Paired Load Deflection Calculator
Midspan deflection of two equal loads, each at distance a from the nearer support. δ = P a (3 L² − 4 a²) / (24 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
- Midspan deflection of a simply supported span with 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 8244ea86ec37
- 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
L, E, and I must be positive. a must be greater than 0 and no greater than L/2.
Read the midspan deflection
The sign of P is the sign of δ.
Example calculations
Common configurations with formula and result.
Loads one quarter of the way in on a span of 4
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 Deflection 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 midspan deflection is δ = P a (3 L² − 4 a²) / (24 E I).
- What it calculates
- Midspan deflection of a simply supported span with two equal symmetric point loads.
- Inputs
- P
- a
- L
- E
- I
- Outputs
- delta
- Formula
δ = P a (3 L² − 4 a²) / (24 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 puts both loads at midspan and matches one load of 2P on the beam-deflection 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=88
- 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=88
- 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: Midspan δ = P a (3 L² − 4 a²) / (24 E I) when each load is a distance a from the nearer support.
- 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 midspan deflection of a simply supported span with two equal loads, each the same distance from the nearer support.
Supported and not supported
Supported: δ = P a (3 L² − 4 a²) / (24 E I). a = L/2 matches a single midspan load of 2P.
Not supported: unequal loads, a past midspan, and a cantilever. /calc/mechanical is not open.
Agent / API notes
Capability id: mechanical.statics.paired_load_deflection · tool id: paired-load-deflection · 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.
What if a is past midspan?
The two positions would cross. Keep a at most L/2, measured from each support toward the center.