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gcfreem (Structural) (OP)
13 Nov 07 14:27
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 (Structural)
13 Nov 07 14:54
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 (Structural)
13 Nov 07 18:37
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.

Helpful Member!(2)  rapt (Structural)
14 Nov 07 22:56
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 (Structural)
15 Nov 07 0:00
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 (Structural) (OP)
15 Nov 07 18:35
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 (Structural)
15 Nov 07 23:48
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.
Helpful Member!  gsmith22 (Structural)
21 Nov 07 22:08
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 (Structural)
22 Nov 07 16:34
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 (Structural)
22 Nov 07 22:39
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 (Structural)
23 Nov 07 1:37
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 (Structural)
23 Nov 07 12:16
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 (Structural)
23 Nov 07 17:49
gsmith22,

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

Your quote:

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 (Structural)
24 Nov 07 0:42
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 (Structural)
24 Nov 07 10:06
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 (Structural)
24 Nov 07 12:15
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 (Structural)
24 Nov 07 16:03
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 (Structural)
24 Nov 07 18:57
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 (Structural)
24 Nov 07 20:08
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 (Structural)
25 Nov 07 0:35
One case I saw was definitely your item 1).  Spider cracking around the columns in all directions and 3 1/2" to 4" cover.



rapt (Structural)
25 Nov 07 22:06
Everyone,
This will become obvious below but we must distinguish between FEM analysis and software that produces reinforcement/prestress requirements based on FEM analysis. All FEM produces is a set of stresses which, when convereted to moments, describe the moments on the floor system that have to be designed for.
A tacked on design program then designs reinforcement. FEM does not produce reinforcement drawings, someones interpretation of FEM results does, whether it be done manually or by computer.

1    FEM vs EFM: There is no difference in the overall moment over a panel width between the 2. This can be easily verfied by setting up a simple square grid of columns in FEM and the same EFM sample and comparing the results. The whole thing should add up to wL^2/8 in each direction (same as for EFM) for a uniform load. If it does not, change FEM programs because the one you are using is WRONG.

The difference is that FEM tells us the distribution of thre moments across the slab based on elastic analysis while with EFM we have to guess the distribution based on experience, eg 75/25 for maximum negative moment and 60/40 or 55/45 for maximum positive moments and varying between.
Both methods should give the same total area of reinforcement over the width of a panel. There is no saving using FEM.
If software tells you there is a difference, question it because it is wrong. For example, if an FEM program allows for Mxy moments in the analysis and then ignores them in design (as several prominant ones do), then the difference will be at least 15% and possibly up to 25% UNDER estimation of the reinforcement requirements. This does not mean that you can use 15-25% less reinforcement, it means it has underdesigned by 15-25%.
It does not mean that FEM is wrong. FEM is reporting Mx, My and Mxy. It means that the design application tacked onto the end of the FEM is wrong because the developer does not understand design using FEM, or they are trying to cheat (hopefully it is the first but either is worrying).

2     I have no problem with EFM. It is how I design most times. What I do have a problem with is the assumption that the design moment on a PT flat slab is a total moment spread over the total width of a panel.

In RC design, ACI tells us to distribute the moments between column and middle strips in different propertions depending on whether it is at support or mid span. This fairly closely models the results of an FEM distribution of moments and I agree entirely with it.

In PT design ACI tells us to use the total moment over the total panel width (resulting in an average moment and averaged stresses over the entire width of the panel). This is blatently incorrect.

2--1   As I explained in earlier posts, for flat slabs where the tendons and reinforcement are placed in a pattern that provides a load path to the supports, it is possible to do the ultimate strength calculation the ACI way and work out a total capacity over the width of a panel rather than dividing into column and middle strips. The justification of this comes back to a yield line solution and the slab will stand up.
The 2 generally accepted tendon patterns for this are
      1    a column/middle strip pattern in each direction with about 70% of the tendons in the coilumn strip and 30% in the middle strip in each direction - result is similar to the FEM moment result and the elastic response of the slab
      2    a banded/distributed pattern with tendons equally spaced in one direction and concentrated over the columns in the other direction - result is a one way failure pattern completely different to the FEM moment result and to the elastic response of the slab
      3    a third solution is similar to 1 but the ratios in each direction are varied but still consistent with each other. In this scenario, solution 2 is one extreme of the solutions possible.

In all cases, all of the laod is carried in each direction and there is a load path to the supports in the reinforcement pattern.

