Rotational Fixity of a Pad Footing

[asixth]

Hi guys, there has been a couple threads lately about semi-rigid design of columns, thread744-260012 and thread507-261922, and now I want to put the theory into practice. I have a steel-frame building which relies on frame action to brace the structure in one direction. I want to reduce the drifts for service conditions and reduce the column moments for ultimate conditions, so I am designing a semi-rigid base. Please note that I only intend on resisting a minor amount of moment using a rotational spring stiffness at the base of 0.1*4*E*Ic/Lc.

Because this is a steel-framed structure, there is not a great amount of dead load compression force on the column and thus uplift does result. What would be the most ethical approach to take out the base moment (referring to the attached sketches). Would it be best to assume an unbalanced slab-on-ground load or would it be assuming some passive soil pressure is developed on the pad footing to resist applied moment. My thoughts are that I should look at designing the slab-on-ground to span onto the pad to provide additional hold-down resistance. This will mean designing the slab on ground with bottom reinforcement locally around the column.

All help will be appreciated.

 

[hokie66]

It is legitimate to use some of the slab on ground to resist uplift and overturning, but I have never thought of using passive soil resistance with a pad footing. That comes into play with a bored pier.

 

[rowingengineer]

I agree with Hokie, suggest you make the footing larger. I prefer piers for this application.

Arguing with an engineer is like wrestling with a pig in mud. After a while you realize that they like it

 

[Ron]

Piling on here, I agree with hokie and RE. I use part of the slab routinely for embedded columns in lightweight structures (aluminum). In most cases, we embed the column in a separate square or rectangular footing, then place the floor slab over the footing and around the column. The slab is minimally reinforced just to hold it together as uplift is mobilized.

I consider the point of fixity at the top of the slab and check for localized crushing of the concrete at that point. The footing is designed to take the entire moment of the column (and lateral load), with the slab providing uplift resistance only.

 

[paddingtongreen]

Looking at the diagram, the footing has to move to develop the passive pressure. Even if the slab was not preventing this, the footing would rotate out of the ground long before any significant passive pressure could develop.

I have, with light weight structures, with high overturning loads, put grade beams between the footings and included them in the calculation/model. the foundations would be smaller in plan but a little deeper than yours. This gains in Pp to counter the horizontal loads and gives an almost uniform soil pressure under the vertical loads.

It is all a balancing act between the weights and forces and soil pressures.

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[BAretired]

180 kN (40.5 k) is a pretty substantial uplift. You might want to make the footing larger and deeper with a capital on top for the column to bear on. The weight of soil will help to resist uplift.

BA

 

[asixth]

Thanks for everyone's input. I did overestimate the design uplift, it gets reduced by 20% when I include area reduction and combination factors.

For another example when I do have bearing under the footing (compression load). Can a varying pressure distribution be assumed to balance the applied moment. For example, say I have a 150kN (34kips) compression load and applied moment of 20kN-m (15kip-ft) applied to a footing 2100 x 2100 (7' x 7'). To balance these applied loads the bearing pressure distribution varies from 47kPa to 21kPa (1kips/ft^2 to 0.45kips/ft^2). Would it be acceptable to say that this resists to moment because I would believe that the foundation settlement would vary across the footing with varying pressure distribution and this differential settlement would be a source of rotation which would alleviate the moment attracted by the foundation.

Any opinions?

 

[paddingtongreen]

asixth, the soil is an elastic material, it is normal to get a pressure gradient under eccentric resultant loads, always provided of course, the footing can distribute that load to the soil.

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[DaveAtkins]

Trapezoidal or triangular bearing pressure under a spread footing is how I always handle moment on the footing.

DaveAtkins

 

[letrab]

Very small rotations are normally all that is required to drop the moment in the column to zero while fairly large deformations are required to mobilise passive resistance. I cannot see how both can be mobilised in a single application. Your footing seem stiff enough to transfer a moment to the soil but it seems a bit small or shallow to be able to receive sufficient reaction from the soil to ensure rigidity

 

[jike]

You need a safety factor on the dead weight versus uplift like....
0.6D + W

I use a rectangular footing to resist the uniaxial moment/rotation. I do not rely on active/passive pressure on the sides of the footing. I use a trianugular bearing pressure on the bottom of the footing.

For uplift, I would suggest a) larger/heavier footing or b) embedding the footing deeper and using (overburden + footing weight) to help resist uplift.

 

[ToadJones]

I guess I would never count on lateral soil pressures for a footing.
For uplift, I'd say lower the footing and add a pier. Trapezoidal soil pressures are pretty common.

 

[BAretired]

The footing can be modeled as a rotational spring if you know the properties of the soil. It is not a fixed support for the column.

BA

 

[ToadJones]

BA-
IS it necessary to model this type of footing?

 

[BAretired]

No, it is not necessary. Another method would be to assume a fixed base, then adjust the frame moments using sound engineering judgment. To assume that calculated frame moments are "exact" is a fallacy in any case, but if a frame program is being used, the introduction of a rotational spring is not difficult to do.

BA

 

[ToadJones]

Is there an easy way to determine the spring stiffness?

 

[paddingtongreen]

If you assume that the footing is rigid and use a default value for the soil modulus you can calculate a spring rate.

A source of guidance on default soil moduli:

http://www.rinkerpipe.com/Technical...Series/IB 4003 Modulus of Soil Reaction E.pdf

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[BAretired]

"Is there an easy way to determine the spring stiffness?".

The units of rotational spring stiffness are Moment per unit rotation or M/[Θ]. The Modulus of Subgrade Reaction, 'k' should be available from the geotech. It is usually expressed as pressure per unit of settlement MPa/mm or psi/inch.

If the footing undergoes a rotation of [Θ] one edge drops [Θ]b/2 where b is the width of a square footing. The opposite edge rises by the same amount. This corresponds to a stress of +/-k[Θ]b/2 which can be converted to a moment for a particular footing size.

The rotational spring stiffness will be a function of both k and b.

BA

 

[asixth]

Making the assumption the footing behaves like and infinitely rigid beam, which for my example would be an appropriate assumption considering the depth, length and reinforcement in the footing.

 

[rowingengineer]

at the end of the this article is a way to quickly take into account footing rotation

http://www.steelbiz.org/Discovery/ResourcePreview.aspx?ID=mYA+ddIXuT1og3WNrFXJ9A==

Arguing with an engineer is like wrestling with a pig in mud. After a while you realize that they like it