STRUCTURES · CANTILEVER DEFLECTION

How much will it bend?

Explore an end-loaded rectangular beam with a fixed support. Inputs, equations, scenario checks and the deformation drawing stay connected.

A FEW LINES OF ENGINEERING

The model, written down.

Dimensions, equations, and a limit.
One readable .napkin file.

cantilever.napkin / editable

Current, unloadedDeflected ×30

XZ / DEFLECTION EXAGGERATED ×30FIXED END ALIGNED

Cantilever selected · related inputs are marked.

tip deflection0.72 mm✓ passes

BASELINE INPUTS

load20 Nmodulus69 GPa

CALCULATED

inertia3600 mm^4

deflection0.72464 mm

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Aluminium cantilever · fixed at one end
length = 300 mm in 100..500
width = 25 mm
depth = 12 mm in 6..30
load = 20 N
modulus = 69 GPa "Illustrative aluminium stiffness"

part beam "Cantilever": box length, width, depth

inertia := width * depth^3 / 12 [mm^4]
deflection := load * length^3 / (3 * modulus * inertia) [mm]
deflectionAt(x: mm) := deflection * (x/length)^2 * (3 - x/length) / 2 [mm]
check tip deflection: deflection <= 2 mm

scenario more reach: length = 500 mm
scenario deeper section: length = 500 mm, depth = 20 mm

Calculated from your source · not saved

Baseline · 300 mm reach · 12 mm depth

tip deflection0.72 mm ✓ passes

more reach · 500 mm reach · 12 mm depth

tip deflection3.35 mm × fails

deeper section · 500 mm reach · 20 mm depth

tip deflection0.72 mm ✓ passes

Edit a number, equation, or check. Results update automatically. Fixed support, end load, small deflections; shear and self-weight omitted.

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What this calculator shows

The source calculates section inertia and tip deflection. The authored deflectionAt function supplies the displacement along the beam. XZ and ISO views show the unloaded outline, deformed shape, load and displacement arrows; scenario views also compare baseline geometry.

Displacement may be exaggerated to make the change visible. The labelled numerical results remain the calculated values. This example assumes small deflections and omits shear and self-weight.

Explore the model

Use Model to change inputs or choose a scenario. Use Source to inspect the equations, change a check, or add a scenario. The anonymous browser example is temporary; use the plugin to save a Study.

Follow the source-editing guide ↗