Truss and frame calculator: member forces, reactions and deflections by the direct stiffness method

What it does

This is a small structural analysis program for flat (2D) structures. You describe the structure as nodes (joints), members joining them, supports and loads, and it solves it with the direct stiffness method, the method inside professional analysis software:

• Truss mode: members are pin-jointed and carry only axial force. You get each member’s force and whether it is in tension or compression, coloured on the drawing.
• Frame mode: joints are rigid, so members also bend. You get each member’s axial force N, and the shear V and bending moment M at both ends. A frame member can also carry a uniform load along its length, such as its own weight or a floor load.
• Support reactions, every node’s displacement (and rotation in a frame), and an equilibrium check that loads and reactions add up to zero.
• A drawing of the structure with its supports and loads and the deflected shape, drawn larger by a factor you can set, plus CSV files of the member forces and node results.

For study and planning, not a substitute for professional judgement. Check your local code and a qualified engineer.

How to use it

1. Pick truss or frame, or fill in one of the made-up examples.
2. Nodes: one row per joint, with a name and x and y in metres.
3. Members: a name, the two node names, Young’s modulus E in GPa and area A in cm². For a frame, add the second moment of area I in cm⁴ and, if you want, a uniform load w in kN per metre of member length (in the y direction, negative for gravity).
4. Supports: node and type. pin holds x and y; roller holds only y (a roller on a level surface); roller-y holds only x; fixed holds x, y and rotation.
5. Loads: node, Fx and Fy in kN (right and up are positive) and a moment M in kN·m (anticlockwise positive).

You can paste each table from a spreadsheet, or open a CSV or Excel file. A header row is skipped.

Worked example

The made-up Pratt truss the page opens with spans 12 m in four 3 m panels, 3 m deep, with a pin at node 1, a roller at node 5 and 20 kN hanging at each of the three inner bottom nodes. Each support takes 30 kN. By the method of joints, the bottom chord carries 30 kN tension, the top chord 40 kN compression, the end diagonals 42.43 kN compression, the verticals beside the ends 20 kN tension, the middle vertical nothing, and the inner diagonals 14.14 kN tension. The solver gives the same, and with 20 cm² steel members the middle of the bottom chord drops 1.899 mm.

The portal frame example is 6 m wide and 4 m tall with fixed feet, a 10 kN/m load on the beam and 15 kN pushing sideways at the top left. The top sways 6.46 mm, and the largest moment is 34.44 kN·m at the right end of the beam.

FAQ

Why does it say the structure is a mechanism? The supports or members cannot stop some movement: a truss with too few members, a roller-only structure that can slide, or a node not connected to anything. A stable plane truss needs at least as many members plus reactions as twice the number of nodes, arranged in triangles.

Can a frame have pinned joints? Not yet in one model: all frame joints are rigid. Model a pinned frame as a truss if its loads are only at the joints.

What about buckling? Compression members can buckle well before they yield. Check them with the column buckling calculator.

Last updated 2026-11-09.