Approximate building period formulas to check structural design software results 4

[concepto.ed]

Nowadays, checking results of structural design softwares is a very important task and using approximate formulas can save a lot of time.

How do you deal with fundamental period of buildings depending on its structural system? Do you think it is a property that can be estimated during structural design?

I have not been able to find something, equations like T= N/10 or the ones included in ASCE 7, are not always adequate, specially for moment resisting frames. ASCE 7 formulas are intended to provide a conservative (short) estimation that results in higher base shear using ELF. In my experience, they differ substantially from that values obtained using a detailed modal analysis of structures.

Thank you all!

 

[KootK]

1) Firstly, I haven't been verifying building periods as you propose and I don't want to be in the position of bullshitting people about that.

2) Were I to attempt such verification, my goto would likely be the Rayleigh Ritz method: [link //pdf.sciencedirectassets.com/282166/1-s2.0-S2212670814X00035/1-s2.0-S221267081400061X/main.pdf?X-Amz-Security-Token=IQoJb3JpZ2luX2VjEAEaCXVzLWVhc3QtMSJIMEYCIQCoTqRpM%2BbU0XlnG0GWHKdZXO%2BHXqfzODk5gt%2FEO7JiAwIhALO%2BhaD7yltNe4PHLzqJ5mGJjSf9pLIryjnCsGXrgL5KKtIECGkQBRoMMDU5MDAzNTQ2ODY1Igxsp%2FJVStfsEsL5%2FKoqrwRODt9bgTgkVk6CL%2FSFC668lI1bBYGX1WVAF01Dr6%2FcNaN8Z%2Fm5cOST9wEXwB7FlNaJi1J8KYddaQmg7emkUe0yM7q1YYKIl3sO1bTnY3D%2By%2B7dwRSGao8%2B6YtY6mMKW9cPaG0JGwUlcR5r%2F0zW9ojowpq4cCyRuBiYs2LAZqecoZ8OumtZy4OO6CHCXyh0lIgWem9qmrSLw5ynrEK6%2Bbe3t7t0yFfxJ1gAIVdlp8eVFyNCcBypuCcOCw801yCMTgWz%2F7D%2Bg68Ug6y0DjD0OYiEQUckGX6S7Lb4dXYG%2ByZwLWTge4D3rCJWBYjFKkp5MpqZNZfN4kYH9CgkMio0j5CJtzmPyP9lVUlx4gQRLYp%2BnntqxJxkHSmVuDexq2empNB%2BAIRWeZWQhV%2FoJ7sPO77MMfSl0DFidODlSp9AB36z8rPbO6e94dxfI%2Bc4pXUDi2FaZWCTo10RMiTJKMOwTJg7gPQNmOkUu%2FJU2FiCwRQwCjsD13hRCGzd%2B05Aw0MicoByWV945xK%2BLQVMYkTkp8rPo73WCMpb%2FeCBoi1P8ddDyPvXHDZ0OLGs1L4w%2FM%2BKsSSBb4cwYwSUW3Hqen6ETp5PQIfUb0a5tx5zMY2MD6d0su0DRAyUITlFUy%2Bz0D5WSGj%2BIG3VkR49as5IKMtzfBl3VdaE2G9g0BgdbySr8OQSUdoo%2FOQuNHvyH31%2B0eimqx%2F7%2FQkmB7loy%2BStKyDEGPgHwXCTI0ZMPuqmevZyG%2Bo4MPi51pcGOqgB2D5mnheLd5Mt%2FdaREnGHrPy7Y6l249WO6MBsHjU7wzwl1j%2F9km9e76jRWrjtpNYN25JrEpLEecet288hO63bLR46sGXVQgKduz%2Bi5Tahz24HuG4gp34mrDiZFdCP3MUFnSBJDLCh5%2BSoxLLI1CQ7B8lHDzknUtYGGtMyspwaOnehWJgyDGNhGyT%2FNJErX6zu7ZUdTNNNyV%2BjIfx6SdgFW4aqLCJTP3jf&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Date=20220812T012526Z&X-Amz-SignedHeaders=host&X-Amz-Expires=300&X-Amz-Credential=ASIAQ3PHCVTYUFJKJETX%2F20220812%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Signature=57a8ed73d8c898cebac6f640bc379fef4049e6a2346efe3e9e531ca9707eec14&hash=31609242ff39ebf750604f1d9a549483e4c862b1e6450dafda61c89eb595bd7b&host=68042c943591013ac2b2430a89b270f6af2c76d8dfd086a07176afe7c76c2c61&pii=S221267081400061X&tid=spdf-56530704-5fee-4245-8382-3602ea5dbf92&sid=b2176a751ee752424469f984025c54e9ede7gxrqa&type=client&ua=4d555c5a540300575007&rr=73956ac73bbac4fd]Link[/url]

