Min Flex. Reinf for Slabs

[JoshPlumSE]

My situation is a 24 inch thick Mat foundation with reinforcement in the top and bottom. It's relatively lightly loaded, so Temperature / shrinkage easily controls over flexure.

Typically I split the temp / shrinkage reinforcement between the top and bottom of the slab. Then I make sure that each one is capable of resisting the demand moment Mu_top and Mu_bot.

Unfortunately, I've got another engineer who is arguing that section 10.5.4 requires that the 0.0018 temp / shrinkage reinforcement should be enforced for BOTH faces of the slab. That would effectively double the amount of reinforcement in my mat foundation.

Does anyone agree with this guys interpretation? To me, section 10.5.4 is given just to make sure that the total reinforcement for flexure design (top and bottom combined) doesn't ever become less that that required for temp / shrinkage.

 

[JoshPlumSE]

EIT -

It wouldn't display on my system.... Does it answer my question about why a beam is allowed to use less than 0.0018 for flexure (because of the 4/3 As_req exception), but not slabs? Would you care to reference the version of the Notes and the example or section #?

I've seen examples where PCA enforces the 0.0018 requirement in a calculation for an elevated slab (which is somewhat different from my situation). But, they didn't give any technical discussions about it. Obviously, they are a respected source, but they have no legal authority over the interpretation of the code. So, unless they give a good argument about what they are doing and WHY they are doing it, then I'm not sure it would add much to this discussion.

 

[JAE]

JoshPlum,

Why do you assert that 0.0018Ag is always more than 4/3As?
That isn't always true.

[red]"My interpretation is now that 10.5.1 DOES apply to slabs and footings.[/red]

I don't agree with that. The direct language of the code is:

....slabs and footings...shall be the same as that required by 7.12.

That's pretty direct and clear to me.

Now I do also check, in high flexural conditions, the earlier sections but I don't see the code as requiring it.

 

[JoshPlumSE]

JAE wrote: "Why do you assert that 0.0018Ag is always more than 4/3As? That isn't always true."

Did I say it was ALWAYS true? I try not to talk in absolutes like that. I meant to say that in the types of Mat foundations that I have been dealing with it is generally true.

I think one of the problems is that everyone STARTS by reading 10.5.4. Instead I think you need to start by reading the GENERAL requirements of 10.5 which require a larger area of steel (in 10.5.1) "except as provided in 10.5.3 and 10.5.4".

If I start there then I can use 10.5.3 and get a smaller amout of steel based on 4/3As_reqd (for my situation).

Then, since this is a mat slab, I need to apply 10.5.4 to make sure that I didn't violate my min temp/shrinkage requirements.... which I would not be required to meet if I had been designing a beam.

Now, I obviously understand that the crux of the disagreement is whether 10.5.4 is a minimum T/S steel requirement or a minimum flexural steel requirement. The section placement (10.5) implies a flexural requirement, but it reference a minimum T/S requirement..... Hence the disagreement/confusion/frustration.

Now, IMHO, we should understand the LOGIC of the code and not just rigidly interpret the words of the code. That is the whole point of my asking the question about WHY you think beams are allowed to get a 4/3 As_required pass (when applicable), but that slabs and footings do not deserve that same pass.

Isn't the theory very similar? The minimum flex. refinforcement section (10.5) is there to prevent sudden failure when the concrete ruptures. That thoery applies to the ENTIRE section. Therefore, why treat beams and slabs so differently?

IMHO, the only logical reason is becasuse the original authors of that section wanted to highlight the fact that the T/S requirements are critical for slabs and the 4/3 As_req liberalization cannot be used for them if it would end up violating the min T/S requirements.

Please, don't just quote code at me.... Instead, Think about making this argument to a member of the code committee (whom I might try to harass later). Why does 0.0018*Agross make sense for slabs but not for beams? Why should 4/3Asreqd be allowed for beams, but not for slabs? How does 0.0018*Agross protect against brittle rupture when 0.0033 would be required for beams.

 

[JAE]

Josh - you said:

"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? "

Your whole beef is based on the concept that 0.0018Ag is somehow a penalty vs. the 4/3As. That's why I supposed you assumed that it always was the case. With most the 1000's of beams I've designed the 4/3As is quite higher than 0.0018Ag.

Don't quote the code at me? When the language is that straight-forward I just couldn't resist, sorry.

But hear me on this - I'm not adamant that you shouldn't apply the 4/3As to slabs/mats. As I mentioned above I have done it before.

I would say we keep researching this a bit and if you know a committee member, hit them up on it. (OK - harass them too).

 

[miecz]

JKW05-

For some previous discussion on ACI350 as it relates to this topic, see thread507-186344.

