Engineering Calc Tools

Statics

Truss Calculator (Method of Joints)

Force in every member of a plane truss, tension or compression, and the support reactions.

Tool no.
ECT-S20
Rev
1.0
Updated
Oct 2026
Method
Method of joints
Examples

Given

One joint per line, like A 0 0. Any length unit works as long as you use the same one throughout.

A roller pushes straight up; write roller x for one that pushes sideways (on a wall).

+ x is right and + y is up, so 20 down is B 0 -20.

Answers

Largest member force = —
Runs in your browser. Nothing you enter is uploaded.Method of joints · 2j equations solved together
How to use this calculator

Give each joint a letter and its coordinates, list the members by the two joints they join, say which joints are supported (a pin holds in both directions, a roller in one) and where the loads act. The calculator writes ΣFx = 0 and ΣFy = 0 at every joint and solves them all at once. Positive member forces are tension, negative are compression.

Method of joints

At every jointΣFx = 0  ΣFy = 0
A member force on a jointF (cos θ, sin θ), with θ the direction from that joint along the member
Determinate and stablem + r = 2j, and the joints can’t move without stretching a member

Worked example

Triangle A(0, 0), B(4, 0), C(2, 3), pin at A, roller at B, 10 kN down at C

  1. By symmetry Ay = By = 5 kN and Ax = 0.
  2. AC has length √13 = 3.606 m. At joint A: ΣFy = 5 + FAC(3/3.606) = 0, so FAC = −6.009 kN (C).
  3. ΣFx = FAB + FAC(2/3.606) = 0, so FAB = 3.333 kN (T). By symmetry FBC = −6.009 kN (C).

Zero-force members

Two quick rules find them before any math: at a joint with only two non-collinear members and no load, both carry zero; at a joint where two members are collinear and a third joins with no load, the third carries zero. They still matter, because they brace the truss and keep compression members from buckling.

Frequently asked questions

What does “statically indeterminate” mean?

There are more unknowns than equations (m + r > 2j), so statics alone can’t share the load between members; you need their stiffness. Remove a redundant member or support to use this calculator.

Can I use the method of sections instead?

Yes, and it is quicker for one member in the middle of a long truss. Both methods give the same forces; this calculator gives all of them at once.