Past Year Questions: Torsion of Shafts & Pressure Vessels | Solid Mechanics - Mechanical Engineering PDF Download

Q.1 A closed thin-walled tube has thickness, t, mean enclosed area within the boundary of the centerline of tube's thickness, A_m and shear stress, τ. Torsional moment of resistance T, of the section would be    [2019 : 1 Mark, Set-ll]
(a) 2τA_mt
(b) 4τA_mt
(c) τA_mt
(d) 0.5τA_mt
Ans. (A)
Solution:

Shear stress,

∴

Q.2 A solid circular beam with radius of 0.25 m and length of 2 m is subjected to a twisting moment of 20 kNm about the z-axis at the free end, which is the only load acting as shown in the figure. The stress component τ_ry at Point ‘ M ’ in the cross- section of the beam at a distance of 1 m from the fixed end is    [2018 : 1 Mark, Set-I]

(a) 0.0 MPa
(b) 0.51 MPa
(c) 0.815 MPa
(d) 2.0 MPa
Ans. (A)
Solution:


The only non-zero stresses are  if θ is 90⁰ then θ = y
Hence
= 16T/πd³ = 0.815 MPa
But in rest of the planes shear stresses are zero, hence,

Q.3 A hollow circular shaft has an outer diameter of 100 mm and inner diameter of 50 mm. If the allowable shear stress is 125 MPa, the maximum torque (in kN-m) that the shaft can resist is _____.    [2017 : 2 Marks, Set-II]
Solution:


⇒ T = 23 kNm

Q.4 A solid circular shaft of diameter d and length L is fixed at one end and free at the other end. A torque T is applied at the free end. The shear modulus of the material is G. The angle of twist at the free end is    [2010 : 1 Mark]




Ans. (b)
Solution:
Angle of twist is given by,

⇒