Calculating the Load Bearing Capacity of Concrete Floors

There isn't any one formula, the selection of which one depends on how the slab is supported, where the rebar is placed, the type and placement of loads, etc. etc.

You need to hire a professional engineer who will properly define the problem and then perform the appropriate calculation.

you can check for helpful-info from the "Wire Reinforcement Institute" ....

link : http://www.wirereinforcementinstitute.org/pages/pubs/structural.htm

I believe WRI YF 700-R-07 should be useful

Good Luck :)

Is this a homework problem?

You actually need to give more information.

What is supporting the floor...Slab on grade? Columns? Where are the columns?

What is the span?

Is the slab designed as a one way or a two way slab?

Where is the rebar located and what is the distance between the layers? what is the clear coverage of the concrete over the rebar?

Any reinforced concrete textbook could help with this. I have "Reinforced Concrete mechanics and design" third edition by James MacGregor. Chapter ten goes into 1-way slabs and continuos beams, and chapter 13 has 2-way slabs. However, without an understanding of the basics of concrete design and analysis you probably won't find what you are looking for.

I suggest though that you follow the previous advice and hire a structural engineer that knows concrete, and you will save a lot of time. Unless this IS homework; in that case you should read your textbook, and then go talk to the TA. That helped me get through all my concrete classes, and I actually became reasonably confident in my work.

Cheers

Oh BTW, if you are a student, register and join the group. I find that I am always getting some tidbits of knowledge about everything I am interested in on this site.

Here's a real-life question/challenge that if someone was inclined to help me out with they would recieve nothing but my immense gratitude ;)

I have a two-car garage, red-brick construction with a sloping floor and a concrete deck as roof and roof deck, built around 1900. The clear span of the concrete deck is 21'-6" X 17'5" and the brick masonry walls which support it are 8". There is steel supporting the garage door openings with the flange being about 4" but the web is not visible(assuming it's an I-beam). The concrete is about 10" thick.

I have to assume that with such a long span that the concrete is reinforced with steel but have no way to confirm this other than the fact that it hasn't collapsed yet in 110 years and it's been used as a roof deck through-out it's life.

Here's the question: How much load can I put on this concrete deck, considering that it is currently empty except for some rubber roofing material and winter snow, rain, a few potted plants and etc? My intention is to put a very substantial wood deck on top, supported only by the concrete and as I transported the wood, I found it to be much heavier than I expected which raised concern about the concrete load capacity being enough. So I want to know what the load capacity is.

I measured the thickness of the roof deck by measuring down from the exterior, subtracting the parapet and the side-entry threshold curb, then measured from the garage floor to a small exposed area of the underside of the deck, did a little math to accomodate the garage floor slope to get a slab thickness of about 10". I was surprised at this but don't know much about conrete deck from the 1900's so maybe it's normal.

here's a picture of the garage:

Hello ACE,

In order to determine the load-carrying capacity of your existing roof slab you are going to need to determine several more items, such as:

1) Concrete compressive strength in Pounds per Square Inch (PSI) as determined by the Windsor Probe method. This is a non-destructive probing method. I would recommend no less than 6 strategically placed tests. This test is usually done by a Certified Tester working for a Materials Testing agency.

2). You need to know the depth of any reinforcing steel bars as well as their size (diameter) and spacing. This can be done with non-destructive sonographic equipment operated by the same testing agency.

3). You going to have to determine several strength characteristics of the reinforcing steel bars: tensile strength and Yield Strength. Your testing agency will need to core the slab in several place to obtain representative samples that will require additional testing back in the laboratory.

IMHO, based on the costs of obtaining the aforementioned data, it may not be worth your while to use the roof for additional purposes. It will be very costly. And in order for a structural engineer to calculate the capacity of the slab you need all of the information....it cannot be done without each and every piece of information that I've listed!

It may be better for you to clear span your wooden deck framing members the short direction (17'6" span) that is supported only by the brick walls only if they're in very good shape (same with the old mortar). Do not support the wood members with the existing concrete roof slab because that's begging for real trouble, such as catastrophic collapse.

I would suggest using Micro=Lam beams capable of supporting a /50 psf Design Live Load for that clear span. The live load deflection should be limited to Span (in inches)/360 = 210"/360 = 0.583" and no more.

You had better first contact your local municipal Building Inspector/Code Enforcement Officer to determine if what you're proposing is even permitted. Do not start any construction without a Building Permit.

In closing, you may be better off obtaining the services of a Licensed Professional Engineer specializing in Structural Engineering to determine your slab strength and load carrying capacity.

I wish I could help you further, but I am not licensed to practice engineering in PA where you're located.

Good luck!

Thank you for your input and suggestions CaptMoosie.

I considered spanning the short direction with deck joists but decided against it because that puts the decking above the parapet and makes the railing useless and the project unsightly from the street.

