A new exhaustive semi-analytical method to calculate stress distribution on the surface of a curved beam with circular cross section, with an application to helical compression springs

In mechanical and in civil engineering, stressed curved beams are found in many applications involving failure and fatigue analysis. However, stress formulas of straight beams cannot be applied to curved beams with any reasonable degree of accuracy. Hence, curved beam theory is yet to be properly defined and is only established for particular sets of loads, particular applications, and particular cross-section geometries. This work proposes the first exhaustive solution of stress field calculation on the surface of a curved beam with a circular cross section, computed with an open-access databank preliminary built with FE simulations and considering every kind of static mechanical load applied and any curvatures. Such data are an important prerequisite for probabilistic fatigue life analysis. A numerical campaign was executed with different relative curvatures and was gathered in an open-access stress coefficient databank to facilitate data use. For any given curvature and wire diameter, the method can obtain the distribution of each stress on the surface of the circular curved beam, calculated with any combination of forces and momenta applied on its centroidal line. This calculation method was successfully verified with an application to a cylindrical compression spring. As a result, the present semi-analytical model has a 99.9% accuracy on the maximal Tresca stress calculation, being more than 43,000 times faster than the most realistic FE model. This is a significant breakthrough for researchers and engineers looking to save industrial time, optimization process or fatigue estimations.