Mohr’s Circle - Stress

 

Example:  (continued)  The figure below shows the element with faces A and B as well

as points  A  and  B  on  Mohr’s Circle.  The principal stresses (max and min) are  σ1  and

σ2  respectively.  The radius of the circle is  √ [ (1250/π)2  +  (2500/π)2 ]  =  889.7 psi

 

  Now    σC  = 1250/π  psi  so  σ1  =  σC  + 889.7  =  1287.6 psi

  and                                         σ2  =  σC  −  889.7  =  − 491.8 psi

 

                                        

 

Next the tan(2θ) = (2500/π) / (1250/π)  =  2  so  2θ =  63.43o .   For the element  θ =  31.71o .  

For the principal stresses on the element rotate face A 31.71o clockwise as shown below.

 

                             

Result

                            

 

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