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Stress in Cylindrical Shell Equation and Calculator

Structural Design and Analysis
Pressure Vessel Design and Engineering

Stress in Cylindrical Shell Equation and Calculator

Uniform internal or external pressure induces in the longitudinal seam two times larger unit stress than in the circumferential seam because of the geometry of the cylinder.

A vessel under external pressure, when other forces (wind, earthquake, etc. ) are not factors, must be designed to resist the circumferential buckling only . When other loadings are present, these combined loadings may govern and heavier plate will be require than the plate which was satisfactory to resist the circumferential buckling only.

The compressive stress due to external pressure and tensile stress due to internal pressure shall be determined by the for the equations:

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Stresses in Cylindrical Shell Calculator:

Circumferential Joint

S₁ = PD/4t

Longitundinal Joint

S₂ = PD/2t

Where:

D = Mean diameter of vessel , inches
P= Internal or external pressure , psi
S₁ = Longitudinal stress, psi
S₂ = Circumferential (hoop) stress, psi
t = Thickness of shell, corrosion allowance excluded, inches

Example:

Given:

D = 96 inches
P= 15 psi
t = 0.25 inches

S₁ = PD/4t = (15 x 96) / (4 x 0.25) = 1440 psi

S₂ = PD/2t = (15 x 96) / ( 2 x 0.25) = 2880 psi

For towers under internal pressure and wind load the critical height above which compressive stress governs can be approximate

H = PD/32t

Where:

H = Critical Height