GATE CE 2024 Set 1 — Question 40
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Structural Engineering → Torsion, Stress Transformation & Columns → Torsion of Circular Shafts
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Question
A homogeneous shaft with fixed supports at both ends is subjected to a torsional moment at point , as shown in the figure. The polar moments of inertia of the portions and of the shaft with circular cross-sections are and , respectively. The torsional moment reactions at the supports and are and , respectively.
(Figure NOT to scale)If and , the ratio of the lengths is
Correct answer
(A) 0.50
Solution
For a shaft fixed at both ends with a torque applied at an intermediate point :
Rearranging for the ratio :
Given
Given
Substituting the values:
Correct option is (A).
1.Equilibrium:
2.Compatibility: The angle of twist at calculated from both ends must be the same.
Rearranging for the ratio :
Given
Given
Substituting the values:
Correct option is (A).
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