Analytical Solutions for Bending Curved Beams with Different Moduli in Tension and Compression

When materials that exhibit different mechanical behaviors in tension and compression must be analyzed, Ambartsumyan's bimodular model for isotropic materials can be adopted. It deals with the principal stress state in a point, which is particularly important in the analysis and design of structures. In this article, an equivalent section method is used to transform the bimodular curved beam into a classical one with singular modulus; consequently, the simplified solution for bending stresses may be easily determined only by changing a few parameters relating to section characteristics. For the determination of the unknown neutral layer, a perturbation method is used to obtain the explicit expression. Based on the known neutral layer, a stress function method is used to obtain the elasticity solution for stresses and displacements via boundary conditions and continuity conditions. Based on the elasticity solution, an initial stresses problem in a bimodular multiply-connected body is considered. The comparison between two solutions shows that the simplified solution agrees very well with the elasticity one. Moreover, the inclusion of shear stress and the application of the equivalent section method in reinforced-concrete curved beams are also discussed. The results indicate that the bimodularity of materials has definite influences on the bending behavior of a bimodular curved beam.