Photoelastic Simulation towards a Study of a Simply Supported Rectangular Beam Carrying a Central Concentrated Force

Abstract

The problem of stress distribution in a rectangular beam is of great practical interest as the beamis used in most structures. This paper presents general mathematical models of a plane-stress problem ofa rectangular beam subjected to a concentrated force at its midspan based on three major theories: theBernoulli-Euler theory, the Wilson-Stokes theory, and the Durant-Garwood theory, and the simulation ofthe stress field on the basis of the principle of digital photoelasticity. Several relevant maps of stresses arealso presented. Comparison of numerical results from these theories reveals that the Durant-Garwood theorygives the stress field being superior to those obtained from the first two theories in the senses of fringes’fineness and continuity. Furthermore, the Bernoulli-Euler theory is shown to be a conservative theory formost regions in the beam except at and near the point of the applied concentrated force.

Keywords : Digital Photoelasticity / Fringe / Isochromatics / Isoclinics / Isopachics / Map / SimplySupported Rectangular Beam