Uni-ch8 Special Design Applications

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

275

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

276


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. In restrained-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)TF

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, oF 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 = SbIc

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, in4 (See Equation 8.4.)

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TABLE 8.1

ALLOWABLE BENDING STRESSES AT 73.4F

Pressure Class Pipe =

4000 -

40002

1.02.5 = 800 lbs/in

2 (5.52 MPa)

Pressure Rated Pipe =

4000 -

40002

1.02.0 = 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 for gasketed pressure pipe.

Non-Pressure Pipe

PVC 12454 = [ ]4000 - 0 1.02.0 = 2000 lbs/in2 (13.79 MPa)

PVC 12364 = [3200 - 0] 1.02.0 = 1600 lbs/in

2 (11.72 MPa)

EQUATION 8.4

I = 64 (Do

4 - Di4) = 0.0491 (Do4 - Di4)

Where: I = moment of inertia, in4 Do = average outside diameter, in Di = 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 I or the allowable bending radius.

279


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 = EIM

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 Rb have 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 profile typically 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 = SbIc L =

Rb90 a


= 360L2Rb

d = Rb cos /2


a = /2 Y = Rb - d


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

C sin /2 = L tan a

282


A 6-in Class 150 PVC pipe (per AWWA C900 Standard) is shown with one length curved in the barrel to required alignment

283


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 required should 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 ft L = (1181)(10 /360 ) = 33 ft 20 ft < 33 ft < 40 ft Use 2 each 8-in x 20-ft lengths L = 2 x 20-ft = 40 ft - Resultant total offset for the pipeline over 2 pipe lengths: Assume: L C Then using Equation 8.9:

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

= 40 (.087) = 3.5 ft

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TABLE 8.2

ALLOWABLE LONGITUDINAL BENDING FOR PRESSURE CLASS PIPE (AWWA C900) IN 20 FOOT LENGTHS

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

Nominal Size,

in 4 6 8 10 12

DR 14 (PC 200) Do, in 4.800 6.900 9.050 11.100 13.200 tnom, in 0.363 0.522 0.685 0.840 0.999 Di, in 4.07 5.86 7.68 9.42 11.20 I, in4 12.5 53.5 158 358 716 M, in-lbs 4,170 12,400 28,000 51,600 86,800 Rb, in (min) 1200 1730 2260 2780 3300 Rb, ft (min) 100 144 188 232 275 , degrees 11.5 7.9 6.1 4.9 4.2 a degrees 5.7 4.0 3.0 2.5 2.1 A, in 24 17 13 10 9 P, lbs 26 77 170 320 540 Ratio Rb/Do 250 250 250 250 250

DR 18 (PC 150) Do, in 4.800 6.900 9.050 11.100 13.200 tnom, in 0.283 0.406 0.533 0.654 0.777 Di, in 4.23 6.09 7.98 9.79 11.65 I, in4 10.3 43.8 130 293 586 M, in-lbs 3,420 10,200 22,900 42,300 71,100 Rb, in (min) 1200 1730 2260 2780 3300 Rb, ft (min) 100 144 188 232 275 , degrees 11.5 7.9 6.1 4.9 4.2 a degrees 5.7 4.0 3.0 2.5 2.1 A, in 24 17 13 10 8.7 P, lbs 21 63 140 260 440 Ratio Rb/Do 250 250 250 250 250

DR 25 (PC 100) Do, in 4.800 6.900 9.050 11.100 13.200 tnom, in 0.204 0.293 0.384 0.471 0.560 Di, in 4.39 6.31 8.28 10.16 12.08 I, in4 7.76 33.1 98.1 222 444 M, in-lbs 2,590 7,700 17,300 32,000 53,800 Rb, in (min) 1200 1730 2260 2780 3300 Rb, ft (min) 100 144 188 232 275 , degrees 11.5 7.9 6.1 4.9 4.2 a degrees 5.7 4.0 3.0 2.5 2.1 A, in 24 17 13 10 9 P, lbs 16 48 110 200 340 Ratio Rb/Do 250 250 250 250 250

