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On the coupled torsional and sway vibrations of a class of shear buildings
Author(s) -
Wittrick W. H.,
Horsington R. W.
Publication year - 1979
Publication title -
earthquake engineering and structural dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.218
H-Index - 127
eISSN - 1096-9845
pISSN - 0098-8847
DOI - 10.1002/eqe.4290070507
Subject(s) - structural engineering , shear (geology) , vibration , normal mode , shear force , torsion (gastropod) , stiffness , geometry , mathematics , engineering , physics , geology , quantum mechanics , petrology , medicine , surgery
This paper is concerned with the free vibrations of a restricted class of multi‐storey shear buildings in which inertial coupling exists between the torsional and the two sway vibrations. The restrictions imposed are that (a) the shear centres of all storeys lie on a vertical straight line, (b) the principal axes of shear are in the same directions in all storeys, (c) the centres of mass of all floors lie on another vertical straight line, (d) the radius of gyration about the shear centre of every floor mass is the same and (e) the ratios of the two shear stiffnesses to the torsional stiffness do not vary from storey to storey. In consequence of the last restriction it is proved that the 3 n natural frequencies, normal modes and generalized masses, where n is the number of storeys, are expressible very simply in terms of products of the three natural frequencies, normal modes and generalized masses of the single‐storey, three‐dimensional building formed by removing everything above the first floor, with the n natural frequencies, normal modes and generalized masses of a certain n ‐storey, two‐dimensional shear frame. In the special case of a uniform building, a simple closed form solution, valid for any number of storeys, is given.