Strength of Shafts in Torsion

Q. A hollow circular shaft has an outer diameter of 100 mm , inner diameter of 50mm and a wall thickness of 25 mm. The allowable shear stress in the shaft is 125 MPa. The maximum torque the shaft can transmit is

1. 46 kN m
2. 24.5 kN m
3. 23 kN m
4. 11.5 kN m

Q. A solid circular shaft has been subjected to a pure torsion moment. The ratio of maximum shear stress to maximum normal stress at any point would be

1. 1 : 2
2. 1 : 1
3. 2 : 3
4. 2 : 1

Q. If a shaft is simultaneously subjected to a torque T and a bending moment M, the ratio of maximum bending stress and maximum shearing stress is given by

1. 2M/T
2. M/T
3. 2T/M
4. T/M

Q. A circular shaft which has a diameter of 100 mm is subjected to torque of 5 kN-m. The shear stress in $N/m{m}^2$, induced in the shaft would be

1. $\frac{160}{\pi }$
2. $\frac{120}{\pi }$
3. $\frac{125}{\pi }$
4. $\frac{80}{\pi }$

Q. Two shafts, one of solid section and the other of hollow section, of same material and weight having same length are subjected to equal torsional force. What is the torsional stiffness of hollow shaft?

1. Equal to that of the solid shaft
2. Less than that of the solid shaft
3. More than that of the solid shaft
4. Exactly half of that of the solid shaft

Q. The maximum shear stress produced in a shaft in $5N/m{m}^2$. The shaft is of 40 mm diameter. What is the approximate value of twisting moment?

1. 628 N-m
2. 63 N-m
3. 126 N-m
4. 251 N-m

Q. A solid shaft has diameter 80 mm. It is subjected to a torque of 4 kN-m. The maximum shear stress induced in the shaft would be

1. $\frac{75}{\pi }N/m{m}^2$
2. $\frac{250}{\pi }N/m{m}^2$
3. $\frac{125}{\pi }N/m{m}^2$
4. $\frac{150}{\pi }N/m{m}^2$

Q. A solid shaft has length and diameter ${}^{\prime }{L}_s^{\prime }$ and D respectively. A hollow shaft of length $L_h$, external diameter D, and internal diameter 'd' repectively. Both are of the same material. The ratio of torsional stiffness of hollow shaft to that of solid shaft is

1. $[1+{\left(\frac{d}{D}\right)}^4].\frac{L_s}{L_h}$
2. $[1-{\left(\frac{d}{D}\right)}^4].\frac{L_h}{L_s}$
3. $[1-{\left(\frac{d}{D}\right)}^4].\frac{L_s}{L_h}$
4. $[1+{\left(\frac{D}{d}\right)}^4].\frac{L_s}{L_h}$

Q. A 40 mm diameter shaft is subjected to a twisting moment $M_t$. If shear stress developed in shaft is $5N/m{m}^2$, what is the value of the twisting moment?

1. 628.8 N-m
2. 328.4 N-m
3. 62.8 N-m
4. 30.4 N-m

Q. What is the Polar Modulus of a solid circular metal shaft of diameter 8 cm?

1. $64\pi c{m}^2$
2. $32\pi c{m}^2$
3. $16\pi c{m}^2$
4. $8\pi c{m}^2$

Q. A solid shaft of circular cross-section is subjected to a torque T which produces a maximum shear stress $f_s$ in the shaft. The diameter of the shaft should be

1. $\sqrt{\frac{\pi f_s}{16T}}$
2. $3\sqrt{\frac{\pi f_s}{16T}}$
3. $\sqrt{\frac{16T}{\pi f_s}}$
4. $3\sqrt{\frac{16T}{\pi f_s}}$

Q. The ratio of torsional moments or resistance of a solid circular shaft of diameter D to that of a hollow shaft with external diameter D and internal diameter d.Both the shafts are of the same material.

1. $\frac{D^4}{D^4-d^4}$
2. $\frac{D^4-d^4}{D^4}$
3. $\frac{D^3}{D^3-d^3}$
4. $\frac{D^3-d^3}{D^3}$

Q. A solid circular shaft has a diameter d. Its polar modulus will be

1. $\frac{\pi }{16}{d}^2$
2. $\frac{\pi }{64}{d}^3$
3. $\frac{\pi }{16}{d}^3$
4. $\frac{\pi }{32}{d}^2$

Q. In a circular shaft of diameter d, subjected to a torque T, the maximum shear stress inducted is

1. proportional to $d^3$
2. proportional to $d^4$
3. inversely proportional to $d^3$
4. inversely proportional to $d^4$

Q. A circular shaft of diameter 30 mm having shear modulus G = 80 GPa is subjected to moment as shown below.

What is the maximum shear stresses developed at periphery of shaft at A?

