Page 210 - Buried Pipe Design

184 Chapter Four

2
2
2
P i a (b /r 1)
Tangential stress: t
2
b a 2
2
2
2
P i a (b /r 1)
Radial stress: r
2
2
b a
where P i internal pressure
a inside radius
b outside radius
r radius to point in question
The maximum stress is the tangential stress t , and it occurs at r a
(Fig. 4.1). Thus,
2
2
2
P i a (b /a 1)
max ( t ) r a
2
2
b a
2
2
P i (b a )
or max (4.1)
2
b a 2
For cylinders (pipe) where a ≈ b and b a t,
2
2
b a (b a) (b a) D t (4.1a)

a 2 b 2
P i
b b 2 a 2

s t 2b 2
P i
a b 2 a 2
+
– P i
s r
–P i s max =(s )
t r = a

Figure 4.1 Thick-walled cylinder with internal pressure.