Equilibrium Branching Due to Flexural Softening

The importance of softening local behavior (decreasing bending moment for increasing flexural deformation) in the inelastic analysis of reinforced concrete beams and frames has been presented elsewhere. Further studies led to a fairly general theory of the implications of flexural softening on the overall stability. However, the bifurcation of equilibrium paths, which can be caused by softening even in the absence of any geometric effects, seems to have escaped attention. This note aims at illuminating this phenomenon that parallels the well-known phenomenon that may occur in structures with stable local behavior when geometry changes affect significantly the equilibrium equations.