Design of Shafts Questions and Answers

Q: 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

The minimum design diameter is 16 mm.The design shear stress is 140/2 = 70 MPa. For a solid shaft in torsion:\[ \begin{aligned} \tau &= \frac{16T}{\pi d^{3}} \\ d^{3} &= \frac{16 \times 50\,000}{\pi \times 70} = 3638\ \text{mm}^{3} \\ d &= 15.4\ \text{mm} \end{aligned} \]The next listed size up is 16 mm, so that is the minimum allowable design diameter. 8 mm is far too small, and without the factor of safety the diameter would be 12.2 mm, which still rounds up to 16 among these options. 24 and 32 mm are safe but not the minimum.

Which of the following factors does NOT directly contribute to the determination of the size and geometry of a shaft?

A.Material of the adjacent components in assembly
B.Maximum torque experienced by the shaft
C.Maximum bending moment experienced by the shaft
D.Rotational speed of the shaft

Exam Year(s)

DSSSB - 2023,

Answer: A

The material of the adjacent components in the assembly does not directly decide the size and geometry of a shaft. The size is fixed by the maximum torque, the maximum bending moment, and the rotational speed (which affects power and critical speed). So the first option is the factor that does not directly contribute.

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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

Exam Year(s)

GATE ME - 2012,

Answer: B

The minimum design diameter is 16 mm.

The design shear stress is 140/2 = 70 MPa. For a solid shaft in torsion:

\[ \begin{aligned} \tau &= \frac{16T}{\pi d^{3}} \\ d^{3} &= \frac{16 \times 50\,000}{\pi \times 70} = 3638\ \text{mm}^{3} \\ d &= 15.4\ \text{mm} \end{aligned} \]

The next listed size up is 16 mm, so that is the minimum allowable design diameter. 8 mm is far too small, and without the factor of safety the diameter would be 12.2 mm, which still rounds up to 16 among these options. 24 and 32 mm are safe but not the minimum.

Discuss in Forum

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