Pipe Stress Calculations - State of · PDF file< 10 > Where: E S = secant modulus of the granular drainage layer, psi = 3,978 M S = one-dimensional modulus, (for 90% standard proctor

ATTACHMENT 7-VI PIPE STRESS CALCULATIONS

DO = = 6.625 in.

t = = 0.602 in.PT = = 28,080 psf

= 195.00 psi

E = = 22,140psi (for 100 yrs, pipe at 90o F)

MS = = 4,200 (for total pressure stated above)

= = 0.15 (value for coarse sand)

= 820 psi, (for pipe at 90o

F)

RF= = 2,156

DF = = 1.42

= = 0.55 (for granular soils)RH = = 1 (for deep burial)

Summary/Conclusion Table

F.S. = 2.3

6" HDPE Leachate Collection Pipes

Ring Deflection (7.5% allowable)Wall Buckling

6.96%

Poisson’s ratio of soil, to model granular drainage layer, (Table 3-13, Plastic Pipe Institute, 2015)

As calculated in ing deflection tab.

6" Leachate Collection Pipe

Table 1: General Calculation Inputs

Deformation Factor, (Figure 3-6, Plastic Pipe Institute, 2015) for RF as in ring deflection.Calibration Factor, (equation 3-29, Plastic Pipe Institute, 2015)Geometry Factor, (equation 3-29, Plastic Pipe Institute, 2015)

The recommended long-term compressive strength design value for HDPE pipe (psi) (Tables B.1.2 & C.1, Plastic Pipe Institute, 2015)

pipe outside diameter, in.pipe wall thickness, in.total external pressure, psf

apparent modulus of elasticity of pipe material, psi

one-dimensional modulus, (for 90% standard proctor and vertical waste and soil stress (Table 3 12, Plastic Pipe Institute, 2015)

Page 1

< 10 >

Where: ES = secant modulus of the granular drainage layer, psi = 3,978

MS =one-dimensional modulus, (for 90% standard proctor and vertical wasteand soil stress (Table 3 12, Plastic Pipe Institute, 2015) = 4,200

=Poisson’s ratio of soil, used to represent the granular drainage layermaterial (Table 3-13, Plastic Pipe Institute, 2015) = 0.15

< 9 >

Where: RF = rigidity factor = 2,156ES = Secant modulus of the soil, psi (see calculated value above) = 3,978DR = dimension ratio, (DR = Do/t) = 11.0

Do = 6.625t = 0.602

E = apparent modulus of elasticity of pipe material, psi = 22,140

< 8 >

Where: PT = total external pressure, psf = 28,080.00ES = Secant modulus of the soil, psi (see calculated value above) = 3,978

= soil strain = 0.049

X/DM = DF x < 7 >Where: X/DM = deflection = 0.0696

DF

= Deformation Factor, (Figure 3-6, Plastic Pipe Institute, 2015) for RF

as calculated above. = 1.42= soil strain = 0.049

Percent Deflection = deflection x 100 = 6.958

Is the ring deflection allowable? (actual < allowable) Yes

The recommended allowable ring deflection for non-pressure pipe is 7.5% which provides a large factor of safetyagainst instability and strain (Plastic Pipe Institute, Chapter 6, 2015).

Calculate the secant modulus of the soil, ES, using equation 10; determine the rigidity factor, RF, using equation 9and the soil strain using equation 8. The rigidity factor is used to determine the deformation factor which is usedto calculate the percent deflection, X/DM x 100, of the pipe using equation 7.

