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Pinned base in a concrete wall - is it really achievable?
3

Pinned base in a concrete wall - is it really achievable?

Pinned base in a concrete wall - is it really achievable?

(OP)
I have a somewhat theoretical question regarding concrete walls as they are a reasonably popular topic of discussion on this forum.
I, as many others, often design concrete foundation walls as pinned-pinned when there is a first floor diaphragm to tie into.  I understand people have been doing this forever and I am not questioning the practice.  My question is this: Is a pinned base really able to be achieved in any typical detailing that anyone does?
I am thinking that any rebar tying the wall to the footing is providing some moment capacity.  I understand the pinned-pinned case is the worst case for the wall, so that is being conservative is you get some end moment capacity out of the foundation to footing connection.  Assuming a pinned base is unconservative for the footing since there WILL be some moment at the base.  Even if the steel yields and a "plastic hinge" forms at the base it doesn't lose its moment capacity.
Also, there must be some steel at the interface of the footing/wall since they are usually seperate pours and the steel is need for shear.
Any opinions on this would be greatly appreciated.

RE: Pinned base in a concrete wall - is it really achievable?

The term "yielding" that you have used is associated with large rotation at that loaction, which dissipates the energy. On top of that the amount of reinforcement that are usually provided at the joints is quite small than the amount that will require the joint to act as fixed.  In other words the small amount of moment that may generate due to the placement of the minimum reinforcements at the joint should not change the design assumptions (pinned-pinned).

RE: Pinned base in a concrete wall - is it really achievable?

(OP)
shin-
I understand that a large rotation is required.  I also understand that this is not overly relevant for the wall since the most conservative case for the wall is pinned-pinned (assuming that you are placing the rebar in the center of the wall).  
That being said, the rebar you provide at teh interface will provide some moment capacity.  Why wouldn't you take that phiMn at ultimate and dump that into the footing?  I realize that this phiMn will likely be smaller than that for the wall at midspan, but is a moment nonetheless and should probably be accounted for.  
I have never put any numbers to this, so it is possible that it is very small and negligible, but given the way moments affect footing design, shouldn't it at least be checked?
Just thinking out loud here, but if you have #6@12" for the wall reinforcing (not unreasonably small) and #5@18" for the dowels (not unreasonably high), phiMn at the base is about half of that for the wall section.  That is not insignificant in my estimation.
Also, given that the wall will act as fixed at the base until the reinforcement yields, it will attract moment.  Is that a fair statement?

RE: Pinned base in a concrete wall - is it really achievable?

I think you're missing a big source of flexibility at the wall base: the footing.  

I've never modeled it, but I suspect that the footing will rotate to relieve most of the moment in most cases. It would be pretty easy to test this.  Create a model of the wall and footing in your favorite program.  Use the subgrade modulus to determine spring stiffnesses to model the soil below the footing.  Run it and see how much moment is generated at the base.

Granted, there are exceptions such as pile supported grade beam as the base or a strip footing on solid rock.

RE: Pinned base in a concrete wall - is it really achievable?

211828
Or a foundation wall to a rigid mat. zero rotation of mat.

RE: Pinned base in a concrete wall - is it really achievable?

connect2, I agree.  I'm sure there are lots of examples.  

Most walls are supported on narrow strip footings supported on plain ole soil.  Those are the cases I was typing about.

RE: Pinned base in a concrete wall - is it really achievable?

(OP)
271828 and connect2-
Please excuse me if I am missing something that is staring me in the face.  
If you have a narrow strip footing on plain soil and the footing rotates, how do you automatically assume pinned?  The rotation of the footing may cause the bearing pressure to be exceeded, correct?  The rotation is caused by the moment at the base of the wall, correct?  I am not understanding why that amount of moment can be just neglected.
If you have a rigid mat this is less of an issue because the moment thrown in by one section of wall footing will likely be much less significant with respect to the capacity of the footing than for an isolated strip noted above.  That being said, the lack of rotation of the mat doesn't mean zero moment being transferred from the footing to the mat, does it?
All I am saying is this.  We obviously have our choice when we begin the design process of designing as a fixed base or not.  If we arbitrarily decide to design as not fixed does not necessarily mean it will behave that way.  I am trying to understand how you neglect the moment that will be transferred.  As I stated in the second post, the base connection will have some moment capacity, that is not debateable in my opinion unless someone can impart something to me that I haven't learned yet (I know there is a ton I haven't and I am always looking to learn, so please pass the wisdom along!).  That moment capacity does not go away when the rebar yields and the walls gains curvature (a plastic hinge forms).  That plastic hinge maintains that moment capacity and I do not see how it does not get transferred into the footing.

