Partial Uniform Load plus Tip Load Calculator
Deflection at distance x from the wall for a uniform load from the wall to a plus a tip load. x = L adds the partial tip page and the tip-load page. 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 partial uniform load plus a tip load.
- 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 5f648b33e8e1
- 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 tip load, the loaded length, the station, the length, the modulus, and the area moment
a and x may reach the free end.
Read the deflection
The signs of w and P are the signs of their parts of δ.
Example calculations
Common configurations with formula and result.
At the free end
w = 24, P = 48, a = 1, x = 2, L = 2, E = 1, I = 1
Partial Uniform Load plus Tip Load 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 carries uniform intensity w from the wall to a and a tip load P. Deflection at distance x from the wall is the sum of those two elastic curves.
- What it calculates
- Deflection at a stated distance from the wall for a partial uniform load plus a tip load.
- Inputs
- w
- P
- a
- x
- L
- E
- I
- Outputs
- delta
- Formula
Sum of the partial-uniform curve and the tip-load curve.- Assumptions
- Calculation runs locally in the browser; values are not uploaded.
- Keep units consistent with the labels on each field.
- x = L recovers the partial tip page plus P L³/(3 E I).
- Units
- w, P, a, x, L, E, and I set the deflection unit.
- Boundary conditions
- missing w, P, 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 P=48 a=1 x=2 L=2 E=1 I=1 → δ=135
- Validation cases
2 published on this page · 2/2 tests · Production surface contract 6/6 · View evidence
- w=24 P=48 a=1 x=2 L=2 E=1 I=1 → δ=135
- a=3 → INVALID_INPUT
- Sources
- Hibbeler, Mechanics of Materials — Deflection of beams — superpositionSupports: A partial uniform load and a tip load on a cantilever superpose.
- Gere and Goodno, Mechanics of Materials — Deflection of beams — cantilever with several loadsSupports: Supports adding the elastic curves measured from the wall.
- 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 for a uniform load from the wall to a plus a tip load.
Agent / API notes
Capability id: mechanical.statics.cantilever_partial_tip_at_deflection · tool id: cantilever-partial-tip-at · pin 1.0.0.
{ "w": 24, "P": 48, "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 two tip pages?
Yes. x = L gives δ = 7 + 128 = 135 for w = 24, P = 48, a = 1, and L = 2.