Warping stresses of a rectangular single leaf flexure under torsion

We describe a stress analysis of a single leaf flexure under torsion in which the warping effect is considered. The theoretical equations for the warping normal stress (oxx) and shear stresses (oxz and oxy) are derived by applying the warping function of a rectangular cross-sectional beam and the twist angle equation that includes the warping torsion. The results are compared with those of the non-warping case and are verified using finite element analysis (FEA). A sensitivity analysis over the length, width, and thickness is performed and verified via FEA. The results show that the errors between the theory of warping stress results and the FEA results are lower than 4%. This indicates that the proposed theoretical stress analysis with warping is accurate in the torsion analysis of a single leaf flexure.