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 be ams 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 whe n the beam undergoes flexural and axial loads. Based on Winkler's theory fo r circumferential stresses, the equation shows the extent to which trapezoi dal and triangular cross-sections can develop equal peak stresses for an as sortment of loading conditions. Several three-dimensional finite element an alyses of reference configurations are performed that confirm the theoretic al findings.