Torsion
Torsion is the twisting of a structural member caused by an applied torque (moment). For circular shafts, the shear stress due to torsion varies linearly from zero at the center to maximum at the outer surface. The torsion formula is τ = (T × r) / J, where T is the torque, r is the radius, and J is the polar second moment of area.
Knowledge Check
1.A solid circular shaft of radius 50 mm is subjected to a torque of 5 kN·m. What is the maximum shear stress? (J = πr⁴/2)
2.The angle of twist (θ) of a shaft under torque is given by:
3.In a circular shaft under torsion, the shear stress distribution is:
4.For a solid circular shaft, the polar second moment of area (J) is:
5.A hollow circular shaft has an outer diameter of 100 mm and inner diameter of 80 mm. The polar moment of inertia (J) is:
6.What is the relationship between shear modulus (G), Young's modulus (E), and Poisson's ratio (ν)?
7.A shaft of length 2 m with G = 80 GPa and J = 1×10⁶ mm⁴ is subjected to a torque of 2 kN·m. What is the angle of twist in degrees?
8.The maximum shear stress in a circular shaft occurs at:
9.In torsion, the shear strain (γ) is related to the angle of twist (θ) by:
10.A solid shaft of diameter 40 mm is subjected to a torque that produces a maximum shear stress of 60 MPa. What is the applied torque?