Consider the indeterminate beam of Example 5.15 (Figure E5.15). Let the beam material be e...

Consider the indeterminate beam of Example 5.15 (Figure E5.15). Let the beam material be elastic–perfectly plastic (Figure 4.4a). Let the cross section be rectangular with width b and depth h.

a. Determine the magnitude of the uniform load w = wY that causes yielding to initiate and locate the section at which it occurs.

b. Determine the magnitude of the uniform load w = wP that causes a plastic hinge to form at the wall support.

---

c. Determine the magnitude of the uniform load w = wPCthat causes the beam to form a plastic hinge to occur at the section of maximum positive moment. The load wPC is called the plastic collapse load for the member.

---

d. Construct a moment diagram for the beam for load wPC.

---

e. Draw a sketch of the deformed shape of the beam for w = wPC.

Note: The elastic segments of the beam rotate about a plastic hinge as rigid bodies. For this reason, the response of the beam at w = wpc is like a mechanism that rotates kinematically about hinges. Therefore, the term mechanism or kinematic mechanism is used in plastic collapse analysis (limit analysis) to describe this process.