Last reviewed 16 Sept 2026 · 7 min read
What a truss is
A truss is a framework of straight members connected at their ends to form triangles. Because a triangle cannot change shape without changing the length of a side, a triangulated frame carries load mainly by axial forces — tension or compression — which uses material efficiently. Roof trusses, bridge trusses, transmission towers and cranes are trusses.
Assumptions of ideal truss analysis
- Members are connected at frictionless pins (hinges).
- Loads and reactions act only at the joints.
- Members are straight and their centroidal axes meet at a point at each joint.
- Self-weight of members is neglected or applied at joints.
So each member is a two-force member carrying only axial force. In real riveted or welded trusses the joints are partly rigid and small secondary stresses (bending) arise; they are usually ignored in basic analysis.
Perfect, deficient and redundant frames
With members and joints (plane truss, reactions counted separately as determinate supports):
| Condition | Name | Meaning |
|---|---|---|
| Perfect frame | Just enough members to be stable and determinate | |
| Deficient (imperfect) frame | Unstable — a mechanism | |
| Redundant frame | Statically indeterminate internally |
Including reactions: (see Determinacy, Indeterminacy & Stability).
Types of trusses
| Truss | Typical use and feature |
|---|---|
| King post, queen post | Small timber roof trusses |
| Fink (French) | Steel roofs of moderate span; short compression members |
| Howe | Verticals in tension, diagonals in compression (timber bridges) |
| Pratt | Verticals in compression, diagonals in tension under gravity load — efficient for steel |
| Warren | Diagonals alternately in tension and compression; with or without verticals |
| K-truss | Short compression panels; deep bridge trusses |
| Fan, north-light (saw-tooth) | Industrial roofs; north-light admits diffuse daylight |
| Bowstring, Baltimore, Parker | Long-span bridges with curved or polygonal top chords |
Long members are better in tension (no buckling). The Pratt truss puts its long diagonals in tension under gravity loads, so it suits steel. The Howe truss puts its diagonals in compression and its (steel rod) verticals in tension, historically suiting timber diagonals with iron rods.
Method of joints
Take each joint as a free body with forces concurrent at the pin. Two equations per joint, so start at a joint with no more than two unknown member forces.
- Find the support reactions.
- Assume every unknown member force is tensile (arrow pointing away from the joint).
- Solve and .
- A negative answer means compression.
- Move to the next joint with at most two unknowns.
Best when forces in all members are needed.
Method of sections (Ritter's method)
Cut the truss through not more than three members whose forces are unknown (and not all concurrent or all parallel). Take one part as a free body.
- Take moments about the point where two of the cut members meet — this gives the third member's force directly.
- Use for a diagonal when both chords are horizontal.
Best when forces in a few members (say the middle panel of a long truss) are needed.
Zero-force members
Identifying these first saves time.
- If two non-collinear members meet at an unloaded joint, both are zero-force members.
- If three members meet at an unloaded joint and two are collinear, the third is a zero-force member.
If a load or reaction acts at the joint along one member's line, apply the rules with that force treated as a member.
Zero-force members are not useless: they brace compression chords against buckling, carry load under other load cases and support the self-weight of other members.
Tension coefficient method
Useful for trusses with many inclined members and especially for space trusses. For a member AB of length carrying tension , define the tension coefficient . Then at joint A:
(and a equation in 3-D), where , are external loads at A. Solve for the values, then .