handbook of pvc pipe chap8.pdf

8/10/2019 Handbook of PVC pipe Chap8.pdf

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CHAPTER VIII - SPECIAL DESIGN APPLICATIONS

CHAPTER VIII

S P E C I A L D E S I G N A P P L I C A T I O N S

Summary of Recommendations, Relationships and

Data Essential to the Design of PVC Piping Systems

Relative to:

Longitudinal Bending

Support Spacing

Thermal Expansion and Contraction

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HANDBOOK OF PVC PIPE

CHAPTER VIII

SPECIAL DESIGN APPLICATIONS

LONGITUDINAL BENDING

The response of PVC pipe to longitudinal bending is considered a

significant advantage of PVC pipe in buried applications. Longitudinal

bending may be done deliberately in PVC pipe installations to make

changes in alignment to avoid obstructions, or it may also occur in

response to various unplanned conditions or unforeseen changes in

conditions in the pipe-soil system such as:- Differential settlement of a manhole, valve or structure to which the

pipe is rigidly connected.

- Uneven settlement of the pipe bedding.

- Ground movement associated with tidal or ground water conditions.

- Erosion of bedding or foundation material due to pipeline leakage.

- Seasonal variation in soil conditions due to changes in moisture

content (limited to expansive or organic soils).

- Improper installation procedures, e.g., non-uniform foundation,unstable bedding, inadequate embedment consolidation.

- Seismic activity.

Through longitudinal bending, PVC pipe provides the ability to

deform or bend and move away from external load concentrations. The

use of flexible joints also enhances a pipe's ability to yield to these forces,

thereby reducing risk of damage or failure. Good engineering design and

proper installation will eliminate longitudinal bending of PVC pipe from

being a critical design consideration.Allowable Longitudinal Bending: When installing PVC pipe, some

changes in direction may be necessary which can be accomplished without

the use of elbows, sweeps, or other direction-changing fittings. Controlled

longitudinal bending, within acceptable limits, can be properly

accommodated by PVC pipe.

Depending upon individual joint design, some amount of axial joint

deflection may be possible in gasketed PVC pipe joints. The pipe

manufacturer should be contacted for allowable joint deflection

recommendations. Additional joint deflection may be possible in

specially designed gasketed joints. Solvent cemented joints allow for no

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axial joint deflection. When applying joint deflection to achieve a change

in system alignment, the pipe barrel should not be bent intentionally.

For pressurized tubes, mathematical relationships for longitudinal

bending have been derived by Reissner.2 These relationships compare

favorably to those of Timoshenko6 and others. One critical limit to

bending of PVC pipe is long-term flexural stress. Axial bending can also

cause a very small amount of ovalization or diametric deflection of the

pipe.

PVC pipe has short-term strengths of 7,000 to 8,000 lbs/in2(48.26 to

55.16 MPa) in tension and 11,000 to 15,000 lbs/in2(75.84 to 103.42 MPa)

in flexure. The long-term strength of PVC pressure pipe in either tension,compression, or flexure can conservatively be assumed as equal to the

hydrostatic design basis (HDB) of 4,000 lbs/in2(27.58 MPa). Applying a

2:1 safety factor results in an allowable long-term tensile or flexural stress

equal to the recommended hydrostatic design stress (S) of 2,000 lbs/in2

(13.79 MPa) for PVC pipe at 73.4o

F (23o

C). This 2,000 lbs/in2 (13.79

MPa) allowable long-term flexural stress may be used for gasketed joint

pipe. That is because the very slight longitudinal strain that occurs in

PVC pipe when it is pressurized is absorbed harmlessly at the joint. Inrestrained-joint pipelines (using solvent-cemented joints, for example) the

longitudinal strain results in a longitudinal stress with a value of one-half

the hoop stress. Therefore, the available conservative tensile stress for

bending is 2,000 - (2,000/2) = 1,000 lbs/in2 (6.89 MPa) in a restrained-

joint system.

From this rationale the equation for allowable bending stress (Sb) is:

EQUATION 8.1

Sb= (HDB - St)T

F

Where: HDB = hydrostatic design basis, lbs/in2(4,000 for PVC)

St = HDB/2 = tensile stress from longitudinal thrust,

lbs/in2

F = safety factor (2.0 for pressure rated pipe or non-pressure pipe, and 2.5 for pressure class pipe)

T = thermal de-rating factor (See Chapter V Table

5.1.)

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Note: The longitudinal stress from thermal expansion and

contraction can be ignored in buried gasketed-joint PVC piping

due to the gasketed-joints ability to accommodate these changes.

Longitudinal thermal stresses should be considered in restrained

pipes such as lines with solvent-cemented joints and restrained

supported piping.

These stresses in restrained-joint piping systems should be considered

using the following equation:

EQUATION 8.2

S = ECT(t1-t0)

Where: S = stress, lbs/in2

E = modulus of tensile elasticity, lbs/in2

CT= coefficient of thermal expansion, in/in/oF

t1 = highest pipe wall temperature,oF

t0 = lowest pipe wall temperature,o

F

Using Equation 8.1, the maximum allowable bending stresses (Sb) for

PVC pipe at 73.4o

F (23o

C) are given in Table 8.1. The mathematical

relationship between stress and the moment induced by longitudinal

bending of pipes is:

EQUATION 8.3

M =SbI

c

Where: M = bending moment, in-lbs

Sb = allowable bending stress, lbs/in2(See Table 8.1.)

c = Do/2 = distance from extreme fiber to neutral axis, in

I = moment of inertia, in

4

(See Equation 8.4.)

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TABLE 8.1

ALLOWABLE BENDING STRESSES AT 73.4F

Pressure Class Pipe =

4000 -4000

21.0

2.5 = 800 lbs/in

2(5.52 MPa)

Pressure Rated Pipe =

4000 -4000

21.0

2.0 = 1000 lbs/in

2(6.89 MPa)

Note: Difference between allowable bending stresses for Pressure Class and Pressure

Rated Pipe relates to difference in selected factors of safety. The allowable bending

stresses above are based on restrained-joint systems and are, therefore, conservative forgasketed pressure pipe.

Non-Pressure Pipe

PVC 12454 = [ ]4000 - 01.0

2.0 = 2000 lbs/in

2(13.79 MPa)

PVC 12364 = [3200 - 0]1.0

2.0= 1600 lbs/in

2(11.72 MPa)

EQUATION 8.4

I =

64(Do4- Di4) = 0.0491 (Do4- Di4)

Where: I = moment of inertia, in4

Do = average outside diameter, inDi = average inside diameter, in

= Do- 2t avg, where:

tavg = tmin+ 6% tmin= average wall thickness, in

tmin = minimum wall thickness, in

Note: This equation does not apply to profile wall products. Due to

their complex geometry, the manufacturer should be consulted

for the appropriate values of Ior the allowable bending radius.

