This is more of a general conceptual question than a specific homework problem. I know how to do these problems, but I'm not understanding part of them. So, with a given stress element, I first look at one specific face, and plot a two-dimensional Mohr's circle. Then, I find the center, radius, and principle stresses. I could also find θp, but I'm not sure I need to in this case. If I do, that's what I'm not understanding. I know rotating the circle by 2θp and thus the element by θp yields a no shear state in the first orientation considered. My question: To plot the other two circles, I have drawn the stresses on the remaining two planes of the element. In order for the circles to work, x' and y' (each from one of the planes) must equal the principle stresses. I am confused as to why they don't equal the stresses in their planes. I know it has something to do with the angle of rotation, but I'm not exactly sure what. An explanation would be greatly appreciated. Thank you!