Elastic versus plastic bending capacity of Timoshenko-Ehrenfest beams

The Timoshenko-Ehrenfest beam theory is widely applied in structural analysis to simplify mathematical modeling when the beam can be considered as a long structural element. In the literature, the flow resistance of the material is the limit state in most applications of this structural element. However, in some situations, this design limit state can be improved to the plastic limit, increasing the structural capacity to support loads. Henceforth, in this article, the elastic and plastic bending capacity of the Timoshenko-Ehrenfest beam is presented in terms of its concepts and formulation. This theory was applied to a simply supported rectangular beam subjected to a point load. In this specific example, the results show that when the design limit state is changed from the yield limit to the plastic limit, there is a 50% increase in the bending capacity of the beam. Based on the comparison between the two limit states performed here, the bending capacity of a structural system can be improved in terms of a higher limit state, allowing the designer to increase the potential of a beam-like structure.