I don't understand why my code is displaying 1x1 sym rather than numbers. I just don't know where I went wrong.

clc; clear; close all;
 
%We have to figure out the lengths for all of the bars
%The distance formula is D = sqrt(((x2-x1)^2)+((y2-y1)^2))
 
fprintf('These are the lengths for each of the pieces\n');
 
fprintf('\n');
 
LAB=sqrt(((-58.97-0)^2)+((-12.14-0)^2));
LBD=sqrt(((-108.21+58.97)^2)+((-86.31+12.14)^2));
LCDE=sqrt(((-185.96+35)^2)+((-107.94+70)^2));
LCF=sqrt(((-334+185.96)^2)+((-74.27+107.94)^2));
LFG=sqrt(((-312+334)^2)+((90+74.27)^2));
 
fprintf('Length AB = %x cm\n',LAB);
fprintf('Length BD = %x cm\n',LBD);
fprintf('Length CDE = %x cm\n',LCDE);
fprintf('Length CF = %x cm\n',LCF);
fprintf('Length FG = %x cm\n',LFG);
 
fprintf('\n');
 
%Now we can use the length values to calculate the volumes
%But first we have to find the volume of each of the round tips of each bar
%The two tips form a full circle with a radius of 10cm or 0.1m and a
%thickness of 5cm or 0.05m
 
VTIP=pi*(10^2)*(5);
 
fprintf('Now we can use the length values to calculate the volume of each bar\n');
 
fprintf('\n');
 
VAB=(((LAB)*(20)*(5))+VTIP);
VBD=(((LBD)*(20)*(5))+VTIP);
VCDE=(((LCDE)*(20)*(5))+VTIP);
VCF=(((LCF)*(20)*(5))+VTIP);
VFG=(((LFG)*(20)*(5))+VTIP);
 
fprintf('Volume AB = %x cm^3\n',VAB);
fprintf('Volume BD = %x cm^3\n',VBD);
fprintf('Volume CDE = %x cm^3\n',VCDE);
fprintf('Volume CF = %x cm^3\n',VCF);
fprintf('Volume FG = %x cm^3\n',VFG);
 
fprintf('\n');
 
%now we can find the mass of each bar
%The density I am using for the steel alloy is 0.00775 kg/cm^3
 
DEN=0.00775;
 
fprintf('Now we can find the mass of each bar');
 
fprintf('\n');
 
MAB=(VAB*DEN);
MBD=(VBD*DEN);
MCDE=(VCDE*DEN);
MCF=(VCF*DEN);
MFG=(VFG*DEN);
 
fprintf('Mass AB = %x kg\n',MAB);
fprintf('Mass BD = %x kg\n',MBD);
fprintf('Mass CDE = %x kg\n',MCDE);
fprintf('Mass CF = %x kg\n',MCF);
fprintf('Mass FG = %x kg\n',MFG);
 
fprintf('\n');
 
%now we can find the weights
 
fprintf('Now we can find the weight of each bar');
 
fprintf('\n');
 
g=9.81;
 
WAB=MAB*g;
WBD=MBD*g;
WCDE=MCDE*g;
WCF=MCF*g;
WFG=MFG*g;
 
fprintf('Weight AB = %x N\n',WAB);
fprintf('Weight BD = %x N\n',WBD);
fprintf('Weight CDE = %x N\n',WCDE);
fprintf('Weight CF = %x N\n',WCF);
fprintf('Weight FG = %x N\n',WFG);
 
fprintf('\n');
 
%I'm just calculating the mass of the casting really quick
 
WCASTING=100;
 
MCASTING=WCASTING/g;
 
fprintf('Mass of the casting is %x kg\n',MCASTING);
 
fprintf('\n');
 
%Now we are going to find the vector components for each bar at the first
%position
 
ABxi=-58.97-0;
AByi=-12.14-0;
BDxi=-108.21+58.97;
BDyi=-86.31+12.14;
CDExi=-185.96+35;
CDEyi=-107.94+70;
CFxi=-334+185.96;
CFyi=-74.27+107.94;
FGxi=-312+334;
FGyi=90+74.27;
 
