Vibration assessment of lightweight pedestrian bridge

[Agent666]

Hi

We have a pedestrian/cycle bridge to design which has multiple simply supported spans of ~11.5m length, with lightweight timber deck + handrail/barrier.

We were hoping for simplicity that we could use 2 simply supported steel beams between intermediate supports (one either side of the deck) with some steel cross members supporting timber joists with timber decking.

I am currently working out vibration performance in accordance with AISC design guide 11 (second edition), our code also refers us specifically also to a procedure in appendix C of BS5400 bridge standard that we need to demonstrate compliance with.

The BS5400 design guidance notes for bridges with the 1st fundamental frequency greater than 5 Hz that a specific assessment is not required. Our first cut beam size was such that the natural frequency was just under 5 Hz, so we then went about evaluating the max acceleration only to find it was about 70%g under running excitation when worked out in accordance with AISC design guide 11 …..(lightweight decking and only 1% damping, so not surprising to us after rechecking the numbers (essentially following the design example 4.5 in DG11)).

The question is, I could have a structure just over 5Hz that would by the code not require a specific evaluation of accelerations, but if I do evaluate the max acceleration with the higher than 5Hz fundamental frequency, then we find it is an order of magnitude greater than any commonly accepted acceleration limits. For example even we much stiffer beams and a 9Hz fundamental frequency, we still evaluate about a 30%g acceleration.

Are we safe to ignore this as being above 5Hz means lesser chance of stepping action exciting the span? Or should we irrespective of the fundamental frequency adhere to some acceleration limits because they might occur in accordance with what is being estimated by DG11? I guess more than anything after working out this large acceleration I'm not 100% convinced we should be ignoring it.

AISC design guide 11 suggests a 5%g acceptable limit for an outdoor footbridge, which seems quite onerous if we need to make this work.

If we do need to meet some acceleration limits even with >5Hz, what is appropriate?

Any advice based on previous experience with similar is appreciated, as it’s the first time we have looked at a footbridge, usually for vibration of composite beams we have more mass and damping and it just works (most of the time).

 

[KootK]

I don't have your answer but thought you might be interested in another source reference and some additional evaluation strategies. This is from AASHTO's guide specification for pedestrian bridges and would seem to be even more permissive than your other references.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[Agent666]

Yeah I did find that in my search for answers, but you can't get away from the DG11 example that has greater than 6 Hz and finds acceleration unacceptable...

I'll keep reading!

 

[gravityandinertia]

I have no experience in the AISC Design Guide, but much experience in vibration analysis of frames and the like. But as to the question:

"The question is, I could have a structure just over 5Hz that would by the code not require a specific evaluation of accelerations, but if I do evaluate the max acceleration with the higher than 5Hz fundamental frequency, then we find it is an order of magnitude greater than any commonly accepted acceleration limits. For example even we much stiffer beams and a 9Hz fundamental frequency, we still evaluate about a 30%g acceleration."

Let me propose a thought to you.

Imagine a sine curve that has an amplitude of 1g. Now imagine your standing a bridge deck and its vibrating with that sine curve. As you're standing there, imagine the frequency of the sine curve is swept through a range of 0 to 10 Hz, while keeping that same amplitude of 1g. How do you imagine 1Hz feels compared to 10Hz?

While acceleration matters, its the combined amount of acceleration with frequency that tells us how it feels to be on it. Higher frequencies don't apply the acceleration for nearly as long due to their period being so short, so it doesn't feel like much.

You could have a peak acceleration of 100g but at 1,000,000Hz you wouldn't feel much at all. That's an exaggeration of course, but you get the picture.

 

[MotorCity]

Keep in mind that AISC pertains to buildings, not bridges. As such, I would expect more stringent vibration requirements for buildings than bridges.

 

[Tmoose]

If the walking surface was planks running longitudinally and bolted, the bolted joints would likely provide some frictional damping that might knock down the amplitude a bit
if the roving punks played bouncing pranks and excited a resonance.

 

[JoshPlumSE]

You can also run a time history analysis or run a FRF (Frequency Response Function) for your bridge. There is some guidance on this in the 2nd edition of Design Guide 11.

 

[Agent666]

Motorcity, Aisc does cover pedestrian bridges in passing. Refer design example 4.5 for example. It has specific advice in other sections also.

Gravityandinertia, good explanation. A calculation at 4.9 Hz and 5.1 Hz yield almost the same acceleration, but guidance suggests to ignore one. Generally what you are discussing is in line with figure 2.1 of the Aisc design guide, after about 8Hz tolerance limits with respect to acceleration are more relaxed (similar below 4Hz) using the iso baseline curves. The acceleration limit doesn't dissappear,requirement just becomes more relaxed if we are interpreting this correctly.

I've noted Design guide 11 does note in section 2.2.1 that you need to only evaluate the acceleration for the lowest harmonic which matches the natural frequency of the floor. I think this is what we are doing wrong and ending up with a large acceleration based off the first harmonic for walking. We have been looking at the first harmonic frequency when we should be looking at the 2nd or 3rd driving any resonance (that which more closely matches the natural frequency of the bridge)?

Does that make sense as I'm not sure if this is 100% correct?

With walking being 1.6 to 2.2 Hz, general advice results in being greater than at least 3Hz to avoid resonance with the first harmonic frequency. I'm guessing that the 5Hz limit in BS5400 is to ensure you also avoid the second harmonic frequency (see table 2-1 in DG11).

 

[PengStruct]

Not sure how useful this is but I once designed a steel stair, which, when built had a measured frequency of 11Hz. There was very little dead load so the vibrations were not damped and if you did a heel-drop at mid-span of the stair run you could definitely feel the vibrations.

 

[gravityandinertia]

Agent666,

As I said, I'm not that familiar with the design guide, the work I do requires more FEA based analysis outside of codes. If I get a chance at lunch I'll take a look and see if I can clarify anything for you.

 

[gravityandinertia]

After looking through that design guide, I would say that if your 1st natural frequency of the bridge is around 5Hz then I would be concerned with the 2nd and 3rd harmonics of walking producing the largest accelerations.

 

[Trenno]

Perhaps have a read of this report/thesis on two pedestrian bridges designed by Arup here in Brisbane.

HUMAN INDUCED VIBRATIONS ON FOOTBRIDGES