Grade Beam Analysis 1

[anthonyc007]

I've been wrestling with a problem lately; hopefully somebody can help me out.

The soils engineer will often give a differential settlement deflection value with an associated span. Usually 1/2" in 40 feet or something similar.

How do you design a grade beam section given this data? (assume conventional 2-pour foundation for slab-on-grade residential foundation)

I tried backing a uniform load out based upon the span and delta. Then generate an actual Moment from this. Compare this moment with the allowable and voila!

But this is clearly incorrect. Uniform load is directly proportional to Moment of Inertia. Therefore, the larger the section, the larger the moment! No Good!

Any ideas??

 

[structural01]

Normally when you have to design a grade beam, that means the soils is really bad. What I would do is ignore the contribution from the soils capacity. I would design the grade beam as a normal beam with whatever load is applying to it.

 

[archeng59]

when designing concrete members, you use strength design and factored loads. when checking deflection, you use unfactored loads. structural01 is correct in that the soil settlement parameters typically do not apply when designing a grade beam, unless you have some very expansive soils that may produce uplift. For a grade beam and pier foundation, I use carton forms under the grade beams so they are not in contact with the soil. however, the settlement will be applicable for a continuous footing supporting a wall or a spread footing at a column.

 

[SlideRuleEra]

Concur with structural01 and archeng59. I have been working on a pile supported grade beam system this week - best to assume the soil is "worthless".

http://www.SlideRuleEra.net

 

[anthonyc007]

Thanks for the input, but this does not solve the problem.

Lets assume the soils engineer gave me a deflection of 1/2" in 40 feet. Do I check the footing size (assume 10"x12" w/ 1-#4 T/B) for all the tributary wall/floor/roof loads for a clear span of 40 feet?

Its not gonna work. no way, no how. Not even close.

I don't think that is how you do it. I don't think that is the intent of the info given by the soils engineer.


Anthony W. Chute, P.E.
Option One Consulting Engineers
Newport Beach, Calif.

 

[1254BW]

The approach to be a beam on elastic foundation. Apply the moment due to the differential settlement specified by the soils engineer in addition to the gravity loads and the thrust from shear walls. In the process, you may need to make a judgement which area is critical situation - will it be building corner, or mid portion of building or particular area with colum load? Eventually you may need to increase the rebar size or footing depth depending on the input from soils engineer. The 1/2" differential settlement over 40' span is quite usual number and convetional continuous footing might work.

 

[anthonyc007]

You said "Apply the moment due to the differential settlement".

This is exactly what I thought to do. But how? I used the fixed-fixed beam model and backed out a uniform load from the delfection equation. Then, use plug this into the formula for moment and design accordingly. But this doesn't work! if you increase your section (b & d), this increases moment of inertia then increase moment. A larger section should not make it worse!

How should you determine the moment from the deflection??

Anthony W. Chute, P.E.
Option One Consulting Engineers
Newport Beach, Calif.

 

[1254BW]

Remember that no loading, no settlement; but even with a perfect uniform loading or some variation of uniformity, soils engineer warn us to expect 1/2" differential settlement over 40' span. There are upper limit of deflection and maximum building loads and our job is to find a optimum stiffness of the footing and flexural capacity with rebars. You can design a footing with excessive stiffness and flexural capacity beyond the maximum or critical building load but it will be noticed - Is it true that the Imperial Hotel was the only building survived from atomic bomb because Frank Lyoid Wright insisted a massive concret structure for his design?
BTW, AISC manual beam formula might be good enough for most of engineers who are farmilar with statically indeterminate structures but have not enough time to plug in Roark's formula, or at least one time throughly gone thru textbook to blakbox run.

 

[MWPC]

Anthony,

I hope other SE's have been sandbagging on this.

I always look at the maximum differentioal settlements given and compare them to my building type. If I am designing a wood framed building I can accept a lot of settlement. If it is a masonry or glass box, not so much. You did not say what type of building.

To look at it another way, 1/2" in 40 feet is L/960. If I was sizing a beam to support masonry I might check deflection for L/600. L/960 looks pretty good in that respect.

