How Can RC Two-Way Solid Slab on Beams Be Analysed with Higher Accuracy? 4

[Huck85]

Hi, everyone

I am a structural engineer graduated 2 years ago. Currently I'm working in construction management; however I like structural design (my major) and I am planning to pursue practicing after completing my current project.

I'm trying to analyze/design a reinforced concrete solid slab on beams flooring system for a single family residence (please check the attached drawing). As you can see, there are one-way and two-way slabs (Non-uniform loads) and the spans are different in each direction. Therefore, ACI Direct Design Method can't be applied considering its limitations.

I really wanted to understand the moment distribution and behavior of two-way slabs at various situations (different loads, spans, boundary conditions), so I referred to the ACI Code and read many books and material about the subject but they briefly talk about two-way slab action and then immediately explain the DDM and EFM methods and their limitations (Don't they realize that architects and owners don't care about those limitations during planning?). I just couldn't find a comprehensive explanation source for two-way slabs behavior and moment distribution that considers the various situations.

Lately I found a design method called Marcus' method that can be used for analyzing and designing two-way slabs with different spans and can be applied for the attached building plan? but I don't know how accurate Marcus Method is.

The questions include
1- Could you please tell me how to analyze and design two-way slabs on beams with non-uniform loads and spans (any sources I could read)? Is there something I am missing about this subject?

2- How accurate is Marcus' Method?

3- I just started studying Finite Element Analysis after hearing of its power. Still not finished with it yet but it seems to me that it depends on the assumptions and inputs one makes(0.0). What is the most accurate FEA model that best represents RC slabs-on-beams? Is there anything I should carefully pay attention to during slab modeling using FEA from your experience?

Your help is appreciated
Thanks in Advance

A. Huckamee

 

[dik]

I would treat this as a regular two-way slab supported on beams with sufficient negative reinforcing to accommodate the unequal spans. It appears to be a 'one off' and is not repeated any significant number of times. It's a price the Architect/Owner has to pay for the irregular layout.

Little or nothing will be gained from a FEA approach. Your beam width may be a tad off because of the high torsional and flexural loads that can be created. An 8" beam only allows a couple of bars to be placed per layer... and may not provide the stiffness required for a two way slab.

If you can output a *.pdf, it may be possible for other engineers to more readily view the plan.

Dik

 

[BAretired]

Higher accuracy is not really the goal in a slab like this. The main goal is to select the most economical system. I do not know what that is because the location of columns and walls below the slab is not available, but my guess is that you would be better off to use a flat slab and get rid of all of those interior beams. It would be much easier to form.

Yield Line Analysis and Hillerborg Strip Method are two ways of dealing with unusual layouts. They are both good but they each have their limitations. Yield Line Analysis provides an upper bound to strength, so if you do not guess the correct pattern your solution may not be safe. The strip method provides a lower bound to strength and is the safer method. Neither of these methods tells you anything about deflections, so Finite Element Analysis may be a better choice but it requires a computer and the proper software whereas the other two are hand methods.



BA

 

[dik]

BA... I don't have a high degree of confidence about FEM deflections...

Dik

 

[BAretired]

dik, you may be right, but at least FEM considers them whereas the other methods do not.

BA

 

[hokie66]

Hard to give advice on framing this without knowing where the supports are, but 200 wide cast in place beams are not in my vocabulary.

 

[Huck85]

Yield Line Analysis and Hillerborg Strip Method.
Thank you Dik and BA.

In the above situation I have constraints:
1- Wall foundation and bearing walls below the beams are the supporting system. Columns are only used at the staircase which is not a problem here since it's easy to analyze.
2- I can't change the supporting system. it's under construction. Therefore, I have to use band beams around the slabs to connect them to the bearing walls.
3- For architectural reasons, in case beams are used they must be 8" wide and depth of not more than 30".

It's a private house with 40-lb/ft² live load and maximum span length not exceeding 16 ft. I think the torsional and flexural loads that will be created in the beams won't be very high. Yes I am limited to 8"-wide beam, however strength of an 8"-wide beam can be increased by increasing the beam depth (arm), adding more closed stirrups and providing more layers of re-bars(4no.7/3no.6). Beams are not the issue here.
A 8x30" rectangular section singly reinforced with six #6 bars is capable of resisting 280 K-ft applied moment and is tension-controlled.


