Question

Determine the fully plastic moment capacity of the frame as shown in figure, if the moment of inertia of the beam and columns is same.

• A. 80 kN-m
• B. 120 kN-m
• C. 100 kN-m
• D. 160 kN-m

Answer 1

The correct option is D 160 kN-m

1. Beam Mechanism :


Internal work done = External work done

$\Rightarrow Mp\theta +Mp(\theta +\theta )+Mp\theta =80\times (4\times \theta )$
$=M_p=80KN-m$

2. Sway Mechanism :



Internal work done = External work done
$Mp\theta +Mp\theta +Mp\theta =60\times (8\times \theta )$

$\Rightarrow M_p=160KN-m$

3. Combined Mechanism :

Internal work done = External work done

$\Rightarrow Mp\theta +Mp(\theta +\theta )+Mp(\theta +\theta )=80\times (4\times \theta )+60\times (8\times \theta )$

$\Rightarrow M_p=160kN-m$

$\text{Therefore, The section has to have Mp = 160 KN-m}$