GATE 2024 ME – Question 56
A solid massless cylindrical member of 50 mm diameter is rigidly attached at one end, and is subjected to an axial force $P = 100$ kN and a torque $T = 600$ N.m at the other end as shown. Assume that the axis of the cylinder is normal to the support. Considering distortion energy theory with allowable yield stress as 300 MPa, the factor of safety in the design is _____ (*rounded off to 1 decimal place*).
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 4.48 to 4.52
Explanation
The axial stress is $\sigma = \frac{P}{A} = \frac{100\,000}{\frac{\pi}{4}(50)^2} = 50.93$ MPa. The torsional shear stress is $\tau = \frac{16T}{\pi d^3} = \frac{16 \times 600\,000}{\pi(50)^3} = 24.45$ MPa. The von Mises (distortion energy) stress is $\sigma_e = \sqrt{\sigma^2 + 3\tau^2} = \sqrt{50.93^2 + 3(24.45)^2} = 66.2$ MPa. The factor of safety is $\frac{300}{66.2} = 4.5$.