Strain Hardening Beams under Shear, Bending, and Axial Forces

The load carrying capacity of a rectangular section is investigated. Using Hencky's total strain theory, interaction relations between axial force, shear and bending moment are obtained for an elastic‐linear strain hardening material. A unified set of equations are presented which can be reduced for any combination of forces and any simpler modeling of materials, including the elastic‐perfectly plastic material. Although the results are generally limited to proportional loading, the accuracy is quite acceptable in most cases, as long as all the applied loads increase monotonically in a quasi‐proportional manner. As a demonstration of the possible broader usage of the derived equations, beam columns under combined loading are examined using the existing approximate beam‐column theory. The results indicate that strain hardening is important in certain situations, particularly when the beam is bulkier. The same principle can be applied to other types of structural sections such as I‐beams.