Interpreting ACI Frame Design 3

[KootK]

I'm working on my first concrete building. It's a five story moment frame and has an odd geometry that precludes the use of simplified methods (ACI 8.3.3). The building is shaped like a square with chamfered corners on one side.

I have numerous questions regarding the analysis approach that should be used in the analysis of this building. If anybody could help with any or all of them, that would be great.

Question #1

ACI 8.8.4 says

Resistance to moments at any floor or roof level shall be provided by distributing the moment between columns immediately above and below the given floor in proportion to the relative column stiffness and conditions of restraint.

ACI 8.9.1 says

The live load is applied only to the floor or roof under consideration and the far ends of columns build integrally with the structure are considered fixed.

Does that mean that I only load one floor at a time when determining col & beam moments? Also, does it mean that I pretend the cols above and below the floor are fixed as in "rigid support" or merely fixed to the members that they frame into. If it is the latter, then wouldn't I still have to calculate the moments from all the other floors to determine how much gets transfered into the floor that I'm working on?

Question #2

ACI 8.9.2 says to design to the worst case given by:

Factored dead load on all spans with full factored live load on two adjacent spans and factored dead load on all spans with full factored live load on alternate spans and factored dead load on all spans with full factored live load on alternate spans?

That's fine in two dimensions but, how do I apply it in three dimensions? Would that not require the use of several permutations of loading? Also, I've build a complete computer model of the structure. If I need to use this method, then I will have to basically build a new set of load cases for every single beam. If that's the case, then why even bother with a model.

Question #3

ACI 10.11.1 makes recommendations on what moments of inertias to use in the design of columns. What guidance is there on what moments of inertias to use for getting the maximum moments for beams? Also, what "I" values should be used for the lateral analysis.

If you've read this far, thanks for your patience. Please advise.

 

[LPPE]

Excellent questions. Use steel instead.

Sorry, not the answer you're lookin for. As for question #2, you must skip load the frame to get your worst case scenario. I would analyze a typical frame in one plane of the building, then another perpendicular to that one. That may take the dreaded third dimension out of your equation. However, if you already have a computer model, would it be that difficult to skip load bays? Your results may prove interesting.

 

[whymrg]

Questions 1 & 2: If you read Sec 8.9 ACI it says: "it shall be permitted..." This is for simplified analisis you may do on back side of used envelope talking to foreman at job site. If you have computer model, do not worry about it. Load all floors at the same time, or part of floors according to your judgement.

Question 3: According to 10.11.1 ACI Moment of Inertia for Beams equal to 0.35*Ig.

I hope it helps.

 

[ishvaaag]

I have not the vigent ACI code, but is obvious as the first answer points the specifications for moment distribution are of a simplified method.

Event Deans of Sstructures courses in Madrid state (I have heard it at a conference) the alternance of loads be non required -as long as no important difference between the spans is present. In any case, when I have had and wanted to meet this clause in 3 D I do hypotheses for bands and checkered loads.

Then, even the use of simplified reduced inertias to model material nonlinearities is subject to some restrictions in the intended structure, so ensure you have read properly if the simplified method of reduced inertias can be applied to your case.

The situation is not very dissimilar in Spain, once exceeded the simplified models one enters one unknown code realm, and one must rely purely and simply in extant structural design knowledge.

 

[JAE]

Agree with above....the ACI provision for fixing the far ends of columns really comes from earlier days when computer programs were definitely 2D and limited in scope and affordability. With your 3D model, just go ahead as you planned.

For alternating loads, most codes require you, as the engineer, to consider the fact that loads will not always be uniform. Thus, whether 3D or 2D analysis is used, you must take alternating live loads into consideration. Your model could include the following live load cases:
1. Checkerboard pattern on each floor
2. Another checkerboard pattern, just on opposite bays.
3. Adding 1 and 2 above gives you full live load.
4. A striped loading pattern on each floor (similar to stripes on the American flag) with each stripe taking up two bays to get an adjacent loading.
5. A similar pattern to 4 above, but with the stripes shifted one bay
6. A similar pattern to 5 above, but shifted over another bay.
7. Repeat 4 thru 6 above only in a perpendicular direction.

This seems rather intense, but to truly consider the alternating bay loadings you need to do something like it.

