British Floor Vibration Design Guide Question

[271828]

Considering that this is an international forum, maybe someone from across the pond can offer some help.

I'm trying to figure out how to use the latest UK Vibe Design Guide: "Design of Floors for Vibration: A New Approach," 2007 and am having trouble with the resonant build-up factor given in Eq. 37, Page 43.

If I have a walking path length of 9.14m, a step frequency of 2.0 Hz, 0.011 damping ratio, then I get a resonant build-up factor of 0.340 from this equation.

Just below the equation, Fig. 6.4 shows the supposed results from plotting this equation. For the same parameters, the factor seems to be about 0.59.

The 2006 Concrete Centre "Predicting Footfall Induced Vibration of Structures," 2006, Eq. 4.2, page 26 gives a very similar factor. It has a slightly different form, requiring some other info. If I use the same walking path length and damping, a stride length of 0.75m, and am exciting the structure with the 3rd harmonic of the walking force, this factor comes out to 0.751.

From looking at test results, I believe that this factor should be much higher than 0.340, so am inclined to believe the latter two.

Does anyone know the source of either of these equations? I've seen one of them semi-derived months ago, but I've spent hours trying to find the paper, to no avail.

Any advice would be greatly appreciated.
100,000e

 

[SmithAL]

Apologies for any confusion. I will investigate this when I get into the office tomorrow.

Andy

 

[271828]

Andy, thank you very much.

I am especially interested in the source of the equation in the SCI document. I've seen it before, but can't put my hands on it.

 

[SmithAL]

The equation is in texts such as Clough and Penzien, and is used in papers such as "On the response of long-span floors to walking loads generated by individuals and crowds" by B.R. Ellis (published in The Structural Engineer). There is indeed a mistake in the publication, however. The exponential term should include the frequency of the walk, fp.

The full equation is

rho = 1 - exp(-2 pi fp c Lp / v)

The graph should be correct.

I hope that answers your question!

Andy

 

[271828]

Thanks Andy for your fast response. I went back and looked at one of my calculations and that seems to make the equation match the graph.

The answer is still a bit different from the Concrete Centre equation, but at least they're reasonably close now (not like 0.75 vs 0.34).