Underground Pipe Stress Check
9
Design Calculation Project No. Project Title: Checked By: Date: Aug/25/22 Date: PIPE STRESSES - WHEELS ON RIGID PAVEMENT Earth Loading Pipe Size = 42 in. Conc. Thick. hc = 8 in. O.D. = 42 in. wd = Cd w Bd^2 = 1316.6 lb / lin ft. where: w = 120 lb/ft^3 soil unit wt. Bd = 5 ft. (actual width) Bd = 5.0 ft. (effective width) Bc = O.D. = 3.50 ft Cd = 1 - e^ (-2 ku'(H/Bd)) 2 ku' = 0.439 H = 2.33 ft. ku' = 0.13 lb / in^3 ku' = modulus of subgrade reaction Saturated clay = 0.110 Ordinary clay = 0.130 Saturated topsoil = 0.150 Sand and gravel = 0.165 Bd max. = Transitional trench width from table below Ref. 1 = 5 ft. Table 13 to 28 Bd = Max. effective transitional trench width Bd Pipe Cover = H ( ft. ) Pipe Dia. 5 6 7 8 9 10 15 20 6 1.42 1.5 1.58 1.67 1.75 1.75 2.08 2.33 8 1.75 1.83 1.92 2 2 2.08 2.42 2.75 12 2.5 2.58 2.75 2.83 2.92 3 3.33 3.67 16 3 3.08 3.17 3.25 3.33 3.42 3.83 4.25 18 3.42 3.5 3.58 3.75 3.83 3.92 4.33 4.75 24 4.25 4.33 4.5 4.58 4.67 4.83 5.25 5.67 30 4.83 5.17 5.33 5.42 5.58 5.67 6.17 6.67 36 5.42 5.75 6.17 6.25 6.42 6.58 7.08 7.58 42 5.92 6.33 6.67 7.08 7.25 7.42 7.92 8.42 48 6.5 6.92 7.25 7.67 8.08 8.17 8.83 9.33 54 7.08 7.42 7.83 8.17 8.58 9 9.67 10.25 60 7.67 8 8.42 8.75 9.08 9.5 10.5 11.08 For shallow depths (< 4ft.) use : wd = H Bc w = 978.6 lb / lin ft. Therefore wd = 978.6 lb / lin + wt. of concrete 350 lb / lin. Ft. wd total = 1328.6 lb / lin ft. N:\civil\spreadsh\UGPipes\u-g pipe.xls (1 of 3) Wheel Loading From Individual Wheel Loads Tire Pressure = 80 psi. Impact Factor = Fi = 1.267 1.5 at surface Ref. 2 , 4.7.2.2.2 Underground Pipe Stress Check - UGP 2 Bc Bd H P X
Transcript of Underground Pipe Stress Check
Design Calculation Project No.
Project Title:Checked By: Date: Apr/07/23Date:
PIPE STRESSES - WHEELS ON RIGID PAVEMENT
Earth Loading
Pipe Size = 42 in. Conc. Thick. hc = 8 in.O.D. = 42 in.
wd = Cd w Bd^2 = 1316.6 lb / lin ft.where: w = 120 lb/ft^3 soil unit wt.
Bd = 5 ft. (actual width)Bd = 5.0 ft. (effective width)
Bc = O.D. = 3.50 ft
Cd = 1 - e^ (-2 ku'(H/Bd))2 ku'
= 0.439
H = 2.33 ft.ku' = 0.13 lb / in^3
ku' = modulus of subgrade reactionSaturated clay = 0.110Ordinary clay = 0.130Saturated topsoil = 0.150Sand and gravel = 0.165
Bd max. = Transitional trench width from table below Ref. 1= 5 ft. Table 13 to 28
Bd = Max. effective transitional trench width
Bd Pipe Cover = H ( ft. )Pipe Dia. 5 6 7 8 9 10 15 20
6 1.42 1.5 1.58 1.67 1.75 1.75 2.08 2.338 1.75 1.83 1.92 2 2 2.08 2.42 2.75
12 2.5 2.58 2.75 2.83 2.92 3 3.33 3.6716 3 3.08 3.17 3.25 3.33 3.42 3.83 4.2518 3.42 3.5 3.58 3.75 3.83 3.92 4.33 4.7524 4.25 4.33 4.5 4.58 4.67 4.83 5.25 5.6730 4.83 5.17 5.33 5.42 5.58 5.67 6.17 6.6736 5.42 5.75 6.17 6.25 6.42 6.58 7.08 7.5842 5.92 6.33 6.67 7.08 7.25 7.42 7.92 8.4248 6.5 6.92 7.25 7.67 8.08 8.17 8.83 9.3354 7.08 7.42 7.83 8.17 8.58 9 9.67 10.2560 7.67 8 8.42 8.75 9.08 9.5 10.5 11.08
For shallow depths (< 4ft.) use :wd = H Bc w = 978.6 lb / lin ft.
