From this picture, we see that the principal normal stresses occur at the farthest right and left points of the circle.

 

s_max = C + R                  s_min = C - R

 

We also see that these points are on the s axis, that is, the shear stress is zero at both points.

 

 

 

Also, the maximum shear stress occurs at the top and bottom of the circle.  The maximum shear stress is equal to the radius, t_max = R.  We also note that at the top and bottom of the circle, there is a normal stress equal to the s coordinate of the center of the circle.

 

Lets set a procedure for constructing and using Mohr’s circle using an example.  Consider a point which has the state of stress shown.

 

1. First, we set up our coordinate system with s on the x axis and t on the y axis.  Our convention is to measure normal stress positive if tensile and negative if compressive.  For shear stress, we use a positive sign if the stress rotates the element counterclockwise and negative if it rotates the element clockwise.  For reasons to be explained later, we need to plot t positive down and negative up.  So as not to get confused, I like to label the axes using rotation direction with up being CW and down being CCW.

 

2. Next, we will plot two known points.  The x face of the given element has stresses of s = 16 ksi and t = 3 ksi  CCW

 

So we plot a point X = (16, 3 CCW)

 

The y face of the element has

 

stresses of s = 8 ksi and t = 3 ksi CW

 

So we plot a point Y = (8, 3 CW).

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