Cantilever With Tip Load

Purpose

This case validates the most basic Euler–Bernoulli beam response in the solver:

• tip deflection of a cantilever under a concentrated end load
• fixed-end reaction force
• fixed-end moment
• basic design/evaluation wiring for a simple bending case

Tests in the repository

The current implementation already has this benchmark in several places:

• CoreBeamTests.CantileverBeam_PointLoadAtTip_CorrectDeflection
• CoreBeamTests.CantileverBeam_PointLoad_CorrectReactions
• CoreBeamTests.CantileverBeam_PointLoad_CorrectMomentAtFixedEnd
• AnalysisAndEvaluationTests.Cantilever_TipLoad_AnalysisAndEvaluation_BendingCheck

If one page becomes the canonical benchmark page, those tests should be linked from it rather than described separately in multiple places.

Model

• Length: L = 5.0 m in the pure beam validation tests
• Support condition: fixed at one end
• Load: tip point load P = 10 kN downward
• Material stiffness: E = member.Material.YoungsModulus
• Bending inertia used by the test: I = member.Section.Ixx

The design/evaluation test uses a 3 m cantilever with a 10 kN tip load. That is useful as a separate pipeline check, but the 5 m beam case is the cleaner closed-form benchmark.

Reference solution

For a cantilever with point load at the free end:

• tip deflection:

δ = P L^3 / (3 E I)

• vertical reaction at the fixed end:

R = P

• fixed-end bending moment magnitude:

M = P L

Armatura result

Fill this table from an actual test run.

Quantity	Reference	Armatura	Abs. error	Rel. error
Tip deflection	TODO	TODO	TODO	TODO
Fixed-end vertical reaction	TODO	TODO	TODO	TODO
Fixed-end moment	TODO	TODO	TODO	TODO

Existing tolerances in the tests

The current tests already set a sensible first-pass expectation:

• tip deflection: within 0.1%
• reaction force: within 0.01%
• fixed-end moment: within 1.0% in the moment test, and 0.01% in the reaction-equilibrium test

That means this page can be populated directly from existing assertions rather than inventing a new acceptance criterion.

Suggested interpretation notes

• This is the best first benchmark because the closed-form solution is unambiguous.
• If this case fails, the problem is likely fundamental: element stiffness, DOF ordering, support application, or result recovery.
• This page should probably be the first validation page linked from the overview.

Optional design/evaluation extension

The Cantilever_TipLoad_AnalysisAndEvaluation_BendingCheck test is a good second table on the same page or a short callout. It validates not just analysis, but the evaluation pipeline:

• reaction recovery
• bending check creation
• Eurocode clause wiring
• low expected utilization for a lightly loaded cantilever