RE: Pinned base in a concrete wall - is it really achievable?

"If you have a narrow strip footing on plain soil and the footing rotates, how do you automatically assume pinned?  "

Design simplification.  Because the moment will probably be small and, like you typed earlier, it's on the safe side to assume it's zero.

"The rotation of the footing may cause the bearing pressure to be exceeded, correct?"

Seems unlikely to me because the rotation angle will be extremely small.

"The rotation is caused by the moment at the base of the wall, correct?"

Not really.  Imagine the end of a simply supported beam.  There's no moment there, but it certainly has some rotation due to curvature along the beam's length.

RE: Pinned base in a concrete wall - is it really achievable?

(OP)
""The rotation is caused by the moment at the base of the wall, correct?"

Not really.  Imagine the end of a simply supported beam.  There's no moment there, but it certainly has some rotation due to curvature along the beam's length."

The simply supported beam has no end restraint, a wall with reinforcement does have end restraint.



""If you have a narrow strip footing on plain soil and the footing rotates, how do you automatically assume pinned?  "

Design simplification.  Because the moment will probably be small and, like you typed earlier, it's on the safe side to assume it's zero."

It is only conservative for the design of the wall.  It is UNconservative for the design of the footing.



- I understand there is a lot of design simplification involved in this.  What I am trying to understand is whether someone has run any numbers at any point to determine if it is actually negligible.  Maybe I should make the question a little more clear, also.  While I am talking about the wall/footing assembly, I am more concerned with the moment at the base of the wall going into the footing, not the wall design.


RE: Pinned base in a concrete wall - is it really achievable?

I've never heard of anybody running such a number.  Maybe you can be the first and report back the result!

RE: Pinned base in a concrete wall - is it really achievable?

StructuralEIT

Need to really hone in on soil spring constants.  If the soil deflects enough to create an active pressure on the main vertical span of the wall, it will certainly deflect enough  below the basement slab where the passive pressure exists.  

If your wall has enough moment capacity to span vertically 10' or 12' to resist the active pressure moment, it will likely have enough reinforcement carried through to the footing to resist the passive pressure moment.

BTW, footing failure is relative to the amount of deflection one can sustain.  The building isn't going to crack in half if you exceed the bearing capacity on the toe of a strip footing.

RE: Pinned base in a concrete wall - is it really achievable?

(OP)
I appreciate everyone's responses with this.
Atomic-
I understand that the building is not going to crack in half, but if you take moment on the footing into account you will get a larger footing.  The soil bearing pressure being exceeded may not cause the building to crack in half but it could cause serviceability issues, no?
Again, I am not concerned about the moment in the wall.  I am concerned about the moment being transferred into the footing.

RE: Pinned base in a concrete wall - is it really achievable?

I think it gets back to deformation compatibility.

How much does the typical strip wall footing (not widened to take any assumed fixed base moment) need to rotate to create a pin condition at the base of the wall?  (Answer--wL^3/24EI).  Assuming this rotation, how much bearing pressure is generated under the footing?

DaveAtkins

RE: Pinned base in a concrete wall - is it really achievable?

Think about what happens when load is shared by two springs, a stiff one and a flexible one.  The stiff one gets most of the load.  

If you made a model of this, you'd have a wall with a certain EI and L.  In effect, you'd have a rotational spring at the bottom from the soil subgrade modulus.  

I'm speculating that the spring at the bottom is so flexible for a soil-supported footing that it won't take much moment.

Here's an exercise that might help.  Calc the rotation in degrees at the bottom of the wall considering it simply supported.  Then calculate how much the corner of the footing dips downward due to this rotation.  I think it'll be a tiny number, just guessing something like 0.1" or less.  Then try to imagine a soil bearing failure due to the footing corner (only, the rest is less) pushing into the soil that tiny distance.  Turning the problem around and thinking about it from a flexibility standpoint instead of a stiffness standpoint.

