Question 18.5: The simply supported beam ABC shown in Fig. 18.10(a) has a c...

The bending moment diagram for the beam is constructed using the method of Section 3.4 and is shown in Fig. 18.10(b). Clearly as W is increased a plastic hinge will form first at \mathrm{D}, the point of application of the 4 W load. Thus, at collapse

\frac{3}{4} W_{\mathrm{U}} L=M_{\mathrm{P}}

so that

W_{\mathrm{U}}=\frac{4 M_{\mathrm{P}}}{3 L}

where W_{\mathrm{U}} is the value of W that causes collapse.