Physics calculator
Center-Peaked Triangle, Uniform Load, and One End Moment Calculator
Deflection at a stated station for a center-peaked triangle, a uniform load, and one end moment. The check station is the sum of two already-landed pages. 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 a center-peaked triangle, a uniform load, and one end moment.
- 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 16333554c016
- 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
STALE · Build schema 1.0.0 ready · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · CVP STALE · attestation STALE — Production CURRENT withheld
Full verification
Formulas
Core equations used by this calculator.
iThe check station recovers 8.2 + 4.
How to use
Enter the triangle intensity, the uniform intensity, the end moment, the station, the length, the modulus, and the area moment
x must lie strictly between the supports and is measured from the unloaded end.
Read the deflection
The signs of w0, w, and M are the signs of their parts of δ.
Example calculations
Common configurations with formula and result.
ϟ
δ = δ_distributed(x) + δ_moment(x)Check station
w0 = 24, w = 24, M = 16, x = 1, L = 2, E = 1, I = 1
δ = 12.2
Center-Peaked Triangle, Uniform Load, and One End Moment calculator specification
Version 1.0.0 · Engine tested
Calculation status
- Engine tested 2/2 tests · Production surface contract 6/6
- Named expert review Not performed
- Calculation version 1.0.0
- Definition
- The beam carries a center-peaked triangle, a uniform load, and one end moment. Deflection at x is the sum of those elastic curves.
- What it calculates
- Deflection at a stated station for a center-peaked triangle, a uniform load, and one end moment.
- Inputs
- w0
- w
- M
- x
- L
- E
- I
- Outputs
- delta
- Formula
Sum of the uniform-triangle curve and the one-end-moment curve.- Assumptions
- Calculation runs locally in the browser; values are not uploaded.
- Keep units consistent with the labels on each field.
- The check station recovers 8.2 + 4.
- Units
- w0, w, M, x, L, E, and I set the deflection unit.
- Boundary conditions
- missing w0, w, M, x, L, E, or I → MISSING_REQUIRED_INPUT
- L ≤ 0, E ≤ 0, or I ≤ 0 → VALUE_MUST_BE_POSITIVE
- x ≤ 0 or x ≥ L → INVALID_INPUT
- Example
- w0=24 w=24 M=16 x=1 L=2 E=1 I=1 → δ=12.2
- Validation cases
2 published on this page · 2/2 tests · Production surface contract 6/6 · View evidence
- w0=24 w=24 M=16 x=1 L=2 E=1 I=1 → δ=12.2
- x=0 → INVALID_INPUT
- Sources
- Hibbeler, Mechanics of Materials — Deflection of beams — superpositionSupports: A triangular load, a uniform load, and an end moment superpose.
- Gere and Goodno, Mechanics of Materials — Deflection of beams — superpositionSupports: Supports adding the elastic curves of the three 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 a center-peaked triangle, a uniform load, and one end moment.
Agent / API notes
Capability id: mechanical.statics.center_uniform_moment_at_deflection · tool id: center-uniform-moment-at · pin 1.0.0.
{ "w0": 24, "w": 24, "M": 16, "x": 1, "L": 2, "E": 1, "I": 1 }
Related tools
Other calculators in this family: Component curve .
Frequently asked questions
Key distinctions behind the calculation.
Does the check station match the landed pages?
Yes. It gives δ = 8.2 + 4 = 12.2.