Outer Uniform Load at a Station Calculator
Deflection at distance x from the wall when the uniform load starts at a and runs to the tip. x = L is the tip page. a = 0 is the full uniform curve. Runs locally.
Trust summary CVP VERIFIED · production STALE · CVP protocol 1.0.0-proposed · Engineering assurance
- Input interpretation
- Enter values to calculate.
- Result
- —
- Assurance
- Engineering
- Declared partition coverage
- PASS · 2/2 declared partitions (domain, invalid-domain) · Matrix
- Known limitations
- Physics L1 gap capability
- Core CVP does not include live graph, viewport, or pointer interaction.
- Model
- Deflection at a stated distance from the wall for a uniform load on the outer part of a cantilever.
- Scope
- Calculation runs locally in the browser; values are not uploaded.
- Verification
- Engine tested · Source checked · v1.0.0 · CVP VERIFIED · production STALE · CVP protocol 1.0.0-proposed · Engineering assurance· View Manifest · CVP overview · Specification
- Versions
- Calculation 1.0.0 · CVP protocol 1.0.0-proposed
- CVP identity
- 0/0 property · digest 5317fac62c23
- Legacy regression
- 2/2 tests · Production surface contract 6/6
- Trust layers
- Verification VERIFIED · Production STALE · overall VERIFIED_STALE
- CVP status
- STALE · Capability production binding: STALE · Site report: STALE · Evidence changed after the last successful production attestation. Re-attestation required.
- Reference
- O1 model · O2 expected_values · O2 numerical_behavior
- Interfaces
- PASS · UI (SSR) / REST / MCP
- Supplemental domain review
- Not performed
- Named expert review
- Not performed
- CVP suite
- 1/1 golden · 1/1 CVP boundary · 1/1 invalid · 1/1 cross-interface · 6/6 CVP contract · Manifest
- Sources
- Hibbeler, Mechanics of Materials
- Gere and Goodno, Mechanics of Materials
- Evidence
- 1 legacy golden · 1 legacy boundary · legacy regression suite · 1/1 oracle-backed golden · 1/1 invalid · Artifact integrity PASS
- Semantic contract
- PASS
Full verification
Formulas
Core equations used by this calculator.
How to use
Enter the intensity, the unloaded length, the station, the length, the modulus, and the area moment
a is shorter than L. x may reach the free end.
Read the deflection
The sign of w is the sign of δ.
Example calculations
Common configurations with formula and result.
At the free end
w = 24, a = 1, x = 2, L = 2, E = 1, I = 1
Outer Uniform Load at a Station calculator specification
Version 1.0.0 · Engine tested
- Engine tested 2/2 tests · Production surface contract 6/6
- Named expert review Not performed
- Calculation version 1.0.0
- Definition
- A cantilever is unloaded from the wall to a, then carries uniform intensity w to the tip. The curve is the full uniform curve minus the partial-from-wall curve. At the tip this is the outer-uniform page.
- What it calculates
- Deflection at a stated distance from the wall for a uniform load on the outer part of a cantilever.
- Inputs
- w
- a
- x
- L
- E
- I
- Outputs
- delta
- Formula
Full uniform curve minus the partial-from-wall curve. x = L is the tip page.- Assumptions
- Calculation runs locally in the browser; values are not uploaded.
- Keep units consistent with the labels on each field.
- x = L recovers w [3 L⁴ − a³ (4L − a)]/(24 E I). a = 0 is the full uniform curve.
- Units
- w, a, x, L, E, and I set the deflection unit.
- Boundary conditions
- missing w, a, x, L, E, or I → MISSING_REQUIRED_INPUT
- L ≤ 0, E ≤ 0, or I ≤ 0 → VALUE_MUST_BE_POSITIVE
- a < 0, a ≥ L, x ≤ 0, or x > L → INVALID_INPUT
- Example
- w=24 a=1 x=2 L=2 E=1 I=1 → δ=41
- Validation cases
2 published on this page · 2/2 tests · Production surface contract 6/6 · View evidence
- w=24 a=1 x=2 L=2 E=1 I=1 → δ=41
- a=2 → INVALID_INPUT
- Sources
- Hibbeler, Mechanics of Materials — Deflection of beams — superpositionSupports: An outer uniform load is the full uniform load minus the same load on the inner length.
- Gere and Goodno, Mechanics of Materials — Deflection of beams — cantilever partially loadedSupports: Supports the tip value w [3 L⁴ − a³ (4L − a)]/(24 E I).
- Hibbeler, Mechanics of Materials — Deflection of beams — superposition
- Calculation version
- 1.0.0
Background
Interpretation and common distinctions.
Find the deflection at a stated distance from the wall when the uniform load starts at a and runs to the tip.
Agent / API notes
Capability id: mechanical.statics.cantilever_outer_at_deflection · tool id: cantilever-outer-at · pin 1.0.0.
{ "w": 24, "a": 1, "x": 2, "L": 2, "E": 1, "I": 1 }
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Frequently asked questions
Key distinctions behind the calculation.
Does the tip match the outer-uniform page?
Yes. x = L gives δ = 41 for w = 24, a = 1, and L = 2, which is the full tip 48 minus the partial tip 7.