Torsional Moment - Footings

[slickdeals]

Just wondering on a Sunday morning, if there are procedures for designing a spread footing for torsional moment?

Imagine those cantilevered signs on the sides of roads. They have biaxial moment (due to gravity in one direction and wind in the other). Also wind will produce a torsional moment.

It appears that the footings can develop torsional resistance from lateral bearing on the sides. Will the coefficient of friction at the bottom provide a restraint to torsion? Are there ways to quantify this?

 

[Lion06]

I've never considered the friction at the bottom. If you have moment such that the bearing pressure isn't uniform, it's seems like it would be unreliable, at best.

I have, however used passive pressure on the corners to counteract a torsional moment.

 

[slickdeals]

You would use passive pressure on 2 sides (similar to a handrail post in grout?) + a skin friction on the other 2 sides ? Or just passive pressure on all 4 sides?

 

[Lion06]

I used passive pressure on all four sides (triangular distribution).

 

[msquared48]

I agree wth Lion, but the distribution would be triangular, with tne moment arms to resist the torsion at the CG of each triangle.

Mike McCann
MMC Engineering
Motto: KISS
Motivation: Don't ask

 

[msquared48]

Each of the four sides would see soil pressure, triangularly distributed on half the length, not the whole length, due to the soil movement.

Mike McCann
MMC Engineering
Motto: KISS
Motivation: Don't ask

 

[slickdeals]

Thanks guys. It makes sense.

 

[Lion06]

I'm pretty sure we're on the same page, Mike.

I'm attaching a sketch that shows my approach. Of course this assumes torsion only and no direct shear. The direct shear complicates the matter and will change the soil pressure distributions.

 

[Lion06]

I think a different approach would be to use the maximum passive pressure to calculate an allowable torsion. Without a starting point for pressures, how would you arrive at P1 and P2?

 

[slickdeals]

I think I started with a square footing. In that case determining P would be easy, since it would be 4*P*B/3 = Moment. Then I get P. Once I get P, I can figure out what passive pressure yields P (based on area of triangle). But I extended it to a rectangle, and it was not making sense.

 

[slickdeals]

Lion: Your approach makes more sense though.

 

[Lion06]

slick-
I'm with you if it's a square, but, like you said, it's not as simple for a rectangle.

 

[msquared48]

It's really no different with a rectangle, there is just more torsional capacity to develop with the longer sides. The longer sides will take a larger portion of the torsion. No worries.

Mike McCann
MMC Engineering
Motto: KISS
Motivation: Don't ask

 

[msquared48]

Oh, but not to complicate the analysis, but the allowable lateral bearing will increase with the depth of the footing. So you might want to analyze this on an average depth for thinner footings, or stepped blocks of 1 to 2 feet for thicker ones.

Obviously, this would not work for a drilled shaft footing.

Mike McCann
MMC Engineering
Motto: KISS
Motivation: Don't ask

 

[Lion06]

Good point on the passive pressure increasing with the depth.

 

[dhengr]

The foundation rotates as a rigid body, so the long sides will see a higher pressure at their corners, than the short sides will. For a degree of rotation, the longer distance to a long side corner will cause more angular movement there than at a short side corner; thus the soil compression and passive pressures will be greater in direct proportion to these angular movements. I would liken this to the rotation of a conc. retaining wall under loading, causing higher pressure under the toe of footing and a lesser, or no pressure under the heel. And, I would compare the sum of these pressures, caused by your torsional moment, against the allowable for the given soil conditions. I’ll have to think on your exact formulas a bit more. I’d just be sure to lock my steel column into the found. so it can transmit this torque.

 

[Lion06]

dh-

The difference I see is that the passive pressure is limiting value. If two retaining walls move, they both develop the active pressure. I've never heard anyone try to calculate something other than the active or passive based on actual movements.

I agree with the statement, in general, but I think from a design standpoint, any movement develops the passive pressure.

 

[BAretired]

In addition to the passive pressure on each side, you have the coefficient of friction on the bottom of the footing which will also contribute to torsional resistance.

BA

 

[msquared48]

I agree dhengr - the lateral bearing tables in the IBC are set up based on 1" of lateral deflection.

You could apportion the relative forces of the short and long sides based on a geometric ratio of the relative rotational deflections.

Mike McCann
MMC Engineering
Motto: KISS
Motivation: Don't ask

 

[csd72]

For a rectangular footing, I would attribute the bearing pressure to the sides in proportion to the amount of movement.

So the short sides will be taking a lesser pressure than the long sides.

I agree with Lion06 regarding the base friction, it is probably too complicated to accurately asess so I would tend to ignore it also.