P

Unrestricted plastic flow

Load

Unrestricted plastic flow

Load

by SL Deflection

FIGURE 2.92 Force redistribution in a three-bar system: (a) elastic, (b) partially yielded, (c) fully plastic, and (d) load-deflection curve.

The corresponding displacement at first yield is

After bar 2 is yielded, the system continues to take additional load until all the three bars reach their maximum strength of oyA, as shown in Figure 2.92c. The plastic limit load of the system is thus written as ft = 3syA

The process of successive yielding of bars in this system is known as inelastic redistribution of forces. The displacement at the incipient of collapse is

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Figure 2.92d shows the load-displacement behavior of the system when subjected to increasing force. As load increases, bar 2 will reach its maximum strength first. As it is yielded, the force in the member remains constant, and additional loads on the system are taken by the less critical bars. The system will eventually fail when all three bars are fully yielded. This is based on an assumption that material strain hardening does not take place.

2.11.4 Concept of Plastic Hinge

A plastic hinge is said to form in a structural member when the cross-section is fully yielded. If material strain hardening is not considered in the analysis, a fully yielded cross-section can undergo indefinite rotation at a constant restraining plastic moment Mp.

Most of the plastic analyses assume that plastic hinges are concentrated at zero-length plasticity. In reality, the yield zone is developed over a certain length, normally called the plastic hinge length, depending on the loading, boundary conditions, and geometry of the section. The hinge lengths of beams (DL) with

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