vpasolve returns empty syms 0x1

I'm not able to figure out what is going on with this system. My other systems are getting solved but not this one. Can anyone help me figure this one out?

rho = 0.289018; % [lb/in^3]; density of material
Sy = 30000; % [psi]; yield strength of material
E = 27992280; % [psi]; Youngs modulus of material
V = 2158.689078; % [in^3]; volume of ENTIRE structure with solid legs, from SolidWorks
L = 118.25; % [in]; length of box structure, perpendicular to truck pulling force
w = 26; % [in]; width of box structure
l = 36; % [in]; height of legs
h = 9.1; % [in]; height of box structure only
Dl = 4; % [in]; outer diameter of legs
W = rho*V; % [lbf]; weight load of structure (conservative, treats legs as solid)
P = 16*20*2 + W; % [lbf]; centroidal load due to weight and PTDs w/ safety factor

Ry = 1250; % [lbf]; rxn in dir of pulling

Mx1 = (2500*2)*(l+h)/4 - P*w/8;
My1 = P*L/8;
MR1 = sqrt(Mx1^2 + My1^2); %total moment

syms I A t1x tau sigz R1 R3 %Leg 1, x-max
%Leg 1, x-max
eqns = [I == (pi/64)*(Dl^4 - (Dl-2*t1x)^4), A == (pi/4)*(Dl^2 - (Dl-2*t1x)^2), ...
    tau == (3/2)*Ry/A, sigz == R1/A + My1*(Dl/2)/I, R1 == (P/2)-R3, ...
    R3 == P/2 - (P*(w/2) + 5000*(l+h))/(2*w), Sy == sqrt(sigz^2 + 3*tau^2)];
S1 = vpasolve(eqns, [I,A,t1x,tau,sigz,R1,R3]);

Answer 1

[Star Strider]

One option is to use solve first rather than vpasolve, then use vpa later.

Example —

S1 = solve(eqns, [I,A,t1x,tau,sigz,R1,R3]);

I_num = vpa(S1.I)
A_num = vpa(S1.A)

producing:

I_num =
 -1.5809251179322542233857232451522
 -1.5809251179322542233857232451522
  1.5598335563826831618612834229733
  1.5598335563826831618612834229733
  1.2534178213176158442695309403285
  1.2534178213176158442695309403285
 -1.2380191890238977904464145042831
 -1.2380191890238977904464145042831
 
A_num =

 -0.76705210311723380012877421564178
 -0.76705210311723380012877421564178
  0.80574886841346695683272432220417
  0.80574886841346695683272432220417
   24.489573101112048426635864036903
   24.489573101112048426635864036903
   25.737212591028410232062479989006
   25.737212591028410232062479989006

Do the same for the others.

[Shrikrishna Basude]

Wow, thanks! I wonder why this is the case...

[Star Strider]

As always, my pleasure!

The only explanationi I can offer is that it’s just the way the Symbolic Math Toolbox works. Other symbolic engines, such as Maple, might provide more direct results.