Moment Magnification Origin 2

[gonutsdonuts]

Hello, I'm curious about the origins of the moment magnification approach for considering second-order effects. Does anyone know if it is based on a mathematical derivation? Or was it instead based on experimental research? Does anyone know the original source for the moment magnification approach?

Thank you!

 

[JAE]

If you are referring to the ACI chapter 10 approach - I believe it is a combination of both analyses and tests.

Try this - go through Chapter 10 and look at the references provided in the commentary for Section 10.10 (R10.10).

There are several there - including articles from MacGregor, Chang, Breen and others.

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[MrHershey]

It's been in ACI 318 for a long time. First rendition it appeared in was ACI 318-71. I don't believe is has changed significantly since.

An old paper with discussion on the topic back when it was first introduced can be found here: Link (PDF). My recollection is it was a combination of math and testing but leaned heavier on the math side.

I'll usually default to moment magnification, as do most design programs. But it can be incredibly conservative, especially for lightly loaded columns. Can't find it now, but read an article a while ago that mentioned the design moments from moment magnification being sometimes in the neighborhood of 5 times what they are if an elastic second order analysis is done.

 

[JoshPlumSE]

Austin, WJ(1961): " Strength and Design of Metal Beam-Columns" Journal of Structural Division, ASCE Vol 87.

I believe this paper first introduced the Cm/(1-fa/Fe) type of equation which later was revised into the B1 portion of the AISC B1/ B2 equations.

 

[sticksandtriangles]

MrHershey,

I would be very interested if you could find that article that mentioned the 5 times number on moment magnification between differing methods.

I am currently looking at tilt panel wall designs for our company.
I am comparing the results of the a non-linear second order elastic analysis verse the alternate method for out of plane slender wall design method (ACI 318-14 11.8).

The difference in moment between the (2) methods is staggering when comparing ETABs non-linear second order results versus the alternate method. I thought I was going crazy, but the 5.0 term could help me feel more rationale that my results are correct.

Thanks!

 

[Hokie93]

This is discussed in a fair bit of detail for beam-columns, including derivation of a moment-magnifier term, in Chapter 1 of "Theory of Elastic Stability" by Timoshenko and Gere (second edition).

 

[MrHershey]

Found it: Link

The provisions in the moment magnification procedure allow for a column to be designed using a conventional first order analysis provided that the moments calculated by the analysis are increased to account for second order effects. Considerable inconsistencies can exist between the results obtained from an elastic second order analysis and the moment magnification procedure. These inconsistencies cause confusion amongst practitioners and result in wide variations in their use and/or interpretation. Simply put, moments estimated by the moment magnification procedure may be upwards of five times larger than those estimated by a second order analysis. As a result, engineers often discount the moment magnification procedure in favor of the more manageable results obtained from an elastic second order analysis.

 

[sticksandtriangles]

Star for you MrHershey.
You just made me look good at the office.

 

[KootK]

I am also grateful for your efforts MrHershey. I'd been looking for the source McGregor stuff for some time.

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.

 

[MrHershey]

A few words of caution before just jumping into a second-order analysis.

[ol 1]
[li]Play around with your boundary conditions. They can make a big difference. Don't assume, for instance, that just because you're a shear wall building that your columns are 'braced' at every floor. If columns are far from any walls or if you don't qualify as a rigid diaphragm you may not actually be 'pinned' at the level. There's restraint but it's more like a spring. Every situation is different so just run it a few different ways to get an idea for how big the influence is and settle on something that's comfortable and defensible. Would also recommend passing your analysis by a friendly colleague with the mandate that they should try to poke holes in it.[/li]
[li]Try to include whatever initial imperfections your specifications allow in your analysis. Contractor isn't going to build your column perfectly plumb. That's part of what moment magnification's minimum moment tries to account for, though they go a little overboard (at least in my opinion, your mileage may vary, and I recognize that may be more feature than bug in an approximate method like moment magnification).[/li]
[li]Unless you have a real good reason to do otherwise, stick with code stiffness modifiers (often ACI 318, sometimes ASCE 41 or other standards depending on what your situation is and what jurisdiction requires). There's a whole slew of people with a whole slew of opinions on the topic of effective stiffness. It's one of the areas where there really doesn't seem to be a great consensus. When that happens, it's my opinion that safest bet is to go with whatever standard is in force barring compelling reasons to do otherwise. You can certainly still be wrong, but if you are you at least did things 'by the book'.[/li]
[/ol]