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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.

Injection Molding Design Guide

Guide for high quality and cost-effective plastic injection molding.

CNC Machining Design Guide

Optimize your designs, reduce machining time, and lower your costs.

Selecting the Right 3D Printer

Discover how to choose the right 3D printer for your needs and the key performance attributes to consider.

Negotiate Your Salary

Learn the best principles to negotiate the salary you deserve!