Floor vibration — EN 1995-1-1 §7.3
Fundamental frequency, deflection under 1 kN and unit impulse velocity response, for timber floors in residential buildings.
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Tool information
What this page computes
The page checks a timber floor for vibration, to EN 1995-1-1 §7.3.3 — the clause covering floors in residential buildings. It computes the fundamental frequency, then the two criteria the code imposes.
Why it is separate from deflections
For timber floors with long spans, vibration often governs before deflection does: the floor passes the deformation check and still feels uncomfortable to walk on.
It is not the same calculation with a different coefficient. Deflection is a static response to the imposed load. Here we compute the natural frequency and the response to an impulse — a different phenomenon, different quantities, a different load case. Hence a page of its own rather than an extension of the deflection page.
The floor is analysed unloaded
§7.3.3(3) is explicit: the mass is only that of self-weight and other permanent actions. The imposed load is not added.
This is counter-intuitive. Extra mass would lower the frequency, so including it seems conservative. But discomfort arises precisely when the floor is unoccupied — someone walking through an empty room feels the vibration; the same room full of furniture and people is damped and heavier. The code asks for the case that produces the problem, not the one that looks safer.
The 8 Hz threshold is not a check
\(f_1 = \frac{\pi}{2\ell^2}\sqrt{\frac{(EI)_\ell}{m}}\)
§7.3.3(1) states that below 8 Hz a special investigation is required. That does not mean the floor fails — it means the simplified method of clause (2) no longer applies, because at low frequencies resonance with the human pace comes into play and the impulse model no longer describes the response correctly.
The page gives no verdict there. It shows the two criteria for guidance, but says explicitly that the method's range has been left.
One detail that explains why vibration appears abruptly at long spans: f₁ falls with the square of the span. Doubling the span quarters the frequency. A 4 m floor well clear of the threshold drops below it at 6 m, even if you make it proportionally stiffer.
The two criteria
If f₁ > 8 Hz, the code requires:
\(\frac{w}{F} \le a \quad \text{[mm/kN]} \qquad\text{and}\qquad v \le b^{(f_1 \zeta - 1)} \quad \text{[m/(Ns²)]}\)
The first is a static stiffness criterion: how far the floor deflects under a 1 kN force — roughly a person's weight. The second is dynamic: the peak initial velocity of the vibration produced by a 1 Ns impulse, ignoring components above 40 Hz.
The second depends on the number of modes below 40 Hz:
\(n_{40} = \left\{\left(\left(\frac{40}{f_1}\right)^2 - 1\right)\left(\frac{b}{\ell}\right)^4 \frac{(EI)_\ell}{(EI)_b}\right\}^{0.25}\)
The more modes the floor has in the perceptible range, the larger the impulse response — hence the form of the relationship.
a and b are national parameters
The code does not fix them. Figure 7.2 gives only the recommended range — a between 0.5 and 4 mm/kN — and the relationship between them: a small a (stiff floor) goes with a large b (greater tolerance on velocity), and vice versa. The upper curve is labelled "better performance", the lower one "poorer performance".
The page reads b from the figure for the given a, unless you enter it directly. Being a graph, the values are approximate by the nature of the source — and the page says so.
Watch the damping
ζ appears in the exponent of the velocity limit. A small change — from 1% to 2% — alters the result considerably. §7.3.1(3) recommends 0.01 where no other values are given, and the page flags any departure from it.
What is not from the code
§7.3.3(2) asks for the deflection under 1 kN "taking account of load distribution", without prescribing how that distribution is computed. This is a genuine gap in the code, not in the implementation.
The page accepts w/F as an input — if you have it from your own analysis, that is the value that counts. If you leave it blank, it uses an estimate based on the effective width from orthotropic plate theory, capped at the real floor width. The estimate is our choice, it is flagged every time it is used, and it should not be mistaken for a code requirement.
What it does not cover
- Machine-induced vibration (§7.3.2), which is checked against ISO 2631-2.
- Floors with other support conditions than simply supported on all four sides — expressions 7.5 and 7.6 are written for that case.
- Floors other than residential; the code treats only residential buildings explicitly in §7.3.3.
- Ultimate limit states — vibration is a serviceability check.
Expressions 7.4–7.7 are transcribed from SR EN 1995-1-1:2004, pages 54–56, and each has a test that reproduces it by hand.