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 Nm 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)

Explanation:

Given:

D = 50 mm; S_yt = 300 MPa

Axial stress due to P, σ_x = σa = \(\frac{P}{A}=\frac{100 \times 10^{3}}{\left(\frac{\pi \times 50^{2}}{4}\right)}=50.93 \mathrm{MPa}\)

Shear stress due to T, τ_xy = (τ_t)_max = \(\frac{16 \times T}{\pi D^{3}}=\frac{16 \times 600 \times 10^{3}}{\pi \times 50^{3}}=24.446 \mathrm{MPa}\)

σ_y = 0

\(\left(\sigma_{t}\right)_{\text {per }} \geq \sqrt{\sigma_{x}^{2}+3 \tau_{x y}^{2}}\)

⇒ \(N \leq \frac{300}{66.232}\)

⇒ N ≤ 4.529

⇒ N = 4.5