The mohr’s circle is a method of analyzing stress ( tensile, shear) at a given body using geometrical figures and methods. This involve some simple and basic calculations of geomatry that’s why Mohr’s circle give a flexible approch to solve a mechanic problem related to analyzing for stresses and strains.
Mohr’s Circle Sing Convention.
1) Tensile stress will be positive if it tends to elongate the body you can see both ?x and ?y are positive in the figure.
2) Shear stresses tending to rotate the element clockwise (cw) are plotted above the
• Shear stresses tending to rotate the element counterclockwise (ccw) are plotted below
the ? axis.
in some books this convention is taken as
Shear stress ( applied perpendicular to ?x at the right side of the body ) will be positive if it tends to rotate the body in counter clock wise.
1) create a coordinate system with normal stresses plotted along the abscissa and shear stresses plotted as the ordinates.
2) On the abscissa, tensile (positive) normal stresses are plotted to the right of the origin O and ompressive (negative) normal stresses to the left. On the ordinate, clockwise (cw) shear stresses are plotted up; counterclockwise (ccw) shear stresses are plotted down.
3) If ?x is positive and the shear stress ?xy is ccw as shown in Fig.1 , we can establish point A with coordinates (?x , ?-xy ccw ) in Fig 2
4) For ?y repeat the process to obtain point B with coordinates (?y , ?-xy cw )
5) The line that join point A with point B is the diameter of the circle.