column at corner of footing qmax formula

[pattontom]

The above is very typical in our plans. Where there is any column at edge, it comes hand in hand with column at corner of footing (see right lower picture above).

For column at edge (beyond the kern) of footing but not at corner, the formula to get qmax is:

qmax = 2P/(3bm)

b comes from rectangular footings of size l x b
so if the P is say 730kn. And b is 3 meter and m is 0.2 meter, the qmax is:

qmax = 2P/(3bm) = 811 kpa

Now I'd like to know the formula for column located at corner of footing. What is the corresponding formula? I can't find it in any books. Or how do you derive the qmax=2P/3bm for column at edge so we can derive the column at corner of footing formula. Thanks.

 

[BAretired]

Assuming you have a 10' x 10' footing and two theoretical scenarios.

1. Column (24" x 24") transferring a moment M and axial load P, such that eccentricity is outside middle third.
2. A wall element (6' long x 12" thick) transferring the same moment M and P.

Are there closed-form solutions that account for the stiffness of the column/wall (with proper subgrade modulus of soil) and provide a formula for reduced soil pressure for Case (2) compared to Case (1)?

Yes, I believe there are. The subgrade reaction on the footing can be directly related to a rotational spring. A frame analysis can be carried out on the structure using the appropriate rotational spring constant at the bottom of the columns or wall.

BA

 

[pattontom]

We used tie beams above footings and below slabs to support walls or even to prevent said differential settlement. But how many use tie beams to make the columns resist the moments of eccentric column at edge footings. To what extend can it work for those who have tried it or have thought of it?

 

[BAretired]

Your diagram is excellent. It shows precisely how the system works. I have used it on a number of occasions. The tie beam prevents the two footings from rotating freely. If the columns are rigidly connected to their respective footings, then the soil pressure will tend to be more uniform.

Good for you, pattontom. I think you now understand what we have been talking about.

BA

 

[dhengr]

Except, after all the talk about hinged and pinned columns at the foundations, the column and the connection btwn. the column and the footing must be designed strong enough to take the accompanying axial loads, shears and moments caused by that system.

Given normal column sizes and rebar detailing, it might be easier and cheaper to make combined footings take these unbalanced loads and moments, right down at that level.

 

[pattontom]

Complete edge eccentric spread footings only ok if the span is short or load low. But then the rebars cost of combined footings are 4 times that of spread footings as I have recently found out from the contractor estimates.

But then the advantage of combined footings is the moments reserve are not eaten resisting the eccentric isolated footings. Meaning in earthquakes the moments reserve can be used to resist seismic instead of resisting eccentric footing. Agree?

 

[pattontom]

what I meant by moments reserve above was the column moments capacity that would be used to resist seismic instead of eccentric footing

 

[BAretired]

Complete edge eccentric spread footings only ok if the span is short or load low. But then the rebars cost of combined footings are 4 times that of spread footings as I have recently found out from the contractor estimates.

Not true. Why does the span have to be short? Why does the load have to be low? The cost of combined footings is nowhere near four times the cost of spread footings. How do you manage to consistently come up with such garbage, pattontom?

BA

 

[pattontom]

According to Hokie66, for a 730kn axial load at edge of eccentric footing. The footing portion 1 meter away from face of column at edge at most have moment of 730kn. The column has to resist that much moment and for a small column of size 0.5x0.5 mtr. It can't resist it. It's moment capacity is just less than 400 kn. You need column that is very large.

Now the 4 times price difference. Well. The combined footings plan you guys suggested is already done and the total amount of kilograms of the rebars is 7040 kilograms compared to the isolated footing which is just 1326 kilograms. In fact it is 5.4 times (7040/1326 kg). The reason there is so much steel in the combined footing is there is massive top bars versus the isolating footing with only bottombar. And the spread footings are much smaller maybe because the old engineer understimated the axial load. Construction will start soon and you guys convinced me to let client go for it.

 

[ishvaaag]

All types of shallow edge (or corner) foundations

1. isolated footings
2. footings making use of a horizontal tensile force atop the column and a compressive horizontal force at the footing forming a pair counteracting the moment caused by the eccentricity of the load and the reaction (what here is labeled "viga tirante" solution, I don't know the english translation)
3. footings with centering beams to the next inner columns
4. combined footings

are used in Spain.

