$20$ Truss Analysis $-$ Method of Joints

Draw the FBD for the truss, adding in

the $($unknown$)$ reaction forces.

So we have a total of $9$ unknowns: $6$

strut forces, and $3$ reactions.

We have $5$ joints, with $2$ equilibrium

equations per joint $({\displaystyle \underset{?}{\overset{?}{}}}{F}_x=0$ and

${\displaystyle \underset{?}{\overset{?}{}}}{F}_y=0),$ so a total of $10$ available

equilibrium equations.

Note that we appear to have more equations then unknowns, but we have

already implicitly used one equation to establish that the reaction at $C$ has only

one component.

We can solve this problem by creating a matrix of $9$ equations $($excluding

${\displaystyle \underset{?}{\overset{?}{}}}{F}_y=0$ at $C)$ and $9$ unknowns. But we can usually solve this by being strategic

about the sequence of our solution.