two way slab strong bands one direction

[structSU10]

I am looking at an existing two way concrete slab with drop caps from the mid 60s that has one direction very heavily reinforced - good for 2x the stated design live load - while the other direction has much less reinforcing and doesn't quite achieve the stated design live load. I am using RAM concept for this analysis right now. Is anyone aware of an different analysis method for these systems they may have used? I would be surprised if load can be redistributed the other way, or that treating one direction as a one way slab supported by the stronger bands would change things too much, but maybe I am off with that thought.

The odd thing is other floors in the same structure are reinforced as a more conventional two way system, with similar bars each way.

 

[KootK]

It's hard to say...

Something can certainly be said. In the jurisdictions that pay attention to redistribution, you'll not get the ability to redistribute more than about 15% of the hogging moment. And even that's only on the table if:

1) The top mat reinforcing is so sparse that it doesn't trigger reductions in the available redistribution and;

2) Redistribution wasn't assumed to begin with. It may well have been if this was a direct design method thing.

 

[structSU10]

Some update - the positive steel and negative steel in one direction has capacity for about 60 psf. the negative steel in the strong direction has capacity for 100 psf, while its positive reinforcement is at about 70 psf. The C shaped band can generally handle about 90 psf. As stated above I think I would be chasing something that may only get a little extra capacity if anything.

This is a retrofit with added load, and there is an idea to do a bonded topping to increase slab strength to what is required (generally about 80-85 psf).

 

[dik]

I don't know... that may be enough...

Thanks, that may not be enough... what load capacity do you need it to meet? What is the strength in the other direction? Can you load test it? A bunch of questions...

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Do you feel any better?

-Dik

 

[hokie66]

structSU10,

As to the bonded topping idea, would the topping be reinforced?

 

[rapt]

Dik,

The rounding effect was to reflect the "reverse bending" over the length of the column. You basically applied the reaction at the column as a reverse UDL over the length of the column. For UDLs, it resulted in a moment reduction of 2/3 of the difference between the moment at the centre of the column and the moment at the face of the column.

Most design codes these days say to design for the moment at the face of the column, so a slightly larger reduction.

Interestingly AS3600 uses the moment at .7 times the distance to the face, which is pretty close to the .66 figure!

Interestingly from what I have observed in practice, this should only be done for the column strip moment. Middle strip should be at the centreline of the supports.

centondollar
And how does a linear elastic FEM model accurately show the design actions in a cracked concrete flat slab which never experiences a UDL loading, creeps, shrinks and may often be over loaded at well below full concrete strength during construction?

And how do you detail the reinforcement to exactly match the variations in the BM pattern - you do it in strips!

 

[dik]

thanks for the added info, rapt... it also 'appears', as you noted, if you consider the reaction as a UDL concentrated over the column, and it was only done for column strips. It's just a means of eliminating the cusp in the BMD and reducing the design moment a tad (not unsafely). I'd forgotten that I used to use that approach for highrise stuff. In a real continuous plate, there should not be a cusp in the column strip, either, but I've never seen that addressed. Other than 'simple stuff'... grade beams and foundations and the odd floor beam, I haven't done any serious concrete design in decades.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Do you feel any better?

-Dik

 

[rapt]

dik

If you do an FEM analysis and define the column as a stiff area rather than just a node, you will get a similar effect.

But most FEM analyses do not go to that detail!

 

[centondollar]

"In my experience that statement is wholly inaccurate. "
Do elaborate on that. I am sure that you are aware of what moments plate theory predicts, and that a slab is not a collection of "unit-width beams" due to the Poisson effect.

 

[centondollar]

"And how does a linear elastic FEM model accurately show the design actions in a cracked concrete flat slab which never experiences a UDL loading, creeps, shrinks and may often be over loaded at well below full concrete strength during construction?

And how do you detail the reinforcement to exactly match the variations in the BM pattern - you do it in strips!"

The first question is an oxymoron. There is no accuracy to be found if the assumptions made are absurd. Overloading during construction is a mistake on the part of either designer, contractor or both, and is thus not a relevant matter in this discussion. Creep does not affect the ultimate limit strength of a slab. Shrinkage can be modeled reasonably accurately and added as a load in a FEM program. Finally, the question of whether the slab experiences a proposed design load is not relevant - there is always an inherent uncertainty in determining actions, and the purpose of structural design is to pick the most likely worst-case scenarios and to ensure that a structural members withstands those actions. If you want to do things "exactly", mathematics is the field you should study!