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Assuming that the bent length of pipe conforms to a circular arc after

backfilling and installation, the minimum radius in inches of the bending

circle (Rb) can be found by Timoshenko's equation:

EQUATION 8.5

Rb=EI

M

Figure 8.1 describes the variables in the following equations. Combining

Equations 8.3 and 8.5 gives:

EQUATION 8.6

Rb=E Do2 Sb

The central angle () subtended by the length of pipe (L) is:

EQUATION 8.7

=bR2

360L

=57.30L

Rb

Where: L and Rbhave the same units of length, and the angle of

lateral deflection (a) of the curved pipe from a tangent to

the circle is:

EQUATION 8.8

a =

/2, degrees

The distance offset at the end of the pipe from the tangent to the circle

is defined in the equation below:

EQUATION 8.9

A = 2Rb(sin2/2 = 2Rb(sin2a)

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Assuming that during installation the pipe is temporarily fixed at one

end and acts as a cantilevered beam, then the lateral force required at the

free end to achieve the offset (A) may be determined by the equation:

EQUATION 8.10

P =3EIA

L3

Where: P = lateral offset force, lbs

E = modulus of tensile elasticity, lbs/in2*

I = moment of inertia, in4

(See Equation 8.4.)A = offset at free end, in

L = pipe length, in

*Note: E will change with temperature (refer to Chapter VII).

Longitudinal bending of PVC pipe without allowance for joint

deflection should not exceed limits given in Tables 8.2 through 8.4. In the

tables, limits of longitudinal bending are expressed for appropriate pipe

lengths as follows:- Maximum bend allowable defined in terms of minimum bending

radius, Rb

- Maximum pipe end offset from the tangent to the circle, A

- Angle of longitudinal deflection from a circular tangent by pipe

bending, a

- Lateral offset force to effect bending, P

The mathematical relationship between the bending deflection angle

(a), the offset (A), the lateral offset force (P), and the minimum bending

radius (Rb) are defined in Figure 8.1. Longitudinal bending limits given

in Tables 8.2 through 8.4 are calculated without allowance for joint

deflection and without consideration of the stresses imposed upon the joint.

Because of the characteristics of a particular joint design, it is possible that a

manufacturer's recommended bending radius may be greater or lesser than

those tabulated. Profile-wall pipes may not duplicate the longitudinal

bending performance of solid-wall PVC pipes. Pipes with an open profiletypically can be bent to the same radii as solid wall pipes with a similar pipe

stiffness. However, the load (P) may be lower. Pipes with a closed profile

typically are limited to larger bending radii. The pipe manufacturer should

be consulted for specific recommendations and limits.

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FIGURE 8.1

PVC PIPE ALLOWABLE BEND

CALCULATIONS MADE AT 73o F (23o C)

(EQUATION 8.3) EQUATION 8.11

M =SbI

c L =

Rb90

a


=360L

2Rbd = Rbcos /2


a= /2 Y = Rb- d


A = 2Rb(sin2/2) = C = 2Rbsin /2 L

Csin /2 = L tan a

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Load application at 73F (23C) required to effect maximum allowable

longitudinal bending in PVC pipe is given in Tables 8.2 through 8.4.

Longitudinal bending of PVC pipe effected through mechanical means must

be controlled to prevent excessive loading of the pipe. In many cases,

bending of PVC pipe can and should be accomplished manually.

When longitudinally bending PVC pipe, the joint shall be blocked or

braced to ensure straight alignment of the joint and to prevent axial

deflection in the gasketed or mechanical joint. Excessive axial-joint

deflection may result in damaging stresses or leakage. If bending

requirements are followed, diameters larger than those shown in Tables

8.2 through 8.4 may be longitudinally bent; however, the forces requiredshould be considered.

When the desired change of direction in a PVC pipeline exceeds the

permissible bending deflection angle () for a given length of pipe, the

longitudinal bending required should be distributed through a number of

pipe lengths. Calculation of required distribution of longitudinal bending

in PVC pipe is demonstrated in the following example.

Example: Calculate the number of pieces of pipe and the total offset,A, required to achieve a 10 change in pipeline direction using only

longitudinal bending of the pipe barrel.

- Pipeline using AWWA C900 8-in PVC DR 18 pipe in 20 ft lengths

See Figure 8.1 and Table 8.2

Rb= 2260 in or 188 ft

Circumference = 2Rb= 2(3.14)(188) = 1181 ftL= (1181)(10 /360) = 33 ft

20 ft < 33 ft < 40 ft

Use 2 each 8-in x 20-ft lengthsL= 2 x 20-ft = 40 ft

- Resultant total offset for the pipeline over 2 pipe lengths:

Assume: LCThen using Equation 8.9:

A = Csin /2= 40 sin (10 /2)

= 40 (.087) = 3.5 ft

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TABLE 8.3

ALLOWABLE LONGITUDINAL BENDING

FOR PRESSURE RATED PIPE (ASTM D 2241, DR = 21, 26, 32.5)IN 20 FOOT LENGTHS

(Sb= 1000 lbs/in2, E = 400,000 lbs/in

2)

Nominal Size,

in1.5 2 2.5 3 4

DR 21

Do, in 1.900 2.375 2.875 3.500 4.500

tnom, in 0.096 0.120 0.145 0.177 0.227

Di, in 1.71 2.14 2.58 3.15 4.05

I, in4 0.221 0.540 1.161 2.55 6.97

M, in-lbs 233 455 807 1,460 3,100

Rb, in (min) 380 475 575 700 900

Rb, ft (min) 31.7 39.6 47.9 58.3 75.0

,degrees 36.2 29.0 23.9 19.6 15.3

adegrees 18.1 14.5 12.0 9.8 7.6

A, in 73 59 49 41 32

P, lbs 1.4 2.8 5.0 9.0 19

RatioRb/Do 200 200 200 200 200

DR 26Do, in 1.900 2.375 2.875 3.500 4.500

tnom, in 0.077 0.097 0.117 0.143 0.183

Di, in 1.75 2.18 2.64 3.21 4.13

I, in4 0.18 0.45 0.97 2.12 5.79

M, in-lbs 194 379 672 1,210 2,580

Rb, in (min) 380 475 575 700 900

Rb, ft (min) 31.7 39.6 47.9 58.3 75.0

,

degrees 36.2 29.0 23.9 19.6 15.3

adegrees 18.1 14.5 12.0 9.8 7.6

A, in 73 59 49 41 32

P, lbs 1.2 2.3 4.1 7.5 16RatioRb/Do 200 200 200 200 200

DR 32.5

Do, in 1.900 2.375 2.875 3.500 4.500

tnom, in 0.062 0.077 0.094 0.114 0.147

Di, in 1.78 2.22 2.69 3.27 4.21

I, in4 0.15 0.37 0.79 1.74 4.75

M, in-lbs 159 310 551 990 2,110

Rb, in (min) 380 475 575 700 900

Rb, ft (min) 31.7 39.6 47.9 58.3 75.0

,

degrees 36.2 29.0 23.9 19.6 15.3

adegrees 18.1 14.5 12.0 9.8 7.6

A, in 73 59 49 41 32

P, lbs 1.0 1.9 3.4 6.1 13

RatioRb/Do 200 200 200 200 200

Note: Larger diameters of pressure rated pipe are shown on the next page.

