Post-tensioned slab applicabilty 5

[gcfreem]

Under what circumstances is it appropriate/efficient to use post-tensioning for an elevated (i.e. not slab on grade) concrete slab? Specifically, I am desiging a storage building with column spacing of either 20' or 30' in each direction. I don't have experience with post-tensioned slabs, but my feeling is that it may not be appropriate for the heavy live loads (125 psf) of a storage building. Thanks.

 

[civilperson]

An alternate method to take advantage of prestress concrete qualities is to use factory made hollowcore planks with a topping. The precaster has expertise for this product and the assembly is very quick and not dependent on good weather. The post-tensioning is also viable if the contractor has required experience with this construction method. The loading cited is within the range of prestressed design, (either pre-tensioned or post-tensioned).

 

[JAE]

Two-way post-tensioned slabs is a very good system to use in storage facilities with high loads. I'm working with a building now that has 30 ft + bays with two-way post-tensioned flat slabs. LL = 250 psf heavy storage.

 

[rapt]

gcfreem,

Agree with JAE but I would not call 250psf heavy storage.

Main thing to consider with these types of loads is that the concrete tensile stresses will be fairly high and the most economical design will be to use partial prestress. Allowing for pattern loading will result in a need for both top and bottom reinforcement as well as the PT tendons.

To do this poroperly, you cannot use the banded/distributed logic and especially the "average moment" logic of the PTI and ACI. You need to consider actual stress concentrations and design for each area accordingly. Averages simply are not logical.

It is also more logical to use bonded PT to gain the extra crack control advantages post cracking.

Flat plates will normally not be the most economical solution for these types of slabs. Flat Slabs with Drop Panels are far more efficient and will give you much strength, crack control and deflection better results but must be designed properly (see above).

 

[JAE]

rapt - the IBC (ASCE 7) live loads list 250 for heavy storage, 125 psf for light storage.

The banded/distributed method prescribed in ACI Chapter 13 has been used on hundreds of flat slabs for many years with good success...and they do get designed for patterned loading.

I'm not sure what you mean by "actual stress concentrations". Perhaps you could elaborate?

 

[gcfreem]

Thanks for all of your input. What (post-tensioned) slab thickness would I need for a building with 30' bays and 125 psf live load?

 

[rapt]

JAE,

There are 2 parts to this,
- Banded/Distributed
- Average moment design of flat slabs

Banded/Distributed system
The banded/Distributed system works ok as long as
- concrete shape is uniform - no drop panels, beams, band beams etc
- light uniform loads - no load concentrations (as you get with heavy storage), point loads, heavy wall loads, wheel loads etc
- stresses (real stresses, not average values) and including restraint effects are kept very low at service so that there is no cracking in the slab under service loads. Otherwidse redistribution begins to occur under service loads and this is not allowed

Average Moment Design
Average Moment design is an abomination. The people who invented it, do not understand slab design, PT design, cracking, deflections, statics and a lot more.
While it may be possible to justify the ultimate strength of a banded/distributed FLAT PLATE slab based on average moment calculations by requiring specific tendon layouts that will provide adequate load paths (either a proper 2way pattern or a banded/distributed 1way pattern) and using yield line logic to actually justify the collapse capacity, the same logic cannot be applied to service calculations for crack control and deflection calculations.
This is how it is done in ACI and PTI methodology and it is completely illogical and leads to gross underdesign of slabs for serviceability. Concrete cracks based on the elastic moment and stress pattern, not some average moment across a full panel width. The ACI rules lead designers to think that a slab is uncracked based on an average stress across the width while the real stress for half of that width is 1.5 - 3 times the average. If you are trying to push slab design to the limits and allow partial prestressing (and if the tensile stress based on average moments is at the ACI limit then the slab is cracked and is partially prestressed and being designed to the limits) then you need to design based on real stresses in the area where they occur, not average values.
This has to be done for both crack control and deflection calculations. None of the USA design software does this by default and a lot of it does not allow for it at all, eg Adapt PT or PTData or Posten etc.

