GATE CE 2016 Set 2 — Question 18
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Structural Engineering → Statics & Rigid Bodies → Equilibrium Equations
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Question
An assembly made of a rigid arm A-B-C hinged at end A and supported by an elastic rope C-D at end C is shown in the figure. The members may be assumed to be weightless and the lengths of the respective members are as shown in the figure.
Under the action of a concentrated load at C as shown, the magnitude of tension developed in the rope is
Correct answer
(B) P√(2)
Solution
Taking moments about hinge A:Clockwise moment due to load at C:
Counter-clockwise moment due to tension in rope CD:
The rope CD makes an angle of with the horizontal (since horizontal and vertical projections are both ).
The tension acts at point C.
Horizontal component
Vertical component
Moment of about A: (CCW)
Moment of about A: (CCW)
Total CCW moment
Equating moments:
Counter-clockwise moment due to tension in rope CD:
The rope CD makes an angle of with the horizontal (since horizontal and vertical projections are both ).
The tension acts at point C.
Horizontal component
Vertical component
Moment of about A: (CCW)
Moment of about A: (CCW)
Total CCW moment
Equating moments:
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