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TABLE 8.3 (continued)


FOR PRESSURE RATED PIPE (ASTM D 2241, DR = 21, 26, 32.5)IN 20 FOOT LENGTHS

(Sb= 1000 lbs/in2, E = 400,000 lbs/in

2)

Nominal Size,

in5 6 8 10 12

DR 21Do, in 5.563 6.625 8.625 10.750 12.750

tnom, in 0.281 0.334 0.435 0.543 0.644

Di, in 5.00 5.96 7.75 9.66 11.46I, in4 16.27 32.7 94.0 227 449

M, in-lbs 5,850 9,880 21,800 42,200 70,400

Rb, in (min) 1110 1330 1730 2150 2550

Rb, ft (min) 92.5 111 144 179 213

,degrees 12.4 10.3 7.9 6.4 5.4

adegrees 6.2 5.2 4.0 3.2 2.7

A, in 26 22 17 13 11

P, lbs 36 61 140 260 440

RatioRb/Do 200 200 200 200 200

DR 26

Do, in 5.563 6.625 8.625 10.750 12.750tnom, in 0.227 0.270 0.352 0.438 0.520

Di, in 5.11 6.08 7.92 9.87 11.71

I, in4 13.5 27.2 78.2 189 373

M, in-lbs 4,870 8,220 18,100 35,100 58,600

Rb, in (min) 1110 1330 1730 2150 2550

Rb, ft (min) 92.5 111 144 179 213

,

degrees 12.4 10.3 7.9 6.4 5.4

adegrees 6.2 5.2 4.0 3.2 2.7

A, in 26 22 17 13 11

P, lbs 30 51 110 220 370

RatioRb/Do 200 200 200 200 200DR 32.5

Do, in 5.563 6.625 8.625 10.750 12.750

tnom, in 0.181 0.216 0.281 0.351 0.416

Di, in 5.20 6.19 8.06 10.05 11.92

I, in4 11.10 22.3 64.1 155 306

M, in-lbs 3,990 6,740 14,900 28,800 48,000

Rb, in (min) 1110 1330 1730 2150 2550

Rb, ft (min) 92.5 111 144 179 213

,degrees 12.4 10.3 7.9 6.4 5.4

adegrees 6.2 5.2 4.0 3.2 2.7

A, in 26 22 16.6 13.4 11.3P, lbs 25 42 93 180 300

RatioRb/Do 200 200 200 200 200

Note: The larger diameters of pressure rated pipe are not shown because the large forces involved

make longitudinal bending impractical. The allowable bending stresses above are based on

restrained joint systems and are, therefore, conservative for gasketed pressure pipe.

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FOR PRESSURE RATED PIPE (ASTM D 2241, DR = 41)IN 20 FOOT LENGTHS

(Sb= 1000 lbs/in2, E = 400,000 lbs/in

2)

Nominal Size,

in3 4 5 6

DR 41Do, in 3.500 4.500 5.563 6.625

tnom, in 0.090 0.116 0.144 0.171

Di, in 3.32 4.27 5.28 6.28I, in4 1.41 3.84 8.98 18.1

M, in-lbs 800 1,710 3,230 5,450

Rb, in (min) 700 900 1110 1330

Rb, ft (min) 58.3 75.0 92.5 111

,

degrees 12.9 10.0 8.1 6.8

adegrees 6.4 5.0 4.1 3.4

A, in 18 14 11 9.3

P, lbs 2.2 4.6 8.7 15

RatioRb/Do 200 200 200 200

Nominal Size,

in8 10 12

DR 41Do, in 8.625 10.750 12.750

tnom, in 0.223 0.278 0.330

Di, in 8.18 10.19 12.09

I, in4 51.9 125 248

M, in-lbs 12,000 23,300 38,900

Rb, in (min) 1730 2150 2550

Rb, ft (min) 144 179 213

,

degrees 5.2 4.2 3.5adegrees 2.6 2.1 1.8

A, in 7.2 5.8 4.9

P, lbs 32 63 105

RatioRb/Do 200 200 200

Note: The larger diameters of pressure rated pipe are not shown because the large forces involved

make longitudinal bending impractical. The allowable bending stresses above are based on

restrained joint systems and are, therefore, conservative for gasketed pressure pipe.

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TABLE 8.4

ALLOWABLE LONGITUDINAL BENDING FOR DR 35

SEWER PIPE IN 13 AND 20 FOOT LENGTHS

(Sb= 1,600 lbs/in2, E = 500,000 lbs/in

2)

Nominal Size,

in4 6 8 10 12 15

13 LengthsDo, in 4.215 6.275 8.400 10.500 12.500 15.300

tnom, in 0.128 0.190 0.254 0.318 0.379 0.463

Di, in 3.96 5.89 7.89 9.86 11.74 14.374

I, in4 3.42 16.8 54.0 132 265 594.4

M, in-lbs 2,600 8,570 20,600 40,100 67,700 124,317

Rb, in (min) 659 980 1310 1640 1950 2,391

Rb, ft (min) 54.9 81.7 109 137 163 199.0

,degrees 13.6 9.1 6.8 5.5 4.6 3.6

adegrees 6.8 4.6 3.4 2.7 2.3 1.8

A, in 18 12 9 7 6 5

P, lbs 25 82 200 390 650 1,330

RatioRb/Do 156 156 156 156 156 156

20 Lengths

Do, in 4.215 6.275 8.400 10.500 12.500 15.300tnom, in 0.128 0.190 0.254 0.318 0.379 0.463

Di, in 3.96 5.89 7.89 9.86 11.74 14.374

I, in4 3.42 16.8 54.0 132 265 594.4

M, in-lbs 2,600 8,570 20,600 40,100 67,700 124,317

Rb, in (min) 659 980 1310 1640 1950 2,391

Rb, ft (min) 54.9 81.7 109 137 163 199.0

,degrees 20.9 14.0 10.5 8.4 7.1 5.8

adegrees 10.4 7.0 5.2 4.2 3.5 2.9

A, in 43 29 22 18 15 12

P, lbs 16 53 130 250 420 780

RatioRb/Do 156 156 156 156 156 156

Note: The larger diameters of DR 35 sewer pipe are not shown because the large forces involved

make longitudinal bending impractical. The values shown are conservative for sewer pipes

manufactured with lower modulus materials.

When longitudinal bending of the PVC pipe barrel is not practical,

such as in large diameter pipelines, axial deflection in the pipe-joints may

be possible. Contact the pipe manufacturer for joint-deflection

recommendations. The recommended axial joint-deflection is representedby in Figure 8.2.

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FIGURE 8.2

COMPOUND CURVILINEAR ALIGNMENT FROM

BENDING MULTIPLE PIPES

The radius of curvature,

Rbis related to

(the jointdeflection):

Performance Limits in Longitudinal Bending: The performance

limits for permanent longitudinal bending in a buried PVC pipe

application must not be confused with the coiling limits established for

temporary coiled storage where the bending stress approaches the short-

term tensile stress. (See Table 8.5 - Longitudinal Bending Stress and

Strain.) Coiling of unplasticized PVC pipe is not a common practice, but

may be permissible for small diameters where the minimum bending

radius ratio (Rb/Do) is not less than 25 and the bending strain (

b) is notgreater than 0.020 inches per inch.

Bending Strain. Longitudinal bending strain (b) and longitudinal

bending stress (Sb) for PVC pipe at different degrees of axial flexure are

tabulated in Table 8.5 from Equation 8.15. The bending stresses

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291

calculated are the initial stresses, which decrease over time when the strain

stays constant.