While we are on this USA software topic,
You cannot calculate PT slab or beam deflections based on either average moments or long term deflection multipliers. ACI code specifically says this does not apply and for very good reason. It is completely irrelevant.
IN 3D design programs, ignoring the Mxy momnets in design as is done by all of this software is blatantly incorrent and grossly unconservative. Any concrete slab designed with this software is underdesigned by at least 15% (both strength and serviceability) and possible more.
Banded/Distributed slab systems can only be designed in 3D software if the column areangements are regular. As soon as the column arrangement becomes irregular the results become less accurate and the more irregular the less accurate and more unconservative the design.

 

[gsmith22]

gcfreem,
Generally, a good slab thickness starting point is Ln/45 for PT two way slabs-I wouldn't go less, and you may want to go more due to your high live load and long spans. You may want to limit how small columns get (not sure how many stories you have) and consider drop panels to make sure punching shear/moment transfer is adequately designed for as well as for obtaining extra depth at the columns to handle the high moments and reduce top bars. Slab thickness tends to be something that everyone including the owner (and lots of other non-technical people) has an opinion on so be prepared to defend your reasons for what you have choosen.

rapt,
I don't generally disagree with all that you have to say regarding the actual slab response vs the banded/distributed tendon layout and the use of average moments for design simplifications. Clearly, the ultimate strength of a two way slab is satisfied with these assumptions since the conrete will crack and will only be able to distribte load across cracks depeding on how the rebar/tendons are laid out and crossing these cracks. It may not be pretty from a serviceability/cracking standpoint, but it won't fall down if you have met statics.

However, where I do differ with the above is that I don't see concrete structures in general or specifically post-tensioned concrete structres in the dire state of service performance that you seem to indicate-actually I generally see the oposite. This could be due to some of the simplifications/over-conservativeness in design such as the actual live load has not approached the design live load, concrete f'c was higher than assumed, additional bars for tendon drapes supports adding crack control, etc. The entire practice of engineering in general is based upon a general simplification of the true, unknown, and highly complex state of stress, cracking, and load distribution among various elements. We aren't physicists! Clearly methods such as equivalent frame are not the true and actual load distribution but that doesn't matter. Assume a load path, place rebar/tendons to work for that load path, and everything will be okay.

At some point, I would think that the overwhelming evidence of the good in-service performance of literally thousands of slabs constructed and resisting load in the manners described here would convince you of the suitability of these simplified but reliable design algorithms.

 

[JAE]

Most every two-way flat slab that I have seen or inspected has cracks on the top surface, but not on the bottom. Not sure what relevence this has but always found it curious.

The ACI Equivalent Frame analysis has always been, in my opinion, essentially over-conservative in its results. Essentially you are designing the slab twice, once for each direction and providing reinforcing twice for the same load.

Do a finite element analysis on the slab (with the Mxy included) and the resulting rebars are much smaller than the ACI methods.

 

[rapt]

JAE,

Bit hard to comment on why cracks have formed somewhere without seeing the design and knowing the actual crack pattern. But a lot of redistribution has to happen to get a banded/distributed design to work at ultimate.

RE your second comment, you should get a new FEM program. You "designing the slab twice" arguement is the one used as a sales point by some FEM companies but its basis is unfounded because they are not including all effects in the design moments and giving unconservative designs. It is a furphy. The only way to get a benifit out of an FEM program for design is to not use orthogonal reinforcement patterns, but that is not possible. Once you decide you have to use orthogonal reinforcing patterns , both methods give the same results.

FEM (including Mxy effects in the design moments using a Wood Ahmer conversion) will give exactly the same result as an Equivalent Frame Analysis for a regular grid of columns. There is no difference. I am not sure which American program you are suggesting includes Mxy in the design moments, the 2 major prestress ones do not (as yet).

