Paired Point Loads plus Equal End Moments Calculator
Deflection at station x for two equal point loads plus equal sagging end moments. x = L/2 adds the paired 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 for two equal point loads plus equal end moments.
- 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 95ce3976b189
- 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 point load, the moment, the inset, the station, the span, the modulus, and the area moment
a lies between a support and midspan. x lies strictly between the supports.
Read the deflection
The signs of P and M are the signs of their parts of δ.
Example calculations
Common configurations with formula and result.
Midspan
P = 48, M = 16, a = 1, x = 2, L = 4, E = 1, I = 1
Paired Point Loads plus Equal End Moments 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 two equal loads P, each at distance a from the nearer support, and equal sagging end moments M. Deflection at x is the sum of those curves.
- What it calculates
- Deflection at a stated station for two equal point loads plus equal end moments.
- Inputs
- P
- M
- a
- x
- L
- E
- I
- Outputs
- delta
- Formula
Sum of the paired-load curve and the equal-end-moment curve.- Assumptions
- Calculation runs locally in the browser; values are not uploaded.
- Keep units consistent with the labels on each field.
- x = L/2 adds the paired midspan page. x = a adds the under-load page.
- Units
- P, M, a, x, L, E, and I set the deflection unit.
- Boundary conditions
- missing P, 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/2, x ≤ 0, or x ≥ L → INVALID_INPUT
- Example
- P=48 M=16 a=1 x=2 L=4 E=1 I=1 → δ=120
- Validation cases
2 published on this page · 3/3 tests · Production surface contract 6/6 · View evidence
- P=48 M=16 a=1 x=2 L=4 E=1 I=1 → δ=120
- a=3 → INVALID_INPUT
- Sources
- Hibbeler, Mechanics of Materials — Deflection of beams — superpositionSupports: Two equal point loads and equal end moments superpose.
- Gere and Goodno, Mechanics of Materials — Deflection of beams — several loads and end momentsSupports: Supports adding the elastic curves of the point loads and the end moments.
- 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 two equal point loads plus equal sagging end moments.
Agent / API notes
Capability id: mechanical.statics.paired_end_moments_at_deflection · tool id: paired-end-moments-at · pin 1.0.0.
{ "P": 48, "M": 16, "a": 1, "x": 2, "L": 4, "E": 1, "I": 1 }
Related tools
Other calculators in this family: Angled Pull Calculator, Angled Pull on an Incline Calculator, Area Moment Calculator, Beam Deflection Calculator, Beam Moment Deflection Calculator, Beam Moment Maximum Deflection Calculator, Bending Stress Calculator, Cantilever Deflection Calculator . Explore all Statics & Strength.
Frequently asked questions
Key distinctions behind the calculation.
Does midspan match the paired midspan page?
Yes. x = L/2 gives δ = 88 + 32 = 120 for P = 48, M = 16, a = 1, and L = 4. Under either load, δ = 88.