1. 20.6 MPa
2. 15.3 MPa
3. 7.4 MPa
4. Zero

Q. A solid circular shaft of diameter 'd' is subjected to a twisting moment T. The maximum shear stress in the shaft is proportional to

1. $d^2$
2. $d^2$
3. $1/d^2$
4. $1/d^3$

Q. 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 .

1. 23

Q. A bar AB of diameter 40 mm and 4 m long is rigidly fixed at its ends. A torque 600 N-m is applied at a section of the bar, 1 m from end A. The fixing couples $T_{A}and{T}_B$ at the supports A and B, respectively are

1. 200 N-m and and 400 N-m
2. 300 N-m and 150 N-m
3. 450 N-m and 150 N-m
4. 300 N-m and 100 N-m

Q. A solid shaft of 100 mm diameter in a small hydraulic turbine is subjected to an axial compressive load of $100\pi kN$ and a torque of $5\pi kN-m$. The maximum shearing stress induced in the shaft is

1. $20\sqrt{3}N/m{m}^2$
2. $20\sqrt{8}N/m{m}^2$
3. $20\sqrt{15}N/m{m}^2$
4. $20\sqrt{17}N/m{m}^2$

Q. A circular shaft of diameter 'D' is made of a material for which Young's Modulus of Elasticity is 'E' and Poisson's Ratio is 'v'. The ratio of flexural rigidity to torsional rigidity for the shaft is

1. $4(1+v)$
2. $15(1-2v)$
3. $(1+v)$
4. $0.25(1+v)$

Q. If a circular shaft is subjected to a torque T and a bending moment M, the ratio of the maximum shear stress to the maximum bending stress is given by

1. $\frac{2M}{T}$
2. $\frac{T}{2M}$
3. $\frac{2T}{M}$
4. $\frac{M}{2T}$

Q. The polar moment of inertia of the cross-section of the member is required to assess the strength of the member in

1. bending
2. torsion
3. axial force
4. shear

Q. Consider the following statements :
If a solid circular shaft and a hollow circular shaft have the same torsional strength, then

1. the weight of the hollow shaft will be greater than of the soild shaft
2. the external diameter of the hollow shaft will be greater than of the solid shaft
3. the stiffness of the hollow shaft will be equal to that of the solid shaft

Which of these statements is/are correct?

1. 1, 2 and 3
2. 2 and 3
3. 1 alone
4. 1 and 2

Q. A 60 mm dia. shaft is subjected to a torque of 6 kNm. $C=8\times {10}^{4}N/m{m}^2$. The maximum shear stress induced in the shaft in $N/m{m}^2$, is nearly

1. $\frac{8000}{9\pi }$
2. $\frac{4000}{9\pi }$
3. $\frac{12000}{9\pi }$
4. $\frac{16000}{9\pi }$

Q. For the circular shaft AB, as shown in the figure below, a torque 'T' is applied at section XX at C, such that b/a = 1.5. The shaft is uniform in section.


What is the ratio of $\frac{T_A}{T_B}$?

1. 2
2. 1.5
3. 0.67
4. 0.5

Q. A circular shaft of diameter D is subjected to a torque T. The maximum shear stress of the shaft will be

1. proportional to $D^3$
2. proportional to $D^4$
3. inversely proportional to $D^3$
4. inversely proportional to $D^4$

Q. A solid shaft of circular cross-section is subjeted to torque T which produces a maximum shear stress $\tau$ in the shaft. The diameter of the shaft will be

1. $3\sqrt{\frac{16T}{\pi \tau }}$
2. $\sqrt{\frac{\pi \tau }{16T}}$
3. $3\sqrt{\frac{\pi \tau }{16T}}$
4. $\sqrt{\frac{16T}{\pi \tau }}$

Q. Statement (I) : Hollow shafts are preferred in propeller shafts of airplanes

Statement (II) : Use of hollow shafts affords considerable reduction in the weight of the shaft for equal performance.

1. Both Statement (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (I)
2. Both Statement (I) and Statement (II) are individually true but Statement (II) is NOT the correct explanation of Statement (I)
3. Statement (I) is true but Statement (II) is false
4. Statement (I) is false but Statement (II) is true

Q. A circular shaft is subjected to a bending moment $M_b$ and a twisting moment $M_t$. What is the ratio of maximum shear stress and the maximum bending stress?

1. $\frac{2M_t}{M_b}$
2. $\frac{M_t}{M_b}$
3. $\frac{M_t}{2M_b}$
4. $\frac{1.5M_t}{M_b}$