New method of deriving stresses graphically from photo-elastic observations

Abstract

In transparent bodies under plane stress the difference and directions of the two principal stresses are obtained by observations with polarized light. To separate the stresses either additional measurements can be used, for instance changes of thickness; or we may resort to any method of graphical integration. Although several different methods exist, all are based upon the equations of equilibrium and involve considerable time. A new method, which has now been worked out by the writer, based entirely upon elastic equations , enables us to trace those lines, along which the sum of the principal stresses has a constant value. Since we can assign to each line its appropriate parameter, we know in this way the sum of the principal stresses at any point of the plate. This method is very accurate and is carried out quite simply as follows. (I) Theory. (1) General Relations. The lines of principal stress 1 and 2, fig. 1, give at all points the directions of the two principal stresses (σ 1 and σ 2 ); where ϕ is the angle between the directions 1 and Y, or 2 and Z respectively (Y-Z are Cartesian co-ordinates).