Physics calculator

One-Sided Triangle, Uniform, Midspan Point Load, and One End Moment Calculator

Deflection at a stated station for a one-sided triangle, a uniform load, a midspan point load, and one end moment. The check station is the sum of two already-landed pages. Runs locally.

Instant result

Result

—

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 a one-sided triangle, a uniform load, a midspan point load, and one end moment.
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_load(x) + δ_moments(x)

iThe check station recovers 15.5 + 4.

How to use

1

Enter the loads, the moment, the station, the length, the modulus, and the area moment

x must lie on the beam.

2

Read the deflection

The signs of the loads are the signs of their parts of δ.

Example calculations

Common configurations with formula and result.

ϟ

Check station

w0 = 24, w = 24, P = 48, M = 16, x = 1, L = 2, E = 1, I = 1

δ = δ_load(x) + δ_moments(x)

δ = 19.5

One-Sided Triangle, Uniform, Midspan Point Load, and One End Moment 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

Definition: The beam carries a one-sided triangle, a uniform load, a midspan point load, and one end moment. Deflection at x is the sum of those elastic curves.
What it calculates: Deflection at a stated station for a one-sided triangle, a uniform load, a midspan point load, and one end moment.
Inputs: w0
w
P
M
x
L
E
I
Outputs: delta
Formula: Sum of the load curve and the moment curve.
Assumptions: Calculation runs locally in the browser; values are not uploaded.
Keep units consistent with the labels on each field.
The check station recovers 15.5 + 4.
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 out of range → INVALID_INPUT
Example: w0 = 24, w = 24, P = 48, M = 16, x = 1, L = 2, E = 1, I = 1 → δ=19.5
Validation cases: 2 published on this page
w0 = 24, w = 24, P = 48, M = 16, x = 1, L = 2, E = 1, I = 1 → δ=19.5
x=0 → INVALID_INPUT
Sources: Hibbeler, Mechanics of Materials — Deflection of beams — superposition
Supports: The listed actions superpose.
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.

Agent / API notes

Capability id: mechanical.statics.triangular_uniform_point_moment_at_deflection · tool id: triangular-uniform-point-moment-at · pin 1.0.0.

{
  "w0": 24,
  "w": 24,
  "P": 48,
  "M": 16,
  "x": 1,
  "L": 2,
  "E": 1,
  "I": 1
}

Other calculators in this family: Component curve .

Frequently asked questions

Key distinctions behind the calculation.

Does the check station match the landed pages?

Yes. It gives δ = 15.5 + 4 = 19.5.