L shaped wall footing 1

[LicensedToPEe]

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

 

[hokie66]

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.

 

[csd72]

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.

 

[kslee1000]

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.

"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."

 

[hokie66]

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.

 

[kslee1000]

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.

 

[hokie66]

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.

 

[kslee1000]

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.

 

[hokie66]

I give up.

 

[kslee1000]

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.

 

[miecz]

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.