Ring Deflection Analysis

)(1)x2(1x)(1xSMSE

E

31)(DRxsEx12FR

sEx144TP

Page 2

< 11 >

Where: PCR = allowable buckling pressure, psi = 453= Calibration Factor (equation 3-29, Plastic Pipe Institute, 2015) = 0.55

RH = Geometry Factor, (equation 3-29, Plastic Pipe Institute, 2015) = 1DM = mean diameter (DO – t), in. = 6.023DO = pipe outside diameter, in. = 6.625t = pipe wall thickness, in. = 0.602E = apparent modulus of elasticity of pipe material, psi = 22,140I = pipe wall moment of inertia, in4/in (t3/12) = 0.0182ES* = ES/(1- ), psi = 4,680ES = Secant modulus of the soil, (see calculation in Ring Deflection) = 3,978

= Poisson’s ratio of soil, (from Table 3-13, used to represent thegranular drainage layer material, Plastic Pipe Institute, 2015) = 0.15

Actual, psi: PT = 195Allowable, psi: PCR = 453

Factor of safety for wall buckling is:F.S. = PCR / PT = 2.32

Pipe Wall Buckling Analysis

Calculate the allowable pipe wall buckling pressure, PCR.

The allowable buckling pressure should be compared to the total “static load” pressure, PT, on the pipe.

32*)S(E x 31I) x (E x MD

HR x x 2.4 CRP

Page 3

DO = = 6.625 in.

t = = 0.432 in.PT = = 28,080 psf

= 195.00 psi

E = = 75,000psi (for 50 yr, pipe at 90o F)


= = 0.15 (value for coarse sand)


F)

RF= = 1,861

DF = = 1.42

= = 0.55 (for granular soils)RH = = 1 (for deep burial)


F.S. = 2.4

6" Sch 80 PVC Leachate Collection Pipes


6.96%



6" Sch 80 PVC LeachateCollection Pipe



The strength design value for PVC pipe (psi), reduced 50% to consider long term conditions.




Page 4

< 10 >


MS =one-dimensional modulus, (for 90% standard proctor and vertical wasteand soil stress (Table 3 12, Plastic Pipe Institute, 2015) = 4,200

=Poisson’s ratio of soil, used to represent the granular drainage layermaterial (Table 3-13, Plastic Pipe Institute, 2015) = 0.15

< 9 >


Do = 6.625t = 0.432


< 8 >



X/DM = DF x < 7 >Where: X/DM = deflection = 0.0696

DF





The recommended allowable ring deflection for non-pressure pipe is 7.5% which provides a large factor of safetyagainst instability and strain.

Calculate the secant modulus of the soil, ES, using equation 10; determine the rigidity factor, RF, using equation 9and the soil strain using equation 8. The rigidity factor is used to determine the deformation factor which is usedto calculate the percent deflection, X/DM x 100, of the pipe using equation 7.


)(1)x2(1x)(1xSMSE

E

31)(DRxsEx12FR

sEx144TP

Page 5

< 11 >


RH = Geometry Factor, (equation 3-29, Plastic Pipe Institute, 2015) = 1DM = mean diameter (DO – t), in. = 6.193DO = pipe outside diameter, in. = 6.625t = pipe wall thickness, in. = 0.432E = apparent modulus of elasticity of pipe material, psi = 75,000I = pipe wall moment of inertia, in4/in (t3/12) = 0.0067ES* = ES/(1- ), psi = 4,680ES = Secant modulus of the soil, (see calculation in Ring Deflection) = 3,978


Actual, psi: PT = 195Allowable, psi: PCR = 474





32*)S(E x 31I) x (E x MD

HR x x 2.4 CRP

Page 6

DO = = 18 in.

t = = 1.636 in.PT = = 4,800 psf

= 33.33 psi

E = = 22,140psi (for 100 yrs, pipe at 90o F)


= 0.15 (value for coarse sand)


F)

RF= = 2,156

DF = = 1.42

= 0.55 (for granular soils)RH = = 1 (for deep burial)


F.S. = 13.6

18" Leachate Collection Pipe



The recommended long-term compressive strength design value for HDPE pipe (psi) (Tables B.1.2 & C.1, Plastic Pipe Institute, 2015)




18" HDPE SDR 11 Sump Riser Pipes


1.19%



Page 7

< 10 >


MS =one-dimensional modulus, (for 90% standard proctor and vertical wasteand soil stress (Table 3 12, Plastic Pipe Institute, 2015) = 4,200Poisson’s ratio of soil, used to represent the granular drainage layermaterial (Table 3-13, Plastic Pipe Institute, 2015) = 0.15

< 9 >


Do = 18t = 1.636


< 8 >



M = DF < 7 >Where: M = deflection = 0.0119

DF





The recommended allowable ring deflection for non-pressure pipe is 7.5% which provides a large factor of safetyagainst instability and strain (Plastic Pipe Institute, Chapter 6, 2015).

