I assume you are using the ACI/PTI banded/distributed tendon layout. And unbonded PT.

If yes, bottom reinforcement is definitely required for both of those.

For unbonded because you need something bonded.

For banded/distributed because your reinforcing pattern one way) is completely different to your loading pattern (two way).

Added to that you probably have concentrated loads for a podium transfer, so you need something to distribute those to the average you have assumedin the full panel width analysis.

If you designed using a more rigorous method than full panel with banded/distributed, you could use Partial Prestressing to provide a much more logical design, but that is not possible with the design assumptions normally made to achieve the above to ACI code.

I have no idea how column dowels will affect anything.

Rapt - Thanks for the response! Yes, ACI/PTI, unbonded, banded/distributed method.
It sounds like you are suggesting a mat of reinforcement regardless of whether or not the slab is a podium slab. FWIW, most PT slabs using this method do not have a mat of rebar. I generally only see them in podium slabs (but not always). Not saying it's right or wrong, but that just seems to be the case. These slabs do have bonded reinforcement, but generally only where required (i.e. minimum top bars over columns, or exceeding service load tension requirements).

Column dowels - I'm kinda taking that back. Intent was to figure out the best way to reinforce the underside of the slab at the column joint where slab lifting might occur during stressing where there is a large "overbalance" load.

Are we talking about the kind of podium that supports light frame construction above?

_{That's a horrible idea. What time?}

Yeah, I probably should have been more specific.

RFrued,

I think unbonded always needs it.

And banded distributed if there is any tension in the bottom.

But as most readers know I think unbonded and banded/distributed are abominations to concrete engineering logic!

Amen to that!

When I started designing these slabs (thick transfer slabs supporting 2-5 levels of light-framed construction), we always put in a uniform mat of bottom reinforcement regardless of code requirements. Similarly, I was challenged on this several times and found that many engineers in the US are no longer doing this, and rather are only providing bonded reinforcement where required per ACI. The table below from ACI 318-14 spells out the requirements. Not that As,min in the positive moment region is "Not Required" if fc <= 2sqrt(f'c).

Whatever your opinion is on the issue, it is my understanding that the ACI does not require a continuous mat of rebar in unbonded 2-way prestressed slabs. If you are finding that you need bottom rebar in the span and over columns, it might improve constructability to simply provide the continuous mat.

For positive moments over columns resulting from over-balancing during the initial stressing, you will need to provide bonded reinforcement per section 24.5.3. You can also consider stage-stressing the tendons so you avoid over-balancing effects.

Check out Tech Note 8: Link. While I understand where rapt is coming from (he is probably one of the two most knowledgeable PT guys on here, KootK being the other - I actually learned most of what I know about PT from KootK); it does appear that bottom bars are not technically required in the US if certain conditions are met with stresses.

1) Most of my PT work has been in the same market that RFreund is working in: the midwestern United States.

2) Currently, I only provide passive, bottom reinforcement when that is driven by demand. If that comes to pass, then I weigh the pros and cons of rationalizing the rebar disposition into a continuous mat in the usual way, just as I would with a mildly reinforced concrete slab.

3) In my opinion, these podium + light frame slabs have a uniquely annoying feature: loads that are difficult and cumbersome to model accurately. Consider:

a) Relative to "all concrete" construction, the ratio of live loads to dead loads is high.

b) The live loads are often unit residential / hospitality loads that, statistically, come in around 6-8 PSF even though we ULS design for 40 PSF+.

c) The loads manifest themselves as line loads running around all over the place.

d) Some manner of load patterning is surely appropriate but, at the same time, it's difficult to know how to apply that appropriately and efficiently.

e) Live load reduction is surely appropriate but, at the same time, it's difficult to know how to apply that appropriately and efficiently.

f) There will usually be some significant point loads that will make all of this stuff that much messier.

g) Even light frame walls will posses significant in plane stiffness. Stacked on a flexural spanning structure, what we assume to be linear loads may well be concentrated loads at slab "hard spots".

4) Because of all of the stuff in [#3], I feel that the question of whether or not to have bottom steel is intimately related to the degree of simplification taken in the slab modelling. If one is just smearing out all of the load and then coming up with no bottom steel demand, it becomes questionable how reasonable that is. I myself am doing this smearing business for preliminary design, simultaneously multiplying my loads by an extra Koot-Factor of 1.25. This is necessary for me to be able to guide and inform my clients within an acceptable time frame. I've also let a few of these smeared designs slip past the goalie into final design. Is what it is.

