Vibration Analysis in Long Span Slab

[NAFTALI-HAKOHEN]

HI all,

Im designing a concrete reinforced slab (not PT) , for a large span 32metres by 26metres, supported by thick (45cm) concrete walls) and have few questions regarding vibrations.

The slab thickness is 79cm (extra dead load 1kPa and live is 3kPa)

The FE analysis shows natural frequency of around 4.5Hz , above the lower limit rule of thumb 4Hz i see quoted as acceptable

However according to basic estimate formula quoted in design guides as F=18/sqrt(deflection - mm) , for the long term deflection of 10cm the frequency is 1.7Hz, much lower than the FE result.

What value does this formula have if it doesnt consider boundary conditions/thicknesses/stiffness/fixity at supports etc?

THanks

N

 

[271828]

Don't use the long-term deflection in the 18/sqrt(delta) equation. Compute the instantaneous deflection due to the weight of the slab and any superimposed loads that would be there during the vibration event you're checking. Typically, the superimposed loads would only be a small fraction of the superimposed dead load and live load. No load factors.

The classical equation for a simply-supported beam with uniform mass, m, and constant EI, is fn = pi/2*sqrt(EI / mL^4). That has quite a few of the variables for sqrt(1/delta) already in it. With some algebra, it can be written in terms of sqrt(1/delta), which is a lot easier for structural engineers to remember.

Because your slab isn't PT, it's not clear whether you should use a cracked moment of inertia. The CRSI design guide mentions this. For lightly reinforced slabs, they recommend an effective MOI equation. My inclination is to use the gross MOI, but you'll have to use some judgment.

 

[271828]

What vibration event is of concern? That slab mass is enormous, so it's hard to see how walking or running could be a problem. Rhythmic group loads like dancing or a concert could be a big problem if it applies, though.

 

[rapt]

I would be more worried about long term deflection. Where did you get 10cm from? It sounds low.

 

[ThomasH]

I'll start with someting relating to the natural frequency. If you check the equation for deflection of a simply supported beam with a uniform load and compare it to the equation for natural frequency of the same beam. Assuming that the load is the mass, the parameters are the same .

The natural frequency is a good measure for stiffness, nothing more and nothing less. To get an idea for how you slab will respond to a certain load, you need that load. The rules of thumb are based on experience with similar designs and similar activities on the floors. People walking and people running jumping or dancing have very different dynamic loads on a floor.

Regarding your slab, it is very large so it will be a large mass the put into motion. But that does not make it impossible. You mention a live load 3 kPa, I doubt the that live load will be more or less permanent. For the calculation of the natural frequency and ultimately the comfort acceleration, if you what to check that, you need to consider the mass that is part of the dynamic system. That is not the design load but rather the actual people expected on the floor, say 0.2 pers/m2. Your floor is so heavy that the extra mass will probably be insignificant.

My first question in this situation would be, what is the floor used for? Type of activity?

 

[NAFTALI-HAKOHEN]

OP here

Thanks for response, the short term deflection is 2-3cm, which gives frequency of 3-4Hz which compares somewhat with the FE results

The slab is a kind of museum/ study area in a University campus

The slab mass is very large, but the span is also large! The interaction between this could theoretically cause vibration issues that im trying to investigate

Is anyone familiar with the minimum 4Hz natural frequency lower limit for slab?

Thanks

 

[271828]

Is anyone familiar with the minimum 4Hz natural frequency lower limit for slab?

People can jump in place or bob up and down at about 3 Hz. They walk up to about 2.2 Hz. Run up to about 3 Hz.

If the natural frequency is below 3 Hz (used in the US) then the first harmonic of these forces can cause resonance and high accelerations. The limit is intended to make sure this doesn't happen.

 

[XR250]

Man it is hard to imagine a slab of this mass and span vibrating at 3-4 hz.

 

[WesternJeb]

The slab is a kind of museum/ study area in a University campus

IMO, you will have enough bookcases, tables, etc. to help dampen any natural frequencies. Make sure you are accurately modeling these as well instead of lumping them into your live load.

 

[ThomasH]

The slab is a kind of museum/ study area in a University campus

The slab mass is very large, but the span is also large! The interaction between this could theoretically cause vibration issues that im trying to investigate

So you have a huge mass but also a potentially large dynamic load, due to the large area. If is is a study area then you may have a situation when a large portion of the people will leave and that may potentially cause unwanted vibrations. You will probably not have people walking or jumping at the natural frequency but there will be dynamic loads.

Is there any risk that people will start some activity, like jumping, on the floor? That is usually a nasty load from a dynamic perspective.

Why don't you simply assume a reasonable load and test what accelerations you will have. That may answer the question if it is a potential problem or not.