Outer Uniform Load plus Tip Moment Calculator
Deflection at distance x from the wall for an outer uniform load plus a tip moment. x = L adds the outer-uniform tip page and the tip-moment 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 an outer uniform load plus a tip moment.
- 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 40517f091bf6
- 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 moment, 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 signs of w and M are the signs of their parts of δ.
Example calculations
Common configurations with formula and result.
At the free end
w = 24, M = 4, a = 1, x = 2, L = 2, E = 1, I = 1
Outer Uniform Load plus Tip Moment 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, plus a tip moment M. Deflection at x is the sum of those two elastic curves.
- What it calculates
- Deflection at a stated distance from the wall for an outer uniform load plus a tip moment.
- Inputs
- w
- M
- a
- x
- L
- E
- I
- Outputs
- delta
- Formula
Sum of the outer-uniform curve and the tip-moment 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 outer-uniform tip page plus M L²/(2 E I).
- Units
- w, M, a, x, L, E, and I set the deflection unit.
- Boundary conditions
- missing w, M, 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 M=4 a=1 x=2 L=2 E=1 I=1 → δ=49
- Validation cases
2 published on this page · 2/2 tests · Production surface contract 6/6 · View evidence
- w=24 M=4 a=1 x=2 L=2 E=1 I=1 → δ=49
- a=2 → INVALID_INPUT
- Sources
- Hibbeler, Mechanics of Materials — Deflection of beams — superpositionSupports: An outer uniform load and a tip moment 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 an outer uniform load plus a tip moment.
Agent / API notes
Capability id: mechanical.statics.cantilever_outer_moment_at_deflection · tool id: cantilever-outer-moment-at · pin 1.0.0.
{ "w": 24, "M": 4, "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 = 41 + 8 = 49 for w = 24, M = 4, a = 1, and L = 2.