# Sign convention in Mohr's circle

I don't really understand the explanation in the circled part of the image below (from here).

From the diagram, we can see that the shear stress that cause the element to turn clockwise is positive, but in the text there, the author stated that the shear stress that cause the element that to turn clockwise is negative. So, which is correct?

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• Anyone can check my concept correct or not ? – kitzlong Dec 17 '16 at 8:12
• have you read all the discussion on the Wikipedia talk page? There are battling editors that cant decide what they are trying to say. My advice take wikipedia for what its worth and go look at a good engineering text book for a clear and correct treatment. – agentp Dec 17 '16 at 14:40
• @agentp , can you provide some link that explain about the sign convention of the mohr's circle ? I spent whole day searching it , but stil cant get it – kitzlong Dec 18 '16 at 1:02

The sign convention for Mohr's Circle is dependent on the user. The direction of $\tau_n$ can be used in both ways, but you need to make sure that if you do it in the opposite method, that everything is opposite. Standard mohr's circle is what is used in Method 2 with $\tau_n$ pointing down and $\sigma_n$ pointing to the right ($\sigma_n$ will always point to the right no matter what method you use). In any of my classes that I use Mohr's Circle in, I never use method 1 as it has confused me too much with the change in direction of all of the elements.
If you are dealing with a situation that is similar to method 3, then you simply invert the direction of $\tau_n$ to get the proper sign convention. For example if you took a square bar of rubber that was mounted to a solid immovable wall and twisted it towards you with one hand, the positive $\tau_n$ ($\tau_y$) would be in the closest and farthest sides from you because those are in tension while the top and bottom are in compression meaning that $\tau_n$ is negative ($\tau_x$). This results in the picture seen in method 2. Now twist it the other way and the torsional stresses change in direction. This would result in the picture having $\tau_{xy}$ in the top left corner and bottom right corner rather than what is seen in method 2. They fix this method by inverting the signs resulting in the $\tau_{xy}$ being located where that are in method two, but the values of these stresses are now all opposite due to their change in direction. The Mohr's Circle used in method 3 depicts this.
if you were to use the values in method 3 in the Mohr's circle right away you would end up with something similar to method 1, there isn't anything wrong with that but because all the values are opposite it would be very easy to confuse signage during the calculations, so the $\tau_n$ is inverted so that you end up with something similar to method 2 that is easier to use. Then you just solve using the values you have and you should get your proper answer while making sure to pay attention to the direction of the values (positive/negative) that you get from your calculations.