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L shaped wall footing

L shaped wall footing

L shaped wall footing

(OP)
I am designing a strip footing that is, due to a property line restriction, constructed as an L. The wall (stem) is propped at the top with a floor diaphragm and at the bottom with a slab on grade. In other words, the foundation system (wall + footing) cannot rotate and can only move in the vertical direction. There is about 6 kips/ft (5 story bldg) of gravity load at the top of the wall with 7" eccentricity to the center of the footing (click on the link to see the section).

My question is, under these conditions, is the pressure under the footing uniform? If the L-bar is designed for the negative moment at the fixity between the footing and the wall, the system is assumed to act as rigid (i.e. the angle stays 90deg).

I am just so used to be anylyzing footings with the good old p_max = Q/A + (6Q*e)/(B^2L) whic always results in no-uniform pressure distribution when load eccentricities are present. This formulation also assumes a pinned stem at the footing to allow rotation of the footing.

Is my approach correct to assume uniform pressure distribution as long as the stem/footing interface is designed (i.e. has enough rebar) to transfer the negative moment and the floor at the top and slab on grade at the bottom prevet rotation?

Any input/comments are appreciated,

Adam U
G M Structure LLC  

RE: L shaped wall footing

Per your detail, ignore the slab on grade, it contributes very little compared to the loads from floors above.

You may make this system simpler by lowering the slab on grade to the strip footing level, and make it a mat foundation. It may cause you more concrete (I would prefer 8" mat as the minimum to allow for double layer reinforcement), but simplify the excavation/backfill/compaction efforts.  

RE: L shaped wall footing

AdamU

Diagrams always help a lot.  In your formula, how do you account for earth pressure thrust?   

It is not a uniform pressure due to two reasons.  First, you have 7" eccentricity & the center of the stem does not coincide with the center of the footing. Second, you have earth pressure thrust which will cause higher bearing pressures on the right edge of the footing.

I am getting 1.93 ksf for comparison.


 

RE: L shaped wall footing

(OP)
Making it simpler might be the case but I would also make it SO much more expensive. 2 layers of rebar make residential contractors cringe!!!

If the footing were to becentered, I would only need about a 3 foot wide strip footing (given 2,500 psf allowable bearing). But it is the eccentricity that, given the standard non-uniform pressure distribution approach, creates a bearing problem at the shorter end (the heel?).

However, there are footings like this constructed all the time, I just need to "prove" it on paper that it works...

RE: L shaped wall footing

(OP)
STVU,

if the stem/footing is not rotating (fixed at the interface, propped at footing and top of wall) how can there be a pressure variation? the footing can only move up an down, theoretically, so it will always be loaded uniformly? Am I not seeing this right?

RE: L shaped wall footing

The pressure will not be uniform.  The soil load will tend to even out the distribution, but the pressure will still be trapezoidal.  You just have to sum the forces to get everything in equilibrium.

RE: L shaped wall footing

(OP)
Also for STVU,

I would say the pressure is larger on the left edge of the footing (at the shorter side).

RE: L shaped wall footing

(OP)
Hokie,

if the footing had no heel, the longer I would make the toe, the higher the pressure I would get since the eccentricity is moving away from the center of the footing. By the trapezoidal approach, you will never get the footing to work since your pressure will always increse linearly at the corner of the L...

RE: L shaped wall footing

That's correct.  Just increasing the width of an offset footing doesn't help.  The pressure goes to a triangular distribution, with the remote toe carrying no load.  When a footing has to be totally offset, no heel, you have to have a rectifying force to keep the toe down.  This is commonly achieve by a "strap" to a footing within the building.

RE: L shaped wall footing

"if the stem/footing is not rotating (fixed at the interface, propped at footing and top of wall) how can there be a pressure variation? the footing can only move up an down, theoretically, so it will always be loaded uniformly? Am I not seeing this right?"

Again, per your detail, the stem (wall) and the footing is connected by a single bar in the middle of the wall (as pinned condition - no moment capacity at the joint), and the slab is simply sitting on the footing, while the lateral movement is prevented by the slab, how could rotation not to occur with the build in eccentricity?

Worst of all, when the footing rotates, the water can seep through, and a gap may form at the slab/footing interface, the gap could be filled by fines, then what?

Double the bars in stem (wall) make it a rigid joint? Now you have moment on footing to deal with, not a solution.

Tie the slab to footing? You are going to have deal with severe cracks, also not a solution.

