Zero-force members in a trussHow to spot them without calculation
Zero-force member = a member with no resistance along its direction at the joint it is connected to. No other force at the joint "pulls against it" — so the force in it is 0.
You spot it by eye, with two rules.
Condition for both: at the joint there is no load and no support.
- Rule 1 Two members, not on one line → both are 0
- Rule 2 Three members, two on one line → the third is 0
-
01
Why does it work? (30 seconds)
- A member carries a force only if the joint has something resisting it along its direction.
- Rule 2: the two members on one line act only along their line — they cannot resist the third member. No resistance → it is 0.
- Rule 1: the same thing twice: neither member resists the other → both are 0.
Rule 1 — both are 0 Rule 2 — the third member is 0 -
02
4 zero-force members — without a single equation
An 8 m truss, a load of 6 t at joint G. Let's find the zero-force members:
Zero-force members — in dashed blue · scroll the drawing sideways - Joint CN1 and N2 on one line, no load → N9 has no resistance → N9 = 0 Rule 2 ✓
- Joint ESame thing → N11 = 0 Rule 2 ✓
- Joint IOnly two members, no load → neither resists the other → N14 = 0, N15 = 0 Rule 1 ✓
That's it. 4 zero-force members, zero calculations. The rest you solve as usual — and the zero-force members are already in your pocket.
The full solution of the truss (for checking)
Reactions: AY = 3 t, BY = 3 t Member Between joints Force State N1 A–C 3 t Tension N2 C–D 3 t Tension N3 D–E 3 t Tension N4 E–B 3 t Tension N5 A–F 4.243 t Compression N6 F–G 6 t Compression N7 G–H 6 t Compression N8 H–B 4.243 t Compression N9 C–F 0 Zero-force member N10 D–G 6 t Compression N11 E–H 0 Zero-force member N12 F–D 4.243 t Tension N13 D–H 4.243 t Tension N14 H–I 0 Zero-force member N15 I–B 0 Zero-force member - Joint C
-
03
4 pitfalls everyone falls into
- Joint G looks exactly like C. But it has a load — and the load is the resistance to N10. So N10 = 6 t in compression, not 0.
- Support = external force. A reaction can also resist a member → at a joint with a support the rule does not work.
- "Almost on one line" does not count. Only an exact straight line.
- Zero-force member ≠ redundant member. It holds the structure, and works under other loadings.
Bonus: the joint has a load — but exactly along the straight line? Rule 2 still works: this load does not resist the third member.
And that's not all: 3 members at a joint and no two on one line? No rule — you solve. And the rules find only the zero-force members you can see by eye: sometimes the calculation also returns 0 — that is a zero-force member too.
Note: the names here (C, D, N1…) belong to the truss on this page only. The other pages have a different truss with its own names.
Trusses binder · BST · beamsolvertool.com/en/learn/trusses/zero-force-members/
All pages as a print-ready PDF — in the Binders to download of BST PRO