Mohr's circle & Principle Stresses
It is a useful graphical technique for finding principal stresses and strains in materials. Mohr’s circle also tells you the principal angles (orientations) of the principal stresses without your having to plug an angle into stress transformation equations. The Mohr circle is then used to determine graphically the stress components acting on a rotated coordinate system, i.e., acting on a differently oriented plane passing through that point.
There will be one plane on which normal stress value is maximum, this plane is known as Principal plane ( more precisely maximum principal plane) and normal stress on this plane is known as principal stress (more precisely maximum principal stress). Similarly there will be one more plane on which normal stress value is minimum, this is also a principal plane (minimum principal plane) and normal stress on this plane is known as Principal stress (minimum principal stress).
Starting with a stress or strain element in the XY plane, construct a grid with a normal stress on the horizontal axis and a shear stress on the vertical. (Positive shear stress plots at the bottom.) Then just follow these steps:
- Plot the vertical face coordinates V(σxx , τxy).
- Plot the horizontal coordinates H(σyy, –τxy).
- Draw a diameter line connecting Points V (from Step 1) and H (from Step 2).
- Sketch the circle around the diameter from Step 3.
- Compute the normal stress position for the circle’s center point (C).
- Calculate the radius (R) for the circle.
- Determine the principal stresses σP1 and σP2.
- Compute the principal angles ΘP1 and ΘP2.