How to solve a symbolic equation that uses conditional statements?

Hello everyone,

I'm currently facing the following issue:

I need to solve an equation with a single variable "c_". But, this equation relies on a function called "sigmaSteel", note that this function uses a symbolic vector variable. The code I've developed is the following:

% I've all the double variables (fc=300,beta1_val=0.83, b=30, as=[11.4040; 11.4040], fy=4200, Es=2.1*10^6, Pu=0, ecu=0.003) 
% defined above this section. Here I'm looking to determine the value of c_ and then save it in c as a double. 
d = [5; 55];
syms c_  % c_ must be real and positive
es = (c_ - d)/c_*ecu;  % this is a vector in function of c_ (symbolic)
eqn = 0.85*fc*beta1_val*c_*b + sum(as.*sigmaSteel(es,fy,Es)) - Pu; % eqn == 0
c = solve(eqn,c_);
c = double(c)

I think, that the problem is in my sigmaSteel() function. I can't find a way to convince matlab that I want the "condition" (if abs(es) < fy/Es so the value of sigma is ... ) to be incorporated into the equation as a symbolic variable.

% This function takes "es" that is a symbolic variable (or a vector of symbolic variables as ca), and if "es" is greater than fy/Es (fy/Es is a double) then return 
% es*Es for that row of the vector if not so return sign(es)*fy. Note that this is because sigma is es*Es until a limit that is the value of fy or -fy 
function sigma = sigmaSteel(es, fy, Es)
    sigma = sym(zeros(length(es),1));
    condition = abs(es) <= fy/Es;         %% How to change this line to work with vector of symbolic variables?
    sigma(condition) = es(condition)*Es;
    sigma(~condition) = sign(es(~condition))*fy;
end

Note that abs(es) <= fy/Es does not work with symbolic variables, I cant work with the numerical es values because

the're in function of c_ that is the value that I want to determine using solve(eqn,c_).

The way that I used to solve this is to make assumptions, for example:

% if es < fy/Es --> sigma = es*Es. The equation that I've to use to find
% c_ is:
eqn = 0.85*fc*beta1_val*c_*b + as*(es*Es) - Pu;

And if the assumption is incorrect (I just have to evaluate c in es = (c-d)/c*ecu), so I switched to the opposite assumption:

% if es > fy/Es --> sigma = fy. The equation that I've to use to find c_
% is:
eqn = 0.85*fc*beta1_val*c_*b + as*(fy) - Pu;  

As you see, this approach is not efficient, specially when there is no only one layer of steel (as1*fy + as2(es*Es) + as3*(fy)..... and all the possible combinations for multiple layers).

I'm open to any solution to address this issue, even if it requires a significant change. My primary goal is to successfully solve this equation.

Best regards,

[Walter Roberson]

piecewise()

[Nathan Hardenberg]

In your condition you write: , but es is a 2D-vector and is a scalar. This gives you two conditions. What do you want to do with that?

Answer 1

[Alexis]

Walter and Nathan,

Yes, with a piecewise() now it works. I also used assume(c_, 'positive') and used this sigma function

function sigma = sigmaReinf(es, fy, Es)
    sigma = sym(zeros(length(es),1));
    for i = 1:length(es)
        sigma(i) = piecewise(abs(es(i)) < fy/Es, es(i)*Es, abs(es(i)) >= fy/Es, sign(es(i))*fy);
    end
end

Thank you both so much.