Dik, how a regular two-way slab supported on beams is treated? and how can I approximate my analysis as much as possible for irregular layout?
BA, What do you mean "if incorrect pattern is assumed the solution may not be safe"?


Hokie66 You said 200-mm wide cast in place beams were not in your vocabulary. I've been practicing for only 2 years and I'm seeing a lot of constraints already (economical, architectural, mechanical, environmental, sustainability and from safety and health people), this reminds me of junior year courses, engineers solve problems considering available sources and realistic constraints. That's our profession.

 

[dik]

You may have some problems if you are limited to 8" wide beams.

Design moments for 2 way slabs if fairly easy to obtain. It used to be available in some ACI pubs as well as in the NBCC Design Manual from a couple of decades back. I'll see if I can dig up a recent source.

Dik

 

[hokie66]

My objection to beams of that width is purely from a constructability standpoint, not that they don't work technically. If you use 40 mm cover each side, which I think should be the minimum for beams in order to assure adequate consolidation, 10 mm stirrups, 20 mm bars each side, that theoretically leaves 60 mm for concrete placement and compaction. I know it is achievable, but most builders of my acquaintance will manage to screw it up. 250 wide works well. The other issue, which most folks seem not to worry about, is that beams should ideally not be the same width as their supporting columns, so that the reinforcement doesn't clash.

If the maximum span length doesn't exceed 16 ft, or about 5 metres, you probably don't need many beams. As BA suggested, a flat plate should work in most part. If you do need to use beams in some areas, "band beams", which are wide, shallow beams, may be the best solution. Why would there be an architectural limitation on width of beams in a residence? Isn't there a ceiling?

 

[BAretired]

2- I can't change the supporting system. it's under construction. Therefore, I have to use band beams around the slabs to connect them to the bearing walls.

That is not good. Design should be completed before construction starts, particularly if the engineer is inexperienced.

I don't think you will have time to familiarize yourself with the Yield Line Method or the Hillerborg Strip Method for this project. Maybe another time. When you do, you will learn that the Yield Line Method is an upper bound theory. For now, I would use conservative coefficients.

8"x24" or 30" beams are used commonly as grade beams in my locale, so I don't share hokie's concern about their use.

Good luck.

BA

 

[TXStructural]

Economy is seldom achieved on a small, or any low rise, project by minimizing materials. Formwork is about half the cost of any concrete construction. Stay simple and consistent. One of the problems we see in all kinds of construction is changes in slab reinforcement from span to span. It is simply not useful. Serviceability and deflections will be best served by not trying to squeeze every bit of capacity out of the slab on small projects, and by trying to thin up the slab unnecessarily. For high rise and large projects, economy comes from cutting small amounts in each members, as the weights build down the structure. In low rise and residential, you might save $100 to $500 for every $1000 in complexity you add - not really a good use of engineering time and construction labor (even more so in expensive labor markets.)

I have not had a chance to look the file you provided (PDF next time would make it easier), so I can't comment on the details. Be cautious about forces and pressures where your proposed 200 mm beams bear. Consider the difficulty forming theses beams and where they intersect supporting members. Consider shear in small bean sections carefully, and be mindful of the minimum bend diameter for stirrups.

 

[dik]

TXS... I posted a *.pdf copy of his file.

Dik

 

[dcarr82775]

Look up Equivalent Frames. That is how two way slabs were done before everybody went FEM crazy.

 

[JAE]

Huck85 - be careful with "six number 6 bars" in an 8" wide beam. The most #6 bars you can get in an 8" width are two. Three bars don't fit.
So you would have three layers of double bars to get six of them in that web. That reduces your bending moment by reducing d.

 

[dik]

JAE... he only needs 3 in the bottom... the 6 in the top can be placed in the slab <G>. Most code beam stiffness for 2 way slabs almost preclude the use of 8" wide let alone trying to put rebar in it.

Dik

 

[TXStructural]

dik, thanks, not sure how I missed that the first time through.

Based on what I see, the slabs will go one-way (but not all the same way), once your account for support conditions (oddly spaced beams creating odd end/restraint conditions.) Depending on how you load the slabs, you could end up with uplift on some beam spans.