Note: AWWA C905 pipe sizes (larger diameters) are not shown because the larger 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. 285


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/in2)

Nominal Size, in 1.5 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 a degrees 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 Ratio Rb/Do 200 200 200 200 200

DR 26 Do, 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 a degrees 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 16 Ratio Rb/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 a degrees 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 Ratio Rb/Do 200 200 200 200 200

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

286


TABLE 8.3 (continued)

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/in2)

Nominal Size, in 5 6 8 10 12

DR 21 Do, 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 11.46 I, 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 a degrees 6.2 5.2 4.0 3.2 2.7 A, in 26 22 17 13 11 P, lbs 36 61 140 260 440 Ratio Rb/Do 200 200 200 200 200

DR 26 Do, in 5.563 6.625 8.625 10.750 12.750 tnom, 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 a degrees 6.2 5.2 4.0 3.2 2.7 A, in 26 22 17 13 11 P, lbs 30 51 110 220 370 Ratio Rb/Do 200 200 200 200 200

DR 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 a degrees 6.2 5.2 4.0 3.2 2.7 A, in 26 22 16.6 13.4 11.3 P, lbs 25 42 93 180 300 Ratio Rb/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.

287


TABLE 8.3 (continued) ALLOWABLE LONGITUDINAL BENDING FOR PRESSURE RATED PIPE (ASTM D 2241, DR = 41) IN 20 FOOT LENGTHS

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

Nominal Size,

in 3 4 5 6

DR 41 Do, 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 6.28 I, 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 a degrees 6.4 5.0 4.1 3.4 A, in 18 14 11 9.3 P, lbs 2.2 4.6 8.7 15 Ratio Rb/Do 200 200 200 200

Nominal Size,

in 8 10 12

DR 41 Do, 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 3.5 a degrees 2.6 2.1 1.8 A, in 7.2 5.8 4.9 P, lbs 32 63 105 Ratio Rb/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.

288


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/in2) Nominal Size,

in 4 6 8 10 12 15

13 Lengths Do, 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 a degrees 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 Ratio Rb/Do 156 156 156 156 156 156

20 Lengths Do, 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 20.9 14.0 10.5 8.4 7.1 5.8 a degrees 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 Ratio Rb/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 represented by in Figure 8.2.

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FIGURE 8.2

COMPOUND CURVILINEAR ALIGNMENT FROM BENDING MULTIPLE PIPES

The radius of curvature, R b is related to (the joint deflection):

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 not greater 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 290


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 2,500 200 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 on longitudinal bending. Ring deflection is usually expressed as:

EQUATION 8.16

Deflection = = DY or

EQUATION 8.17

% Deflection = 100 = 100DY


Where: Y = the reduction in outside diameter, in D = 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

= DY = (A1 a2)

2

3 + 71 + 4135 + 9 (A1 a

2)

with and (A1 a2) defined as:

EQUATION 8.19

= 12(1 - v2)PDm3

8Et3

EQUATION 8.20

(A1 a2) = 116

18(1 - v2)

12 + 4 Dm4R2t2

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 of elasticity to a minimum bending radius of 156 times the pipe diameter, as shown in Table 8.4.

292


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

(A1 a2) = 116

18(1 - 0.382)

12 + 4 Dm4R2t2

= 116

86.01218

(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(0135071

32

= 0.00324 [0.667 + 0.00170] = 0.002 = 0.2% ring deflection

Example: Calculate the percent ring deflection after pressurization to 100 lbs/in2 which 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

= 116

+

32.21286.018

)132.0)(000,440,1(2.387

293


294

= 0.000138

= 0.000138

++

+

000138.0

)584.0(9135)584.0(471

32

= 0.000138

+ 000722.032

= 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

= mDY =

23 (A1 a

2) = (1 - v2)Dm4

16R2t2

Where: = ring deflection v = Poisson's Ratio (0.38 for PVC) Dm = mean pipe diameter, in R = 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 0.06 percent for all PVC pipes marketed today in North America.