Only case 1 uses to show entirely the moment of the eccentricity in the column that pattontom refers to; even in that solution is usual modeling the column hinged at the footing and then proceed with the design; I have never seen a hinged detail there from anyone, but could be implemented.

Case 2 is suspect of not entirely relieving the moment in the column, particularly if a tie beam materializing the compressive horizontal force is not in place, yet it can be entirely effective ... I think it was far more common in the past where the tensile anchor needed to be materialized effectively. Today I have seen this less in practice. Some uncertainty about the path loads of the tensile force atop the column is also a factor in the issue.

Case 3 I have practiced extensively both with footings and pile caps, in the hundreds and maybe thousands, and, well, the centering beams are not cheap but if one wants a solution this may be thought a conceptually simple and sound solution.

Case 4 I have rarely practiced in particular relation with edge loads, even if in design converted to edge loads for economy; normally I see them where columns are very close and/or irregular plans are asking for some integrity.

Just to add the human and local factors, the custom of using centering beam I took from a colleague that studied and worked at Barcelona where some soils are reclaimed (but not neccesarily bad since centuries old); when I joined a team that learnt and practiced first in Madrid, when sounder soils are more common, isolated footings was the rule ... till I came. In general it will be very rare to see me doing any footings not having at least some tie; if you see, it will be surely an imposition of someone or of the logic of the problem.

 

[pattontom]

In normal RC beams. We don't put more bars than needed so that beams are weaker than column and plastic hinges can form in the beams for ductility to avoid sudden concrete compressive failure. What about in combined footings. The axial loads are fixed. Would it hurt to add more bars? How much more than needed added would there be a counterpart of compressive failure in the beams? I can't find reference about this in any books. In the design of my seniors. They put many transverse bars in the top portion of the combined footings. Ordinary. We put only transverse bars at bottom. So I wonder what would happen if more bars are more. Remember the axial loads are fixed with no overloads and we can't see the combined footings failing in flexure before they are hidden underground.

 

[ishvaaag]

Masybe the seniors are not as convinced of that the loads are so well stated that a bit more of reinforcement do any harm ... one would need to analyze the particular case of a foundation beam in the soil to see if any adverse effects of that excess of reinforcement can develop ... one first would think that on some cases shrinkage could show over the bars if too massive etc, on strength terms it would be very rare to prefer some particular part of the foundation fail before than most of the rest of the structure except to protect some other structural item etc ... it would be necessary to study the case and normally not an issue in most designs.

 

[BAretired]

I looked up the meaning of "viga tirante" in a Spanish/English translator and it said "tight beam" or "beam brace", so I am not too clear on the precise meaning either, ishvaaag.

In the case of an isolated footing with gravity load 'P' applied outside the kern of the footing, soil pressure will vary linearly from a maximum pressure to zero but will not extend over the entire footing.

A column with axial load 'P' located at distance 'e' from the centroid of a footing will behave as a gravity load unless it applies moment to the footing. If the column applies a moment to the footing, the effective load point shifts a distance M/P. [ul]
[li][/li]
[/ul]If M/P = e directed toward the c.g. of footing, the eccentric column is effectively a concentric column insofar as soil pressure is concerned.

BA

 

[pattontom]

ishvaaag, what do you mean "one first would think that on some cases shrinkage could show over the bars if too massive etc".

Were you referring to the shrinkage of the bars? or shrinkage of the concrete, or shrinkage of the footings as a whole or settlement. I don't get what you meant. Pls. be clear on the descriptions.

Maybe there are tranverse bars on top of the combined footings in addition to longitudinal to avoid overturning of the combined footings along the east-west axis?

Imagine there are 3 columns aligned horizontally with rectangular combined footings with the edge at both ends holding the 2 columns and one at center and distance edge to edge is 11 meters and it's hold the east-west axis. While the top is north-south axis. Lateral force from moment frames in north-south axis have to be resisted by the combined footings and I think the tranverse bars make the width stronger. Does this make sense?

 

[ishvaaag]

Well, I only meant that with big diameter bars it is a frequent problem to have concrete shrinkage problems directly on the vertical of the same (drying shrinkage) in some cases like windy hot weather. I doubt your seniors are not aware of this particular circumnstance and provide a reinforcement prone to the problem.

