Expression for the maximum shearing stress, Mechanical Engineering

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Expression for the maximum shearing stress:

Obtain expression for the maximum shearing stress and maximum shearing planes.

Sol.: The condition for maximum shearing stress is given below,
1606_Expression for the maximum shearing stress.png 
This expression gives value of maximum shearing plane. The other plane that carries maximum shearing stress is normal to this plane. Substituting value of θ in  τ expression with he following rearrangement.
237_Expression for the maximum shearing stress1.png 
1301_Expression for the maximum shearing stress2.png 

44_Expression for the maximum shearing stress3.png

 


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