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) 73.4o F (23o C) 120 o F (49 o C) 140 o F (60 o C)

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




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




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)

298



Nominal Tensile PVC Pipe Support Spacing, ft (m) Pipe Size Product Dimension Modulus (in) Standard Ratio (lbs/in2) 73.4o F (23o C) 120 o F (49 o C) 140 o F (60 o C) 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 movement perpendicular 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

299


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

wEI154.0

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) 0.88 110 (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.

300


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 specific gravities:

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

Where: Sb = bending stress, lbs/in2 M = bending moment, in-lbs I = moment of inertia, in4 (See Equation 8.4.) Do = average outside diameter, in The moment for an end-supported simple beam with single span may

be calculated as follows: EQUATION 8.26

M = wL2

8

301


Where: M = bending moment, in-lbs w = load, lbs/in L = support spacing or span length, 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

Where: Sb = bending stress, lbs/in2 w = load, lbs/in L = support spacing or span length, in Do = average outside diameter, in Di = average inside diameter, in

EXPANSION AND CONTRACTION All 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.

302


303

TABLE 8.8

COEFFICIENTS OF THERMAL EXPANSION

Coefficient Expansion Coefficient Expansion Piping Material in/in/ oF in/100 ft/10o F in/in/ oC mm/10m/10o C

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 1.2 Clay 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 T PVC 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 accommodate substantial 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.


304

FIGURE 8.3

PVC PIPE LENGTH VARIATION DUE TO TEMPERATURE CHANGE

(F)

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

0.050.040.030.020.010

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 or contract 3/8" per 100'.

LENGTH VARIATION, in/ft


305

FIGURE 8.4

PVC PIPE LENGTH VARIATION DUE TO TEMPERATURE CHANGE

(C)

Coefficient of Thermal Expansion = 5.4 x 10-5 mm/mm/ oC

3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0

5

10

15

20

25

30 35

40

45

50

55

60

PVC

pAs a general rule, for tem erature change of 10C PVC pipe will expand or contract 5.4 mm per 10 m.

LENGTH VARIATION, mm/m

TEM

PER

ATU

RE

CH

AN

GE

INC


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

ALLOWABLE LONGITUDINAL BENDING FOR PVCO PRESSURE RATED PIPE (ASTM F 1483)

IN 20-FOOT LENGTHS

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


Pressure Rated 200 Do, in 4.500 6.625 8.625 10.740 12.750 tnom, 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 a degrees 7.6 5.2 4.0 3.2 2.7 A, in 32 22 17 13 11 P, lbs 11 37 81 158 263 Ratio Rb/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 a degrees 7.6 5.2 4.0 3.2 2.7 A, in 32 22 17 13 11 P, lbs 14 45 99 192 321 Ratio Rb/Do 200 200 200 200 200

306


TABLE 8.11

ALLOWABLE LONGITUDINAL BENDING FOR PVCO PRESSURE CLASS PIPE (AWWA C 909)

IN 20-FOOT LENGTHS

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


Pressure Class 200 Do, 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 a degrees 5.7 4.0 3.0 2.5 2.1 A, in 24 17 13 10 9 P, lbs 16 48 107 198 333 Ratio Rb/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 a degrees 5.7 4.0 3.0 2.5 2.1 A, in 24 17 13 10 9 P, lbs 13 38 85 157 265 Ratio Rb/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 3,300 Rb, ft (min) 100 144 189 231 275 , degrees 11.5 8.0 6.1 5.0 4.2 a degrees 5.7 4.0 3.0 2.5 2.1 A, in 24 17 13 10 9 P, lbs 9 27 62 114 192 Ratio Rb/Do 250 250 250 250 250

