Mechanical 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 · offset point-load max |δ| = P c (L²−c²)^{3/2}/(9√3 E I L); + O3 mpmath tabulated δ.

Input interpretation: Enter values to calculate.
Result: —
Verified scope: offset point-load max |δ| = P c (L²−c²)^{3/2}/(9√3 E I L); + O3 mpmath tabulated δ.
Assurance: Engineering
Declared partition coverage: PASS · 5/5 declared partitions (main, alias, signed, awkward, invalid-domain) · Matrix
Deferred: Not δ under the load, not midspan under the same load, and not a station curve.
Numerical scope: O2: delta vs a separate-module identity (≤2 ULP). Not δ under the load, not midspan under the same load, and not a station curve. ≤2 ULP vs O3 applies only to the published tabulated offset-load-maximum vectors.
Known limitations: 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 · offset point-load max |δ| = P c (L²−c²)^{3/2}/(9√3 E I L); + O3 mpmath tabulated δ.· View Manifest · CVP overview · Specification
Versions: Calculation 1.0.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-27.o2-o3
Verification revision: 2026-09-27.o2-o3 · 1/1 property · digest 8351127c0ffd
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 · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Interfaces: PASS · UI (SSR) / REST / MCP — ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 1/1 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only.
Supplemental domain review: Not performed
Named expert review: Not performed
CVP suite: 4/4 golden · 1/1 CVP boundary · 3/3 invalid · 1/1 property · 1/1 metamorphic · 8/8 O3 · 2/2 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 · 4/4 oracle-backed golden · 3/3 invalid · Artifact integrity PASS
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

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.

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.

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

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

Engine tested 3/3 tests · Production surface contract 6/6
Named expert review Not performed
Calculation version 1.0.0

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: Beam Deflection Calculator, Beam Moment Deflection Calculator, Beam Moment Maximum Deflection Calculator, Cantilever Deflection Calculator, Cantilever Intermediate Deflection Calculator, Cantilever Load at a Station Calculator, Cantilever Moment at the Couple Calculator, Cantilever Moment Deflection Calculator . Explore all Beams & Deflection.

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).