# Method of Joints

When analyzing a joint you will solve for the forces in all of the members connected to it.

Lets start with H, draw the two unknown forces $F_{HE}$ and $F_{HF}$ in tension (away from H).

You already know the downward force is $5k$. $F_{HE}$ is the only member with a vertical component so you can solve for it.

Ok so you know $F_{HE}$. Use the horizontal component of $F_{HE}$ to solve for $F_{HF}$:

Note: $\frac{10}{\sqrt{1000}}$ is from the geometry of the structure. $\sqrt{1000} = \sqrt{10^2 + 30^2}$ andÂ $\frac{10}{\sqrt{1000}} = \sin\theta$ (where $\theta$ is the angle of the pointy end).

### Jumping over toÂ B

You do not know any of these forces. $F_{BA}$Â is a Â doozy though. Summing the vertical forces reveals that..

$F_{BA}$ is zero. You can calculate the horizontal reaction at B by taking moments of the entire truss at A.

Now sum the horizontal forces to find $F_{BD}$

### Sliding on over toÂ D

At this joint we know that $F_{DB} = 60k( Compression)$ (so the arrow should actually point inward for compression), and that the downward force is 5k. We have three unknowns and only two equations ($\sum{F_x}$ and $\sum{F_y}$). This joint is unsolvable so you must move on to another joint before coming back to it.

After practice you start to see the paths to take. At this point E is solvable (secret zero-force member), and then F will be solvable, and then D would be too.

Combining the Method of Joints with the Method of SectionsÂ makes things even faster because you can often jump straight to a joint or area that you need for the problem (it may only ask you to find one member for example).