Two hemispherical shells of inner diameter 1m are joined together with 12 equally spaced bolts. If the interior pressure is raised to 300kPa above atmospheric pressure, determine the tensile force in each bolt.

F = 2,355 10⁵ N

Explanation:

The pressure is distributed throughout the sphere with the same value and is defined by

P = F / A

F = P A

Therefore, on each bolt there is an internal force and external force

∑ F = F_int - F_ext

∑ F = P_int A - P_atm A

F = A (P_int - P_atm)

P_int = 300 10³ + P_atm

F = A 300 10³

The area of the sphere layer is

A = π r² = π / 4 d²

A = π / 4 1²

A = 0.785 m2

F = 0.785 (300 10³)

F = 2,355 10⁵ N