Related Resources: pressure-vessel

### Cone Cylinder Stress and Deflection Equations and Calculator

Cone Cylinder Stress and Deflection Filled to Depth with Liquid Tangential Edge Support Equation and Calculator. Per. Roarks Formulas for Stress and Strain for membrane stresses and deformations in thin-walled pressure vessels.

 Cone Cylindrical

At any level y below the liquid surface y < d

Meridional Stress

Circumferential or Hoop Stress

Radial Displacement of Circumference

Change in height dimension y

Rotation of a meridian from its unloaded position

At any level y above the liquid level

Note: There is a discontinuity in the rate of increase in fluid pressure at the top of the liquid. This leads to some bending in this region and is indicated by a discrepancy in the two expressions for the meridional slope at y = d.)

Meridional Stress

Circumferential or Hoop Stress
σ2 = 0

Radial Displacement of Circumference

Change in height dimension y

Rotation of a meridian from its unloaded position

Rotation of a meridian from its unloaded position
Where used:
E = Modulus of Elasticity (lbs/in2)
v = Poisson's ratio
δ = Liquid density (lbs/in3)
σ1,2 = stress, (lbs/in2)
y = At some level of the cone (in)
d = Liquid fill level, (in)
t = Wall thickness (in)
α = 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

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