Min Flex. Reinf for Slabs

You are correct - 0.0018 is total, not per face.

Another minimum from ACI 318, 10.5, gets to a higher percentage for a minimum. Either 4/3 As required for flexure, or 3((f'c)<1/2)/fy. Having bending in both directions, (and thus reinforcement in both faces), could have an area of steel close to the amount given by double the temperature/shrinkage percentage. However, your interpretation of the minimums is correct.

Civilperson -

I believe that the 10.5.1 section specifically excludes the 3(f`c)^0.5 / Fy requirement for structural slabs and footings. Therefore, the ONLY minimum flexural requirement for slabs is the 0.0018 temp / shrinkage requirement.

I would somwhat agree with that JoshPlum.

The code reads that "where tensile reinforcing is required by analysis" that section 10.5.1 is required except as provided in....10.5.4.

Mat footings many times (if not always) has applied bending moments and thus would initially fall into 10.5.1. The commentary for 10.5.1 suggests the reason for this minimum steel is to avoid sudden failures with low amounts of flexural steel. Since mat footings rest on the ground, a sudden failure usually doesn't occur and if some sort of flexural failure did occur, it might not result in a catastrophic collapse or instability.

Section 10.5.3 tempers the rebar somewhat when the moments are low and allow the 1.33 x As instead of that required by Equation 10-3.

Section 10.5.4 is for structural slabs and footings, which a mat footing would fall into. Thus 10.5.4 is applicable except for cases where the footing doesn't have uniform thickness.

Also, in my own view, if the mat footing was a significant element in my structure, taking some larger moments, and its flexural failure might cause some serious instability, I might still stay under 10.5.1.

For the original question - agree with WillisV - the 7.12 minimum steel is for the entire sectional area. For a mat that is say 18" thick, the required area of steel would be

0.0018 x 18" x 12" = 0.389 sq. inches per foot width of mat.

Thus you'd probably provide #4 @ 12" o.c. each face. which totals 0.4 sq. inches per foot.

Sorry for chiming in late, but I just got home after being out of the country for the week. ACI does state, as JAE mentions above, "...where tensile reinforcement is required by analysis...".
To me, that means any location where the plain concrete section is not adequate to resist the loads, you need to provide the minimum (which is 0.0018bh for your case). If the section is not adequate as plain concrete at the top face AND at the bottom face, then why would you not need 0.0018bh on BOTH faces. If both faces are not adequate as plain concrete, I think you should provide it on both faces. I don't believe that 0.009bh on one face will exceed the flexural capacity of plain concrete, and you have done nothing to increase the flexural capacity above the inadequate plain concrete section. Well, it might by the equations in the plain concrete chapter of ACI, but that is extremely conservative for the actual capacity (ph=0.55 and they use the modulus of rupture as 5*rootf'c, plus you are required to decrease your section by 2"). The actual behavior would be that once your section cracks, the reinforcement is not adequate and the section immediately fails.
That section of ACI does specifically reference footings, so I have a hard time believing that you can neglect it for....... a footing.

StructuralEIT-

That is precisely the argument that the other engineer is making. But, if this is the argument, then why is this flexural reqmt based on Rho_gross when every other flexural reqmt in the whole code is based on rho?

I've never seen anyone try to invoke this in a real design. So, my follow up question becomes "is this really how you are designing your structural slabs on grade?".

In my opinion, Slabs offer a lot more ductility / moment re-distribution than beams do. The moment doesn't just re-distribute one way along the span, but rather two ways.

Plus, the only catastropic / non-ductile failure that I have seen written about for slabs is the punching shear failure. So, perhaps this type of plain concrete failure (while valid for beams) is not a real failure for slabs. Or, at least not a failure that has been proven to occur in the field or in the test lab.

I do this in my designs. I never use less than 0.0018bh for any face where steel is required. If it's required on both faces, then that's what I provide.
It may very well be that slabs offer more moment redistribution than beams, but the minimum steel for slabs/footings is less than that for beams (which would say to me that it is already taken into consideration), 0.0018bh vs. 0.0033bd.
At the end of the day, if ACI meant for you to use only total T&S steel without regard to which faces it is required on, I don't believe they would have included it as a minimum FLEXURAL REINFORCEMENT requirement and would have left it as T & S steel only.

