# Math Help - Mohr Circles ?? how to creat a tangent for a set of Circle equations ??

1. ## Mohr Circles ?? how to creat a tangent for a set of Circle equations ??

hi guys i'm studying civil engineering , and part of it we study Mohr Circles of stress analysis But we still do it Graphically and that is not off course as accurate as you want, anyway i did my part summarizing it .

So first let explain to you what we do here ,

[*]we do Lab experiments to find 2 things called Sigma 1 (vertical Stress) Sigma 2 ( horizontal Stress) and we make this more than one time.
[*]we plot those sigmas as circles ( i will explain later)

[*]then we find a tangent (line=Liner equ) for those circle that touches them all (My problem )

[*]and for that we make an calculation of at X=0 , Y=??? and we call that Y ==> C (Cohesion), and the Angle of the Slop of the line we call Phaie
so here is what i did so far :

equ for Circles : $(X-h)^2+(Y-k)^2=R^2$
and R = (\[Sigma]1-\[Sigma]3)/2
and K=0 since all Circles at X axis.
and h=(\[Sigma]1+\[Sigma]3)/2

so if we give an example that
we have 2 Circles equ. , where in

1. [Sigma]1 = 5 and \[Sigma]3 = 2, so R = 1.5 and h = 3.5

2. [Sigma]1 = 6 and [Sigma]3 = 4so R = 1 and h = 5

it Will give you that Plot in Mathmatica :

ContourPlot[{(-5 + x)^2 + y^2 == 1, (-3.5 + x)^2 + y^2 ==
2.25}, {x, -2.346083333333333,
7.012749999999999}, {y, -2.346083333333333, 7.012749999999999}]

so My problem is how to Solve this Two (and May be three or Four) of those circles equations in only Y>=0 (we use only First quarter) ,to find a liner equ , that is the tangent of the both circles equ.

i don't know if i have to D them then solve them together or what since $Dy/Dx$ (tangent is what i want) But for which that each $dy/dx$ of each circle is equal the other ones ????