Overhang Span at a Station Calculator
Deflection at station x on the span when a load sits at the end of an overhang. x = L/2 is the span-midspan 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 on the span of an overhanging beam.
- 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 3ce51dad0198
- 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 load, the overhang, the station, the span, the modulus, and the area moment
x must lie strictly between the supports.
Read the deflection
Positive P downward on the overhang gives a negative span deflection.
Example calculations
Common configurations with formula and result.
Midspan of the span
P = 48, a = 1, x = 1, L = 2, E = 1, I = 1
Overhang Span at a Station 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 beam of span L has an overhang a beyond the right support, with load P at the overhang end. On the span, at station x, δ = −P a x (L² − x²)/(6 E I L). Midspan is the span-midspan page.
- What it calculates
- Deflection at a stated station on the span of an overhanging beam.
- Inputs
- P
- a
- x
- L
- E
- I
- Outputs
- delta
- Formula
Overhang span curve. x = L/2 is the span-midspan page.- Assumptions
- Calculation runs locally in the browser; values are not uploaded.
- Keep units consistent with the labels on each field.
- x = L/2 recovers −P a L²/(16 E I). A downward overhang load lifts the span.
- Units
- P, a, x, L, E, and I set the deflection unit.
- Boundary conditions
- missing P, a, x, L, E, or I → MISSING_REQUIRED_INPUT
- L ≤ 0, a ≤ 0, E ≤ 0, or I ≤ 0 → VALUE_MUST_BE_POSITIVE
- x ≤ 0 or x ≥ L → INVALID_INPUT
- Example
- P=48 a=1 x=1 L=2 E=1 I=1 → δ=−12
- Validation cases
2 published on this page · 2/2 tests · Production surface contract 6/6 · View evidence
- P=48 a=1 x=1 L=2 E=1 I=1 → δ=−12
- x=2 → INVALID_INPUT
- Sources
- Hibbeler, Mechanics of Materials — Deflection of beams — overhanging beamSupports: The span deflection from an overhang load is −P a x (L² − x²)/(6 E I L).
- Gere and Goodno, Mechanics of Materials — Deflection of beams — beam with an overhangSupports: Supports the elastic curve on the span between the supports.
- Hibbeler, Mechanics of Materials — Deflection of beams — overhanging beam
- Calculation version
- 1.0.0
Background
Interpretation and common distinctions.
Find the deflection at a stated station on the span when the load sits at the end of an overhang.
Agent / API notes
Capability id: mechanical.statics.overhang_span_at_deflection · tool id: overhang-span-at · pin 1.0.0.
{ "P": 48, "a": 1, "x": 1, "L": 2, "E": 1, "I": 1 }
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Frequently asked questions
Key distinctions behind the calculation.
Does midspan match the span page?
Yes. x = L/2 gives δ = −12 for P = 48, a = 1, and L = 2.