magnitude of the load - hollow cast iron

Question

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/m². Assume that the Young's modulus for cast iron as 1.5 x 10⁸ KN/m²  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/m²

E = 1.5 x 108 kN/m²

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 (D₂  - d₂)

= 75000 × Π /4 (0.32 - 0.22)

or P = 2945.2 kN                                                             .......ANS