Calculate the secant modulus of the soil, ES, using equation 10; determine the rigidity factor, RF, using equation 9and the soil strain using equation 8. The rigidity factor is used to determine the deformation factor which is used

M x 100, of the pipe using equation 7.


(1x2(1x(1xSMSE

E

31)(DRxsEx12FR

sEx144TP

Page 8

< 11 >


RH = Geometry Factor, (equation 3-29, Plastic Pipe Institute, 2015) = 1DM = mean diameter (DO – t), in. = 16.364DO = pipe outside diameter, in. = 18t = pipe wall thickness, in. = 1.636E = apparent modulus of elasticity of pipe material, psi = 22,140I = pipe wall moment of inertia, in4/in (t3/12) = 0.3649ES* = ES = 4,680ES = Secant modulus of the soil, (see calculation in Ring Deflection) = 3,978


Actual, psi: PT = 33.333Allowable, psi: PCR = 453





32*)S(E x 31I) x (E x MD

HR x x 2.4CRP

Page 9

Material Properties

Apparent Elastic Modulus for 73°F (23°C)

Duration of Sustained Loading

Design Values For 73°F (23°C) (1,2,3)

PE 2XXX PE3XXX PE4XXX

psi MPa psi MPa psi MPa

0.5hr 62,000 428 78,000 538 82,000 565

1hr 59,000 407 74,000 510 78,000 538

2hr 57,000 393 71,000 490 74,000 510

10hr 50,000 345 62,000 428 65,000 448

12hr 48,000 331 60,000 414 63,000 434

24hr 46,000 317 57,000 393 60,000 414

100hr 42,000 290 52,000 359 55,000 379

1,000hr 35,000 241 44,000 303 46,000 317

1 year 30,000 207 38,000 262 40,000 276

10 years 26,000 179 32,000 221 34,000 234

50 years 22,000 152 28,000 193 29,000 200

100 years 21,000 145 27,000 186 28,000 193

(1) Although there are various factors that determine the exact apparent modulus response of a PE, a major factor is its ratio of crystalline to amorphous content – a parameter that is re ected by a PE’s density. Hence, the major headings PE2XXX, PE3XXX and, PE4XXX, which are based on PE’s Standard Designation Code. The rst numeral of this code denotes the PE’s density category in accordance with ASTM D3350 (An explanation

of this code is presented in Chapter 5).

(2) The values in this table are applicable to both the condition of sustained and constant loading (under which the resultant strain increases with increased duration of loading) and that of constant strain (under which an initially generated stress gradually relaxes with increased time).

(3) The design values in this table are based on results obtained under uni-axial loading, such as occurs in a test bar that is being subjected to a pulling load. When a PE is subjected to multi-axial stressing its strain response is inhibited, which results in a somewhat higher apparent modulus. For example, the apparent modulus of a PE pipe that is subjected to internal hydrostatic pressure – a condition that induces bi-axial stressing – is about 25% greater than that reported by this table. Thus, the Uni-axial condition represents a conservative estimate of the value that is achieved in most applications.

It should also be kept in mind that these values are for the condition of continually sustained loading. If there is an interruption or a decrease in the loading this, effectively, results in a somewhat larger modulus.

In addition, the values in this table apply to a stress intensity ranging up to about 400psi, a value that is seldom exceeded under normal service conditions.

