Distributed Gravity and Temperature Loading in Two-Dimensional Elasticity Replaced by Boundary Pressures and Dislocations

Abstract

This paper deals with two-dimensional stresses due to an important class of body forces. Gravity stresses and temperature stresses are produced by body forces of the type investigated. In the case of gravity stresses it is proved that these stresses may be calculated by forgetting about the action of gravity on the body and applying instead only external normal loads that are identical with a hydrostatic pressure. This opens the possibility of applying photoelastic tests to the measurement of gravity stresses; a model loaded by these external pressures would show an isochromatic fringe pattern identical with the one that would appear in a model submitted to an intense gravity field. In Fig. 5 is shown the type of external loading to be applied to find the gravity stresses in a dam. In the case of two-dimensional temperature stress in cylindrical bodies where the temperature distribution is stationary, it is shown that a distinction is to be made between solid and hollow cylinders. For a solid cylinder the only thermal stress component appearing is an axial stress acting perpendicularly to cross-sectional planes. In other words, the solid cylinder expands freely along the cross-sectional planes. For a hollow cylinder a general stress condition may arise which is identical with the stresses produced by cutting a longitudinal slit of a certain small width in the cylinder wall and sticking together the two sides of the slit (dislocation).