Principal Values and Mohr's Circle for Planar Stresses
This Demonstration generates Mohr's circles for planar stresses. The inputs are stress values for at the and orthogonal faces oriented at zero angle. The Demonstration calculates a Mohr's circle and generates other plots to illustrate how stress changes at different orientations as the angle of the plane is changed, using the slider. Planar stress is assumed, therefore stresses in the direction are assumed to be zero.
For plane stress, components vanish and the 3D stress tensor reduces to . Assuming , , and are given at 0°, the stresses at a different angle are found from .
The angles and at which the maximum and minimum normal principal stress occurs are given by and , respectively. The maximum and minimum normal principal stresses are given by , where is taken as the larger of the two principal stresses in absolute terms. The maximum shear stress is at 45° from the principal plane and is given by . At the principal planes the shear stress is always zero. Mohr's circle for plain stress can be viewed from the pull-down menu. You can view polar plots that show how the normal and shear stress change with the angle. You can select the angle to view the stresses by using the slider or select specific planes using the pull-down menu. SI units are used throughout.
 A. C. Ugural and S. K. Fenster, Advanced Strength and Applied Elasticity, New York: Elsevier, 1987.
 M. Fogiel (ed.), REA's Problem Solvers: Strength of Materials & Mechanics of Solids, Piscataway, NJ: Research and Education Association, 1996.
 I. H. Shames, Mechanics of Deformable Solids, Englewood Cliffs, NJ: Prentice-Hall, 1964.