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/m^{2}. Assume that the Young's modulus for cast iron as 1.5 x 10^{8} KN/m^{2} 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/m^{2}
E = 1.5 x 108 kN/m^{2}
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