Effect of Compressibility on Strain Hardening Beams under Combined Loading

The effect of material compressibility on the load-carrying capacity of rectangular section beams is studied in this work by using the Hencky's total strain theory of plasticity. Interaction relations between axial force, shear, and bending moment are obtained for an elastic-linear hardening material. The general form of the obtained equations yields the cases of a reduced combination of applied forces, an incompressible material, and the simpler modeling by the elastic-perfectly plastic behavior. As is well known, results obtained from this modeling coincide with those of the more accurate flow theory only for proportional straining. However, the accuracy remains quite acceptable when the applied loading increases monotonically in a quasi-proportional manner. The constructed model is a generalization of a number of previous works that all dealt with the case of incompressible materials. Demonstration of the important role of Poisson's coefficient is made in the case of short beams for which the load-carrying capacity is not determined by elastic buckling but by a condition of stability corresponding to the existence of a limit loading point in the plastic range of deformation.