For this problem, create at MATLAB script called statics.m and a diary called statics. txt$.$

The plane truss shown below has $13$ members $($the numbered lines$)$ and $8$ joints $($the numbered circles$).$ The indicated loads are applied at joints $2,5,$ and $6$ as shown.

For the truss to be in static equilibrium, there must be no net force, horizontally or vertically, at any joint. For the eight joints, this yields $16$ equations, which is more than the $13$ unknown forces to be determined. For the truss to be statically determinate $($a unique solution$),$ it is assumed that Joint $1$ is rigidly fixed both horizontally and vertically and that Joint $8$ is fixed vertically. Thus, we do not consider those joints in our system of equations.

Resolving the forces into horizontal and vertical components and defining $=\frac{\sqrt[\phantom{2}]{2}}{2},$ yields the following system of equations for the member forces $f_i$ :

Joint $2$: $-f_2+f_6=0$

Joint $3$: $-f_1+f_4+f_5=0$

Joint $4$: $-f_4+f_8=0$

Joint $5$: $-f_5-f_6+f_9+f_{10}=0$

Joint $6$: $-f_{10}+f_{13}=0$

Joint $7$: $-f_8-f_9+f_{12}=0$

Joint $8$: $-f_{13}-f_{12}=0$

$f_3-10=0$

$-f_1-f_3-f_5=0$

$f_7=0$

$f_5+f_7+f_9-20=0$

$f_{11}-10=0$

$-f_9-f_{11}-f_{12}=0$

All members are assumed to be in tension, thus positive force values in the solution will denote tension and negative values will represent compression. Solve this system of equations to determine the force in each member.

Arrange the system of equations such that the solution vector is $x=\{[f_1],[f_2],[vdots],[f_{13}]\}kN.$