HomeCalculatorsPhysicsStatics & StrengthOffset Load Maximum Calculator
Physics calculator

Offset Load Maximum Calculator

Largest deflection of a simply supported span with an offset point load. δ = P c (L² − c²)^(3/2) / (9 √3 E I L). 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
Largest deflection of a simply supported span with one offset concentrated load.
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 f17ad1012ccc
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 — concentrated load at an intermediate point
  • Gere and Goodno, Mechanics of Materials — Deflection of beams — simply supported beam with an intermediate 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.

Largest deflectionδ = P c (L² − c²)^(3/2) / (9 √3 E I L)
Shorter segmentc = min(a, L − a)
ix is measured from the left support. a = L/2 recovers the midspan point-load page. The value under the load is a different page.

How to use

1

Enter the load, its position, the span, the modulus, and the area moment

L, E, and I must be positive. a must lie strictly between the supports.

2

Read the largest deflection and its position

The peak sits in the longer segment, not under the load, unless the load is at midspan.

Example calculations

Common configurations with formula and result.

ϟ

Load at one quarter of a span of 4

P = 48, a = 1, L = 4, E = 1, I = 1

δ = 20 √5
δ = 44.7214 at x = 4 − √5
ϟ

Same load at midspan

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

δ = P L³ / (48 E I)
δ = 8 at x = 1

Offset Load Maximum calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
A simply supported span of length L carries one concentrated load P at distance a from the left support. b = L − a. c is the shorter of a and b. The largest deflection is δ = P c (L² − c²)^(3/2) / (9 √3 E I L), in the longer segment.
What it calculates
Largest deflection of a simply supported span with one offset concentrated load.
Inputs
  • P
  • a
  • L
  • E
  • I
Outputs
  • delta
  • x
  • b
  • c
Formula
δ = P c (L² − c²)^(3/2) / (9 √3 E I L).
Assumptions
  • Calculation runs locally in the browser; values are not uploaded.
  • Keep units consistent with the labels on each field.
  • x is measured from the left support. a = L/2 recovers the midspan point-load page. The value under the load is a different page.
Units
  • P, a, L, E, and I set the deflection unit.
Boundary conditions
  • missing P, 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
P=48 a=1 L=4 E=1 I=1 → δ=20√5
Validation cases

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

  • P=48 a=1 L=4 E=1 I=1 → δ=20√5
  • P=48 a=1 L=2 E=1 I=1 → δ=8
  • a=0 → INVALID_INPUT
Sources
  • Hibbeler, Mechanics of Materials — Deflection of beams — concentrated load at an intermediate point
    Supports: The largest deflection is in the longer segment, δ = P c (L² − c²)^(3/2) / (9 √3 E I L).
  • Gere and Goodno, Mechanics of Materials — Deflection of beams — simply supported beam with an intermediate load
    Supports: Supports the page formula for the largest deflection when the load is not at midspan.
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Find the largest deflection of a simply supported span when one concentrated load is not at midspan.

Supported and not supported

Supported: δ = P c (L² − c²)^(3/2) / (9 √3 E I L). x is the position from the left support. a = L/2 recovers δ = P L³/(48 E I).

Not supported: the value directly under the load, a cantilever, a uniform load, and an end moment. /calc/mechanical is not open.

Agent / API notes

Capability id: mechanical.statics.offset_load_max_deflection · tool id: offset-load-maximum · pin 1.0.0.

{ "P": 48, "a": 1, "L": 4, "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.

→ Angled Pull Calculator Pull at an angle above the horizontal that puts a block on a level surface at impending slip. The normal is W − P sinα. Runs locally. › → Angled Pull on an Incline Calculator The pull at an angle above the horizontal that puts a block on an incline at impending slip. α = 0 is horizontal. α = θ is parallel to the plane. Runs locally. › → Area Moment Calculator Second moment of composite plane areas about the composite centroid. Supply each part's centroidal Ix and Iy. Runs locally. Not a section modulus and not a beam calculator. › → Beam Deflection Calculator Midspan deflection of a simply supported span with one concentrated load. δ = P L³/(48 E I). I is an input. Runs locally. › → Beam Moment Deflection Calculator Midspan deflection of a simply supported span with one end moment. δ = M L²/(16 E I). I is an input. Runs locally. › → Beam Moment Maximum Deflection Calculator Largest deflection of a simply supported span with one end moment. δ = M L²/(9√3 E I) at x = L/√3. I is an input. Runs locally. › → Bending Stress Calculator Elastic bending stress from a moment and a section modulus. S can also be formed from Ix and c. Runs locally. › → Cantilever Deflection Calculator Free-end deflection of a cantilever with one concentrated load at the tip. δ = P L³/(3 E I). I is an input. Runs locally. ›

Frequently asked questions

Key distinctions behind the calculation.

Is this the deflection under the load?

No. That value is P a² b² / (3 E I L). This page is the largest deflection, farther toward midspan when the load is offset.

Where is x measured from?

From the left support. When a is at least L/2, x = √((L² − b²)/3). Otherwise x = L − √((L² − a²)/3).