Square Tube Deflection Calculator

Inputs

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Support condition and load: simply supported with a central point load, or a cantilever with the load at the free end.
Outside width of the tube — the dimension along the bending axis.
mm
Outside height (depth) of the tube — the dimension that resists bending. Orient the larger dimension vertically.
mm
Wall thickness. Must be less than half of both b and h.
mm
Span between supports (simply supported) or the cantilever length from the fixed end.
mm
Applied point load — at mid-span (simply supported) or at the free end (cantilever).
N
Elastic modulus of the material — steel ≈ 200 GPa, aluminum ≈ 69 GPa.
GPa
Serviceability target as span divided by n. Common checks use L/360, L/240, L/180 or stiffer shop targets.
Allowable bending stress after your material strength and safety-factor choice. Example: 250 MPa yield / 1.67 ≈ 150 MPa.
MPa

Results

Default result
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Max deflection(δ)
0.9992mm

δ = F·L³ / (48·E·I)

Maximum elastic deflection at the load point.

Also computed

Allowable deflection(δ_allow)2.778mm

Limit uses L/360.

Entered L/n serviceability target.

Deflection utilization(U_δ)Pass35.97%

Deflection is within the L/360 target.

Actual deflection ratio(L/δ)1,001

Actual ratio based on span L.

Max bending stress(σ)59.95MPa

M = F·L/4

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

Stress utilization(U_σ)Pass39.97%

Stress is within the entered allowable stress.

Second moment of area(I)20.85cm⁴

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

Method notes 5 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.
  • Deflection utilization compares the elastic deflection against L/360; stress utilization compares σ against the entered allowable stress.
  • 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.

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