Therefore wd = 978.6 lb / lin ft. + wt. of concrete = 350 lb / lin. Ft.wd total = 1328.6 lb / lin ft.
N:\civil\spreadsh\UGPipes\u-g pipe.xls (1 of 3)
Wheel LoadingFrom Individual Wheel Loads
Tire Pressure = 80 psi.Impact Factor = Fi = 1.267 1.5 at surface Ref. 2 , 4.7.2.2.2
1.0 @ H = 5 ft.k mod. of subgrade reaction = 200 lb / in^3
Ec conc. = 3400000 psi Ref. 4
Underground Pipe Stress Check - UGP 2
Bc
Bd
H
P
X
X
Sum loadsat this point
r
P1
P2P3
P4
hc
L
Wheel P X A contact L H / L X / L Press. Coef. Pressure# ( lbs. ) ( ft. ) ( ft. ^2 ) ( ft. ) ( C from below) Top Pipe (lb./ft^2)1 17500 0.00 1.92 2.45 0.95 0.00 0.0825 Ref 4 1204.22 17500 7.00 1.92 2.45 0.95 2.86 0.013 Table 1 189.73 17500 21.20 1.92 2.45 0.95 8.67 0 0.04 17500 20.00 1.92 2.45 0.95 8.18 0 0.05 0.00 0.00 2.45 0.95 0.00 0.06 0.00 0.00 2.45 0.95 0.00 0.0
Total: = 1393.9Pressure Coeficient C
C X / LH / L 0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 40.0 0.113 0.105 0.089 0.068 0.048 0.032 0.020 0.011 0.006 0.002 0.0000.4 0.101 0.095 0.082 0.065 0.047 0.033 0.021 0.011 0.004 0.001 0.0000.8 0.089 0.084 0.074 0.061 0.045 0.033 0.022 0.012 0.005 0.002 0.0011.2 0.076 0.072 0.065 0.054 0.043 0.032 0.022 0.014 0.008 0.005 0.0031.6 0.062 0.059 0.054 0.047 0.039 0.030 0.022 0.016 0.011 0.007 0.0052.0 0.051 0.049 0.046 0.042 0.035 0.028 0.022 0.016 0.011 0.008 0.0062.4 0.043 0.041 0.039 0.036 0.030 0.026 0.021 0.016 0.011 0.008 0.0062.8 0.037 0.036 0.033 0.031 0.027 0.023 0.019 0.015 0.011 0.009 0.0063.2 0.032 0.030 0.029 0.026 0.024 0.021 0.018 0.014 0.011 0.009 0.0073.6 0.027 0.026 0.025 0.023 0.021 0.019 0.016 0.014 0.011 0.009 0.0074.0 0.024 0.023 0.022 0.020 0.019 0.018 0.015 0.013 0.011 0.009 0.0074.4 0.020 0.020 0.019 0.018 0.017 0.015 0.014 0.012 0.010 0.009 0.0074.8 0.018 0.017 0.017 0.016 0.015 0.013 0.012 0.011 0.009 0.008 0.0075.2 0.015 0.015 0.014 0.014 0.013 0.012 0.011 0.010 0.008 0.007 0.0065.6 0.014 0.013 0.013 0.012 0.011 0.010 0.010 0.009 0.008 0.007 0.0066.0 0.012 0.012 0.011 0.011 0.010 0.009 0.009 0.008 0.007 0.007 0.006
Total Wheel Pressure at Top of Pipe = 1393.9 lb / ft.^2
Pipe Stresses
Pipe Dia. O.D. = 42 in. Young's Mod. E = 30000000 psi.Wall thickness t = 0.50 in. Poisson's Ratio = 0.3
Pipe Grade = X65 Coef. Thermal Exp. = 0.0000065 per deg FSMYS = 65000 psi.
