Question

A pipe has an outside diameter of 25 mm, an inside diameter of 15 mm and length 0.40 m and it supports a compressive load of 40 kN. The pipe shortens by 0.5 mm when the load is applied. Determine (a) the compressive stress, (b) the compressive strain in the pipe when supporting this load. 

Answer 1

Compressive force F = 40 kN = 40000 N,

and cross-sectional area A = π/4 (D² − d²)

where D = outside diameter = 25 mm and 

d = inside diameter = 15 mm. Hence

(a) Compressive stress

(b) Contraction of pipe when loaded, 

x = 0.5 mm = 0.0005 m, and original length 

L = 0.40 m. Hence, compressive strain,

ε = x/L = 0.0005/0.4

= 0.00125 (or 0.125%)