Truss Force Lab
Build an ideal planar pin-jointed truss from straight two-force members. Enter joint positions in mm, signed joint loads and support restraints. The solver assembles all joint x/y equilibrium equations: positive member force means tension and negative means compression; positive load and reaction components point right or up. Only a unique, well-conditioned determinate system receives forces. Counting members plus reaction components against twice the joints is necessary but not sufficient, so matrix rank also checks geometry and support directions. This preliminary statics model does not evaluate deflection, buckling, construction or structural safety.
Key features
- Actual 2D joint-equilibrium matrix with axial member and support-reaction columns
- N/kN load selection that preserves physical load on unit changes; both output units and mm geometry
- Separate underrestrained, statically indeterminate and equal-count singular diagnoses
- Matrix/augmented rank, numerical pivot guard and joint/global force/moment residuals
- Editable joints, supports, loads and members with four examples and strict JSON restore
- Labeled SVG, member/reaction CSV, full result JSON and project JSON
How to use
- Enter joint x/y positions in mm and right/up positive joint loads in N or kN.
- Select a pin (x+y reactions), X roller (x only), Y roller (y only) or free joint.
- Connect distinct joints with straight members; drawn crossings are not connections unless a joint is defined.
- Analyze unknown count m+r versus 2j and matrix rank. Only a unique well-conditioned system has numeric forces.
- Read positive tension, negative compression and signed reactions; inspect residuals, then download or restore local files.
Use cases
- Teach the method of joints with a hand-checkable triangle
- Show why m+r=2j cannot prove a collinear truss stable
- Compare a missing member with a redundant support
- Inspect force balance after changing a joint load
Frequently asked questions
What is modeled?
Straight ideal two-force members joined by frictionless planar pins, with loads only at joints. A pin resists x and y, while a roller resists only the chosen global axis. Member bending and distributed loads are excluded.
How are force signs interpreted?
Positive member force pulls away from both joints (tension); negative means compression. Positive external and reaction components point right (+x) or up (+y).
Does m+r=2j prove stability?
No. It counts unknowns and equations but misses dependent supports, collinear bars or mechanisms. The actual equilibrium matrix must have full rank; equal-count rank defects are reported as singular without invented forces.
What about underrestrained or indeterminate structures?
Fewer unknowns than 2j means underrestrained. More unknowns with full row rank are statically indeterminate because equilibrium does not select unique forces. Rank-deficient systems are unstable or dependent. No stiffness or compatibility analysis is performed.
What are the units and residuals?
Joint positions and bar lengths use mm. Loads may be entered in N or kN; switching units preserves physical load. Results show both. Joint residuals are ΣFx/ΣFy in N; global moment residual is N·mm about the first joint.
Can this certify a real truss?
No. Strength, buckling, joints, load combinations, deflection, wind/seismic effects, fabrication, codes, site safety and professional review are outside this preliminary equilibrium tool.
Is my truss uploaded?
No. The browser calculates locally. Files are generated only when downloaded, and JSON restore reads a local or pasted project.
Privacy
Joints, loads, supports and results remain in this browser tab. Downloads are local; no truss model is submitted to an application API.
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