Question

$\text{A propped cantilever ABCD is loaded as shown in}$
$\text{figure. If it is of uniform cross- section, the collapse}$
$\text{load of the beam is}k\frac{M_p}{L}\text{, The value of}k\text{will be\_\_\_\_\_.}$

Answer 1

$I^{st}possibility,$
Plastic hinge at C alone

$\therefore \frac{W_u}{4}\times (\frac{L}{3}\times \theta )=M_P\theta$

$\Rightarrow W_u=\frac{12M_P}{L}$

$I{I}^{nd}possiblility,$
Plastic hinges at A and B

$\Rightarrow W_u\times (\frac{L}{2}\times \theta )-\frac{W_u}{4}(\frac{L}{3}\times \theta )=M_P\left(\theta \right)+M_P(\theta +\theta )$

$\Rightarrow W_u=\frac{7.2M_P}{L}$

So, Collapse load,

$W_u=\frac{7.2M_P}{L}=K\frac{M_P}{L}$

$So,K=7.2$