K factor for sidesway--gravity column

[haynewp]

What is the correct way to assign the K factor for a pin-pin gravity column that is experiencing sidesway from an adjacent moment frame? In other words, I have 4 columns along a column line. The first 2 columns are a moment frame rigid connections at the top. The last 2 are just typical pin-pin gravity columns that are displacing at the top from the sway of the moment frame.

By looking at the AISC alignment chart, p.16.1-192 of LRFD 3rd, if the girder stiffness is zero, the K factor would go to infinity for a sidesway uninhibited column. If you go by the footnote on p.16.1-191, G can be taken as 10 for pinned ends at the foundation.

Is this what you do for pinned end columns experiencing sidesway from adjacent moment frames? Use G=10 at the bottom(per note) and G=infinity at the top, and get K=4.5 from the chart?

 

[UcfSE]

A column that is not part of the moment frame and only resists gravity does not depend on its own stiffness for stability. That makes it non-sidesway in my book. You could design the moment frame with or without those columns attached and it wouldn't make a real difference.

 

[JAE]

....agree...so the columns that are just "going along for the ride" would use a k = 1.0.

 

[haynewp]

Thanks, so the only difference for the gravity columns should be a slight increase in axial load due to the displacement. And the moment frames would be picking up the small horizontal component from the gravity colummns. And just design the gravity columns for K=1.

 

[JAE]

Yes, that's the way I do it. When designing a braced frame system or a moment resisting frame system, the members doing the bracing take, theoretically, all the lateral load.

But as they do this, they (and the whole diaphragm) deflect laterally, and this results in secondary effects (pdelta forces). So if the whole diaphragm deflects laterally, say 1", then we sometimes add to the original lateral force a force equal to the sustained dead load x 1" divided by the diaphragm height. For flexible diaphragms, this can be sometimes substantial. For seismic, there are provisions given in the code (I'm thinking IBC here) where this pdelta effect can be neglected if the lateral deflections are small enough.

 

[Murali27]

Nice post. How the deformation compatibility is achieved for gravity columns ith lateral system?

Instead of increasing K value, can we perform P-Delta analysis for the structure and design the gravity columns for the second order moments with K = 1.

Thanks
Murali

 

[UcfSE]

Murali, I wouldn't do that. P-delta effects and column instability are two independent phenomena. A p-delta analysis will capture effects of second-order moments but will not affect the column buckling.

 

[JAE]

UcfSE - I agree with you. Just wanted your opinion, though, on modeling the columns with multiple joints along the length of the member. Such as spacing joints every foot or so. This would include (in a rough sense) the second order effects of the frame drift as well as the second order effects of the column buckling (pdelta effects due to curvature of the column). While not perfect, it does take into account the buckling behavior.

 

[Murali27]

Can this P-Delta effect capture the global effect (sway) on column instability?

The local column instability due to slenderness can be captured based on its size?

Please explain on this or site some reference for the same.

Thanks
Murali

 

[NewImhotep]

This is a related topic

http://www.eng-tips.com/viewthread.cfm?qid=151341

Murali27

P-Delta capture some (may be not all) stability issues, like in ACI-318 chapter 10.13.6 where the magnified moment from P-Delta limited to be sure the column is stable.
That was for concrete column.Iam not sure if similar limits avaliable for steel columns.

Regards

Ahmed

 

[haynewp]

JAE, when you are adding back to the lateral due to p-delta, aren't you supposed to be taking that all the way to convergence? (Unless you use the AISC first order magnifiers method.)

 

[JAE]

haynewp - yes, you are technically correct (which means you are really correct). I just returned from an all-day AISC seminar on the new ASD/LRFD Manual and spec.

Chapter C, which deals with stability and Pdelta issues offers three analysis methods and within that, two analysis/design types - very convoluted and I've not yet had time to study it all in depth. But what I did take out of it was that you can perform a 3D analysis via computer but the program must be able to provide for both P(DELTA) forces and P(delta) forces....overall frame DELTA and member curvature delta. Most programs only do the DELTA part.

Usually, the second order interation that I described above (manually placing pdelta forces in addition to the main lateral forces) takes into account a very large percentage of the total. Subsequent interations would add to that but they are usually much smaller and we have usually added some conservatism to the results to account for that.

 

[Galambos]

I'm suprised that no one has brought up leaning columns. the effective length factors for the LFRS columns must be increased to account for the K=1 columns per AISC. note that this is not a code specific effect and is applicable to ASD designs, as well. can someone tell me if this procedure has been reworked with the new AISC Chapter C?