Concrete floated floor resonant frequency calculation

[John Mor]

Hello everyone,

I tried using Gregwor's MSM calculator but i am not sure if i am using it correctly when it comes to floors.
What troubles me the most is, what value should i enter in LEAF 2 SUPPORT STRUCTURE MATERIAL thickness when it comes to
the concrete floor of a basement that has earth underneath. Should i go for infinite/maximum value or just the basement concrete thickness?


I know some will suggest not to float, but my situation is this:

I have access to a basement that is beneath a 5 store building with residents on the 1st floor and up.
The building is made from big concrete pillars & columns reinforced with steel and the walls are from bricks ( except the walls in the basement which are 200mm concrete. Ceiling is 160mm )
It is a typical greek building. Noise transmission through the structure is HORRIBLE in these. Ceiling height, 3 meters.
The basement has a 100mm to 150mm concrete floor before earth.


There will be 2 live rooms, one for ultra loud band rehearsals, with very low bass guitar tunings.
The other one for recordings, one loud instrument at the time in there.
Control room irrelevant for now.

I am going to need the best isolation i can get. Room in a room construction, at least for the rehearsal room is going to be needed i believe, based on my reading so far.
I was going for 100mm of concrete floated on 50mm rubber pads and filling the gap with insulation. I'm in contact with a structural engineer for calculating the loads and number of pads, right now my
focus is to lock this decision about the above materials with regards to isolation.


When i take the earth into account and insert a thinkness of lets say 9999 for the subfloor i get F0 of 12hz approximately.
When i enter 150mm i get F0 of 16hz approx.

Is this even applicable to calculate floating floors?
Any suggestions are welcome.

I've attached the two sheet snapshots too.

Thank you for reading!

[John Mor]

Anyone? I have searched every possible keyword for this. Let's forget about the long post above, i will narrow it down to a "simpler" question.

How does one calculate the resonant frequency of a floated concrete floor?

I've read the discussions here, most of them end up leading to broken links of older forums and sites that are not around anymore, this is why i persist.

Cheers

[Bastiaan]

Hi,

There is a difference between a wall and a floor, which has to do with gravity. The rubber that you want to use must carry the load of the floating floor, the walls and ceiling that rest on it, the equipment in the room and also the people in the room.

The rubber (or springs) work within specification only in a certain area of compression. If you would compress them out of spec, the rubber will not work as an isolator but as a flanking path, and this impacts the resonance frequency and the transmission loss of the floating floor.

This is why Rod Gervais advises in his book to contact the manufacturer of the product you intend to use for a calculation. I have once spent some time to investigate a floating floor, and came across this website: https://www.farrat.com. However, I went for an isolated slab instead as I could start from scratch.

[John Mor]

Hi,

There is a difference between a wall and a floor, which has to do with gravity. The rubber that you want to use must carry the load of the floating floor, the walls and ceiling that rest on it, the equipment in the room and also the people in the room.

The rubber (or springs) work within specification only in a certain area of compression. If you would compress them out of spec, the rubber will not work as an isolator but as a flanking path, and this impacts the resonance frequency and the transmission loss of the floating floor.

This is why Rod Gervais advises in his book to contact the manufacturer of the product you intend to use for a calculation. I have once spent some time to investigate a floating floor, and came across this website: https://www.farrat.com. However, I went for an isolated slab instead as I could start from scratch.

Hi Bastiaan, thank you. I am in contact with my structural engineer for the live and dead loads. The company we have contacted also walked us through with which product to go in order to be in the "sweet spot" for that, so my engineer calculated how many per square meter are needed. However the company didn't do any calculations regarding the resonant frequency of this system as a whole. Their product states that it can support isolation down to 4hz (if the rest of the system is designed & constructed perfectly) and when in max load it goes to 7hz. This doesn't tell us much though. I know some companies offer that for free when you buy their product, and we could ask them too i guess.

I just hoped that the MSM calculator would assume an ideal spring/rubber pad and that i could use it to have an idea if my concrete thickness and gap is sufficient.i think I've seen people using it for ceilings, which gravity affects them too, but yeah, they could also be wrong too.

[gullfo]

it's actually a simple mass-spring calculation to identify the resonant frequency - first of the mass (concrete) and second the suspension of the mass - the end frequency desired should be no more than 1/3rd the resonant frequency of the mass - and generally we prefer that to be 15Hz or less. so the reason it's often suggested to skip floating a lightweight floor is that the resonant frequency is much higher and to get the right spring + stability to get down even less than 30Hz is difficult at best.
i don't have the formula handy but a quick search for mass spring resonant frequency should find it quickly.

[John Mor]

it's actually a simple mass-spring calculation to identify the resonant frequency - first of the mass (concrete) and second the suspension of the mass - the end frequency desired should be no more than 1/3rd the resonant frequency of the mass - and generally we prefer that to be 15Hz or less. so the reason it's often suggested to skip floating a lightweight floor is that the resonant frequency is much higher and to get the right spring + stability to get down even less than 30Hz is difficult at best.
i don't have the formula handy but a quick search for mass spring resonant frequency should find it quickly.

Hey Gullfo, thank you! I've seen a few formulas but i am not sure i have grasped what's going on behind them completely and i don't know how to express my "understanding" of those. And i've done quite some reading too. I will try to, let me know if i got anything wrong please:

All objects have a natural frequency in which they resonate to, right? Here we have a system of those, the concrete slab which is to be floated, the spring/rubber pad itself (which has a resonant frequency depended on its material characteristics and on the load it carries too) and finally the subfloor which in my case, is concrete and has condensed earth underneath it, with a resonant frequency extremely low. Those somehow are related and produce a combined(?) resonant frequency, which we need to be under 10 hz, in my case at least.

