sway frame - columns design 2

[ZoranB]

As far as I can figure it, there are two ways to design slender columns in sway frames.

** 1st:
ACI-318 10.11.1
Generaly slender columns could be designed using magnified first order moments.
It shell be permitted (in the absence of more accurate methods) to use moments of inertia reductions: 0.35 for beams and 0.7 for columns.

Correct me if I'm wrong: I can reduce stifnesses of frame members and perform linear, FIRST order analysis.
Obtained forces (factored) I can use for cross-section design (after magnification?).

** 2nd
ACI-318 10.13.3
The moments M_1 and M_2 at the ends of column shell be calculated according to:

M_1 = M_1ns + delta_s * M_1s
M_2 = M_2ns + delta_s * M_2s
where:
M_1s - factor end moment on a compression member at the end at which M_1 acts, due to load that cause no appreciable sidesway, calculated using first order elastic frame analysis (Sway moment)
M_1 - factored end moment

Question:
How to get M_1ns and M_1s?
I understood that non-sway moment results from a vertical load and sway moment from a horizontal load. What if I have load which acts vertical and lateral? Should I split it into two loads and use only vertical component for the M_1ns and horizontal for the M_1s, or should I use complete load to calculate just M_1s?

ACI-318 10.13.4.1
The magnified sway moment (delta_s * M_1s) shell be taken as the column end moment calculated using SECOND order analysis based on the REDUCED member's stifness (10.11.1 - stated above).

What does it mean?
Doesn't that assume that I performed a SECOND order analysis of a whole loading (vertical and horizontal)?
If it does, isn't it in contradiction with 10.11.1 where it is noted that one can use FIRST order analysis with REDUCED stifnesses?
Additionaly, I shell magnify that moment using non-sway procedure (delta_ns):
delta_ns * (M_ns + delta_s * M_s)

SAP2000 uses this (2nd) procedure. It calculates sway and non-sway moments using P-delta analysis (kind of second order analysis), but it does not reduce member's stifness. Is it allowable?

The differences obtained using these two procedures could be drastic. Second procedure reduce stifnesses, calculates second order moments and magnify them.
I'm sure I misunderstood something. Can you help me?

sorry for long question
thanks

 

[JAE]

ZoranB

The two "methods" that ACI allows are:

1. A complete second order analysis taking into account material non-linearity, cracking, member curvature, drift, shrinkage, etc.
This is a complete, thorough analysis and design that does NOT use any delta factors or other kinds of magnification. It is outlined in ACI 10.10.1.

2. An approximate method where the designer is allowed to use first order moments and magnify them under certain rules.

All of your comments are based on the second method, using magnified moments which are outlined in 10.11 through 10.13.

With a sway frame, you are primarily dealing with 10.13. Note that 10.11.4.2 gives you a method to determine whether your frame is sway (10.13) or non-sway (10.12).

If it is a sway frame, then, under 10.13, you need to determine non-sway moments and then sway moments. How you divide your forces to get these two different moments can be dealt with in two ways.
A. Identify the load CASES which tend to be primarily vertical and consider them as non-sway. Identify the load CASES which tend to be primarily horizontal (wind, seismic, lateral soil) and consider them as sway forces. Get moments from each and utilize them in the ACI provisions as sway or non-sway moments.

B. If you forces are a bit confusing in terms of sway/non-sway, some engineers will place imaginary lateral supports at each floor, and run each and every load combination (factored), getting moments in the frame which are then identified as non-sway moments. Then, get the REACTIONS at each of the imaginary supports for each combination. Then re-run your model for each combination without the supports, but with these reaction forces at each level applied in the opposite direction. This will produce a swayed condition, with the resulting sway moments.

Now, it gets a little sticky. You are correct that 10.13.3 defines M1 and M2 moments as a combination of the determined non-sway moment (M_ns) PLUS your determined sway moments factored by delta_s (delta_s*M_s).

The value of delta_s*M_s can be calculated by your choice of THREE methods:

Method 1 (ACI 10.13.4.1) - Perform a SECOND ORDER analysis to find M_s based on the reduced stiffnesses in 10.11.1

Method 2 (ACI 10.13.4.2) - Using your M_s from A or B above, calculate a delta_s*M_s using the Q factor from 10.11.4.2.

Method 3 (ACI 10.13.4.3) - Using your M_s from A or B above, calculate a delta_s*M_s using the older equation from previous ACI 318-89.

Note the limitations on delta_s*M_s given in 10.13.6

All of the above was taken from ACI 318-99.

Hope it helps.

One comment: The ACI concrete design method has gotten more and more complex over the last 20 years or more. We engineers should complain. Note that each delta factor is based on M_s and possibly other axial loads for EACH LOAD COMBINATION. Therefore, for each load combination, there is a different delta.

