Post-Tensioned Beams Parallel to Slab 2

[MikeT14]

I'm designing a two-story parking garage using post-tensioned beams and slabs. It will be ordinary moment frames with three nominally 62' spans in one direction and 7-9 spans of between 22' and 32' in the other direction. My one-way slabs range in thickness from 7" to 9" and run in the short (22-32') direction.

My question is in regards to those 22'-32' beams running parallel to the slab. During a meeting with a PT supplier, they mentioned that you need to post-tension the beams parallel to the one-way slab to the same P/A value in the slab. I've searched though my mountain of literature and can't find a reference or guide to this situation. My question is this: How much slab do I consider in the design of those beams? Will I be accumulating prestressing if the slab is already prestressed to a P/A value and then I add more through the prestresssing of my beam?

Tech support at ADAPT stated that it didn't matter as long as my tendons were anchored at the CG for the tributary cross-section. Well, the tributary for my cross section is 31' or 62'! Should I just be using the area and CG of the beam itself? I'm worried that I will be introducing a significant moment in the beams if the tendons are anchored higher/lower than they should have been. As these beams aren't carrying a significant gravity load except selfweight (since they're parallel to the one-way slab), I'm concerned that they wouldn't be adequate if a moment did develop.

Any help or insight would be appreciated.

 

[haynewp]

"As these beams aren't carrying a significant gravity load except selfweight (since they're parallel to the one-way slab)"

What are the beams there for?

 

[MikeT14]

hayneswp,

They are the lateral force resisting system (ordinary moment resistant frames) for the direction perpendicular to the long 62' beams.

 

[haynewp]

You are planning on pouring the slab at the same time as the beams, correct?

 

[MikeT14]

Yes, as far as I know. Not as sure about the stressing schedule though, as the PT supplier will be responsible for that.

 

[haynewp]

I had written up a long reply but I just accidentally deleted it.

Anyway, I think you should design the beam as post tensioned (draped strands) with an effective flange width at on side per ACI or whatever your Code says. I am assuming your beams are only at the ends of the slab and none in the interior?

You can have some extra tendons without any drape running within the effective flange width if you are concerned about a minimum P/A. I think Adapt was implying you should anchor the tendons at the centroid of the beam+effective flange width (this is somewhere within the beam). I wouldn't just assume the beam is only taking its own self weight.

There will be some deflection compatibility issues between the beam and adjacent slab as you move away from the beam, but assuming there are no heavy line loads, I don't think it will be a problem.

 

[14159]

I don't know the technical answer, but the following is my idea:

Provide mild steel to resist a reasonable amount of tributary area and then...

For example, say the slab is designed to have P/A=200. Your drawings show enough tendons in the slab to create 200 for the entire slab, including the part of the slab within the ACI effective width, which is fictitious for a PT beam anyway. Now provide P/A for the rectangular part of the beam. You have approximately 200 everywhere in this case. Put the beam tendons at d/2.
DBD

 

[AUCE98]

MikeT14,

Mike, DBD is correct regarding the addition of pt tendons in the beams. The addition of the tendons is to ensure that the slab cross section has the correct amount of precompression with the presence of the perimeter beams.

AUCE98

 

[rapt]

MikeT14,

If the beam is there it will be stiffer than the slab and will support some of the slab load. The beam and the attached slab must deflect the sams amount for compatibility so the beam will attract some of the slab load.

In terms of the amount of PT required in the beam, you could put none in there if you want as long as you put enough reinforcement to provide strength to support the loads that the beam will attract and make sure that the slab parallel to the beam has sufficient P/A + reinforcement. The slab for about 6 to 8' on either side of the beamn will be supported by the beams anyway, not by the parallel slab, so if the P/A in this parallel slab is slightly reduced because some of the prestress force leaks into the beam it does not matter as the bending stresses in the slab are much reduced as the slab in this area is actually spanning as a 2way slab.