RE: Pinned base in a concrete wall - is it really achievable?

Dave, you fiend!  You beat me by 5 min.

RE: Pinned base in a concrete wall - is it really achievable?

StructuralEIT  correct me if I'm wrong, but you are talking about a typical concrete wall, on a continuous narrow footing, with a slab acting as the "pinned" support?  If the slab is there, then whatever moment does or does not pass thru from the wall to the footing is irrelevant.  If the dowels don't have the moment capacity, OK.  The footing can still take gravity load, and the slab is still there providing the "pin".

If the slab is not there, then yes I would agree that there is a moment across the wall/footing interface to consider.  But assuming pinned again, that moment will not be as large as the maximum in the wall, and the dowels will probably be sufficient.

I think the real answer to your question is that if you assume pinned, then there isn't much else you have to do.  It's an easy detail, everybody understands it.  If you assume fixed, then there is calculation and detailing rigor that must follow to assure you will get fixed behavior.  I do not think it would be good engineering practice to try and "massage the numbers" to justify a narrow footing acting as fixed, when everyone else in the world sees as pinned.

RE: Pinned base in a concrete wall - is it really achievable?

This takes some amount of energy to put the connection into yielding and cause rotation in the inelastic range. This energy is contributed by the moment generated at the joint by virtue of little bit of steel at that joint.

Now, since the energy from the moment is used up to cause a rotation at the joint,the energy is lost, then theoretically the moment should not transfer into the footing.

RE: Pinned base in a concrete wall - is it really achievable?

(OP)
OK, let me restate my question with an exaggerated situation so that everyone can clearly understand my question and concern.  It seems that many people are missing the point of my question.
The question is regarding the actual bearing pressure of the footing and has nothing to do with the wall except how it interacts with the footing.  
Assume a 16" restrained retaining wall.  It is restrained at the top by a floor diaphragm and at the bottom (either by a slab for sliding only or the ftg is acceptable against sliding on its own).  Let's say we start by assuming the wall is pinned-pinned and the moment requires #9@12" each face.  Now, we detail the wall/footing interface to have #5@12" each face for the dowels.  There is no dead load on the wall other than self weight.  
The footing is sized as gravity only and a very small footing width is required because there is little dead load, and say that the actual bearing pressure is about 95% of allowable (3.8 ksf vs. 4.0 ksf allowable).
Now, we assumed a pinned base, but those #5@12" have a moment capacity of 17 K-ft/ft of wall.  This connection is going to act fixed until the base connection reaches it moment capacity at which time that connection will become a plastic hinge and the wall will act as pinned-pinned for any additional load, but that 17 K-ft/ft of wall moment is still there, it doesn't disappear.  Once you add that 17K-ft/ft of wall moment to the footing that was just sized for gravity only it is going to exceed the allowable bearing pressure considerably.

PMR-
I understand that everyone in the world sees this as pinned.  I am not trying to reinvent the wheel.  As I stated in the OP, this is a somewhat theoretical question, but I would like to understand it better.  

RE: Pinned base in a concrete wall - is it really achievable?

EIT, 271828's example is what I'm talking about.

No serviceability issues for something like this.

RE: Pinned base in a concrete wall - is it really achievable?

"This connection is going to act fixed until the base connection reaches it moment capacity at which time that connection will become a plastic hinge and the wall will act as pinned-pinned for any additional load, but that 17 K-ft/ft of wall moment is still there, it doesn't disappear.  Once you add that 17K-ft/ft of wall moment to the footing that was just sized for gravity only it is going to exceed the allowable bearing pressure considerably."

The footing won't have 17 kip-ft/ft unless it's stiff enough compared to the wall EI to attract that much moment.  Again, go back to my analogy.  You have a wall with a HUGE EI and fairly short L.  You also have a teeny, tiny, strip footing supported on soil springs.  The springs aren't very stiff and the strip footing is narrow.  The bottom of the wall will rotate a little, but its own EI will limit the rotation to be very small.

