grade beam analysis

huangyhg

grade beam analysis
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??
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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.
when designing concrete   
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".
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.
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.
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.
re  
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.
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.
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.