Relative Lateral Stiffness of Braced Frames 8

[CivilSigma]

Hi everyone,

To calculate a floor's center of rigidity, and distribute shear forces in a building's lateral system with a rigid diaphragm, you need to determine the relative lateral stiffness of your lateral force resisting elements.

For concrete shear walls, the relative rigidity is: 1 / [ 4*(h/L)^3 + 3 (h/L) ]
For concrete columns (moment-moment boundary), the relative rigidity is : 1 / [ 6EI/L^3 ]

So, I am wondering, is there an equation that approximates the lateral deflection of a steel braced frame like in the above examples?

 

[CURVEB]

I think you would be better off running the frame in a program because the deflection is a function of the elongation of the brace, as well as the rotation due to elongation in the columns. I'm not sure it can be easily done in a simplified equation such as the examples above, but it's certainly possible. Just break it down into the different components that contribute to the deflection. Rigidity is the inverse of deflection.

 

[CivilSigma]

Ok, I see.

So technically, I need to determine the axial elongation of the strut, in addition to the lateral deflection of the column, which gives the lateral displacement and therefore relative rigidity of the brace

 

[dik]

I cannot find one of the lateral spreadsheets, I've done it in. I've done this numerous times for mixes of concrete walls, X-bracing and rigid frames. It's just a matter of calculating the relative stiffnesses... no big deal. I'll keep looking. No 3D frame anlaysis required.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[dold]

From: Seismic Principles ASCE 7-10/2016 CBC, Paul W. Richards, PhD, PE 2017

 

[jayrod12]

I always use this one for lateral deflection of braced frames.

 

[dik]

Still cannot find it... I quit. The above is the metodology that I've used. It's just a matter of using the various stiffnesses for the frame system. The last project I used this for was for a church addition and the x-bracing was 'strap' material attached to a CFS wall. Calcs are off site, so don't have access to the spreadsheet for lateral.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[CivilSigma]

Thank you for the references Dold and Jarrod, that's exactly what I was looking for !

I agree Dik, I will be using the above formulas to determine member stiffness and go from there

 

[CivilSigma]

@dold, do you recommend the text book you referenced?

Does it include chapters on the design of braces or other elements ?

 

[phamENG]

I used to have the one jayrod posted pinned to a bulletin board in my old office. Quite handy.

 

[dold]

@CivilSigma

If you haven't been exposed to much seismic design and are interested in learning more about it I think it would be worth the investment. It a good refresher when i'm working on a topic I haven't visited in a while. It covers a lot of the basics and a bit of analysis. If you're looking for a reference with more component-level (braces, connections, etc) you might look elsewhere. AISC 341 has quite a few good design examples within. Here's an overview of the seismic principles book: [URL unfurl="true"]http://seismicprinciples.com/preview.html[/url]

 

[CivilSigma]

I'm just getting started with seismic design.

Are you aware of any books with reference to Canadian code? I guess it wouldn't matter too much, as the ideas for design and analysis carry over from the US to Canada?

 

[dold]

Welcome to the lovely world of earthquakes.

I'm not familiar with any books that discuss Canadian code. Surely one of our Canadian fellows would know of some - I think Koot does a fair bit of seismic design. I can't imagine that the fundamentals and goals of seismic design would be all that different but i can't speak to any of the differences between the codes (force derivation/generation, resisting system classifications, equations....).

 

[KootK]

1) We don't have much in Canada I'm afraid. The book shown below is the only seismic text that comes to mind and it's a little pricy. You can also find examples of various things in Canadian authored books on the various materials: Metten's steel book, Brzev's concrete book, etc.

2) The concepts used in Canada do carry over very well from the US. And, in my opinion, the US treatment is much more comprehensive and cohesive.

3) I was glad to read dold's review of the Seismic Principles book. I've been curious about that for a while. Whenever I see excerpts, the formatting and presentation seems exceptional compared to the stuff that you usually see in the exam prep space. The only things holding me back from purchasing it so far are:

a) I'm done with exams, at least in North America and;
b) I suspect that I already have most of the information in the book scattered amongst other, older generation exam prep books.
c) I want it as a PDF.

4) I'm a pretty big fan of the free NEHRP seismic guides: Link

 

[TLHS]

The Elements of Earthquake Engineering and Structural Dynamics book is great for more detailed work and touches on both theory and practice. If you are doing small buildings and trying to whip things out without making them too complicated, I'd agree that Metten's book is great for that and for all sorts of related steel building work.

Keep an eye on SEABC. Hopefully they keep up the web option for classes post-pandemic. They will have one or two seismic focused courses per year, and their material specific courses (steel/concrete/timber) will also include seismics. They are generally good value for money.

https://seabc.ca/certificate-program/current-term/

Canadian seismic stuff is a little weird. It's got some quirks and some really good people that do work on it, but there isn't the manpower to properly maintain the code. So you'll get super detailed changes to theory in some parts of the code, clauses that are trying to solve a problem but were written as definitive requirements not realizing that they've got consequences outside of the direct area they were trying to fix in another, and then really vague requirements about entire methods of analysis elsewhere.

On top of that, the steel and concrete codes contain some of the basic requirements for seismic design, and you'll sometimes get mismatches between things.

I also think there's a general reticence to do things the same way as the Americans. Lots of things are generally compatible, but it's weird that things aren't cribbed from NEHRP more often.

 

[dold]

+1 for the NEHRP documents. Excellent resources.