Design the beam as a standard T/L beam with the code flanges (I disagree with DBDavis that the effective flange width is fictious for PT beams, there are too many people designing PT beam/slab systems on the basis that the P/A completely averages over the full width including some stupid illogic put out by some PT software companies) and put the anchors at the centroid of that beam shape. Put enough PT in the beam for strength and serviceability checks but it does not have to exactly equal the P/A in the slab.

Also, the slab perpendicular to these beams will experience bending stresses and you will need to reinforce the slab in this direction with top reinforcement over the beams and possibly bottom reinforcement as well as you move away from the beams.

 

[MikeT14]

Thanks for the responses. The approach of designing the beam PT considering an effective width of slab is what I was planning on doing, but limiting the P/A to the rectangular area of the beam, not the effective flanges.

Adapt seems to anchor at the CG of the tributary cross-section, not the effective cross section. Which is right? Rapt, is this what you are talking about with regards to the P/A across the full width?

 

[PTslab]

MikeT14:

A few bigger picture notes on PT design - Is it neccessary to drop the beams in question? The economy of PT design is keeping the slab thickness the same. The additional formwork for drop beams in the direction parallel to the slabs may be costly. Also, The spans between 22' and 32' appear to range in thickness from 7" to 9". Coming from a contractor background - We'd rather pour one thickness of slab even if it meant increasing the thickness of all spans. Simplify. Simplify. Simplify. I'll now step down from my GC soapbox.

Specifically to your question: "What effective flange width should you use?" This is more of an art form gained through experience. I've practiced with some heavily experienced PTI members and most agree with around four to eight times the slab thickness approach. Using the CG associated with that flange width.

 

[rapt]

MikeT14,

Yes, that is what I was referring to. It is based on some warped logic that because the P/A distributes evenly over the width of the concrete section (according to their logic), then the effective flange width can be the full tributary flange width.

Unfortunately ther are 2 main problems with this,

1 the effective flange width in flexure is completely unrelated to the distribution of the prestress across the width of the slab. It is related to the width of flange which will me mobilized in flexure. As PTSlab says, it is normally between about 4 to 8 times the slab thickness but does vary depending on the overall arrangement. Most non-ACI codes base it on the distance between the points of contraflexure of the member (about 10% of this on either side of the beam), thus relating it more to the overall span arrangement rather than just the slab thickness.

2 The P/A does not distribute evenly over the width of the tributary section (read on before jumping into an answer). If concrete were elastic, linear, homogeneous, did not experience differential shrinkage etc, yes the P/A would distribute fairly evenly. Unfortunately it is none of these and the P/A distribution cannot be based on an elastic distribution as Adapt and some of the PT FE software tries to predict. Even membrane action, which the PT FE programs ignore, will make the distribution uneven in a slab made from an elastic material.
As concrete experiences all of these other inelastic and non-linear properties, a purely elastic analysis is meaningless in attempting to determine the real distribution of prestress.

Unfortunately, the even distribution of prestress logic has become entrenced in the industry in some areas because it makes life easy for designers as has the PT flat slabs act differently to RC flat slabs logic expoused by the PTI. Unfortunately for thise expousing these concepts, you cannot tell nature how to act.

 

[MikeT14]

PTSlab,

The architect REALLY doesn't want shear walls in this garage, therefore we're relying on Ordinary Moment Resisting Frames for a Lateral System, so the beams do have to be dropped parallel to the slab. Not for gravity load so much as for lateral.

Thanks for the recommendation on effective flange width.

The different slab depths are in different portions of the garage that are seperated by EJ's so the GC won't be dropping his forms within one "Phase" but will have different depths due to different uses in different phases. For example, one phase was designed to potentially have retail loading on nominally 22' spans, while another will have fire truck loading, and a third will have normal garage loading on 32' spans that match an adjacent buildings column spacing. They've really made it more difficult for themselves more than any decision we've made.

Rapt,

Thanks for the explanation. I was wondering why ADAPT did this. They have yet to respond to my question regarding which CG to use, but I'm inclined to use the effective width CG for future designs. We've already bid a portion of this job where I used the 22' tributary CG on 30x48" beam with a 5" slab. Is it worth looking at those beams again with the effective CG's??

Thanks again for all the responses.

