Three-dimensional effects in beams: Isodyne assessment of a plane solution

The stress distribution in a homogeneous beam subjected to three-point bending is investigated using the method of optical isodynes. The three stress components_xx,_yy and_xy acting in the planes formed by the longitudinal and vertical axes of the beam are determined in three planes situated at different through the thickness locations with respect to the beam's midplane. The experimental results are subsequently correlated with the two-dimensional elasticity solution. It is illustrated that at locations sufficiently removed from the centrally applied concentrated load, good correlation between theory and experiment is obtained. In the regions where high stress gradients exist however, differences are observed in the in-plane stress distributions in the different planes. These differences are explained by the presence of the out of plane normal stress_zz using the relations of optical isodynes. Greatest differences between theory and experiment are obtained for the in-plane shear stress component_xy.