A straight member ten meters long is fixed at one end and free at the other. A lateral force of 6.0 N acts at the tip. How far does the tip deflect, and what moment does the fixed end carry? This bending case has one element and one load.

This page preserves a recorded benchmark and its expected values. The dated run below is not a new run of the current product.

Independent numerical comparison. The recorded test exercises a benchmark crate. It does not exercise the desktop product route.

1.Inputs.

Illustrative values, taken from no standard and chosen so the arithmetic can be followed by hand. Most do not describe a real pipe; read them in any consistent set of units.

2.Method.

The reference uses elementary cantilever results. Tip deflection is PL³/(3EI). The fixed-end moment magnitude equals force times length. Recovery from the solved displacements gives the moment that the root restraint must supply. This reaction opposes the applied moment: −60.0 N·m, with magnitude 60.0.

3.Results.

The case record describes these checks:

• The solver builds one frame element, fixes all six freedoms at the root and solves for the tip.
• The solved tip deflection in Y matches the hand value.
• The fixed-end reaction moment recovered from the solution is −60.0 N·m, the hand magnitude with the reaction’s sign.

What it shows. Compared with an independent hand calculation.

Path exercised. The benchmark calls the solver’s components directly: elements, loads, frame solver and stress recovery. It does not go through the program’s own model-to-solve path.

Agreement. Each computed value must match the reference within an absolute difference of 1.0 × 10⁻⁹ in the case’s own units. Counts and structural outcomes must match exactly. Long values are shown here to seven significant figures; the tests compare the full values in the record.

4.Recorded command.

This command belongs to the archived source at 462f66975d36cd10d5b8455193ada9517d28d353. Use a checkout of that exact revision. This edition did not run the command. The recorded result does not establish current product support.

git checkout --detach 462f66975d36cd10d5b8455193ada9517d28d353
cd projects/chirality-piping
cargo test --manifest-path validation/benchmarks/mechanics/Cargo.toml cantilever_tip_force_matches_open_mechanics_formula

Hand calculation: validation/hand_calcs/mechanics/cantilever_tip_force.md. Test record, with the recorded run of 2026-07-10, with the strengthened check first run on 2026-09-22: mech-cantilever-tip-force.md.