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# Pedestrian bridge vibrations and the AASHTO pedestrian bridge specification

## Pedestrian bridge vibrations and the AASHTO pedestrian bridge specification

(OP)
Hi all, long time lurker, first time posting.

I’m designing a long span pedestrian bridge. It's a multispan steel girder bridge. A computer vibration analysis shows a vertical frequency of 1.9hz which is less than 3hz which is less than the AASHTO allowable in the pedestrian bridge spec. AASHTO allows the frequency below 3hz if the weight of the structure meets the alternate criteria of f>=2.86ln(180/W) or if W>=180e^-0.35f. Does any one know how this works for multispan bridges? Do you just use the largest span length to compute W?

Alternatively, I found the AISC design guide for vibration of steel framed structures, there is a section on pedestrian bridges. If the peak acceleration of a single walker Poe^-0.35 / BW is less than their limit of 5% , using the recommended values for B (0.01), and Po (92lbs), it works out to be the same equation as in AASHTO.

However, AISC has a second formula to check the vibration from running- acceleration < 0.79Qe^-173f / BW, where Q (168lbs). If I assume that W is the span length, the bridge will pass the AASHTO criteria, but fail the one for a runner in the AISC design guide. To pass the runner I need to add a lot of dead load, like 1k/ft more. Which, is just not going to happen.

This is a very large signature structure we are designing, is it adequate to just meet AASHTO? Or should we look at installing some dampers, which could be expensive. I know AASHTO really doesn't go to the level of say the Eurocode for vibration analysis and keeps it simple. Do I need to perform a more refined analysis?

To add, to the assumption of W being the span length, the AISC guide does discuss vibrations of floor system and increasing W 1.5x if the adjacent spans are great that .7x the span under consideration which leads to me to believe that I am correct in using the span length for W but it makes no explicit mention of how to analysis a continuous span bridge. The AISC guide says the effective weight, W, is taken as the total weight of the bridge so its not clear and need to make sure I'm understanding it correctly. In contrast, the AISC guide has an equation of f = 0.18*sqrt(g/delta), if I use the deflection get from the computer analysis in this equation, the frequency is over 3, which all leads me to believe these equations don't work for multispan bridges.

Has anyone had to address this and can offer any insight, any information would be appreciated.

### RE: Pedestrian bridge vibrations and the AASHTO pedestrian bridge specification

I tend to agree that the AASHTO equations are not for continuous bridges - vibrations are not my area of expertise. The vibration requirements in the LRFD guide spec for ped bridges are the same as the guide spec for the Standard Specifications. However, the commentary in the LRFD version, AASHTO suggests using the attached European guidelines. There is an example for a two span continuous bridge.

### RE: Pedestrian bridge vibrations and the AASHTO pedestrian bridge specification

This is a signature ped bridge that was built in Brooklyn a few years ago. Unfortunately, it had to be demolished because of too much bounce.

### RE: Pedestrian bridge vibrations and the AASHTO pedestrian bridge specification

(OP)
Thanks for this.

EDIT: Ok, so I spent all day researching this. AASHTO says to keep the frequency over 3hz to be certain, but according to Technical guide linked above, they break it down into risk categories, where over 2.6hz there is a low risk of resonance, between 2.1 and 2.6 a moderate risk, and 1.7 to 2.1 posing a high risk or resonance. From there you calculate the acceleration that defines the comfort. Easy enough.

Here is my dilemma, my structure, designed for strength, has a frequency of ~1.9hz. I can get that up over 2.1 and close to 2.5 or 2.6 by making the girders deeper. I can get it to over 3hz by getting creative with the depth and optimizing the flanges to keep the weight in check while increasing stiffness. I'm going to have to go back and check the strength requirements but it should be ok. I also need to check to make sure the profile can accommodate this added depth. Its just a lot of more steel and Its going to be adding quite a bit of fill to get up to grade, since there are under clearance restrictions.

so... what to do? If the vibration checks work out according to this technical guide is that sufficient or do I should I stiffen it up all the way to 3hz to satisfy AASHTO? Obviously this needs to be run by the client, but my concern is in service how the bridge will perform, if we get them to sign off on this alternate analysis. I just don't have any experience to give me confidence as to how this structure will perform in service. The technical guide has a bunch of real world examples that fall in the 2hz zone.

thoughts or experiences?

### RE: Pedestrian bridge vibrations and the AASHTO pedestrian bridge specification

You state that this is a signature structure so I assume it’s going to be a fairly expensive structure to begin with. If you’re only talking about adding more structural steel, how much are you really increasing the cost of the structure compared to the overall project cost?

I would lean towards seeing what it took to meet the AASHTO code so that I didn’t have to worry about this. It seems like pedestrian bridges are always having issues with vibration and that’s something I’d want to keep my name out of when the media gets a hold of it.

### RE: Pedestrian bridge vibrations and the AASHTO pedestrian bridge specification

(OP)
Thanks. Its not going to be really expensive, but there are constraints on the approach walkways where increasing the profile will pose some challenges with matching existing grades and staying within ADA grade limits.

