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MECHANICS - EXAMPLE


Mohr's Circle
  Example

 

Which Mohr circle is correct for the given stress state

 

 

 

 

 

 

   
  Solution

 

The given stress components for the stress element are,

       σx = 30 MPa
     σy = -60 MPa
     τxy = 50 MPa

     

Rotated Stress Element
 

Mohr's Circle center will be at the normal stress average,
     σaverage = [30 + (-60)]/2 = -15 MPa

which is plotted on the diagram at the left. Next, a point on the circle is needed. Two different points can be used,

     Point 1: (σx , τxy) = (30, 50)
     Point 2: (σy, -τxy) = (-60, -50)

Remember, the shear stress is plotted positive in the downward direction. From the plotted center and points on the circle, the radius (shear maximum) can be determined.

     R = τmax = [(30+15)2 + 502]1/2 = 67.3 MPa

Principal stresses are

     σ1 = -15 + 67.3 = 52.3 MPa
     σ2 = -15 - 67.3 = -82.3 MPa

The principle direction is      

tan 2θ1 = 50/(15+30)
      2θ1 = 48.0o

The correct diagram is 1)

     
   
 
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