This is just like having a steel beam with a simple shear connection.  A rigorous model of that would have rotational springs at the ends.  These springs would be very flexible, so won't pick up much moment for the tiny rotations at the end of the beam.  We rightfully ignore moment going to these connections.

RE: Pinned base in a concrete wall - is it really achievable?

StructuralEIT,

The point everyone else here is trying to make is that load is attracted to the stiffest path.  Forget about moment capacity in the wall-footing interface for a minute.  If the footing can rotate enough to "pin" the base of the wall, then the fixed end moment at the base of the wall will go somewhere else (up into the span).  We're saying that the wall-footing assembly pins itself at the bottom of the footing.  There won't be 17kf under the footing, because the rotation of the bottom of the footing has already released the moment to go elsewhere (up into the span).

Oh, and for the record, the rotation formula I listed above is for uniform load on a simple span.  If this is a basement wall, with triangular load, the formula would be a little different.

DaveAtkins

RE: Pinned base in a concrete wall - is it really achievable?

StructuralEIT, I sometimes design basement wall as pinned at the bottom (fixed fixed pinned at bottom).  The reason you can say it is pinned is because the footing is so narrow therefore it cannot perform like a cantilevered retaining wall.  The toe pressure from the overturning moment is so large so the sub-grade should fail and the footing should rotate (pinned) against the slab.  That's the way I look at it.  Correct me if I am wrong.

RE: Pinned base in a concrete wall - is it really achievable?

(OP)
AlmostPE-
Thank you!!  You are the first person to say that.  So the soil at the toe would have exceeded the allowable bearing pressure and it will allow the footing to rotate, relasing the moment back into the wall?!
That is what I was getting at.  
The question I was asking is if this is acceptable to have the allowable soil bearing exceeded and does this cause any serviceability issues?

RE: Pinned base in a concrete wall - is it really achievable?

StructuralEIT:
You are correct in your last post.  Technically the soil would have to yield or "fail" just a small amount for the footing to rotate.  However, the length that would have failed is very, very small and the remaining footing still has full bearing capacity.

At this point the footing has rotated a very small amount releasing the moment back into the wall, and you have essentially full axial bearing capacity beneath the footing.  No serviceability issue here.

RE: Pinned base in a concrete wall - is it really achievable?

Structural EIT

You are correct that there is additional soil pressure at the bottom of the wall due to the moment at the bottom of the wall.  You are also correct that the maximum moment at the bottom of the wall is limited by the strength of the vertical reinforcing at the top of the footing.  However, the maximum moment at the bottom of the wall is also limited by the strength and stiffness of the soil at the interface with the bottom of the footing.  If your soil were very strong and stiff, then the reinforcing limit would govern.  In most cases, though, the soil stiffness governs the upper limit of the moment.

If the soil governs, the moment at the bottom of the footing is proportional to the soil stiffness and the rotation at the bottom of the wall.  The rotation at the bottom of the wall is indeterminate, but itself has an upper limit.  The maximum possible wall rotation is the rotation that the wall would have if it were pinned at the bottom.

So, if you calculate the maximum possible rotation at the bottom of the wall and multiply that by the width of the footing, you have the soil deflection due to the maximum rotation.  If you multiply that deflection by the soil stiffness (k/in) you have the maximum additional soil pressure due to the wall rotation.  If you compare the moment due to the additional soil pressure to the upper limit due to the wall reinforcing, the soil limit should (hopefully) govern.  And, the additional soil pressure should (again, hopefully) be small enough to be ignored.

RE: Pinned base in a concrete wall - is it really achievable?

The soil doesn't have to exceed the bearing capacity to allow rotation, it moves as a function of the loading and subgrade reaction modulus.

RE: Pinned base in a concrete wall - is it really achievable?

(OP)
The soil bearing capacity doesn't need to be exceeded to allow the rotation, but would you agree that a higher bearing stress will occur at the toe as a result of this rotation?  It may not necessarily exceed the allowable, but it will be higher than under pure gravity load, correct (and lower at the heel)?

RE: Pinned base in a concrete wall - is it really achievable?

