Dynamics of a Class of Horizontal Setback Buildings
Publication: Journal of Engineering Mechanics
Volume 129, Issue 9
Abstract
Dynamics of a class of horizontal setback buildings with flexible floor diaphragms has been studied by developing a “separable model.” A rectangular plan building, with flexible floor diaphragms, is a particular case of the horizontal setback building. The mass and stiffness matrices have been written in terms of direct products of matrices. The separable buildings have two types of natural modes of vibration: (a) those which involve in-plane floor deformation, and (b) those in which the floors do not undergo in-plane deformation. Further, spatially uniform ground motion does not excite the modes involving in-plane floor deformation. Therefore, the problems associated with diaphragm flexibility, e.g., stress concentration at the re-entrant corners, are avoided in separable buildings. General conditions for a building to be separable have been obtained. In simplistic terms, these conditions imply that (a) all wings of the building should have identical value of lateral stiffness per unit plan area divided by mass per unit plan area in either of the principal directions of the wings, and (b) all of the floor diaphragms should have same ratio of lateral stiffness to mass. In other words, the building should be configured so that the fundamental period of vibration of each wing in either direction is the same, and that of all the floors for in-plane vibrations is the same.
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References
Halmos, P. R. (1958). Finite dimensional vector spaces, Van Nostrand, Princeton, N.J.
Jain, S. K. (1983). “Analytical models for the dynamics of buildings.” Earthquake Engineering Research Laboratory Rep. No. 83-2, California Institute of Technology, Pasadena, Calif.
Jain, S. K.(1984). “Seismic response of buildings with flexible floors.” J. Eng. Mech., 110(1), 125–129.
Jain, S. K., and Mandal, U. K.(1992). “Dynamics of buildings with V-shaped plan.” J. Eng. Mech., 118(6), 1093–1112.
Jain, S. K., and Mandal, U. K.(1995). “Dynamics of buildings with Y-shaped plan and flexible floor diaphragms.” J. Struct. Eng., 121(6), 1004–1012.
Lynch, R. E., Rice, J. R., and Thomas, D. H.(1964a). “Tensor product analysis of partial differential equations.” Bull. Am. Math. Soc., 70, pp. 378–384.
Lynch, R. E., Rice, J. R., and Thomas, D. H.(1964b). “Direct solution of partial differential equations by tensor product methods.” Numerische Mathematik,6, pp. 185–199.
Maybee, J. S., Goldberg, J. E., and Herness, E. D.(1966). “Dynamics of separable multistory buildings.” J. Eng. Mech., 92(2), 153–176.
SAP2000 nonlinear: Integrated finite element analysis and design of structures, Computers and Structures Inc., Calif.
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Information
Published In
Journal of Engineering Mechanics
Volume 129 • Issue 9 • September 2003
Pages: 1092 - 1103
Copyright
Copyright © 2003 American Society of Civil Engineers.
History
Received: Dec 3, 1999
Accepted: Feb 12, 2003
Published online: Aug 15, 2003
Published in print: Sep 2003
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