EQUATION 8.15

b= Sb/E = Do/2Rb

Where: Sb = bending stress, lbs/in2

E = modulus of tensile elasticity, lbs/in2

Do = outside diameter, in

Rb = bending radius, in

TABLE 8.5

LONGITUDINAL BENDING STRESS AND STRAIN IN PVC PIPE

Bending Radius Bending Strain Bending Stress, Sb(lbs/in2)

Ratio, Rb/Do b, (in/in) E = 400,000 E = 440,000 E = 500,000

25 0.0200 8,000 8,800 10,000

50 0.0100 4,000 4,400 5,000

100 0.0050 2,000 2,200 2,500200 0.0025 1,000 1,100 1,250

250 0.0020 800 880 1,000

300 0.0017 667 748 833

500 0.0010 400 440 500

Bending Ovalization (diametric or ring deflection). As a thin tube is

bent longitudinally, it will ovalize into an approximately elliptical shape.

This effect has been ignored as insignificant in previous calculations onlongitudinal bending. Ring deflection is usually expressed as:

EQUATION 8.16

Deflection = =D

Y or

EQUATION 8.17

% Deflection = 100= 100D

Y


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Where: Y = the reduction in outside diameter, inD = original pipe outside diameter, in

For thin pressurized tubes, the mathematical relationship between ring

deflection and axial bending has been derived by E. Reissner as follows:

EQUATION 8.18

=D

Y= (A1 a2)

2

3+

71 + 4

135 + 9

(A1a2)

with and (A1a2) defined as:

EQUATION 8.19

=

12(1 - v2)PDm3

8Et3

EQUATION 8.20

(A1 a2) =1

16

18(1 - v2)

12 + 4

Dm4

R2t2

Where: Dm = mean pipe diameter, in

v = Poisson's Ratio (0.38 for PVC)P = internal pipe pressure, lbs/in2(gauge)

E = modulus of elasticity, lbs/in2

t = pipe wall thickness, in (use tnom= 1.06 x tmin)

R = bending radius of pipe, in

Example: Calculate the percent ring deflection which results from

bending a 15" DR 35 PVC sewer pipe with a 400,000 lbs/in2

modulus ofelasticity to a minimum bending radius of 156 times the pipe diameter, as

shown in Table 8.4.

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Since P= 0, = 0 for sewer pipe and:

(A1 a2) =1

16

18(1 - 0.382)

12 + 4 Dm4

R2t2

=1

16

86.0

12

18

(15.3 - 0.463)4

(2387)2(0.463)2

=(0.214)105.597

60)0.080(48,46

= 0.00324

= 0.00324

++

+ )00324.0(0135

071

3

2

= 0.00324 [0.667 + 0.00170] = 0.002

= 0.2% ring deflection

Example: Calculate the percent ring deflection after pressurization to

100 lbs/in2which results from bending a 4" DR 14 PVC pressure pipe to a

minimum bending radius of 250 times the diameter, as shown in Table

8.2.

=12(1 - 0.382) 100 (4.800 - 0.364)3

8 (400,000)(0.364)3

=)0482.0(000,200,3

)29.87)(86.0(1200 = 0.584

(A1a2) = 116 18 (1 - 0.382

)12 + 4 (0.581) (4.800 - 0.364)

4

(1,200)2(0.364)2

=1

16

+

32.212

86.018

)132.0)(000,440,1(

2.387

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294

= 0.000138

= 0.000138

+

++

000138.0)584.0(9135

)584.0(471

3

2

= 0.000138

+ 000722.0

3

2

= 0.000092

= 0.009% ring deflection

From an analysis of the above examples, it has been determined that at

the recommended maximum bending (minimum bending radius) for 4" to

15" PVC pressure pipes and non-pressure pipes, a close approximation of

deflection can be calculated from the equation:

EQUATION 8.21

=mD

Y=

2

3(A1 a2) =

(1 - v2)Dm4

16R2t2

Where: = ring deflectionv = Poisson's Ratio (0.38 for PVC)

Dm = mean pipe diameter, inR = bending radius of pipe, in

t = pipe wall thickness, in (use tnom= 1.06 x tmin)

Analysis of these relationships also establishes that the amount of

deflection resulting from bending is negligible in the case of pressure

pipes, and the amount has very little significance in the case of non-

pressure pipes. Generally, at bending radii of 300 times the diameter, the

percent diametric ring deflection from bending will be less than 0.06percent for all PVC pipes marketed today in North America.


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SUPPORT SPACING

PVC pipe, when installed without uniform longitudinal support as

provided in a properly bedded underground application, requires supports

with proper spacing. In various above-ground applications, PVC pipe is

suspended on "hangers" or "brackets." Proper bearing and spacing of pipe

supports in such an application is required to prevent excessive stress

concentration due to load bearing, to prevent excessive bending stress, and

to limit pipe displacement or "sag" between supports to acceptable

tolerances. Recommended support spacing or length of pipe spanning

between supports for PVC pipe in above-ground applications is shown in

Table 8.6.

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TABLE 8.6

SUPPORT SPACING FOR SUSPENDED HORIZONTAL

PVC PIPE FILLED WITH WATER

Note: Support spacing recommendations shown in Table 8.6 are based on the following design

limitations:

1. Initial pipe vertical displacement (sag) limited to 0.2 percent of span length based on

calculations using Equation 8.22, so that long-term sag is limited to approximately 0.5

percent.

2. Pipe bending stress values limited to values defined in Table 8.1.

3. All calculated values greater than 20.0 have been reduced to 20.0, which is the

maximum length for gasketed PVC pipe.

Nominal Tensile PVC Pipe Support Spacing, ft (m)

Pipe Size Product Dimension Modulus

(in) Standard Ratio (lbs/in2) 73.4oF (23

oC) 120

oF (49

oC) 140

oF (60

oC)

4 AWWA C900 14 400,000 8.3 (2.5) 7.7 (2.3) 7.4 (2.2)4 AWWA C900 18 400,000 7.8 (2.3) 7.3 (2.2) 7.0 (2.1)4 AWWA C900 25 400,000 7.2 (2.1) 6.7 (2.0) 6.4 (1.9)6 AWWA C900 14 400,000 10.6 (3.2) 9.9 (3.0) 9.4 (2.8)6 AWWA C900 18 400,000 10.0 (3.0) 9.3 (2.8) 8.9 (2.7)6 AWWA C900 25 400,000 9.2 (2.8) 8.5 (2.5) 8.1 (2.4)8 AWWA C900 14 400,000 12.8 (3.9) 11.8 (3.5) 11.3 (3.4)8 AWWA C900 18 400,000 12.0 (3.6) 11.1 (3.3) 10.6 (3.2)8 AWWA C900 25 400,000 11.0 (3.3) 10.2 (3.1) 9.8 (2.9)

10 AWWA C900 14 400,000 14.6 (4.4) 13.6 (4.1) 13.0 (3.9)10 AWWA C900 18 400,000 13.8 (4.2) 12.8 (3.9) 12.2 (3.7)10 AWWA C900 25 400,000 12.6 (3.8) 11.7 (3.5) 11.2 (3.4)12 AWWA C900 14 400,000 16.4 (4.9) 15.2 (4.6) 14.6 (4.4)12 AWWA C900 18 400,000 15.4 (4.6) 14.3 (4.3) 13.7 (4.1)12 AWWA C900 25 400,000 14.2 (4.3) 13.1 (3.9) 12.6 (3.8)

