# 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.

$$\sum{F_y} = \frac{10}{\sqrt{1000}}F_{HE} – 5k=0$$

$$F_{HE} = 5k\frac{\sqrt{1000}}{10}\approx 15.8k (Tension)$$

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

$$\sum{F_x} = -\frac{30}{\sqrt{1000}}F_{HE} – F_{HF} = 0$$

$$F_{HF} = -\frac{30}{\sqrt{1000}} 15.8k \approx -15k (Tension) = 15k (Compression)$$

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

### Jumping over to B You do not know any of these forces. $$F_{BA}$$ is a  doozy though. Summing the vertical forces reveals that..

$$\sum{F_y} = F_{BA} = 0$$

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

$$\sum{M_A} = 10k(10ft) + 10k(20ft) + 10k(30ft) – 10ft(R_{Bx}) = 0$$

$$R_{Bx} = \dfrac{(100 + 200 + 300)k*ft}{10 ft} =60k$$

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

$$\sum{F_x} = 60k + F_{BD} = 0$$

$$F_{BD} = -60k (Tension) = 60k (Compression)$$

### Sliding on over to 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 Sections 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). 