RE: Concrete Sway Column - Moments

[ooox]

I'm looking at the design of an unbraced column in accordance with the Australian code, AS3600. The frame is single span with a small cantilever at one end and I have assumed the base to be fixed.

The question I have is how do I determine the end moment at the top of the column? I have a large moment over the column at the cantilever, does this get factored down due to the relative stiffness between the beam and column?

 

[apsix]

1. You have to do better than assume the base to be fixed, you need to design the footing to provide a fixed base (which may not be easy).

2. A 2-D frame analysis will provide the column moments. Assuming that the large moment is due to the cantilever, then yes, it will be distributed according to relative stiffness. I would favour a conservative approach and assume all the cantilever moment is taken by the beam for the beam design.

 

[asixth]

It is a good question, the design of sway frames is something that I had trouble with when I first started out because I couldn't find any resources that where appropriate for the design I was doing at the time.

Your example, you say that you assummed the bases are fixed. Can you prove that the foundations can resist moment, for an embedded pile, I would say the base is fixed but I wouldn't be making that assumption for a pad footing unless the footing can be shown to resist the moment at the base. Being a single span, you are designing edge columns so all the negative moment in the slab at the slab-column joint will need to be transferred into the column, so the stiffer the column is (eg. fixed base versus pinned base) the more moment it is going to attract at the slab-column joint.

You will need to perform an elastic analysis to determine what the end moments of your columns are. I will assume that you are only designing for vertical loads at the moment but be mindful that lateral forces may indeed require you to increase the amount of reinforcement in your column. To design for vertical loads I would assume that the column remains uncracked and use the gross I value for design (even though you may be able to prove that the column cracks, loses stiffness and redistributes moment back midspan).

You will also need to make a valid assumption for the stiffness of the slab. There is a section in the code that will enable you to make an estimate for the effective moment of inertia based on the ratio of the service moment to the cracking moment. Going through this calc you may find the effective inertia of the beam to somewhere between 0.4 to 0.6*Ig.

You will need to determine what is the governing load case in which the most moment is transferred into the column. Because the cantilever will counterbalance the span, I would apply live load to both the cantilever and the span in separate load cases to see which load case creates the greatest unbalanced moment to be transferred into the column with minimum axial force (closer to the pure bending point on the interaction diagram). Once you determining the end moments at the top and bottom of the column, you can run through the code clauses to find the moment magnifier (should be one because the columns are in double curvature) and then design the column using an interaction diagram.

Let us know if you are having any trouble. There was a good post recently about what Ieff to use for reinforced concrete so you might want to do a search for that. I can post a diagram with the showing what assumptions you should be making with regard to stiffness.

 

[fa2070]

There was a good post recently about what Ieff to use for reinforced concrete so you might want to do a search for that.

asixth,
Are you talking of this post?

http://www.eng-tips.com/viewthread.cfm?qid=252848

 

[asixth]

fa2070

thanks, that was the one I was referring to.

 

[ooox]

asixth,

Thanks for your comments.

Would I be right in saying that the moment transferred to the column from the slab would then be:

Mcol = Mslab x (Icol/(Ieff slab + Icol))

Could you post your diagram on what assumptions should be made.

Cheers,
999

 

[asixth]

I don't think that analogy is right at all. It has been a long time since I have gone through the equations to calculate what moment is transferred into the column. If you just consider the slab, fixed-ended moments are w*L^2/12. So when the columns are very stiff compared to the slab the moment transferred into the column is w*L^2/12. i.e.

Mcol=w*L^2/12 when Kcol>>Kslab where K is the rotational stiffness (K=I*E/l^2) but it depends on other factors as well like far end restraint.

When the column is very weak compared to the slab, the moment transferred into the column is 0. i.e.

Mcol=0 when Kcol<<Kslab

What is Mslab that you are refering to, is it w*L^2/12? If so then your equation is semi-correct but the member lengths and the end-restraints will also contribute to the distribution of moment, it is not just dependent on I.

I will post a diagram shortly.

 

[asixth]

So I built up a frame 4000 high, 6000 long with a 1500 cantilever (13' high, 20' long, 5' cantilever).

I assumed a beam strip thickness of 350mm (14') and a column dimension of 400 x 400 (14'x14'). Reduced the stiffness of the beam strip by 50% to account for cracking and didn't reduce the stiffness of the column at all even though analysis will prove that the section has cracked and redistibution of moment has occured back to the span.

The total moment that found its way into the column was roughly 75% of w*L^2/12. Again, you won't be able to distribute moments based on I alone because there are other factors that will affect the stiffness of the beam and columns such as far end restraint and length.

 

[paddingtongreen]

nineninenine, no insult intended here, but I find it unsettling that you are trying to perform a statically determinate analysis on a statically indeterminate frame.

Understand that if you just distribute the cantilever loads to the beam and column according to their stiffnesses, you will be left with an unbalanced horizontal force unless you let the frame sway and the moments re-distribute around the frame. You need to run it through an analysis program.

I think one of the benefits of learning analysis before the computer arrived, using Moment Distribution for example, provided a greater insight to the behaviour of structures under load.

Timing has a lot to do with the outcome of a rain dance.