Daily Concept Booster Mechanical Engineering: Thin spherical vessel

Thin spherical shell

In this case Hoop stress and longitudinal stress are equal
σ_L = σ_h = pd/4t
And Also Hoop strain and longitudinal strain are equal
∈_L= ∈_h = pd/4tE (1 – μ)
So, Volumetric strain of in spherical shell is
∈_V = 3pd/4tE (1 – μ)

Important points:

The thickness ratio for thin cylindrical shell (t_c) and thin spherical shell (t_s), for same strain
t_c/t_s = (2-μ)/(1-μ)
The thickness ratio for cylindrical shell (t_c) and sphere (t_s), for same maximum stress
t_c/t_s = 2

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