I have the need to use a MathCAD function (possibly) but I am not sure how to achieve what I would like the program to try to do.
My situation is essentially I havea fixed-fixed beam of circular cross section with a known span L anda uniformly distributed load w.
So using standard beam equations I have the max moment is M = wL^2/12 so the max stress is S = [(wL^2/12)(OD/2)]/I
where I = (pi/64)(OD^4-ID^4), OD is known
and the max deflection is y = wL^4/384EI where E is a known constant.
What I would like to eventually find is the thickness t = 0.5*(OD-ID) which just satisfies y = 0.1 and S = 2000.
Usually by hand, I would work use S = 2000, find the value of I and work out ID, then find t, substitute into the formula for y and see if equal to 0.1. I can probably assess it graphically but that would probably not give me too exact of an answer.
However I am not sure what functions would help me get MathCAD to automate this for me. Can anyone shed any light on how to go about doing this ?
Note that I is the same value, for each of the four solutions, the second solution gives a negative ID and the last two of the solutions for ID are pure complex (imaginary) numbers.
As Terry indicates you may not be able to satisfy both equalities at the same time. I rewrote your equations for y and S putting in t (ID = (OD -2t). If I divide S by y I can get:
You can solve either equation of S or y for t:
Whichever is more critical will depend on the actual problem.
Depending on the problem one of your two limits will be more restrictive than the other. You can derive an expression between y and S that does not involve the thickness:
The attached sheet gives a starting point. (In my experience, designing for deflection is usually more restrictive than designing for stress.