Mohr's circle formula

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foo9008
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  • #2
haruspex
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Homework Statement



https://web.iit.edu/sites/web/files/departments/academic-affairs/Academic Resource Center/pdfs/Mohr_Circle.pdf[/B]
why will σ_xl disappear in the equation ? [ [σ_xl - (σx -σy)/ 2 ] ^2 ] = ( [ (σx -σy)/ 2] ^2 ) is it wrong ?

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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.
 
  • #3
foo9008
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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
 
  • #4
haruspex
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can you show me the proof ? the link doesn't provide the proof
It has what looks to me as a claimed proof. At "Equation of the Mohr Circle" it obtains expressions for σn and τn as functions of θ. Then it eliminates θ between these two equations to obtain a relationship between σn and τn. This produces the equation you queried.
 

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