5) When doing a podium + light frame transfer slab, my primary goal for the PT is deflection control. And the only deflection that I care about is the deflection that takes place after the super structure is erected. The only feature of a PT slab that improves this is the pre-compression on the tensile face of the slab which creates an an un-cracked / closed cracked slab that responds to service loads with I_gross. In broad strokes, this pre-compression is brought about in two ways:

a) Straight up P/A. I love me gobs of P/A for transfer slabs. Why? Because it's effectiveness is fairly insensitive to the actual loading pattern. See [#3].

b) Drape. I feel that drape is used most effectively when the loading pattern is known with confidence. Per [#3], podium + light frame a'int that.

[a + b] = I usually design podium slabs with a higher ratio of [P/A : Drape Balancing] than I use for common PT slabs.

6) I don't believe that I've ever, deliberately over balanced a PT slab. I've overbalanced a lot of precast girders but that's a different animal. [#5], combined with a judicious column layout, eliminates a lot of situations where I might be tempted to over balance PT slabs. When that's not enough I use other strategies:

a) Local slab thickenings.

b) Introduction of local PT that does not run the whole length of the slab. Again, I'm mostly in it for the P/A.

c) Good old fashioned bottom steel if I feel that it's just a ULS problem.

d) I would consider staged pre-stressing but, thus far, have only done that for discrete transfer beams. This ties back in with [5b]. Staged pre-stressing only makes sense to me if one is wielding drape as a significant design tool. And, as I mentioned, I don't love drape for the loadings that these kinds of building generate.

@RFreund: that was a pretty big rant. I hope that you find something useful in there. TLDR is an ever present threat...

_{That's a horrible idea. What time?}

Quote (Aesur)

I actually learned most of what I know about PT from KootK)

Aren't you the charmer? *blush*.

That said, I know full well that you've been lovin' on Bondy behind my back.

_{That's a horrible idea. What time?}

Quote (KootK)

That said, I know full well that you've been lovin' on Bondy behind my back.

I knew there were cameras somewhere in my office, where did you hide them?

In my "would always have it"I would include Kootk's point 3.

Where load effects are simplified for ease of design, a bottom mat is needed to account for the actual versus assumed moments and stresses. That is a feature of banded/distributed also as it does not account for stress distribution across the slab.

Kootk,

Relying on P/A is dangerous where there is significant restraint, which often happens with podiums connected to retaining walls and cores.

Thanks again for the responses.

Quote (rapt)

But as most readers know I think unbonded and banded/distributed are abominations to concrete engineering logic!

While I'm fully aware of this, it still kinda blows my mind that there is such a divide about this. I've seen Kootk ask this question before, so I'm not actually asking it again, but I'd love a reference similar to Bondy's "Principles and practice". It's not that "your method" is such a stretch to learn. From posts I've read, it's actually more intuitive. I just think it's a confidence thing. I need an example or something.

Quote (KootK)

@RFreund: that was a pretty big rant. I hope that you find something useful in there. TLDR is an ever present threat...

NHo worries there, if someone is taking the time to respond to my thread, I'm going to read it.
My issues arise mostly due to column layout and load placement. There are typically a couple of long spans with some heavier loads (maybe brick, or a concentrated post load). The easiest solution is thicker slab, but it seems like contractors want to avoid changes in slab thickness like the plague and I don't want to penalize the entire slab for one or two areas.
So the workflow/problem is this:
1) ULS are satisfied with either passive reinforcement or even P/T from the following steps. The real problem is meeting the allowable service tension stress (i.e. <6*sqrt(f'c)).
2) Increase P/A as much as practical, but I like to limit this to say 250psi for a podium. Maybe some go higher here?
3) Increase drape until you satisfy your allowable service tension stress.
4) Problem: Due to #3 you are "overbalanced" and you may or may not be within the allowable tension stress at transfer (i.e. >3*sqrt(f'c), too much tension on the top side at mid-span and/or too much tension on the bottom side at the support). This is where I suppose my question really exists - If you end up being overbalanced (and possible still within allowalbe transfer stress), how 'bad' is that? In my mind, let's just add some top bars at midspan and some bottom bars over the columns. ACI 24.5.3.2.1 allows you to do just that if you exceed the allowable tension transfer stress. This seems easier than thickening the slab. I'm trying to think, why that won't work. One thing that comes to mind would be if the tendon could "split" the slab even with the reinforcement there.

RFreund,

Why do you need a reference book?

Just go back to common sense engineering.

I assume You have a slab that has high concentrated loads in some areas and none in other areas, and are basing a design on the average of those. That is not logical. I could use other words but will be polite). You need to allow forthe concentration effects to get over the problems you are having. Using ACI flat slab logic is all based on averages, It does not apply where you want to control the effects of load/moment concentrations.

