clarifier effluent bo

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clarifier effluent box
i have a circular clarifier with an effluent box that cantilevers off the clarifer wall.  my concern is that this results in a bending moment that gets applied to the clarifier wall at the location of the effluent box.  how do you account for this in the design of the clarifier walls?  this moment would tend to distort the clarifier walls so that they are no longer circular. the clarifer has an interior diameter of 30 feet, and the effluent box is about 9' long and cantilevers about 4.5'.
note, this is not a moment that is applied around the corcumference of the clarifier, it is only applied at the location of the effluent box.
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this would be a difficult analysis to simplify - you could try assuming a certain width of clarifier wall that participates in resisting the moment -
we would most likely develop a finite element model using 6 dof plate elements and analyze for moments in the plates.  just a 3d situation and difficult to approximate by hand.
i have tried to look at it by assuming that a certain width of the clarifier wall is effective in acting like a circular ring, and then using the equations in roark.  the resulting moments were very large, and i don't have a lot of faith in that approach.  maybe another way to look at it would b
one way to make this problem go away is to extend the walls of the effluent box down to the base slab elevation and put footings under them.
...or perhaps run some diagonal wall struts from the underside of the box to the base of the clarifier...sort of like triangular walls acting like corbels.
might be tough to build them though.
what i have decided to do is extend some of the walls down and give them footings.  there are 3 walls that are perpendicular to the clarifier, and i will extend these down to footings.  they were so low anyway that i just had to make them a couple of feet longer.  this way, i am not creating any enclosed space under the effluent box, and i think that the formwork will be simplified for constructing the effluent box.
it would be interesting to create a finite element model and see what the effect of a cantilevered effluent box is.  unfortunatley i have no experience creating models for something like a concrete plate structure.  we have risa 3d, but i mostly use it for analyzing steel framing.
i wonder how cantilvering the effluent box would have been handled in the "old" days of no computers and just calculators or slide rules. i love my hp, but i couldn't imagine doing a finite element analysis using it.
thanks for your input jae
how tall are your walls?  we have in the past cast concrete underneath right down to ground level so the box just sits on top, this transfer the weight of (what was a launder channel in this instance) directly to the foundation and not the wall.  the contractor liked it as well as it allowed him to do away with the soffit shutters and form the launder at the same time as the walls.  
however, you do need to be aware that this large dollop of concrete with increase the heat of hydration and induce cracking if not designed for.
my walls are about 12'-5" tall.  i was planning on just extending the walls that cantilever from the clarifer down to a rectangular extension of the base slab.