Q40
When a machine member is subjected to torsion, the torsional shear stress set up in the member is
A.
Zero at both the centroidal axis and outer surface of the member
B.
Maximum at both the centroidal axis and outer surface of the member
C.
Zero at the centroidal axis and maximum at the outer surface of the member
AnswerD.
Maximum at the centroidal axis and zero at the outer surface of the member
Answer: Option C
Solution
Answer: Option C
Solution:
The torsional shear stress in a circular shaft varies linearly from the centre to the outer surface of the shaft.According to the torsion equation:
τ = (T × r) / J
Where:
τ = Torsional shear stress
T = Applied torque
r = Radial distance from the centre
J = Polar moment of inertia
Since the stress is directly proportional to the radial distance (τ ∝ r):
• At the centroidal axis (r = 0): Shear stress is zero.
• At the outer surface (r = R): Shear stress is maximum.
Therefore, the correct statement is that the torsional shear stress is zero at the centroidal axis and maximum at the outer surface of the member.