Source: "PPI Handbook of Polyethylene Pipe", downloaded February, 2015;http://plasticpipe.org/publications/pe_handbook.html

Attachment 1

Page 10

Material Properties

The multipliers listed in Table B.1.2 when applied to the base temperature value (Table B.1.1) yield the value for another temperature.

Temperature Compensating Multipliers for Determination of the Apparent Modulus of Elasticity at Temperatures Other than at 73°F (23°C)

Equally Applicable to All Stress-Rated PE’s (e.g., All PE2xxx’s, All PE3xxx’s and All PE4xxx’s)

Maximum Sustained Temperature of the Pipe °F (°C)

Compensating Multiplier

-20 (-29) 2.54

-10 (-23) 2.36

0 (-18) 2.18

10 (-12) 2.00

20 (-7) 1.81

30 (-1) 1.65

40 (4) 1.49

50 (10) 1.32

60 (16) 1.18

73.4 (23) 1.00

80 (27) 0.93

90 (32) 0.82

100 (38) 0.73

110 (43) 0.64

120 (49) 0.58

130 (54) 0.50

140 (60) 0.43

Attachment 1 cont.

Page 11

Design of PE Piping Systems

crown may completely reverse its curvature inward and collapse. See Figure 3-1A. A de ection limit of 7.5% provides at least a 3 to 1 safety factor against reverse curvature.

Bending strain occurs in the pipe wall as a result of ring de ection — outer- ber tensile strain at the pipe springline and outer- ber compressive strain at the crown and invert. While strain limits of 5% have been proposed, Jansen (12) reported that, on tests of PE pipe manufactured from pressure-rated resins and subjected to soil pressure only, “no upper limit from a practical design point of view seems to exist for the bending strain.” In other words, as de ection increases, the pipe’s performance limit will not be overstraining but reverse curvature collapse.

Thus, for non-pressure applications, a 7.5 percent de ection limit provides a large safety factor against instability and strain and is considered a safe design de ection. Some engineers will design pro le wall pipe and other non-pressure pipe applications to a 5% de ection limit, but allow spot de ections up to 7.5% during

eld inspection.

The de ection limits for pressurized pipe are generally lower than for non-pressurized pipe. This is primarily due to strain considerations. Hoop strain from pressurization adds to the outer- ber tensile strain. But the internal pressure acts to reround the pipe and, therefore, Eq. 3-10 overpredicts the actual long-term de ection for pressurized pipe. Safe allowable de ections for pressurized pipe are given in Table 3-11. Spangler and Handy (13) give equations for correcting de ection to account for rerounding.

Safe De ection Limits for Pressurized Pipe

DR or SDR Safe De ection as % of Diameter32.5 7.5

26 7.5

21 7.5

17 6.0

13.5 6.0

11 5.0

9 4.0

7.3 3.0

* Based on Long-Term Design De ection of Buried Pressurized Pipe given in ASTM F1962.

Attachment 1 cont.

Page 12

Material Properties

Table C.1 lists allowable compressive stress values for 73°F (23°C). Values for allowable compressive stress for other temperatures may be determined by application of the same multipliers that are used for pipe pressure rating (See Table A.2).

Allowable Compressive Stress for 73°F (23°C)

Pe Pipe Material Designation Code (1)

PE 2406 PE3408

PE 4710PE 2708

PE 3608

PE 3708

PE 3710

PE 4708

psi MPa psi MPa psi MPa

Allowable Compressive

Stress800 5.52 1000 6.90 1150 7.93

(1) See Chapter 5 for an explanation of the PE Pipe Material Designation Code.

Poisson’s Ratio for ambient temperature for all PE pipe materials is approximately 0.45.

This 0.45 value applies both to the condition of tension and compression. While this value increases with temperature, and vice versa, the effect is relatively small over the range of typical working temperatures.

Attachment 1 cont.

Page 13


One-dimensional modulus values for soil can be obtained from soil testing, geotechnical texts, or Table 3-12 which gives typical values. The typical values in Table 3-12 were obtained by converting values from McGrath (20).

