HomeCalculatorsPhysicsStatics & StrengthCantilever Partial Load Calculator
Physics calculator

Cantilever Partial Load Calculator

Deflection where a uniform load that starts at the wall stops. δ = w a⁴ / (8 E I). 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 the end of a uniform load that starts at the fixed end of a cantilever.
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 13d507a009ae
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 — 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 — cantilever with a partial uniform load
  • Gere and Goodno, Mechanics of Materials — Deflection of beams — partial uniform load
Sources
Evidence
2 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 aδ = w a⁴ / (8 E I)
ia = L is the full uniform-load page. The free-end deflection is a different page.

How to use

1

Enter the intensity, the loaded length, the cantilever length, 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 deflection at the end of the load

The sign of w is the sign of δ.

Example calculations

Common configurations with formula and result.

ϟ

Load over the inner half

w = 24, a = 1, L = 2, E = 1, I = 1

δ = 24 × 1⁴ / 8
δ = 3
ϟ

Load over the whole length

w = 24, a = 2, L = 2, E = 1, I = 1

δ = w L⁴ / (8 E I)
δ = 48

Cantilever Partial Load calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
A cantilever of length L is fixed at one end. Uniform intensity w runs from the fixed end to distance a and is zero beyond a. The deflection at a is δ = w a⁴ / (8 E I).
What it calculates
Deflection at the end of a uniform load that starts at the fixed end of a cantilever.
Inputs
  • w
  • a
  • L
  • E
  • I
Outputs
  • delta
Formula
δ = w a⁴ / (8 E I).
Assumptions
  • Calculation runs locally in the browser; values are not uploaded.
  • Keep units consistent with the labels on each field.
  • a = L is the full uniform-load page. The free-end deflection is a different page.
Units
  • w, a, L, E, and I set the deflection unit.
Boundary conditions
  • missing w, a, L, E, or I → MISSING_REQUIRED_INPUT
  • L ≤ 0, E ≤ 0, or I ≤ 0 → VALUE_MUST_BE_POSITIVE
  • a ≤ 0 or a > L → INVALID_INPUT
Example
w=24 a=1 L=2 E=1 I=1 → δ=3
Validation cases

3 published on this page · 3/3 tests · Production surface contract 6/6 · View evidence

  • w=24 a=1 L=2 E=1 I=1 → δ=3
  • w=24 a=2 L=2 E=1 I=1 → δ=48
  • a=3 L=2 → INVALID_INPUT
Sources
  • Hibbeler, Mechanics of Materials — Deflection of beams — cantilever with a partial uniform load
    Supports: The deflection at the end of a load that starts at the wall is w a⁴ / (8 E I).
  • Gere and Goodno, Mechanics of Materials — Deflection of beams — partial uniform load
    Supports: Supports the page formula. a = L recovers w L⁴ / (8 E I).
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Find the deflection where a partial uniform load ends on a cantilever. The load starts at the fixed end.

Supported and not supported

Supported: δ = w a⁴ / (8 E I). a = L is the full uniform-load page.

Not supported: the free-end value when a is shorter than L, and a load that starts away from the wall. /calc/mechanical is not open.

Agent / API notes

Capability id: mechanical.statics.cantilever_partial_deflection · tool id: cantilever-partial-deflection · pin 1.0.0.

{ "w": 24, "a": 1, "L": 2, "E": 1, "I": 1 }

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Frequently asked questions

Key distinctions behind the calculation.

Is this the free-end deflection?

Only when a = L. Otherwise the free end moves farther, and that value is a different page.