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Mohr's Circle Plane Shear Strain

Mohr's circle is a two-dimensional graphical representation of the transformation law for the Cauchy stress tensor. Strain is a description of deformation in terms of relative displacement of particles in the body that excludes rigid-body motions.

The shear strain in the new x\[Hyphen]y coordinates increases with the normal strain in the x and y directions (though a larger normal strain in the y direction will increase it more). Increased shear strain in the x\[Hyphen]y coordinates will also increase it.

Formula

QuantityVariable[Subscript["γ", Superscript["x⁣y", "′"]], "Unitless"]/2 == (Cos[2*QuantityVariable["θ", "Angle"]]*QuantityVariable[Subscript["γ", "x⁣y"], "Unitless"])/2 - ((QuantityVariable[Subscript["ε", "x"], "Unitless"] - QuantityVariable[Subscript["ε", "y"], "Unitless"])*Sin[2*QuantityVariable["θ", "Angle"]])/2

symbol description physical quantity
γx⁣y′ shear strain in new x­y coordinates "Unitless"
θ plane angle "Angle"
γx⁣y shear strain in x­y coordinates "Unitless"
εx normal strain in x direction "Unitless"
εy normal strain in y direction "Unitless"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Mohr's Circle Plane Shear Strain"]
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Get the formula:

In[2]:=
FormulaData[ResourceObject["Mohr's Circle Plane Shear Strain"]]
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Use some values:

In[3]:=
FormulaData[ ResourceObject["Mohr's Circle Plane Shear Strain"], {QuantityVariable[ \!\(\*SubscriptBox[\("\[Gamma]"\), \("x\[InvisibleComma]y"\)]\), "Unitless"] -> 0.00005`, QuantityVariable["\[Theta]","Angle"] -> Quantity[0, "Radians"], QuantityVariable[ \!\(\*SubscriptBox[\("\[Epsilon]"\), \("x"\)]\),"Unitless"] -> 0.0001`, QuantityVariable[ \!\(\*SubscriptBox[\("\[Gamma]"\), TemplateBox[{"\"x\[InvisibleComma]y\"","\"\[Prime]\""}, "Superscript"]]\),"Unitless"] -> 0.00005`}]
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