Page 211 - Buried Pipe Design

Design of Pressure Pipes 185

where D average diameter b a and t thickness b a. Also,
2
2
2
2
(b a) D b a 2ab (4.1b)
D 2
2
2
2
2
2
2
b a D 2ab ≈ D 2 r D
2
Thus Eq. (4.1) can be rewritten using Eqs. (4.1a) and (4.1b) as follows:

2
P i D
P i (D /2)
max (4.2)
D t 2t
Equation (4.2) is recognized as the equation for stress in a thin-
walled cylinder (Fig. 4.2). This equation is sometimes called the
Barlow formula, but is just a reduction from Lamé’s solution. This
equation is the form most often recognized for calculating stresses due
to internal pressure P .
i
If the outside diameter D is the reference dimension, Eq. (4.2) can
o
be put into another form by introducing
D D D o t
That is, the average diameter is equal to the outside diameter minus
thickness. Equation (4.2) becomes
P i (D o t)
max (4.3)
2t

t

P i

P D P i D
i
s max
D 2t

P i D P i D

Figure 4.2 Free-body diagram of half section of pipe with
internal pressure.