anchor bolt group in circular layou

huangyhg

anchor bolt "group" in circular layout
aci-318, app. "d", includes equations for the pull-out strength of groups of anchor bolts, but assumes that the bolts are in a rectangular pattern.  what do you do if the bolts are in a (large) circular pattern?  taking the rectangular area around the whole group includes a bunch of area inside the circle that isn't necessarily close to the bolts.  using an annular area around the bolt circle doesn't meet the "rectilinear geometrical figure" specified.  any ideas?
what is the proposed embedment depth of the anchors and what is the proposed bolt circle diameter?  taking the large area of concrete between bolts seems too conservative.  i think the annular ring idea seems realistic.  it might not actually break like that, but it seems conservative enough to justify.
is the entire ring in uplift?  if so i would use a "donut" with the inside and outside circular edges based on the dimension to the bolt centerline +-1.5(embedment length) as the group area.  if only a portion of the ring is in tension (as would probably be the case with typical base moments) then you could draw a reasonable rectangular area around the bolts in tension and go with that.  

i'm working on a standard detail, but typically, the anchor bolt circle would range from 12' to 20' diameter, with bolt embedments of around 2'-4' (ie, run to the bottom mat of the slab).  in most cases, the bolt uplift would be from wind, so only part of the bolt pattern would be in tension.  however, it is simpler to assume all bolts are stressed like the highest-stressed bolt, rather than work out individual bolt loadings around the circle.
check awwa d-100 "welded steel tanks for water storage"  the design tension loading per anchor bolt is:
p = 4m/nd - w/n
p = design tension loading per anchor, #
d = diameter of anchor bolt circle, feet
n = number of anchors
m = wind load moment, ft-lbs
w = tank dl resisting wind load, lbs
best, tincan
tincan, that's what i'm doing.  (it's not obvious, but that equation is just mc/i +/- p/a, adjusted to give load on one bolt).  anyway, it gives the highest stressed bolt load only.  but the question still remains of calculating the pullout strength in the concrete once you have that load.  or more properly, once you have the factored load.
what is the spacing between bolts?
can you just use the cone method, and if the spacing is less than diameter, neglect part of the area that overlaps?
spacing varies.  (this on tanks, by the way, not the power-pole type arrangement of big bolts).  of course, if the pull-out areas don't overlap, it's not a "group", it's just individual anchors.
as to cone method, annular ring, etc.- yes, i can use these (annular ring idea sounds best).  but it doesn't actually fit the aci requirements.  i'have to play with the rectangular-area-on-partial-group idea a bit to see what kind or results it gives.
if the normal embedment length cone pullout dosn't work, try placing a plate at the end of the anchor bolt.  use a
6" x 6" x 1/2" plate welded to the end of the bolt.  we normally use 1 1/2" to 2" bolts with the plate affixed.
tincan
the term "rectilinear geometrical figure" in article d.5.1.2 refers to shape of the failure surface, not the layout of the bolts.  it is meant to distinguish the assumed failure surface from that of previous models, which had overlapping cones.  as long as you develop your failure surface according to the rules of d.5.2.1, i believe you meet the intent of the code, even if your failure surface is not rectangular in shape.