Typical Values of Ms, One-Dimensional Modulus of Soil

Vertical Soil Stress1 (psi)Gravelly Sand/Gravels 95% Std. Proctor (psi)

Gravelly Sand/Gravels 90% Std. Proctor (psi)

Gravelly Sand/Gravels 85% Std. Proctor (psi)

10 3000 1600 550

20 3500 1800 650

40 4200 2100 800

60 5000 2500 1000

80 6000 2900 1300

100 6500 3200 1450

* Adapted and extended from values given by McGrath(20). For depths not shown in McGrath(20), the MS values were approximated using the hyperbolic soil model with appropriate values for K and n where n=0.4 and K=200, K=100, and K=45 for 95% Proctor, 90% Proctor, and 85% Proctor, respectively.

1 Vertical Soil Stress (psi) = [ soil depth (ft) x soil density (pcf)]/144

The radial directed earth pressure can be found by multiplying the prism load (pressure) by the vertical arching factor as shown in Eq. 3-23.

(3-23)

PRD = radial directed earth pressure, lb/ft2

w = unit weight of soil, pcf

H = depth of cover, ft

The ring compressive stress in the pipe wall can be found by substituting PRD from Equation 3-23 for PE in Equation 3-13 for DR pipe and Equation 3-14 for pro le wall pipe.

Determine the earth pressure acting on a 36” pro le wall pipe buried 30 feet deep. The following properties are for one unique 36” pro le pipe made from PE3608 material. Other 36” pro le pipe may have different properties. The pipe’s cross-sectional area, A, equals 0.470 inches2/inch, its radius to the centroidal axis is 18.00 inches plus 0.58 inches, and its apparent modulus is 27,000 psi. Its wall height is 2.02 in and its DO equals 36 in +2 (2.02 in) or 40.04 in. Assume the pipe is installed in a clean granular soil compacted to 90% Standard Proctor (Ms = 1875 psi), the insitu soil is as stiff as the embedment, and the back ll weighs 120 pcf. (Where the excavation

RDP = (VAF)wH

Attachment 1 cont.

Page 14


this method is that it assumes a constant Deformation Factor independent of depth of cover and it does not address the effect of the presence of ground water on the Deformation Factor.

To use the Watkins-Gaube Graph, the designer rst determines the relative stiffness between pipe and soil, which is given by the Rigidity Factor, RF. Equation 3-24 and 3-25 are for DR pipe and for pro le pipe respectively:

(3-24)

EIDE = R m

3S

F

EDRER S

F

3)1(12

S SE = (1+ )(1- 2 )(1- )

(3-25)

DR = Dimension Ratio

ES = Secant modulus of the soil, psi

E = Apparent modulus of elasticity of pipe material, psi

I = Pipe wall moment of inertia of pipe, in4/in

Dm = Mean diameter (DI + 2z or DO – t), in

The secant modulus of the soil may be obtained from testing or from a geotechnical engineer’s evaluation. In lieu of a precise determination, the soil modulus may be related to the one-dimensional modulus, MS, from Table 3-12 by the following equation where is the soil’s Poisson ratio.

(3-26)

Typical range of Poisson’s Ratio for Soil (Bowles (21))

Soil Type Poisson’s Ratio, μSaturated Clay 0.4-0.5

Unsaturated Clay 0.1-0.3

Sandy Clay 0.2-0.3

Silt 0.3-0.35

Sand (Dense) 0.2-0.4

Coarse Sand (Void Ratio 0.4-0.7) 0.15

Fine-grained Sand (Void Ratio 0.4-0.7) 0.25

Attachment 1 cont.

Page 15


Next, the designer determines the Deformation Factor, DF , by entering the Watkins-Gaube Graph with the Rigidity Factor. See Fig. 3-6. The Deformation Factor is the proportionality constant between vertical de ection (compression) of the soil layer containing the pipe and the de ection of the pipe. Thus, pipe de ection can be obtained by multiplying the proportionality constant DF times the soil settlement. If DF is less than 1.0 in Fig. 3-6, use 1.0.

