Consider the indeterminate beam of Figure P4.27. Let the beam material be elastic–perfectl...

Consider the indeterminate beam of Figure P4.27. Let the beam material be elastic–perfectly plastic (Figure 4.4a). Also let the cross section be rectangular with width b and depth h. Treat the internal moment at A as the redundant one. Under sufficiently high load P,the moment at A will reach its limiting value MP, the fully plastic moment. Thus, the redundant moment is known.

a. Determine the magnitude of the force P = PPC that will cause a second hinge to form at B.

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b. Construct a moment diagram for the beam for load P = PPC.The load PPCis called the plastic collapse load for the member.

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c. Draw a sketch of the deformed shape of the beam for P = PPC.

FIGURE P4.27

FIGURE 4.4 Idealized stress–strain curves. (a) Elastic–perfectly plastic response. (b) Elastic–strain hardening response.