Plastic Moment

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In plastic limit analysis of members subjected to bending, it is assumed that an abrupt transition from elastic to ideally plastic behaviour occurs at a certain value of moment, known as plastic moment (Mp). Member behaviour between My and Mp is considered to be elastic. When Mp is reached, a plastic hinge is formed in the member.

$M p = σ Z p$

If, for example, a beam has an increasing applied moment on it, the beam will begin by deforming slightly. This small deformation is still in the elastic region of the beam. Once the beam yields, the deformations become larger as the moment increases. This continues until the moment becomes so large that the material becomes fully plastic, and therefore it will not take a larger moment to cause infinite deflection. The beam has no more ability to prevent bending.