Example #$6$

At a point in a member subjected to load the stress system induced is defined by the stresses acting on the elemental prism shown in figure. Determine the principle stresses and the orientation of the principle planes. Also determine the magnitude and direction of the maximum shearing stress.

${}_x=80$MPa

${}_y=50$MPa

$=40$MPa

Mohr's Circle for Plane Stress

With the physical significance of Mohr's circle for plane stress established, it may be applied with simple geometric considerations. Critical values are estimated graphically or calculated.

The graphical procedure to obtain the principle stresses is as follows:

Draw the perpendiculars axes $x-x$ and $y-y$ and mark off the following intercepts on the x $-$axis, plotting tensile stresses to the right of y $-$axis and compressive stresses to the left.