I have done comparisons between FEM analysis results (European ones that include Mxy) for flat plates and equivalent frame and the answers were within less than 1% for the cases I checked.

 

[JAE]

Hmmm...the ones I cross checked were always quite a bit smaller (M values) for FEM analysis. I'll try to back check it again but perhaps your statement "for a regular grid of columns" is what made the difference. I don't think I always had regular (i.e. square) grids.

But think about the Equivalent Frame Analysis. You take ALL the loads and design essentially a wide beam (made up of a column strip and two middle strips) with a complete load path for ALL the loads in one direction.

Then you do the same thing in the orthogonal direction....taking ALL the loads the other way. Just stepping back and seeing the forest for the trees, that tells me I have two load paths taking one load, each independently.

But you might be right...I haven't done the numbers in a long while.

 

[gsmith22]

JAE,
Cracking in concrete is not the smoking gun of poor design methods. The stuff just cracks sometime. Assuming the design was not flawed, I can think of several reasons why you would see cracks on top but not at the bottom: moments are higher at columns than at midspan so cracking would naturally occur here first or possibly poor curing methods. rapt is correct that without firsthand knowledge, this is basically impossible to diagnose.

While on the surface, equivalent frame may seem overly conservative since you think you are taking all load in both directions, think about this:

The EFM reduces joint stiffness at the column-slab connection since all slab is not connected directly to the column. However,it does not reduce vertical stiffness across the entire slab width-i.e. your strip does not cantilever off of the column perpendicular to the stip direction. EFM assumes you have a vertical support across the entire strip width (0.5middle+column+0.5middle) that is stiff flexurally at the centerline like a beam-column connection and is increasingly less stiff flexurally (more like a beam on knife support connection) as you move away from the stip centerline.

Now, how does the slab that is not directly connected to the column or even within the 1.5h+c2+1.5h width around the column get its beam support reaction from the EFM back to the column? You need a girder in the perpendicular direction and that "girder" is your EFM run in the perpendicular direction. THIS IS YOUR COMPLETE LOAD PATH. If you take all the load in one direction with EFM, and then don't correspondingly design for a very large percentage of that same load in the perpendicular direction, you haven't completed a load path because the EFM assumption of a vertical support across the strip width will not therefore hold.

Is it conservative to assume all load needs to be resisted in both directions with EFM? Absolutely. Could you take 1/2 the load in each direction on a slab with column supports? Not unless you wanted it to collapse almost instantaneously. Maybe in reality you need to take 100% of load in one direction and 80-90% of total load in the other direction (say 1-(1.5h+c2+1.5h)/total strip width)), but if you remove this simplification, you have better take a look at what other things you may need to increase. Aagin, this goes back to my previous post. Codes have simplified the true response so that things can actually be analyzed and built with some reasonable distribution of bars, slab thickness, etc. in a time frame that allows for relatively fast construction. The EFM as a whole has produced buildable, reliable slabs. If you begin to tinker with some of its simplifications, you may need to look a the whole method.

As for finite anaylsis, this is just an improvement over the EFM so yes, you will get less bars becasue this analysis is closer to the true response of the slab to loading-hence it is more efficient. The fact remains however, that no one is gong to place bars in such a manner that the spacing and bar size is changing throughout the entire slab to closely resemble the output from the finite element analysis. Which is why the EFM is so powerful since it has simplified an otherwise complex behavior and reinforcement pattern into a series of bars and spacing within the column strip and a series of bars and spacing within the middle strip or in the case of PT, only one big column strip with no middle strip.

I am not arguing that the EFM is the end-all-be-all to concrete slab design-it certainly has its limitations. Finite element is probably better but I am not sure how much better. For instance, my car now has GPS navigation, but amazingly, I was able to get to where I wanted to go a very large % of the time prior to obtaining this feature! I am not suggesting that finite element doesn't have its place, but to me this is like driving a ferrari to pick up milk when an accord would have done the job just fine.

