Sway Column Stabilty Index 2

[ahmedhegazi]

Hi All,

I am referring to ACI 318-11 and same applicable to 2014 code version
Two questions as follow

1-For Stability Index (Q)equation 10.10 , should Δo ( the first-order relative lateral deflection between the top and the bottom of that story ) be multiplied by Cd ( deflection amplification factor) ,
my personal opinion it should not as seismic story shear is divided by R ( Response modification factor)


2-Clause 10.10.2.1 — Total moment including second-order effects in compression members, restraining beams,or other structural members shall not exceed 1.4 times the moment due to first-order effects

This statement is bit confusing to me , i have seen column design software such as Spcolumn , apply this formula to moment magnification for non sway ,which simply means (δns) should not exceed 1.4
I believe this clause should apply only to sway component magnification P - Delta ( Large delta)

Any thoughts on the above

 

[Celt83]

1. I mispoke initially - Cd should be included as this check is similar to the ASCE stability coefficient.

2. This clause assumed you performed a second order analysis so the moment magnification procedure would no longer apply for P-Delta(Large Delta). SpColumn and the like are using clause 10.10.2.2 to then capture P-delta (little delta) so δns may be larger than 1.4. This seems to be an overly conservative approach in my opinion to capture P-delta, hopefully ACI goes in a similar direction as AISC and introduces notional loads or some similar approach. Note also that most of these software packages as far as I have seen are checking the slenderness to enter 10.10.2.2 against equation for columns braced against sway(10-7 in ACI 318-08) which can lead to some slender sway columns checking out as non-slender and getting no amplification, I've artificially bumped K to 1.8=(40/22) to guaranty columns that would check out slender for Kl/r <= 22 still check out slender for Kl/r <= 40, this can also be very conservative.

Open Source Structural Applications:

https://github.com/buddyd16/Structural-Engineering

 

[ahmedhegazi]

Thanks Celt83 for your prompt reply ,

1- I checked ASCE 7-10 Stability Coefficient equation (12.8-16)

​

it has (Δ/cd) for displacement , so it means Elastic displacement(δe ) should be used for Stability Index (Q)

2- I agree with what you write there , however i was reviewing other engineers calculations prepared by spColumn and the output made me confused
Non sway Column
δns=1.7
Software reported Magnified Second order moment exceeds 1.4 times first order moment .Revise Design !
anyway , it seems like software issue

One more question , For sway columns , if we calculate δns ( small delta ) should k non sway (i.e k<1.00 ) be used , i have seen some reference use k sway such as SP-17 (14) and some use k nonsway such as PCA notes

 

[KootK]

1) I agree that Cd should not be applied to the drift used in the calculation of the stability coefficient. I disagree with your reasoning for it however. The stability coefficient actually has nothing at all to do with any particular set of lateral loads. It's really a shame that the presentation of the equation suggests otherwise. The calculation is about comparing axial load to lateral story stiffness to asses buckling -- the end. Story shear / drift is simply a way to arrive at the lateral stiffness of the story (k spring constant in my own vernacular). For all the difference it would make, you could use the seismic load, the wind load, 1000 kips, 1 kip, or -73 kip. Viewed in this light, I think that it makes sense for this to be a check base on elastic drift.

2) I believe that 10.10.2.1 applies to both sway and non-sway members and that it applies regardless of whether the moment amplification was determined via a true second order analysis or an approximate method like moment magnification. It's simply an upper limit on how slender we allow our framing members to get. A good example of a non-sway member that might be limited by 10.10.2.1 is a slender precast wall panel. It's quite common for such members to be significantly influenced by P-baby-delta effects.



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.

 

[Celt83]

That is some good insight on the stability coefficient and makes good sense, seems there may be few things defined in the specific sections of ASCE 7 that should/could really apply more generally.

Agree on 10.10.2.1 applying to both sway and non-sway columns, I need to reread the section but based on my memory it is vague at best if the 1.4 limit applies if your doing the magnification procedure, although it makes sense that it would if your going to limit a second order analysis to that value why wouldn't you limit the approximate method. I think ACI needs to do a bit of rework to this section in general.

One more question , For sway columns , if we calculate δns ( small delta ) should k non sway (i.e k<1.00 ) be used , i have seen some reference use k sway such as SP-17 (14) and some use k nonsway such as PCA notes

I'd say if you performed a second order analysis you should be entering δns with a K<=1 as your moments would be inclusive of P-D effects and you are now using δns to capture P-d effects by magnifying the P-D moments. As I was hinting at in my previous post though there is a subset of columns that would be slender when considered as a sway column but non-slender when considered as a non-sway column so there are instances where you may need to artificially inflate K in software to get the δns magnification applied, though this may result in an overly conservative amplification of the second order moments.

