Reinforced Concrete Flat Slab 1

[micana]

Hi All,

I'm a Graduate Engineer and have been tasked with designing a part of a RC building. The building shall have a central RC core and columns only around the edge of the floor plate. Thefloor plate is somewhat elliptical, whilst the core is circular. The intention is to design the slab spanning between the perimeter columns and the central core walls as a FLAT SLAB, ie without any drops for beams.

The spacing between the perimeter columns and the core varies between 7 and 9 meters, so we are also contemplating the option of having a post-tensioned system, but this is perhaps irrelvant for this question.

My query which i hope somebody could help me with is whether or not to consider the slab as a flat slab in the design, or otherwise. The reason is that typically with flat slab design examples and theory, the slab is always supported on all 4 edges by a column. In this case however, each bay only has two columns on one side, and a RC wall on the other side. Would this in your view still be considered as a typical flat slab in terms of design?

Any thoughts on this would be appreciated. Thanks and regards.

 

[CELinOttawa]

The method of analysis is what you need to choose here, flat slab being the intended goal, not a type of design as you imply.

I would use yield line analysis to determine the requited slab thickness as well AA bar size, distribution, and placement. That is what you need to figure out.

Good luck!

CEL

P.S. For your first one, you should be either provided a detailed design example or simply be running the numbers on someone else's job. See one, assist one, do one is not only useful as a process for Doctors, but perfectly suited to Structural Engineering as well.

 

[micana]

Thanks for your prompt reply CEL.

I agree with your reasoning in that it's the method of analysis that i need to choose. I'm familiar with Yield line analysis, but in this case the slab bays are not very regular which in my opinion complicates this method as the choice of yield line is not straight forward. The bays are basicially in a fan shape with a curved inner and outer edge (due to the circular core and curved outer edge respectively). I will give Yield line analysis some thought, but in the mean time i would be interested to hear your thoughts on the use of what is known as the 'Equivalent Frame'. Have you ever applied this and do you think it could be used here given that in one direction i have a wall support on one edge, and a column on the other edge?

Thanks also for the reccomendation you made at the end. In reality maybe i made it sound like all the responsibility for the design is mine, which in reality it's not as i will have my work checked. Nonetheless i dont want to look like a complete idiot at work so im doing some extra home-work before next week

Thanks once again and i look forward to any additional feedbck you, or anyone else, could provide.

 

[ukbridge]

Micana, have a look for the book "Practical Yield Line Design" which is a good practical text on the subject. The book gives details on how to analyse slabs for non-straight forward situations. The method requires some knowledge of identifying failure mechanisms that could/may be overlooked by inexperienced graduates (like myself).

It might be worth trying a number of analyses and comparing the results. For example you could do a relatively simple FE plane analysis to determine peak wood-armer moments, use the equivalent frame method and (if you have time which is a rarity in a consultancy!) have a go at a yield line analysis.

It sounds like you're in a fantastic position which will give you a lot of experience, don't hesitate to sit down with your director/senior eng to discuss the problem as its not straight-forward as their experience will be very beneficial to you.

 

[micana]

Thanks for the feedback UKbridge, will have a look at the book you recommended. I have in fact already prepared a FE model using Staad and want the hand calculation to verify these results. Thanks again and best regards

 

[CELinOttawa]

Hi Micana:

Yield line analysis can be undertaken for any shape, and is particularly useful for regularised shapes (of any form) such as those of a multi-storey structure.

Learn the method. Don't apply canned formulae, but instead work out the yield lines from first principles. You'll be surprised just how useful genuinely understanding yield line analysis will be!

The caution offered by UKBride is tremendously important. If you can, and you'd like, post the floor plate and support conditions, and I'll sketch you a head start.

 

[ukbridge]

*bridge .

You should be able to download it on IHS/CIS if you're based in the UK and your company has a subscription.

 

[rapt]

Micana,

Yield line analysis may give you an ultimate strength solution to your design, but it does nothing to satisfy deflections or crack control. And it is deflections that will control the section depth, not ultimate strength. Yield line will give you the reinforcement pattern for strength, but you will need to add extra reinforcement in other areas to provide crack control, as yield line allows redistribution from some tension areas to provide a load path but that is only an ultimate strength solution. Crack control is still required in areas where stresses have been redistributed from.