14 AWWA C905 18 400,000 17.3 (5.3) 16.0 (4.9) 15.3 (4.7)14 AWWA C905 21 400,000 16.7 (5.1) 15.4 (4.7) 14.8 (4.5)14 AWWA C905 25 400,000 15.8 (4.8) 14.7 (4.5) 14.1 (4.3)14 AWWA C905 32.5 400,000 14.7 (4.5) 13.6 (4.2) 13.1 (4.0)14 AWWA C905 41 400,000 13.8 (4.2) 12.8 (3.9) 12.3 (3.7)16 AWWA C905 18 400,000 18.8 (5.7) 17.4 (5.3) 16.7 (5.1)16 AWWA C905 21 400,000 18.2 (5.5) 16.8 (5.1) 16.1 (4.9)16 AWWA C905 25 400,000 17.3 (5.3) 16.0 (4.9) 15.3 (4.7)16 AWWA C905 32.5 400,000 16.1 (4.9) 14.8 (4.5) 14.3 (4.3)16 AWWA C905 41 400,000 15.0 (4.6) 13.9 (4.2) 13.4 (4.1)18 AWWA C905 18 400,000 20.0 (6.1) 18.8 (5.7) 18.0 (5.5)

18 AWWA C905 21 400,000 19.5 (5.9) 18.0 (5.5) 17.3 (5.3)18 AWWA C905 25 400,000 18.6 (5.7) 17.2 (5.3) 16.5 (5.0)18 AWWA C905 32.5 400,000 17.3 (5.3) 16.0 (4.9) 15.4 (4.7)18 AWWA C905 41 400,000 16.2 (4.9) 15.0 (4.6) 14.4 (4.4)18 AWWA C905 51 400,000 15.3 (4.6) 14.1 (4.3) 13.5 (4.1)20 AWWA C905 18 400,000 20.0 (6.1) 20.0 (6.1) 19.3 (5.9)

296


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(in) Standard Ratio (lbs/in2) 73.4oF (23oC) 120oF (49oC) 140oF (60oC)

20 AWWA C905 21 400,000 20.0 (6.1) 19.3 (5.9) 18.5 (5.7)20 AWWA C905 25 400,000 19.9 (6.1) 18.4 (5.6) 17.7 (5.4)20 AWWA C905 32.5 400,000 17.3 (5.3) 16.0 (4.9) 15.4 (4.7)20 AWWA C905 41 400,000 17.4 (5.3) 16.1 (4.9) 15.4 (4.7)20 AWWA C905 51 400,000 16.4 (5.0) 15.1 (4.6) 14.5 (4.4)24 AWWA C905 18 400,000 20.0 (6.1) 20.0 (6.1) 20.0 (6.1)24 AWWA C905 21 400,000 20.0 (6.1) 20.0 (6.1) 20.0 (6.1)24 AWWA C905 25 400,000 20.0 (6.1) 20.0 (6.1) 19.9 (6.1)24 AWWA C905 32.5 400,000 20.0 (6.1) 19.3 (5.9) 18.5 (5.6)24 AWWA C905 41 400,000 19.6 (6.0) 18.1 (5.5) 17.4 (5.3)24 AWWA C905 51 400,000 18.4 (5.6) 17.0 (5.2) 16.3 (5.0)30 AWWA C905 21 400,000 20.0 (6.1) 20.0 (6.1) 20.0 (6.1)30 AWWA C905 25 400,000 20.0 (6.1) 20.0 (6.1) 20.0 (6.1)30 AWWA C905 32.5 400,000 20.0 (6.1) 20.0 (6.1) 20.0 (6.1)30 AWWA C905 41 400,000 20.0 (6.1) 20.0 (6.1) 20.0 (6.1)30 AWWA C905 51 400,000 20.0 (6.1) 19.7 (6.0) 18.9 (5.7)36 AWWA C905 21 400,000 20.0 (6.1) 20.0 (6.1) 20.0 (6.1)36 AWWA C905 25 400,000 20.0 (6.1) 20.0 (6.1) 20.0 (6.1)36 AWWA C905 32.5 400,000 20.0 (6.1) 20.0 (6.1) 20.0 (6.1)36 AWWA C905 41 400,000 20.0 (6.1) 20.0 (6.1) 20.0 (6.1)36 AWWA C905 51 400,000 20.0 (6.1) 20.0 (6.1) 20.0 (6.1)42 AWWA C905 25 400,000 20.0 (6.1) 20.0 (6.1) 20.0 (6.1)42 AWWA C905 32.5 400,000 20.0 (6.1) 20.0 (6.1) 20.0 (6.1)42 AWWA C905 41 400,000 20.0 (6.1) 20.0 (6.1) 20.0 (6.1)42 AWWA C905 51 400,000 20.0 (6.1) 20.0 (6.1) 20.0 (6.1)48 AWWA C905 32.5 400,000 20.0 (6.1) 20.0 (6.1) 20.0 (6.1)48 AWWA C905 41 400,000 20.0 (6.1) 20.0 (6.1) 20.0 (6.1)48 AWWA C905 51 400,000 20.0 (6.1) 20.0 (6.1) 20.0 (6.1)

1.5 ASTM D2241 21 400,000 4.2 (1.3) 3.8 (1.2) 3.7 (1.1)1.5 ASTM D2241 26 400,000 3.9 (1.2) 3.6 (1.1) 3.5 (1.1)2 ASTM D2241 21 400,000 4.8 (1.5) 4.5 (1.4) 4.3 (1.3)2 ASTM D2241 26 400,000 4.6 (1.4) 4.2 (1.3) 4.0 (1.2)

2.5 ASTM D2241 21 400,000 5.5 (1.7) 5.1 (1.5) 4.9 (1.5)2.5 ASTM D2241 26 400,000 5.2 (1.6) 4.8 (1.5) 4.6 (1.4)3 ASTM D2241 21 400,000 6.3 (1.9) 5.8 (1.8) 5.6 (1.7)3 ASTM D2241 26 400,000 5.9 (1.8) 5.5 (1.7) 5.2 (1.6)4 ASTM D2241 21 400,000 7.4 (2.3) 6.8 (2.1) 6.6 (2.0)4 ASTM D2241 26 400,000 7.0 (2.1) 6.5 (2.0) 6.2 (1.9)5 ASTM D2241 21 400,000 8.5 (2.6) 7.9 (2.4) 7.6 (2.3)5 ASTM D2241 26 400,000 8.0 (2.5) 7.4 (2.3) 7.1 (2.2)6 ASTM D2241 21 400,000 9.6 (2.9) 8.8 (2.7) 8.5 (2.6)6 ASTM D2241 26 400,000 9.0 (2.8) 8.4 (2.5) 8.0 (2.4)8 ASTM D2241 21 400,000 11.4 (3.5) 10.5 (3.2) 10.1 (3.1)8 ASTM D2241 26 400,000 10.8 (3.3) 10.0 (3.0) 9.6 (2.9)

8 ASTM D2241 32.5 400,000 10.1 (3.1) 9.4 (2.9) 9.0 (2.7)8 ASTM D2241 41 400,000 9.5 (2.9) 8.7 (2.7) 8.4 (2.6)10 ASTM D2241 21 400,000 13.2 (4.0) 12.2 (3.7) 11.7 (3.6)10 ASTM D2241 26 400,000 12.5 (3.8) 11.5 (3.5) 11.1 (3.4)10 ASTM D2241 32.5 400,000 11.7 (3.6) 10.8 (3.3) 10.4 (3.2)10 ASTM D2241 41 400,000 11.0 (3.3) 10.1 (3.1) 9.7 (3.0)12 ASTM D2241 21 400,000 14.8 (4.5) 13.7 (4.2) 13.1 (4.0)

