Plastic moment

In structural engineering, the plastic moment (Mp) is a property of a structural section. It is defined as the moment at which the entire cross section has reached its yield stress. This is theoretically the maximum bending moment that the section can resist - when this point is reached a plastic hinge is formed and any load beyond this point will result in theoretically infinite plastic deformation. In practice most materials work harden resulting in increased stiffness and moment resistance until the material fails. This is of little significance in structural mechanics as the deflection prior to this occurring is considered to be an earlier failure point in the member.

Mp for a rectangular section can be calculated with the following formula: ${\displaystyle M_{p}=(bd^{2}/4)\sigma _{y}}$

For other sections it is normal to calculate ${\displaystyle Z_{P}}$ then substitute it into the formula as follows: ${\displaystyle M_{p}=\sigma Z_{p}}$

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