Graduate Thesis Or Dissertation
 

A photoelastic stress analysis of a beam under shear and compressive loads

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  • The determination of failure is complicated when a structural element is subjected to combined rather than simple stresses. This is especially true when the principle of superposition does not apply. For such cases, tests of the element under the expected loads are required to determine its failure criteria. In this investigation, a rectangular beam is subjected to combined shear and axial loads and studied experimentally. It is the object of this investigation to determine the effect of the axial compression on the maximum stresses created by the shear load. As a preliminary objective, the stress distribution along the shear plane will be determined using photoelastic techniques. The distortion energy theory of failure, and its corollary the octahedral shear stress theory, establish a relationship between the combined applied loads and the yield stress of the material and will be used in this investigation. The distortion energy theory shows that, as axial compression increases, the distortion energy (and octahedral shear stress) increases indicating that the beam is approaching failure along the shear plane. The normal stress distributions at the shear plane were determined and the effect of axial compression established. The shear stress was found to be a maximum near the edges of the beam. Under axial compression the shear stresses near the edges were reduced and the minimum stresses (at the midsection) were increased somewhat. The normal stresses perpendicular to the plane of investigation were found to be compressive near the edges and tensile in the midsection. Axial compression is superimposed on the original profile, thereby increasing the stresses uniformly over the entire cross section. The normal stresses parallel to the shear plane are of the same general shape and magnitude as the shear stress and are effected only under high axial compressive loads, probably due to the poisson effect.
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