**Related Resources: pressure-vessel**

### Toroidal Shell Internal or External Pressure Formulas and Calculator for Stress and Deflection

Toroidal Shell Stress and Deflection Equation and Calculator.

Uniform Internal or External pressure, q force/unit area.

Per. Roarks Formulas for Stress and Strain for membrane stresses and deformations in thin-walled pressure vessels.

Preview: Toroidal Shell Stress and Deflection Calculator

Toroidal shell |

For b/t > 10

Meridional Stress

at point O

Circumferential Hoop Stress

Radial Displacement of Circumference

Where used:

E = Modulus of Elasticity (lbs/in^{2})

*v* = Poisson's ratio

q = ^{2})

σ_{1,2} = Stress, (lbs/in^{2})

a = Distance (in)

b = Radius (in)

r = Torid radius (in)

t = Wall thickness (in)

y = Vertical level from bottom of vessel (in)

θ = Angle (deg.)

ψ = Rotation of a meridian from its unloaded position, positive when that meridional rotation represents an increase in ΔR when y or θ increases;

Reference:

Roarks Formulas for Stress and Strain, 7th Edition