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Mohr's Circle Plane Normal Stress X Direction

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

Formula

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

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

Forms

Examples

Get the resource:

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

Get the formula:

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

Use some values:

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

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