Min. reinforcement in footing question 1

[danm494]

Hello all, I'm investigating a footing with an eccentric load which results in a partial triangular soil pressure response. When I calculate bending moments I get negative values in the area where soil pressures are zero because of the footing concrete weight (footing is 4' thick). I checked the uncracked moment resistance and it is much greater than the neg. BM. Do I still need to provide the min. reinforcing steel at the top as per code Asmin= 0.0018 bh? thx. for any guidance

 

[DaveAtkins]

I don't think it is necessary, because the footing qualifies as a plain concrete member per ACI 318.

DaveAtkins

 

[danm494]

There is bottom steel though... I'm not sure I'm comfortable labeling this footing as plain concrete(?)

 

[JAE]

Just because you add rebar doesn't negate the use of the footing as unreinforced if the footing can work fine without the rebar.

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[danm494]

Supposing the footing exceeds Mcr for positive moment (which it does) how would I compute the neg. moment capacity of the footing? Could I use the uncracked value? (the neg. BM is only a tiny tiny fraction of Mcr as mentioned previously)... or something else?

 

[JoshPlumSE]

You could let the plain footing resist the negative bending as a plain concrete section as long as it is allowed. There are some seismic zones, I believe, which will not allow you to use the un-reinforced design provisions from ACI. I remember running into a problem with someone awhile back about this exact issue.

The other odd thing is if you decide you want to put ANY reinforcement in the top, then ACI now obligates you to put in the full 0.0018.

 

[danm494]

"You could let the plain footing resist the negative bending as a plain concrete section as long as it is allowed"

That's exactly the point I'm unsure about, is it still allowed when I've surpassed Mcr in positive bending?
Does not plain concrete design require everything remain uncracked for all loading conditions?

 

[KootK]

That's exactly the point I'm unsure about, is it still allowed when I've surpassed Mcr in positive bending?
Does not plain concrete design require everything remain uncracked for all loading conditions?

This is exactly right and something that seems to get missed by most. You can't very well have positive moment capacity coming from a cracked, reinforced section and then assume the same section to be uncracked for negative moment.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[CBSE]

I always put a top mat in my negative moment sections. For the small additional cost, I don't get too worked up about it.

 

[msquared48]

UBC Seismic D and above do require reinforcing, regardless of the size or thickness of the footing.

I think the IRC may be a little more lax on that though. I would have to check.

Mike McCann, PE, SE (WA)

 

[JoshPlumSE]

You CAN assume cracking on one side and not on the other. I don't know of any code provisions which disallow this.

Certainly it is a matter of engineering judgement / preference. Those who lean toward least cost / value engineering solutions would allow it. Those who are more conservative would not and would want to force top bars to be there.


I've gotten a number of requests by engineers over the years to add this option into RISAFoot / RISAFoundation. We eventually added it. Around the same time we added an option to let the engineer force the program to add top bars.

This footing example is the classic case of when you do this. The normal behavior of your footing is to have pressure from below. This will likely produce cracking in the bottom of the footing. But, that is resisted by reinforcement. Then in the very unusual overturning event, you have some negative moment on the footing. This moment will close the bottom crack. And, it will act as a plain concrete section with the corresponding strength.


What I was pointing out (though inarticulately) was that I remember some code provisions that disallowed plain concrete for certain seismic regions. Looking it up, I believe this was 1997 UBC section 1922.10. That tells you how long ago the project was where we got questioned about this. It may not even be in the code anymore. Baring a similar code provision existing now in ACI or IBC, I believe you would be free to use plain concrete capacity to resist the negative bending.

 

[msquared48]

It is required per the IBC for C, D and above except under specific circumstances....

Look in IBC section 1905.1.8 where it amends ACI section 22.10., specifically 22.10.1

Mike McCann, PE, SE (WA)

 

[KootK]

You CAN assume cracking on one side and not on the other. I don't know of any code provisions which disallow this.

Well, no, it's not explicitly prohibited. But then neither is urinating into a stiff wind. I challenge anyone to submit their calculation algorithm for the negative, uncracked moment capacity of a section previously cracked in positive, ULS bending.

Consider:

1) One method could be to estimate how much of the section remains uncracked after positive bending and then use just that section as un-reinforced concrete to resist negative bending. Of course, after ULS positive bending, that's likely to be less than 25% of the cross section.

2) Another method could be to use the estimated, uncracked portion of the cross section as the tension force in a moment couple that includes the rebar as the compression force. Given what we know of concrete and fracture mechanics, however, how confident would we be in having made a correct estimate of the depth over which a concrete tension crack has run?

3) When a crack closes, it doesn't get its reliable tension capacity back. Maybe just some voodoo adhesion business.


