Unified formulation of the stress field of saint-Venant's flexure problem for symmetric cross-sections

• A closed form engineering stress field is proposed for elastic flexure of beams.
• A modified stress field is also introduced for Saint-Venant's flexure problem.
• The modified stress field is a unified formulation of Saint-Venant's solution.
• The introduced stress field recovers solutions available from theory of elasticity.
• An explicit solution form for the shear flexibility factor is also presented.

The flexure problem of Saint-Venant's elastic beam under lateral traction is revisited. First an engineering stress field is proposed with the explicit closed form solution that results in shear stress distribution determined by mechanics of materials theory. Afterward a modified stress field is introduced for Saint-Venant's flexure problem with uniaxial symmetric cross-sections that recovers the solutions available from the theory of elasticity. The modified stress field which is a unified formulation of Saint-Venant's solution confirms the main features of shear stress distribution found in the earlier investigations and has an excellent agreement with the results of the theory of elasticity. Also the shear flexibility factor is comprehensively discussed and an explicit solution form is presented based on the modified stress field.