The mohr’s circle is a method of analyzing stress ( tensile, shear) at a given body usingÂ geometrical figures andÂ methods. This Â 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.
Mohrâs Circle Sing Convention.
1) Tensile stress will be positive if it tends to elongate the body you can see bothÂ ?x andÂ ?y are positive in the figure.
2) Â Â Shear stresses tending to rotate the element clockwise (cw) are plotted above the
â¢ Shear stresses tending to rotate the element counterclockwise (ccw) are plotted below
the ? axis.
in some books this convention is taken as
Â Shear stress ( applied perpendicular toÂ ?x Â at the right side of the body )Â will be positive if it tends to rotate the body in counter clock wise.Â
1)Â create a coordinate system with normal stresses plotted along theÂ abscissa and shear stresses plotted as the ordinates.
Â 2) Â On the abscissa, tensile (positive)Â normal stresses are plotted to the right of the origin O and Â ompressive (negative) normalÂ stresses to the left. On the ordinate, clockwise (cw) shear stresses are plotted up;Â counterclockwise (ccw) shear stresses are plotted down.
3)Â If ?x is positive and the shear stress ?xy is ccw as shown in Fig.1 , we canÂ establish point A with Â coordinates (?x , ?-xy ccw ) in Fig 2
4) For Â ?yÂ repeat the process to obtain point B withÂ coordinates (?y , ?-xy cw )
5) The line that join point A with point B is the diameter of the circle.