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

 

[KootK]

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.

This would be the case only if the the tensile cracks did not extend beyond the portions of the section that later found themselves in compression. And, as I mentioned above, that strikes me as a very unlikely scenario that would be difficult to verify reliable.

It's worth remembering that no crack ever closes perfectly. In the process of closing a a crack, imperfect re-mating must be over come. And, with each cycle of that, your brittle, crack grows... and grows... and grows. Fracture mechanics is not a forgiving mistress.

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]

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.

If footings can be said to be restrained in most cases per your argument above, then please explain to me section 22.7 for Plain Concrete Footings. It would seem odd to have a section of the code that is directly in contradiction to the previously listed limits of the main section....


We will agree to disagree on the rest of your comments. To me, the critical question remains one of the desired or required ductility... not a question of cracking.

 

[KootK]

If footings can be said to be restrained in most cases per your argument above, then please explain to me section 22.7 for Plain Concrete Footings. It would seem odd to have a section of the code that is directly in contradiction to the previously listed limits of the main section....

The sections do not contradict one another at all. Chapter 22 says two things, among many others:

1) blah, blah ... you can design yourself some un-reinforced footings if you like ... blah ... here's some moment and shear capacity provisions for that.

2) blah... if you design something in plain concrete thou shalt consider creep, shrinkage... blah-blah.

So chapter 22 clearly endorses plain concrete footings (uncracked ones at least). And I've never once claimed that not to be the case. The only question, in my mind, is whether or not statement #2 means means that footings, like other plain concrete members, must be checked to see if they will crack and become structurally neutered. Chapter 22 doesn't give them a pass but, at the same time, I've never known anyone to consider it in practice.

Since your still firing riddles my way, I've got one for you. If plain concrete members can be cracked, why all the extra warnings about creep, shrinkage, thermal, and joint spacing? Chapter 22 is plain saturated with them. What on earth could possibly explain all that concern for the development of tensile stresses in plain concrete members...

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]

...was hoping to reach some consensus here...if I state 0018bh is required for the top when Mcr is exceeded in +BM but don't need any top steel when +BM stays below Mcr would that be ok? (again, -BM <<< +BM). And then, which Mcr do I use? theoretical or factor reduced? I would like to save my client some $$$ if possible but still stay within the code...thanks again.

 

[KootK]

...was hoping to reach some consensus here...

Not looking promising unless some new blood starts chiming in. Josh and I seem to be at an impasse.

My practical recommendation is identical to CBSE's:

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.

The $$$ are small. Don't get too worked up about it. In any practical uplifting situation, I'd want some top bars for shear / punching shear resistance anyhow.

if I state 0018bh is required for the top when Mcr is exceeded in +BM but don't need any top steel when +BM stays below Mcr would that be ok? (again, -BM <<< +BM). And then, which Mcr do I use? theoretical or factor reduced? I would like to save my client some $$$ if possible but still stay within the code...thanks again.

To be logically consistent, I think that it would be as simple as this: if you could design the footing unreinforced for positive bending, then you're at liberty to do the same for negative bending.

 

[danm494]

k, thanks KootK, I follow your reasoning =)... actually thanks to everyone who contributed, you've all been helpful

 

[jayrod12]

Late to the party, I'm not sure which camp I would be in, however, I don't see how cracks that have developed from positive bending (exceeding Mcr) would have any impact on the cracking moment in the negative bending since it would be in compression and in fact closing those cracks.

That being said, just add the rebar, it can't be that many bars or that many pads. If there were a thousand pads and it was going to be more than 6-15m per pad, maybe I'd re-evaluate my position.

 

[KootK]

Late to the party, I'm not sure which camp I would be in, however, I don't see how cracks that have developed from positive bending (exceeding Mcr) would have any impact on the cracking moment in the negative bending since it would be in compression and in fact closing those cracks.

For plain concrete negative bending resistance, some of the section would need to be in tension (normally half of it). The problem, given the nature of fracture mechanics of concrete and possible repeated opening and closing of the cracks, is guaranteeing that the cracks will not extend into the portions of the section that you need to resist tensile stresses. A typical, mildly reinforced concrete member will have cracks extending 60-90% of the member depth after initial, serviceability level cracking (read that last night by accident in Gilbert's prestressed concrete book).

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.

 

[jayrod12]

Understood. But if it never reaches Mcr, does it really crack beyond possible shrinkage cracking (which I deem as low probability in a buried situation).

 

[KootK]

If it doesn't exceed Mcr in positive or negative bending then sure, no problem. But if it exceeds Mcr in positive bending, there's a very good chance that the ensuing cracks would extend into the portion of the cross section assumed to be in tension using the plain concrete provisions for negative bending.

I would expect that shrinkage cracking would cause similar issues. Every provision in the plain concrete section depends on the tensile modulus of rupture of the concrete. Cracks, open or closed, negate any capacity associated with modulus of rupture in my opinion.



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.

 

[jayrod12]

I avoid having to think about this stuff by just putting the bars in anyways. I think I'm conceding the point on this one barring a significant epiphany. It makes sense that you cannot design half of one member as plain concrete, and the other half as reinforced, all or none would likely make the most sense.

 

[KootK]

I think that this is a very interesting point and one that I'd not considered until OP brought it up the first time: Link. Not much discussion that time around though.

I've actually done unreinforced footings in uplift on many occasions in the past without thinking about the impact of positive flexure cracking.

Along similar lines, slab designers will often reduce the reinforcing impact of unbalanced loads and/or unequal spans by letting small amounts of negative moment near mid-span be handled by plain concrete in negative bending. I even have a textbook that advocates this strategy. I would think that to be a very similar issue.

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]

The only thing that KootK has said that gets me to question the use of plain concrete for negative bending is:

A typical, mildly reinforced concrete member will have cracks extending 60-90% of the member depth after initial, serviceability level cracking (read that last night by accident in Gilbert's prestressed concrete book).

That level of cracking is higher than I would have thought. If the cracking is at 60% of depth, then I think we're probably still okay because that center 10% is at very low stress location. If, however, the cracks really extend to 90% of the depth of the member, then it's certainly not okay. So, at least we're speaking the same language now....

This whole time, I've been thinking that KootK was assuming design strength / failure levels of cracking on the reinforced side. That (in my opinion) would be excessive. We know that this is a non-ductile structure and cannot go through multiple design level load reversals. So, to assume the level of cracking associated with design capacity / failure would seem to be excessive.

However, if the service level cracking is truly likely to be that severe, then I would concede.... Though I'd have to see more research on the subject to actually believe it.

 

[KootK]

This whole time, I've been thinking that KootK was assuming design strength / failure levels of cracking on the reinforced side.

That's precisely what I was assuming until about 10pm last night when I read that blurb in Gilbert's work. To say that ULS uplift capacity is only available so long as ULS downwards capacity has never previously been reached is a sketchy proposition in my book. The serviceability cracking business is just icing on the cake.

Another interesting Gilbert finding is that, for mildly reinforced concrete members, apparently the depth of cracking doesn't really change much beyond SLS first cracking. You go straight to 60-90% at Mcr and then pretty much stay there the rest of the way. This has little relevance to this discussion but was a surprise to me.

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.