Magnitude of the load - hollow cast iron cylinder:
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 Magnitude of the load,
Sol.: 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
Magnitude of load P:
By using the relation, σ =P/A
or P = σ × A = 75000 × Π /4 (D_{2} - d_{2})
= 75000 × Π /4 (0.32 - 0.22)
or P = 2945.2 kN .......ANS