Square Tube Deflection Calculator

Inputs

Load case

Support condition and load: simply supported with a central point load, or a cantilever with the load at the free end.

Outside width (b)

Outside width of the tube — the dimension along the bending axis.

Outside height (h)

Outside height (depth) of the tube — the dimension that resists bending. Orient the larger dimension vertically.

Wall thickness (t)

Wall thickness. Must be less than half of both b and h.

Span / length (L)

Span between supports (simply supported) or the cantilever length from the fixed end.

Load (F)

Applied point load — at mid-span (simply supported) or at the free end (cantilever).

Young's modulus (E)

Elastic modulus of the material — steel ≈ 200 GPa, aluminum ≈ 69 GPa.

GPa

Default result

Max deflection(δ)

0.9992mm

δ = F·L³ / (48·E·I)

Maximum elastic deflection at the load point.

Also computed

Max bending stress(σ)59.95MPa

M = F·L/4

σ = M·c / I at the extreme fibre (c = h/2).

Second moment of area(I)20.85cm⁴

I = (b·h³ − bᵢ·hᵢ³) / 12 about the bending axis.

Method notes 4 notes

Simply supported, central point load. Second moment of area I = (b·h³ − bᵢ·hᵢ³)/12 with bᵢ = b − 2t and hᵢ = h − 2t.
Simply supported with a central point load: δ = F·L³/(48·E·I), maximum moment M = F·L/4 at mid-span.
Max bending stress σ = M·c / I with c = h/2 (distance to the extreme fibre). Bending is about the axis parallel to width b — the depth h resists bending, so orient the larger dimension vertically.
Euler–Bernoulli elastic beam theory — small deflections, material below yield, self-weight ignored. Add the beam self-weight as a distributed load for long, lightly loaded spans.