Question

A steel portal frame has dimensions, plastic moment capacities and applied loads as shown in the figure. The vertical load is always twice of the horizontal load. The collapse load P required for the development of a beam mechanism is _______.

• A. $\frac{8M_p}{L}$
• B. $\frac{4M_p}{L}$
• C. $\frac{6M_p}{L}$
• D. $\frac{3M_p}{L}$

Answer 1

The correct option is D $\frac{3M_p}{L}$


Degree of static indeterminacy = 3

Maximum number of hinge for collapse of structure = 3 + 1 = 4

However, for Beam Mechanism in BC we need only 3 hinges.
For beam mechanism number of hinge required =3
One under the load and two at supports B and C


Applying principle of virtual work

$\Rightarrow -M_p\theta -2M_p\theta -2M_p\theta -M_p\theta +2P\Delta =0$

$\Rightarrow 6M_p\theta =2P.\theta .L$

$P=\frac{3M_p}{L}$