Free Truss Calculator: Member Forces & Reactions

How to use the truss calculator

This free truss calculator analyses any 2D pin-jointed truss and returns the axial force in every member, the reactions at each support and the displacement of every joint. It uses the matrix stiffness method, the same approach as commercial structural analysis software, so it handles both statically determinate and indeterminate trusses.

1. Place the nodes

Open the Nodes tab and enter the x and y coordinates of each joint. The default model is a simple Warren truss, which is a good starting point for homework problems and for checking a hand solution by the method of joints.

2. Connect the members

In the Members tab, join pairs of nodes. Each member has a cross-sectional area and an elastic modulus. For a determinate truss the member forces do not depend on these values, but they do change the displacements and are needed for indeterminate trusses.

3. Add supports and loads

Add a pin support (restrains x and y) and a roller (restrains one direction) so the truss is stable, then apply point loads at the joints in the Loads tab. Loads on a truss always act at the nodes.

4. Read the results

The diagram updates as you type. Members in tension and compression are coloured differently, support reactions are listed in the results panel, and the deflected shape is drawn at an exaggerated scale. Zero-force members show a force of 0, which is a quick way to confirm what you found by inspection. For the exam-style walk-through, see the FE Civil method of joints example, or switch to the beam calculator for shear and moment diagrams.

Method of joints, method of sections and the stiffness method

You can check any result from this truss solver by hand. The three standard methods give the same member forces for a statically determinate truss:

• Method of joints: isolate one joint at a time and solve ΣF_x = 0 and ΣF_y = 0. Start at a joint with no more than two unknown member forces.
• Method of sections: cut through no more than three members, then take moments about the point where two of the cut members meet to get the third force directly. Best when you only need one or two members in the middle of a long truss.
• Stiffness method (what this calculator uses): works for every truss, including indeterminate ones, and also gives joint displacements.

Worked example: a simple triangular truss

Joints A (0, 0) and B (6, 0) are 6 m apart with a pin at A and a roller at B. The apex C is at (3, 4), and a 30 kN load acts downward at C. Members AC and BC are each 5 m long.

• Reactions: by symmetry A_y = B_y = 15 kN, and A_x = 0.
• Joint A, vertical: 15 + 0.8 F_AC = 0, so F_AC = −18.75 kN (compression). The 0.8 is the sine of the member angle (4/5).
• Joint A, horizontal: F_AB + 0.6 F_AC = 0, so F_AB = +11.25 kN (tension).
• By symmetry F_BC = −18.75 kN. Check at joint C: 2 × 18.75 × 0.8 = 30 kN, which balances the load.

Enter the same three joints in the calculator above to see these forces and the deflected shape.

How to spot zero-force members

• At an unloaded joint with only two non-collinear members, both members carry zero force.
• At an unloaded joint with three members, two of them collinear, the third member carries zero force.

Zero-force members still matter: they brace compression members against buckling and carry load when the loading changes.

Truss calculator FAQ