another ACI slender column question 3

[Lion06]

I am having a bit of trouble checking some slender columns. ACI really only gives guidance for columns that are a part of frames. How do you approach a column that is truly a gravity only column? I have a P.C. column that is supporting a WF that bears on top of the P.C. column and is not rigidly attached. The only end moments are due to the minimum e of 1" and I can't imagine this qulaifies as a frame. I was thinking I could just treat it as a non-sway frame anyway (since it is not a lateral column), but the problem I am having is that my kl/r>100 (107), which means I need a true second order analysis (I can't use the ACI method), but this column is not actually part of a frame so I am having trouble figuring out how to do a true second order analysis.
Any guidance here would be greatly appreciated!!

 

[WillisV]

Move the top of the column over the 1" in an analysis program to capture P-delta effects (e.g. analyze as a sloping column), split the column into 4 or 5 segments over its length to capture slenderness (little P-delta) effects, and run a 2nd order analysis on it. This will give you the moments required for design and meet the intent of ACI.

 

[Lion06]

willisv-
MUCH APPRECIATED. I see the reason for the 1" movement of the top of the column (Is this a seemingly arbitrary, assigned story drift?). What is the reason for breaking the column into 4 or 5 parts (wouldn't the P-small delta effects be taken care of with the second order analysis?)?

 

[WillisV]

Structural EIT - 1" was from your minimum eccentricity calc - the movement would be whatever you calculated that to be. It depends on the abilities of the program you are using (its actual beam element formulation) as to whether or not it will take into account the slenderness of the column within its second order analysis. Splitting the column into multiple pieces forces the program to take into account slenderness effects even if the program doesn't have that advanced capability built in.

 

[Lion06]

Moving the topof the column would be comparable to a drift. I was thinking I would account for the 1" e by applying a moment at the top and bottom of the column.
I have tried modelling the column in 4 pieces and running a second order analysis on it with equal end moments in single curvature and I am getting smaller moments in the middle of the column - that is completely baffling me.
I am using RAM Advanse - it allows me to input a cracked factor for the concrete.

 

[WillisV]

Modeling the eccentricity explictly rather than as a moment gives the program a perturbation to run its second order analysis on (it gives it the "delta" part of the P-Delta).

 

[Lion06]

but I can't specify the 1" e. If I move the top of the column by 1" it will still apply it at the center of the top of the column. It will get an e as it works its way down the column, but won't get it at the top or bottom (for the reaction).
You do have to assume the e at the bottom as well, right?

 

[271828]

Make a 1" long rigid link at the top of the column and apply the load to it.

To get P-(LittleDelta) effects, give the volumn some sweep also.

 

[haynewp]

How do you plan on including the "material nonlinearity and cracking" required by 10.10.1 in the analysis?

 

[271828]

Hopefully with such a tiny eccentricity, there won't be any tensile stresses. Actually, thinking about it now, 1" is less than the column dimension divided by 6, so I think that means that there's no tensile stresses for this particular column, right?

One question. KL/r=107. What L did you use? I don't have my Code in front of me and it's been a while, but can't you use the clear distance for L? Hopefully you used the centerline dimension and KL/r<100.

Reading back through the thread, I don't agree with just moving the top of the column over 1". You need to use a 1" long rigid link at the top and bottom. Use a pin restraint at the bottom one and apply the vertical load at the end of the top one, so you have a constant 1" eccentricity over the entire column. Break up your column into several segments, using trial and error to see how many are required, probably 5-6. Then run your 2nd-order analysis and get your design forces.

Check to make sure that no part of the section has a stress exceeding the modulus of rupture (shouldn't be a problem). If there's cracking, then change Ig to Icr and re-run the 2nd-order analysis. The next step up in rigor is an event-to-event analysis changing Ig to Icr after each load step that results in a little part of the column cracking. I can't imagine anybody doing this, though, LOL.

 

[Lion06]

tunacan-
I was accounting for this by using a cracked factor that incorporated both factors into it.

271828-
This Precast column sits directly on a footing and has a WF riding over top of it. I took the unbraced length as the bottom of column to the top of column - I don't think I can reduce this at all.
Do you see a problem in modelling it with axial loads and end moments?

General-
My intent was to get the moment from RAMAdvanse (using the second order analysis), and design the reinforcing in PCA Column as a short column with the second order moments already added in. Does this seem reasonable?

 

[271828]

There's no problem modeling it with axial loads and end moments. The end moments will cause deflections along the member so you can capture your P-(Little Delta) effects, which are the only 2nd-order effects you'll care about.

Your last paragraph makes perfect sense to me.

 

[WillisV]

Agree with 271828 - for this gravity only column as long as you split the column into enough segments to properly capture slenderness effect magnification you should be fine modeling with axial load and end moments. Checking using that load & moment and PCA column is good to go. Offsetting the column as I talked about previously would also apply the correct moments but there is really no need to do that.

 

[Lion06]

271828 & willisv-
I appreciate both of your help. Can either of you tell me the significance of breaking the member into 4-6 pieces? I know both of you said that this would capture the slenderness effects, but if these 4-6 pieces are rigidly connected how is it different from using one piece? Also, if a program offers a second order analysis wouldn't this take the slenderness into account? What kind of second order anaylsis could it do that wouldn't take slenderness into account?
I was applying a modified cracked factor to a (roughly) equivalent square section (RamAdvanse doesn't offer round sections for RC columns). This cracked factor was the 0.25 shown in ACI and modified to get the square section down the the circular section. I assumed this would also take care of the Ec modification (RamAdvanse doesn't let you play with that either).

 

[271828]

When the program runs a second-order analysis, it monitors the change in nodal displacements, not internal member displacements. There are different types of member stiffness matrices, but it's usually important to create several internal nodes along the member.

 

[271828]

Oops, forgot to answer this one:

"What kind of second order anaylsis could it do that wouldn't take slenderness into account? "

Hmmm, I can't think of one. There are two basic types of second-order analyses: geometric nonlinear analyses and material nonlinear analyses, although they might go by different names than that in some circles. Geometric nonlinear analyses take into account nodes moving by considering equilibrium of the deformed geometry. Material nonlinear usually consider geometry effects, but also consider plastic hinge formation, changes in MOI (like Ig -> Icr) as load increases, etc.

It would be possible to consider material effects, but still consider equilibrium of the undeformed geometry, which would do what you asked about. I've never seen this done, though.

Usually the geometric nonlinearities are accounted for using geometric stiffness matrices. Some use these on the element level, but some do it on the system level. Some iterate and some don't need to.

Material nonlinear analyses can be done different ways, but the easiest to explain is event-to-event. Add load until properties need to change, then re-formulate the stiffness matrix, add more load, etc. until all the load is there.

Large displacement analyses, like the ones for cables, are another step up from these. These are really hard to understand, IMO, and use various schemes.

Probably a lot more than you wanted to know! It's a really interesting subject, usually covered in a second semester matrix analysis class.

 

[Lion06]

271828-
second star from me. That clears it up - Thank you!!