Stair Vibration for Floating Landing

[jsmr]

I am attempting to design a stairway meant for an open lobby with a floating unsupported landing. I have been asked to perform a vibration analysis for human perception and am unsure how to proceed. Reviewing design guide 11 seems to pertain to floor slab systems, and I cannot think of a proper way to apply it to this case.

Does anyone have any suggestions on how to proceed or a place I can look for additional information?

 

[PEinVA]

jsmr,
What is the landing being supported on? I know I've checked the supporting floor system in this case. As well as the stringers as a beam from floor to hanging support.




RC
All that is necessary for the triumph of evil is that good men do nothing.
Edmund Burke

 

[jike]

I remember researching some criteria for a cantilevered balcony years ago (but cannot remember where I found that). That same criteria might be applicable.

 

[jsmr]

The landing is being supported by the stringers going from the ground to the intermediate landing, then from the landing up to a walkway bridge. We are assuming a fixed connection to the floor and a continuous stringer framing into the bridge with a moment connection.

 

[Lion06]

jsmr-

Are you in the Philadelphia area?

I would probably do a dynamic analysis in something like RAM Advanse to get the frequency of the stair. Using that, I would go into DG # 11 and use the equations for accelerations.

 

[WillisV]

Stairs differ from the assumptions used in DG#11 in several ways that in my opinion make it invalid for this case. Generally footfalls on stairs are much more forceful than those based on typical walking. Also the forced stride pattern due to the fixed stair tread length can result in higher force functions for groups. I would recommend reviewing the following paper for some good suggestions on how to tackle the problem:

http://www.sciencedirect.com/scienc...serid=10&md5=c667d6dd1db1e1bb6fcd7a65d25fe157

 

[youngstructural]

I would approach this similarly to StructuralEIT, however I would caution you that whereas the end fixity on a floor is of moderate assistance, it is of critical consideration on a staircase. Particularly if you are in a seismic area and will be isolating the bottom of the stair to prevent unexpected load path effects (thus a true pin, rather than the semi rigid connections that are more typical).

I would caution you about this situation. Be conservative. You'd be surprised how ineffective what little damping that is present in a staircase can be... In my experience the behaviour is more akin to a beam equivalent to the length of the staircase (the hypotenuse) running horizontally.

You're going to need sufficient stiffness and weight in the staircase proper. If your weight of your staircase is less than ten times the weight of a single user, that's not good. If your span/depth ration is more than twenty for timber, or more than fifteen for concrete, you need to start being very careful to ensure vibration is satisfied.

Good luck, and let us know how it goes,

YS

B.Eng (Carleton)
Working in New Zealand, thinking of my snow covered home...

 

[kslee1000]

Not familar with DG11. However, while I agree you can not follow is step after step, but can you utilize some of the concepts such as how the loads are introduced, and what are the suggested tollerance levels of vibration? From there, you might be able to gather some information to perform your own model analysis.

Other than that, make sure the stringers are sturdy, and deflections (both ways) are much tighter than stairs with supports in the mid-landing, it may help.

 

[271828]

WillisV is correct. Do not use DG11 for a stair, period.

First off, the loading is completely different. On a floor, people walk between 1.6 Hz and 2.2 Hz. Average people can descend a stair at 3-3.5 Hz, and very slightly athletic people can descend at 4-4.5 Hz.

Secondly, the forces are a lot higher for stairs than floors, whether we're talking ascending or descending. The DG11 forcing function is way too low.

There was a paper presented at the Arch. Engineering Conference last fall by Davis and Murray on the subject of stair vibrations. If you can get your hands on the proceedings, you can see the method they suggest, based on tests run on a monumental stair. They give recommendations for harmonic loads.

Using their harmonic loads, do a time history analysis or frequency domain analysis to predict the response.

Next is figuring out what limit to use. Somewhere between 1.5%g and 2%g, peak is reasonable, if not a bit conservative.

Finally, there's one huge issue with some stairs that's totally different from floors: crowd synchronization. If 10 people walk on a floor, they won't sync their steps, so the response to their combined loading won't be more than that of a single person. They don't sync because their stride lengths are different. On a stair, the stride lengths are fixed, so a group syncs up and causes a lot higher acceleration than does a single person. An amplification of 3.0 is sometimes recommended in Europe for this case. The problem is that your stair won't have a snowball's chance in you know where of meeting 1.5%g-2%g, so you'll have to use judgment to see if you want to consider groups for your stair.

 

[271828]

Oh yeah, I forgot one more thing that's different. Do not use any stair with a natural frequency below about 5 Hz, ever. The first harmonic of the walking force is monstrously huge, so if you allow someone's step frequency to match the natural frequency, you're in deep trouble.

And yet another thing. In some cases, you'll need to consider lateral vibrations. Some monumental stairs have very little lateral stiffness, so someone could get it moving pretty easily. This is worse if the stair is a bit unsymmetrical so that the main vertical mode also has a lateral component.

And yet yet another thing. Watch out for handrail lateral movement. This can be severe enough to catch people's attention. To my knowledge, nobody has ever set a limit on displacement (would seem to be the appropriate parameter) for this. Of course, if the guardrail is put into the analysis, it's displacement can be predicted.

 

[WillisV]

Thanks for the backup 271828 - I was going to mention the Davis and Murray paper but thought it was unpublished as of yet.

 

[Lion06]

Does anyone know where to find the paper that 271828 references?

 

[271828]

If you're interested enough and in enough of a hurry, you can order it for a fairly high price at:

http://www.proceedings.com/04137.html

I have heard that a more detailed journal paper will be published in the ASCE Journal of Architectural Engineering sometime in the near future. If you can wait, it'll probably be better and cheaper.

 

[Lion06]

Ouch!!! That's expensive. Thanks for the link, though.

 

[271828]

I suspect the journal paper will be something like $25. unless you're in a hurry, that would be better anyway.

 

[HouseBoy]

Is the "Journal" paper available yet?
Can someone provide a link to this or any other similar refs?