I searched after your post and i came across this formula which i also had in the past, but i had trouble finding "K"
It looks simpler than the explanation that i had in mind. :

The natural frequency, Fn,
is dependent upon the stiffness of the
spring, K, and the mass of the load that
it is supporting (M), and can be deter-
mined by the following equation:

Fn=1/2 π√K/M

where K is the stiffness in newtons per
meter (N/m) and M is the mass in kilo-
grams (Kg)


Should "K" be stated on the product specs?

Thank you for your time.

Cheers!

[gullfo]

yes the K value is usually defined as compression typically up to 25% and sometimes as much as 50%. so durometer specs will often include compression numbers as well - some translation is needed unless they use the N/m here's a useful paper on understanding the floor controls: https://www.mne.psu.edu/lamancusa/me458 ... ration.pdf

[John Mor]

yes the K value is usually defined as compression typically up to 25% and sometimes as much as 50%. so durometer specs will often include compression numbers as well - some translation is needed unless they use the N/m here's a useful paper on understanding the floor controls: https://www.mne.psu.edu/lamancusa/me458 ... ration.pdf

Bless! This is great, thank you.
I gave it a quick read but i still didn't see something related to the air gap between subfloor and floated floor.
I'm trying to wrap my head on how is that expressed in the equation. Will read it more thoroughly for sure later.

[John Mor]

i still didn't see something related to the air gap between subfloor and floated floor.
I'm trying to wrap my head on how is that expressed in the equation.

Is it because that's for another equation maybe?

... first of the mass (concrete) and second the suspension of the mass - the end frequency desired should be no more than 1/3rd the resonant frequency of the mass .

by "end frequency" did you mean the resonant frequency of the system as a whole, or the resonant frequency of just the spring?

Maybe this is what i've been failing to understand all that long: Should i be using the formula once for the Concrete slab and once for the Spring, seperately?


And then what happens next, don't i need another formula for those two? in order to find the resonant frequency of the system as a whole?

I got confused with the formula and was thinking of it as a general one that includes them both, more specifically the "K" for the spring and the "M" for the Concrete mass. Seeing "K" being reffered as "Spring Stiffness" got me thinking that this is something that applies to springs only. But yeah, missing variables.

[gullfo]

the air gap should have minimal impact on a heavy floating floor unless you seal it tight and then you have another spring in the equation.

[John Mor]

I see.

I would really appreciate your comment on this too, as i am still deeply confused on how to use the formula.

Should i be using the formula once for the Concrete slab and once for the Spring, seperately?

Or do i use it like "k" is the stiffness of the spring, and "M" is the mass of the Concrete?

[gullfo]

K is the spring - the isolators for example - either rubber type or spring type. M is the concrete mass. assume for now the air cavity is not sealed only damped by light semi-rigid insulation.

[John Mor]

K is the spring - the isolators for example - either rubber type or spring type. M is the concrete mass. assume for now the air cavity is not sealed only damped by light semi-rigid insulation.

Ok, that helps a lot, thank you so much! That's what i initially thought but then i got paranoid there, haha.

[John Mor]

Hey all, after clearing things up with the equation and what is what, i tried doing the calculations and it feels like the result i'm getting is a bit too good to be true i'm afraid. Mostly because i'm the worst in calculations, lol.

The room is 25 m^2 with 10cm concrete which roughly weights 6250kg.
The walls, ceiling and equipment will be around 3000kg. A total of 9250kg.

Reading the specs sheet and dynamics of the rubber pads, (see attached image - i translated the diagrams),
and having 6hz as a target resonant frequency, i solved the equation for "X" which is the deflection of the spring.
Note, i am going for double layer of pads (25mm x 2)


K = F/X where F = W * g , where g = 9.8 m/s (acceleration of gravity). so in the equation we have:


Fn=1/2 π√K/M => 6 = 1/2π √[(W*g/X)/M] => 6 = 1/2π √[(9250 * 9.8/X)/9250] => 6 = 1/2π √[(9250 * 9.8/X)/9250] => X= 6.8mm

Link for the equation calculation : https://www.symbolab.com/solver/equatio ... D?or=input

I am no good at math and physics, so there's big chance i messed up something, replacing the variables for example. If you've spotted something wrong so far, disregard the following as they all would be made on a wrong assumption, lol.

If i get this rubber pad, and my calculations are right, i am near the sweet spot regarding the Fn. I don't expect more than 10 people in the room, nor any heavy pianos/consoles etc.

So, i expect a maximum live load of lets say 1000 to 2000kg extra, worst case scenario.

The calculation of how many pads i will need, is going to be based on the static load right? I may be oversimplifying here, please correct me:

Judging from the diagrams, the maximum load per pad seems to be 420 kg roughly. These are 12.5 x 12.5 cm x 25mm, 2 layers.
The load for Fn=6hz with the room empty is roughly at 330kg. If it goes to max load it will go as low as 5.6 hz.

All i have to do now is to divide the total static load (9250kg) by 330kg to find how many pads i need?
In that case it looks like i need 28 pads x2.

From a rough calculation it looks like 11200kg is the max operating load for the room. Is any of that realistic, or a bunch of bs?
Where's the catch? Even if you tell me everything is right, i'm still gonna have a bit of a hard time believing it, haha.
Thank you so so much for reading & commenting.

[gullfo]

so, another thought - let's assume the room with equipment etc will be 12000Kg. no one ever put less stuff in a studio you might think it would be better to go with spring-based isolators rather than pads. and it would also behoove you to consider calling Mason Industries or Kinetics Noise engineering to discuss as they can readily identify the correct products and quantities. typically the edge isolators need more resistance than middle of the room because of the difference in pressures as that even concrete with rebar can flex.