Respect the final paragraph question, normally a solicitation that shows significantly in some direction will be best addressed with reinforcement in that direction. The particulars always pertains to the case. However it is in the best tradition of monolithism wanted from reinforced concrete to provide at least 1/4 or 1/3 of the main reinforcements transversally precisely to enable through the width distribution of the solicitations to be met by extant capacity.

 

[pattontom]

ishvaaag, you mentioned: "Well, I only meant that with big diameter bars it is a frequent problem to have concrete shrinkage problems directly on the vertical of the same (drying shrinkage) in some cases like windy hot weather.

The bar size is 20mm.. do you consider it big diameter bars? Also I can't understand what you meant that "to have concrete shrinkage problems directly on the vertical of the same"? Can you please rephrase it? Do you mean the concrete would shrink? Also how can windy hot weather get inside the foundation??

 

[ishvaaag]

Concrete whilst setting normally shrinks, other thing is that it causes a problem or not. Special mixes (more commmon in mortars for specialty use) with additives may undergo small (low-shrink) volume change, or even expand; for even expansive mixes are wanted on occasion. But the normal occurrence is to shrink, from that "shrinkage", a word to describe the rheological phenomenon.

http://www.concrete.org.uk/fingertips_nuggets.asp?cmd=display&id=22

I don't think 20 mm is particularly "thick" to this purpose (in fact is the thickest diameter you can routinely use in design without starting to have to give some thought to rebar diameter matters) but too small cover, liquid bleed atop, and the hot and windy weathers could produce the defects.

This article seems to be a good primer on the matter.

http://rollcov-r.com/hot_weather_curing.html

Proper jointing, cover of reinforement, surface secondary reinforcement if neccesary, mixes (with admixtures, usually) targeting to prevent the shrinkage bad effects in hot weather, and proper curing all may help with the difficult cases.

 

[pattontom]

After talking about eccentric footings for 2 weeks. We didn't mention the fact that for columns located at external end. It automatically has moments due to the beams at top (ceiling level) not centered and on one side only even when the column is at center of footing (see above). Now is it not possible that when you use eccentric footing, somehow the moments introduced by eccentric footing cancels the moments created by the one sided ceiling beam (see right side of picture above)?? Not exactly cancelled 100% but at least each can help each other out? Or could the combination be worse because the column body is pulling itself apart? How do you analyze such case?

 

[ishvaaag]

See attachment for the "VIGA TIRANTE" solution.

This is an old and limited solution for the problems caused by edge footings. When it was practiced, mostly masonry structures times, the difficulty was to get integrity between walls and floors and so finding the force T, to be provided by some actual and effective anchorage was paramount. You can see that you have in place a device to ensure the centering of the reaction if you have something to deliver C and T, forces to be surmised equal and of opposite direction. C being weak, it was assumed many times to be taken by the lateral strength to compression of the soil, or better, if materialized, provided by some tie at ground level.

However by no means it is warranted the footing will not attempt to rotate under the N·e pair and so subject the column to additional moment, except hinged. A hinged support for masonry or steel could maybe accepted, more rarely for concrete. In masonry, some eccentricity at bottom support of the wall would be resulting, anyway; actual hinges would have their own constructive issues.

It is for this reason that the "viga tirante" solution is practiced less and less today, it having being substituted by the superior "centering beam" solution, a beam that occupies the dashed portion between external and 1st inner footings in our drawing, and by its flexural strength provides at the -in our drawing- right side of our edge footing a moment counteracting N·e that directly forbids the worrying rotation, then negating any additional moment in the column from edge footing.

 

[pattontom]

Instead of using a centering or strap beam. What's wrong if you just combined all the footings into rectangle. This would mean making the footings larger than needed. Is the disadvantage only costs? This is the solution we used. The 3 columns separate only has axial load of 3500 kn. We made combined footings of the 3 column that can take 5000 kn. The increased width is also to strengthen the seismic resistance in the perpendicular axis.

 

[ishvaaag]

Centering beams use to need big depths, whereas the transverse solicitations look to be scarcely problematic.

Except someone is keeping a close eye on the design from an economy viewpoint, the choice is usually made by the structural designer without further problems. One structural designer is not challenged on economy matters each and every time something; it is only a matter of charging more where feasible for additional design or review time that the client should keep amenable to some divergence of thought with its design team. You can design 100 solutions for one structural problem, but you should not do that for the price of one.

So be assured that I only was describing some things, not saying that you should follow what explained.