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What is the maximum torque transmitted by a hollow shaft of external radius ‘R’, internal radius ‘r’ and maximum allowable shear stress τ?

This question was previously asked in
UPPSC AE Mechanical 2019 Official Paper I (Held on 13 Dec 2020)
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Detailed Solution

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Explanation:

Torque transmission by a hollow shaft: 

Torsion equation = 

Torque transmission 

where, T = Torque, J = polar moment of inertia , R = Outer radius of shaft , r = internal radius of shaft

Zp = Polar modulus of the section

For hollow shaft

J = Ixx + Iyy = 

Zp = 

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More Equation of Torsion Questions

Q1.If the external diameter of a hollow shaft is three times greater than its internal diameter, what is the ratio of its torque-carrying capacity compared to that of a solid shaft of identical material and the same outer diameter?
Q2.Calculate the polar moment of inertia and the maximum torque transmitted by a solid shaft of diameter 100 mm and length 1.0 m. Let the angle of twist be 2° and the modulus of rigidity, G = 80 GPa. 
Q3.If the diameter of a solid steel bar is to be designed for torque T, then the permissible shear stress is considered as:
Q4.A 2.5 m long steel shaft of circular cross-section is subjected to torques as shown in the following figure. Torque at B = 500 Nm (anti-clockwise). Torque at C = 1000 Nm (clockwise). Determine the diameter of the shaft if permissible shear stress is 6000 kN/m2. Modulus of rigidity = 80 GN/m2.
Q5.A circular solid shaft of span L = 5 m is fixed at one end and free at the other end. A torque T = 100 kN.m is applied at the free end. The shear modulus and polar moment of inertia of the section are denoted as G and J, respectively. The torsional rigidity GJ is 50,000 kN.m2 /rad. The following are reported for this shaft: Statement i) The rotation at the free end is 0.01 rad Statement ii) The torsional strain energy is 1.0 kN.m With reference to the above statements, which of the following is true?
Q6.The magnitude of shear stress induced in a shaft due to applied torque varies from: 
Q7.Which of the following assumptions are True for torsion theory for axisymmetric sections?
Q8.The angle of twist is _______ proportional to the twisting moment.
Q9.The maximum torque that can be safely applied to a shaft of 100 mm diameter if the permissible angle of twist is 1 degree in a length of 3 m and the permissible shear stress is 30 N/mm2. Take G = 0.8 × 105 N/mm2.
Q10.Outside diameter of a hollow shaft is twice its inside diameter. Ratio of torque carrying capacity to that of a solid shaft of same outside diameter and same material is

More Torsion of Shaft Questions

Q1.Which of the following represents the polar modulus of the hollow shaft? [ If Do = External diameter and Di = Internal diameter ]
Q2.If the external diameter of a hollow shaft is three times greater than its internal diameter, what is the ratio of its torque-carrying capacity compared to that of a solid shaft of identical material and the same outer diameter?
Q3.For a thin planar ring of radius ‘r’ mm and thickness ‘t’ mm, its radius of gyration about the polar axis in mm is:
Q4.Two shafts, A and B, are of the same material. If the diameter of A is thrice the diameter of B, then the torque that can be transmitted by A will be:
Q5.If torsional rigidity increases in the torsion equation, then the:
Q6.A rectangular bar of width b and height h is being used as a cantilever. The loading is in a plane parallel to the side b. The section modulus is
Q7.If a shaft rotates at 120 rpm under a torque of 1200 Nm, the power transmitted is:
Q8.A beam of uniform rectangular cross - section is under a transverse load. The stress along the neutral axis of central cross - section is
Q9.A solid shaft of 'D' mm diameter is used to transmit torque, if maximum shear stress induced to the shaft is 'τ' N/mm2, what will the maximum torque transmitted by the shaft? 
Q10.Calculate the minimum diameter of the shaft, such that the shearing stress does NOT exceed 50 N/mm2 during torque transmission of 15000 N-m.
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Q4.Which of the following represents the polar modulus of the hollow shaft? [ If Do = External diameter and Di = Internal diameter ]
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