I would use FEM to determine my load elastic paths and reinforce for them, rather than yield line. And remember for deflections, STAAD is giving you short term uncracked deflections. If reinforced for the elastic moment pattern in the slab, actual long term deflections will be about 6 times the STAAD result. If reinforced for a yield line pattern that requires substantial redistribution from the elastic moment pattern, this deflection estimate could increase significantly.

 

[hokie66]

I agree with rapt. For a check, I would just do several sections as one ways slabs, spanning from perimeter to core. The curves complicate things, but you can overcome that with conservatism. Don't skimp on depth in a flat plate. And the design at the perimeter will be the most challenging, unless you have spandrel beams.

 

[micana]

Firstly, thansk a lot for your comments, each have been helpful.

CELinOttawa, thanks for your offer to help out - i really appreciated it. For now though i think i'll continue with the FE analysis and try some more trivial ways of verifying these results. If eventually i do resort to using the yield line method, i'll repost here with an update

To UkbridGe , i actually managed to find a PDF copy of the book you mentioned for free

To Rapt... Thanks for your feedback and it's for this reason that i have decided not to look further into Yield line analysis for now as i tend to agree with your reasoning, based also on other info i have found. With regards to your comment about the slab deflection, i was aware of this however you have concerned me by saying it could realistically be higher by a factor of 6. What i have been doing till now to account for creep and shrinkage was to modify the concrete stiffness in the Servicieability Load Combination by a factor stipulated, i believe, in the Eurocode (as i am based in UK). The reduction factor is = 0.5E/(1+creep coefficient). So basically, i am carrying out normal Elastic Analysis but with a reduced concrete stiffness in order to approximate deflections. I am aware its an approximation, but hopefully the margin of error would not be too large (i have found that it could be +/- 15%). Would you agree with this?

To Hokie66, thanks for your thoughts. I originally wanted to avoid an edge/spandrel beam in order to speed up construction, but i will ultimately decide on this after checking deflections and sagging moments that result without it. My guess is that i will surely need a beam for the largest of the bays, but could maybe do without it for teh smaller bays.

 

[hokie66]

Without spandrel beams, punching shear quickly becomes an issue for flat plates at edge and corner columns. You must allow for the unbalanced moments in analysing for punching shear.

 

[CELinOttawa]

*sigh* Sorry for missing the 'G' UKBridge...

I'm surprised to see such criticism of yield line analysis, particularly from some of our most esteemed members. It is true that yield line analysis can only find the ultimate limit state, but that's the same for manybof our methods of analysis. It is a part of the total solution, just as PhiM for your bending moment would be in a beam design. Both are strength checks which then require a suitable serviceability check, and the OP was looking for a method to check the computer results by hand. I think that is highly admirable, not being one to trust the idiot boxes without good cause myself.

All that said I have to admit that you gentlemen have me a bit worried... I've always used yield line to double check black box results. In the case of complex tilt up panel design, I've often used it exclusively.

For the serviceability check there are some very easy options. I don't know if it is common practice, but I complete a yield line analysis with a detailed review of span to depth ratios against the ultimate moments I've calculated. This is consistebt with the serciceability provisions used for the design of flat slabs in A23.3. Frankly I've always found the results to be pretty close to FEM.

Note that I've never seen a major discrepancy in the adjusted yield line to FEM results without finding an error in the model or the yield line analysis.

RAPT: Can you give an example of significant discrepancy? I'm very interested, and you have a heck of a lot more experience than me, so I trust you to be able to reach me something here!

 

[rapt]

Micana,

With a creep factor of 2,
.5/(1+creep factor) = 1/6!

Being an old school engineer (though younger than Hokie66), I think there should always be edge/spandrel beams. Unfortunately the form workers have won in UK/Europe and they tend to build flat plates without them. I think it is a bad idea.

CELinOttawa ,

It depends on the yield line pattern adopted. In some cases an elastic based solution is difficult to detail and yield line is appropriate, but in my thinking any concrete member should be designed as close as possible to the elastic action of the member to avoid significant redistribution. That way crack control will always be satisfied and you do not have to try to figure out what is happening with deflections.
FEM is giving you the elastic uncracked (normally) deflection result. Not the cracked, redistributed deflection.