I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[JoshPlumSE]

KootK -

I believe you're confusing the strength of plain concrete section per ACI Chapter 22, with the assumption of an uncracked section. Your member does NOT have to be un-cracked for you to use Chapter 22 to calculate it's strength.

It sounds like you're trying to re-invent a design provision by which a plain concrete section could be used. But, that's unnecessary. The provisions of Chapter 22 are pretty well defined.

Now, you could certainly make an argument based on the code and commentary of Chapter 22 of whether or not this example meets the intent of that section of the code. But, I haven't seen that yet.

Pick up ACI and read Chapter 22. There is even a section of the provision (22.7) that specifically covers plain concrete footings. I fail to see why this section cannot be applied to the design of this guy's footing?

 

[KootK]

Your member does NOT have to be un-cracked for you to use Chapter 22 to calculate it's strength...Pick up ACI and read Chapter 22.

As you wish. I just read the chapter cover to cover, including the commentary, but not all of the zillion referenced sections elsewhere in 318-11. What can I say? I'm lazy with my Friday night homework assignments.

Anyhow, I did not see a single statement in chapter 22 that would lead me to believe that that chapter 22 could be used for cracked concrete. If you know of one, please point me to it. I did, however, bump in to the statement below which would seem to imply that, all other issues aside, a cracked plain concrete member would have no shear capacity.

There is even a section of the provision (22.7) that specifically covers plain concrete footings. I fail to see why this section cannot be applied to the design of this guy's footing?

I think that it can't be applied to OP's footing because:

1) OP's footing is cracked.
2) I believe that Ch.22 flexural resistance involves the tensile resistance of concrete.
3) I don't believe that you can transfer concrete tensile stress across a crack, open or closed.

Of course, if you're not buying that cracked concrete has compromised tensile capacity, then you're obviously not going to be on board with this either.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[danm494]

I believe ACI limits concrete tensile stress to 5*SQRT(f'c) for plain concrete design. The modulus of rupture of concrete is usually taken as 7.5*SQRT(f'c) so it appears ACI does not want you to approach cracking levels. Also, ACI uses a reduction factor of .6 for plain concrete which is quite conservative, it looks like it doesn't want you to approach cracking under any circumstances and anywhere inside the section.

 

[KootK]

Chapter 22 also makes a pretty big deal about:

1) Considering creep, shrinkage, thermal forces , and restraint.
2) Dividing larger members up with joints and considering the concrete between them discontinuous.

This points to basing capacity on swaths of concrete assumed to be uncracked in my opinion.

Even for regular, non-uplift, unreinforced footings, I've always wondered how one should satisfy the requirements for considering this stuff. Friction with the ground is likely to provide a fair bit of restraint to a loaded footing. If a 20'X20' unreinforced footing develops a restraint crack at mid-span, that would be bad news. Fortunately, unreinforced footings don't tend to make much economic sense for large footings.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[JoshPlumSE]

KootK -

Good points. Some food for thought, certainly. In response to your comments:

1) I don't believe the OP never said that his footing was cracked. Only that the positive moment would exceed Mcr. You're assuming that it will eventually crack. That's a reasonable assumption. But, I don't know that this really negates the use of these design provisions.

2) If the top of the footing is essentially uncracked until the ultimate design load is reached, then you're not trying to transfer tensile stresses across a crack. Maybe you have limited cracking at the bottom of the footing if you've gone through a design level event in the other direction. But, that's on the compression side of the footing for the negative bending load case. And, the level of cracking has been limited by the presence of the reinforcement.

3) Commentary says, "Use of structural plain concrete should be limited to members that are primarily in a state of compression, members that can tolerate random cracks without detriment to their structural integrity, and members where ductlility is not an essential feature of the design."

To me this is pretty clear that some cracking is allowed / assumed. You're just not going to get any ductility out of your structure.

4) This type of footing does not have the type of "restraint" from creep, shrinkage or temperature effects that are generally of a concern. Right? The top face of an individual spread footing is essentially unrestrained. This seems to be exactly the type of situation ACI is talking about for this chapter.

5) When the commentary says that the shear requirements assume an uncracked section, they are talking about the stress model used to derive the equation. v = VQ/Ib and the dimensions used to calculate these values. They also talk about how this will rarely control the design of a plain concrete member.

Certainly if you get uncomfortable with the nature of these shear provisions, you could be justified in used reduced properties for the calculation of the shear capacity. Though, again, they have said that shear is unlikely to control.

 

[JoshPlumSE]

My last post on this subject:

To me, the use of these provisions really comes down to a question of ductility. As engineers, we generally want our structures to perform in a ductile manner. So, for seismic (where ductility is inherent in our design assumptions), design to these plain concrete provisions may be a poor choice. Even in non-seismic concrete, we are taught to make sure our beams and columns fail in a ductile manner. That's why we have limits on steel strain and why we used to limit our steel to 0.75 of rho_balanced.