 

[JAE]

gsmith22,

Yes...quite obvious that there is a "true" sharing of load in some percentage in the two orthogonal directions.

Your quote:

The EFM as a whole has produced buildable, reliable slabs. If you begin to tinker with some of its simplifications, you may need to look a the whole method.

is pretty much the point I was making. The EFM has produced good designs.

The cracking in the top that I mentioned was simply to say that if the EFM is such an awful way to design two-way flat slabs (which was implied in some posts above) then why does it look so good from below and perform so well in general?

The cracks in the top are usually the result of what you imply...higher concentrations of stress at the column in conjunction with a sort of fatigue cracking (most of these were in parking garage applications).

There are so many engineers that seem to slam (or feel uncomforable with) finite element analysis. Yes your results come out in a non-uniform scatter of required reinforcing, but the engineer can still successfully lay out a reinforcing scheme that is both more economical than the EFM and uniform enough to be constructable. In fact, my use of FEA has taken advantage of the "expected" column strip-middle strip layouts.

Essentially though, I don't have too much to disagree with you at all. I just tried, awkwardly I guess, to respond to the posts that implied the EFM in ACI was somehow all screwed up and incorrect.

 

[hokie66]

JAE,

Your arguments are usually well presented, but you seem to be on both sides of the fence on this one. I didn't have a dog in the fight (oops, that is now politically incorrect, I guess), but have read the posts. I didn't read that anyone else had implied that the EFM was so bad. You were the one who opined that the EFM was too conservative.

 

[JAE]

hokie66,

On Nov. 14th above, I got the impression rapt was implying that the ACI "method" wasn't very good, correct, right, whatever. I responded that it (the ACI EFM method) has produced many good designs. rapt then responded further with a well presented description of a "banded" system and an average moment system. Both of which, in rapt's opinion, were seriously flawed or had enormous limitations.

I came back on the 22nd and essentially stated that the EFM was, if anything, over-conservative, despite cracks I'd seen in the top of some slabs. I wasn't trying to decry the use of EFM, but reinforce it as being a good system, just fairly conservative with respect to finite element analysis.

Sorry for the confusion - with the holidays I've been typing too fast I guess.

 

[gsmith22]

no worries. I didn't agree with the initial slamming of EFM by rapt but maybe I was a little too hard on finite element too! They each have their place. The truly ciritcal thing I wanted to point out though, was that EFM is required to design for the total load in both directions due to the methods assumptions/limitations not necesserily becasue in reality that is what happens. Happy Holidays

 

[hokie66]

Guys, I just didn't read that rapt was slamming the equivalent frame method. In fact, he says that the results obtained are the same as by FE. What he obviously doesn't like is "banded/distributed system" and "average moment design", and I don't know enough about those to comment.

 

[JAE]

I guess I assumed that the average moment design was the same as the equivalent frame analysis. If not - rapt, sorry I mis-understood.

I've never heard those two terms before.

 

[hokie66]

Maybe Rapt will come back and give us a definition of "average moment design".

In the meantime, about your question about cracking in the top but not the bottom of flat slabs. When i see this, and I have a few times, I look for:

1) Too much cover on the top bars due to improper height chairs being used or not maintaining the correct location of the reinforcement during placement. I have seen on more than one occasion a concreting crew displace the top mat and intend to do nothing about it until directed to rectify. There is no substitute for continuous inspection, although I know it is seldom done.

2) Not enough concentration of top bars going directly through and adjacent to columns.

3) Plastic settlement cracking if the cracking pattern is regular.

But as gsmith pointed out, sometimes it just cracks. Flexural cracking is to be expected more in the top than bottom as the moments are higher. If there is a lot of cracking in the bottom, direct tension is likely involved.

 

[JAE]

One case I saw was definitely your item 1). Spider cracking around the columns in all directions and 3 1/2" to 4" cover.