%Now we have to solve for all the reaction forces
 
syms Ax Ay Bx By T Dx Dy Cx Cy Ex Ey Fx Fy Gx Gy;
e1 = -Ax + Bx == 0;
e2 = Ay - By - WAB == 0;
e3 = -(ABxi*By) - (AByi*Bx) + T == 0;
e4 = -Bx + Dx == 0;
e5 = By - Dy - WBD == 0;
e6 = -(BDxi*Dy) - (BDyi*Dx) == 0;
e7 = -Dx + Cx + Ex == 0;
e8 = -Ey + Dy + -Cy - WCDE == 0;
e9 = -(CDExi*Cy) - (CDEyi*Cx) == 0;
e10 = -Cx + Fx == 0;
e11 = Cy - Fy - WCF - WCASTING == 0;
e12 = -(CFxi*Fy) - (CFyi*Fx) == 0;
e13 = Gx - Fx == 0;
e14 = -Gy + Fy - WFG == 0;
e15 = -(FGxi*Gy) - (FGyi*Gx) == 0;
 
sol1 = solve([e1, e2, e3, e4, e5, e6, e7, e8, e9, e10, e11, e12, e13, e14, e15],[Ax, Ay, Bx, By, T, Dx, Dy, Cx, Cy, Ex, Ey, Fx, Fy, Gx, Gy]);
 
display(sol1);
 
%Now we are going to find the vector components for each bar at the second
%position
 
ABxf=60.182-0;
AByf=1.716-0;
BDxf=-28.793-60.182;
BDyf=4.748-1.716;
CDExf=-26.314+35;
CDEyf=-85.412+70;
CFxf=-162.536+26.314;
CFyf=18.381-85.412;
FGxf=-312+162.536;
FGyf=90-18.381;
 
%Now we have to solve for all the reaction forces
 
syms Axf Ayf Bxf Byf Tf Dxf Dyf Cxf Cyf Exf Eyf Fxf Fyf Gxf Gyf;
e16 = -Axf + Bxf == 0;
e17 = Ayf - Byf - WAB == 0;
e18 = -(ABxf*Byf) - (AByf*Bxf) + T == 0;
e19 = -Bxf + Dxf == 0;
e20 = Byf - Dyf - WBD == 0;
e21 = -(BDxf*Dyf) - (BDyf*Dxf) == 0;
e22 = -Dxf + Cxf + Exf == 0;
e23 = -Eyf + Dyf + -Cyf -WCDE == 0;
e24 = -(CDExf*Cyf) - (CDEyf*Cxf) == 0;
e25 = -Cxf + Fxf == 0;
e26 = Cyf - Fyf - WCASTING - WCF == 0;
e27 = -(CFxf*Fyf) - (CFyf*Fxf) == 0;
e28 = Gxf - Fxf == 0;
e29 = -Gyf + Fyf - WFG == 0;
e30 = -(FGxf*Gyf) - (FGyf*Gxf) == 0;
 
sol2 = solve([e16, e17, e18, e19, e20, e21, e22, e23, e24, e25, e26, e27, e28, e29, e30],[Axf Ayf Bxf Byf Tf Dxf Dyf Cxf Cyf Exf Eyf Fxf Fyf Gxf Gyf]);
 
display(sol2);

Answer 1

[Walter Roberson]

The first set of equations is inconsistent.

 eqn = [e1, e2, e3, e4, e5, e6, e7, e8, e9, e10, e11, e12, e13, e14, e15];
 sol = solve(eqn(1:14));
 E15 = subs(eqn(15), sol);
 
 E15 = 151767382664397973517046363/294104539013337579520 == 0

In particular, e9 has consequences that are incompatible with e15

 solve(eqn(9:15))  %-> empty
 solve(eqn(10:15)) %-> non-empty