I'm not sure who or why they laid it out like that, but efficiency of the slabs is NOT the problem, and if you want acceptable performance, it should not be taken to the thinnest or least reinforced section you can compute. Check various loading patterns (such as loading the large spans and not the narrow ones) and you may find that you need top reinforcing across the narrow (hall?) spans - and this is likely to exist in uniformly loaded conditions also.

As far as 8 inch / 200 mm beams, CRSI provides the following guidance:
ONLY 2 bars of #5, 6 or 7 only, with #4 stirrups, 1-1/2" cover, and 3/4" aggregate.
This does not work for 1" and larger aggregate, or #8 or larger bars. (Beware of crushed aggregate using nominal sizes, as these can be 3x nominal in the long axis, per ASTM)
Also, be aware that you will lose some "d" because the bars must be tied to the vertical legs of the stirrups to get permissible space between them. This requires them to "ride the radius" of the bend. Minimum bend diameter for stirrups are: #3 - 1-1/2", and #4 - 2"
bars will move 1/2" to 1" farther up from the bottom on the beam than in wider beams.

 

[dik]

TX:
I was more concerned about the odd beam arrangement and flexure and torsion... the latter being a bigger problem for narrow beams.

Dik

 

[TXStructural]

I agree that the beam arrangement is the issue. Making the slab stiffer can diminish the torsion issue, and is probably the best solution to keep the slab serviceable.

 

[Huck85]

I've been busy studying Arne Hillerborg Design Method. Thanks BA and dik.
TXStructural, the halls need top reinforcement for the negative moment created in the short span. That's actually one of the reasons I posted this thread. Thanks for your input.

Thank you gentlemen for your interaction. I agree with all of your inputs
This site is great. It's really good to find a place where you can find someone with whom you can find regular contact as a Mentor, someone understands what you are trying to become and can offer guidance and help in achieving that goal.


As I mentioned before I'm working in Project Management & Execution Division, where I am a member of a team who's responsible for planning, organizing, monitoring, controlling and managing the construction of projects to achieve time/cost/quality targets. At the beginning of my current project the contractor were to choose whether a paneled slabs system or solid slabs system. They actually chose the solid slabs even-though the solid slabs have more steel and concrete and the measuring unit of this pay item in the bill of quantities is squared meter. They were more concerned with the complexity than the material cost. My current project is 12000-m² (129,150-ft²)building. I am on site 70% of the time.
Hokie66 you're absolutely right; I've noticed that 200-mm (8")elements (beams/walls) are the most critical parts of concrete structures that suffer honeycomb and require extra care during concrete placement and compaction. The changes in slab reinforcement from span to span are just a headache for workers and site engineers.
Yesterday at the site, we made a sample of 8"-wide form with 3no.6 bars I couldn't see what below them. Yes, dik, TX and JAE (3 bars no.6) three 20-mm bars in a 200-mm beam! don't fit. A prudent structural engineer should avoid such sections during design. Now I understood why my department insists that fresh engineers must work on-site with the Execution Division team at least one year before they decide moving to the Design Section.

To answer some of the questions:
Hokie66 the flat soffit of the RC slab will be used as the ceiling. The walls are 200mm. The owners don't want beams projected from the walls.
BAretired Don't worry. Five months ago, I started preparing myself by designing/analyzing structures that had already been designed (case study). Then I'd compare my results with the design drawings. I've designed three structures but one design (a museum being the second in the series of my exercises) I couldn't do coz it had an irregular layout. As far as the attached plan, it belongs to a couple friends to the family. When I met them at a wedding, they showed me their house project and asked if i could design their slabs. The minute I saw the plan, I noticed the irregular layout (my weakest point) and told them to consult a structural firm, since the plan is a little alien to me and requires time to study it. They said that their schedule was after completing the walls they would stop for four months before proceeding to the slabs; as they save a percentage of their salaries and use it for building their home (a way of saving money and evading loans). This is my chance to work hard and overcome this obstacle. "if you avoid failure, you also avoid success". I don't have to design their unusual slabs. But if I did complete it on time it'd be conservative (for now), consistent and considering the constructibility issues.


P.S. Helpful resources for analyzing two-way irregular slabs will be appreciated.

A. Huckamee

 

[dik]

This is my chance to work hard and overcome this obstacle. "if you avoid failure, you also avoid success". I don't have to design their unusual slabs. But if I did complete it on time it'd be conservative (for now), consistent and considering the constructibility issues.


Not something I strive for...