HomeCalculatorsPhysicsStatics & StrengthOffset Load Deflection Calculator
Physics calculator

Offset Load Deflection Calculator

Deflection under a concentrated load that is not at midspan. δ = P a² b² / (3 E I L). I is an input. 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 under one concentrated load on a simply supported span, at a stated distance from the left support.
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 ac2a96a937bb
Legacy regression
4/4 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 · 2/2 CVP boundary · 2/2 invalid · 1/1 cross-interface · 6/6 CVP contract · Manifest
Sources
  • Hibbeler, Mechanics of Materials — Deflection of beams — simply supported beam with a concentrated load at an intermediate point
  • Gere and Goodno, Mechanics of Materials — Deflection of beams — simply supported beam with a concentrated load at an intermediate point
Sources
Evidence
2 legacy golden · 2 legacy boundary · legacy regression suite · 1/1 oracle-backed golden · 2/2 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 under the loadδ = P a² b² / (3 E I L)
Right-hand segmentb = L − a
iI comes from a section page. a = L/2 recovers the midspan point-load page. The largest deflection, when the load is not at midspan, is not under the load and is not this 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. P may be negative. Positive P is the positive deflection direction. P, a, L, E, and I share one unit system, and δ then has the unit of L.

2

Read the deflection under the load

δ = P a² b² / (3 E I L), with b = L − a. The sign of P is the sign of δ.

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, in one consistent unit system

δ = 48 × 1² × 3² / (3 × 1 × 1 × 4)
δ = 36
ϟ

Same load at midspan

P = 48, a = 1, L = 2, E = 1, I = 1 matches the beam-deflection page

δ = 48 × 1² × 1² / (3 × 1 × 1 × 2)
δ = 8

Offset Load Deflection 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. The other segment is b = L − a. The deflection under the load is δ = P a² b² / (3 E I L). E is the elastic modulus. I is the centroidal area moment, typed in.
What it calculates
Deflection under one concentrated load on a simply supported span, at a stated distance from the left support.
Inputs
  • P
  • a
  • L
  • E
  • I
Outputs
  • delta
  • b
  • P
  • a
  • L
  • E
  • I
Formula
δ = P a² b² / (3 E I L), b = L − a.
Assumptions
  • Calculation runs locally in the browser; values are not uploaded.
  • Keep units consistent with the labels on each field.
  • I comes from a section page. a = L/2 recovers the midspan point-load page. The largest deflection, when the load is not at midspan, is not under the load and is not this page.
Units
  • P, a, L, E, and I set the deflection unit. δ has the unit of length when those five are consistent.
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=36
Validation cases

3 published on this page · 4/4 tests · Production surface contract 6/6 · View evidence

  • P=48 a=1 L=4 E=1 I=1 → δ=36
  • P=48 a=1 L=2 E=1 I=1 → δ=8
  • a=0 → INVALID_INPUT
Sources
  • Hibbeler, Mechanics of Materials — Deflection of beams — simply supported beam with a concentrated load at an intermediate point
    Supports: The deflection under the load is P a² b² / (3 E I L) when b = L − a.
  • Gere and Goodno, Mechanics of Materials — Deflection of beams — simply supported beam with a concentrated load at an intermediate point
    Supports: Supports the page formula: δ = P a² b² / (3 E I L)
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Find the deflection under one concentrated load on a simply supported span. The load sits at distance a from the left support.

Supported and not supported

Supported: δ = P a² b² / (3 E I L), with b = L − a. Positive P is the positive deflection direction. Aliases are load, force, F, position, span, length, youngs, modulus, Ix, and inertia.

Not supported: a load at a support, the off-load maximum, a cantilever, a uniform load, an end moment, and rebuilding I from a section. /calc/mechanical is not open.

Agent / API notes

Capability id: mechanical.statics.offset_load_deflection · tool id: offset-load-deflection · pin 1.0.0.

{ "P": 48, "a": 1, "L": 4, "E": 1, "I": 1 }

Share the link with P, a, L, E, and I. The result is not written into the link.

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.

Where is the deflection reported?

Directly under the concentrated load. When the load is not at midspan, the largest deflection is farther toward the middle and is not this page.

Does this rebuild the area moment?

No. I is an input. A rectangle, a circle, and a hollow circle stay on their section pages.

What if the load is at midspan?

a = L/2 gives δ = P L³/(48 E I), the same number as the midspan point-load page.