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

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Nathan Ong
Nathan Ong on 13 Nov 2017
Edited: Karan Gill on 20 Nov 2017
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!

Answers (1)

Karan Gill
Karan Gill on 14 Nov 2017
Edited: Karan Gill on 20 Nov 2017
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.

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