Shear‐Stress Distribution in Symmetrically Tapered Cantilever Beam

Shear-stress distribution is investigated for the case of a symmetrically tapered cantilever beam subjected to simultaneous axial and transverse loading. An analytical solution is developed by expanding on earlier work involving tapered beams subject to transverse loading. The solution is compared to a finite element model for both long, slender beams and short, stubby beams. The model is in good agreement with the theoretical predictions for the long, slender beams at the middle and free end but shows a significant discrepancy at the fixed end, i.e., a stress concentration of greater than 2. This discrepancy is to be expected since the fixed end is not free to distort. Similar correlations were obtained for the short, stubby beam. The finite element analysis indicated that these stress concentrations dissipated at approximately 15% of the beam length.