Offset Point Load plus Equal End Moments Calculator
Deflection at station x for an offset point load plus equal sagging end moments. 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 an offset point load 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 0855deb5fdb2
- 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 point load, the moment, the load 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 P and M are the signs of their parts of δ.
Example calculations
Common configurations with formula and result.
Under the point load
P = 48, M = 16, a = 1, x = 1, L = 4, E = 1, I = 1
Offset Point Load 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 a point load P at distance a from the left support and equal sagging end moments M. Deflection at x is the sum of those two elastic curves.
- What it calculates
- Deflection at a stated station for an offset point load plus equal end moments.
- Inputs
- P
- M
- a
- x
- L
- E
- I
- Outputs
- delta
- Formula
Sum of the offset-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 = a adds the under-load page. x = L/2 adds the offset midspan 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, x ≤ 0, or x ≥ L → INVALID_INPUT
- Example
- P=48 M=16 a=1 x=1 L=4 E=1 I=1 → δ=60
- Validation cases
2 published on this page · 3/3 tests · Production surface contract 6/6 · View evidence
- P=48 M=16 a=1 x=1 L=4 E=1 I=1 → δ=60
- x=4 → INVALID_INPUT
- Sources
- Hibbeler, Mechanics of Materials — Deflection of beams — superpositionSupports: An offset point load and equal end moments superpose.
- Gere and Goodno, Mechanics of Materials — Deflection of beams — beam with a concentrated load and end momentsSupports: Supports adding the elastic curves of the two actions.
- 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 an offset point load plus equal sagging end moments.
Agent / API notes
Capability id: mechanical.statics.offset_end_moments_at_deflection · tool id: offset-end-moments-at · pin 1.0.0.
{ "P": 48, "M": 16, "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 = 36 + 24 = 60 for P = 48, M = 16, a = 1, and L = 4. Midspan is δ = 76.