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August 14th, 2014, 03:48 AM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 343 Thanks: 1  how to find max shear stress at a given point?
The state of planestress at a point is given by σx = 200 MPa, σy = 100 MPa, σxy = 100 MPa The Maximum shear stress (in MPa) is: A) 111.8 B) 150.1 C) 180.3 D) 223.6 Explain Procedure also with Answer. 
August 26th, 2014, 08:42 AM  #2 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,150 Thanks: 730 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
According to the Wikipedia page, Plane stress  Wikipedia, the free encyclopedia, the maximum shear stress is given by $\displaystyle \tau_{max} = \frac{1}{2}\left(\sigma_1  \sigma_2\right)$ where $\displaystyle \sigma_{1} = \frac{1}{2}\left(\sigma_x + \sigma_y\right) + \sqrt{\left[\frac{1}{2}\left(\sigma_x  \sigma_y\right)\right]^2 + \tau_{xy}^2}$ and $\displaystyle \sigma_{2} = \frac{1}{2}\left(\sigma_x + \sigma_y\right)  \sqrt{\left[\frac{1}{2}\left(\sigma_x  \sigma_y\right)\right]^2 + \tau_{xy}^2}$ Plugging in your numbers ($\displaystyle \sigma_x = 200$MPa, $\displaystyle \sigma_y = 100$MPa and $\displaystyle \tau_{xy} = 100$MPa) I get $\displaystyle \tau_{max} = 180.28$ so the answer is c). I would make sure you understand all the mathematics on that wikipage! 

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