297


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(in) Standard Ratio (lbs/in2) 73.4oF (23oC) 120oF (49oC) 140oF (60oC)

12 ASTM D2241 26 400,000 14.0 (4.3) 12.9 (3.9) 12.4 (3.8)12 ASTM D2241 32.5 400,000 13.1 (4.0) 12.1 (3.7) 11.7 (3.6)12 ASTM D2241 41 400,000 12.3 (3.7) 11.4 (3.5) 10.9 (3.3)14 ASTM D2241 21 400,000 16.5 (4.8) 14.5 (4.4) 13.9 (4.2)14 ASTM D2241 26 400,000 14.8 (4.5) 13.7 (4.2) 13.1 (4.0)14 ASTM D2241 32.5 400,000 13.9 (4.2) 12.8 (3.9) 12.3 (3.8)14 ASTM D2241 41 400,000 13.0 (4.0) 12.0 (3.7) 11.6 (3.5)16 ASTM D2241 21 400,000 17.1 (5.2) 15.8 (4.8) 15.2 (4.6)16 ASTM D2241 26 400,000 16.2 (4.9) 14.9 (4.6) 14.3 (4.4)16 ASTM D2241 32.5 400,000 15.2 (4.6) 14.0 (4.3) 13.5 (4.1)

16 ASTM D2241 41 400,000 14.2 (4.3) 13.2 (4.0) 12.6 (3.9)18 ASTM D2241 21 400,000 18.5 (5.6) 17.1 (5.2) 16.4 (5.0)18 ASTM D2241 26 400,000 17.5 (5.3) 16.3 (4.9) 15.5 (4.7)18 ASTM D2241 32.5 400,000 16.4 (5.0) 15.2 (4.6) 14.6 (4.4)18 ASTM D2241 41 400,000 15.4 (4.7) 14.2 (4.3) 13.7 (4.2)20 ASTM D2241 21 400,000 19.8 (6.0) 18.3 (5.6) 17.6 (5.4)20 ASTM D2241 26 400,000 18.7 (5.7) 17.3 (5.3) 16.6 (5.1)20 ASTM D2241 32.5 400,000 17.6 (5.4) 16.3 (5.0) 15.6 (4.8)20 ASTM D2241 41 400,000 16.5 (5.0) 15.3 (4.7) 14.7 (4.5)24 ASTM D2241 21 400,000 20.0 (6.1) 20.0 (6.1) 19.9 (6.1)24 ASTM D2241 26 400,000 20.0 (6.1) 19.6 (6.0) 18.8 (5.7)24 ASTM D2241 32.5 400,000 19.9 (6.1) 18.4 (5.6) 17.7 (5.4)

24 ASTM D2241 41 400,000 18.6 (5.7) 17.2 (5.3) 16.6 (5.0)

4 ASTM D3034 26 400,000 6.7 (2.0) 6.2 (1.9) 5.9 (1.8)6 ASTM D3034 26 400,000 8.7 (2.7) 8.1 (2.5) 7.7 (2.4)8 ASTM D3034 26 400,000 10.6 (3.2) 9.8 (3.0) 9.4 (2.9)

10 ASTM D3034 26 400,000 12.3 (3.7) 11.4 (3.5) 10.9 (3.3)12 ASTM D3034 26 400,000 13.8 (4.2) 12.8 (3.9) 12.2 (3.7)15 ASTM D3034 26 400,000 15.8 (4.8) 14.6 (4.4) 14.0 (4.3)4 ASTM D3034 35 400,000 6.1 (1.9) 5.7 (1.7) 5.5 (1.7)6 ASTM D3034 35 400,000 8.0 (2.4) 7.4 (2.3) 7.1 (2.2)8 ASTM D3034 35 400,000 9.7 (3.0) 9.0 (2.7) 8.6 (2.6)

10 ASTM D3034 35 400,000 11.3 (3.4) 10.4 (3.2) 10.0 (3.1)

12 ASTM D3034 35 400,000 12.7 (3.9) 11.8 (3.6) 11.3 (3.4)15 ASTM D3034 35 400,000 14.5 (4.4) 13.4 (4.1) 12.9 (3.9)4 ASTM D3034 35 500,000 6.5 (1.9) 6.0 (1.8) 5.7 (1.7)6 ASTM D3034 35 500,000 8.4 (2.5) 7.8 (2.3) 7.5 (2.2)8 ASTM D3034 35 500,000 10.2 (3.1) 9.5 (2.8) 9.1 (2.7)

10 ASTM D3034 35 500,000 11.9 (3.6) 11.0 (3.3) 10.6 (3.2)12 ASTM D3034 35 500,000 13.4 (4.0) 12.4 (3.7) 11.9 (3.6)15 ASTM D3034 35 500,000 15.3 (4.6) 14.2 (4.3) 13.6 (4.1)

18 ASTM F679 T-1 400,000 16.5 (5.0) 15.3 (4.7) 14.7 (4.5)18 ASTM F679 T-2 500,000 17.3 (5.3) 16.0 (4.9) 15.4 (4.7)21 ASTN F679 T-1 400,000 18.4 (5.6) 17.0 (5.2) 16.4 (5.0)

21 ASTM F679 T-2 500,000 19.3 (5.9) 17.9 (5.4) 17.2 (5.2)24 ASTM F679 T-1 400,000 19.9 (6.1) 18.4 (5.6) 17.7 (5.4)24 ASTM F679 T-2 500,000 20.0 (6.1) 19.3 (5.9) 18.6 (5.7)27 ASTM F679 T-1 400,000 20.0 (6.1) 19.9 (6.1) 19.2 (5.8)27 ASTM F679 T-2 500,000 20.0 (6.1) 20.0 (6.1) 20.0 (6.1)

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(in) Standard Ratio (lbs/in2) 73.4oF (23

oC) 120

oF (49

oC) 140

oF (60

oC)

30 ASTM F679 T-1 400,000 20.0 (6.1) 20.0 (6.1) 20.0 (6.1)30 ASTM F679 T-2 500,000 20.0 (6.1) 20.0 (6.1) 20.0 (6.1)33 ASTM F679 T-1 400,000 20.0 (6.1) 20.0 (6.1) 20.0 (6.1)33 ASTM F679 T-2 500,000 20.0 (6.1) 20.0 (6.1) 20.0 (6.1)36 ASTM F679 T-1 400,000 20.0 (6.1) 20.0 (6.1) 20.0 (6.1)36 ASTM F679 T-2 500,000 20.0 (6.1) 20.0 (6.1) 20.0 (6.1)

Note: Due to the various profile designs that are available, manufacturers of profile pipe should

be contacted concerning the recommended support spacing of their products.

In common practice, a support is secured within two feet of and on

both sides of pipe joints. Pipe supports should provide a smooth bearing

surface conforming closely to the bottom half of the pipe. The bearing

surface in contact with the pipe should be at least 2 inches (50 mm) wide.

Supports should permit longitudinal pipe movement in expansion and

contraction without abrasion, cutting or restriction. Supports should be

mounted rigidly to prevent lateral or vertical pipe movementperpendicular to the longitudinal axis in response to thrust from internal

pressure. Changes in pipe line size and direction should be adequately

anchored.

