Cantilever Partial Tip Calculator
Free-end deflection when a uniform load starts at the wall and stops at a. δ = w 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
- Free-end deflection of a cantilever whose uniform load starts at the wall and stops before the tip.
- 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 fbf4b2de8b29
- 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 loaded length, the cantilever length, the modulus, and the area moment
L, E, and I must be positive. a must be greater than 0 and no greater than L.
Read the free-end deflection
Past a the beam is straight, at the slope it already has.
Example calculations
Common configurations with formula and result.
Load over the inner half
w = 24, a = 1, L = 2, E = 1, I = 1
Load over the whole length
w = 24, a = 2, L = 2, E = 1, I = 1
Cantilever Partial Tip 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. Uniform intensity w runs from the fixed end to distance a and is zero beyond a. The free-end deflection is δ = w a³ (4L − a) / (24 E I).
- What it calculates
- Free-end deflection of a cantilever whose uniform load starts at the wall and stops before the tip.
- Inputs
- w
- a
- L
- E
- I
- Outputs
- delta
- Formula
δ = w 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 = L recovers δ = w L⁴ / (8 E I). The deflection at a is a different page.
- 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=7
- 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=7
- w=24 a=2 L=2 E=1 I=1 → δ=48
- a=0 → INVALID_INPUT
- Sources
- Hibbeler, Mechanics of Materials — Deflection of beams — cantilever with a partial uniform loadSupports: The free-end deflection is w a³ (4L − a) / (24 E I).
- Gere and Goodno, Mechanics of Materials — Deflection of beams — partial uniform loadSupports: Supports the page formula. a = L recovers w L⁴ / (8 E I).
- Hibbeler, Mechanics of Materials — Deflection of beams — cantilever with a partial uniform load
- Calculation version
- 1.0.0
Background
Interpretation and common distinctions.
Find the free-end deflection of a cantilever when a uniform load starts at the wall and stops at a.
Supported and not supported
Supported: δ = w a³ (4L − a) / (24 E I). a = L is the full uniform-load page.
Not supported: the value at a when a is shorter than L, and a load that starts away from the wall. /calc/mechanical is not open.
Agent / API notes
Capability id: mechanical.statics.cantilever_partial_tip_deflection · tool id: cantilever-partial-tip · pin 1.0.0.
{ "w": 24, "a": 1, "L": 2, "E": 1, "I": 1 }
Related tools
Other calculators in this family: Angled Pull Calculator, Angled Pull on an Incline Calculator, Area Moment Calculator, Beam Deflection Calculator, Beam Moment Deflection Calculator, Beam Moment Maximum Deflection Calculator, Bending Stress Calculator, Cantilever Deflection Calculator . Explore all Statics & Strength.
Frequently asked questions
Key distinctions behind the calculation.
Why is the tip farther than the end of the load?
Past a the beam stays straight. For w = 24, a = 1, and L = 2 the tip moves 7 while the end of the load moves 3.