## GATE ME solved Questions on Torsion (Strength of Materials)

Question #1

The cross sections of two hollow bars made of the same material are concentric circles as shown in the figure. It is given that r3 > r1 and r4 > r2 and that the areas of the cross-sections are the same. J1 and J2 are the torsional rigidities of the bars on the left and right, respectively. The ratio J2/J1 is

[GATE 2016 Set 1, 1 mark]

(A) > 1

(B) < 0.5

(C) =1

(D) between 0.5 and 1

Question #2

A rigid horizontal rod of length 2L is fixed to a circular cylinder of radius R as shown in the figure. Vertical forces of magnitude P are applied at the two ends as shown in the figure. The shear modulus for the cylinder is G and the Young’s modulus is E.

[GATE 2016 Set 2, 2 marks]

The vertical deflection at point A is

(A) $PL^3$ / $\pi$ $R^4G$

(B)   $PL^3$ / $\pi$ $R^4E$

(C) $2PL^3$ / $\pi$ $R^4E$

(D) $4PL^3$ / $\pi$ $R^4G$

Question #3

Two circular shafts made of same material, one solid (S) and one hollow (H), have the same length and polar moment of inertia. Both are subjected to same torque. Here, $\LARGE \tau$S is the twist and $\LARGE \tau$ S is the maximum shear stress in the solid shaft, whereas $\LARGE \tau$H is the twist and $\LARGE \tau$H is the maximum shear stress in the hollow shaft. Which one of the following is TRUE?

[GATE 2016 Set 3, 2 marks]

(A) $\theta$ s  = $\theta$ H and $\tau$ s = $\tau$ H
(B)$\theta$ S > $\theta$ H and $\tau$ S > $\tau$ H
(C)$\theta$S < $\theta$H and $\tau$S < $\tau$H
(D)$\theta$S = $\theta$H and $\tau$S <$\tau$H

Question #4

Consider a stepped shaft subjected to a twisting moment applied at B as shown in the figure. Assume shear modulus, G = 77 GPa. The angle of twist at C (in degrees) is __________

[GATE 2015 Set 1, 1 mark]

Question #5

A rope-brake dynamometer attached to the crankshaft of an I.C. engine measures a brake power of 10 kW when the speed of rotation of the shaft is 400 rad/s. The shaft torque (in N-m) sensed by the dynamometer is ___________

[GATE 2015 Set 2, 1 mark]

Question #6

A hollow shaft of 1 m length is designed to transmit a power of 30 kW at 700 rpm. The maximum permissible angle of twist in the shaft is 1°. The inner diameter of the shaft is 0.7 times the outer diameter. The modulus of rigidity is 80 GPa. The outside diameter (in mm) of the shaft is__________

[GATE 2015 Set 2, 2 marks]

Question #7

Two solid circular shafts of radii R1 and R2 are subjected to same torque. The maximum shear stresses developed in the two shafts are $\tau$  and $\tau$  . If R1/ R2=2 , then $\frac{\tau_{1}}{\tau_{2}}$is _______

[GATE 2014 Set 3, 1 mark]

Question #8

A solid circular shaft needs to be designed to transmit a torque of 50 N.m. If the allowable shear stress of the material is 140 MPa, assuming a factor of safety of 2, the minimum allowable design diameter in mm is

(A)8

(B) 16

(C) 24

(D) 32

[GATE 2012, 2 marks]

Question #9

A torque T is applied at the free end of a stepped rod of circular cross-sections as shown in the figure. The shear modulus of the material of the rod is G. The expression for diameter to produce an angular twist $\theta$ at the free end is

(A) $\left(\frac{32TL}{\pi \theta G} \right)^{1/4}$

(B) $\left(\frac{18TL}{\pi \theta G} \right)^{1/4}$

(C) $\left(\frac{16TL}{\pi \theta G} \right)^{1/4}$

(D) $\left(\frac{2TL}{\pi \theta G} \right)^{1/4}$

[GATE 2011, 2 marks]

Practice other topics from Strength of Materials:

Stress and strain

Bending