Strain-gradient stress analysis in saint-venant bending

Light beam deflections caused by stress or strain gradients are investigated analytically and experimentally in homogeneous beam specimens which are subjected to a particular case of flexure with shear. This study is a generalization of the prior analytical-experimental examination of strain-gradient light deflections produced in stressed plates, which had concentrated on the simplest case where information of interest is collected along a line of symmetry of the stress field. Main purpose of the present investigation is to document the efficacy of the strain-gradient method in analysis of the general case of stress state. The most interesting stress state is that in a beam subjected to the Saint-Venant bending, where the transversal and the longitudinal axes of the beam are in pure shear. The obtained results are compared with the predictions of the developed analytical models and with the predictions of Filon's stress function. The procedures of evaluating the photoelastic and material coefficients using strain-gradient techniques were tested positively. Dedicated to Prof. Dr. Horst Lippmann, Muenchen, on the occasion of the 65th anniversary of his birthday The project was supported by the Natural Sciences and Engineering Research Council of Canada and the NATO Scientific Affairs Division