Mohr's Circle For The Analysis Of State Of Stress:
Mohr's circle is a graphical method of finding normal, tangential and resultant stresses on an oblique plane. Mohr's circle would be drawn for the subsequent cases:
(a) A body subjected to two equally perpendicular principal tensile stresses of unequal intensities.
(b) A body subjected to two mutually perpendicular principal stresses that are unequal and unlike (i.e. one is tensile and other is compressive).
(c) A body subjected to two equally perpendicular principal tensile stresses accompanied through a easy shear stress.
The circle in above figure is known as the Mohr's Circle of stress. Mohr's circle is extremely useful in graphical analysis of state of stress at a point.
Given the state of stress (defined through σx, σy and τxy), the procedure for construction of the Mohr's circle was discussed later. The determination of principal stresses and principal planes from the Mohr's circle was also implies. Here let us learn a few applications of stress analysis with the help of the Mohr's circle.
Suppose we need to search the normal and shear stress components on a plane whose inclination to x plane is θD. We required only drawing a radial line OD making an angle 2θD along with the radial line OX. A coordinates (σD, τD) of the point D will provide the normal and shear stress components on the plane. Therefore, once the Mohr's circle is constructed, the stress components on any plane might be readily acquired.