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August 14th, 2014, 03:48 AM   #1
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how to find max shear stress at a given point?

The state of plane-stress 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.
Ganesh Ujwal is offline  
August 26th, 2014, 08:42 AM   #2
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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

$\displaystyle \tau_{max} = \frac{1}{2}\left(\sigma_1 - \sigma_2\right)$


$\displaystyle \sigma_{1} = \frac{1}{2}\left(\sigma_x + \sigma_y\right) + \sqrt{\left[\frac{1}{2}\left(\sigma_x - \sigma_y\right)\right]^2 + \tau_{xy}^2}$


$\displaystyle \sigma_{2} = \frac{1}{2}\left(\sigma_x + \sigma_y\right) - \sqrt{\left[\frac{1}{2}\left(\sigma_x - \sigma_y\right)\right]^2 + \tau_{xy}^2}$

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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