Question

A hollow pipe inside diameter 40 mm and outside diameter 50 mm is compressed by a an axial force of 55 kN. Calculate compressive stress in the material of the pipe.
1. 77.80 N/mm²
2. 75.80 N/mm²
3. 70.80 N/mm²
4. 78.80 N/mm²

Answer 1

Correct Answer - Option 1 : 77.80 N/mm²

Concept:

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

\(σ = \frac {F}{A}\)

Where, F = Force, A = Area

Calculation:

Given:

Di = 40 mm, Do = 50 mm,  F = 55 kN

Area, A = \(=\frac{\pi}{4}(D_o^2-D_i^2)=\frac{\pi}{4}\times (50^2-40^2)=706.85~mm^2\)

Using \(σ = \frac {F}{A}\)

\(σ = \frac {F}{A}=\frac{55\times 10^3}{706.85}=77.80~\) N/mm2