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Mohr's Circle Plane Shear Stress

Mohr's circle is a two-dimensional graphical representation of the transformation law for the Cauchy stress tensor. Stress is a physical quantity that expresses the internal forces that neighboring particles of a continuous material exert on each other.

The shear stress in a new frame increases with the shear stress and normal stress in the x and y directions (though a larger normal stress in the y direction will increase it more). The angle of the stress also modifies it.

Formula

QuantityVariable[Subscript["τ", Superscript["x⁣y", "′"]], "Stress"] == Cos[2*QuantityVariable["θ", "Angle"]]*QuantityVariable[Subscript["τ", "x⁣y"], "Stress"] - ((QuantityVariable[Subscript["σ", "x"], "Stress"] - QuantityVariable[Subscript["σ", "y"], "Stress"])*Sin[2*QuantityVariable["θ", "Angle"]])/2

symbol description physical quantity
τx⁣y′ shear stress in new frame "Stress"
θ plane angle "Angle"
τx⁣y shear stress "Stress"
σx normal stress in the x direction "Stress"
σy normal stress in the y direction "Stress"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Mohr's Circle Plane Shear Stress"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Mohr's Circle Plane Shear Stress"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject["Mohr's Circle Plane Shear Stress"], {QuantityVariable[ \!\(\*SubscriptBox[\("\[Tau]"\), \("x\[InvisibleComma]y"\)]\), "Stress"] -> Quantity[50, "Kilopascals"]}]
Out[3]=

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