calculating moment capacity and section modulus for pipescy

huangyhg

calculating moment capacity and section modulus for pipes/cy
the awwa m11 gives
section modulus  =  i/c  =  π * r^2 * t
however, i found in the mcgraw hill civil engineering formulas textbook,
section modulus  =  i / c  =  π (od^4 - id^4)/(32 * od)
the results are totally different.
has anybody done any bending moment checks on large pipes/cylinders?
thanks.
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mcgraw hill is correct.  
so i take it that m11 is wrong? for anyone who are interested, this is in the m11 pg 86.
the first one is a close approximation for thin-walled pipes.  for instance, if i use it to find the modulus of a 30" diameter, 0.05" w.t. pipe, i'd get:
15^2 * 0.05 = 11.25 in^3
using the mcgraw formula:
(30^4 - 29.9^4)/(32 * 30) = 11.19 in^3
a change of less than 1/2 of a percent.
it doesn't work so well when the wall gets thick compared to the diameter, though:
10" diameter, 1/2" w.t. pipe:
5^2 x .5 = 12.5 in^3
now if i use the mcgraw formula:
(10^4 - 9^4)/(32 x 10) = 10.75 in^3
which comes in at 16% off...
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