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.

 

[atrizzy]

In plain flexure, the tensile stress would always govern. If the footing as in significant compression (granted such a condition is a long shot) then the compression stress might become governing. I imagine CSA simply included this for completeness. This compression limit is, after all, lower than the compression limit given for reinforced flexural members.

 

[Shotzie]

@atrizzy That makes sense, for whatever reason I thought the code was trying to imply that you could develop the full compression stress and tensile stress simultaneously. I'll continue on with limiting my compression stress to an equal and opposite value from the maximum tension stress.

 

[atrizzy]

Shotzie, think of it this way. They wouldn't instruct you to limit the tension AND compression stress to the lower value, since the compression stress obviously need not be limited to that value. The fact that the tension component tends to govern is incidental.

 

[Shotzie]

@atrizzy That's a good way to look at it. Thanks!

 

[KootK]

There's one thing that I've never been able to reconcile myself with in plain concrete footings: design to a uniform moment across the footing. I'd expect moment to peak under columns as with a two way slab. That moment would be intense and hard to determine accurately. And with concrete being brittle in flexural tension, there would be little capacity for redistribution.

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.

 

[dik]

You can calculate it roughly by considering the compression load as a force on the footing. This will give rise to a slightly curved moment diagram rather than the discontinuous 'cusp'. We used to use the reduced moment for design of flat slabs and plates for multistorey concrete buildings.

Dik

 

[KootK]

Can you elaborate upon that method dik? I don't get it... but I'd like 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.

 

[haynewp]

Look at the moment diagram at the cantilevered edge of a strap/combined footing. The moment in the footing is lowered by accounting for the compression force along the column interface in the FBD instead of considering the columns as point loads.

 

[KootK]

Ah, I see. Thanks haynewp. Two things though:

1) It's actually the moment distribution in the other direction that worries me.

2) I've seen that method presented for two way slabs as the reason that we're able to design for flexure at the column face. So I imagine that it's also the reason that we design footings for flexure at the column face (or near it). So would it not be double dipping to design for flexure at the column face AND take the reduction accrued by looking at the compression load?

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.

 

[atrizzy]

I don't see how the compression from the column counteracts the flexural tension at the bottom of the footing. They act in opposite directions.

 

[KootK]

Just the difference between treating the column load as a point load or a distributed load over a finite width.

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]

1) I'm not clear on this.
2) For isolated column footings, I would use either the moment at the face for the footing design or the maximum moment that occurs in the footing when accounting for the reduction in the moment diagram under the distributed bearing area of the column. Designing at the face of the column always assumes the max moment occurs.

 

[KootK]

1) I'm not clear on this.

Consider the moment diagram that you're imagining in you head and that you would draw on the sketch of the strap beam etc. Now imagine the moment diagram that runs perpendicular to that. That's what concerns me.

2) For isolated column footings, I would use either the moment at the face for the footing design or the maximum moment that occurs in the footing when accounting for the reduction in the moment diagram under the distributed bearing area of the column. Designing at the face of the column always assumes the max moment occurs.

Is it not standard practice to design for the moment of the face of the column? If so, then it seem to me that we should just leave it at that and let the compression business be interesting background trivia.

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]

interesting background trivia

Your bread and butter right there

 

[KootK]

That was the old me. Now it's Koot-"Dolla Bill"-K. Eatin' profitability sandwiches 24/7.

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]

It’s standard practice for isolated footings but I don’t know for sure there isn’t another case where that isn’t true. I think for combined footings with a mix of uplift and downwrd loads and/or column moments that might not always be a safe assumption. Would you take it to the face of the column on all sides if it was a small axial load and high moment on an isolated ftg? Maybe to the rebar location countering the negative bending.

 

[KootK]

Would you take it to the face of the column on all sides if it was a small axial load and high moment on an isolated ftg?

I would, yes, based on the same theory. I think that I saw the derivation in William Gamble's concrete slab text in reference to two way slabs. I suppose it's a bit different because, in most cases, you're sandwiched between a column above and below. In truth, right now is the first time that I've really thought about this is such detail. A little late to the party perhaps.

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.

 

[dik]

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...

Dik

 

[haynewp]

I had a lot typed up and lost it. Anyway, I don’t think it matters for isolated footings, I’m not convinced on combined footings given all the load possibilities.