Question

A propped cantilever of span L is carrying a vertical concentrated load acting at mid-span. The plastic moment of the section is $M_p$. The magnitude of the collapse load is ______.

• A. $\frac{2M_p}{L}$
• B. $\frac{8M_p}{L}$
• C. $\frac{6M_p}{L}$
• D. $\frac{4M_p}{L}$

Answer 1

The correct option is C $\frac{6M_p}{L}$


No. of plastic hinge required for collapse of structure = Degree of indeterminacy + 1 = 1 + 1 = 2

One plastic hinge will form at the fixed support and other will form at the location of point load.

From BMD
$\frac{wL}{4}=M_p+\frac{M_p}{2}$

$\frac{wL}{4}=\frac{3}{2}\frac{M_p}{L}$

$w=\frac{6M_p}{L}$