HomeCalculatorsPhysicsStatics & StrengthOverhang Arm at a Station Calculator
Physics calculator

Overhang Arm at a Station Calculator

Deflection at station z on the overhang, measured from the right support out to the load. z = a is the load page. 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 on the overhang.
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 c98e07088e2c
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 — overhanging beam
  • Gere and Goodno, Mechanics of Materials — Deflection of beams — beam with an overhang
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 z on the overhangδ = P a L z/(3 E I) + P z² (3a − z)/(6 E I)
iz = a recovers P a² (L + a)/(3 E I).

How to use

1

Enter the load, the overhang, the station, the span, the modulus, and the area moment

z is measured from the right support and may reach the load.

2

Read the deflection

The sign of P is the sign of δ.

Example calculations

Common configurations with formula and result.

ϟ

At the load

P = 48, a = 1, z = 1, L = 2, E = 1, I = 1

δ = P a L z/(3 E I) + P z² (3a − z)/(6 E I)
δ = 48

Overhang Arm at a Station calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
A beam of span L has an overhang a beyond the right support, with load P at the overhang end. At distance z from the right support, δ = P a L z/(3 E I) + P z² (3a − z)/(6 E I). z = a is the load page.
What it calculates
Deflection at a stated station on the overhang.
Inputs
  • P
  • a
  • z
  • L
  • E
  • I
Outputs
  • delta
Formula
Overhang arm curve. z = a is the load page.
Assumptions
  • Calculation runs locally in the browser; values are not uploaded.
  • Keep units consistent with the labels on each field.
  • z = a recovers P a² (L + a)/(3 E I).
Units
  • P, a, z, L, E, and I set the deflection unit.
Boundary conditions
  • missing P, a, z, L, E, or I → MISSING_REQUIRED_INPUT
  • L ≤ 0, a ≤ 0, E ≤ 0, or I ≤ 0 → VALUE_MUST_BE_POSITIVE
  • z ≤ 0 or z > a → INVALID_INPUT
Example
P=48 a=1 z=1 L=2 E=1 I=1 → δ=48
Validation cases

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

  • P=48 a=1 z=1 L=2 E=1 I=1 → δ=48
  • z=2 → INVALID_INPUT
Sources
  • Hibbeler, Mechanics of Materials — Deflection of beams — overhanging beam
    Supports: Deflection along the overhang is P a L z/(3 E I) + P z² (3a − z)/(6 E I).
  • Gere and Goodno, Mechanics of Materials — Deflection of beams — beam with an overhang
    Supports: Supports the elastic curve measured from the right support.
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Find the deflection at a stated station on the overhang, measured from the right support out to the load.

Agent / API notes

Capability id: mechanical.statics.overhang_arm_at_deflection · tool id: overhang-arm-at · pin 1.0.0.

{ "P": 48, "a": 1, "z": 1, "L": 2, "E": 1, "I": 1 }

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Frequently asked questions

Key distinctions behind the calculation.

Does the load station match the overhang page?

Yes. z = a gives δ = 48 for P = 48, a = 1, and L = 2.