 

[rapt]

There are 2 reasons for minimum reinforcement

Shrinkage and Temperature - This requirement is satisfied by ensuring that the total reinforcement in the 2 faces is covered by 10..7.4 (7.12). This requirement is normally applied where there is no significant flexural action and if in cases where the slab would not fail if this reinforcement were to fail, in other words if a load path still exists without this reinforcement,. eg transverse reinforcement in a one way slab. ACI318 does suggest that this requirement also applies in raft slabs but I cannot understand why as there is significant flexural stress. Just because it is on the ground does not mean that failure of the reinforcement is not critical so, personally, I would ignore this as a code slip up.

Strength/Brittle failure - This requirement is satisfied by 10.5.1 etc and requires a minimum area of reinforcement at each face of the concrete in tension. The reason given in the commentary is that the cracked strength must be greater than the uncracked strength, and there is good reason for this as it explains. The other forgotten reason is that we never check the strain level in reinforcement at ultimate strength. The smaller the area of reinforcement , the higher the strain in the reinforcement at the tension face The minimum reinforcement rule is also meant to limit this strain in the reinforcement to avoid snapping of the reinforcement which is a brittle and possibly catastrophic failure. So, where there is significant flexure and the load path for the slab requires strength at a cross-section, minimum reinforcement is required at an section where there is tension at a concrete face. This does not necessarily require reinforcement at both faces everywhere as someone suggested, only at locations where there is flexural tension.

So, in conclusion, if you are relying on reinforcement to provide flexural strength and to support the structure, the minimum is required on any face that requires tension reinforcement.

The 4/3 rule is technically incorrect for flexural minimum reinforcement as it allows the steel strain to be much higher than it should be.

 

[JKW05]

EIT, Sorry, I couldn't get the link to open either, but I would be interested in reading it. What reference is that out of?

miecz, thanks for the link to the 350 discussion. The more I read, the more I scratch my head. No wonder my hair is getting so thin up there

I need to examine this thread and the previous two threads again to try to figure this out.

 

[miecz]

JKW05

Some of us have been at this for a while now. If you read the three threads carefully, you'll see that some of us have changed our minds. Some of us, more than once. I think it helps to limit the discussion to one code or the other (318 vs 350), as they may (and seem to) say different things. Early on, I tried to apply 350 reasoning to 318 and quickly got confused.

Here's my current thinking on slab/wall reinf.:

For ACI350, flexural minimum per 10.5.1 and 10.5.3. T/S minimum per 7.12. Ignore 10.5.4.

For ACI318, I'd say Taro's argument is pretty solid. 10.5.4 has the minimum flexural reinforcement ratio of .0018. (T/S is then automatically satisfied.) However, as I tend to be the conservative type, I follow the same procedure as above for ACI350.

 

[JKW05]

Miecz,

I think I am leaning toward that same conclusion: the two codes have similar wording with different intent (and neither one is particularly clear). I noticed that none of the committee members that developed ACI 350 were involved in ACI 318 (at least not on the last revisions). The only reason I keep comparing the two is because at the ACI-350 seminar I attended, the instructors said that ACI 350 was intentionally re-written to parallel 318 so I would assume that the provisions are based on similar rationales and theories (maybe not a wise assumption?!?). But I've spent too much time writing this, so I'm going to post it anyway…..

I've re-read everything and have come up with some additional thoughts, some of which I've already said, and some of which may have already been said by someone else in the related threads. So my apologies if I am repeating anything and for the long-windedness….

I must admit, based on the definition of As,min in 318 Chapter 2 that 10.5.4 does indeed pertain to flexural reinforcement. But going back to the parallel sections in ACI-350 and the considering the poor wording in 318, I'm still not convinced about how it is to be distributed.

EIT

I don't understand the relevance of your comment regarding the load being applied to the footing "by the ground". My interpretation is that if a member is subject to flexure, whether it is a slab, beam, wall, or footing, regardless of what the load is from, or what direction, that 10.5.1 and, in particular, 10.5.4 ensures adequate reinforcing from flexural failure.

I saw from your posts last spring that you asked a couple of times why the (4/3)*Asreq'd is permitted in lieu of 200/fy. This is answered in the 318 Commentary (R10.5.3):

"…this exception provides sufficient additional reinforcement in large members where the amount required by 10.5.1 or 10.5.2 would be excessive."