Regarding reinforcement detailing, I do not understand your claim. Designing reinforcement according to a calculated moment and shear envelope, and ensuring proper bond lengths and lap lengths, is not the same as designing a slab according to the "strip method"!

 

[dik]

Thanks rapt... pretty much thought that... I hate one dimensional knife edges, myself. Now that the slab is inadequate... it's a matter of finding a way forward. Evaluate the load requirement or restricting occupancy, testing, or reinforcing.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Do you feel any better?

-Dik

 

[Settingsun]

I would think that fiddling with the stiffness would only be worthwhile if the weaker direction has some spare capacity in the middle strip. But you could instead do a service load analysis as a two-way slab with typical stiffness values then do a separate ultimate analysis by hand for such a regular layout, and likely squeeze more out of the existing reinforcement.

 

[dik]

It's not really fiddling with stiffness, except as caused by local cracking. It's a matter of gaining a little residual strength by redistribution of load due to partial 'failure'. The added strength being able to accommodate the load. In this case it's insufficient, it would appear.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Do you feel any better?

-Dik

 

[hardbutmild]

Plastic analysis yields great results, of course if done within reason. Hillerborg method, strut and tie method or other plastic methods provide safe results (this was experimentally verified).
No analysis is "correct", as you yourself mentioned, but you insist that plastic methods do not provide adequate results.

You have to use both elastic and inelastic aspects, no matter how you design. It's not very reasonable to make a distribution that's far away from an elastic solution, but you can not use only elastic assumptions.

One fantastic example of this is the way boundary conditions are considered in RC. For slabs usually a pinned connection at the edges is assumed. This fundamentally requires some amount of plastic redistribution since there is actually no hinge there, right?
Another is a singularity where you have a huge value of some internal force at one point. you don't actually put in enough reinforcement to cover that, do you? you usually say "oh, this is local and will redistribute", but you never actually check will it be able to redistribute, you just do it by the feeling... why not use a plastic method where you can exactly track your redistribution and control it?

I think that what rapt was trying to say with his last remark (please correct me if i'm wrong) is that you design in strips. It is impossible to do it any other way. you certainly don't place reinforcement to follow BM or shear diagram exactly, you pick a region and put in the same reinforcement in it... or better yet, you put the same mesh over the whole plate and add additional reinforcement where needed.

 

[centondollar]

Just a few comments:

The reduction of moments over supports is not based on feeling, but rather on experimental results performed in the last century. The support is not a pin, but rather has finite width, and thus creates a moment in the opposite direction of the hogging moment, reducing the absolute value of the moment in the vicinity of the support.

Furthermore, it is strictly speaking not possible to track redistribution with plastic methods, since they are based on assumptions of where yield lines will form, and those assumptions are up to the designer to evaluate. Choosing the correct model (yielding the lowest energy and smallest collapse load) is more of an art than a science, which is why many codes (including EC2) do not allow it for e.g., bridges of many types.

I cannot speak for what rapt was trying to say with his last sentence, but my impression was that he was equating discrete (non-continuous) design of the reinforcement with calculation methods that are based on strips. This, of course, is not necessary at all: it is possible to use elastic methods, find the "exact" (as far as plate theory reflects reality) elastic internal forces, and to design against those with a finite set of reinforcement laps and splices. This, in my experience, is how most commercial large-scale and technically demanding RC design is done these days; it requires very little guesswork or knowledge of art (yield line analysis) and is based on structural mechanics.

Using the same mesh over the whole plate will make it locally over-reinforced (unless the plate has uniform moment, which doesn´t usually occur), and should thus be avoided.

 

[hardbutmild]

The reduction of moments over supports is not based on feeling, but rather on experimental results performed in the last century. The support is not a pin, but rather has finite width, and thus creates a moment in the opposite direction of the hogging moment, reducing the absolute value of the moment in the vicinity of the support.

I was not talking about that. I was talking about when you have a large concentration like in this picture.

What will you do?

The support is not a pin

I agree... how do you model the plate edge? as a fixed edge or a pinned edge?

is more of an art than a science, which is why many codes (including EC2) do not allow it for

EC2 allows plastic methods and what you're describing are UPPER-bound solutions, I'm talking about LOWER-bound solutions.
EC2 has a whole section on strut and tie and specifically allows for moment redistribution and plastic design.

it requires very little guesswork or knowledge of art (yield line analysis) and is based on structural mechanics.

yield line method is only one of the methods... and i never mentioned it, i specifically mentioned STM and hillerborg method.

