Page 116 - Trenchless Technology Piping Installation and Inspection

82 Cha pte r T w o

Design Calculations for CIPP
I. Buckling due to external water pressure (modified Timoshenko)
Restrained buckling analysis

×
2 × KE 1 C
P = L × ×
1 (– v 2 ) (DR –) 3 N
1
Solve for t,
t = D
⎡ × KE × ⎤ 3 1
×
⎢ 2 L C ⎥ + 1
×
⎢ ⎣ PN × ( 1 –v 2 ) ⎦ ⎥
where D = mean I.D. of existing pipe (or Liner pipe outside
diameter), in.
t = liner 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, psi, reduced to
L
account for long-term effects
C = ovality reduction factor
⎡ ⎛ ⎤ 3
⎢ ⎜ 1– q ⎞ ⎟ ⎥
⎢ ⎝ 100 ⎠ ⎥
= ⎢ 2 ⎥
⎢ ⎛ q ⎞ ⎥
⎟
⎢ ⎜ ⎝ ⎣ 1+ 100 ⎠ ⎦ ⎥
q = ovality
⎛ maximum diameter – mean diameter ⎞
q = 100 × ⎜ ⎟
⎝ mean diameteer ⎠
N = factor of safety, typical value = 1.5 to 2
υ = Poisson’s ratio = 0.3

a. Calculate external pressure
.
H × 62 4
P = w = 5.20 psi
144
b. Calculate thickness
t = 0.88 in.