Pipe Operating Pres. = 1000.0 psi. Temp. @ Pipe Installation = 10 deg. FSMYS design factor F = 0.8 Max./Min. Operating Temp. = 170 deg. F
Circumferential Stress Due to Earth LoadRef. 2
She = Khe Be Ee lamda D = 2756.3 psi. where: Khe = soil/pipe stiffness coef. = 4500 Fig. 3t / d = 0.011905 (set E' = 1.0)
Value by Ref 1 (above) = 978.6 psi. Be = 0.21 Fig. 4where H/Bd = 0.665714 (Soil Type B for trenches)
Use largest Value set SHe = 2756.3 psi. Ee = 1 (for trenched constuction)
+ wt. Concrete = She tot. = 2756.9 psi. lamda = unit wt. Soil = 120 lb / ft^3D = 42 in (2 of 3)
Wheel Load Stress
w = 9.68 psi. from above
where: KHh = circumf. stiffness factor = 12.5 Fig. 14Cyclic Circumferential Stress where: t / d = 0.011905 Set Er = 10
SHh = KHh GHh R L Fi w GHh = geometry factor = 0.96 from Fig. 15
= 86.10 psi.GHh H, soil cover ( ft. ) Fig. 15
Pipe dia. 3 - 4 6 8 10Cyclic Longitudinal Stress 6 1.45 1.15 0.9 0.7
12 1.28 1.05 0.85 0.67SLh = KLh GLh R L Fi w 18 1.08 0.95 0.77 0.63
= 55.96 psi. 24 1.12 0.85 0.73 0.5830 1.07 0.8 0.68 0.5436 1.01 0.76 0.64 0.5
Internal Pressure Circumferential Stress 42 0.96 0.72 0.6 0.4648 0.92 0.69 0.55 0.43
Shi = p (D - t ) / 2 t 54 0.87 0.66 0.51 0.41
= 41500 psi. 60 0.85 0.63 0.47 0.38
R = pavement factor = 0.90 Ref. 2 ==>L = Axle configuration = 0.65 Table 2
Limits of Calculated StressKLh = long. Stiffness factor = 10 Fig. 16
1.) Check Pressure Stress using Barlow formula where t / d = 0.0119048 Set Er = 10GLh = geometry factor = 0.78 from Fig. 17
SHi (Barlow) = p D / 2 t< or = F E T SMYS (natural gas) GLh H, soil cover ( ft. ) Fig. 17< or = F E SMYS (liquids) Pipe dia. 3 - 4 6 8 10
6 1.55 1.45 1.35 1.25where:F = design factor = 0.8 Ref. 3 10 1.23 1.1 1 0.9
E = joint factor = 1.0 Ref. 2 12 1.15 1.02 0.88 0.8T = temp. derating = 1.0 18 1.1 0.93 0.83 0.7
24 1.02 0.87 0.75 0.5730 0.94 0.8 0.69 0.53
SHi (Barlow) = 42000 psi 36 0.86 0.73 0.63 0.48< = 52000 (nat. gas) OK 42 0.78 0.65 0.58 0.44< = 52000 (liquids) OK 48 0.7 0.58 0.52 0.4
54 0.62 0.51 0.46 0.3660 0.54 0.44 0.41 0.32
2.) Check Total Effective Stress
Seff =SQRT [ 1/2 ( (S1 - S2)^2 + (S2 - S3)^2 + (S3 - S1)^2)] < or = SMYF F
S1 = SHe + SHr + SHi = 44343 psiS2 = SLr - Es Coef. Thermal Exp. (T2 - T1) + poisons ratio ( SHe + SHi) = 44533 psiS3 = - P = -1000.0 psi
S eff = 32130 psi < or = 52000 psi OK -- Stress within allowables
References:1. ) Concrete Pipe Design Manual ACPA 5th Printing June 1980
2. ) API Recommended Practice 1102 Steel Pipelines Crossing Railroads and Highways 6th Editition 1993
3. ) CAN/CSA Z183 - M90
4. ) PCA Vertical Pressure on Culverts Under Wheel Loads on Concrete Pavement Slabs
5. ) PCA Concrete Floors on Ground (3 of 3)
Design Calculation Project No.
Project Title: 014173Checked By: Date: Apr/07/23Date:
PIPE STRESSES - WHEELS ON UNPROTECTED FILL
Earth Loading
Pipe Size = 42 in.O.D. = 42 in.
wd = Cd w Bd^2 = 1666.6 lb / lin ft. Ref. 1where: w = 120 lb/ft^3 soil unit wt.
