ELASTIC-PLASTIC ANALYSIS OF A BEAM WITH ONE DEGREE OF INDETERMINACY UNDER AN EVEN LOAD

By using of virtual work principle and the unit-load method, the elastic-plastic process of loading and deflection of a beam with one degree of indeterminacy under an even load is analyzed. The process is divided into four stages: an elastic state in the whole beam, an elastic-plastic state in the region close to the fixed end, an unloading state in the plastic region with a plastic hinge at the fixed end, and an elastic-plastic state in the region near the middle of the beam till the formation of plastic flow state with a plastic hinge at the fixed end. The formulae of the moment and displacement and reaction force at the support of the beam are derived at the four stages. The results are applicable to engineering structure design as well as teaching.