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Mechanical Stresses on a Thin-Walled Hoop

A cylinder stress is a stress distribution with rotational symmetry, one that remains unchanged if the stressed object is rotated about some fixed axis.

Hoop stress equals pressure times the inner radius divided by the wall thickness. The axial stress equals the pressure times the inner radius divided by twice the wall thickness. Radial stress equals the negative of half the pressure.

Formula

{QuantityVariable[Subscript["σ", "θ"], "Stress"] == (QuantityVariable["P", "Pressure"]*QuantityVariable["r", "Length"])/QuantityVariable["t", "Length"], QuantityVariable[Subscript["σ", "z"], "Stress"] == (QuantityVariable["P", "Pressure"]*QuantityVariable["r", "Length"])/(2*QuantityVariable["t", "Length"]), QuantityVariable[Subscript["σ", "r"], "Stress"] == -QuantityVariable["P", "Pressure"]/2}

symbol description physical quantity
σθ hoop stress "Stress"
P pressure "Pressure"
r inner radius "Length"
t wall thickness "Length"
σz axial stress "Stress"
σr radial stress "Stress"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Mechanical Stresses on a Thin-Walled Hoop"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ ResourceObject["Mechanical Stresses on a Thin-Walled Hoop"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Mechanical Stresses on a Thin-Walled Hoop"], {QuantityVariable[ "r","Length"] -> Quantity[1, "Meters"]}]
Out[3]=

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