Bounds on the Maximum Thermoelastic Stress and Deflection in a Beam and Plate

[+] Author and Article Information
Bruno A. Boley

Institute of Flight Structures, Columbia University, New York, N. Y.

J. Appl. Mech 33(4), 881-887 (Dec 01, 1966) (7 pages) doi:10.1115/1.3625197 History: Received May 24, 1965; Revised January 17, 1966; Online September 15, 2011


It is shown in this paper that the thermal stress in a beam or plate cannot exceed the value kαEΔT, where ΔT is the maximum instantaneous temperature excursion in a cross section, and k is a coefficient dependent on the shape of the cross section. A simple general formula for k is found, and results for several special cases of practical interest are given. For rectangular beams (suitably oriented) and for plates, for example, k = 4/3. For any section, k = 1 if the thermal moment is zero; simplifications also occur if the thermal force is zero. The corresponding results for beam deflections are also carried out: The maximum deflection cannot exceed the value kδ kδ ′ αLΔT, where kδ and kδ ′ are coefficients depending respectively on the cross-sectional shape and on the end conditions. For example, for rectangular cross sections, kδ = 3/4; and for a simply supported beam, kδ ′ = 1/8.

Copyright © 1966 by ASME
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