the problem and to calculate the seismic response of structures with flexible floor slabs. Unlike other currently available dynamic condensation techniques, this approach is applicable to classically as well as nonclassically damped structures. The approach is also applicable to structures divided into substructures. The approach can be used to calculate as many lower eigenproperties as one desires. The remaining higher modal properties can also be obtained, if desired, by solving a complementary eigenvalue problem associated with the higher modes. The accuracy of the calculated eigenproperties can be increased to any desired level by iteratively solving a condensed and improved eigenvalue problem. Almost exact eigenproperties can be obtained in just a few iterative cycles. Numerical examples demonstrating the effectiveness of the proposed approach for calculating eigenproperties are presented. To calculate the seismic response, first the proposed dynamic condensation approach is utilized to calculate the eigenproperties of the structure accurately. These eigenproperties are then used to calculate the seismic response for random inputs such as a spectral density function or inputs defined in terms of design response spectra. Herein, this method is used to investigate the influence of the out-of-plane flexibility of the floor slabs on the response of primary and secondary systems subjected to vertical ground motions. The calculated results clearly show that inclusion of the floor flexibility in the analytical model increases the design response significantly, especially when computing acceleration floor response spectra. This has special relevance for secondary systems and equipment the design of which are based on the floor response spectra. The accuracy of the results predicted by two of the most popular methods used in practice to consider the floor flexibility effects, namely the cascade approach and the modified lumped mass method, is also investigated. The numerical results show that the cascade approach overestimates the seismic response, whereas the modified lumped mass method underestimates the response. Both methods can introduce significant errors in the response especially when computing accelerations and floor response spectra. For seismic design of secondary systems supported on flexible slabs, the use of the proposed condensation approach is thus advocated.
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