JoshPlum,

I have to agree with your colleague.

ACI 318-02 Section 10.5.4 states "...the minimum area of tensile reinforcement in the direction of the span shall be the same as that required by 7.12. ..." (emphasis added)

I believe the use of the word tensile requires the full T&S on the tension face.

Keep in mind that 10.5.4 does NOT apply to slabs-on-grade (see the commentary)

318-05 revised the wording used in 318-02 to omit the word tensile and replaced it with As(min).

For a mat foundation - you may have one of these conditions at any one section of the mat:
1. Positive bending only under all load combinations
2. Negative bending only under all load combinations
3. Both positive and negative bending under all LC.

If you never have negative bending, for example, at one area of the mat, then doubling the 0.0018Ag steel doesn't seem to make sense.

Oh, goodness, don't anyone mention this thread to Taro. See thread507-185223.

After reading through the thread that miecz references, it appears to make sense for slabs and footings (not slabs-on-grade though) to use 0.0018Ag on the tension side of the slab or footing. If moment reverses under different load combinations, use 0.0018Ag on both faces. Don't use 0.0009Ag on each face.

Maybe I'm just jaded, but I'm beginning to think that the wording in ACI is intentionally vague in this case. Otherwise, they would have clarified it at some point over the last 20 years.

I've heard of this sort of thing happening before. Half the committee agrees with one interpretation half agrees with another. Therefore, none of them have enough votes to make the wording changes required so that the code actually makes sense to us practicing engineers.

For non-structural slabs on grade, the issue is clear. But, there is a whole range of "structural" slabs on grade where temp / shrinkage becomes a controlling issue. These mat foundations do not have a history of failure that I'm aware of. So, the committee is free to ignore the poor wording. Urg!

Most of these mats (at least the ones I have seen) are reinforced so that the total steel adds up to 0.0018bh.... But, that still ends up being significantly more than required by analyss.

I don't mean to stir things up here, but I just ran across this thread. I did read through the post from spring '07, but I'm not sold on providing ALL of the T&S steel on tension face.

10.5.4 says that As,min in the direction of the span shall be the same as that required by 7.12. However, 7.12 does not say how that steel is to be distributed in the slab.

A couple of items in ACI 350 suggests to me that the intent is that the T&S reinforcing can be split to each face. ACI 350 parallels ACI 318 with additional restrictions, many for crack control. ACI 350-10.5.4 has similar wording as 318-10.5.4. 350-7.12.2.1 specifically says that for sections that are greater than 24 inches thick, the minimum S&T reinforcing may be based on a 12-inch concrete layer. Under the theory that the S&T reinforcing is required to go on each face, then according to ACI 350, with joints at 20 feet on center:

23" slab would require: .003*23*12=.828 in^2/ft each face

25" slab would require: .003*12*12=.432 in^2.ft each face.

There seems to be a great discontinuity there....

350-7.12.2.1 goes on to allow a 50% reduction for bottom reinforcement of base slabs on soil!! Furthermore, 350-10.5.4 (that same section)goes on to include minimum areas of steel for walls per 14.3.2 and 14.3.3. I don't have my older copies of 318, but I believe it also included walls in the comparable section. Anyway, Chapter 14 of both 318 and 350 specifically requires that the total reinforcing be split between faces when the wall is >10 inches.

I'm still of the opinion that minimum S&T reinforcing and minimum flexural reinforcing are two different requirements. If we have designed the element to meet the requirements of 10.5.1 and 10.5.3, whether it is a "structural slab", footing, or whatever, then we have guarded against flexural failure.

JoshPlum, I agree: it is frustrating that the code committee's can't write clear, concise requirements.

JKW05 -

Thanks for the contribution! I was planning on obtaining a copy of ACI350 to investigate this issue becasue I thought that it might address it better. But, you saved me the trouble.

