Uniform Load plus Offset Point Load Calculator
Deflection at station x for a uniform load plus a point load at distance a from the left support. x = a adds the under-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 station for a uniform load plus an offset point 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 bec243536bf3
- 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 point load, its position, the station, the span, the modulus, and the area moment
a and x must lie strictly between the supports.
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.
Under the point load
w = 24, P = 48, a = 1, x = 1, L = 4, E = 1, I = 1
Uniform Load plus Offset Point Load 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 simply supported beam carries uniform intensity w and a point load P at distance a from the left support. Deflection at x is the sum of those two elastic curves.
- What it calculates
- Deflection at a stated station for a uniform load plus an offset point load.
- Inputs
- w
- P
- a
- x
- L
- E
- I
- Outputs
- delta
- Formula
Sum of the uniform curve and the offset-load curve.- Assumptions
- Calculation runs locally in the browser; values are not uploaded.
- Keep units consistent with the labels on each field.
- x = a adds the under-load page. x = L/2 adds the offset midspan page.
- 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=1 L=4 E=1 I=1 → δ=93
- Validation cases
2 published on this page · 3/3 tests · Production surface contract 6/6 · View evidence
- w=24 P=48 a=1 x=1 L=4 E=1 I=1 → δ=93
- x=4 → INVALID_INPUT
- Sources
- Hibbeler, Mechanics of Materials — Deflection of beams — superpositionSupports: A uniform load and an offset point load superpose.
- Gere and Goodno, Mechanics of Materials — Deflection of beams — several loadsSupports: Supports adding the elastic curves of the two loads.
- Hibbeler, Mechanics of Materials — Deflection of beams — superposition
- Calculation version
- 1.0.0
Background
Interpretation and common distinctions.
Find the deflection at a stated station for a uniform load plus a point load at distance a from the left support.
Agent / API notes
Capability id: mechanical.statics.offset_uniform_at_deflection · tool id: offset-uniform-at · pin 1.0.0.
{ "w": 24, "P": 48, "a": 1, "x": 1, "L": 4, "E": 1, "I": 1 }
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Frequently asked questions
Key distinctions behind the calculation.
Does the load station match the under-load page?
Yes. x = a gives δ = 57 + 36 = 93 for w = 24, P = 48, a = 1, and L = 4. Midspan is δ = 124.