 

[rapt]

MikeT14,

Placing the anchorages at the Tributary width CG rather than the effective width CG and using this Tributary width CG for the full design will have significant unconservative effects on the design. The two main effects will be,

1 Overestimated balanced loads in the end spans due to the unrealistically high positioning of the anchors. The uplift load will be as estimated by the calculations but, because the anchorages are placed well above the actual centroid, there will be an anchorage eccentricity moment at the ends which effectively reduces the balanced moments in the end spans to that calculated using the real eccentricity.
As this moment has not been applied in the calculations, the balancing moments will have been significantly overestimated and the service stress conditions will be much worse than as calculated.

2 The calculated secondary prestress moments will be much larger than they should be and will significantly reduce the negative moments for the ultimate strength calculations and result in an underestimate of the negative moment strength compared to the real moments. The opposite is true at positive moment points where the applied moment will have been increased significantly by the over estimated secondary moemnts and the design here will have been conservative. But the negative result is the worry as the section will be significantly under capacity.

So, yes, I would recheck them.

Also, have you followed the Adapt advice and included the slab tendons parallel to the beams in the beam analysis and design. If so, you are even worse off as they cannot be included in the beam design.

 

[MikeT14]

Rapt,

Thanks for the explanation. I may have been a little unclear in my last question. The beams I was referring to don’t have slab tendons running parallel to them since they are in a portion of the garage that could be converted to retail in the future. We didn’t want to run into any problems with slab coring in the future so we used a joist slab for this portion of the garage and only PT’d the beams in the 62’ garage spans. Therefore, those beams/tendons ARE supporting 22’ tributary. Should I still worry about the tributary vs. effective anchorage depths?

As for your other question, no I haven’t included the slab tendons in the design of beams running parallel to the slab. In discussions with other engineers in my office, and based on the discussion here, we’ve decided to design the beams with about a 5’ tributary width only and anchor at that CG and precompress to the same P/A level as the slab, much like PTSlab’s suggestion above.

 

[rapt]

MikeT14,

The slab supported should be a triangle of 22'/2 = 11'. If you are going to model this as a constant UDL you would normally apply 2/3 of this.

The rest of it I explained above in points 1 and 2 for the reasoning as to why you should recheck it. The comment about parallel slab tendons was just an extra.

 

[concrete28]

Are the parallel beams serving only as lateral, or are they picking up intermediate (perpendicular) beams that do not match the column spacing?

If the beams picking up the one-way slab are supported directly on columns, there is no need for parallel beams in an ordinary moment frame. If the parking structure is relatively short (<5 stories) the lateral should have no problem without the parallel beams. If you still want to keep them in for the lateral, the lateral strength requirements should be addressed with rebar anyway.

The parallel beams are a mess for the contractor to construct. There will be a great amount of rebar/PT congestion at the beam/column joint. Make sure you detail properly and coordinate shop drawings, or you'll have a mess in the field.

To address the P/A compression issue: the PT supplier is really only looking for a minimum P/A within the beam to insure the movement from the initial elastic shortenging is uniform in the slab. It's a serviceability issue, not a strength issue. PT can actually engage a much larger portion of the flange than recommended by some of the other responses. ACI318 only addresses non-prestressed effective flange widths. 12 times the flange thickness (each side) is common practice by those of us that do significant PT design.

For this situation, I would consider at the P/A I already have in the slab. Look at the effective cross-sectional area of the parallel beam+12*slab thickness and determine the P/A based on the tendons that cross through that region. If it meets the 125psi (or 175psi for hihgliy corrosive environment) you do not need to add any tendons. If it is below the minimum amount, add only the number of tendons you need to meet the minimum. You do not want to overcompress the slab, which creates bigger problems.

For example:
8" slab thickness with only 175 minimum psi P/A
12x24d parallel beam should only need 1-2 additional tendons too keep the 175 psi minimum...and they won't need to be at full drape unless you have some load-balancing issues for the longer spans.

 

[rapt]

concrete28

Can you please explain what you mean by
" PT can actually engage a much larger portion of the flange"