How do I solve an equation with multiple symbolic variables with a condition on one of the variables?

I'm trying to program a concrete column interaction curve and one of the points needed is for a column in pure bending. I'm trying to solve for the values 'c' and 'fs' simultaneously, but I need the absolute values of fs to be limited to less than or equal to the yield stress of steel, Fy. Here is the code below:

 Fy = 50;
 B1 = 0.85;
 rows = 3;
 Es = 29000;
 d = [2.5 7.5 12.5];
 As = [5.08 2.54 5.08];
 b =15;
 fc = 4;

 syms c fs
 assume(abs(fs)<=Fy)
 for i = 1:rows
    fs(i) = (0.003/c)*(c-d(i))*Es
    product(i) = As(i)*fs(i)
 end

 eqn = 0.85*fc*B1*c*b + sum(product) == 0
    cM = solve(eqn,c);
    cM = double(cM(cM >= 0));
    fs = double(subs(fs,c,cM))

When I get my output, the absolute values of fs are still greater than Fy. Can anybody give me some advice? Thanks!

Answer 1

[Karan Gill]

You should first solve the equation for c and then use that value to find fs.

Also, your problem sounds like an optimization problem. Consider the Optimization Toolbox: https://www.mathworks.com/help/optim/getting-started-with-optimization-toolbox.html.