This yield line solution is only possible however when tendon layouts as described above are used, loads are uniform, concrete cross-section is uniform and the slab is uncracked at service - see below.

Otherwise solution 1 must be used where the tendon layout matches the elastic moment response of the slab.

2--2    The real problem with the ACI method arises when we come to serviceability design, crack control and deflections.
Concrete cracks based on the stresses at each point in the section, not based on the average stress over a 10m (33') width of slab. A Crack in concrete can only be restrained by reinforcement that crosses the crack. Sounds logical and obvious. But that is not the way ACI works for PT slabs.

The slab cracks based on the elastic moment pattern, not some assumed ultimate failure criterion. It keeps cracking as load is increased until the final ultimate capacity of the slab matches the reinforcement pattern. If that pattern is banded/distributed, then a lot of cracking and redistribution and extra deflection have to occur to achieve the final ultimate capacity.

What we are interested in is the first cracking and that is dependent on the elastic moments and their distribution across the floor panel. ACI ignores this.

Even though 75% of the moment is in only half of the width at the supports, ACI allows you to assume it is spread evenly. This means that you are grossly underestimating the actual stress which will crack the concrete. So ACI designers are assuming slabs are uncracked for cracking and deflection calculations when they are actually cracked. This is very unconservative. Add in the fact that everyone ignores restraing stresses and your software might be ignoring Mxy (15% of the moemnts) and your slabs will be a lot more cracked than you expect and deflections will be much higher.

The further serviceability problem is that banded/distributed slabs cannot be allowed to crack at service unless crack control reinforcememt, calculated based on the requiremnents of all areas of the slab for their actual stresses, is supplied based on the elastic moment pattern not the failure pattern. The decision on this cracking must be based on the elastic stress pattern and allow for restraing stresses due to shrinkage and temperature change.
haynewp (Structural)
26 Nov 07 23:09
JAE,

I have not used FEM for a slab before, in fact, it has been a while since I have even done an EFM. But I do remember that wl^2/8 total moment (positive reinforcing + negative reinforcing for a slab panel in either direction has to add up to wl^2/8) as rapt was talking about to make sure there is a minimum amount of reinforcing required for the slab. Again, the wl^2/8 must apply for EACH direction so you are reinforcing it for that load twice but this is required.

I think this total moment in each direction goes back to a guy name Nichols around 1915 that proved this and changed the way slabs were reinforced. I remember reading that 2 way type slabs were almost all under-designed prior to this guy showing this total moment requirement. The EFM is supposed to be derived from Nichols' analysis. The Nichols' analysis looks at the entire moment in a slab panel.

Regarding PT slabs and serviceability cracking, I really haven't heard of PT slabs designed in the U.S. performing all that poorly either when designed based on EFM. But I do not specialize in just doing one thing all the time (ex. PT concrete slabs) so I am not constantly exposed to designing and inspecting only prestressed slab systems. So maybe I am wrong. Apply carpet as necessary.

hokie66 (Structural)
27 Nov 07 6:27
Intuitively, I think Rapt is right about this banded/distributed arrangement.  I wouldn't do it that way.  What are the reasons it is common practice in the US?  You wouldn't arrange deformed bars that way, so why posttensioning tendons?  When the slab wants to span in both directions, you can't force it to work as a one way system.
csd72 (Structural)
27 Nov 07 8:17
haynewp,
re:"...for EACH direction so you are reinforcing it for that load twice but this is required."

Fundamentally it is no different than a slab supported on beams on 4 sides. except the beams would take the moment in one direction and the slab in the other. The only reason for the different analysis is the difference in relative stiffness.

csd
haynewp (Structural)
27 Nov 07 10:59
csd,

Yes that is right. The load is taken 100% in each direction for both a 2 way flat plate and 2 way slab on beam case. Or even a one way slab and beam system. Just like steel roof joists take the load to girders then the girders take the load to the columns.

For a 2 way flat slab without beams the slab itself takes the load in one direction then in the other.
csd72 (Structural)
27 Nov 07 15:52
haynewp,

not trying to correct you, just trying to make it clearer for anyone that doesnt understand that fact.

csd
JAE (Structural)
27 Nov 07 20:00
Good replies.....and rapt - whew...what a dissertation.  Appreciate the time it took to do it.

As far as load being taken twice...I was using that description to make the point that it seems that SOME of the load is counted twice (and thus there is some level of redundancy in the EFM)...probably not 100% and 100% but some level of duplication.

