In two-dimensional photoelasticity a plate of transparent isotropic material is stressed by a uniplanar force system coplanar with the middle plane of the plate (Fig. I). The material of the plate thereby becomes optically doubly refracting and certain of the resulting optical properties are determined by examining their effects on p61arized light passed through the plate at normal incidence. The state of stress in the plate is then calculated on the basis of experimentally determined relations between stress and optical effect carried out under similar conditions.
The state of stress, at a point in a plate loaded only by forces in its plane, is a particular case of a more general stress condition; the most general being characterized by six independent quantities, namely, the magnitudes and the directions of the three mutually perpendicular principal stresses. The three principal stresses will be denoted in this paper by the symbols ~3, a2, at, and their relative magnitudes will be taken as a3 > as > al.
In a plate loaded in its plane, one of the principal stresses is always normal to the plane of the plate and its magnitude is zero, so that three of the six quantities are known a priori. The remaining three quantities are the magnitudes of the two principal stresses, lying in the plane of the plate, and their orientation. An important characteristic of such a stress distribution is that, at each point in the plate, one principal plane of stress is parallel to the middle plane of the