Physics calculator

Overhang Span, Uniform, Triangular Load, Offset Point Load, and Paired Point Loads Calculator

Deflection at a stated station on an overhanging beam: overhang tip P, uniform w, triangular w0, offset Po at ao, and paired Pp at ap. Superposition of the listed elastic curves on the span. 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_uniform + δ_tri + δ_offset + δ_paired

iThe check station recovers −12 + 5 + 2.5 + 5.5 + 11.

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; other length symbols are span stations.

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, Pp = 48, w = 24, w0 = 24, a = 1, ao = 0.5, ap = 0.5, x = 1, L = 2, E = 1, I = 1

δ = δ_overhang + δ_uniform + δ_tri + δ_offset + δ_paired

δ = 12

Overhang Span, Uniform, Triangular Load, Offset Point Load, and Paired Point Loads 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 uniform load w on the span, a triangular load of peak w0 on the span, an offset span point load Po at ao from the left support (ao is not the overhang a), and a symmetric paired point load Pp at distance ap from each support (ap is not a and not ao). 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
Pp
w
w0
a
ao
ap
x
L
E
I
Outputs: delta
Formula: δ = δ_overhang + δ_uniform + δ_tri + δ_offset + δ_paired. 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 + 5 + 2.5 + 5.5 + 11.
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, Pp = 48, w = 24, w0 = 24, a = 1, ao = 0.5, ap = 0.5, x = 1, L = 2, E = 1, I = 1 → δ=12
Validation cases: 2 published on this page
P = 48, Po = 48, Pp = 48, w = 24, w0 = 24, a = 1, ao = 0.5, ap = 0.5, x = 1, L = 2, E = 1, I = 1 → δ=12
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 P, uniform w, triangular w0, offset Po at ao, and paired Pp at ap.

The overhang length is a. The check midspan recovers −12 + 5 + 2.5 + 5.5 + 11.

Agent / API notes

Capability id: mechanical.statics.overhang_span_uniform_triangular_offset_paired_at_deflection · tool id: overhang-span-uniform-triangular-offset-paired-at · pin 1.0.0.

{
  "P": 48,
  "Po": 48,
  "Pp": 48,
  "w": 24,
  "w0": 24,
  "a": 1,
  "ao": 0.5,
  "ap": 0.5,
  "x": 1,
  "L": 2,
  "E": 1,
  "I": 1
}

Other calculators in this family: Overhang span, uniform, triangular, and offset .

Frequently asked questions

Key distinctions behind the calculation.

What does the check midspan mean?

With E = I = 1 and the listed check loads, midspan recovers the sum of the component midspan values. It gives δ = −12 + 5 + 2.5 + 5.5 + 11 = 12.

Are a, ao, and ap the same?

No. a is the overhang beyond the right support. ao is the offset load distance from the left support. ap is the distance of each paired load from the nearer support.