o

307

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 oncalculations 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 2.14 AWWA C909 150 400,000 6.8 2.1 6.3 1.94 AWWA C909 100 400,000 6.2 1.9 5.7 1.76 AWWA C909 200 400,000 9.4 2.9 8.6 2.66 AWWA C909 150 400,000 8.7 2.7 8.0 2.56 AWWA C909 100 400,000 7.9 2.4 7.3 2.28 AWWA C909 200 400,000 11.2 3.4 10.4 3.28 AWWA C909 150 400,000 10.4 3.2 9.6 2.98 AWWA C909 100 400,000 9.4 2.9 8.7 2.710 AWWA C909 200 400,000 12.8 3.9 11.9 3.610 AWWA C909 150 400,000 11.9 3.6 11.0 3.410 AWWA C909 100 400,000 10.8 3.3 10.0 3.012 AWWA C909 200 400,000 14.4 4.4 13.3 4.112 AWWA C909 150 400,000 13.4 4.1 12.4 3.812 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 1.84 ASTM F 1483 250 400,000 6.7 2.0 6.2 1.96 ASTM F 1483 200 400,000 8.1 2.5 7.5 2.36 ASTM F 1483 250 400,000 8.7 2.6 8.0 2.48 ASTM F 1483 200 400,000 9.7 3.0 9.0 2.78 ASTM F 1483 250 400,000 10.3 3.1 9.5 2.910 ASTM F 1483 200 400,000 11.3 3.4 10.4 3.210 ASTM F 1483 250 400,000 12.0 3.6 11.1 3.412 ASTM F 1483 200 400,000 12.6 3.8 11.6 3.512 ASTM F 1483 250 400,000 13.4 4.1 12.4 3.8

PVCO Pipe Support SpacingNominal Pipe Size

(in)

Product Standard

Pressure Class

TABLE 8.12

SUPPORT SPACING FOR SUSPENDED HORIZONTAL PVCO PIPE FILLED WITH WATER

Tensile Modulus (psi at 73.4oF)


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, Fourth

Edition, 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.

309

Handbook of PVC PipeTitleTitle PageCopyrightPrefaceTable of ContentsChapter I, Polyvinyl Chloride (PVC) PipePVC -- An Engineered ThermoplasticHistorical BackgroundA Rational ChoicePVC Pipe Technology

Chapter II, Raw MaterialsPVC Pipe CompoundsGasket Materials

Chapter III, Resistance to Aggressive EnvironmentsCorrosionChemical AttackPermeationBiological AttackWeatheringAbrasionSoil MovementRepetitive Fatigue

Chapter IV, PVC Pipe Manufacturing and TestingManufacturing ProcessesManufacturing of Profile Wall PipeManufacturing of Injection Molded PVC FittingsFabricated PVC FittingsStandard SpecificationsTestingQualification TestsQuality Control Tests and InspectionQuality Assurance TestingTest Certification and WarrantyPackaging and ShippingManufacturing of PVCO

Chapter V, Pressure Pipe and Fittings, Design and SelectionPressure Pipe Design and SelectionInternal Hydrostatic PressureDistribution MainsTransmission MainsTransmission Pipe Design ExampleDesign of Molded PVC Pressure FittingsFabricated PVC Pressure FittingsSurge Pressures In PVC PipeSewage Force MainsPressure Pipe LongevityMolecularly Oriented PVC Pressure Pipe (PVCO)

Chapter VI, Superimposed Loads on Buried PipeEarth LoadsLive LoadsDesign Software

Chapter VII, Design of Buried PVC PipeSewer Pipe LongevityAlternative Design Methods

Chapter VIII, Special Design ApplicationsLongitudinal BendingSupport SpacingExpansion and ContractionMolecularly Oriented PVC Pipe (PVCO)

Chapter IX, HydraulicsFlow of Water in PVC Pressure PipesGravity Flow in PVC Sewer PipeMolecularly Oriented PVC Pipe (PVCO)

Chapter X, ConstructionReceiving, Storage and HandlingPVC Pipe Joint AssemblyCasingsSliplining ApplicationsPVC Pressure Pipe InstallationPVC Non-Pressure Pipe

Published Design Guides and RecommendationsPVC Pipe DimensionsUnit Conversion TablesIndex

Copyright: Uni-Bell PVC Pipe Association, 2001

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