 

[eric1037]

anthonyc007:

I would take a step back to understand where the estimated differential settlement came from and what it was based on. There will be different settlements depending on loading, soil type, density, etc.

For some reason, there is a misconception that geotechnical engineers provide tolerable settlements. These should be structure specific and determined by the structural engineer.

I always request tolerable total and differential settlements from the structural engineer. I am not in a position to determine tolerable settlements for a structure that I am not intimately familiar. I then provide recommendations to accommodate the tolerable settlements provided.

Since bearing pressure is most often governed by settlement, a higher recommended bearing pressure can be given if higher settlements can be tolerated. Conversely, we can provide a different bearing pressure for low tolerable settlement.

I have been involved in structures that can only tolerate 1/4" of TOTAL settlement. Conversely, I have been involves in projects that can tolerate 2" or higher of total settlement. Obviously, these would result in very different allowable bearing pressures or subgrade moduli.

Sorry for the rant, but this happens all of the time.

To address anthonyc007's original question, there are a couple of things to think about.

If the soils are organic in nature or are very loose/soft, then you shouldn't really count on the soils for any support, especially if grades have been raised significantly.

If there are deep foundations due only to large column loads, then the existing, inorganic soils can be relied upon for some support.

I would request a subgrade modulus or design bearing pressure from the geotechnical engineer. Explain to them what you are trying to do and get their recommendation. As I said before, these things are site specific and structure specific. A differential settlement of 1/2" in 40 feet is not set in stone. They could even provide subgrade preparation recommendations for very low tolerable settlements.

 

[PEStructural]

When designing a grade beam with a "sinking support" (differential settlement amount) there is a formula for the moment from the sinking support.

M = 6EI(Delta)/L^2

where Delta is the 1/2" and the L is your 40feet x 12.

I also design the beam as a beam on elastic foundation from the slab loads on top of it and then add the moment from the elastic beam to the sinking support moment and design for that.

Hope this helps.

 

[anthonyc007]

PEStructural:
Your forumla is the one I initially came up with. But it is clearly wrong. Increasing the section will increase the I. Making the section stronger should not make the moment worse.

 

[Slowzuki]

Anthonyc007

I can't vouch for the accuracy of PE's formula but just sitting back reading this, if you increase the stiffness of the grade beam it can't deflect to match the soil profile and would have to carry larger moments.

 

[PEStructural]

Increasing the stiffness (i.e. the moment of inertia) would increase the moment because the equation is basically stating that given a moment of inertia, what moment would be required to make the beam deflect delta amount.

That's my opinion anyways. Please correct me if I'm wrong.

 

[anthonyc007]

I agree.

So that leads me to my original question: What do I do with this information from the soils guy? (1/2" in 40 feet)

How do I utilize it to design a proper footing? There must be some other analysis that makes sense.

 

[steve1]

I think that the equation stated by PE is correct. It's the interpretation of the equation that is in question. The equation is in essense calculating an "allowable" moment based on an allowable delta and an assumed cross section. This should then be compared against the "actual" moment produced by the design loads. This is calculated, as PE states, by doing a beam on elastic foundation analysis. If you increase the I, in the equation that you are using, then you get a larger value of "allowable" moment not a larger value of "actual" moment.

 

[PEStructural]

Good point, steve1!

 

[MWPC]

Anthony,

How much deflection will your building accept?

 

[anthonyc007]

This is for a two story residential wood framed building.

So.....(forgive me) how do I do this:

"This should then be compared against the "actual" moment produced by the design loads. This is calculated, as PE states, by doing a beam on elastic foundation analysis"

?

 

[steve1]

007,

If you wish to persue an anaytical solution then you need to get a good reference. You should have the theory and calculations in some text from college. Mine is "Advanced Mechanics of Materials", 2nd Ed by Seely and Smith. You could probably find the equations in Roark. A key term will be "k", the Modulus of Subgrade Reaction. Ask the geotech for assistance with this.

Alternatively, as has been suggested by others, you can evaluate the significance of the stated deflection on your structure. Using a combination of engineering judgement along with selected references you may determine that differential settlement is not a problem. If that is the case then you can design your foundation on the basis of bearing capacity only.