I seem to see gsmith22's point about the slab not being fully connected/supported by the column but by the orthoganal slab.

gsmith22 (Structural)
27 Nov 07 21:44
wow. go away for a few days and there is alot to read!

rapt, very nice summary. I was under the impression from your first post that you were bashing the EFM and/or finite element. However, now I see that your only concern is the use of banded/distributed tendons and the fact that their layout does not match the elastic response of the slab.  I can very much concour with most of your thoughts and I too had similar concerns when I first started design with PT.  The one difference that maybe we are all forgetting is that a PT slab is under compression in addition to bending moments.  Hopefully you are using an Mc/I+P/A to analyze the slab when talking about first cracking as that P/A can have a large effect.  Due to the compression, you will most likely not have tension at the top of your slab away from columns and a large portion of the slab will be uncracked and thus stiffer than a similarly designed conventional slab-also required by ACI due to stress limitations. But assuming you have done this, the following may be of help.

Banded/Distributed. As far as I can tell/have read, most of the PT design for buildings in the US was started through contractors experimenting and not engineers designing or professors teaching.  As such, they developed methods that were easy to build.  The engineering industry followed their lead istead of the other way around. The banded/distributed layout of tendons is a contractor favorite because it almost completely eliminates any weaving of tendons. Basically, place all the banded tendons close to column lines first, then place all the uniform tendons.  ACI has done numerous research on the use of different tendon layouts and has concluded that there is no significant difference in the distribution of compression into the slab via the tendons whether the tendons are banded, distributed, or some mix of the two. Compression is basically uniform in the slab away from anchorages.

Cracking.  If we can assume the ACI is correct and that all compression distributes equally into the slab, then the only question here is why the use of full strip width for moment design.  This is clearly conservative from the standpoint of the "middle strip" as it will have lower moments elastically than a neighboring "column strip". Throw in the compression via the tendons and I doubt you have any problem with eliminating top bars at the support line "middle strip." So what then happens at "column strip"? Well limiting the max stress to 6*SQRT(f'c) certainly helps here as well as being forced to provide a minimum amount of top bars at the column (ACI's way of recognizing the flaws in their analysis?) but ultimatly, you are somewhat right in that the stress at the columns is probably higher than being calculated since the column strip beam was artifically too wide.  

I haven't really personally worried about it but that maybe because most things I have designed 2-way flat plate PT have been residential with low live load (40psf and reducible) that is rarely ever achieved in reality.  I think I recall much higher live loads being talked about previously (and probably unreducible) so the stresses are probably much closer to the limits than my buildings.  

Conclusions.  If you are near 6*SQRT(f'c) for negative moment stresses, clearly recognize that the true stress right at the column face maybe much higher and maybe add some extra bars to reinforce it if it bothers you.  The true deflecton calculation will probably be worse than a completely uncracked slab if you are near stress limits but I still would maintain that a large portion of the slab will be uncracked.  The moment of inertia doesn't immediately drop as soon as a single crack develops, but there is a smoothing of the stress/deflection curve-the reason for Ie calculations in Chapter 9 of ACI. It is always best to recognize when a code has simplified a much more complex system and as you near code limits, pay attention to some of the assumptions of the code-which it appears that rapt has to his credit.     
rapt (Structural)
27 Nov 07 22:33
gsmith22,

Yes the axial prestress sort of distributes evenly in a flat plate (except for membrane action, and not with T beams/band beams) but this stress is normally much lower than the bending stresses which do distribute unevenly across a slab panel width. You cannot base the distribution of the moments on the distribution of the P/A which as some "experts" have suggested previously in print.

Yes, the early designs using this method used much lower stress levels so they were ok. Now people want to do partial prestressed design (like we have in the Australia for 30 years). To do this, you have to look at the stress concentrations, not averages, and put the steel where the cracks are.

I have seen people justifying slabs with 30-50kPa live load (600 - 900 psf) and with drop panles using banded distributed tendons and average moment design. Also heavily loaded transfer slabs. Their results are stupid and it is all because they read ACI and PTI documents and get the impression from these that this is how a PT slab actually works rather than it being a simplification with limited applicability.

Deflections do increase significantly on the appearance of the first crack. Branson's formula says that they don't but all approximations have their limitations and this is the main limitation of Bransons formula. It is unconservative at the first crack and for lightly stressed/cracked members. That is why ACXI is the only code that uses it in its original form.
rapt (Structural)
28 Nov 07 21:58
gsmith22,

The other area that worries me with all of this is designs for floors with variable concrete sections, either drop panels or beams and also slabs with large concentrated loads.

