Mohr's circle formula

foo9008

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Homework Statement

why will σ_xl disappear in the equation ? [ [σ_xl - (σx -σy)/ 2 ] ^2 ] = ( [ (σx -σy)/ 2] ^2 ) is it wrong ?

The Attempt at a Solution

I don't think the above equation is supposed to follow from a simple manipulation of one side to produce the other. Rather, this equation is the result of some sequence of steps. Note that you have misquoted it: on the left hand side it should be σxy, not minus.
See if https://en.m.wikipedia.org/wiki/Mohr's_circle helps.

foo9008
foo9008
I don't think the above equation is supposed to follow from a simple manipulation of one side to produce the other. Rather, this equation is the result of some sequence of steps. Note that you have misquoted it: on the left hand side it should be σxy, not minus.
See if https://en.m.wikipedia.org/wiki/Mohr's_circle helps.
can you show me the proof ? the link doesn't provide the proof