Open Source Structural Applications:

https://github.com/buddyd16/Structural-Engineering

 

[ahmedhegazi]

Thanks Gents for your input , appreciated.

I agree with Kootk first point for stability Check according to ASCE 7-10 being more stiffness of structure regardless magnitude of force and its directions. and it should be carried out on elastic member properties.

However for seismic load case,would you apply elastic (Δ) or multiply Δ by Cd for calculating (Q) equation 10-10 ACI318-11?

With Respect to 1.4 upper limit set by ACI in clause 10.10.2.1 , i am doubtful it apply for nonsway columns as this would mean (δns) ACI eq (10-12) should not be more 1.4

 

[KootK]

However for seismic load case,would you apply elastic (Δ) or multiply Δ by Cd for calculating (Q) equation 10-10 ACI318-11?

For all the difference it would make, you could use the seismic load, the wind load, 1000 kips, 1 kip, or -73 kip. Viewed in this light, I think that it makes sense for this to be a check base on elastic drift

If you took Cd into account for seismic, you'd be dealing with some kind of secant story stiffness. That would be a different animal and, in my opinion at least, is not the intent of the provision.

With Respect to 1.4 upper limit set by ACI in clause 10.10.2.1 , i am doubtful it apply for nonsway columns as this would mean (δns) ACI eq (10-12) should not be more 1.4

That precisely what it would mean and I fail to see why that's a problem. R10.10.2.1 does a pretty good job of explaining why the limit makes sense.

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.

 

[KootK]

One more question , For sway columns , if we calculate δns ( small delta ) should k non sway (i.e k<1.00 ) be used , i have seen some reference use k sway such as SP-17 (14) and some use k nonsway such as PCA notes

I'm confused by the question for this part. I was under the impression that δns did not enter into the sway procedure. Are you guys seeing that differently?



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.

 

[ahmedhegazi]

Agree that δns does not enter in sway procedure , however after calculating magnification for sway part we should calculate δns for ( Mns+δs*Ms)
That is carried out using equation (10-12 ACI318-11)
I always use k<= 1.0 for Pc that is logged in equation 10-12 , what shocked me that ACI AP-17(14) used K sway =2.2
Attached screenshot for that

That precisely what it would mean and I fail to see why that's a problem. R10.10.2.1 does a pretty good job of explaining why the limit makes sense.

R10.10.2.1 talks about PΔ and stability index that is why i do not consider it is valid for non sway columns

 

[KootK]

however after calculating magnification for sway part we should calculate δns for ( Mns+δs*Ms) That is carried out using equation (10-12 ACI318-11)

I disagree. Equation 10-12 is part of the non-sway procedure and, in my opinion, does not apply to the sway case. And that makes sense. Rationally, one expects the P-D moment magnification to dwarf any P-d magnification. Moreover, when K>1, P-D really incorporates some P-d because analytical nodes are occurring between the inflection points of your compression members.

I always use k<= 1.0 for Pc that is logged in equation 10-12 , what shocked me that ACI AP-17(14) used K sway =2.2

I agree with the K=2.2 approach. The intent in looking at the Pu/Pc ratio is to assess how much member flexural stiffness is lost as the applied axial load approaches the critical Euler buckling load, where it would be zero. That process is only valid if the Euler load (and K) reflect the actual, expected buckled shape of the compression member. In a sway column, that means K>=1.0. Rational engineering judgment aside, 10.10.7.2 seems to say exactly that.

R10.10.2.1 talks about PΔ and stability index that is why i do not consider it is valid for non sway columns

I see where you're coming from but, frankly, that seems like a pretty weak form of justification. Consider that P-d and P-D are essentially the same phenomenon with the primary difference being merely where the designer has chosen to introduce nodes into the analytical model. Besides, if you're not going to apply 10.10.2.1 as the limit on non-sway member stiffness, then what do you apply as the limit? Surely you're not just allowing these things to be as slender as your calculator will allow?

Thou shall not covet thy neighbor's wife <> Go ahead and covet thy neighbor's girlfriend. Sometimes we gotta read between the lines to satisfy the intent of the provisions rather than just the letter of them.

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.

 

[Celt83]

I was under the impression we were talking about 10.10.2.2 which if you did a second order analysis has you run a non-sway magnification to capture P-d effects.

Agree that the 1.4 limit applies for sway and non-sway a like, the 1.4 limit takes over for the previous limit which I think was based on kl/r.

Open Source Structural Applications:

https://github.com/buddyd16/Structural-Engineering

 

[KootK]

I was under the impression we were talking about 10.10.2.2 which if you did a second order analysis has you run a non-sway magnification to capture P-d effects.

Got it. In that case I see and agree.

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.