Engineering Transactions, 4, 1, pp. 73-86 / 87-97, 1956

Odkształcenia i Naprężenia Termiczne w Płytach na Sprężystym Podłożu / O Poziomym Oddziaływaniu Sprężystego Podłoża na Płyty Poddane Działaniu Zmian Temperatury

Z. Thrun

The application of the well-known method of finite differences to the determination of thermal stresses and strains in plates, in particular in plates resting on elastic foundations is considered. It is assumed that the temperature difference between the upper and the lower layer of the plate is constant for the whole area of the plate. The differential formulae obtained for deflections, bending moments and shearing forces refer to rectangular plates arbitrarily supported and to circular plates on circularly symmetric supports.
Two examples are given to illustrate the computation procedure.


The paper begins with the derivation of differential equations of de- flection, bending and twisting moments, shear and normal forces for a plate resting on an elastic foundation, provoked by temperature changes, the horizontal reaction of the elastic foundation being taken into account. As a particular case of this general equation the familiar differential equation of plate deflection is obtained; the vertical reaction of the foundation being the only reaction considered. Next the author obtains the exact solution of the general differential equation of deflection for a strip and derives formulae for bending moments and normal forces.
Finally, the influence of horizontal reaction of the elastic foundation on extremal normal stresses is illustrated by a numerical example.

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Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).


K. Beyer, Die Statik im Stahl-betonbau, Benlin 1948.

Z. Thrun, Termiczne stany odkształcenia i naprężenia w cienkich płytach, Arch. Mech. Stos. 4 (1954).


S. Timoshenko, Theory of Plates and Shells, New York-Londyn 1940.