The soil layer surrounding the pipe bears the entire load of the overburden above it without arching. Therefore, settlement (compression) of the soil layer is proportional to the prism load and not the radial directed earth pressure. Soil strain, S, may be determined from geotechnical analysis or from the following equation:

(3-27)

EwH=

SS144

w = unit weight of soil, pcf

H = depth of cover (height of ll above pipe crown), ft

Es = secant modulus of the soil, psi

The designer can nd the pipe de ection as a percent of the diameter by multiplying the soil strain, in percent, by the deformation factor:

5 10 50 100 500 1000 5000 10,000

Defo

rmat

ion

Fact

or, D

F

Rigidity Factor, RF

(3-28)

X/D multiplied by 100 gives percent de ection.

D(100) = DF S

Attachment 1 cont.

Page 16


The Moore-Selig Equation for critical buckling pressure follows: (Critical buckling pressure is the pressure at which buckling will occur. A safety factor should be provided.)

(3-29))E()(EI

DR 2.4 = P 3

2*S3

1

M

HCR

P R = Critical constrained buckling pressure, psi

= Calibration Factor, 0.55 for granular soils

R = Geometry Factor

E = Apparent modulus of elasticity of pipe material, psi

= Pipe wall moment of Inertia, in4/in (t3/12, if solid wall construction)

ES = ES /(1- )

ES = Secant modulus of the soil, psi

s = Poisson’s Ratio of Soil (Consult a textbook on soil for values. Bowles (1982) gives typical values for sand and rock ranging from 0.1 to 0.4.)

The geometry factor is dependent on the depth of burial and the relative stiffness between the embedment soil and the insitu soil. Moore has shown that for deep burials in uniform lls, RH equals 1.0.

Determine the critical buckling pressure and safety factor against buckling for the 6” SDR 11 pipe (5.987” mean diameter) in the previous example.

SOLUTION:

Shallow cover presents some special considerations for exible pipes. As already discussed, full soil structure interaction (membrane effect) may not occur, and live loads are carried in part by the bending stiffness of the pipe. Even if the pipe has suf cient strength to carry live load, the cover depth may not be suf cient to prevent

S 2E2000

( 0 328 0 s

in

S PP

350 5

R

E

R 323 2P

2 0 55 05 8

(28250 0 0 8 (28 0 35 sin

(2 000 in2358

358Determine the Safety Factor against buckling:

Attachment 1 cont.

Page 17


OD

Pipe inside

diameter (d)

Minimum Wall

Thickness (t)

Weight (w)

Nominal in.

Actual in.

DR

in.

in.

lb. per foot

7 3.14 0.643 3.384

7.3 3.19 0.616 3.269

9 3.44 0.500 2.737

9.3 3.47 0.484 2.660

11 3.63 0.409 2.294

4 4.500 11.5 3.67 0.391 2.204

13.5 3.79 0.333 1.906

15.5 3.88 0.290 1.678

17 3.94 0.265 1.540

21 4.05 0.214 1.262

26 4.13 0.173 1.030

32.5 4.21 0.138 0.831

7 3.88 0.795 5.172

7.3 3.95 0.762 4.996

9 4.25 0.618 4.182

9.3 4.29 0.598 4.065

11 4.49 0.506 3.505

5 5.563 11.5 4.54 0.484 3.368

13.5 4.69 0.412 2.912

15.5 4.80 0.359 2.564

17 4.87 0.327 2.353

21 5.00 0.265 1.929

26 5.11 0.214 1.574

32.5 5.20 0.171 1.270

7 4.62 0.946 7.336

7.3 4.70 0.908 7.086

9 5.06 0.736 5.932

9.3 5.11 0.712 5.765

11 5.35 0.602 4.971

6 6.625 11.5 5.40 0.576 4.777

13.5 5.58 0.491 4.130

15.5 5.72 0.427 3.637

17 5.80 0.390 3.338

21 5.96 0.315 2.736

26 6.08 0.255 2.233

32.5 6.19 0.204 1.801

Attachment 1 cont.

