Stress Concentrations in Plates Loaded Over Small Areas

Abstract

If a considerable pressure is applied within a small area as a transverse load on a plate or slab, a concentration of stress will occur within and around that area. This stress concentration differs in type from that observed at fillets, re-entrant corners, or holes in solids; it is caused by concentration of the load. If the load on the plate or slab is not too close to any lines or points of concentrated support or to any edge and is neither too concentrated nor too dispersed, and if the material of the plate or slab is homogeneous, isotropic, and elastic, the important features of the stress concentration produced by the load can be expressed conveniently and with good approximation by means of six coefficients, all of which are pure numbers. Three of these-B, C, and D-are called “place coefficients”; they depend on the place of the load, but not on its manner of distribution over the small loaded area. The remaining three-K, S, and Tare called “area coefficients”; they depend on the size and shape of the loaded area and on the manner of distribution of the load over that area, but are independent of the place of the load. When the place coefficients have been determined in m cases and the area coefficients in n cases, solutions are thereby made available in m times n combined cases.