Designing Columns for Concrete Buildings

[Stazz]

I'm designing a 15 story post tensioned building and I'm trying to design the columns in Risa Floor. I'm just wondering what the standard practice is for considering moments from the slab in the design of the column.

1) I want to design the columns as axial compression members only but I know the slab will put moment into the columns. Is this a standard assumption that I am required to make and design for?

2) When I model the floor I connect all the columns with fixed-fixed beams so that the columns will suck in moment in the Finite Element analysis.

- Will this put too much moment into the columns? I have a 3 span condition 13'-27'-13' so theres a lot of unbalanced moment from the dead load alone.

4) If what I'm doing is overkill for the moment, do you model the slab moment connection as spring, and how?

I have slab cantilevers too. Does anyone have the magic bullet for designing these quickly. Thanks!

 

[rapt]

Stazz,

The only PT effect put into the columns for ultimate design is the secondary effects. You cannot reduce the loading by the balanced load as the PT puts a vertical force into the column as well as uplift forces between columns, giving a nett uplift effect of ZERO (gravity still exists and PT is not a skyhook!

The total vertical force going into the columns in DL + SDL + LL all factored + PT Secondary.

PT secondary reaction for the whole floor is ZERO.

So the vertical loads in the columns are the same with/without PT except for some very minor redistribution between columns. Yes, the moments will normally be reduced by the secondary prestress moments, which are significant for end columns.

RE restraint effects, they are maximum for the bottom couple of floors and the roof. They can be much small for the floors between, depending on the stiffness of the end columns or if there are multiple cores. You cannot make a general statement on this.

 

[rowingengineer]

In a PT slab, some engineers would take Ieff=Ig as you suggest. Other engineers would suggest that this be lowered due to restraint effects, for deflection calculations.

Arguing with an engineer is like wrestling with a pig in mud. After a while you realize that them like it

 

[Stazz]

rapt, I'm on the same page, to design the columns I used the axial load from load case DL+LL and I used the moments from load case DL+LL+PTsecondary.

 

[KootK]

Rapt,

Concerning your statement:

"RE restraint effects, they are maximum for the bottom couple of floors and the roof. They can be much small for the floors between, depending on the stiffness of the end columns or if there are multiple cores. You cannot make a general statement on this."

I haven't heard this before. For the lower floors, is it because of the proximity to the foundations and lateral support at grade? What's the rationale for the roof?

Thanks,

KK

 

[rapt]

KootenayKid,

I should have split the restraint effects up a bit.

For shrinkage and temperature shortening and PT shortening, the lower floors are affected badly because there is no movement possible at the foundations. The stiffer the edge supports, the higher up the building this goes. If you have end shear walls, it could be a reasonable height up the building. You would have to analyse the full building for a shrinkage effect to find out hoiwe far up the building is affected.

For PT shortening , the roof is also a problem, depending again on end support stiffness. For lower floors, when you stress at a floor, restraint from the columns below reduces the amount of PT axial force that goes into that floor. But the restraint is caused by the the columns reacting against the floor below, so the axial force that is not going into the current floor gors into the floor below (except for its restraint again), making up for much of its own loss when it was stressed.
For the roof, there is no floor above to be stressed, so it does not get back some of its lost force as the other floors do.
The bottom floor does not get much back because the foundation restraint is so large.

 

[rapt]

Stazz,

The secondary reactions should also be included! The secondary moments are caused by column reactions to the prestressing!

 

[asixth]

rowingengineer

If you are going to design saying that Ieff=Ig (or that Ieff/Ig=1) then you should check to ensure that the section never exceeds it's cracking moment. Every research report or technical document that I have ever read all show a graph plotting deflections versus moment. They all exhibit linear behavior up to the cracking moment and then display non-linear deformation behavior post-cracking.

I make this assumption (Ieff=Ig) when designing prestressed girders (using high performance concrete as you know) but I ensure that at every point along the girder the cracking moment is never exceeded.

Attached is another paper for your collection.

 

[Stazz]

Rapt,

What secondary reactions are on the columns? I'm just assuming moment reactions (M) from eccentrity of the tendons. Don't most of the Fx (horizontal) reactions get absorbed by the slab? and Fy (vertical) reactions are not existant as they disobey the laws of physics (If they push the column down then there must be an opposite and equal force pushing the building up.

Asixth,

Ig is the moment of inertia of the section with only concrete and no steel considered. I think what you meen is that Ieff=I ("I" being just "I" and only "I" with no subscipts because it is the true moment of inertia of the section considering the steel). I'm arguing that Ig is aproximately Ieff for most ranges of cracking. When I visualize a rectangular cross section of just concrete and then juxtupose the same size rectangular section minus the cracked portion plus transformed steel, then the section I feel would have a similiar moment of inertia.

 

[OzEng80]

Stazz

I think you need to put some real numbers to your Ief statement.