Page 18


OD

Pipe inside

diameter (d)

Minimum Wall

Thickness (t)

Weight (w)

Nominal in.

Actual in.

DR

in.

in.

lb. per foot

7 6.01 1.232 12.433

7.3 6.12 1.182 12.010

9 6.59 0.958 10.054

9.3 6.66 0.927 9.771

11 6.96 0.784 8.425

8 8.625 11.5 7.04 0.750 8.096

13.5 7.27 0.639 7.001

15.5 7.45 0.556 6.164

17 7.55 0.507 5.657

21 7.75 0.411 4.637

26 7.92 0.332 3.784

7 7.49 1.536 19.314

7.3 7.63 1.473 18.656

9 8.22 1.194 15.618

9.3 8.30 1.156 15.179

11 8.68 0.977 13.089

10 10.750 11.5 8.77 0.935 12.578

13.5 9.06 0.796 10.875

15.5 9.28 0.694 9.576

17 9.41 0.632 8.788

21 9.66 0.512 7.204

26 9.87 0.413 5.878

32.5 10.05 0.331 4.742

7 8.89 1.821 27.170

7.3 9.05 1.747 26.244

9 9.75 1.417 21.970

9.3 9.84 1.371 21.353

11 10.29 1.159 18.412

12 12.750 11.5 10.40 1.109 17.693

13.5 10.75 0.944 15.298

15.5 11.01 0.823 13.471

17 11.16 0.750 12.362

21 11.46 0.607 10.134

26 11.71 0.490 8.269

32.5 11.92 0.392 6.671

Attachment 1 cont.

Page 19


OD

Pipe inside

diameter (d)

Minimum Wall

Thickness (t)

Weight (w)

Nominal in.

Actual in.

DR

in.

in.

lb. per foot

7 9.76 2.000 32.758

7.3 9.93 1.918 31.642

9 10.70 1.556 26.489

9.3 10.81 1.505 25.745

11 11.30 1.273 22.199

14 14.000 11.5 11.42 1.217 21.332

13.5 11.80 1.037 18.445

15.5 12.09 0.903 16.242

17 12.25 0.824 14.905

21 12.59 0.667 12.218

26 12.86 0.538 9.970

32.5 13.09 0.431 8.044

7 11.15 2.286 42.786

7.3 11.35 2.192 41.329

9 12.23 1.778 34.598

9.3 12.35 1.720 33.626

11 12.92 1.455 28.994

16 16.000 11.5 13.05 1.391 27.862

13.5 13.49 1.185 24.092

15.5 13.81 1.032 21.214

17 14.00 0.941 19.467

21 14.38 0.762 15.959

26 14.70 0.615 13.022

7 12.55 2.571 54.151

7.3 12.77 2.466 52.307

9 13.76 2.000 43.788

9.3 13.90 1.935 42.558

11 14.53 1.636 36.696

18 18.000 11.5 14.68 1.565 35.263

13.5 15.17 1.333 30.491

15.5 15.54 1.161 26.849

17 15.76 1.059 24.638

21 16.18 0.857 20.198

26 16.53 0.692 16.480

32.5 16.83 0.554 13.296

Attachment 1 cont.

Page 20


OD

Pipe inside

diameter (d)

Minimum Wall

Thickness (t)

Weight (w)

Nominal in.

Actual in.

