mat foundation of non-unform thickness

huangyhg

mat foundation of non-unform thickness
i need to design a mat foundation, but we want the type of foundation that does not have uniform thickness. under each column we want the mat to be deeper, and then to be thinner between columns. i am designing this by hand. i have found out how to design mat foundations using the rigid method, but the author (braja das) solves for the effective depth of the mat, d, which seems to be assuming a uniform thickness. how can i design a mat foundation of non-uniform thickness by hand? any references or links would be especially appreciated!
at change of thickness, a stress concentration will occur.  the moment strength of the thinner section and the the shear strength of the thinner section will control.  why change depth?  how is the finish grade elevation varied and how is it constructed when the concrete is plastic?  what reinforcement layer is to be continuous and where are the breaks or bends of the other bars?
thank you for your reply!
this is evidently a not-uncommon way to design mat foundations that reduced the concrete and reinforcement needed by 20-30%. thus we are using a non-uniform mat foundation to save costs.
the non-uniform thickness of the mat will not just be controlled by the thinner section: according to one article i found (
in my opinion, a mat foundation is nothing more than a slab with a reversed load.  as a first approximation, you could try and design it as a slab with drop panels.  you would have to know the pressure distribution below the foundation, which requires some calculation to obtain, but that is beyond the scope of the question.  re  
it seems to me that you will be concentrating the soil pressures near the columns by making the mat thinner and more flexible between columns. at some point you will find that individual isolated footings are the most cost effective.
maybe you could do the equivalent of an all column strip gillage with the inbetween parts filled in but not bearing much if any load.
as civilperson has pointed out, changing mat thickness has problems.  the first problem is the analysis.  these will continue with design, detailing, shop drawing preparation and review, fabrication, grading, construction, and inspection. all the bottom bars now need to be bent.  the extra cost related to these activities should be accounted for in a cost comparison, where you're only saving the cost of the plain concrete.
ugh! i have felt your pain.  
everyone is giving you really good advice.
in my situation, it ended with a compromise.  the client wanted uniform steel throughout the mat.  in order to do that, the mat under the columns needed to be thicker.  this does make the cost increase significantly.  
first, in excavating, the surveyor pins the corners of the mat.  the contractor then excavates down to the thinner portion of the mat.
the surveyor then pins the corners of the thickened portions inside the excavation.
then the contractor excavates down to the bottom of the mat at those locations.
as we all know, contractors are always in a hurry.  chances are good, he has started his excavation w/o the steel being on-site.  delivery of all those bent bars could be delayed.  remember the excavation is open during this time.  if it rains during this delay, that's an "extra".  fabrication cost will be increased.  labor cost in placement is increased.
in my situation, i was able to talk the client into more steel at the column locations and less in the middle of the mat.  the contractor helped me out in acheiving this.  i effectively just doubled the steel in those locations.  it did save them money, even after having to pay for my re-engineering.  
careful on fea.  you've got to do some funky things in staad to get the soil springs to work correctly.  i even sent a model to staad for them to give me some input, and they sent me back my "working" model, but i still had tension reactions.  i did get it figured out on my own (repeat load command).  pcamats works fine.  i'm not sure on other programs.
hope this helps