Accuracy you can check
Every FERS result is produced by a finite-element solver and validated against the closed-form (analytical) solution — the textbook formula. For the standard beam and frame cases below, FERS matches the exact solution to within solver tolerance. That is what makes FERS safe for an AI agent to call and for an engineer to trust.
| Case | Closed-form | Analytical | FERS | Error |
|---|---|---|---|---|
Simply supported beam, uniform load — mid-span deflection L = 6 m, w = 10 kN/m, 200×100 mm steel (E = 210 GPa) | δ = 5wL⁴ / 384EI | 12.05 mm | 12.05 mm | 0.0% |
Simply supported beam, uniform load — maximum moment L = 6 m, w = 10 kN/m | M = wL² / 8 | 45.00 kN·m | 45.00 kN·m | 0.0% |
Cantilever, end point load — free-end deflection L = 5 m, P = 1 kN, IPE180 | δ = PL³ / 3EI | closed form | matches | < 0.1% |
Cantilever, end point load — fixed-end moment L = 5 m, P = 1 kN | M = PL | closed form | matches | < 0.1% |
Simply supported beam, central point load — mid-span deflection closed form | δ = PL³ / 48EI | closed form | matches | < 0.1% |
Cantilever, uniform load — free-end deflection closed form | δ = wL⁴ / 8EI | closed form | matches | < 0.1% |
These closed-form checks are asserted in the open-source FERS test suite and re-run on every release. Beyond hand solutions, FERS also handles second-order (P-Δ) effects, buckling, load combinations, and Eurocode unity checks — each solve returning a transparent hand-calc trace.
Reproduce it yourself
Any agent or script can run these solves. Create an API key at Profile → API Keys, then:
curl -s https://ferscloud.com/api/sdk/solve \
-H "X-API-Key: keyId.secret" \
-H "Content-Type: application/json" \
-d '{ "model": { /* FERS model JSON */ } }'Or connect FERS to Claude, ChatGPT, or Cursor via MCP — see the MCP server guide, or drive the same solver from Python on the structural analysis in Python page. First 100 solves each week are free.
Every case in this table can be rebuilt and re-solved in about a minute. The free 2D frame calculator runs this same engine compiled to WebAssembly in your browser, and its worked example reproduces the simply supported row above exactly. For the standard NAFEMS benchmarks — including the ones a low-order element cannot represent well — the comparison is re-solved live rather than quoted from a table.