Mohr's Circle for Plane Strain
engineering fundamentals Mohr's Circle for Plane Strain
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Mohr's Circle
Strains at a point in the body can be illustrated by Mohr's Circle. The idea and procedures are exactly the same as for Mohr's Circle for plane stress.

The two principal strains are shown in red, and the maximum shear strain is shown in orange. Recall that the normal strains are equal to the principal strains when the element is aligned with the principal directions, and the shear strain is equal to the maximum shear strain when the element is rotated 45° away from the principal directions.

As the element is rotated away from the principal (or maximum strain) directions, the normal and shear strain components will always lie on Mohr's Circle.

Derivation of Mohr's Circle
To establish the Mohr's circle, we first recall the strain transformation formulas for plane strain,

Using a basic trigonometric relation (cos22q + sin22q = 1) to combine the above two formulas we have,

This equation is an equation for a circle. To make this more apparent, we can rewrite it as,

where,

     

The circle is centered at the average strain value eAvg, and has a radius R equal to the maximum shear strain, as shown in the figure below,

Related Topics
The procedure of drawing Mohr's Circle from a given strain state is discussed in the Mohr's Circle usage and examples pages.

The Mohr's Circle for plane stress can also be obtained from similar procedures.

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