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Mohr's Circle Plane Normal Strain X Direction

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

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

Formula

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

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

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Mohr's Circle Plane Normal Strain X Direction"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ ResourceObject["Mohr's Circle Plane Normal Strain X Direction"]]
Out[2]=

Use some values:

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