For lateral analysis, the moments of inertia given in the ACI code are approximate effective values which take into account compression in the columns (which increases Mcr and therefore increases Ie). The ACI code limits you to two methods - a rational analysis or the approximate moment magnification method.

The rational analysis is what you are attempting. Technically, you need to read through section 10.10.1. This requires you to include in your model a second-order analysis, material non-linearity, cracking, effects of member curvature, lateral drift, load duration, shrinkage and creep, and foundation interaction. The last sentence in that section requires you to ensure your approach is consistent with comprehensive tests....whew!

We've attempted to do this in the past by underestimating the Ie of the columns (similar to the .7 x I used in section 10.11.1) which increases the lateral drift of the building, thus maximizing, conservatively, the Pdelta effects. We also model our columns by using short, 1 ft. segments (lots of joints in the model). This includes in your 2nd order analysis (assuming your program does this) the member curvature. If you just model columns as single members with a joint at each floor, you are not including Pdelta effects of the member curvature, only the story drift Pdelta...they are two different things.

Alternatively you can use the approximate moment magnification method given in 10.11, 12, and 13.

 

[KootK]

Thanks guys. In case you end up looking at this thread again...

In all honesty, this is my very first concrete structure outside of the work I did at school. Unfortunately, all of the examples that I looked at at school were glorious rectangular structures with evenly spaced bays.

The building that I'm working on can basically be visualized as three concentric rings of pentagons. In addition, there are transverse beams connecting the corner points on each ring.

The probem that I'm having is that I'm not sure how to apply skip loading when 1) No two bays of the frame are in the same vertical plane and 2) The two directions of framing are not orthogonal to one another.

My office sensai has instructed me to treat all of the beams and joists as simple span. In that way, we hope, the amount of positive moment calculated will exceed whatever would be present in the continuous framing scenario of the real world. Then, for negative moment, we use the amount of moment that would correspond to the amount you would expect if you had that much positive on a beam with fixed supports. Then, we transfer that moment to the columns accoring to relative stiffness assuming that they are pinned supported at their far ends (to draw max moment into the joint under consideration).

It this what other people are doing for oddball framing situations where the logic of pattern loading is not all that clear cut?

 

[ishvaaag]

The thing of all positive moment plus correspondent negative seems to me exaggerate and I don't think anyone is doing this, nor I see it proper. A 3D analysis by whatever assumption should be far better than that. Some banding and checkering may be possible in the different floors; do pairs: whatever you don't put in one, put in the other.
If you feel not confiden in having caught the worst scenario, do other set.

And try to ensure you abide by one of the simplification modes, the rational method may be guessed by some sources, but prequalified as the simplified is not.

 

[KootK]

Thanks ishvaaag. I know what is meant by checkering but I am not sure that I know what you mean by "banding" or using "pairs". If you see this, could you explain a little further? I think that these concepts may be useful for my project. Thanks.

 

[ishvaaag]

Banding, err, my english: using bands: one band loaded, the other no. You can do this by concentrical zones.

Pairs...of load cases: in one checkered, more or less one loadcase would cover half the floor, then the other the other "half". And the same with the "band" load cases.

This is to ensure the intended alternation of loads towards different direction is described in your model; otherwise you would cover the higher loading towards on side, but not the other.

 

[KootK]

Thanks JAE. You're gonna have to send me a bill or somethin'. One last little thing. In analysing the column moments/beams of a particular floor, can you just assume that that is the only floor being loaded. Or do I need to apply the pattern loads that you discussed above to all of the floors simultaneously?

 

[JAE]

AdamP - With your 3D model, you essentially need to include the Live Load with all floors patterned at the same time. (That's what I would do anyway). The checkered pattern would just be opposite down every floor. With 5 stories, your column at the first level would be designed for all the upper floors above.

A couple of things to know: First, the codes allow a live load reduction based upon the tributary area. Thus, your lower columns may allow a greater reduction than your upper ones. This is a bookkeepping headache and may mean that you have to use a special reduction load factor on live load and vary that, running the model a number of times for each column level....or you can just manually adjust the live load axials and moments.

Also, you'll find, in a 3D model, that the upper, corner columns tend to require more reinforcing than the lower corner columns. This is due to the higher bending moments and lower axial forces in the higher levels...pushing your design point way out on the interaction curve. We always balked at detailing more rebar above than below so we just went with the worst case and used the higher rebar all the way down the column.