Bd = 5 ft. (actual width)Bd = 5.0 ft. (effective width)
Bc = O.D. = 3.50 ft
Cd = 1 - e^ (-2 ku'(H/Bd))2 ku'
= 0.556
H = 3 ft.ku' = 0.13 lb / in^3
ku' = modulus of subgrade reactionSaturated clay = 0.110Ordinary clay = 0.130Saturated topsoil = 0.150Sand and gravel = 0.165
Bd max. = Transitional trench width from table below= 5 ft. Table 13 to 28
Bd = Max. effective transitional trench width
Bd Pipe Cover = H ( ft. )Pipe Dia. 5 6 7 8 9 10 15 20
6 1.42 1.5 1.58 1.67 1.75 1.75 2.08 2.338 1.75 1.83 1.92 2 2 2.08 2.42 2.75
12 2.5 2.58 2.75 2.83 2.92 3 3.33 3.6716 3 3.08 3.17 3.25 3.33 3.42 3.83 4.2518 3.42 3.5 3.58 3.75 3.83 3.92 4.33 4.7524 4.25 4.33 4.5 4.58 4.67 4.83 5.25 5.6730 4.83 5.17 5.33 5.42 5.58 5.67 6.17 6.6736 5.42 5.75 6.17 6.25 6.42 6.58 7.08 7.5842 5.92 6.33 6.67 7.08 7.25 7.42 7.92 8.4248 6.5 6.92 7.25 7.67 8.08 8.17 8.83 9.3354 7.08 7.42 7.83 8.17 8.58 9 9.67 10.2560 7.67 8 8.42 8.75 9.08 9.5 10.5 11.08
For shallow depths (< 4ft.) use :wd = H Bc w = 1260.0 lb / lin ft.
Therefore wd = 1260.0 lb / lin ft.
N:\civil\spreadsh\UGPipes\u-g pipe.xls
Underground Pipe Stress Check - UGP 1
Bc
Bd
H
P
X
X
Sum loadsat this point
r
P1
P2P3
P4
Wheel LoadingFrom Individual Wheel Loads
Tire Pressure = 80 psi.Impact Factor = Fi = 1.2
1.5 at surface Ref. 2 , 4.7.2.2.21.0 @ H = 5 ft.
Ref. 4
Wheel P X A contact r H / r X / r Press. Coef.# ( lbs. ) ( ft. ) ( ft. ^2 ) ( ft. ) ( C from below) Top Pipe (lb./ft^2)1 17500 0.00 1.82 0.76 3.94 0.00 0.0872 17500 7.00 1.82 0.76 3.94 9.19 0.0023 17500 21.20 1.82 0.76 3.94 27.83 0.0014 17500 20.00 1.82 0.76 3.94 26.26 0.0015 0.00 0.00 0.00 #DIV/0! #DIV/0!6 0.00 0.00 0.00 #DIV/0! #DIV/0!
Total: = Pressure Coeficient C
C X / rH / r 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.00.0 1.000 1.000 0.000 0.000 0.000 0.000 0.000 0.0000.5 0.911 0.425 0.010 0.001 0.000 0.000 0.000 0.0001.0 0.646 0.350 0.500 0.005 0.001 0.000 0.000 0.0001.5 0.424 0.250 0.075 0.012 0.004 0.001 0.000 0.0002.0 0.284 0.198 0.075 0.020 0.007 0.003 0.001 0.0012.5 0.200 0.145 0.070 0.026 0.010 0.004 0.002 0.0013.0 0.146 0.110 0.066 0.029 0.013 0.006 0.003 0.0023.5 0.110 0.101 0.060 0.031 0.015 0.008 0.004 0.0024.0 0.087 0.081 0.054 0.031 0.017 0.009 0.005 0.0035.0 0.057 0.054 0.041 0.028 0.017 0.011 0.006 0.0046.0 0.040 0.039 0.032 0.024 0.017 0.010 0.007 0.0057.0 0.030 0.029 0.025 0.020 0.015 0.011 0.008 0.0058.0 0.023 0.023 0.020 0.017 0.013 0.010 0.008 0.0069.0 0.018 0.018 0.016 0.014 0.012 0.009 0.007 0.00610.0 0.015 0.015 0.014 0.012 0.010 0.009 0.007 0.006
Total Wheel Pressure at Top of Pipe = 1258.0 lb / ft.^2
Pipe Stresses
Pipe Dia. O.D. = 42 in. Young's Mod. E = 30000000 psi.Wall thickness t = 0.50 in. Poisson's Ratio = 0.3
Pipe Grade = X65 Coef. Thermal Exp. = 0.0000065 per deg FSMYS = 65000 psi.
