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Maximum Shear Stress in Spring

The maximum shear stress in a spring is the maximum shear stress the spring can suffer before permanent deformation.

The maximum shear stress in a spring increases linearly with the free length of a spring and its Young's modulus. It decreases with the Poisson ratio, the spring wire diameter, the number of active windings and the cube of the spring's outer diameter.

Formula

QuantityVariable["τ", "Stress"] == (QuantityVariable["d", "Diameter"]*QuantityVariable["D", "Diameter"]*((0.615*QuantityVariable["d", "Diameter"])/QuantityVariable["D", "Diameter"] + (-1 + (4*QuantityVariable["D", "Diameter"])/QuantityVariable["d", "Diameter"])/(-4 + (4*QuantityVariable["D", "Diameter"])/QuantityVariable["d", "Diameter"]))*QuantityVariable["E", "YoungsModulus"]*(QuantityVariable["L", "Length"] - QuantityVariable["d", "Diameter"]*QuantityVariable["n", "Unitless"]))/(2*Pi*(-QuantityVariable["d", "Diameter"] + QuantityVariable["D", "Diameter"])^3*QuantityVariable["n", "Unitless"]*(1 + QuantityVariable["ν", "PoissonRatio"]))

symbol description physical quantity
τ maximum shear stress in spring "Stress"
d spring wire diameter "Diameter"
D spring outer diameter "Diameter"
E Young's modulus "YoungsModulus"
n number of active windings "Unitless"
L free length of spring "Length"
ν Poisson ratio "PoissonRatio"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Maximum Shear Stress in Spring"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Maximum Shear Stress in Spring"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Maximum Shear Stress in Spring"], {QuantityVariable[ "L","Length"] -> Quantity[0.5`, "Meters"]}]
Out[3]=

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