How can a beam pass every deflection check and still feel wrong?

Because deflection limits are about appearance and about what the finishes will tolerate, and they are checked under a load that is rarely present. Comfort is about frequency and acceleration under the load that is always present. A shallow beam with a long span can sit comfortably inside L/360 under design live load and still drop to five or six Hz under its everyday mass, which is where a normal walking pace can drive it.

What are the walking pace figures in the breakdown telling me?

Walking is periodic, so it excites a floor at its step rate and at whole multiples of it. People walk at roughly 100 to 130 steps a minute. If the pace matching your floor's second or third harmonic lands inside that band, ordinary walking can drive it into resonance; if both figures fall well outside, no one walking normally will find the resonance.

Why does damping only appear in one line?

Because damping does not change the frequency — it changes how big the response gets once resonance is reached, which is the amplification figure. It is deliberately kept separate so nothing implies that adding damping fixes a floor tuned to a walking harmonic. It reduces the symptom; it does not move the frequency.

Is this the AISC Design Guide 11 check?

It is the frequency half of it. The full check compares a predicted peak acceleration against a comfort limit, and that calculation needs the effective weight of the vibrating floor panel, which comes from the guide's joist-and-girder procedure rather than from one beam's properties. This page gives you the frequency and tells you which regime you are in; it does not pretend to be the acceptance test.

Materials & Quantities

Floor Beam Vibration Natural Frequency Calculator

A floor beam's natural frequency and the walking paces that can resonate it, since a beam can meet every deflection ratio and still feel lively underfoot.

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Imperial · sales tax

Beam Span

The clear span between supports, centre to centre of bearing.

Span dominates this calculation more than anything else, because it enters to the fourth power under a square root — frequency falls with the square of the span. Doubling a span at constant section and load quarters the frequency.

Second Moment of Area I (×10⁶ mm⁴)

The section's second moment of area about the bending axis, from its published properties.

Take it from the section tables for the exact serial size. Working from a US table quoted as I in in⁴? Multiply by 0.4162 to get ×10⁶ mm⁴ — a W16x31 at 375 in⁴ is 156 in these units. Where the beam acts compositely with a slab, use the composite value, which can be two or three times the bare section.

Modulus of Elasticity E

The stiffness of the beam material.

Structural steel is 200,000 MPa (29,000,000 psi) and that is the default here. Glulam runs around 11,000 MPa (1,600,000 psi), and normal-weight concrete rather less. For vibration, use the dynamic modulus where one is published — it is typically a little higher than the static value.

Supported Mass per Unit Length

The mass this beam carries along its length, including its own, at the loading present in service.

Vibration is assessed under the load actually there day to day, not the factored design load — the permanent load plus a small allowance for occupancy, often taken as a fraction of the design live load. Loading a floor up for a code check makes it look better than it feels.

Damping Ratio (% of critical)

How quickly the floor's motion dies away, as a percentage of critical damping.

This is an assessment, not a measurement. A bare structure with nothing on it sits near 1 to 2 per cent; an office with ceilings, ductwork and full-height partitions reaches 3 to 5. Partitions are the single biggest contributor, which is why an open plan fit-out can make an acceptable floor unacceptable.

Fundamental natural frequency

5.94 Hz

Medium confidence

This is a low-frequency floor, so a walking harmonic can resonate it and the response is governed by that resonance. Frequency alone does not settle whether it is acceptable — the full Design Guide 11 acceleration check, which needs the effective panel weight, does.

Static deflection under the supported mass: 0.35 in
Dynamic amplification at resonance: 16.67 (× static)
Walking pace whose second harmonic matches this floor: 178.23 steps/min
Walking pace whose third harmonic matches this floor: 118.82 steps/min

Then change the inputs to see how far the answer moves.

Show calculation logic

How this was calculated

Formula source(s)

Fundamental frequency of a uniform simply supported beam, f₁ = (π/2)·√(E·I / (m·L⁴)), with m the supported mass per unit length — the classical closed form, and the same relationship AISC Design Guide 11 expresses as f = 0.18·√(g/Δ) through the static deflection
AISC Design Guide 11, Vibrations of Steel-Framed Structural Systems Due to Human Activity — floors below about 3 Hz can be resonated by the first harmonic of walking, and floors above roughly 9 to 10 Hz respond impulsively rather than resonantly, which is why the two thresholds appear in the note under the result
Dynamic amplification at resonance = 1 / (2ζ) for a single-degree-of-freedom system, which is where the damping ratio enters. Damping ratios for floors are assessed, not measured — a bare structure is nearer 1–2%, a fitted-out office with partitions nearer 3–5%
This page reports FREQUENCY, not the Design Guide 11 acceleration ratio. That check needs the effective weight of the vibrating panel, which comes from the guide's own joist-and-girder panel procedure and cannot be derived from a single beam's properties

Inputs used

Beam Span: 30 ft
Second Moment of Area I (×10⁶ mm⁴): 300
Modulus of Elasticity E: 29007547.55 psi
Supported Mass per Unit Length: 403.18 lb/ft
Damping Ratio (% of critical): 3

Intermediate steps

Static deflection under the supported mass: 0.35 in
Dynamic amplification at resonance: 16.67 (× static)
Walking pace whose second harmonic matches this floor: 178.23 steps/min
Walking pace whose third harmonic matches this floor: 118.82 steps/min

Final result5.94 Hz

Confidence note: This is a low-frequency floor, so a walking harmonic can resonate it and the response is governed by that resonance. Frequency alone does not settle whether it is acceptable — the full Design Guide 11 acceleration check, which needs the effective panel weight, does.

