An optical determination of the variation of stress in a thin rectangular plate subjected to shear

Abstract

The determination of the distribution of shear stress in a body subjected to the action of an arbitrary set of forces applied to its bounding surfaces is often of great importance in constructional work. In most cases mathematical difficulties do not allow of an exact solution, while the simplifying assumptions which are often made to reduce these difficulties lead to formulæ which are probably not correct even to a first approximation. It is important, therefore, to have experimental determinations to compare with the values calculated by approximate methods to determine to what extent the assumptions are correct, and also, if possible, to afford data for better approximations in cases which do not allow of mathematically exact solution. The shear stresses in riveted joints, the stiffened webs of plate girders and such like structures, afford examples of practical problems of extreme complexity from the mathematical standpoint, which are dealt with in practice by rough approximations, using large factors of safety fixed by experience of the behaviour of similar structures, in order to allow for contingencies due to ignorance of the actual stresses and accidental overloading. The experimental determination of the state of stress in a body as inferred measurements of the strains produced at its surface affords a means, which has been used by various investigators, to determine the condition of stress in a body subjected to the action of forces applied at its boundary. In shear problems, with which the present paper deals, this usually involves the measurement of small angular displacements, but these strains are so minute for the materials of construction at ordinary working stresses that it is usually found necessary to make experiments on other materials like indiarubber, plasticine and the like, which afford strains sufficiently large for accurate measurement, while their elastic properties are such that they may be considered to behave like more intractable materials with fair accuracy.