In your posts last spring, you also asked about a code requirement for phi*Mn>Mcr. I must say I've never heard of that either, and I haven't seen any responses in the previous threads regarding that matter (sorry if I missed it somewhere). You also say you wouldn't feel comfortable providing a reinforcing in a member that is less than the cracking moment. In absence of a requirement for phi*Mn > Mcr, would you agree that that is exactly what 10.5.3 is specifically permitting for beams (for which there is less redundancy than a slab)? Otherwise, what is the intent of that Section?

Regarding the concerns about "sudden, brittle failure"… referencing Winter and Nilson's Design of Concrete Structures : "When relatively moderate amounts of reinforcement are employed, at some value of the load the steel will reach its yield point. At that stress the reinforcement yields suddenly and stretches a large amount…." The concluding sentence in that paragraph says, "Such yield failure is gradual and is preceeded by visible signs of distress, such as the widening and lengthening of cracks and the marked increase in deflection." Although there seems to be a contradiction in "sudden yielding" and "gradual yield failure", I think the key here is that the steel yields, it doesn't snap as was suggested by another in a previous post.

ACI 318-05 R10.5 also addresses this: "With a very small amount of tensile reinforcement, the computed moment strength as a reinforced concrete section using the cracked section analysis becomes less than that of the corresponding unreinforced concrete section computed from it's modulus of rupture. Failure in such a case can be sudden. To prevent such a failure , a minimum amount of tensile reinforcement is required by 10.5.1 … I still don't see anything requiring phi*Mn>Mcr.

I'm not trying to challenge your position, just trying to better understand what made you change your interpretation from your original posts last spring. Was it solely the PCA Notes you referenced that convinced you?

JAE

Thank you for you comments, I have great respect for your wisdom. Did you ever feel that the longer we stay in this profession, the less we seem to know?

However, no where in ACI 350 does it say the requirements for S&T reinforcement are just for slabs on grade:

"7.12.2.1 -- For members subjected to environmental exposure conditions or required to be liquid-tight, the area of shrinkage and temperature reinforcement shall provide at least the ratios of reinforcement area to gross concrete area shown in table 7.12.2.1:

Concrete sections that are at least 24 inches may have the minimum shrinkage and temperature reinforcement based on a 12" concrete layer at each face. The reinforcement in the bottom of base slabs in contact with soil may be reduced to 50 percent of that required in table 7.12.2.1"

"7.12.2.2 – ….No less than 1/3 of the required area of shrinkage and temperature steel shall be distributed at any one face."

Unfortunately, 318 does not provide similar guidance to the placement.

"ACI 350-10.5.4 – For structural slabs, mats, and footings of uniform thickness, the minimum area of tensile reinforcement in the direction of the span shall be the same as required by 7.12. For walls, the minimum area of reinforcement steel shall be as required by 14.3.2 and 14.3.3."

It is curious that in this section in 350 still refers to it as "minimum area of tensile reinforcing" while 318 changed it to "As,min". I wonder what the intent was in revising that wording. The instructor at the ACI seminar I attended indicated that 350 is generally being revised subsequent to 318 revisions, so I suspect this may change with the next version of 350…not that that will clarify anything here.

So reading this I would say, based on ACI-350-10.5.4, that the minimum area of tensile reinforcement is 1/3 * Ag * (Reinforcement Ratio from table 7.12.2.1). In addition, I believe 10.5.1 and 10.5.3 must be satisfied. If they only meant to indicate the required ratio was required for the "minimum area", why wouldn't they refer specifically to Section 7.12.2.1 or even better, Table 7.12.2.1, instead of the entire Section 7.12, which includes the placement requirements?

So I guess the first interpretation we must make: For "structural slabs and footings", do we skip 10.5.1 and go directly to 10.5.4 (Do not pass Go, Do not collect $200). Or do we satisfy all of the requirements of Section 10.5?

Second, we must interpret how the distribution of reinforcement per 7.12 is to be made with respect to 10.5.4. EIT's example from PCA notes apparently suggests one interpretation while the PCA Design Guide for Concrete Tanks suggests the opposite. Two committees..two meanings?

To quote Taro from May '07…"My head hurts. Anyone have an aspirin?"

 

[JKW05]

Yeah, it's me again. There had been some previous comments about the relative minor impact that just providing the S&T quantity at the tension face might have. I have analyzed an example slab using 318 and 350 requirements that I would like to share. I would tend to agree that using 318, there isn't a lot of difference (~25% additional steel tonnage). But using the same interpretation under 350 resulted in 220% increase.

Design parameters:
Concrete Mat Foundation Slab
f'c = 4 ksi, fy = 60 ksi
b = 12", h = 22", cover = 2"
Md = 5 k-ft, Ml = 10 k-ft, Mu =1.2D+1.6L

Under 318 I get the following results:

rho required for Mu = 0.0011

For purposes of this discussion, I am going to assume 10.5.1 and 10.5.3 are to be considered.

