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different support and loading conditions are shown in Figure 2.93. Plastic hinges are developed first at the sections subjected to the greatest moment. The possible locations for plastic hinges to develop are at the points of concentrated loads, at the intersections of members involving a change in geometry, and at the point of zero shear for a member under uniform distributed load.

### 2.11.5 Plastic Moment Capacity

A knowledge of full plastic moment capacity of a section is important in plastic analysis. It forms the basis for limit load analysis of the system. Plastic moment is the moment resistance of a fully yielded cross-section. The cross-section must be fully compact to develop its plastic strength. The component plates of a section must not buckle prior to the attainment of full moment capacity.

The plastic moment capacity, Mp, of a cross-section depends on the material yield stress and the section geometry. The procedure for the calculation of Mp may be summarized in the following two steps:

1. The plastic neutral axis of a cross-section is located by considering the equilibrium of forces normal to the cross-section. Figure 2.94a shows a cross-section of arbitrary shape subjected to increasing moment. The plastic neutral axis is determined by equating the force in compression (C) to that in tension (T ). If the entire cross-section is made of same material, the plastic neutral axis can be determined by dividing the cross-sectional area into two equal parts. If the cross-section is made of more than one type of material, the plastic neutral axis must be determined by summing the normal force and letting the force equal zero.

2. The plastic moment capacity is determined by obtaining the moment generated by the tensile and compressive forces.

Consider an arbitrary section with area 2A and one axis of symmetry, which is strengthened by a cover plate of area a as shown in Figure 2.94b. Further, assume that the yield strengths of the original section

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