Where there is a large difference in the load effects across the slab, you cannot logically base the design on averages.

If you can identify the locations and effects of all loads,

- do an FEM analysis.
- instead of designing for each panel, divide each panel in each direction into logical width strips that correspond to moment zones that do not have too much variation across each strip. It will depend on the design, but possibly 10-20% of a panel width for each strip.

- Then place tendons in each strip profiled to the bending moments in each strip and reanalyse the structure with the PT and design each strip accordingly. Or do each strip in a 2D program to include the moments and shears from the FEM analysis and the PT in 2D.

The simplest case of this is a slab with Uniform loading. The logical design strips are the column strip and the middle strip,the same ones you use for RA flat slabs. Column strip has about 75% of the negative moment and 60% of the +ve moment. Middle strip has the rest.

Where loads are not uniform you divide into smaller strip widths to pick up the concentrated effects.

By doing this, the service stress limits in ACI for flat slabs no longer apply as you are not using the average effects. The one way slab rules apply for each design strip and you can do partial prestressing if you want.

The biggest problem you will then run into is that it requires weaving of the tendons in the 2 directions. Good luck fining an American PT company that will be able to do that for you with unbonded PT.

If you like, that is a complete text on the subject. You do not need a book.

Quote (RFreund)

4) Problem: Due to #3 you are "overbalanced" and you may or may not be within the allowable tension stress at transfer (i.e. >3*sqrt(f'c), too much tension on the top side at mid-span and/or too much tension on the bottom side at the support). This is where I suppose my question really exists - If you end up being overbalanced (and possible still within allowalbe transfer stress), how 'bad' is that? In my mind, let's just add some top bars at midspan and some bottom bars over the columns. ACI 24.5.3.2.1 allows you to do just that if you exceed the allowable tension transfer stress. This seems easier than thickening the slab. I'm trying to think, why that won't work. One thing that comes to mind would be if the tendon could "split" the slab even with the reinforcement there.

This is how I would recommend handling the issue. It is permitted by code, so you should feel comfortable proceeding in that direction. I would recommend using FEM or one of the methods described by rapt to determine the moment and stresses in the slabs due to the non-uniform layout and loading. In the US, Adapt, Ram Concept, and CSI safe are all commonly used software packages to accomplish this task. I do not have experience with Safe but both Adapt and Ram Concept will evaluate the design sections for your transfer stress condition and add reinforcement if it exceeds the code-permitted limits.

For what it's worth, I establish slab thickness on the basis of punching shear and deflection. I then start with the minimum required P/A and maximum drape for the PT. I will then increase P/A as much as I feel comfortable doing on that given day if I can't meet stress limits. I will only increase the slab thickness if I still can't get allowable stresses to calc out, and even then I try to only increase thicknesses locally similar to what others have mentioned on this thread.

Although I used to try and keep slabs a uniform thickness throughout for ease of forming, I've changed my mindset on this a bit lately as my priority has turned towards saving raw materials and reducing the overall structural weight. This has a compounding effect on the size of your columns, shear walls, and foundations supporting the slab so there are additional savings just beyond the slab thickness.

I tend to think the reality of these light framed podium slabs is the PT isn't really being used in the most efficient manner. Within the standard of care of most regions, the actual design fee, and the skill level of the labor using the PT in the most efficient manner just isn't practical beyond university study in many regions.

Providing parabolic drapes in each direction, as is typically done in my surrounding region, only efficiently addresses uniform loading and the only "guaranteed" uniform loading in these structures is the slab self-weight. In my region these typically land at around 16-18" flat plates which puts the self-weight in line with the total live load requirement of a residential structure. In my opinion the PT is really being used most efficiently to at best work to counter the stresses generated by the self-weight in these podium structures and the thickness is being used to control the stresses generated by the loading.

If you take the approach of doing maximum drape and min. P/A in these slabs each span will be starting overbalanced against the slab self-weight by around 150%. In my experience I've found that aiming for a self-weight balance of 80-90% and with the overall slab thickness ranges noted above the stresses end up under control when the actual line/point loads are applied.

Quote (rapt)

Relying on P/A is dangerous where there is significant restraint, which often happens with podiums connected to retaining walls and cores.

Thanks for raising that point rapt. I understand and, conceptually at least, I agree. My counter argument would be these.

1) To my knowledge, all commonly designed PT slabs rely upon P/A for flexural strength. It's only a question of degree. I've not yet encountered a software package that allowed me to disregard the benefit of P/A.

2) It is for this reason that I consider the planning of the layout and details to minimize shrinkage restraint to be one of the most critical aspects of PT design. It's never perfect, but smart choices can usually be made none the less.

