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.

 

[dik]

Is what you are trying to describe what we used to call 'slab bands'?

These were like a continuous 'drop panel' in one direction, albeit a little thicker than a normal drop. The slab as designed as a continuous one way slab, adjusted for the haunch. The positive steel would be slightly greater than the +ve reinforcing if you considered the slab edge as fixed at the edge of the slab band. The negative reinforcing would be slightly less than designing the slab over the slab band as a cantilever with a point load and moment at the edge. -ve reinforcing was checked at centerline of the slab band using the greater depth and at the edge of the slab band using the slab depth. The slab band was designed as a wide, flat concrete beam, without stirrups, just hoops for ties.

Is that what you have?

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

 

[dik]

Something like... from 50 years back...

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

 

[structSU10]

There are continuous drop panels around the edge but interior drop panels are standard squares. The band around the edge is also quite heavily reinforced. see image below - the red zones are drop panels. standard slab is 10.5", drop panels are 15", spans are 30' one way 28' the other.

 

[dik]

The continuous 'drops' would be considered as a slab band. Proportions appear to be of the right magnitude, except I would have gone with slight deeper drops and maybe a slightly thinner slab... I don't recall slab to span ratios I used to use... marginally shy and used to check for deflections to thin it down a tad. I used to use slightly deeper drops; it helped with moments, shear, and reinforcing. Depth would be predicated on dimensioned lumber depth+ 3/4" for plywood. It's been several decades since I did any serious concrete design.

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

 

[SethGuthrie]

As for the original question about analysis options, in Ram Concept you can certainly experiment with calling the slab a one-way slab or using some other custom behavior to approximate the directional stiffness of the original design, or you can use a load history analysis to determine the degree of cracking based on the actual reinforcement.

 

[dik]

Thanks, Seth.. I've not used RAM... I'd try it both ways and see what the reinforcing for both methods is. It's a little fuzzy, but I seem to recall the slab for the parking deck for Sears in Regina was 9 or 9-1/2 with 10" drops (total about 19") for 28'x28' bays... but may be out a bit.

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

 

[KootK]

This kind of feels like a genuine error in my opinion. I see nothing about the system that would justify a markedly different design approach in the two directions.

There was actually a time when some folks believed that a slab only needed to be reinforced in one direction. I'd thought that time to have ended well before the 60's though.

 

[dik]

Yup... but if it fails, then it may be a matter of taking a look at the yield line failure to see if it complies and if yield line is acceptable as a rational design method in the code. If it works with one method and not the other, then yield line may yield a 'more correct' solution. It depends on how far off it is and what the effect of 2x the reinforcing is...

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]

Using FEM to analyse a structure where you are completely ignoring 2way action is not logical.

For regular column layouts it will give similar results as long as Mxy moments are included in the design values in each direction, but if the column pattern is irregular the effects of 2way action can give very misleading results compared to 2D analysis of each design strip in each direction which is what you are actually designing and building.

In the 1960's it would have been analysed as 2D design strips in each direction if not done by direct design method factors rather than analysis.

Kootk
ACI still had that logic into the 1950's if I remember correctly, not 50/50, but something like 60% each way.

I had a discussion with a very senior engineer in the early 1980's (probably trained as an engineer in the 1950's) about flat slab design and he still thought you could design for half of the load in each direction in a flat slab and wanted to know why I had grossly over designed his slabs!

 

[bugbus]

Not sure if anyone mentioned this previously, but I would consider doing a FE model with the flexural stiffness of the slab different in the two directions, proportional to the quantity of reinforcement in those respective directions. You will end up with bending moments basically proportional to the quantity of reinforcement and closer to the 'real' behaviour of the slab.

 

[Ingenuity]

ACI still had that logic into the 1950's if I remember correctly, not 50/50, but something like 60% each way.

Along those same lines, it was not until 1971 when ACI 318 required strength design for 100% of statics.

This is from ACI 318 in 1963, where designing for 80% of statics was ok:

J.R Nichols published his paper on the total static moments in flat plates 1919, with much controversy:

 

[dik]

I just remembered... way back when, we used to reduce the max -ve moment slightly to accommodate the 'rounding' effect the reaction has on the SFD... it's not a 'sharp spike' but a slightly rounded point. I don't recall the method, except it was a function of the support dimension, the shear and the slab thickness. I seem to recall it was the result of model studies that Per Christoffersen did on slabs. FEM studies should reflect this...

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

 

[dik]

Part of the fun of engineering is determining why things work, when in all reality, they shouldn't. The old expression that the person that says something is impossible should not interrupt the person that's doing it...

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

 

[centondollar]

Gusmurr,

the reinforcement will not change the flexural stiffness by much, and for a plate model, applying it becomes rather technical and requires input of orthotropic plate parameters. The "real" behavior of the slab, if designed with linear elastic FEA, will be two-way action of various degrees, with design to be done against Mxx, Myy, Mxy (bending and twisting) and Qx, Qy (shear). There really is no way around this, and the various types of "strip methods" are not correct from a structural mechanics perspective and nowadays a relic of the pre-computer era where analysis was tedious and (due to hand-calculations being used) prone to error.

 

[KootK]

...and the various types of "strip methods" are not correct from a structural mechanics perspective...

In my experience that statement is wholly inaccurate.

 

[KootK]

If it works with one method and not the other, then yield line may yield a 'more correct' solution. It depends on how far off it is and what the effect of 2x the reinforcing is... pipe

I don't believe that the yield line method will yield much edible fruit in this situation. That, because it will be limited by the folded plate yield line pattern shown below. And that's basically just one way slab design with redistribution.

 

[KootK]

Not sure if anyone mentioned this previously, but I would consider doing a FE model with the flexural stiffness of the slab different in the two directions, proportional to the quantity of reinforcement in those respective directions. You will end up with bending moments basically proportional to the quantity of reinforcement and closer to the 'real' behaviour of the slab.

I'm skeptical. That would work for something like a wall supported, rectangular panel of modest aspect ratio but here, where the aspect ratio is very large, I doubt that the strong direction slab stiffness is anywhere near stiff enough to make an appreciable difference. As an extreme example, imagine that the slab was actually one way pan joists running left to right in panel drawn in blue below. The joists in the middle of the panel would have such large spans that they would do little to shield the slab from flexing in the perpendicular direction.

 

[Celt83]

If you have the funds this program for yield line analysis of slabs looks promising:
LimitState:SLAB

I'm making a thing:

http://www.thestructuraltoolbox.com

(It's no Kootware and it will probably break but it's alive!)

 

[dik]

It's hard to say...

We don't know how close the positive reinforcing is to failure (he said it had failed, but not by how much), and there may be a little reserve in the negative reinforcing to carry the day... it's a matter of taking another kick at the cat... before looking at other alternatives... I'm no longer up with the concrete code, but I seem to recall a provision that you could re-distribute flexural moment is less than a certain % of reinforcing... I don't recall if it was for beams and/or slabs. This was to reflect plastic redistribution... might be out to lunch... it's been decades since I did any serious concrete stuff.

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