Civil Engineering ETDs

Publication Date

12-9-1972

Abstract

The objective of this investigation is to determine the complete response of undamped structural systems to time-dependent loads. Two systems, continuous beams and plates with equally spaced interior supports, are examined. Both have distributed mass and experience small linearly elastic deflections. The problems are formulated using the discrete mechanics method in which the response of a typical element of the system is first determined. A difference equation for the moments at the support locations is then derived by satisfying the force and compatibility conditions between adjacent elements. Finally, a closed form solution of this equation is obtained in terms of a finite series. Two methods are used to determine the element response. The first is a modified separation of variables technique. The second is the Laplace transform. Using the first method for continuous beams, the moments at the supports are expressed as integral equations which are solved by a numerical procedure. The second method is applied to beams and plates and results in transformed expressions for the moments. The expressions for the moments in real time are obtained from the inversion integral. Three example problems are solved: a two-span beam, a three-span beam and a two-panel plate. The loading is assumed to vary sinusoidally with time, and all systems are taken to be initially at rest and undeformed. The numerical method gives values for the support moments larger than the exact values with span deflections less than the exact values. The second method gives exact closed form solutions for moments and deflections, since the inversion is exact. The numerical method is the simpler of the two solutions to apply for continuous beams. It is suitable for short time periods where only approximate values are required. The Laplace transform solution involves considerable effort in the inversion step but results in a closed form exact solution for continuous beams and plates.

Sponsors

Dr. Cyrus Omid'varan

Document Type

Dissertation

Language

English

Degree Name

Civil Engineering

Level of Degree

Doctoral

Department Name

Civil Engineering

First Committee Member (Chair)

Howard Linn Schreyer

Second Committee Member

Roy Linton Johnson, Jr.

Third Committee Member

Marion Marvin Cottrell

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