I'm designing a free standing exercise platform. How much lateral displacement do you think would be acceptable for human comfort? Thanks for your help.
I've never heard of checking this for rhythmic activities, but it's a good catch on your part.
Lateral forces are a very big deal for footbridges. I just finished a project in which the EOR didn't think of lateral vibe and is in deep trouble now.
Lateral vibe criteria are in their infancy at this point and the only ones I've seen use frequency as the criterion, not displacement or acceleration.
If you can get your lateral natural frequency far outside the range that they can excite it, then you should be fine. See the AISC DG11 Chapter 5 for info on excitation frequencies.
All that is, of course, for vertical vibration. The OP is trying to figure out what to do with lateral vibration, similar to the Millenium Footbridge.
ars001: What you need to do is run an eigenvalue analysis to get the natural frequency of the platform. You're only interested in lateral modes. Make your best estimate of masses, don't bump them up like you would for strength or stiffness design.
You have to estimate the live load mass. The DG11 gives psf that you can use. The aerobics 4.2 psf comes from 150/6/6=4.17 psf for example. Pick the one you have. Convert this to mass units.
If you don't have a program that'll do this, you can do it manually assuming it's a simple single-level platform with symmetric LFRS.
Estimate the mass of the platform in kip*sec^2/in. units. Take the kips of the platform divided by g = 386 in./sec^2.
Calc the lateral stiffness k in kip/in for the more flexible direction -- you had to be able to do this to check drift, although you might not have had it in exactly that form.
The lateral natural frequency in Hz is fn=1/2pi*sqrt(k/m).
If you're using eigenvalue analysis, you should check your frequency number using this manual method. I've been doing this for a long time and I ALWAYS check the program using a calc like this. I don't know about others, but I never get used to mass units, so it's easy to forget something and it's hard to tell from looking at the input if it's right.
271828-Thanks for all your help. It makes sense until I get to the stiffness k in terms of kip/in? I got my story drift number from Risa. It makes me cringe thinking about eigenvalues. I haven't heard that word for 15 years.
If you're using RISA, you can get k in kip/in. very easily.
Apply a 1 kip lateral load at your slab level in the most flexible direction. Run RISA and get the drift for this fake load case. Divide 1 kip load by the deflection to get kip/in.
RISA will do eigenvalue analysis and it's not very difficult. The only weird thing is making sure you have the right mass. It's been 3 years since I used RISA. I think one defines a load case with the vibe loads--the best estimate of DL and LL psfs plus the self weight. Then tell the eigenvalue analysis to use that load case.
If you use RISA's eigenvalue analysis, you should still do some kind of manual calc to make sure the eigenvalue analysis is correct.
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