Designers are treating both of these like lightly loaded flat plates. They are including tendons in slabs a long way fro the changes in depth as having the same effective depth as the tendons in the area of the change in depth, eg tendons in slabs parallel to beams are included in the beam section for design and also include a very wide flange. It is garbage but they are doing it.

Same with drop panel slabs where the tendons between the drop panels are treated as if they are over the drop panels.

The actual capacities of these slabs are significantly lower than the designers think. And they are encouraged to do it by some software developers who simply do not understand design no matter how much they put their names up in lights.

With large concentrated loads, they are treating the design like a normal positive moment area for a uniforn load design but it is actually more like a negative moment area in the way it acts and the tendons and reinforcement have to be arranged accordingly and the design needs to consider this. Basic banded/distributed and "averaged moments" just does not work with this type of design.
gsmith22 (Structural)
29 Nov 07 15:36
rapt,
I realy don't have any problem with what you are suggesting here. Alot of it makes perfect sense and should be checked and not just ignored.

I would offer this though.  Codes are written to be conservative for the average building. What you appear to be designing on some sort of regular basis (Slabs supporting 600-900 psf) are by no means average and in fact I would suggest you are designing something that probably few other people in the world are designing and as such should be looked at with a critical eye. The code was not written for your building and while these loads may seem "regular" to you, I would suggest are far from regular to everyone else and probably the code writers. I would argue that most pT flat plate two-way slabs are used for loads in the 40-150 psf range. Hell, the building code doesn't even list live loads larger than 250psf and that is for supporting truck loading.

To be honest, I am slightly shocked that you would even consider using a flat plate (PT or non PT) for the loading being considered.  I certainly can understand how a partial prestress would have negligible effect on your slabs-I haven't put numbers to it, but a PT slab with service live load of 600-900psf is probably akin to a non-pt slab with srevice live load of 300 psf or more of bending stress. I would guess that you must have slabs measured in feet thick (or centimeter) instead of inches (or mm) based on keeping stresses low at the columns while the center of the bays, there is relatively very low stress. If I had that kind of load, I would be using one way slab and beams (PT or non PT) because at those stress levels, it would seem as though a significant amount of concrete and rebar would be wasted within the interior of a bay where the slab doesn't have to be so thick. In fact, you seem to be suggesting you need this type of layout anyway given your drop panels, thickened slab beams, etc.  
rapt (Structural)
29 Nov 07 20:12
gsmith22,

I am not designing them. They are cases I see quite often around the world and they are fairly common in Europe, Middle East, Asia and Australia.

I am just trying to let people know that they cannot believe everything they read and are told by software salesmen and that is calculated by software, garbage -> garbage.
hokie66 (Structural)
29 Nov 07 22:12
Rapt is correct in that in other countries, floors are often designed for heavier loading than in the US.  For instance,in Australia many supermarkets are in shopping malls on the upper levels, and the loading docks and storage areas in these stores are typically designed for 300 to 400 psf (stacks of cans of peas are heavy).  Also, many tranfer floors between the parking levels and commercial or residential space above are designed with flat plates 2 to 4 ft thick.  
gsmith22 (Structural)
1 Dec 07 0:00
you learn something new everyday!  In my experience, when ever I had a transfer slab or loading of those high magnitudes, I used one-way beam and slabs. It provides a significantly better load path (especially for a transfer slab with column point loads), doesn't waste so much concrete between the beams (at some point repetetive formwork with beams is as cheap as flat formwork with a slab so thick), and as you can attest to, aren't relying on all of these simplified code design methodologies.  2' to 4' thick is just insane for a flat plate. What are the spans? You probably could of had 2'Wx2.5'D beams with 8" slabs between. Computers are only helpful if you understand the math behind the algoriths and can do it by hand without the computer.  Adapt isn't signing and sealing any drawings!  
hokie66 (Structural)
1 Dec 07 0:50
The transfer floors I am talking about are buildings where the architect designs everything above the podium without regard for supporting conditions below.  So the columns or walls above are more or less randomly located, while the columns below are controlled by carparking, but the carparking itself is often irregular.  I couldn't agree more that beams and slabs are a better system, but unfortunately when nothing lines up, beams don't work very well.

A typical example would be a 15 storey residential building over 3 levels of carparking.  The spans are usually in the range of 12 to 15 times the plate thickness.

There are some offsetting advantages: formwork simplication, less excavation, more attractive soffit with better lighting, simpler plumbing are a few.

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