Pipe Operating Pres. = 1000.0 psi. Temp. @ Pipe Installation = 10 deg. FSMYS design factor F = 0.8 Max./Min. Operating Temp. = 170 deg. F
Circumferential Stress Due to Earth Load
She = Khe Be Ee lamda D = 3675.0 psi. where: Khe = soil/pipe stiffness coef. = 4500t / d = 0.011905
Value by Ref 1 (above) = 1260.0 psi. Be = 0.28where H/Bd = 0.857143 (Soil Type B for trenches)
Use largest Value set She = 3675.0 psi. Ee = 1 (for trenched constuction)lamda = unit wt. Soil = 120 lb / ft^3
D = 42 inWheel Load Stress
w = 8.74 psi. from above
X
X
Sum loadsat this point
r
P1
P2P3
P4
where: KHh = circumf. stiffness factor = 12.5Cyclic Circumferential Stress where: t / d = 0.011905
SHh = KHh GHh R L Fi w GHh = geometry factor = 0.96 from Fig. 15= 89.95 psi.
GHh H, soil cover ( ft. )Pipe dia. 3 - 4 6 8 10
Cyclic Longitudinal Stress 6 1.45 1.15 0.9 0.712 1.28 1.05 0.85 0.67
SLh = KLh GLh R L Fi w 18 1.08 0.95 0.77 0.63= 58.46 psi. 24 1.12 0.85 0.73 0.58
30 1.07 0.8 0.68 0.5436 1.01 0.76 0.64 0.5
Internal Pressure Circumferential Stress 42 0.96 0.72 0.6 0.4648 0.92 0.69 0.55 0.43
Shi = p (D - t ) / 2 t 54 0.87 0.66 0.51 0.41= 41500 psi. 60 0.85 0.63 0.47 0.38
R = pavement factor = 1.10L = Axle configuration = 0.65
Limits of Calculated StressKLh = long. Stiffness factor = 10
1.) Check Pressure Stress using Barlow formula where t / d = 0.0119048GLh = geometry factor = 0.78 from Fig. 17
SHi (Barlow) = p D / 2 t< or = F E T SMYS (natural gas) GLh H, soil cover ( ft. )< or = F E SMYS (liquids) Pipe dia. 3 - 4 6 8 10
6 1.55 1.45 1.35 1.25where:F = design factor = 0.8 Ref. 3 10 1.23 1.1 1 0.9
E = joint factor = 1.0 Ref. 2 12 1.15 1.02 0.88 0.8T = temp. derating = 1.0 18 1.1 0.93 0.83 0.7
24 1.02 0.87 0.75 0.5730 0.94 0.8 0.69 0.53
SHi (Barlow) = 42000 psi 36 0.86 0.73 0.63 0.48< = 52000 (nat. gas) OK 42 0.78 0.65 0.58 0.44< = 52000 (liquids) OK 48 0.7 0.58 0.52 0.4
54 0.62 0.51 0.46 0.3660 0.54 0.44 0.41 0.32
2.) Check Total Effective Stress
Seff =SQRT [ 1/2 ( (S1 - S2)^2 + (S2 - S3)^2 + (S3 - S1)^2)] < or = SMYF F
S1 = SHe + SHr + SHi = 45265 psiS2 = SLr - Es Coef. Thermal Exp. (T2 - T1) + poisons ratio ( SHe + SHi) = 44811 psiS3 = - P = -1000.0 psi
S eff = 32555 psi < or = 52000 psi OK -- Stress within allowables
References:1. ) Concrete Pipe Design Manual ACPA 5th Printing June 1980
2. ) API Recommended Practice 1102 Steel Pipelines Crossing Railroads and Highways 6th Editition 1993
3. ) CAN/CSA Z183 - M90
4. ) PCA Vertical Pressure on Culverts Under Wheel Loads on Concrete Pavement Slabs
Ref. 1
Table 13 to 28
(1 of 3)
Bc
Bd
H
P
X
X
Sum loadsat this point
r
P1
P2P3
P4
PressureTop Pipe (lb./ft^2)
1202.727.613.813.80.00.0
1258.0
Ref. 2
Fig. 3
(set E' = 1.0)
Fig. 4
(Soil Type B for trenches)
(for trenched constuction)
(2 of 3)
X
X
Sum loadsat this point
r
P1
P2P3
P4
Fig. 14
Set Er = 10
Fig. 15
Ref. 2 ==>Table 2
Fig. 16
Set Er = 10
Fig. 17
(3 of 3)
