Stress Distribution in Square Plates With Hydrostatically Loaded Central Circular Holes

The stress distribution in square plates with hydrostatically loaded central circular holes was determined using photoelasticity and brittle coatings. Photoelasticity was used to determine the maximum shear lines (isochromatics) and a brittle coating was used to determine the directions of the principal stresses (isostatics). The investigation was conducted for plates with holes producing seven ratios of the diameter to the square side (D/a). Curves are presented which show the distribution of the maximum shear stress along the axis and along the diagonal of the square plate, as a function of D/a, Figs. 3 and 4. The maximum principal stress along the exterior and interior boundaries as a function of D/a, Figs. 5 and 6, has also been given. A comparison is made of the stress ratios (σ₁/P) at a point on the axis of the square at the interior boundary with that calculated for a thick-wall cylinder using Lamé’s equation, Fig. 1. Stress ratios (σ₁/P) also are determined for a point on the diagonal of the square plate at the interior boundary, Fig. 8. A diffused-light polariscope was used. The loading jig consisted of rubber tubing in a grooved block. The photoelastic material (CR39) was calibrated automatically. No new methods are developed in the paper but it is felt that the use of the presently available methods has been simplified appreciably.