Concrete Building Wind Drifts

[RobertHale]

We are having a discussion in our office about checking allowable wind drifts. Based on a paper by Griffis, we had settled for a time on checking drifts of a first order analysis with 10 year MRI wind against a limit of H/400. We also had some discussion about appropriately accounting for cracking in concrete. Based on commentary section R10.10.4.1, it was decided to permit an increase of the allowable drift limit by 1.43 on that first order analysis, where the lateral system was mildly reinforced concrete. I am now rehashing this issue on another project, and upon re-reading I am not so convinced that a first order analysis is okay. Specifically the allowable increase of 1.43 is referenced in section 10.10.4 - Elastic second-order analysis. To me this seems to indicate when using the increase to adjust for cracking at service, one should be using a second order analysis. In light of the ambiguity, what does everyone else, think or do?

 

[Archie264]

Per R10.10.4.1 (with my emphasis and clarification added),

Unless a more accurate estimate of the degree of cracking at service load level is available, it is satisfactory to use 1.0/0.70 = 1.43 times the moments of inertia given here [i.e., the Elastic Second Order Analysis section] for service load analyses.

The 1.43 is simply the inverse of the .70 factor applied to reduce Ig to Icr, to be used in the second order analysis. And the .70 factor contains two factors, .875 x .80 = .70. The 1.43 factor simply backs that out. In other words, the 1.43 factor is to be applied to the .70 factor to bring it back to 1.0. That is, 1.0 Ig, the gross moment of inertia, to be used with uncracked behavior. So if you were applying the 1.43 to Ig then I think you were double counting, but only materially so if you were using service, not factored, loads. To calculate service drift and deflection simply use service loads and 1.0 Ig.

That's how I interpret it, at least. We have a lot of whiz-bang concrete guys on here, though, so if if that's wrong they'll probably weigh in.

 

[MrHershey]

The 1.43 is to convert from ultimate level crack/stiffness factors to allowable level. Has nothing to do with first vs second order. The only reason they're in the elastic second order section is to keep them out of the inelastic section as you shouldn't be applying crack factors if your analysis already accounts for effects of cracking.

They actually used to be in the moment magnification section in ACI 318-05 and earlier and are still referenced as acceptable methods for determining EI in those sections for ACI 318-08 and -11.

 

[wannabeSE]

Have you looked at ACI 318-08 (or 318-11) section 8.8 and the commentary for the effective stiffness for drift calculations.

 

[Archie264]

That section is rather confusingly written, in my opinion. To wit:

As with lateral stability analysis of concrete structures (R10.10.4), a factor of 1.4 times the stiffness used for analysis under factored lateral loads is adequate to model effective section properties for lateral deflection analysis under service loads.

And one has read that carefully and with full knowledge of the rules of English grammar (a lot to require of engineers!) to pick out the nuances. Maybe that’ll keep the Endian ingingeers from being able to compete with us! Oh, except they speak better inglish than we do. Nevermind…

In essence it’s saying to use service loads with (1.4 x .875 x .80)Ig = .98 Ig. I presume that the 1.4 factor is simply 1.43 rounded off, which, as noted in R10.10.4.1, is the reciprocal of .70, which, in turn, is the sum of .875 x .80. Whew!

Another way to have said all of that is to simply say use 1.0 Ig with unfactored service loads to compute elastic deflection, something any engineering student taking an introductory strength of materials class would have assumed in the first place.

This is the Grand Old Duke of York school of code-writing: factor the parameters up to the top of the hill and factor them back down again. And here we are, discussing how to multiply something by 1, hoping we got it right.

 

[RobertHale]

wannabeSE. I completely missed that in my reading of the 08 and 11 codes. I think that makes things less murky.

 

[LehighLarry]

I passed your question onto Larry Novak at the Portland Cement Association. Here was his response:

The industry is currently working on a consensus documents on this very topic (one by ATC, one by ASCE/SEI).

A. For tall buildings one should decompose the deflection into the story racking component (flexure and shear, also called shear sway) and the cantilever component (differential vertical elastic shortening). In many cases the deflections are critical for the exterior wall system.
B. One must analyze the building under service loads and under ultimate loads with different properties (service loads for deflection, ultimate loads for design forces) with the anticipated cracking associated with the magnitude of load (ACI 318-11 section 10.10.4.1 and associated commentary).
C. One must also consider the 2nd order effects for P-delta (for both service and ultimate loads analysis).
a. P-Delta 2nd order effects are critical; it is easy to have a rectangular building have a very large P-delta amplification for wind on the narrow face. The P-delta amplification will increase the overturning moments and the deflections (real world effects). ACI 318-11 section 10.10.2.1 limits the 2nd order amplification to 1.4 (if larger, must modify the structure).
b. (Larry Has some slide he can share with you on the topic.)

Best Regards
Lawrence C. Novak, SE, SECB, F.ACI, F.SEI, LEED® AP
Director of Structural Engineering
Portland Cement Association
5420 Old Orchard Road
Skokie, IL 60077
Tel 847-972-9100
email: LNovak@cement.org



Larry from Lehigh White Cement Company