How do you calculate the forces in a simple truss?

Short answer: treat the truss as pin-jointed, find the support reactions, then balance the forces at one joint at a time. This is called the method of joints. Here is a complete small example.

The example

A triangular truss rests on two supports 300 mm apart. The apex is 100 mm above the middle of the base, and a load P hangs at the apex. There are three members: two sloping sides and a bottom chord.

1. Reactions. The load sits in the middle, so each support carries P/2.

2. The angle. Each sloping side rises 100 mm over a horizontal run of 150 mm, so tan θ = 100/150 and θ ≈ 33.7°.

3. Balance the joint at a support. The upward reaction P/2 must be balanced by the vertical part of the sloping member:

• Sloping member force = (P/2) ÷ sin θ ≈ (P/2) ÷ 0.555 ≈ 0.90 P, and it is pushed (compression).
• Its horizontal part, 0.90 P × cos θ ≈ 0.75 P, must be balanced by the bottom chord, which is pulled (tension).

What the numbers say

For a load P, each sloping stick carries about 0.9 P in compression, and the bottom chord about 0.75 P in tension. Both are close to the load itself, because this truss is shallow.

Try changing the height

Make the apex 200 mm high instead. Then tan θ = 200/150, θ ≈ 53°, the sloping members carry about 0.63 P, and the bottom chord about 0.38 P. A deeper truss lowers the forces. See why deeper trusses are stronger.

Limits of this method

It assumes members carry only push and pull. Real glued joints also carry some bending, and balsa buckles before it crushes. Use these numbers to compare designs and spot the most loaded members, not as a guarantee of the failure load.