The Australian code has a couple of simplified formulas that may help you get a better feel for the large reduction in stiffness.

For reinforced rectangular sections

Ief = (0.02 + 2.5p)bd3 where p < 0.005 (percentage of tensile reinf).
&
Ief = (0.1-13.5p)bd3 where p > 0.005

This results in (approx):
(p = 0.5%) Ig = 0.39 Ig
(p = 0.75%) Ig = 0.465 Ig
(p = 1.0%) Ig = 0.54 Ig
(p = 1.5%) Ig = 0.69 Ig

These are obviously conservative (deemed to comply) but you can see the trend.

Hope this helps.

Rapt - your use of columns to tension lower stories of buildings is impressive! Might be able to utilise this principal to upgrade existing buildings! What would happen at a 'soft story' ie discontinuous shear walls etc..? Haven't got my head half way around all the restraint issues!

 

[rapt]

OzEng80,

Those cracked figures are for flexural members, so no axial compression has been allowed for. The Ief figures would be a lot larger in a column where there is axial compression, and in a 15 storey building, at the lower floors the columns would be in compression under vertical loads, so no cracking. and Ief = Ig.

RE the prestress effect when stressing, it is simple statics.
Actually, the upper floor prestress compresses the floor below if there is restraint from the supports below the floor being stressed!

 

[rapt]

Stazz,

We are talking about Prestress Secondary moments aren't we! I assume you know the difference between the full prestress moment (Mp below) and the prestress secondary moments (Msec below)! The prestress moment is not just the eccentricity moment P * eccentricity!

Mp = P * eccentricity + Msec

Wherever there is a moment in a frame, there is a shear and therefore a reaction.

The Msec moments are actually caused by column reactions stopping the slab lifting off the columns under the prestress forces because they are connected to the columns.

The secondary moment case puts moments and reactions into the columns. The total of the prestress reactions for a member or a floor is zero so there is no net vertical force generated, but there is a rearrangemenmt of column reactions due to these forces.

So each column gets a Mp and an Rp from the prestress which needs to be included in the column forces. Note that Rp is normally realitively small compared to the other reactions.

 

[rowingengineer]

OzEng80 & asixth,
Note we are discussing a post tensioned building,what the P/A is I have not idea, but the Ig for a Pt slab after cracking is different to a reinforced beam.

I would never design a pre-stressed slab to crack under service loads, would be counter productive. also after cracking the PT slab behaves in a completely different manner compared to a reinforced slab. The restraint and temp effects may cause some cracking and a reduction in Ieff (I like to use about 0.7Ieff for slabs), but i will let other argue that point.

If you are however concerned that you may get different moment at ultimate state due to cracking of the concrete, generally this would only be of consequence for torsion beams thus i wouldn't get all that worried for a beam and slab arrangement due to cracking of the concrete.

asixth,
Thanks for the paper, but his book is a better read.

Arguing with an engineer is like wrestling with a pig in mud. After a while you realize that them like it

 

[asixth]

which one, prestressed concrete or time-effects in concrete structures. I was looking through the later a few weeks ago because I am trying to develop a spreadsheet for prestresses concrete bridge girders and I can't find a good example of time-history long-term calculations in other texts.

 

[rowingengineer]

never opened the pre-stressed concrete, guess i got the warner et al book and stopped looking for other references for aust design but time effects in concrete is worth the money in my humble opinion.

Arguing with an engineer is like wrestling with a pig in mud. After a while you realize that them like it

 

[rapt]

rowingengineer,

"I would never design a pre-stressed slab to crack under service loads, would be counter productive. also after cracking the PT slab behaves in a completely different manner compared to a reinforced slab. The restraint and temp effects may cause some cracking and a reduction in Ieff (I like to use about 0.7Ieff for slabs), but i will let other argue that point."

Most PT slabs designed in Australia over the last 35 years have been designed to crack, at least at the critical sections. It is not economical to design PT slabs as uncracked and their performance is far better than RC slabs.

How do they act in a different manner to RC slabs after cracking and why is it a problem?

Yes, Time-effects in Concrete Structures is a great book, but I thought it was out of print!

 

[rowingengineer]

Rapt did you read this part "under service loads" ie for deflections not ultimate calculations, or maybe i wasn't clear.

no problems with the way concrete cracks I was just pointing out that the %Ig value given by OzEng80 are not applicable to post tension slabs.

"Time effects in concrete" is ou of print is news to me, but i did buy mine a while back.

Arguing with an engineer is like wrestling with a pig in mud. After a while you realize that them like it

 

[KootK]

An excellent, modern book on time-dependent effects in concrete structures is:

Concrete Structures - Stresses & Deformation
Mamdouh M. El-Badry

I had the good fortune to take a class from Dr. El-Badry. The methods presented in his book represent the state of the art and are a considerable improvement upon the methods traditionally used.

I don't mean to take anything away from Gilbert's work of course. I revere the classics as much as anybody.