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.

 

[msquared48]

Well, the resultant of the pressure prism would be at the CG of an inverted quarter pyramid shape.

Page 280 of my Bowles "Foundation Analysis and Design", fourth edition, has an example that might be helpful. They use an itterative process to solve it.

Mike McCann
MMC Engineering

http://mmcengineering.tripod.com

 

[ishvaaag]

I made this worksheet from a table said to come from Betonkalender, I think to remember. pdf printout attached. Just a matter of reading a value in a table.

Please note that this seems to be for isolated footings, since when using centering beams the situation should be designed to be more favorable.

 

[ishvaaag]

Also, the table is built for a central column. However for a rigid distribution of the pressures you can place the resultant from a corner (or edge) column and proceed from the eccentricities to the center of the rectangle as in the intent of the table. You can also add any centering effect from the footing weight when placing the resultant for the case.

 

[pattontom]

Mike,

The Foundation Analysis and Design, 5th edition I just got has over 1000 pages.. what is the particular topic subject title in page 280 because the 4th and 5th edition has different page numbers so I don't know what particular pages you are referring to. Thanks.

 

[BAretired]

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

qmax = 2P/(3bm)

That is true when the column is pinned to the footing. But if (a) the column and footing are rigidly connected to each other and (b) the top of column is prevented from translating horizontally, q[sub]max[/sub] is much smaller and pressure extends over the entire footing. The pressure distribution in that case is variable depending on the column stiffness and the modulus of subgrade reaction.

In the case of a corner column, if it is hinged to the footing, the soil pressure will vary from a maximum value at the corner to zero at a diagonal line determined by the geometry of the column. But if the column and footing are rigidly connected, a larger portion of the footing will be engaged. The pressure distribution will depend on the column stiffness and the modulus of subgrade reaction .

BA

 

[fcu45]

You will find great help in this book, "Reinforced Concrete: Analysis and Design" by S. S. Ray.

 

[pattontom]

BA

I thought it is a law that if column goes beyond the kern, the opposite side of the footing connected to the column would have uplift. This is the reason we did the combined footings thing last week. So you are saying if the column and footing connected rigidly. Pressure extends throughout the footings and no uplift?? I thought all isolated spread footings are hinged and anything any column beyond the kern can cause uplift.

 

[hokie66]

You misunderstood. BA is correct. A force applied to the footing within the centre third, in the absence of an applied moment, does not result in an "uplift" situation, but...

We discussed, in one of your other threads, how if a column could apply a resisting moment, the distribution of pressure could be changed. But in your case, your columns were quite small relative to the footing, so the column stiffness would not help much.

Don't try to make everything black and white. There are shades of grey in between.

 

[pattontom]

There seems to be subtle difference between pinned and hinged column footing connections.

1. Are all isolated footings hinged? What does it mean to have pinned isolated spread footing? Can one gives example? But the book analysed it in terms of pinned, why not hinged?

2. Combined footings have pinned columns. Isolated spread footing have hinged columns. Which has greater base shear effect or seismic response? I heard pinned columns have the moments transferred to the column joints above. It's means pinned is weaker?

3. Is it possible to make hinged combined footings columms? Is this stronger than pinned?

 

[hokie66]

Hinge = pinned. No difference in this context. No column to footing connection is truly pinned, but that is normally the way we analyze them.

 

[ishvaaag]

Other very useful trick (even if not the maximum pressure under a corner) is to use just the plastified response on the maximum area centered on the applied resultant on the soil. This way you don't only know the pressure (the applied load divided by the effective area) but you have a loading scheme for the reinforcement of the footing, all this with minimum conceptual and numerical effort.

 

[slickdeals]

There are some good charts in Teng's books. There is also another thread in this forum, where meicz (sp?) has posted a mathcad worksheet which is based on Teng's curves.

 

[ishvaaag]

For an approach where a modulus of subgrade reaction is given (and quite surely a good soil is implied in the betonkalender table, to get conservative statements of the soil pressure) you can use the following zipped Mathcad 2000 professional worksheet to find a solution. It serves for all central, edge and corner column placements.

Or you can do even better the same with your preferred FEM software setting some compression-only springs under the nodes of the elements in which you will be dividing your footing.

 

[slickdeals]

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)?

 

[ishvaaag]

Taking into account the structure and the soil is soil-structure interaction and it is normally dealt with with some model that has both the structure and soil characteristics. Other than that, in the more simplified ways, the column action is resumed in resultants, here M and P (for which hence my worksheet would give common results, being the actions the same); using more loads as a set of M components and P components as you would do to mimick the wall applying the loads is already even more in the way of FEM (my worksheet itself allready decomposes the plan of the footing in elements to establish equilibrium).

One can't say something has not been done so I will refrain from saying there are not closed form solutions for your question but I would say that instead of trying to seek benefit from a different setup on the column for a common geommetrical footing, I would be contrarily working in the way of making it irrelevant to the design ... I am not confident in shaving close to structural strength and if compromised I just better choose some alternative and if possible well proven solution.

 

[pattontom]

If one puts more bars in columns... moment capacity increase.
If the axial load is low and it is eccentric outside the middle third. There is moments equal to axial load multiply by the distance of the eccentricity. Now that moments can be resisted by the columns if the column is sufficiently stiff (more bars).

So all in all. What do you think is the theoretical maximum axial load and smallest columns and footing where column can be safely be put at edge of footing (not corner)? Anyone has tried this combination and come up with a theoretical maximum limit or threshold? Please give the values. I don't use mathcad.

 

[ishvaaag]

You call a to the distance from where the resultant of the axial load, plus moment, plus centering moment places it to the edge. That is, the distance to the edge to the resulting load. Since you are investigating a case that places the edge at the limit stress sigmamax,

in a elastic setup the maximum load is:

Rmax = sigmamax·3·a / 2

in a plastic setup:

Rmax = sigmamax·2·a

that is, 1.33 times the elastic capacity if the same maximum stress is accepted for the elastic and plastic case (which is not necessarily the case).

 

[ishvaaag]

Of course, depending upon the case, the 3a or 2a widths of footing need be available.

 

[ishvaaag]

... and multiplied by the depth.

Rmax = sigmamax·3·a·L / 2

in a plastic setup:

Rmax = sigmamax·2·a·L

that is, 1.33 times the elastic capacity if the same maximum stress is accepted for the elastic and plastic case (which is not necessarily the case).