GATE CE 2016 Set 2 — Question 43
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Structural Engineering → Determinate Structures & Energy Methods → Determinate Structures
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Question
The portal frame shown in the figure is subjected to a uniformly distributed vertical load (per unit length).
The bending moment in the beam at the joint ‘Q’ is
Correct answer
(A) zero
Solution
In the given portal frame, support P is a hinge and support S is a roller.
1.Since there are no horizontal loads acting on the frame, the horizontal reaction at the hinge support P () must be zero ().
2.The bending moment at any point in the column PQ is given by , where is the distance from P. Since , the bending moment throughout the column PQ is zero.
3.At joint Q, by equilibrium of the joint, the moment in the beam QR must equal the moment in the column PQ. Since the moment in the column at Q is zero, the bending moment in the beam at joint Q is also zero.
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