Page 113 - Trenchless Technology Piping Installation and Inspection

Existing Pipeline Renewal and Replacement Methods 79

2. Live load

W = 0.35 psi (from I1)
s
a. Calculate deflection
D 48.00
Dimension ration (DR) = = = 47.6
t 1.01
×
[
Y = 0 083 × 1 25 9 85) + 0 35] × 100
.
(
.
.
.
,
D 250 000 + + (.061 1000 )
×
0
−
15 × 476 1) 3
.
.
(
Y
= 1.68 % < 5 % allowable? O.K.
D
III. Buckling due to external water pressure (modified Timoshenko)
restrained buckling analysis
×
2 × KE 1 C
P = L × ×
2 3
1
1 (– v ) (DR –) N
solve for t,
D
t =
1
⎡ 2 × KE × C ⎤ 3
×
⎢ L ⎥ + 1
×
⎣ PN × 1 (– v ⎦ )
2
where D = mean inside dia. of existing pipe (or liner pipe outside
dia.), in.
t = liner pipe thickness, in.
D
DR = dimension ratio,
t
P = allowable restrained buckling pressure, psi (or allowable
external pressure measured above the pipe invert)
K = enhancement factor (typically 7)
E = flexural modulus of elasticity of liner pipe, psi, reduced
L
to account for long-term effects
C = ovality reduction factor
⎡ ⎛ q ⎞ ⎤ 3
⎢ ⎜ 1 – ⎟ ⎥
⎢ ⎝ 100 ⎠ ⎥
= ⎢ 2 ⎥
⎢ ⎛ 1 + q ⎞ ⎥
⎟
⎢ ⎜ ⎝ ⎣ 100 ⎠ ⎦ ⎥