Question

The plastic moment capacity for the propped cantilever as shown in figure is W.

• A. 1.364

Answer 1

The correct option is A 1.364

Number of independent mechanisms = Number of possible plastic hinges - Number of redundancies
= 2 - 1 = 1

The mechansim is shown in figure.
$\Delta =5\theta =3\varphi$
From principal of virtual work,
$W.\Delta =M_P\theta +M_P(\theta +\varphi )$
$\Rightarrow W\left(5\theta \right)=M_P\theta +M_P(\theta +\varphi )$
$\Rightarrow W\left(5\theta \right)=M_P\theta +M_P(\theta +\frac{5\theta }{3})$
$\Rightarrow M_P=\frac{15}{11}W=1.364W$