3) If a slab is to benefit from the effect of drape only, then I believe that the post tensioning then does not contribute to the flexural strength of the slab. All that the post tensioning does in this case is apply a negative load to the floor system. So, if one is to not rely on P/A for flexural capacity, I imagine that all of the flexural capacity would have to come from passive reinforcement. And, perhaps, this is one of the reasons that you favor the inclusion of some passive reinforcement.

Quote (Celt83)

I tend to think the reality of these light framed podium slabs is the PT isn't really being used in the most efficient manner.

I think that's a pretty astute observation.

I currently live in Calgary, Alberta. And you pretty much cannot do PT in this city because of paranoia over some bad experiences we had with corrosion back in the 70's before the extrusion stuff got sorted out.

We still do these podium slabs though, we just do them mildly reinforced. Surprisingly, the thicknesses of these slabs winds up being about the same as PT or pretty close to it. I think this kind of speaks to the inefficiency that you mentioned.

Two provinces over, PT is likely used even less. We only touch it to fix old PT, as far as I'm aware, there have been no new PT structures in a really long time. There's very few contractors (less than 5 likely) who will even touch the PT work that we do have.

Maybe if you switched over to bonded PT, it would be more palatable to builders. Partially prestressed, bonded PT is the norm in Australia, and builders here are not doing it just to be different.

Quote (hokie66)

...and builders here are not doing it just to be different.

I suspect that they are doing it because the engineering community in their locale doesn't really give them the ability to use unbonded systems.

Quote (hokie66)

Maybe if you switched over to bonded PT, it would be more palatable to builders.

That's actually a pretty good idea. It's the insurers that need to be persuaded. The builders that are comfortable with PT in general love unbonded. Same fundamental concept though: bonded = more convincing durabilty.

Quote (RFreund)

This is where I suppose my question really exists - If you end up being overbalanced (and possible still within allowalbe transfer stress), how 'bad' is that?

Truly, I do not know. And I want to be forthcoming about that. As I said, I've never overbalanced as a deliberate design strategy. Nor do I know of anyone who has. I also have never seen any kind of detailed discussion of what might happen if one did overbalance. Who knows though, maybe my reluctance to try this has been nothing more than me failing to think outside of the box. Consider what follows to be nothing more than me trying to create a detailed discussion of what might be problematic about an unbalanced design.

1) Reinforcing complexity. To limit cracking well, I would think that you would have to detail your bottom steel in much the same way that one details their top steel. Bottom mats where you have top mats and that kind of thing. I could see builders responding unfavorably to that. That said, you can just show your builders what this looks like and let them be the judge of its desirability.

2) Deflection. Utilizing the reinforcing intended to deal with the overbalance means cracking the concrete. And by definition that means that, during the initial stages of loading, the slab will deflect in accordance with it's cracked moment of inertia. As such, you've somewhat undone what I consider to be the major benefit of using PT in the first place: kick ass deflection control. Theoretically, I think that you're back to I_gross once you've closed the cracks. That said, I kind of question whether or not a crack truly closes up in this sense in the real world. Lastly, if there's a software package capable of dealing with this aspect of things well, I'm not aware of it.

I think it's important to remember that balancing is not really a design consideration but more of a rule of thumb practice, it's a means to relate the quantity of PT relative the loading condition being balanced. I tend to think of balancing as the percent of tensile stress of the loading I'm trying to balance being negated by the PT. So at any cross section whatever and wherever the tensile stress is under the loading condition the relative reduction of that tensile stress by the PT is the "balance" on the cross-section.

Assuming all stress requirements are satisfied the implication of "over balancing" to the extent that it usually happens is likely more a serviceability concern for humping of the floor. From a mechanics perspective "over balancing" results in a reversal of curvature from that of the applied loading at each section that is over balanced.

Thanks again for the responses.

@Rapt - I appreciate that design summary. I think it is well said and you're right, it does make a lot of sense.

For some reason Unbonded P/T in the Midwest US is a dominating force right now. Not really sure what is driving it. We've had to redesign a couple mild slabs with fairly short spans to P/T even though we only saved 1/2" of concrete.

US building PT went the unbonded route back in the 1960's. It is hard to change once the whole system has gone that way. It was basically a factory manufacturing operation delivering pre-assembled tendons to site where the site works were done by others. Bonded PT is the opposite and all works need to be done by the PT company. In recent years the US has realised the deficiencies of the system and have at least started to use trained operatives on site rather than untrained labourers for very specialised work.

Australia went bonded at the same time. We looked at unbonded in the late 1970's because it was being pushed so hard by the PTI but after a few months review decided to stay with bonded because of the design advantages and the low level of the unbonded technology at the time.