GATE CE 2026 Set 2 — Question 49
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Structural Engineering → Connections & Plastic Analysis → Plastic Analysis (Frames)
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Question
A rigid-jointed portal frame, shown in the figure, consists of beam and columns of equal length . The frame has a fixed support at one end and a roller support at the other end. The frame is subjected to a uniformly distributed load and a lateral load as shown in the figure. The plastic moment capacity of the beam and column sections is . Consider a combined beam-column mechanism for plastic collapse. By applying the virtual work equation corresponding to the combined plastic collapse mechanism, is expressed as where and are constants.The value of is ______ (in integer).
Correct answer
4 to 4
Solution
For a combined mechanism in the given portal frame:
1.External Work ():
- Work done by lateral load :
- Work done by UDL : W_w = \int_0^L w \cdot y(x) dx = w \cdot rac{1}{2} \cdot L \cdot rac{L heta}{2} = rac{wL^2 heta}{4}
- Total
- Plastic hinges form at the fixed base (rotation ), mid-span of the beam (rotation ), and the top-right rigid joint (rotation due to combined sway and beam rotation).
- Total
- M_p = rac{1}{5}PL + rac{0.25}{5}wL^2 = 0.2PL + 0.05wL^2
- rac{C_1}{C_2} = rac{0.2}{0.05} = 4
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