Mohr's Circle
A graphical way to transform plane stress and find principal stresses
Difficulty
Advanced
Read time
11 min
Review status
Needs review
Concept sketch
Principal stress and maximum shear on one circle
Plane stress view
Overview
Mohr's circle converts a plane stress state into a graph that shows normal stress, shear stress, principal stresses, maximum in-plane shear stress, and stress values on rotated planes.
How to read it
- Read the horizontal axis as normal stress and the vertical axis as shear stress.
- Find principal stresses where the circle intersects the normal-stress axis.
- Read maximum in-plane shear stress from the circle radius.
- Remember that angular movement on the circle is twice the physical plane rotation.
When to use it
- Plane stress transformation problems.
- Finding principal stresses and principal planes.
- Finding maximum in-plane shear stress.
- Interpreting stress states before applying failure criteria.
What the circle represents
Mohr's circle is a graphical representation of the plane stress transformation equations. Each point on the circle corresponds to the normal and shear stress acting on a plane at a particular orientation in the material.
Principal stresses
The points where the circle crosses the normal-stress axis represent the principal stresses. At those planes, in-plane shear stress is zero. These values are often important for failure checks and material design.
Maximum shear stress
The top and bottom of the circle represent maximum in-plane shear stress. The radius of the circle is the magnitude of that maximum shear stress for the plane stress state.
Angle interpretation
Angles on Mohr's circle are doubled compared with physical material angles. A rotation of theta in the material corresponds to a 2 theta rotation on the circle, which is a common source of student errors.