Thickness Calculations- Hoops Stress
If Working Pressure is Used
The Nominal Thickness of steel pipe is calculated as given
below, Plus the permitted manufacturing tolerence for
reduction in Thickness.
t =
pD
2afe+p
t = Thickness of the Pipe in mm
p = internal pressure Kgf/ cm2
D = OD of the pipe in mm
a = design factor ( 0.6 if p is the working pressure and 0.9 if
p is the test pressure inclusive of surge pressure ).
f = Minimum yield stress of the steel Kgf/ cm2
e = Weld efficiency of the joint ( 0.9 for shop welding and
0.8 for field welding ).
Thickness required
II
6.45 Kgf/ cm2
1804 mm
0.6
2500 Kgf/ cm2
0.8
4.84 mm
If hydraulic test Pressure is Used
t =
PD
2afe+P
P = Hydraulic test pressure
t = Thickness of the Pipe proposed in mm
D = OD of the pipe in mm
a = design factor ( 0.6 if p is the working pressure and 0.9 if
p is the test pressure inclusive of surge pressure ).
f = Minimum yield stress of the steel Kgf/ cm2
e = Weld efficiency of the joint ( 0.9 for shop welding and
0.8 for field welding ).
S = 60% of Yield stress
P = 2 ST
D
Hydraulic Test pressure
Thickness of pipe required for this hydraulic test
pressure
12 mm satisfies this criteria
12
1804 mm
0.9
2500 Kgf/ cm2
0.8
19.96 Kgf/ cm2
9.94 mm
Pipe Diamete
Dia
Inside Ling
Tk
OD
Mean Dia
Shell ID
Pipe Diameter
1750
15
12
1804
1792
1780
Thickness Calculations- Deflection
The deflection is given by Spangler,s Theory ( AWWA
Manual M11)
a)
x =
D1
KW r3
EI + 0.06 E' r3
x = Deflection Cm
W = Load per unit length of pipe due to soil overburden
Kgf/ cm2
r = Pipe radius cm
E = Modulus of elasticity of steel Kgf/ cm 2
b)
I = Transverse Moment of Inertia per unit length of pipe
wall Cm3
E' = Modulus of soil reaction Kgf/ cm2
x =
D1=1 for lined and gunited pipe
W = s D H
100
D = Mean diameter of pipe mtr
H= Heigth of backfill above pipe top Mtr
s = Specific weigth of backfill material Kgf/ cm2
The division by 100 is to convert the load per mtr length
to load per cm length.
W=
Delection should be less than 2% of the Mean
diameter
2% of the mean dia
Deflection is less than 2% of mean dia, Hence Safe.
Cm
32.26 Kgf/ cm2
89.6 Cm
2100000 Kgf/ cm2
0.1440 Cm3
40 Kgf/ cm2
1.144 Cm
1.792 Mtr
1 Mtr
1800 Kgf/ cm3
32.26 Kgf/ cm2
3.584 cm
Thickness Calculations- Buckling
The allowable buckling pressure is given by ( AWWA Manual M11)
qa = 1
a)
32 RwB' E' EI
FS
D3
qa = Allowable buckling pressure Kgf/ cm2
Kgf/ cm2
FS = design factor ( 2 as per 4th edition of AWWA manual M11)
Rw = water buoyancy factor given by 1-.33 (Hw / H)
2
1
Hw = heigth of water surface above top of pipe cm
H = Heigth of backfill above top of pipe cm
E' =Modulus of soil reaction Kgf/ cm2
E = Modulus of elasticity of steel Kgf/ cm 2
0 Cm
100 Cm
40
2100000 Kgf/ cm2
I = Transverse Moment of Inertia per unit length of pipe wall Cm 3
D = Diameter
0.144 Cm3
180.400 Cm
Calculations are done for 1 Mtr overburden of soil with no
waterlogging in the trench, that is Hw =0 as Hw is 0, Rw = 1. The
value of B' is calcualted based on H value in Ft, as follows.
qa =
b)
B' =
1
1+ 4 e ( -0.065 H)
B' = empirical constant given by
H is in ft
e is mathematical constant
B' =
c)
1.974 Kgf/ cm2
3.28 Ft
2.732
0.236
The requirement of safety from buckling is verified by the following
Equation
w Hw + Rw W + Pv
qa
w = Specific Wt of water Kgf/ cm3
W = Load per cm length due to soil overburden Kgf/ cm2
Pv = Internal vacuum Pressure Kgf/ cm2
Hw =
Actual buckling Pressure =
0.001
32.47 Kgf/ cm2
1
0
1.180 Kgf/sq cm
W = s D H
100
s= Specific weigth of backfill material Kgf/ cm2
D= dia in Mtr
H= Heigth of backfill Mtr
W=
1800 Kgf/ cm2
1.804
1
32.47 Kg/ Cm2
Assuming
water
logging
Actual Buckling pressure is Less than Allowable Pressure ,
Hence Safe.
Thickness Calculations- Collapse Pressure
For truly circular pipe, The critical copplase pressure is
given by Following ( AWWA Manula M11)
3
Pc = 2 E
t
( 1 - 2 )
Pc= Critical collapse pressure
Kgf/ cm2
Kgf/ cm2
E= Youngs Modulus of steel
= Poissons Ratio.
t= Thickness of wall in mm
D is diameter in mm
D/t raio
For steel pipe in FPS units the formula reduces to.
Pc = 66 x 10^ 6
t
3
12 mm
1780 mm
148.3 less than 165
D
Pc =is in PSI
AWWA recommends more conservative formula
3
Pc = 50.2 x 10^ 6
t
D
Where Pc is in PSI
Pc
Pc
Critical pressure is more than1kg/sq cm ie
atmospheric pressure . Hence OK.
15.38 PSI
1.082 Kgf/ cm2