Cheap has a price! (Sorry, not an attack, just express personal feeling. I didn't do the math, your system colud be worked out just fine)

RE: L shaped wall footing

kslee,

The wall to footing joint shown by AdamU's section is not a pinned joint.  The bar has an effective depth of roughly half the wall thickness, 5".  It takes bending.  Whether or not it is strong enough, I don't know.  His solution may work, he just has to do the numbers to find out.

RE: L shaped wall footing

(OP)
Exactly what Hokie66 says, the section is designed with d=5" for the negative moment resulting at the interface.

If the joint is rigid, the lateral support provided against the stem by the slab on grade provides a "roller" support, allowing up and down movement only, i.e., no rotation.

I am not trying to convince anyone on the right approach, I am just saying these footing ARE build like this in residential construction and the footing don't experiance a bearing failure nor settlement even though the analysis (trapezoidal pressure) shows high overstress. But I guess this will only lead us into the whole discussion into the accuracy of allowable pressure guess (I don't call that a calculation ha-ha).

RE: L shaped wall footing

(OP)
STVU,

if the wall is propped at the top, the condition that develops is the "at rest" and Ko needs to be used in lieu of Ka. That's just a side note.

Also, you are missing the axial load at the top of the wall (Q = 6 kip/ft) contribution to the pressure under the footing given e=7" (per sketch). In other words, the q_max needs an additional term in the form of  

+ [(6,000*(7"/12")]/[(4^2*1)/6] = + 1,312 psf

This is waht kills the pressure diagram, it adds 1,312 psf to the tip (if trapazeidal distribution is used).

RE: L shaped wall footing

hokie:

I agree it has some moment capacity, but not to the extent of fixidity for 10" wall (the tension side wall-footing interface will open up as a triangle wedge). I believe you know very well that finding degree of support fixidity is not a simple task, even for overhead beam-columns, not to mention there is effect from the soil to be considered. Therefore, for practical concerns in the US, single layer bar in the center of wall is most likely to be considered as pinned connection.

Also, will moment be helpful/desirable for his case (he can move the bar to the outer face)? I doubt, and rather to have single vertical load to be dealt with, not both. However, as both of us have pointed out that we didn't do the math, so, his detail may turn out just fine without all these arguments.

RE: L shaped wall footing

You are correct-Ko applies instead of Ka.  Only exception would be if you backfill before the floor beams are installed. In which case the wall has already rotated and Ka is fine.

The formula I used assumes the axial load is in the center and not 7" off.  Let me digest that. I don't know if it is going to add 1312 psf though. I will repost later.

RE: L shaped wall footing

(OP)
It's Friday 8pm and I am still at the office...

Thanks for your contributions, I will reply to additianal posts on Monday...

RE: L shaped wall footing

I just looked at my reference "Structural Concrete" 2nd edition, by Hassoun.  If the eccentricity is less than B/6, then only one formula applies. So, for e=0 to e=B/6 or 8" qmax is the same 2.53 ksf per my previous post. I learned something!:)

Once you have "e" = B/6 or 8" exact we jump into the triangular distribution, where qmin is zero and q max is still 2.53 ksf.  

When "e" > B/6 it is triangular, but the zero portion of the triangle moves to the right.  

RE: L shaped wall footing

One more note:

No matter the fixidity of the lower joint, your wall could have positive moment on the inside face, how do you take care of it, by using the same bar in the middle? Won't there be cracks on the wall? Double check your forces along the wall.  

RE: L shaped wall footing

kslee,

You need to stop talking about the fixity of the joint.  You can only fix a joint if there is a rigid support, and in this case neither the footing or wall is rigid enough for that to occur.  Fixity = no rotation, while there will clearly be rotation in this instance.  But there is no reason why centrally reinforced elements cannot carry bending moment.  Otherwise, reinforced masonry walls and tilt up concrete walls don't work, and this is true regardless of the country.  If the moment at the base of the wall causes the steel to yield, a hinge could form, but that is certainly a lot different from a pin.   

RE: L shaped wall footing

A few notes.

Have you actually checked the truss joists for the reaction from the wall, this can be very large.

If you take the dead load from the basement slab this will help to even out the eccentricity.

If the soil fails from bearing pressure then it would have a tendency to rotate, but how will it rotate with all that retained soil pusshing the other way - i.e. the retaining wall will play a part in the bearing oressure whether you design for it or not, luckily it is in your favor.

