Slender Concrete Columns in Sway Frames 2

[mrengineer]

Every time I have to design a reinforced concrete frame I have to wrap my head with duct tape to keep it from exploding. I am wondering which ACI method other engineers are using to find the magnified column moments in sway frames (non-linear second order analysis, or one of the 2 approxiate methods in 10.13.4). With regards to the non-linear second order analysis referred to in 10.10.1, does anyone just use a simple P-delta analysis available in such programs as RISA, or is that not sophisticated enough? How is everyone handling the requirement that beam moments be increased by the amount of the magnified column moments? Any thoughts on any of this would be appreciated. If you lie, cheat and steal your way thru concrete column design, I would love to hear about whatever shortcuts you are taking.

 

[JAE]

The process that I have used in the past is based on the language in ACI 10.10 (I think that's the paragraph) - where they essentially say that you HAVE to do a full blown "rational" second order design UNLESS you use their approximate methods (delta magnification).

If you model your frame with end joints only, such as the following model:

j========j
| |
| |
| |
| |
j j

and run a Pdelta analysis, you will ONLY get the primary second order effects due to frame sway. What the ACI code requires, though, is a full consideration of ALL second order effects.

There are two sources of second order effects.
1. Frame second order effects (Pdelta due to the beam end joints swaying sideways and the axial load causing an additional moment on the frame).

2. Member second order effects (Pdelta due to curvature in axial loaded members along their length)

Both of these are affected by loss of stiffness in the columns and beams due to cracking.

So I model the beam as a full, single member (like the sketch above) but I model the columns with 1 ft. little segments (lots of joints along the length).

I run a first order analysis and verify, at service loads, whether any sections have cracked, calculating Mcr considering axial load effects on Mcr (compression elevates the Mcr).

Then, I adjust the A, Ix of the beams and columns and cycle through the analysis again, until I get convergence.

Then, I run the factored combinations and get full Pu and Mu values and design the column (no use of delta's are necessary as they are in the model).

The numerous joints along the length of the columns create little Pdelta effects as the RISA program uses the deflected position of these joints for the subsequent runs until the interation stops. This successfully models the full second order effects.

Sounds like a lot of work, but compare that to the head exploding duct tape method of the ACI deltas and I'd take this every time. With the ACI method, you have to calculate a delta for each member, under each load combination - this results, sometimes, in hundreds of deltas in a single model.

One last warning, though; ACI also added a statement in Chapter 10.10 saying something to the effect that this "rational analysis" must be backed up with tests. I've called various experts on this and no one seems to know what this means in actuality.

 

[shepherd]

JAE-
Do you find that your second source of second order effects (member curvature) to be significant in a sway frame? With typically no transverse loads on the columns, doesn't the end moment usually control?

I've also searched for explanation of the requirement of 10.10 that states "...refined second order analysis procedure should have been shown to predict ultimate loads within 15 percent of those reported in tests...". If anyone has insight on this, I'd love to hear it.

Regards,
Shepherd

 

[JAE]

I've never done a study of comparing the two Pdeltas to see what the relative magnitudes are. But even without lateral forces on the columns, there is still a curvature that does occur. And since multiple joints along a column are really not that hard to deal with, I just do it to "be rational".

In RISA, I set the number of sections to output to 2 so I just get the end Pu and Mu at each 1' segment - keeps the output smaller and easier to coordinate.

 

[JedClampett]

I've never used it and hope to never use it, but at least there's an example in the "Notes on ACI 318-02 Building Code Requirements for Structural Concrete" by PCA. It's Example 11.2 and takes 12 pages to design two columns. They do some comparisons, however.

 

[haynewp]

JAE, do you know if you still have to use your proposed method with the new RISA version that has concrete capability? I assume you are using an older version and inputting in a user defined shape to model as a concrete column?

 

[JAE]

Honestly, although we have the RISA Concrete version, we have not yet utilized it on a project so I just don't know. I do know that they have yet to put in flanged beam design so even if you have a beam integral with a floor slab (almost 99% of building beam designs) you can't use any T-beam design feature which makes it useless until they get it in there.