Daily Concept Booster Mechanical Engineering: Thin cylinder

Important formulas for thin cylinder

Let p = Pressure of fluid
t = Thickness of the cylinder
d = Inside diameter of the cylinder
μ = Poisson’s ratio
Longitudinal Stress (σ_L) = pd/4t
Hoop Stress (σ_h) = pd/2t
Longitudinal Strain
∈_L=σ_L/E-〖μσ〗_h/E
∈_L=pd/4tE (1-2μ)
Hoop Strain
∈_h=σ_h/E-〖μσ〗_L/E
∈_h=pd/4tE (2-μ)

Ratio of Hoop Strain to Longitudinal Strain
∈_h/∈_L = (2-μ)/(1-2μ)

Volumetric Strain (∈_V) of Cylinder
∈_V = pd/4tE (5 – 4μ)

Note: If fluid is compressible, volumetric strain will be
∈_V = pd/4tE (5 – 4μ) + p/K
Where, K = Bulk modulus of fluid

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