Mohr’s circle is a very useful method to define the unknowns of specific problems of classical mechanics. In a typical stress analysis, there are tensile and compression stresses and torsional stresses appear. The strength state of systems can be assessed in mechanics by using these values in general.
Principal stresses and principal planes can be obtained from these stress values. There is a numeric method to do it. But also you can use Mohr’s circle method to define principal stresses and principal planes of a system.
As we stated above, you need to start with the definition of stress situations in a stress element. You need to define;
You need to select a proper set of X and Y axis values to represent stresses on it. Y-axis will be the axis of torsional stresses and the X-axis will be de axial stresses.
As we stated above, you need to have two planar stresses both can be compression or tensile stresses. Place these axial stress values on the X-axis of the drawn coordinate system.
We stated that the Y-axis is for torsional stresses. And torsional stresses are represented both negative and positive.
Connect these two points with a straight line, then draw the circle that this line is the diameter. You obtained the Mohr’s circle.
You can find the angle of the principal stress element on the Mohr’s circle as stated in the illustration above. The slope of the diameter line that is drawn is two-fold of the angle of the principal stress element.
There can be some special conditions that may occur as stress elements.
This is the most basic explanation of drawing Mohr’s circle to find principal stresses and angles from stresses acting on stress elements.
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