Question

A hollow steel tube with an inside diameter of 100 mm must carry a tensile load of 300 KN. Determine the outside diameter of the tube if the stress is limited to 100 mN/m²
1. 219.22 mm
2. 118.22 mm
3. 117.57 mm
4. 130.12 mm

Answer 1

Correct Answer - Option 3 : 117.57 mm

Concept:

Stress: Internal resistance offered by the material to the deformation given by,

\(σ = \frac {F}{A}\)

Where, F = Force, A = Area

Calculation:

Given:

D_i = 100 mm = 0.1 m, F = 300 KN = 300000 N, σ = 100 MN/m2 = 10⁸ N/m2, D_o = ? 

Area, A = \(\frac{\pi}{4(D^2_o-D^2_i)}=\frac{\pi}{4(D^2_o-0.1^2)}\)

Using \(σ = \frac {F}{A}\)

\(10^8 = \frac {4\times 300000}{\pi (D_o ^2 \ -\ 0.1^2)}\)

\(D_o ^2 = 0.00382 + 0.01\)

Do = \(\sqrt{0.01382}\) 

Do =0.11757 m

Do = 117.57 mm