StructuralEIT, when I desing a basement wall with pinned at the bottom, I do not reinforce the concrete footing.  The only thing it has is the dowel going into the wall.  I am just using the footing as a base for the wall.  I dont really care  if it cracks since you wont see it anyway.  So theoratically it should rotate at the stem connection onto the footing.  

Now if you do reinforce the footing and also has enough hook embedment length, it will rotate at the base of the footing.  Yes, the soil will not be able to resist the toe pressure and it will start to rotate but it will only rotate so much because the horizontal rebar will transfer the moment to the both sides of the wall.

I am just using my engineering judgement on this design(I am sure you do that a lot).  Other engineers in my office seem to agree with me.  The didnt agree with me at first.

RE: Pinned base in a concrete wall - is it really achievable?

StructuralEIT-

I think you are right.  There is some additional bearing pressure at the toe due to the rotation.  However, I think the additional pressure is small and can be ignored, in most cases.

RE: Pinned base in a concrete wall - is it really achievable?

(OP)
AlmostPE-
You do reinforce it transversely, don't you?  If you do not and it cracks, such that your 3'0" wide ftg is now 2'0" then you will likely exceed your allowable bearing stress and have problems, no?
I can almost see not reinforcing it longitudinally, because no load is getting transferred in that direction, it is really on for T&S.

RE: Pinned base in a concrete wall - is it really achievable?

Usually we let the narrow footings (2 or 3 feet wide) work as plain unreinforced concrete. We have longitudinal bars for shrinkage and add transverse bars at 48" oc to wire them to so that they don't roll off the bricks into the sand as they are pouring concrete.

RE: Pinned base in a concrete wall - is it really achievable?

(OP)
jmeic-
Thank you.  That is all I was looking for.  

All,
This is my understanding now (which makes sense) - There will be some moment at the base of the footing due to the reinforcement from wall into footing.  Unless the subgrade is infinitely stiff, this will be less than the capacity of the connection at the wall/ftg interface due to the finite stiffness (some give) of the soil.  This moment can be ignored as long as the wall is designed as pinned at the base.

RE: Pinned base in a concrete wall - is it really achievable?

The unreinforced footing I use is 1'-6.  It is only sticking out 4" both sides of the wall.  Plus it does have a hook @ 16" o.c.  

RE: Pinned base in a concrete wall - is it really achievable?

A couple more thoughts.

First, the vast majority of these footings are have design bearing pressures nowhere near the allowable.  Thinking back, I can't think of a single one I've ever designed that wasn't like this.  I'd make the footings 2'-0" just by default.  If I have 3 ksf soil, I need 6 klf to have a problem.  It's fairly hard to have a wall with 6 klf, although I'm sure they exist.  All the heavily loaded walls I can recall ended up on footings on solid rock.

Second, the allowable bearing pressure in your geotech reqport is for larger scale bearing failure, like the pressure bulb stuff you see in geotech books.  I'm not sure whether very localized little areas of high pressure really are of any consequence.  

I still invite you to do one or both of the following:

1. Make a little model of a wall with footing on soil springs.  See what moment is generated at the base.

2. Calc the rotation at the bottom fo the wall in the upper bound case of being pinned.  Calc how much the footing tip would be pressed into the soil to make that rotation happen.

RE: Pinned base in a concrete wall - is it really achievable?

Stiffness attracts load, if you reinforce you must then account for the potential to attract load.  If sufficiently reinforced you must take the load into the connected element the footing the mat what ever it is. Modulus of sub-grade reaction the final stiffness your dealing with.  Where the heck does it come from? Spring constants leave it to the dirt guys. pinned pinned well then ensure you reinforce accordingly and pick up the remaining resultants.  In anycase fixed at the base of the wall we do and then transfer this load into the sub-soil at the toe(S) rocking otherwise.  We keep all our foundations in the elastic realm period.  Not sure about this plastic hinge thing would imply yielding and ability to transfer load ie fixed.  Anyways what's the slab in the basement have to do with it, unless you detail it accordingly? Never designed a mat that wasn't rigid which was my comment, long ago, otherwise. You can detail a pinned connection or fixed connection and a footing size will result based on the dirt guys opinion of either the allowable bearing capacity or the modulus of sub-grade reaction,one ULS and the other SLS.

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