So, if you are comfortable with a design that has low ductility, then the use of these plain concrete provisions would be acceptable. It's an engineering judgment call. The code doesn't forbid it, nor does it encourage it. So, it is matter of engineering judgment and comfort level.


KootK, you certainly have a right to disagree with the use of the moment capacity equation in negative bending when the section could have been cracked in positive bending. Though, if you plot out the stresses, you would see that the derivation would be assumed to be exactly the same as an uncracked section.

The difference is likely the levels of cracking that we are assuming. You're probably taking it all the way to positive moment failure (and the large cracks that occur), then this stress profile wouldn't work. But, that's at a load factor of 1.6 times your design level event. If you look at it actual cracking anticipated in the structure when your negative bending is present, (even for a max wind load event) then the cracking would likely be minor.


You really cannot get much capacity out of these plain concrete sections. So, this discussion is really about when you have a very minor (but non-zero) amount of negative moment. Can you save a few bucks by keeping the steel in bottom of the footing or do you have to double the amount of reinforcement (because ACI 318-14 requires the full 0.0018 as a minimum) by also placing bars in the top.

If it were me, by preference would be use 0.0018 TOTAL reinforcing with more bars on bottom than on top. But, ACI won't let us do that anymore.

 

[KootK]

1) I don't believe the OP never said that his footing was cracked. Only that the positive moment would exceed Mcr. You're assuming that it will eventually crack. That's a reasonable assumption. But, I don't know that this really negates the use of these design provisions.

I'm pretty sure that OP is concerned about a cracked footing. And, clearly, whether or not cracking invalidates the plain concrete provisions is the crux of this debate.

Does not plain concrete design require everything remain uncracked for all loading conditions?

2) If the top of the footing is essentially uncracked until the ultimate design load is reached, then you're not trying to transfer tensile stresses across a crack. Maybe you have limited cracking at the bottom of the footing if you've gone through a design level event in the other direction. But, that's on the compression side of the footing for the negative bending load case. And, the level of cracking has been limited by the presence of the reinforcement.

This essentially amounts to my proposed, but not recommended, design strategy #1 above. Additional thoughts:

a)I find it hard to imagine that any engineer would want life safety hinging on their ability to estimate the depth of flexural tension crack accurately.

b) If a footing's ULS uplift capacity is dependent upon that footing never having previously reached ULS gravity capacity, I would definitely question the soundness of the design strategy.

c) To use the full section in plain concrete flexure post-cracking, you'd need to ensure that the cracking didn't extend past mid-depth. Even early in the loading history, there's pretty good chance that a member will see cracks penetrating deeper than that.

d) A small crack is no better at transferring tensile stress than a large crack is.

3) Commentary says, "Use of structural plain concrete should be limited to members that are primarily in a state of compression, members that can tolerate random cracks without detriment to their structural integrity, and members where ductlility is not an essential feature of the design."

How are we to know that members able to tolerate cracks aren't just members loaded primarily in compression? Or members not requiring water tightness? I get what you're pointing to here but, for me, it would take a far more definitive statement of intent before I'd be willing to conclude that chapter 22, which mentions concrete modulus of rupture every other paragraph, applies to cross sections already cracked in tension.

4) This type of footing does not have the type of "restraint" from creep, shrinkage or temperature effects that are generally of a concern. Right? The top face of an individual spread footing is essentially unrestrained. This seems to be exactly the type of situation ACI is talking about for this chapter.

I disagree. A large, heavily loaded footing on sedimentary bedrock will experience restraint at the bottom due friction with the bearing surface. And the top of the footing will be similarly restrained by it's horizontal shear connection to the bottom of the footing. Chapter 22 clearly is meant to apply, at least, to footings that are uncracked. Chapter 22 also makes much of considering creep, shrinkage, etc for plain concrete members. And they make no mention of excluding footings from such consideration. As I mentioned above, I'm really not sure if footings are meant to be excluded from such scrutiny. I've never personally known anyone to consider it in design.

5) When the commentary says that the shear requirements assume an uncracked section, they are talking about the stress model used to derive the equation. v = VQ/Ib and the dimensions used to calculate these values. They also talk about how this will rarely control the design of a plain concrete member.

I disagree. The statement made is simply that "the shear requirements for plain concrete assume an uncracked section". To me, the fact that the VQ/Ib method also assumes an uncracked section only reinforces the notion that chapter 22 shear capacity is intended for uncracked concrete. And, if a cracked section means zero shear capacity, then you can bet that it will govern.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.