HomeCalculatorsPhysicsStatics & StrengthOne-Sided Triangle plus Equal End Moments Calculator
Physics calculator

One-Sided Triangle plus Equal End Moments Calculator

Deflection at station x for a one-sided triangle plus equal sagging end moments. x = L/2 is the sum of the two midspan pages. Runs locally.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
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 one-sided triangle 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 e64ec9fd95d8
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 — ui-ssr is query-result HTML, not a live browser session.
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 — Deflection of beams — superposition
  • Gere and Goodno, Mechanics of Materials — Deflection of beams — distributed load and end moments
Sources
Evidence
1 legacy golden · 1 legacy boundary · legacy regression suite · 1/1 oracle-backed golden · 1/1 invalid · Artifact integrity 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
Semantic contract
PASS
Full verification

Manifest identity, reference classes, interfaces, suite, and production records.

Formulas

Core equations used by this calculator.

Deflection at xδ = δ_triangle(x) + δ_end moments(x)
ix = L/2 recovers 5 w0 L⁴/(768 E I) + M L²/(8 E I).

How to use

1

Enter the peak intensity, the moment, the station, the span, the modulus, and the area moment

x must lie strictly between the supports.

2

Read the deflection

The signs of w0 and M are the signs of their parts of δ.

Example calculations

Common configurations with formula and result.

ϟ

Midspan

w0 = 24, M = 16, x = 1, L = 2, E = 1, I = 1

δ = δ_triangle(x) + δ_end moments(x)
δ = 10.5

One-Sided Triangle plus Equal End Moments calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
A simply supported beam carries a triangle that is 0 at the left support and w0 at the right, plus 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 a one-sided triangle plus equal end moments.
Inputs
  • w0
  • M
  • x
  • L
  • E
  • I
Outputs
  • delta
Formula
Sum of the one-sided triangle 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 recovers 5 w0 L⁴/(768 E I) + M L²/(8 E I).
Units
  • w0, M, x, L, E, and I set the deflection unit.
Boundary conditions
  • missing w0, 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 M=16 x=1 L=2 E=1 I=1 → δ=10.5
Validation cases

2 published on this page · 2/2 tests · Production surface contract 6/6 · View evidence

  • w0=24 M=16 x=1 L=2 E=1 I=1 → δ=10.5
  • x=2 → INVALID_INPUT
Sources
  • Hibbeler, Mechanics of Materials — Deflection of beams — superposition
    Supports: A one-sided triangular load and equal end moments superpose.
  • Gere and Goodno, Mechanics of Materials — Deflection of beams — distributed load and end moments
    Supports: Supports adding the elastic curves of the two actions.
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Find the deflection at a stated station for a one-sided triangle plus equal sagging end moments.

Agent / API notes

Capability id: mechanical.statics.triangular_end_moments_at_deflection · tool id: triangular-end-moments-at · pin 1.0.0.

{ "w0": 24, "M": 16, "x": 1, "L": 2, "E": 1, "I": 1 }

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.

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Frequently asked questions

Key distinctions behind the calculation.

Does midspan match the two midspan pages?

Yes. x = L/2 gives δ = 2.5 + 8 = 10.5 for w0 = 24, M = 16, and L = 2.