DR

in.

in.

lb. per foot

7 13.94 2.857 66.853

7.3 14.19 2.740 64.576

9 15.29 2.222 54.059

9.3 15.44 2.151 52.541

11 16.15 1.818 45.304

20 20.000 11.5 16.31 1.739 43.535

13.5 16.86 1.481 37.643

15.5 17.26 1.290 33.146

17 17.51 1.176 30.418

21 17.98 0.952 24.936

26 18.37 0.769 20.346

32.5 18.70 0.615 16.415

9 16.82 2.444 65.412

9.3 16.98 2.366 63.574

11 17.76 2.000 54.818

11.5 17.94 1.913 52.677

22 22.000 13.5 18.55 1.630 45.548

15.5 18.99 1.419 40.107

17 19.26 1.294 36.805

21 19.78 1.048 30.172

26 20.21 0.846 24.619

32.5 20.56 0.677 19.863

9 18.35 2.667 77.845

9.3 18.53 2.581 75.658

11 19.37 2.182 65.237

11.5 19.58 2.087 62.690

24 24.000 13.5 20.23 1.778 54.206

15.5 20.72 1.548 47.731

17 21.01 1.412 43.801

21 21.58 1.143 35.907

26 22.04 0.923 29.299

32.5 22.43 0.738 23.638

Attachment 1 cont.

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6

In summary, as pipe diameter increases, less resistance to ring bending is required for the same handling and installation capacity. Useful measures that compare handling and installation capacity without regard to pipe size include AASHTO flexibility factor, FF, and ring stiffness constant, RSC. Pipe stiffness, PS, however, is sensitive to pipe size, and is not useful for comparing the handling and installation capacities between larger and smaller pipes.

STRAIN CAPACITY

When subjected to earth loads, strain in the pipe wall results from deflection and ring compression. If the pipe material has a low tolerance for strain, it is usually necessary to limit strain by limiting pipe deformation.

There are two levels of deformation in buried pipe. One is elliptical deflection due to uniform earth load; the other is a second order deformation from uneven loads around the pipe circumference such as point loads that cause localized deviation from an elliptical shape. Second order deformations are generally small but may induce high strains, and they are directly proportional to the pipe's stiffness. Second-order deformations are of little consequence with strain-tolerant pipes such as HDPE because of the high strain capacity. In an eight-year study of pipes made using pressure-rated HDPE material, Janson reports that for practical design purposes such as for gravity sewers, there does not appear to be an upper limit on design strain [2]. This essentially means that a design for pipes made from pressure-rated grades of HDPE does not need to address strains from second order deformations when overall deflection and buckling are controlled.

BURIED PIPE PERFORMANCE

Buried pipe must possess sufficient stiffness to mobilize backfill soil resistance and resist buckling. Deflection must be limited to a value that will not disrupt flow or cause joint leakage. Extensive field experience with high DR stress-rated HDPE pipes and stress-rated HDPE, profile wall pipes speaks to the capability of low stiffness pipes to perform under soil loads.

Flexible pipe deflection depends on the combined contribution of its pipe stiffness and the embedment soil stiffness (E'), but primarily on embedment soil stiffness. Considerable testing and field measurements have established that for low stiffness pipes, deflection is almost exclusively controlled by the embedment soil surrounding the pipe. This is true for any flexible pipe, whether metal or plastic. Spangler's Iowa formula can be used to demonstrate that the soil's contribution to resisting deflection is much more significant than the pipe's contribution. Although Spangler’s Iowa formula was developed using pipes of 25-psi stiffness and higher, considerable field experience has demonstrated its applicability to low stiffness pipes [3]. For example when pipes of 46 psi PS and 4.6 psi PS are installed with a properly selected and compacted embedment, there is little difference in either pipe’s deflection. On the other hand, when pipe is not installed properly, a low embedment soil E' can result in excessive deflection for both 46 psi and 4.6 psi pipes.. It can be shown mathematically that a 46 psi pipe supplies a stiffness to the soil/pipe system

Attachment 3: From Plastic Pipe Institute TN-19/2010

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Pipe Stress Calculations - State of · PDF file< 10 > Where: E S = secant modulus of the granular drainage layer, psi = 3,978 M S = one-dimensional modulus, (for 90% standard proctor