Cantilever Outer Uniform Calculator
Tip deflection when a uniform load starts away from the wall. δ = w [3 L⁴ − a³ (4L − a)] / (24 E I). 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
- Tip deflection of a cantilever whose uniform load starts at distance a from the fixed end.
- 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 109d566a9b47
- Legacy regression
- 3/3 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
- 2 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 cantilever length, the modulus, and the area moment
L, E, and I must be positive. a must be at least 0 and strictly less than L.
Read the tip deflection
The sign of w is the sign of δ.
Example calculations
Common configurations with formula and result.
Load on the outer half
w = 24, a = 1, L = 2, E = 1, I = 1
Load over the whole length
w = 24, a = 0, L = 2, E = 1, I = 1
Cantilever Outer Uniform calculator specification
Version 1.0.0 · Engine tested
- Engine tested 3/3 tests · Production surface contract 6/6
- Named expert review Not performed
- Calculation version 1.0.0
- Definition
- A cantilever of length L is fixed at one end. Intensity is zero from the fixed end to distance a, then uniform w to the free end. The tip deflection is δ = w [3 L⁴ − a³ (4L − a)] / (24 E I).
- What it calculates
- Tip deflection of a cantilever whose uniform load starts at distance a from the fixed end.
- Inputs
- w
- a
- L
- E
- I
- Outputs
- delta
- Formula
δ = w [3 L⁴ − a³ (4L − a)] / (24 E I).- Assumptions
- Calculation runs locally in the browser; values are not uploaded.
- Keep units consistent with the labels on each field.
- a = 0 is the full uniform-load page. This is the full uniform load minus the partial load that stops at a.
- Units
- w, a, L, E, and I set the deflection unit.
- Boundary conditions
- missing w, a, L, E, or I → MISSING_REQUIRED_INPUT
- L ≤ 0, E ≤ 0, or I ≤ 0 → VALUE_MUST_BE_POSITIVE
- a < 0 or a ≥ L → INVALID_INPUT
- Example
- w=24 a=1 L=2 E=1 I=1 → δ=41
- Validation cases
3 published on this page · 3/3 tests · Production surface contract 6/6 · View evidence
- w=24 a=1 L=2 E=1 I=1 → δ=41
- w=24 a=0 L=2 E=1 I=1 → δ=48
- a=2 L=2 → INVALID_INPUT
- Sources
- Hibbeler, Mechanics of Materials — Deflection of beams — cantilever with a uniform load on the outer portionSupports: The tip deflection is the full uniform load minus the partial load that stops at a.
- Gere and Goodno, Mechanics of Materials — Deflection of beams — superpositionSupports: Supports δ = w [3 L⁴ − a³ (4L − a)] / (24 E I). a = 0 recovers w L⁴ / (8 E I).
- Hibbeler, Mechanics of Materials — Deflection of beams — cantilever with a uniform load on the outer portion
- Calculation version
- 1.0.0
Background
Interpretation and common distinctions.
Find the tip deflection of a cantilever when the uniform load starts away from the wall.
Supported and not supported
Supported: δ = w [3 L⁴ − a³ (4L − a)] / (24 E I). a = 0 is the full uniform-load page.
Not supported: a load that starts at the wall and stops early, and a simply supported span. /calc/mechanical is not open.
Agent / API notes
Capability id: mechanical.statics.cantilever_outer_uniform_deflection · tool id: cantilever-outer-uniform · pin 1.0.0.
{ "w": 24, "a": 1, "L": 2, "E": 1, "I": 1 }
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Frequently asked questions
Key distinctions behind the calculation.
Why is this the full load minus the inner load?
A full uniform load minus the load that stops at a leaves the outer piece. For w = 24 and L = 2 the full tip is 48 and the inner-load tip is 7, so the outer tip is 41.