GATE CE 2019 Set 1 — Question 49
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Structural Engineering → Determinate Structures & Energy Methods → Unit Load Method
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Question
A portal frame shown in figure (not drawn to scale) has a hinge support at joint P and a roller support at joint R. A point load of is acting at joint R in the horizontal direction. The flexural rigidity, , of each member is . Under the applied load, the horizontal displacement (in , round off to 1 decimal place) of joint R would be __________
Correct answer
24.9 to 25.1
Solution
To find the horizontal displacement at joint R, we use the unit load method.1. Reactions and Internal Moments due to Applied Load ():
- Support P is a hinge, R is a roller. Let be the vertical reaction at R.
- Taking moments about P: (upwards).
- Member QR (origin at R, ): .
- Member PQ (origin at Q, ): .
- Vertical reaction at R: (upwards).
- Member QR: .
- Member PQ: .
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