Paired Load at the Load Calculator
Deflection under either of two equal loads. δ = P a² (3L − 4a) / (6 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
- Deflection under either of two equal symmetric point loads.
- 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 72c41c459dc3
- 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 each load, its distance from the nearer support, the span, the modulus, and the area moment
a must be greater than 0 and no greater than L/2.
Read the deflection under a load
The two loads deflect by the same amount.
Example calculations
Common configurations with formula and result.
Loads one quarter of the way in
P = 48, a = 1, L = 4, E = 1, I = 1
Both loads at midspan
P = 48, a = 2, L = 4, E = 1, I = 1
Paired Load at the 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 span of length L carries two equal loads P, each at distance a from the nearer support. The deflection under either load is δ = P a² (3L − 4a) / (6 E I).
- What it calculates
- Deflection under either of two equal symmetric point loads.
- Inputs
- P
- a
- L
- E
- I
- Outputs
- delta
- Formula
δ = P a² (3L − 4a) / (6 E I).- Assumptions
- Calculation runs locally in the browser; values are not uploaded.
- Keep units consistent with the labels on each field.
- a = L/2 matches one midspan load of 2P. The midspan value, between the loads, is a different page.
- Units
- P, a, L, E, and I set the deflection unit.
- Boundary conditions
- missing P, a, L, E, or I → MISSING_REQUIRED_INPUT
- L ≤ 0, E ≤ 0, or I ≤ 0 → VALUE_MUST_BE_POSITIVE
- a ≤ 0 or a > L/2 → INVALID_INPUT
- Example
- P=48 a=1 L=4 E=1 I=1 → δ=64
- Validation cases
3 published on this page · 3/3 tests · Production surface contract 6/6 · View evidence
- P=48 a=1 L=4 E=1 I=1 → δ=64
- P=48 a=2 L=4 E=1 I=1 → δ=128
- a=3 L=4 → INVALID_INPUT
- Sources
- Hibbeler, Mechanics of Materials — Deflection of beams — two symmetric concentrated loadsSupports: The deflection under each load is P a² (3L − 4a) / (6 E I).
- Gere and Goodno, Mechanics of Materials — Deflection of beams — symmetric point loadsSupports: Supports the page formula. a = L/2 recovers one midspan load of 2P.
- Hibbeler, Mechanics of Materials — Deflection of beams — two symmetric concentrated loads
- Calculation version
- 1.0.0
Background
Interpretation and common distinctions.
Find the deflection under either load when two equal loads sit the same distance from each support.
Supported and not supported
Supported: δ = P a² (3L − 4a) / (6 E I).
Not supported: the midspan value between the loads, and unequal loads. /calc/mechanical is not open.
Agent / API notes
Capability id: mechanical.statics.paired_load_at_deflection · tool id: paired-load-at · pin 1.0.0.
{ "P": 48, "a": 1, "L": 4, "E": 1, "I": 1 }
Related tools
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Frequently asked questions
Key distinctions behind the calculation.
Is midspan the same number?
Only when the loads meet at midspan. For a = 1 and L = 4, under each load is 64 and midspan is 88.