Truss Analysis — 2D Truss Solver

2D truss member force analysis using the matrix stiffness method. Calculates axial forces, reactions, and joint deflections for statically determinate trusses. Educational use only.

This page documents the scope, inputs, outputs, and computational approach of the Truss Analysis tool on steelcalculator.app. The interactive calculator runs in your browser; this documentation ensures the page is useful even without JavaScript.

What this tool is for

Solving for member axial forces, support reactions, and joint deflections in 2D pin-jointed trusses.
Visualising the truss geometry, deformed shape, and force diagram.
Verifying hand calculations for simple Pratt, Warren, and Howe truss configurations.

What this tool is not for

It does not handle 3D space trusses or members with bending stiffness (use a frame analysis tool instead).
It does not check member capacity, buckling, or connection design.
It does not account for self-weight, thermal effects, or fabrication imperfections.

Key concepts this page covers

matrix stiffness method for truss structures
member axial force (tension and compression)
support reactions and equilibrium
joint deflections

Inputs and outputs

Typical inputs: joint coordinates, member connectivity (which joints each member connects), support conditions (pin or roller), applied loads at joints, and member properties (E, A).

Typical outputs: member axial forces (positive = tension, negative = compression), support reactions, joint deflections, and a visual force diagram with colour-coded tension/compression members.

Computation approach

The solver assembles the global stiffness matrix [K] from individual member stiffness contributions. Each truss member contributes a 4x4 stiffness matrix (2 DOF per joint) transformed from local to global coordinates. The system [K]{d} = {F} is solved for unknown joint displacements, then member forces are computed from the relative displacements of each member's end joints. Reactions are recovered from the constrained DOFs.

Frequently Asked Questions

What is the difference between a truss and a frame? In structural analysis, a truss has pin-connected joints and carries loads only through axial forces in its members (no bending moments). A frame has rigid or semi-rigid joints that transfer bending moments. Real steel trusses have gusset-plated connections that provide some moment fixity, but the truss idealisation is valid when loads are applied at joints and members are slender enough that bending effects are secondary.

How do I check if a truss is statically determinate? For a 2D truss, the condition for static determinacy is m + r = 2j, where m is the number of members, r is the number of support reactions, and j is the number of joints. If m + r > 2j, the truss is statically indeterminate (redundant). If m + r < 2j, the truss is a mechanism and is unstable. The stiffness method handles both determinate and indeterminate trusses, but this tool is primarily intended for determinate configurations.

Why might the solver give unexpected results? Common issues include: (1) an unstable truss geometry that is a mechanism, causing a singular stiffness matrix; (2) loads applied at unsupported joints without adequate member connectivity; (3) collinear members that create a zero-stiffness mode. Always check that your truss geometry forms a stable triangulated structure before interpreting the results.

Disclaimer (educational use only)

This page is provided for general technical information and educational use only. It does not constitute professional engineering advice, a design service, or a substitute for an independent review by a qualified structural engineer. Any calculations, outputs, examples, and workflows discussed here are simplified descriptions intended to support understanding and preliminary estimation.

All real-world structural design depends on project-specific factors (loads, combinations, stability, detailing, fabrication, erection, tolerances, site conditions, and the governing standard and project specification). You are responsible for verifying inputs, validating results with an independent method, checking constructability and code compliance, and obtaining professional sign-off where required.

The site operator provides the content "as is" and "as available" without warranties of any kind. To the maximum extent permitted by law, the operator disclaims liability for any loss or damage arising from the use of, or reliance on, this page or any linked tools.