The roof was designed as an occupiable deck space so it surely holds more than the load of a few people considering it's size and that it was built with concrete and not wood joists-I would assume 8 or more people, iron furniture, planted pots and etc. With that assumption, what if I make some other safe assumptions,

-let's say the compressive strength of the concrete is 2500psi

-let's say the rebar was the minimum used for such a slab, and the spacing was the minimum as well.

Will I be able to get an answer that, although may be minimal, at least it will be something to go with?

The other option I was considering was to simply halve the distance of the long span with a beam underneath or a column in the center.

Thoughts?

Making those assumptions would get you a conservative capacity since 2500 psi is generally used on sidewalks, but steel would be a slightly harder thing to guess at. The amount of steel need is related to many things including the depth of the concrete, and strength of concrete. Looking in ACI318-05 you would find the formulas for A_smin which would give you the minimum amount of steel required by code. If you know what year the structure was built, and then looked in the ACI code book for that time frame, you would find what the minimum for that time would have been. Once you found that you could then find the moment and shear capacity of the slab and work backwards to get a psf loading.

That's a great idea! I didn't know that information was kept. Thanks that helps a lot!

Dear Ace,

IMHO you should not follow Idrivetrain's advice. His advice would be valid if the concrete slab was much more modern and not nearly 100 years old.

The reason why is fairly simple: when your roof slab was constructed Contractors generally did not use deformed steel reinforcing bars as they do use today. If fact, the steel rebar or wire mesh that must likely was used in your slab most likely has smooth surfaces, not deformed, thereby allowing much less bonding between the concrete and steel.....ie, it'll slip under moderate to significant loading. Also, concrete slabs way back then (and into the early 1960's) were generally designed using the "Working Stress Method", which affords you very little Factor of Safety against Catastrophic Collapse with no warning. Today, the American Concrete Institute handbooks and specifications use what is called the "Ultimate Strength Method" of concrete design where all design is based on high strength tensile steel deformed reinforcing bars and a host of Factors of Safety to prevent Catastrophic Collapse or failure and give the occupants a lot of early warning.....ther slab is designed around the ductility of the steel rebar. You slab isn't. Additionally, I doubt very much that any Licensed Professional Engineer designed your rood slab nearly 100 years ago. Back then the Building Codes and the licensing of engineers was very lax and most contractors just threw up constructs willy nilly without solid engineering behind everything they built....most often they stand for years untested until someone down the pike ultimately tests the construction with heavy enough load to break it.

Also, don't safely assume that 2,500 psi is the actual concrete compressive strength that is in your roof slab because it might be as low as 600 psi or all the way up to 5000 psi or even higher. You just don't know until you actually test it! To make such assumptions to quantify strength of a composite member such as your slab is VERY DANGEROUS because there are too many unknowns that must be eventually qualified (see my check list in my previous posting above).

If you're very serious about going forward with your roof deck project then I strongly suggest that you at least sit down and talk face to face with a Registered Professional Engineer who is also a qualified Structural Engineer. Generally, a consultation meeting will most likely cost you nothing or a very small fee and very well worth it.

One last thing, you may not even get a Building Permit from your municipality without a PE's signed seal affixed to any construction drawing that you will most likely need to submit to the Code Enforcement Officer. I beg you not to build that deck without going through the Building Permit process! The reason why is that if go ahead and buil;d you deck without a permit and the slab failes for whatever reason, then you will be held legally liable for any persons injuries or death as well as any related property damage.

If you need to talk to a LPE such as myself then I'm willing to talk to you on the telephone or Skype.....just PM me account here and I'll call you or you can call me. Unfortunately I will not be able to help you out later on since I do not practice Professional Engineer in PA where you are...only in NYS for now.

Good luck!

The Capt is correct again GA+. I must have missed how old the structure was. Since it is as old as it is, it's not within my realm of experience, and I should have read more carefully. I should have paid more attention; a mistake I shall work harder at not repeating. In this case the situation is more complicated than I had assumed (yes, I know what happens when I assume and it happened), and I agree with CaptMoosie. His list in the previous post is the best route to take considering the age of the structure. Thanks for the good catch CaptMoosie.

Hello All,

Is it me, or does it seem that lately that there is a surge of (a). Students submitting their homework problems in CR4 Forum, or (b). Guests looking for "Freebie" engineering advice and solutions rather than hire the services of a Licensed Professional Engineer to solve their problem(s) (case in point: like this OP)?

Have a great day day!

I was just thinking that this morning as I was perusing the latest discussions. For the students I would think it is near the end of the term, and they are trying to get the last of their homework finished. I am having that problem with my high school kids. I have all but given up on my college kids, its time they learned on their own to perform what's required. Other than that I am not sure.

Cheers to one and all