Physics calculator

Overhang Span, Triangular Load, Offset Point Load, and Equal End Moments Calculator

Deflection at a stated station on an overhanging beam: overhang tip P, triangular, offset Po at ao, and end moment(s). Check station sums landed pages. Runs locally.

Instant result

Result

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Enter values to calculate.

Inputs—

Mode—

Formula—

Trust summary Engine tested · Source checked · v1.0.0

Input interpretation: Enter values to calculate.
Result: —
Model: Deflection at a stated station for this overhang-span superposition.
Scope: Calculation runs locally in the browser; values are not uploaded.
Verification: Engine tested · Source checked · v1.0.0
Named expert review: Optional · Not performed
Sources: Hibbeler, Mechanics of Materials — Deflection of beams — superposition
Gere and Goodno, Mechanics of Materials — Deflection of beams — superposition
Sources

Formulas

Core equations used by this calculator.

Deflection at xδ = δ_overhang + δ_tri + δ_offset + δ_MM

iThe check station recovers −12 + 2.5 + 5.5 + 2.

How to use

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

x must lie strictly between the supports. a is the overhang; ao is the offset load position.

Read the deflection

A downward overhang load lifts the span; span loads and sagging moments keep their usual signs.

Example calculations

Common configurations with formula and result.

Check station

P = 48, Po = 48, w0 = 24, M = 4, a = 1, ao = 0.5, x = 1, L = 2, E = 1, I = 1

δ = δ_overhang + δ_tri + δ_offset + δ_MM

δ = −2

Overhang Span, Triangular Load, Offset Point Load, and Equal End Moments calculator specification

Version 1.0.0 · Engine tested

Calculation status

Engine tested 2 published cases
Named expert review Not performed
Calculation version 1.0.0

Review policy

Definition: A beam of span L has an overhang a beyond the right support, with load P at the overhang end, a triangular load of peak w0 on the span, an offset point load Po at station ao from the left support (ao is not the overhang a), and equal sagging end moments M on the span. Deflection at station x on the span is the sum of those elastic curves.
What it calculates: Deflection at a stated station for this overhang-span superposition.
Inputs: P
Po
w0
M
a
ao
x
L
E
I
Outputs: delta
Formula: δ = δ_overhang + δ_tri + δ_offset + δ_MM. x = L/2 recovers the listed midspan pages.
Assumptions: Calculation runs locally in the browser; values are not uploaded.
Keep units consistent with the labels on each field.
The check station recovers −12 + 2.5 + 5.5 + 2.
Units: The inputs set the deflection unit.
Boundary conditions: a required input missing → MISSING_REQUIRED_INPUT
L ≤ 0, E ≤ 0, or I ≤ 0 → VALUE_MUST_BE_POSITIVE
x ≤ 0 or x ≥ L → INVALID_INPUT
Example: P = 48, Po = 48, w0 = 24, M = 4, a = 1, ao = 0.5, x = 1, L = 2, E = 1, I = 1 → δ=−2
Validation cases: 2 published on this page
P = 48, Po = 48, w0 = 24, M = 4, a = 1, ao = 0.5, x = 1, L = 2, E = 1, I = 1 → δ=−2
x out of range → INVALID_INPUT
Sources: Hibbeler, Mechanics of Materials — Deflection of beams — superposition
Supports: The listed actions superpose on the span.
Gere and Goodno, Mechanics of Materials — Deflection of beams — superposition
Supports: Supports adding the elastic curves.
Calculation version: 1.0.0

Background

Interpretation and common distinctions.

Find the deflection at a stated station for this superposition: overhang tip load P, triangular on the span, offset Po at ao, and equal end moments M.

The overhang length is a. The offset position is ao (not a). The check midspan recovers −12 + 2.5 + 5.5 + 2.

Agent / API notes

Capability id: mechanical.statics.overhang_span_triangular_offset_end_moments_at_deflection · tool id: overhang-span-triangular-offset-end-moments-at · pin 1.0.0.

{
  "P": 48,
  "Po": 48,
  "w0": 24,
  "M": 4,
  "a": 1,
  "ao": 0.5,
  "x": 1,
  "L": 2,
  "E": 1,
  "I": 1
}

Other calculators in this family: Overhang span triangular offset .

Frequently asked questions

Key distinctions behind the calculation.

Does the check station match the landed pages?

Yes. It gives δ = −12 + 2.5 + 5.5 + 2 = −2.

Is ao the same as the overhang a?

No. a is the overhang beyond the right support. ao is the span station of Po from the left support.