PVC pipe conveying fluids while suspended in horizontal

configuration by rigid supports displays response to load which conforms

to design theory for suspended beams. Maximum span vertical

displacement (sag) may be calculated as follows:

Two supports per continuous length of pipe - (one span)

EQUATION 8.22

y =0.0130wL4

EI

Where: y = mid-span vertical displacement (sag), in

w = weight of pipe filled with water, lbs/in

L = support spacing or span length, in

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E = modulus of elasticity, lbs/in2

I = moment of inertia, in4(See Equation 8.4.)

Consequently, Equation 8.22 can be rearranged in order to calculate the

maximum support spacing as a result of short-term or initial sag:

EQUATION 8.23

L =

3/1

w

EI154.0

Since the modulus of elasticity of PVC is temperature dependent, a

multiplier should be applied to the room temperature modulus for

applications at higher temperatures. Simply multiply the modulus for

PVC at 73.4oF by the correction factor shown in Table 8.7 to obtain an

accurate E value, which can be used in the vertical displacement and

support spacing calculations.

TABLE 8.7

TEMPERATURE CORRECTIONS FOR E

Temperature Modulus of Elasticity

F C Correction Factor

90 (32) 0.93

100 (38) 0.88110 (43) 0.84

120 (49) 0.79

130 (54) 0.75

140 (60) 0.70

NOTES:

1. The maximum recommended temperature for the wall of PVC pipe and fittings is

140F (60C).2. Interpolate between the temperatures listed to calculate other factors.

3. The factors in Table 8.7 assume sustained elevated service temperatures. When the

contents of a PVC pipe are only intermittently and temporarily raised above the

service temperature shown, a multiplier may not be needed.

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Weight of PVC pipe filled with water is calculated as follows:

EQUATION 8.24

w = 0.0113 (3.5 Do2- Di2)

Where: w = weight of pipe filled with water, lbs/in

Do = average outside diameter, in

Di = average inside diameter, in

Note: Derivation of Equation 8.24 is based on the following specificgravities:

SGPVC = 1.40

SGH2O = 1.00

Normally, specific gravity of sewage can be assumed to be 1.0. If

higher specific gravities are anticipated, Equation 8.24 should be

factored by the particular fluid specific gravity.

Maximum bending stress in the pipe wall may be calculated as

follows:

EQUATION 8.25

Sb=M Do

2I


M = bending moment, in-lbs

I = moment of inertia, in4(See Equation 8.4.)


The moment for an end-supported simple beam with single span may

be calculated as follows:EQUATION 8.26

M =wL2

8

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Where: M = bending moment, in-lbs

w = load, lbs/in


Substituting equations for M and I in Equation 8.25 results in the

following equation for maximum bending stress:

EQUATION 8.27

Sb=1.273wL2Do

Do4

- Di4


w = load, lbs/in



Di = average inside diameter, in

EXPANSION AND CONTRACTIONAll pipe products expand and contract with changes in temperature.

Variation in pipe length due to thermal expansion or contraction depends

on the coefficient of thermal expansion of the pipe material and the

variation in temperature (T). It should be noted that change in pipe

diameter or wall thickness, with pipe material properties remaining

constant, does not effect a change in rates of thermal expansion or

contraction. Approximate coefficients of thermal expansion for different

pipe materials are presented in Table 8.8.

Expansion and contraction of PVC pipe in response to change in

temperature will vary slightly with changes in PVC compounds.

However, the coefficients in Table 8.8 are accurate for practical purposes.

Table 8.9 displays typical length variation of PVC pipe due to thermal

expansion and contraction. PVC pipe length variation due to temperature

change is shown graphically in Figures 8.3 and 8.4.

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303

TABLE 8.8

COEFFICIENTS OF THERMAL EXPANSION

Coefficient Expansion Coefficient Expansion

Piping Material in/in/oF in/100 ft/10

oF in/in/

oC mm/10m/10

oC

PVC 3.0 x 10-5 0.36 5.4 x 10-5 5.4

HDPE 1.2 x 10-4 1.44 2.2 x 10-4 21.6

ABS 5.5 x 10-5 0.66 9.9 x 10-5 9.9

Asbestos Cement 4.5 x 10-6 0.05 8.1 x 10-6 0.8

Aluminum 1.3 x 10-5 0.16 2.3 x 10-5 2.3

Cast Iron 5.8 x 10-6 0.07 1.0 x 10-5 1.0

Ductile Iron 6.2 x 10-6 0.07 1.1 x 10-5 1.1

Steel 6.5 x 10-6 0.08 1.2 x 10-5 1.2Clay 3.4 x 10-6 0.04 6.1 x 10-6 0.6

Concrete 5.5 x 10-6 0.07 9.9 x 10-6 1.0

Copper 9.8 x 10-6 0.12 1.8 x 10-5 1.8

TABLE 8.9

LENGTH VARIATION PER 10F TPVC PIPE

PIPE LENGTH LENGTH CHANGE

ft (m) in (mm)

20 (6.1) 0.072 (1.83)

13 (4.0) 0.047 (1.19)

12.5 (3.8) 0.045 (1.14)

10 (3.0) 0.036 (0.91)

A good rule of thumb in design of PVC piping systems is to allow 3/8

inch of length variation for every 100 feet of pipe for each 10 F change in

temperature (5.4mm/10m/10 C). The relationship is shown graphically in

Figures 8.3 and 8.4.

Allowance for Thermal Expansion and Contraction: PVC pipe

with gasketed joints, if properly installed (i.e., with pipe spigot inserted

into bell joint up to manufacturer's insertion mark), will accommodatesubstantial thermal expansion and contraction. If gasketed joints are used

within the accepted range of operating temperatures for PVC pipe, thermal

expansion and contraction is not a significant factor in system design.


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304

FIGURE 8.3

PVC PIPE LENGTH VARIATION

DUE TO TEMPERATURE CHANGE(F)

Coefficient of Thermal Expansion = 3 x 10-5in/in/ o

F

0.050.040.030.020.01

0

10

20

30

40

50

60

70

80

90

100

110

120

PVC PIPE

As a general rule, for everytemperature change of 10F,PVC pipe will expand orcontract 3/8" per 100'.

LENGTH VARIATION, in/ft


31/35


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MOLECULARLY ORIENTED PVC PIPE (PVCO)

The principles and design approach described in this chapter apply to

PVCO as well. PVCO has the same coefficient of thermal expansion as

PVC. However, due to the differences in the pipe wall and material

properties, the following tables are provided for design with PVCO

pipe. Bending tables and support spacing tables are provided below:

TABLE 8.10


FOR PVCO PRESSURE RATED PIPE (ASTM F 1483)IN 20-FOOT LENGTHS

(Sb= 1000 lbs/in2, E = 400,000 lbs/in

2)

