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??

 

[1254BW]

Anthony, which textbook are you referring to? Any deflection formula?
Classical solution of beam on Elastic Foundation in the "Foundation Analysis and Design" by Joseph E. Bowels listed formulas for deflection, slope, moment and shear along with coefficients table. Hope following steps can be any help.
1st - initial size up by plug in the upper deflection and upper moment from actual building loading to the formula PEStructural mentioned. BTW the formula is the AISC manual beam formula for a concentrated load with fixed ends; and understood deflected shape and boundary condition.
2nd - plug in moment due to deflection and actual loading to Bowels formula; pick a modulus of subgrade from soil type or bearing value. Tweak out the upper limit deflection while optimizing the gradebeam size while doing so, you can have a feel for which affects what. BTW soils engineer did not pick up the settlement number from the sky; structural engineer supply the expected maximum wall load and column load in addition to construction types, so the number is somewhat specific for subject building.
3rd - try Enercalc in quick way to compare and for concrete design.
4th - be aware liquefaction effect and expect larger magnitude seismic induced differential settlement. BTW USGS posted liquefaction map for California and USC published the DMG SP 117 – Guidelines for Analyzing and Mitigating Liquefaction in California.

 

[MWPC]

anthony,

If you do not wish to design this to death, you are done. One half inch in 40 feet is quite good compared to what I normally see. A wood framed structure with normal finishes should accept that easily. I suspect that with nominal width footings your bearing pressures will also be well below the allowable. If you or your client is sensitive to settlements you could size your footings for service loads. That would probably help more than anything. Ask your soils engineer. Be it my design, I would put minimum reinforcing in the walls with a couple #5 top and bottom to make them act as beams and a few control joints to avoid unsightly cracks. This would reduce the differential deflection even more and avoid calls if there is enough moment to overstress the reinforcing. Hope this helps.

Good luck.

 

[malhas]

http://geotechnic.ucsd.edu/footing/footing.html

This may help for your calc.