What do you do with seismic design (keep in mind that this is often the most dominant load for RC structures)? "very little guesswork" suddenly becomes a whole lot of guesswork when using linear fea. your "structural mechanics" fails miserably unless you plan on using nonlinear dynamic analysis.
This is a huge problem... you were talking about EC so I'll assume that you're from europe. Most people do use FEA method as you mentioned and most of the ones I worked with do not respect capacity design rules or special wall or column detailing or anything. They see results from FEA and do not understand why it needs to be modified.

Using the same mesh over the whole plate will make it locally over-reinforced (unless the plate has uniform moment, which doesn´t usually occur), and should thus be avoided.

For a 20 cm thick plate 257 mm2 mesh is usually minimum reinforcement. For many houses or smaller projects this can be enough to cover much of the plate. You either do not provide minimum reinforcement or you're deliberately yanking my tail. It's probably the second one because you're suggesting that reinforcement should follow the BM diagram exactly. That will produce at least a 1000 different rebar lengths, absurd.

 

[centondollar]

"I was not talking about that. I was talking about when you have a large concentration like in this picture."
You were talking about exactly that, since what your figure shows is the internal force (bending or shear) diagram that reflects a plate supported by a line with infinitesimal width.

"I agree... how do you model the plate edge? as a fixed edge or a pinned edge?"
I already explained the procedure commonly adopted for estimating the effect of a support with finite thickness, which tends to reduce the maximum hogging at intermediate supports.

"EC2 allows plastic methods and what you're describing are UPPER-bound solutions, I'm talking about LOWER-bound solutions."
All plastic methods are upper-bound solutions.

"EC2 has a whole section on strut and tie and specifically allows for moment redistribution and plastic design."
The bridge EC2 does not allow for plastic design - as in, determining internal forces based on hypothesized plastic collapse mechanisms. Furthermore, strut-and-tie is not based on yield lines (plasticity theory), but rather on a truss model.

"yield line method is only one of the methods... and i never mentioned it, i specifically mentioned STM and hillerborg method."
Strut-and-tie is more or less based on educated guesses. The principle behind the method and the literature will support this finding.

"What do you do with seismic design (keep in mind that this is often the most dominant load for RC structures)? "very little guesswork" suddenly becomes a whole lot of guesswork when using linear fea. your "structural mechanics" fails miserably unless you plan on using nonlinear dynamic analysis. "
You said it yourself: the most accurate results require nonlinear dynamic analysis. I might add that the material model for concrete is difficult to estimate correctly. In spite of this, linear elastic analysis and plastic sectional design (compression block and rebar) will give a conservative estimate for strength regardless of cracking, as I´ve already explained in the thread "Moment redistribution - Concrete Continuous Beams".

"This is a huge problem... you were talking about EC so I'll assume that you're from europe. Most people do use FEA method as you mentioned and most of the ones I worked with do not respect capacity design rules or special wall or column detailing or anything. They see results from FEA and do not understand why it needs to be modified."
I cannot comment on what others do, but I am aware of the fact that not everyone is interested to learn their trade. I am glad to notice that people who frequent this forum at least give the pretense of caring about their work.

"You either do not provide minimum reinforcement or you're deliberately yanking my tail. It's probably the second one because you're suggesting that reinforcement should follow the BM diagram exactly. That will produce at least a 1000 different rebar lengths, absurd."
I did not mention minimum reinforcement, nor did you, which is why I wrote the comment. Furthermore, I did not suggest 1000 different rebar lengths: please re-read the third paragraph.

 

[rapt]

Centondollar,

No, I was saying what hardbutmild thought I was saying.

 

[centondollar]

Good to know. Do note that I did not equate design according to linear elastic results to design with perfect (i.e., infinitely many strips and laps) rebar placement, so I´m not sure what reason the question was posed for in the first place. The strip method (a quasi-scientific method that ignores plate action (twisting resistance and Poisson´s effect)) is not equivalent to design with a finite set of rebar lengths and laps.

 

[hardbutmild]

The strip method (a quasi-scientific method that ignores plate action (twisting resistance and Poisson´s effect)) is not equivalent to design with a finite set of rebar lengths and laps.

It's not, except that if you have a finite set of rebar lengths you're no longer using your own principles. You no longer have a continuum, you no longer follow the BM, but choose a quasi-scientific method of roughly placing rebars... a mess really.

Your other comments are so absurd that I don't even want to comment them (such as denying the existence of a lower bound theorem of plasticity). I give up, you do you... I guess many buildings just miraculously stand up.

 

[dik]

It goes plastic at the same time... no redistribution; is that good?

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Do you feel any better?

-Dik