Nominal Size, in 4 6 8 10 12

Pressure Rated 200

Do, in 4.500 6.625 8.625 10.740 12.750tnom, in 0.127 0.187 0.243 0.304 0.359

Di, in 4.247 6.25 8.139 10.193 12.031

I, in4 4.163 19.646 56.232 136.06 268.62

M, in-lbs 1,850 5,931 13,039 25,337 42,136

Rb, in (min) 900 1,325 1,725 2,148 2,550

Rb, ft (min) 75 110 144 179 213

,

degrees 15.3 10.4 8.0 6.4 5.4

adegrees 7.6 5.2 4.0 3.2 2.7

A, in 32 22 17 13 11

P, lbs 11 37 81 158 263RatioRb/Do 200 200 200 200 200

Pressure Rated 250

Do, in 4.500 6.625 8.625 10.750 12.750

tnom, in 0.158 0.232 0.302 0.377 0.447

Di, in 4.185 6.162 8.021 9.996 11.856

I, in4 5.071 23.801 68.389 165.37 327.17

M, in-lbs 2,254 7,185 15,858 30,767 51,321

Rb, in (min) 900 1,325 1,725 2,150 2,550

Rb, ft (min)75 110 144 179 213

,

degrees 15.3 10.4 8.0 6.4 5.4

adegrees 7.6 5.2 4.0 3.2 2.7

A, in 32 22 17 13 11

P, lbs 14 45 99 192 321

RatioRb/Do 200 200 200 200 200

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TABLE 8.11


FOR PVCO PRESSURE CLASS PIPE (AWWA C 909)

IN 20-FOOT LENGTHS

(Sb= 800 lbs/in2, E = 400,000 lbs/in

2)

Nominal Size, in 4 6 8 10 12

Pressure Class 200Do, in 4.800 6.900 9.050 11.100 13.200

tnom, in 0.201 0.29 0.375 0.465 0.553

Di, in 4.399 6.321 8.292 10.171 12.094

I, in4 7.672 32.89 97.17 219.8 439.9

M, in-lbs 2,557 7,627 17,179 31,683 53,321

Rb, in (min) 1,200 1,725 2,263 2,775 3,300

Rb, ft (min) 100 144 189 231 275

,degrees 11.5 8.0 6.1 5.0 4.2

adegrees 5.7 4.0 3.0 2.5 2.1

A, in 24 17 13 10 9

P, lbs 16 48 107 198 333RatioRb/Do 250 250 250 250 250

Pressure Class 150

Do, in 4.800 6.900 9.050 11.100 13.200

tnom, in 0.155 0.223 0.293 0.35 0.427

Di, in 4.491 6.454 8.465 10.38 12.35

I, in4 6.086 26.084 77.195 174.59 349.65

M, in-lbs 2,029 6,048 13,648 25,166 42,382

Rb, in (min) 1,200 1,725 2,263 2,775 3,300

Rb, ft (min) 100 144 189 231 275

,

degrees 11.5 8.0 6.1 5.0 4.2

adegrees 5.7 4.0 3.0 2.5 2.1

A, in 24 17 13 10 9

P, lbs 13 38 85 157 265

RatioRb/Do 250 250 250 250 250

Pressure Class 100

D , in 4.800 6.900 9.050 11.100 13.200

tnom, in 0.11 0.157 0.206 0.252 0.3

Di, in 4.579 6.586 8.638 10.596 12.6

I, in4 4.475 18.903 55.961 126.34 252.91

M, in-lbs 1,492 4,383 9,894 18,211 30,656

Rb, in (min) 1,200 1,725 2,263 2,775 3,300Rb, ft (min) 100 144 189 231 275

,

degrees 11.5 8.0 6.1 5.0 4.2

adegrees 5.7 4.0 3.0 2.5 2.1

A, in 24 17 13 10 9

P, lbs 9 27 62 114 192

RatioRb/Do 250 250 250 250 250

o

307


34/35

Note: Support spacing recommendations shown in this table are based on the following

design limitations:

1. Pipe vertical displacement (sag) limited to 0.2 percent of span length based on

calculations using Equation 8.22.

2. Pipe bending stress values limited to values defined in Table 8.1.

ft at

73.4oF

m at

23oC

ft at

120oF

m at

49oC

4 AWWA C909 200 400,000 7.3 2.2 6.8 2.1

4 AWWA C909 150 400,000 6.8 2.1 6.3 1.9

4 AWWA C909 100 400,000 6.2 1.9 5.7 1.7

6 AWWA C909 200 400,000 9.4 2.9 8.6 2.6

6 AWWA C909 150 400,000 8.7 2.7 8.0 2.5

6 AWWA C909 100 400,000 7.9 2.4 7.3 2.2

8 AWWA C909 200 400,000 11.2 3.4 10.4 3.2

8 AWWA C909 150 400,000 10.4 3.2 9.6 2.9

8 AWWA C909 100 400,000 9.4 2.9 8.7 2.7

10 AWWA C909 200 400,000 12.8 3.9 11.9 3.610 AWWA C909 150 400,000 11.9 3.6 11.0 3.4

10 AWWA C909 100 400,000 10.8 3.3 10.0 3.0

12 AWWA C909 200 400,000 14.4 4.4 13.3 4.1

12 AWWA C909 150 400,000 13.4 4.1 12.4 3.8

12 AWWA C909 100 400,000 12.1 3.7 11.2 3.4

4 ASTM F 1483 200 400,000 6.3 1.9 5.8 1.8

4 ASTM F 1483 250 400,000 6.7 2.0 6.2 1.9

6 ASTM F 1483 200 400,000 8.1 2.5 7.5 2.3

6 ASTM F 1483 250 400,000 8.7 2.6 8.0 2.4

8 ASTM F 1483 200 400,000 9.7 3.0 9.0 2.7

8 ASTM F 1483 250 400,000 10.3 3.1 9.5 2.9

10 ASTM F 1483 200 400,000 11.3 3.4 10.4 3.2

10 ASTM F 1483 250 400,000 12.0 3.6 11.1 3.4

12 ASTM F 1483 200 400,000 12.6 3.8 11.6 3.5

12 ASTM F 1483 250 400,000 13.4 4.1 12.4 3.8

PVCO Pipe Support SpacingNominalPipe Size

(in)

Product

Standard

Pressure

Class

TABLE 8.12

SUPPORT SPACING FOR SUSPENDED HORIZONTAL

PVCO PIPE FILLED WITH WATER

Tensile Modulus

(psi at 73.4

o

F)


35/35


CHAPTER VIII

BIBLIOGRAPHY

1. Modern Plastics Encyclopedia, Issued annually by Modern Plastics, McGraw-Hill,

New York, NY.

2. Reissner, E., "On Finite Bending of Pressurized Tubes," Journal of Applied

Mechanics Transactions of ASME, (Sept. 1959) pp. 386-392.

3. "Standard Specification for Poly(Vinyl Chloride) (PVC) Large-Diameter Plastic

Gravity Sewer Pipe and Fittings, ASTM F 679," American Society for Testing and

Materials, Philadelphia, PA (1980).

4. "Standard Specification for Type PSM Poly(Vinyl Chloride) (PVC) Sewer Pipe

and Fittings, ASTM D 3034," American Society for Testing and Materials,

Philadelphia, PA (1981).

5. "Thermal Expansion and Contraction of Plastic Pipe, PPI Technical Report, PPI-

TR-21," Plastics Pipe Institute, New York, NY (Sept. 1973).

6. Timoshenko, S. and D. H. Young, Elements of Strength of Materials, FourthEdition, Van Nostrand Company, Princeton, NJ, p. 111, p. 139.

7. Timoshenko, S. P., Theory of Elastic Stability, Second Edition, McGraw-Hill,

(1961).

8. Timoshenko, S. P., Strength of Materials, Part II - Advanced Theory and

Problems, Van Nostrand Company, Princeton, NJ (1968) pp. 187-190.

handbook of pvc pipe chap8.pdf

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