Long Span Pedestrian Bridge Vibration 1

[bar7h]

I am working on the design of a long span (approx. 200') pedestrian bridge consisting of a steel box truss and concrete deck. The natural frequency of the bridge in the vertical mode is approximately 1.5 Hz, so it does not meet the AASHTO ped. bridge spec minimum requirement of 3 Hz - and there is really no way to get the bridge to 3 Hz with the constraints I have been given. The bridge does, however, meet the alternate mass criteria of f>=2.86ln(180/W), since the bridge is quite massive.

My question is, how comfortable are you all with relying on alternate frequency criteria for justification of the bridge frequencies? Do we need to consider expensive dampers? I have seen bridges of this span with similar depth, width, and member sizes in service without dampers, and I'm wondering how it is justified.

 

[graybeach]

I read somewhere that Professor Murray of Virginia Tech, who established these criteria, never meant the alternate mass criteria to justify frequencies below 3 hz. Maybe you could contact him and ask about this. If dampers are needed, it will be much better to include them in the original design instead of having to retrofit an overly bouncy constructed one.

 

[bar7h]

I'll see if I can contact Professor Murray - although I have never been very successful getting academic folks to respond to questions like this. I agree that it would be much better to make dampers part of the original design, but I want to be sure that they are truly necessary before I incur that expense on the project.

 

[ajose]

I would like to advise about a non structural factor on vibration and it is serviceability. If people get unconfortable to cross the bridge then they could try to avoid it. There is other criteris for vibration besides AASHTO like:

AISC Degin guide 11 Floor vibration due to human activity.

SSEC Practice to prevent floor vibration by Farzad Naeim, this one explain a little about vibration impact on humans.

Tips for desiner of office buildings by Thomas Murray.

 

[graybeach]

Being sure that they are truly necessary is the tough part, especially given the alternate mass criteria in AASHTO. I was in your same position on a design build project. I decided that I would insist that contractor install dampers simply because I couldn't find a good justification for not installing them. Unfortunately the project got canceled before the design really got underway.

If you do end up installing them perhaps you can temporarily disconnect them and get people to jump around on the bridge.

 

[graybeach]

Actually that gave me an idea. How about if you design in connection points for the dampers, do some testing of the completed structure, and only install the dampers if indicated? The dampers could be included in the bid documents as an option, so you would have a price up front.

 

[bar7h]

We have considered designing in connection points for dampers and then leaving the final decision on whether to install them until after the structure is commissioned and "tried out". The bridge is multi-span, so it lends itself nicely to this with relative displacement of the top chords at the bents. Still, I would like go into it with a good idea of what the human comfort level will be.

 

[graybeach]

Well, I hope you will keep us posted on how this turns out. Another source might be Taylor Devices. They designed and supplied the retrofit dampers for the Millennium Bridge in London. Maybe they would be willing to look at your structure and provide an opinion.

 

[gwynn]

The frequency requirement is based on foot fall frequency and amplification of vibrations due to resonance, as I expect you know. However, with a massive bridge the damping inherent to the structure iteslf may drown out the resonance.

Since you know the frequency of the structure, a quick thought would be to assign the bridge 2% damping, apply the live load as a periodic function with the same frequency as the bridge and see what sort of excitation of deflections you get due to the resonance. Obviously conservative since, outside of a platoon marching in step across your bridge, the foot fall pattern will be distributed across a range of frequencies. But that would at least give you a ball park estimate of the worst case scenario.

 

[jorton]

A platoon marching in step may not be completely unrealistic if the deflections are large enough. Check out "Structural Dynamic Design of a Footbridge under Pedestrian Loading" by Blanco, Bouillard, Bodarwe and Ney. They describe a "Lock-in Effect" where pedestrians tend to fall into step in sync with the resonance, further exciting the resonance. I think Newland also noted this phenomenon in "Pedestrian Excitation of Bridges - Recent Results".

 

[gwynn]

Thanks for the references,
The Blanco et al. paper was an interesting read, as were the parts of "Vibrations in structures: induced by man and machines" by Hugo Bachmann and Walter Ammann that address the same issue. I haven't found a way to get a hold of the Bachman paper cited in the Blanco et al work as giving the deflection and acceleration limits without buying the entire conference proceedings, though the deflection criteria are mentioned in the book above. When I have more time next weekend, I think looking into whether there are circumstances differentiating when each limit is appropriate is worthwhile. Using the same references, it also seems 2% damping would be on the low end.

Characterising the vibration of the bridge while including everyone at the same foot fall frequency would still be a reasonable starting point in evaluating whether there is a real need for dampers in my opinion.

 

[jorton]

I haven't read the Bachmann and Ammann book. I'll have to look into it when I get some free time. I've haven't dug that deep into the defection and acceleration limits. I've always been able to meet the 3hz fundamental frequency limit. I agree with your approach.

Of course if the fundamental frequency is close to step frequency it will not take a platoon. I've stood near one end of a local pedestrian bridge and nearly became nauseated due to one person walking from the other end. The amount of movement did not seem to be any different when larger groups crossed together. I did some quick calcs and verified the fundamental frequency nearly matched that of pedestrians.

 

[ajose]

The case cited by Jorton is very important and i would like to take it from this point.

He said he became "nauseated", but that is not the worst impact on humans, the impact could be more severe. It is not casual that the codes state limits number of hours operating some equipment.

So the calculations and the decision have to be carefully evaluated.

To show some effects of vibration i attached two tables taken from Design manual soil mechanics, foundations earth structures - NAVFACENGCOM

http://files.engineering.com/getfil...-10c0a167ce75&file=Frequnecy_vs_Amplitude.jpg

http://files.engineering.com/getfil...d05ca7cbf&file=Frecuency_vs_Peak_velocity.jpg

 

[bar7h]

Thanks for your comments. I'm not sure if my FEA program will allow the periodic application of live load as you have suggested - I'll have to look into that. Also, thank you for the technical paper references. I have some reading to do.