Beam Natural Frequency Calculator
First three bending natural frequencies of a simply supported beam.
INPUTS
m
GPa
×10⁶ mm⁴
kg/m
RESULTS
1st mode f₁ = (π/2L²)√(EI/m̄)
23.03 Hz
2nd mode f₂ = 4·f₁
92.13 Hz
3rd mode f₃ = 9·f₁
207.3 Hz
Period T₁ = 1/f₁
0.043 s
Footfall check
✓ f₁ ≥ 4 Hz — above typical walking excitation
How it works
Every beam has natural frequencies at which it resonates: fn = (n²π/2L²)√(EI/m̄) for simple supports. Frequency falls with the SQUARE of span — doubling the span quarters f₁ — which is why long lightweight floors and footbridges become 'lively'. The London Millennium Bridge famously resonated with pedestrians until dampers were added. Designers keep floor f₁ above about 4 Hz or add mass/damping.
Worked example
IPE 300 (I = 83.6×10⁶ mm⁴) spanning 6 m with total mass 60 kg/m: EI = 16.72×10⁶ N·m², f₁ = (π/72)·√(16.72e6/60) = 23 Hz — far above footfall frequencies, so no vibration issue.
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