CSA A23.3 Plain Footing Bending Resistance 1

[Shotzie]

Hi there,

I'm having some trouble understanding the meaning behind clause 22.6.5 in CSA A23.3-04. It states that for plain footing strength in bending "The factored resistance in bending shall be based on a maximum stress in tension of 0.37*lambda*phi_c*sqrt(f'c) and a maximum stress in compression of 0.75*phi_c*f'c". If I was to do a bending calculation and limit the tensile stress to the value given in the code clause, would the compression side of the footing not just be stressed to the equal and opposite amount, with the neutral axis occurring in the center of the footing? When would the compression stress limit ever apply? I feel like this is a basic question that should be easy to figure out with basic concrete principles, but for some reason it's not making sense to me.

 

[KootK]

KootK... if you draw a BMD, but rather than treat the reactions as point loads at the centerlines, treat them as UDL's equal to the reaction (moment and/or axial) across the width of the support. This will reduce the peak -ve moment at the centerline by a tad.

I get it now post-haynewp. That said, it's the other direction that worries me and this would seem to be double dipping against the usual practice of taking moments at the column face.

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.

 

[BAretired]

Combined footings are usually reinforced. A combined footing using plain concrete would be a rare occurrence.

BA

 

[haynewp]

I don’t think usual practice or ACI differentiates and allows momnts to be taken to the face whether reinforced or not. But I don’t have ACI with me right now.

 

[hokie66]

Perhaps that code contemplates a plain concrete member, footing or whatever, which is not rectangular or symmetric in section.

 

[dik]

The moment at the col face would be less... unless there is a 'bunch'... I usually use the centerline moment... It's the structural system chosen that determines the economy... not a tight design...

Dik

Dik

 

[haynewp]

An extreme case for example, if there is a combined footing where one column is heaviy loaded (vertical and or moments) and there is another column at the other end of the footing that has no load in comparison, how can the moments be justified to be reduced to the faces of the unloaded column at that end of the footing? I think this is getting away from what the OP was looking for so I will stop with that.

 

[haynewp]

kootk; Regarding the double dipping, I don’t see a problem if I think about it in terms of pressures instead of line moments. For an isolated square footing with column axial only for example, assuming the pressure under the footing is only the result of the pressure under the column, the moment reduction under the column should occur the same in each ftg direction. The moment in each footing direction is a result of the soil pressure (that happens because of the column pressure being applied). Total pressures are equal, moments reductions ahould occur equally in each direction, everything is linear.

 

[haynewp]

If that’s confusing, think about a basic square footing. If you take the pressure under one half of the footing and design for that moment and then look at the footing in the orthogonal direction, we take into account that same soil presure overlap again to get the moment in that direction. Why wouldn’t the same concept apply to the column pressure that reduces these incoming orthogonal moments?

 

[KootK]

An extreme case for example, if there is a combined footing where one column is heaviy loaded (vertical and or moments) and there is another column at the other end of the footing that has no load in comparison, how can the moments be justified to be reduced to the faces of the unloaded column at that end of the footing?

Why would such a procedure be unjustified? As I understand it, taking moment at the face is based on the derivation below. It's MacGregor rather than Gamble -- my bad. It seems to me that the same logic could be applied to both columns in a combined footing regardless of the relative loads.

kootk; Regarding the double dipping, I don’t see a problem...Total pressures are equal, moments reductions ahould occur equally in each direction, everything is linear.

I agree that moment peak smoothing can be applied in both directions simultaneously without double dipping. What I do believe is double dipping, however, is to both take moments at the column faces AND reduce moments by explicit consideration of compression / distributed load. That, because they would seem to be mathematically the same phenomenon.

Thus far, I've been misunderstood in my concern. My concern is not about moment peak smoothing but that, in any direction, when we evaluate flexural capacity against what is, implicitly, and average moment demand that does not capture peak stress. That strikes me as a problem when the mode of failure is brittle, tensile concrete failure based on the flexural modulus of rupture. I feel as though we're assuming a redistribution capacity that doesn't exist. I've obviously done a terrible job of expressing my concern so far so I've included a sketch below to try to help with that. If others are doing this kind of thing more rigorously, I'd love to hear about it and how it's being undertaken. As I see it, we're designing to uniform, lateral moment distribution that is fictional.