 

[concepto.ed]

1) Firstly, I haven't been verifying building periods as you propose and I don't want to be in the position of bullshitting people about that.

Totally agree. Please let me clarify something, my intention is not to avoid the use of well-established methods in structural dynamics or to spread misinformation about something so important for seismic design.

I just think that sometimes it is useful to have aids that help us define if the results that structural programs produce are coherent and not blindly believed. Aids in the form of approximate formulas or even own experience solving and studying many structures. Of course, it may be that the period is not a property that can be easily taken.

Thanks for the paper, I will take a look.

 

[JStephen]

Just curious, but how different is "substantially different"?

 

[GregLocock]

For a typical multistorey metal framed structure that looks like a box, if you can estimate the stiffness in response to a force applied laterally at the top then you could just use

f = 0.56 (k / M)^0.5

ie a cantilever encastre with distributed mass, where M is the mass of the building. f is the first resonant frequency in Hz. This is wrong for all sorts of reasons, but it would be interesting to see how it plays out.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?

 

[concepto.ed]

In my experience, up to two times the one calculated using ASCE 7 formulas.

 

[FE_struct1]

Here's a trick I was taught at one point - the first mode frequency of a cantilever can be approximated as 18/sqrt(deflection under lateral UDL). This deflection is in millimeters and is for the case where a cantilever is horizontal and the UDL is applied vertically. The resulting value is in Hz.

For buildings, you can just flip the concept around - get the equivalent stiffness of your building (assume all stiffness comes from your lfrs system), apply all self weight + SDL loads in the lateral direction with the largest stiffness, get the deflection, then plug it into that equation.

It's a bit involved in that you'll now also want some approximate means to calc your building stiffness. I'll admit I've only ever used this method once, but it's given me reasonably close results.

 

[WillisV]

Relevant:

https://www.structuremag.org/wp-content/uploads/2014/08/C-CS-BuildingPeriods-Jacobs-June081.pdf

 

[JoshPlumSE]

Not sure if you're interested or not. But, when I was working for RISA, I put together a few "example" or "verification" problems to demonstrate the accuracy of the programs Eigen Solution (and an estimate of it's flaws since it didn't account for P-Delta softening).

I've attached the write-up to this post. If it would be useful to you, I can probably track down the Excel file and RISA files that were the basis of this write-up. Just let me know.

 

[concepto.ed]

Thank you all!

I've run some numbers using a steel moment frame building I was working on. Six storeys (4m typical heigth), regular building, 10 m bays. See attached picture.

First, I consider Rayleigh method as suggested by KootK and JoshPlumSE. This method has the advantage that is not very sensitive to the lateral load pattern. In this case, I used a uniform load, equal to the storey weigth for seismic design, so we can compare the method suggested by FE_struct1 wich only requires top deflection. As you can see, for this regular example both methods are close to the result reported by the software.

WillisV Great article that clarifies the purpose of the code formulas. By the way, I've checked at New Zealand Standards and they used an approximated period for SLS and another for ULS. In contrast ASCE periods are calibrated from buildings subjected to ground motions that apperar to be at service level.

 

[KootK]

Wow. I'd say that's an astonishing level of agreement really.

 

[concepto.ed]

I was also surprised. May be the ideal building, I will try to check other building models, some of them taller and with irregularities.

 

[Celt83]

I have found the Raleigh method to give a pretty good approximation.

as another reference point here is a comparison with RAM for a 16 story PT concrete structure:

I'm making a thing:

http://www.thestructuraltoolbox.com

(It's no Kootware and it will probably break but it's alive!)