 

[ZoranB]

Wow. I haven't expected that specific answer.
I don't know, is it possible to give someone more than one star for a tip? I'll try.
Anyway, thanks. But, still there is something more.

First, YES, I forgot to note that I'm dealing with approximate methods of sway frame columns design.

Let's concentrate at the following method:
> Method 1 (ACI 10.13.4.1) - Perform a SECOND ORDER
> analysis to find M_s based on the reduced stiffnesses in
> 10.11.1

If one uses second order analysis, why is it necessery to split the total moment into sway and non-sway? I understood that delta_s equals 1.0 in that case.

When M_1 and M_2 moments are determined, why should I additionaly magnify them AFTER (already) reducing members stifnesses and performirng second order analysis? Isn't there too much security?

Please, tell me your opinion abuout that procedure SAP2000 performs using non-reduced stifnesses.

Finally, I must agree with you. Codes are too complicated. I mean (especially) in term of their programmability.
Not only the huge number of possible load combinations, but two directions in 3D structure, could be a real nightmare.
I'm not professionaly oriented to ACI, since I'm from Europe and we use EuroCodes. But, complains are the same.

regards

 

[JAE]

Your first question, why you need to split the moments into sway and non-sway when you perform a second order analysis from 10.13.4.1.

I don't know. I would guess that the ACI committee felt that since the Mns moments did not involve sway, and therefore Pdelta effects, then a second order analysis for that was illogical. What this forces you to do is lump the non-sway loads onto the column ends (to avoid developing M_ns effects in your second order analysis). You also must include all other axial loads in your second order analysis which are from all other columns in that story that are NOT part of your lateral resisting frame. This creates a model where you have very high axial forces (which you don't actually use) and magnified end moments delta_s*M_1s.

Your second question - I think I know what you're asking. If you run a second order analysis, and get from that analysis column end moments - they equal delta_s*M_1s. There is no further magnification. You simply add these moments from the second order run to the non sway moments. the "delta" is already included in the moment. You don't have to further calculate a delta and multiply.

I don't know anything about SAP2000. But I would think that you could by-pass all of the magnified moments and use your computer to determine your member forces per 10.10.1 which is the full second order analysis. The only problem with this is the last sentence of that section which makes a vague statment regarding validating your procedure with tests. I've called a number of professors, engineers, etc. and none seem to know what that means.

In the past, we've modeled our frame columns by breaking them up into many smaller members. You would have a beam represented by a single member, spanning from column to column. The length of column between stories, however, would be made up of perhaps 10 or 12 short members. This creates multiple joints (or nodes) which are represented in your stiffness matrix, deflect laterally during your analysis, and fully represent not only the story Pdelta effects, but also the slenderness column Pdelta effects. You can also adjust the stiffness of the column along its length to represent different degrees of cracking and stiffness. This is a lot of work, though.

 

[ZoranB]

thanks again.

> Your second question - I think I know what you're
> asking. If you run a second order analysis, and get from
> that analysis column end moments - they equal
> delta_s*M_1s. There is no further magnification. You
> simply add these moments from the second order run to the
> non sway moments. the "delta" is already included in the
> moment. You don't have to further calculate a delta and
> multiply.

Yes, it seem reasonable, but...
ACI 10.13.5 says that if slenderness high enough, column end moments (calculated according to 10.13.3, which means that they could be calculated using exact second order analysis) should additionaly be magnified using delta_ns.

 

[JAE]

OK, what about this:

You're right that the "M" from section 10.13.3 INCLUDES a delta magnification. I understand that delta to be a magnification which accounts for second order effects due to lateral story sway....in other words, overall displacement of the entire floor and the resulting second order effects that are produced by that P and that delta.

Now the commentary to 10.13.5 indicates that for more slender columns, the maximum moment will tend to be in the center portion of the column as opposed to the ends of the column. When this happens, there would be additional magnification due to the dislocated shape of the column along its length. This creates an additional second order effect that varies with the slenderness of the column and the magnitude of the axial load relative to the Euler buckling load Pc.

So you have a MACRO Pdelta that deals with story to story deflection (sway) and you have a MICRO Pdelta that accounts for the deflected shape of the column along its length.

Thus, for a slender column in a sway frame, you would have both types of moment magnification. The sway magnification would be accounted for in 10.13.3. Then, the slenderness magnification would be accounted for in 10.12.3.

Sorry for the long drawn out verbage, but this helps me sort through ACI as well and I appreciate the opportunity to discuss it. If anyone else would like to weigh in and/or correct any mis-application, please feel free.