For what it's worth, I think the consensus of the other thread was that folks were really using the 0.0018 T&S for the entire section like I suggested from the start.

However, many also only felt comfortable with this procedure when they also satisfied the 4/3 As_req'd. They felt it provided some additional safety against sudden failure at cracking.... In my experience the 4/3 As_required is always satisfied for these types of slabs, so there isn't any change to design practice.

For what it's worth, I'm not aware of any structural testing of slabs that showed the type of brittle FLEXURAL failures that Taro was so adamantly concerned about. Rather, punching shear is the brittle failure that is seems to be most common for slabs. I'm far from an expert, but, I'm willing to consider that brittle cracking failure may be a "theoretically" valid failure that just doesn't show up in structural testing or past failure investigations.

All that being said, I feel perfectly comfortable approaching the challenge by saying that I'll be happy to guarantee that we provide more than 4/3 As_required becasue that will always be less than we alreay provided for T&S.

Here, this is right out of PCA Notes on ACI 318-05. Note the highlighted sentence. This makes it pretty clear that the intention is for the minimum FLEXURAL reinforcement be 0.0018bh.

JKW-
If you satisfy 10.5.1 and 10.5.3 for a footing, that will usuall require more steel than 10.5.4, and 10.5.1 and 10.5.3 will require it on the tension face (not split between the two faces).
This isn't about slabs supported by ground. In a footing, it is the ground that is applying the load, the wall/ftg is supporting it.
I haven't run the numbers, but I would bet money that 0.0009bh on the tension face of a ftg will likely provide a smaller reinforced moment than the section has cracking moment. That means there is no warning of failure. This is what 10.5.4 is meant to prevent. See the attachment I provided above, that language is pretty clear to me.
Aside from following the code, I don't feel comfortable providing a reinforced moment which is less than the cracking moment. I'm sure I might take some heat for that, but I just don't like it.

JKW05 - your discussion sounds reasonable as it is - but you keep using the phrase T&S.

In the original post above, the question was for a mat foundation which is not necessarily concerned with Temp & Shrinkage reinforcing.

Mat foundations typically have positive and negative moments where flexural tension steel is required to resist those moments.

ACI 318, section 10.5.4 says that, for slabs and footings, As,min in the direction of the span shall be the same as 7.12.

It doesn't say that for slabs and footings you provide T&S reinforcing per 7.12.

That is the critical distinction here:

min. flexural reinforcing
vs.
temperature & shrinkage reinforcing

They are two separate things.

All your references to 350, I would imagine, are for slabs on grade (which the 318 commentary says is not applicable to this issue).

I think this is just an awkward way that the 318 committee decided to save ink or something to avoid repeating the formulae in chapter 7 to quantify a minimum amount of reinforcing required.

EIT and JAE -

To understand this section, I think you need to read 10.5.4 within the context of the ENTIRE 10.5 section. To paraphrase:
10.5.1 lays out general minimum requirements for flexural reinforcing to prevent brittle failure at cracking loads.
10.5.3 says that you never need to get above 4/3 As_reqd.
10.5.4 then adds that, for slabs and footings, you cannot use the previous section to justify steel that doesn't meet the minimum temperature and shrinkage requirements.

Yes, the wording of the code is vague, but the context of 10.5.4 makes the intent fairly clear to me. Now, you can use the vague code language to interpret the section as you have. But, then please answer the following question:

Why would a beam be allowed to use less than 0.0018 for flexure (because of the 4/3 As_req exception), but not slabs?

I've seen brittle deep beam failures in text books and such, but have not seen a similar brittle slab failure described. So, why would slabs be more restricted than beams?

My interpretation is now that 10.5.1 DOES apply to slabs and footings. And, that I had been mis-interpreting that section for years. That was never a problem though because the 4/3*As_req was likely to govern in those cases. Then (above and beyond the 4/3As_reqd) you need to make sure that you steel meet the T&S requirements of 7.12.

JoshPlum-
Did you miss the attachment I provided right out of PCA Notes?