Question

The plastic collapse load P for the propped cantilever supporting two point loads as shown in figure in terms of plastic moment capacity (Mp) is given by _______.

• A. $\frac{3M_p}{L}$
• B. $\frac{6M_p}{L}$
• C. $\frac{5M_p}{L}$
• D. $\frac{4M_p}{L}$

Answer 1

The correct option is D $\frac{4M_p}{L}$


Degree of static indeterminacy for vertical loading = 1
So number of plastic hinge required for collapse of structure = 1 + 1 = 2

Mechanism-1
One plastic hinge will form at fixed support and other below point load W (at distance L/3 from fixed support)



From BMD, it is clear that value of BM is more at D than value of bending moment at point C. So plastic hinge will form at point D not at C, hence mechanism 1 is not possible.

Mechanism-2
One plastic hinge at A and other at D from collapse BMD

$\frac{PL}{3}=M_p+\frac{M_p}{3}$

$\Rightarrow \frac{PL}{3}=\frac{4M_p}{3}$

$\Rightarrow P=\frac{4M_p}{L}$