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.

 

[haynewp]

Attached where I tried to show a case where I would not reduce the max moment to the column which I made a breezeway column just for the example. I apologize for the lack of neatness.

 

[KootK]

I don't see why the theory wouldn't still apply but it's hard to imagine an engineer bothering with it in a situation like that where the ROI would be vanishingly small. I suspect that many engineers would include a design case that omitted the breezeway column altogether making the reduction moot.

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.

 

[haynewp]

If there’s virtually no load or resistance to the footing bending moments at the center column I don’t see how it can be counted on to reduce moments as the ftg hardly knows it is there in comparison to the other columns.


On the double dipping, starting on page 37 has a good presentation. We may be assuming a lateral distribution that doesn’t exist but it is permitted by my Code and has always worked as far as I know. The column and middle strip method would be better to account for that lack of lateral distribution ability when doing hand calcs.

https://repository.up.ac.za/bitstream/handle/2263/40823/Skorpen_Application_2013.pdf?sequence=1

 

[dik]

Good publication... thanks,

Dik

 

[KootK]

If there’s virtually no load or resistance to the footing bending moments at the center column I don’t see how it can be counted on to reduce moments as the ftg hardly knows it is there in comparison to the other columns.

Right, but that's just a matter of scale and whether or not it's worth the effort to account for the moment peak smoothing. It doesn't invalidate the use of the method on any technical basis. The impact of the central column would be minimal and the analysis would reflect that.

On the double dipping, starting on page 37 has a good presentation.

It's a fine presentation of FEM results (below) but the document is entirely geared towards reinforced footings which will tolerate inaccuracies in the assumed lateral distribution of moment. My concern is for plain footings where, one would assume, first rupture = failure. To my knowledge, we in north america don't even have the SD methods represented by the step functions in the graphs below except to the extent that designers might wisely be doing that of their own volition. Folks just use the straight average moment.

To me, the situation is akin to attempting to design a plain concrete two-way slab using only the averaged panel moment for design. And, of course, that sounds kinda nuts.

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.

 

[haynewp]

Right, but that's just a matter of scale and whether or not it's worth the effort to account for the moment peak smoothing. It doesn't invalidate the use of the method on any technical basis. The impact of the central column would be minimal and the analysis would reflect that.

My analysis would include whether to take the moments to the face of the column/(midpoint of base plate) or not based on assuming the moment is spread equally across the width of the footing in the orthogonal direction. Basic old hand calculation method and whether to use the ACI permitted provision or not.

It's a fine presentation of FEM results (below) but the document is entirely geared towards reinforced footings which will tolerate inaccuracies in the assumed lateral distribution of moment. My concern is for plain footings where, one would assume, first rupture = failure. To my knowledge, we in north america don't even have the SD methods represented by the step functions in the graphs below except to the extent that designers might wisely be doing that of their own volition. Folks just use the straight average moment.

To me, the situation is akin to attempting to design a plain concrete two-way slab using only the averaged panel moment for design. And, of course, that sounds kinda nuts.

There is a significant reduction in the phi value for ACI when designing plain concrete. I would assume part of that is the recognized lack of ductility.

 

[KootK]

@shotzie: this commentary section from ACI may give a clue as to what scenario the code writers had in mind when they decided to present different tension and compression values. Of course, you don't see many footings that would have geometries producing different S_top and S_bot values.

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.

 

[hokie66]

Like I said 28 October, 0447. But that's all right, you fellows have enjoyed your discourse on a different subject.

 

[haynewp]

It was a blast.

 

[KootK]

You get full marks Hokie but I still think that there's value in quoting an "official" source for confirmation. I wouldn't have stumbled across it had haynewp not had me looking into the safety factors for plain concrete.

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.

 

[KootK]

It was a blast.

Uhh.. I feel as though I might be picking up some sarcasm there. Were you not enjoying yourself haynewp? I honestly can't tell a lot of the time around here. In the world of anonymous cyberspace I can't, for the life of me, understand why anybody would bother participating in anything they don't enjoy. Yet some folks seem to.

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.