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# Interpretation of Natural Frequency from SAP20002

## Interpretation of Natural Frequency from SAP2000

(OP)
I'm designing a bridge, and need to check that the natural frequency of my structure is greater than 5 Hz.

I have made 12 numbers of modes, and am getting frequencies at different modes, but have no idea how to interpret this. Do I just use the frequency at a mode where the modal load participation ratio is greater than 90%?

Thanks a lot.
Replies continue below

### RE: Interpretation of Natural Frequency from SAP2000

I take it the VERTICAL direction's natural frequency has to be greater than 5Hz. Is that correct? In that case, you would probably look at the frequencies that have significant mass participation in the vertical direction.

### RE: Interpretation of Natural Frequency from SAP2000

(OP)
Thanks Josh. Should I be taking the frequency with vertical direction only? Or torsional modal shape as well?

### RE: Interpretation of Natural Frequency from SAP2000

What are your worried about exciting the 5Hz frequency? Pedestrians, Wind, Vehicles, Vortex Shedding?

I haven't done much bridge design, so I'm no expert on this topic. At least not for bridges. But, I'd suspect that the torsional mode would be an issue for wind, but not the other loading conditions. And, 5Hz seems pretty fast for wind. and, I have no experience with Vortex shedding for bridges. So, I have no idea if that's a reasonable frequency or not.

### RE: Interpretation of Natural Frequency from SAP2000

As a first pass, the lowest mode with the most vertical mass participation would be relevant. The deflected shape should gives you some clues here.

Also frequency is not always the silver bullet, perhaps have a look at the response factor (vertical acceleration) of the bridge too.

### RE: Interpretation of Natural Frequency from SAP2000

kongkong,

JoshPlumSE's question is important. What are you designing for? Pedestrian vibration resonance or galloping due to lateral wind loads? If the former, and this is a pedestrian bridge, typically 3Hz is the threshold that designers aim to be above. When you run your modal analysis, you should be able to see your mode shapes and their corresponding natural frequency. The visualization of the mode shape will tell you in what direction the bridge is vibrating, i.e. vertical, horizontal, twisting. Visualizing the mode shapes is a nice check to see if your bridge appears to be behaving correctly.

#### Quote (kongkong)

Do I just use the frequency at a mode where the modal load participation ratio is greater than 90%?

You are confusing the 90% modal participation factor as that is utilized when combining modes for use in a response spectrum analysis. What you seem to be looking for are the mode shapes that produce the lowest natural frequency as these prove to be problematic under certain types of loading. Most likely, none of your mode shapes alone contribute over 90% of your mass participation. I hardly ever see a single mode shape contribute over 70% alone. You may have ran a modal analysis for 12 modes but are they all applicable?

Standard highway bridges don't have the same issues as pedestrian bridges with vertical vibration and also don't typically have issues with galloping. It's only when you get into highfalutin long span bridges that these types of things require close attention.

I suggest you read up on the topic. There are plenty of resources out there that deal with this stuff.

### RE: Interpretation of Natural Frequency from SAP2000

(OP)
Thanks everyone.

I am designing a pedestrian footbridge, so I guess 3Hz is the threshold as STrctPono mentioned. I have reviewed the modal shapes, and the first few modes seem to vibrate only part of the footbridge, so deemed not applicable. And the next few modes give lateral/longitudinal/torsional modal shapes with very small vibration in vertical direction.

Afterall, I am using the lowest mode that gives the most mass participation in vertical direction as the natural frequency. Please correct me if I am wrong.

### RE: Interpretation of Natural Frequency from SAP2000

Is this an FRP pedestrian bridge? If so, there are different requirements and your 5 Hz limitation was correct.

If not an FRP pedestrian bridge..... Do you have a copy of AASHTO LRFD Guide Specifications for the Design of Pedestrian Bridges? Refer to Page 7 and 8. They recommend that for the first harmonic (jogging induced vibration) that the fundamental frequency in the vertical mode without the weight of the live load shall be greater than 3 Hz. In the lateral direction, the fundamental frequency shall be greater than 1.3 Hz.

You can isolate your eigenvalue analysis in only the lateral and vertical directions, essentially isolating those modes. You can also run the analysis in combination, however, I would be highly suspicious if your lower modes were not purely lateral or vertical. Typically, combination modes or torsional behavior comes in at higher frequencies with low mass participation (unless it is a long and slender steel bridge).

What is the natural frequency of your lower modes?

When you say the first few modes vibrate only part of the footbridge, what do you mean? If say, you have a 3 span bridge and the middle span is longer then perhaps you will see mostly vibration of the middle span for your first mode. I would not think this is "deemed not applicable." However, if you see an area of your bridge where say a small portion of the deck is vibrating independent of the structure and has low mass participation, then I would say that there is some modeling issues. Typically, I find that if your first few mode shapes don't have high mass participation, it's typically an error with the model. Perhaps boundary conditions are not modeled correctly or elements are not joined correctly. Can you attach a picture of the first few modes so we can see if it appears correct. How are you modeling the foundations? Drilled shafts or spread footings?

If the bridge is pretty straightforward and not skewed or curved, and is on spread footings you should also check the frequencies by hand to see how they compare with your model.

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