HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS		QUICK SEARCH:   [advanced] Author: Keyword(s): Year:  Vol:  Page:

This Article Full Text (PDF) References Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via Google Scholar Google Scholar Articles by GIBSON, R. E. Articles by AYRE, R. S. Search for Related Content GeoRef GeoRef Citation

Free vibration of an unsymmetrical multistoried building modeled as a shear-flexible cantilever beam

DEPARTMENT OF CIVIL ENGINEERING UNIVERSITY OF NEBRASKA AT OMAHA, OMAHA, NEBRASKA 68132
DEPARTMENT OF CIVIL ENGINEERING UNIVERSITY OF COLORADO, BOULDER, COLORADO 80302

Abstract

A solution is presented for the undamped free vibration frequencies and mode shapes of a multistoried building with unsymmetrical floor plan, modeled as a continuous (distributed parameter), shear-flexible cantilever beam. The beam has constant mass per unit length and a linear distribution of elastic shearing resistance (stiffness) along its length. Three coupled, second-order partial-differential equations describe the rotational and lateral motions. Solution of the equations reveals the presence of "coupling modes," which are dependent on the cross-sectional properties of the beam, and "z-modes,", which are independent of cross-sectional properties. An exact solution is presented for the coupling modes, and approximate and exact solutions for the z-modes are obtained. Frequencies are given for different linear variations in elastic resistance, and are presented in dimensionless form. A discrete element analysis has been included for purposes of comparison. The results of this paper will be referred to in the accompanying paper entitled "Response Spectrum Solution for Earthquake Analysis of Unsymmetrical Multi-Storied Buildings."