I spoke with the PM this morning and we are going to develop two cost alternatives, one >2.6hz (Setra minimum for low risk category) and one at > >3hz (AASHTO minimum) and perform the SETRA checks regardless to be certain that user comfort has been established.

All the help has been appreciated.

### RE: Pedestrian bridge vibrations and the AASHTO pedestrian bridge specification

Vibration analysis for pedestrian bridges is not my area of expertise. However, I am interested in this topic.

When you mentioned that your natural frequency is 1.9Hz, I'm assuming that this is your vertical frequency. It seems as if you are aware, but I thought I would point it out that there seems to be different requirements for vertical vs lateral frequency/vibration issues.

What do your support/bearing details look like? It seems that you are trying to increase your frequency to get it out of the resonant range of foot traffic. Just another thought, can you decrease it anymore to get it below that resonant range? I imagine that for a continuous steel bridge, it would probably be pretty hard to introduce enough rotational damping at the supports to reduce your frequency enough below 1.6 Hz. I guess that's where tuned mass dampers come in handy. Something that I don't have experience with.

### RE: Pedestrian bridge vibrations and the AASHTO pedestrian bridge specification

Thanks, we already called High Steel, they provided a cost estimate of $1.65/lb for fabrication and delivery of the plate girders. ### RE: Pedestrian bridge vibrations and the AASHTO pedestrian bridge specification #### Quote: ...cost estimate of$1.65/lb for fabrication and delivery of the plate girders

That sounds about like what I would expect. Given those numbers, you can easily estimate the cost difference for different sized girders. The total fabrication and delivery costs (approximately \$1.05 * current estimated girder weight) won't change much for heavier or deeper girders. The bulk of that cost will be welding, fit up, drilling, shear studs, etc. - things that are similar regardless of the size of the girders.

Rod Smith, P.E., The artist formerly known as HotRod10

### RE: Pedestrian bridge vibrations and the AASHTO pedestrian bridge specification

(OP)
An additional question with respect to a composite concrete deck.

In the Setra Guide and the AISC guide on vibrations, both guide use an increased modular ratio for a steel member with a composite composite deck. The AISC guide uses 1.35Ec when calculating the modular ratio, n. It has some discussion that it is acceptable to do so and includes this 1.35Ec in the bridge sample calculation.

Setra, make no discussion but they do you say in one of the sample calculations that "the moment of inertia is calculated taking into account the concrete
slab with a homogenisation coefficient of 6". But no discussion is made to how 6 was determined instead of the usual n=~8.

An increased EC helps quite a bit in raising the stiffness of the bridge, I'm also looking at using lightweight concrete to help raise the frequency so I'm dealing with a decreased Ec as it is.

Is increasing the Ec by 35% acceptable when determining natural frequencies?

### RE: Pedestrian bridge vibrations and the AASHTO pedestrian bridge specification

The Squib Park Bridge designed by Ted Zoli winner of the "Genius Award". BWHAAHAHAHAHAHAHAHA!

It was supposed to be bouncy, but not that "bouncy". Foolishness.

HNTB = How Not To Build?

### RE: Pedestrian bridge vibrations and the AASHTO pedestrian bridge specification

I deal with this issue routinely. If your bridge is a beam or girder structure then it is a little more of a challenge. That's why most of my work involves trusses. Note that as a structure gets larger and heavier, meeting 3 HZ is essentially impossible, thus the allowed reductions based on mass. Stick to the guidelines you've already mentioned (AASHTO, Setra, and AISC Design guide 11?) and you should be fine.

### RE: Pedestrian bridge vibrations and the AASHTO pedestrian bridge specification

MIKE 311 - You mention it's a large structure, but how large? If you meet the minimum based on the AASHTO reduction formula based on mass then forget about it and move on. If your structure is more than 180K then the minimum fn becomes a negative number which is meaningless. In that case a few people don't have enough energy to create a problem and a large group of people contribute more to the mass. I would use the weight of any particular span under investigation, regardless of the continuity, as the W. The "continuous vs. simple span" question only affects how you calculate your fn.

### RE: Pedestrian bridge vibrations and the AASHTO pedestrian bridge specification

(OP)

#### Quote (I would use the weight of any particular span under investigation, regardless of the continuity, as the W. The "continuous vs. simple span" question only affects how you calculate your fn.)

The pedestrian code is really a mess (i'll be doing another post about this shortly). The bridge is a 4 span continuous structure, three girder. 400' long, 16' feet wide. So it easily meets the W criteria. I thought about just looking at one span but we ultimately just did the modal analysis and we were able to deepen the girders a bit and using a lightweight concrete deck, get the frequency to almost 3 (2.98 something).

### RE: Pedestrian bridge vibrations and the AASHTO pedestrian bridge specification

(OP)

Following the Setra guide, when determining the minus factor, does one use either 0 or 1, or do you interpolate between the points? The examples don't have one where it falls between...

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