3*(f'c)^0.5/fy = 0.0032
200 / fy = 0.0033

(4/3)*(rho req'd) = 0.0015 --> 10.5.3 can be used in lieu of 10.5.1

Therefore the minimum steel ratio = 0.0015

Allowing for ½ of a #5 bar diameter to determine "d",
As = .0015*12*19.69 = .35 in^2/ft, say #5@10"(1.25 psf)

Applying .0018Ag to the tension face,
As = .0018*12*22 = .48 in^2/ft, say #5 @8" (1.56 psf)

Not too bad. Now for ACI-350. For those not familiar with 350, additional consideration of an "environmental durability factor (Sd)" must be included in determining the required strength for liquid-tight structures.

For the same loading and slab I get:

Sd = 1.33

rho req'd for Mu = 0.0011 (same as before)
rho req'd for Sd*Mu = 0.0015

Section 10.5.1:
3*(f'c)^0.5/fy = 0.0032
200 / fy = 0.0033 (same as before)

Section 10.5.3: (To be considered excluding Sd)
(4/3)*(rho req'd) = 0.0015 --> 10.5.3 can be used in lieu of 10.5.1

Therefore the minimum steel ratio = 0.0015

Allowing for ½ of a #5 bar diameter to determine "d",
As = .0015*12*19.69 = .35 in^2/ft, say #5@10"

ACI 350 also has limits to keep fs below fs,max (Section 10.6.4.1). In this case, this requirement ends up reducing my #5 spacing to 9" (0.41 in^2/ft and 1.39 psf)

Assuming the same interpretation that the minimum flexural tension steel is based on the S&T ratio, then with joints at 40 feet o.c.:
As = .0050*12*22 = 1.32 in.^2/ft, say #6@4" (4.51 psf)
(0.0050 is ratio required by ACI 350 for joints at 40 feet or more)

Going back to the actual required ratio calculated for the applied moment, As = .0011*12*19.69 = .26 in^2/ft.

Based on 10.5.1, 10.5.3, and 10.6.4.1, we are already required to provide ~58% more steel than is required for strength alone. And this is understandable, and is explained in the commentary as a control to keep the structure liquid-tight and to prevent "sudden" failure. But the 1.32 in^2/ft is 5 times greater than what is calculated as being required for strength alone. Now I think I'm generally as conservative as the next guy, but that just seems excessive to me…..

 

[miecz]

JKW05-

I'm writing from home now and don't have ACI350 here. In your slab example according to ACI350, I would have included S_d in the calculation for 10.5.3. I wasn't aware that S_d can be excluded there. Also, I would have calculated the T/S A_s=.0050*12"*(22"/2)= 0.66 in²/ft. I realize that this interpretation flies in the face of the "agreed to" interpretation of ACI318, but I believe it is the intent of the ACI350 code writers. As you say, 1.32 in²/ft can't be right.

 

[JAE]

Did you ever feel that the longer we stay in this profession, the less we seem to know?

Since joining Eng-Tips, I have found so many of you throw out questions, and provide answers, that make me take another look at things in a new light and I find myself learning quite a bit.

But even so, I find it amazing that so many of us structurals face similar problems, challenges and frustrations with architects, codes, etc.

Eng-Tips has become for me, and I think should be to all of us, a great place to learn and keep our engineering skills sharp and up to date. Young engineers learn from more seasoned engineers and seasoned engineers can keep up to date with new trends, methods, and codes from the younger engineers..

Dare I say it.....[blue]Engineering Heaven[/blue]

 

[JKW05]

miecz

Thanks for your response. I had missed it earlier, too, but 350 10.5.3 excludes Sd in determining U. And I agree, I would also calculate T/S As as you illustrated. What I was trying to demonstrate is the apparent excessive amount of steel if the other interpretation is used.

 

[miecz]

JKW05

I'm looking at Article 10.5.3 of 350-01 and can't find verbiage that excludes S_d in determining the required tensile reinforcement. Can you help me find that?

 

[JKW05]

In ACI 350-06 The article was changed:

"The requirements of 10.5.1 and 10.5.2 need not be applied if at every section the area of tensile steel reinforcement provided is at least one-third greater than that required by analysis for required strength U, not including the environmnetal durability factor Sd."

If you don't have '06, you may want to consider obtaining a copy. There are significant changes including the determination of Sd, and they followed 318 by eliminating calculation of "z" for crack control. Section 10.6 was essentially re-written with new requirements for limiting steel stresses in order to control crack sizes.

 

[miecz]

JKW05- Thanks. We're a little behind the times here.