GATE CE 2020 Set 2 — Question 39
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Structural Engineering → Determinate Structures & Energy Methods → Determinate Structures
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Question
The planar structure RST shown in the figure is roller-supported at S and pin-supported at R. Members RS and ST have uniform flexural rigidity () and S is a rigid joint. Consider only bending deformation and neglect effects of self-weight and axial stiffening.
When the structure is subjected to a concentrated horizontal load at the end T, the magnitude of rotation at the support R, is
Correct answer
(B) (PL²)/(12EI)
Solution
The horizontal load at T creates a clockwise moment at joint S:
Member RS is a beam of length , pinned at R and rigid at S. The moment is applied at joint S. According to the slope-deflection equations or standard beam formulas, the rotation at the pinned end R due to a moment applied at the other end S is:
Substituting :
Member RS is a beam of length , pinned at R and rigid at S. The moment is applied at joint S. According to the slope-deflection equations or standard beam formulas, the rotation at the pinned end R due to a moment applied at the other end S is:
Substituting :
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