Intro: I am working towards constructing Mohr's circle for stresses at a point. This involves the Plane Stress Transformation equations, one of them being stress=(sigmax+sigmay)/2 + (sigmax-sigmay) Cos[2 phi]/2 + tau Sin[2 phi]
.
I want to determine the angle (preferably in the form Tan[2 phi]
) at which the the stress is maximum, i.e. the principle direction of stress. Using this value I can then determine the principle stresses.
Problem: I do the following:
sol=Solve[D[stress,phi]==0,phi]
hoping it will give me the following:{phi -> (1/2) ArcTan[2 tau / (sigmax-sigmay)]}
but to no avail. It gives a screen full of ConditionalExpressions instead which I don't know how to begin to use.
Question: How to 'solve' for phi
in the above conditions (i.e. when the differential of stress
is 0)?
Thank you inadvance.