Designing the cross-section of curved beams for equal magnitude of peak bending stresses

The paper discusses the problem of designing the cross-section of curved beams to achieve any desired ratio of the stress arising at the inner radius to that arising at the outer radius. A general design equation is developed which identifies the cross-sectional profiles enforcing that condition when the beam undergoes flexural and axial loads. Based on Winkler's theory for circumferential stresses, the equation shows the extent to which trapezoidal and triangular cross-sections can develop equal peak stresses for an assortment of loading conditions. Several three-dimensional finite element analyses of reference configurations are performed that confirm the theoretical findings.