What this calculation does not cover

A single simply supported beam. A real floor vibrates as a panel of joists on girders, and the panel frequency is lower than any of its parts — Design Guide 11's combined-mode procedure exists for exactly that reason.
Continuity, fixity and adjacent bays are not modelled. A continuous beam over several supports is stiffer and its frequency higher than this.
Says nothing about acceleration, which is what people actually feel. Two floors at the same frequency can be worlds apart in comfort depending on effective panel weight and damping.

Add the equipment this sizes

This result is a specification — 5.94 Hz — not a quantity. Put the thing it sizes into your project: how many, what you call it, and your supplier’s price.

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Schematic, drawn to the proportions you entered — not to scale on screen.

Computed in your browser — nothing you enter is uploaded. Presented in US customary units and US trade terminology. Where a formula follows a published standard, that standard and its edition are cited beside it on this page; where none governs, the page says so. Local amendments override model codes — verify against the code in force where you build.

Sources checked 2026-08-30 · in the site-wide review of 2026-09-06 · v1.0.0

Regulatory standards & verification citations4

Fundamental frequency of a uniform simply supported beam, f₁ = (π/2)·√(E·I / (m·L⁴)), with m the supported mass per unit length — the classical closed form, and the same relationship AISC Design Guide 11 expresses as f = 0.18·√(g/Δ) through the static deflection
AISC Design Guide 11, Vibrations of Steel-Framed Structural Systems Due to Human Activity — floors below about 3 Hz can be resonated by the first harmonic of walking, and floors above roughly 9 to 10 Hz respond impulsively rather than resonantly, which is why the two thresholds appear in the note under the result
Dynamic amplification at resonance = 1 / (2ζ) for a single-degree-of-freedom system, which is where the damping ratio enters. Damping ratios for floors are assessed, not measured — a bare structure is nearer 1–2%, a fitted-out office with partitions nearer 3–5%
This page reports FREQUENCY, not the Design Guide 11 acceleration ratio. That check needs the effective weight of the vibrating panel, which comes from the guide's own joist-and-girder panel procedure and cannot be derived from a single beam's properties

Cite this page

Your workspace

Most jobs need more than one number. Add the calculators you need next and they open right here, underneath this one — your figures stay on screen and nothing is lost to a page change.

Now that you have the number

These guides cover the work this quantity is for — the first ones run this calculator inside the section that raises the question.

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A whole structure squeezed into one bay of a running warehouse: slab, grid, deck span, bolt group and edge, in the order each one bites.
Sizing a Floor That Does Not Bounceuses this calculator
A floor can pass span over 360 and still move underfoot. Span, depth and everyday mass set its frequency, and frequency is what the client feels.
Stopping Impact Noise Between Floorsuses this calculator
A gym going in over occupied offices: what a floating sports floor can reach, what an isolated ceiling has to finish, and what neither of them touches.

Called something else where you work? Joist, rafter and centres — the term in each market, how close the equivalence really is, and the standard that governs it.

Still deciding? Deflection Limit vs Floor Vibration — the factors that actually differ, with no invented prices.

Already gone wrong? My floor bounces or feels springy · The tiles on my floor are cracking

How to calculate floor beam vibration natural frequency in 6 steps

Beam SpanThe clear span between supports, centre to centre of bearing.
Second Moment of Area I (×10⁶ mm⁴)The section's second moment of area about the bending axis, from its published properties.
Modulus of Elasticity EThe stiffness of the beam material.
Supported Mass per Unit LengthThe mass this beam carries along its length, including its own, at the loading present in service.
Damping Ratio (% of critical)How quickly the floor's motion dies away, as a percentage of critical damping.
Fundamental natural frequencyThe tool computes the fundamental natural frequency from those figures and shows the formula, its sources, and a confidence rating alongside it.

Fundamental natural frequency by beam span

Page defaults, not your figures above.

Beam Span	Fundamental natural frequency (Hz)
20 ft	13.4
30 ft	5.94
40 ft	3.34
50 ft	2.14

Frequently asked questions

How can a beam pass every deflection check and still feel wrong?: Because deflection limits are about appearance and about what the finishes will tolerate, and they are checked under a load that is rarely present. Comfort is about frequency and acceleration under the load that is always present. A shallow beam with a long span can sit comfortably inside L/360 under design live load and still drop to five or six Hz under its everyday mass, which is where a normal walking pace can drive it.
What are the walking pace figures in the breakdown telling me?: Walking is periodic, so it excites a floor at its step rate and at whole multiples of it. People walk at roughly 100 to 130 steps a minute. If the pace matching your floor's second or third harmonic lands inside that band, ordinary walking can drive it into resonance; if both figures fall well outside, no one walking normally will find the resonance.
Why does damping only appear in one line?: Because damping does not change the frequency — it changes how big the response gets once resonance is reached, which is the amplification figure. It is deliberately kept separate so nothing implies that adding damping fixes a floor tuned to a walking harmonic. It reduces the symptom; it does not move the frequency.
Is this the AISC Design Guide 11 check?: It is the frequency half of it. The full check compares a predicted peak acceleration against a comfort limit, and that calculation needs the effective weight of the vibrating floor panel, which comes from the guide's joist-and-girder procedure rather than from one beam's properties. This page gives you the frequency and tells you which regime you are in; it does not pretend to be the acceptance test.

Preliminary estimate, not certified engineering. This tool produces an indicative quantity calculation for planning purposes only — it is not a certified structural analysis, a guaranteed material takeoff, or a substitute for building department approval. Always verify measurements on-site and have a licensed contractor or structural engineer review any load-bearing, code-sensitive, or safety-critical work before purchasing materials or starting construction. Spotted an arithmetic or standards error? Report it to contact@craftquantities.com with your inputs — a confirmed fix gets a permanent check of its own, so the same mistake cannot come back.