out-of-round steel pipe

huangyhg

out-of-round steel pipe
i've got a situation where a 69" diameter 7/16" wall pipe has been pushed inward, with up to 2" change in the horizontal diameter, due to external grout pressure. i am trying to determine at what point if at all the pipe wall is overstressed and needs replacement. the following was my attempt which seemed to yield invalid results:
max allowable plate bending = 0.75*fy*b*t^2/6
  where b = 1 in (assumed unit width)
  t = 7/16 and fy = 50 ksi
using roark's formula #1 in table 9.2 (pg 314 of 7th ed.) i back calculated the maximum load w:
  w=ma*pi/r (k2 assumed unity) = 110 lbs
this value was input into dh = 0.1366*w*r^3/(e*i) = 3.66e-7 which i would think is too small.
any input or recommendations would be greatly appreciated.
thanks in advance.
you might check b31.8 for the max allowable dent and then use some good engineering judgement.  b31.8 will probably give you a more severe limitation than this application justifies but it is a starting point.
i might add that you have a d/d ratio of 157 which is pretty high for me.  i personnly would like to see the d/d be 100 or less.
it seems to me that pressurizing the pipe will just tend to round it back up, which may not be that big of a deal.  if the grout is still in place, you may have more problem with the grout and whatever is on the other side of it being moved than with the pipe itself.  if you have grout all around the pipe, adequately stiff to hold the pipe in a particular shape, i don't think you'll have a stress problem in the pipe.
here's some more background: the 69" diameter pipe is ml&tws inside a 3/4" steel casing with the annulus grouted (trenchless installation). we didn't design the pipe or casing, we're working on behalf of the contractor that did the grouting and we need to provide justification to the owner of the pipe for how much, if any, of the damaged pipe gets cut out and replaced. as you can imagine, this is not an easy process.
again, thanks in advance.
did anyone give you the max grout pressure that was allowed? what pressure was used to grout? prssure on a pipe is a little different than a plate. look in astm f-1216 for some formulae for buckling, etc. liners are designed for less than 5% deflection. 2/69 is about 2.8%. may not be a problem.
richard a. cornelius, p.e.