total decrease in lengthq a hollow cast iron

Question

Total decrease in length:

Q: A hollow cast iron cylinder 4 m long, 300 mm is the outer diameter, and thickness of metal 50 mm is subjected to central load on top when standing straight. The stress generated is 75000 kN/m². Assume that the Young's modulus for cast iron as 1.5 x 10⁸ KN/m²  find out Total decrease in length?

Outer diameter, D = 300 mm = 0.3 m Thickness, t = 50 mm = 0.05 m

Length, L = 4 m

Stress produced, σ = 75000 kN/m²

E = 1.5 x 108 kN/m²

Here diameter of cylinder, d = D - 2t = 0.3 - 2 × 0.05 = 0.2 m

Total decrease in length, dL: By using the relation,

Strain = change in length/original length =  dL_A/L

0.0005 = dL_A/4

dL_A  = 0.0005 × 4m = 0.002m=2mm

Thus decrease in length = 2 mm                                                          .......ANS