RE: L shaped wall footing

Hokie:

Below is AdamU's write up, not mine. Sure there is a big "IF" at the beginning of the second sentence, but as a whole, it tries to justfy the "uniform reaction under footing", "rigid Joint" & "NO ROTATION", all 3 were the focus of disputes.

I am not familiar with CMU wall design, but has no doubt if it subjects to significant lateral load, the single bar method wouldn't work, rather intermediate piers are required, or more intermediate bond beams to distribute the excessive load to columns. (At least I will do so)

Again, all my responses were pointing to the 3 claims above, not predicating the system works, or not, in his favor. But, as I have already laid down all my thoughts, yes, I am resting my case, waiting to talk to you guys on other topics. 3eyes

"Exactly what Hokie66 says, the section is designed with d=5" for the negative moment resulting at the interface.

If the joint is rigid, the lateral support provided against the stem by the slab on grade provides a "roller" support, allowing up and down movement only, i.e., no rotation."
 

RE: L shaped wall footing

kslee,

I know you have rested your case, but thought I would have one more go to try to clarify one point.

I didn't really understand this statement of AdamU's either, but my last post was strictly to do with your statement that "for practical concerns in the US, single layer bar in the center of wall is most likely to be considered as pinned connection."  I am from the US, and although I now practice in Australia, I don't believe that statement has any validity.

A single layer of reinforcement in the center of a 10" wall, d=5", provides the same moment capacity as the same layer of reinforcement with d=5" in a 7" wall.  When used as in the OP's example, the moment can be of either sign.

RE: L shaped wall footing

Hokie:

It's not just the moment capacity, the likelihood of the joint to maintain right angle should be considered too (it's not a straight cut for this case). If his wall is 7" with bar near the outmost tension face, I would agree fully with the "fixed" assumption, but not 10" wall with bars in the center.

 

RE: L shaped wall footing

I said nothing about "fixed", that is your terminology, which is incorrect.  But the joint in the centrally reinforced 10" wall and a 7" wall with the same d will "maintain right angle" the same, just depending on the area of steel and d.  The joint in the 10" wall would open more at the tension face due to the geometry, but not at an equal distance from the bar.

RE: L shaped wall footing

hokie:

My old pal, you confused me a little here. If the joint is neither fixed, nor pinned, how could one get the reaction at the onset of calculation? It can be done, but as I hinted, it's (partial restrain) not quite straight forward, and very difficult to convince everybody. That's been the reason, let's be safe, call it pinned to maximize positive moment (higher desirable) to round off the uncertainty on the negative moment. Actually, for underground walls, we used to assume both for the lower connection to maximize the reactions along the entire wall. Waste? Not much. I personally have difficulty to grab the idea for a single bar to resist both positive & negative moments.

Finally, all arguments here is trying to straighten the myth from the beginning - uniform stress under the footing with an eccentric load. Can be done mathematically, but not without doubts and uncertainties.

I think both you and I have very different background in practice, though both been trained in the US, that's been the reason we disagree with each others view points when judgement calls are involved. But I do agree that many often you do have quite a few practical points that worth to think about, and to moderate my far-reaching conservative thinkings. That's the beauty of this forum.     

RE: L shaped wall footing

I give up.

RE: L shaped wall footing

Hokie:

Don't be frustrated with diversity on certain engineering practices. I have a personal believe that no theory is perfect, so does the engineering applications - they always subject to arguments & given circumstances. Once my PhD supervisor joked with me: you can always twist the codes/theories in your favor if it is to your advantage. Well, not quite true, but worth to think about.

By the way, I do appreciate your check on me, it forces me go back to foundamentals and think, which I haven't been doing for a while. Thanks. bigsmile

RE: L shaped wall footing

Getting back to the original question;

First, assume zero restraint from the upper floor level. The overturning moment due to the backfill is opposite in sign from the eccentricity due to the vertical load.  The heel and toe dimensions can be adjusted so these effects nearly cancel each other.  When that is accomplished, then the reaction at the top of the wall is small, and the initial assumption is realized.  There may be a small rotation at the joint from the wall to the footing, but it's effect on the footing pressure is negligible.  The footing pressure, then, can be taken as uniform.

This all assumes that the connection from the wall to the footing is capable of transferring the calculated moment, and that the vertical wall reinforcing is capable of resisting the moment in the wall.  Finally, the little shear key shown at the bottom of the wall does nothing and can be eliminated.   

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