a column at center of tank bottom plate

huangyhg

a column at center of tank bottom plate
while reviewing vendor's calculation, i found i am not familiar with their equations although i used computer element modeling.
can anybody advise the equations (or where to find) to calculate the bending stress of a tank bottom plate under a point load when the allowable soil pressure is given? a circular baseplate is used under the column, which is much larger than the cross-sectional area of the column and welded to the bottom plate.
thanks.
this sounds like a slab-on-grade with a point load.  i haven't seen a solution that gives slab bending moments, but there are a couple of resources that give maximum load.  one is "designing floor slabs on grade" by boyd c. ringo and robert anderson.  another is an article by boyd ringo that appeared in the aci journal in november of 1978, title no. 75-61, "design, construction and performance of slabs-on-grade for an industry.
if you are asking about the slab stresses - for a circular tank, the pca circular concrete tanks book has a section for roof slabs with a single column or multiple columns.  by substituting the soil bearing pressure for the overburden this section works just as well for the base slab.
you may have to confirm the actual assumptions used in the design of the base plate with the vender in question, as approaches can vary considerably.
roark's "formulas for stress and strain" includes design equations for circular flat plates, which would typically be used for this type of application.
the design standard for welded steel water tanks is awwa  d100-05. i am not sure if this addresses this particular issue.  often beams are used for this bottom location. say a h shape grid of channels with the column on top.   nevertheless, depending on tank size, the plate may be resting directly on compacted granular fill and all bearing would transfer directly to the sand. assuming gussets are used,and bearing is on sand i would check equivelant bearing for the sand for a diamter of the gussets.  allowable capacity is typically 2-5 ksf.  if it doesn't work, make the contractor prove that it works.
the plates themselves, typically 1/4", will just plastically deform until bearing capacity is developed in the granualar fill.
roark's "formulas for stress and strain" has lots of equations for circular plates, but most of them are structural plates supported along the edge. pca circular concrete tanks book seems most pertinent (but i don't have the book). the best analytical equation i found is in joseph e. bowles' foundation book eq. 10-8, which deals with wheel load on slab on grade.
with this equation and computer modeling, i found that the tank bottom plate bending stress is allowable (the base has no footing under the central column). the vendor claims that the footing is detrimental to the bottom plate. this sounds odd to me.
d100 does not address base plate design in detail.  the h-shape assembly has been used more in oil tanks and is undesirable in water tanks due to corrosion issues.
with the flat plate formulas in roark, you can superimpose the loadings for many cases that are not specifically tabulated.  for example, a simply supported plate with uniform pressure up and a line (circular) load down will give a result similar to the one needed here.  adjust the loads so that the reaction at the edge is zero and you then have a free edge.  that may not be what the vender did, but it is one approach.
concrete footings are very seldomly used under tank columns.
have you checked with the vender concerning the source of their equations?  
is this an api or awwa tank?  these tanks are often built on sand or gravel pad.  the load from a fixed roof support column is distributed to the soil by adding thick plates under the column.  these plates are then uniformly supported with a ring load (if a pipe column is used) on top.  the contribution of the tank bottom plate under the base and wear plates is also taken into account to reduce thickness and size of the base plate.  the plates are basically in bending and some tank builders use simplified formulae to design the plates.  if that is the case you won't find the equations in roarks, etc but you likely could confirm their design using fea or roarks.
if this is an api or awwa tank, the plate under the column is typically not welded to both the column and the tank bottom, there are usually two plates.  one is welded to the column and one is welded to the tank bottom.  the plate welded to the column is restrained from moving laterally but not vertically by the use of clips welded to the bottom plate.
thanks for the input. with the central column on a large base plate but no footing seems acceptable to me. this this from the stress in the baseplate and the differential settlement between central column and the ring beam.
but the settlement at the central column is 0.35" and the corresponding subgrade pressure is about 7ksf. these seem excessive from geotechnical point of view.
did you use a finite element model to get your deflection?