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MECHANICS - EXAMPLE


Stress Element
  Example

 

What is the maximum shear stress in the stress element shown?

   
  Solution

 

The stress state shows the normal stresses, σx and σy, to be positive (tension) but the shear stress arrows are in the negative direction. Thus, the stress state is

     σx = 10.1 ksi
     σy = 6.2 ksi
     τxy = -3.7 ksi

     

Rotated Stress Element
 

The maximum shear stress is,

     

This could be either positive or negative due to the square root. Angle that the max shear stress acts at is,

     

     2θτ-max = 27.79o (or -152.21 )
     θp = 13.90o

     τmax = 4.182 ksi @ 13.90o

It is interesting to note, the new normal stresses are,

          σx' = σy' = (σx+ σy)/2 = 8.15 ksi

     
   
 
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