Wavistrong Engineering Guide [PDF]

Zitiervorschau

Future Pipe Industries

WAVISTRONG ENGINEERING GUIDE

WAVISTRONG

®

FIBERSTRONG

®

WAVIFLOAT

®

FIBERMAR

®

Epoxy Pipe Systems

Title: Engineering Guide for Wavistrong filament wound epoxy pipe systems

Date issued: 01-11-1997 Replaces issue of: 01-04-1995

REP 348/Rev 1/1197

Wavistrong Engineering Guide ES/EW/CS System

Reader Service Card Please find in the back of this brochure a business reply card. In order to inform you about the different applications and latest developments of Wavistrong glass fibre reinforced plastic pipe systems, you are kindly requested to complete and return this card.

All information was correct at the time of going to press. However, we reserve the right to alter, amend and update any products, systems and services described in this brochure. We accept no responsibility for the interpretation of statements made. © Copyright by Future Pipe Industries B.V. formerly Wavin Repox B.V. No part of this work may be reproduced in any form, by print, photoprint, microfilm or any other means without written permission from the publisher.

Table of Contents Section

Page

I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

II. Wavistrong information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 3 3 4 4 4 5 5 5 11 12 18 18 18 23 25 29 33 37 41

II.1. II.2. II.3. II.4. II.4.1. II.4.2. II.5. II.5.1. II.5.2. II.5.3. II.6. II.6.1. II.6.2. II.7. II.8. II.9. II.10. II.11. II.12.

General . . . . . . . . . . . . . . . . Serial identification . . . . . . . . Winding angle . . . . . . . . . . . Joining systems . . . . . . . . . . Tensile resistant joints . . . . . Non-tensile resistant joints . . . System data . . . . . . . . . . . . Pipes . . . . . . . . . . . . . . . . . . Fittings . . . . . . . . . . . . . . . . Combined stresses . . . . . . . . Head loss in pipes and fittings Wavistrong pipes . . . . . . . . . Wavistrong fittings . . . . . . . . Wavistrong pipe properties . . Bending radius . . . . . . . . . . . Fluid (water) hammer . . . . . . Stiffness . . . . . . . . . . . . . . . Buckling pressure . . . . . . . . . Classification . . . . . . . . . . . .

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III. Wavistrong above ground pipe systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

III.1. III.2. III.3. III.4. III.4.1. III.4.2. III.5. III.6. III.7.

Design . . . . . . . . . . . . . . . Supports . . . . . . . . . . . . . Clamps . . . . . . . . . . . . . . Support distance . . . . . . . Single span length . . . . . . Continuous span length . . . Corrected support distance Anchor points . . . . . . . . . . Anchor loads . . . . . . . . . .

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42 42 42 43 43 45 47 52 52

IV. Wavistrong underground pipe systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

IV.1. Design and joining systems . . . . . . . . . . IV.2. Anchor points . . . . . . . . . . . . . . . . . . . . IV.3. Calculation of underground pipe systems IV.3.1. Pipe deflection . . . . . . . . . . . . . . . . . . . IV.3.2. Deflection lag factor . . . . . . . . . . . . . . . IV.3.3. Deflection coefficient . . . . . . . . . . . . . . . IV.3.4. Vertical soil load . . . . . . . . . . . . . . . . . . IV.3.5. Live load . . . . . . . . . . . . . . . . . . . . . . . IV.3.5.1. Live load coefficient single wheel load . IV.3.5.2. Live load coefficient two passing trucks IV.3.6. Pipe stiffness factor . . . . . . . . . . . . . . . IV.3.7. Modulus of soil reaction . . . . . . . . . . . . IV.4. Resulting hoop stress . . . . . . . . . . . . . . IV.5. Allowable combined stress . . . . . . . . . .

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Appendix I

: List of symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

Appendix II

: Conversion tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

Appendix III

: Conversion graph psi vs bar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

Appendix IV

: Conversion graph °C vs °F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

Appendix V

: Examples combined stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

II

I. Introduction This Wavistrong Engineering Guide provides information for the design, specification and installation of Wavistrong glass fibre reinforced epoxy pipe systems in the diameter range from 25 mm up to and including 1200 mm, for above ground and underground applications. For detailed specification, installation information and standard products reference is made to the Wavistrong System Specifications, the Wavistrong Installation Manual and the Wavistrong Product List. Beyond others, this information can be obtained by completion of the reader service card. All conventional methods of calculating stresses in the pipe wall, resulting from internal and external loads, are applicable to the Wavistrong pipe system. The occurring stresses in the structural laminate have to be combined to an equivalent stress and compared with the allowable value of this stress. The allowable equivalent stress has been determined using the Continuum Theory . The engineering of piping systems is complicated and can be simplified with the aid of calculation programs. As a help for the piping engineer, Future Pipe Industries developed computer programs for the calculation of stresses, strains and deformations for underground and above ground applications. On request, computer runs can be made for the calculation of stresses and deformations in a specific underground piping system in accordance with ANSI/AWWA C950-88 (Spangler theories), or ATV A 127-88 (Leonhardt theories). For rigid above ground applications pipe stress analysis can be made with the aid of a computerized flexibility programs. Although our Engineering Department is able to support the pipe system design with individual calculations as described above, Future Pipe Industries will not act as "designer" as described in ASME B31.3-1990, chapter 1, paragraph 300 (b) (2). The design of a pipeline system using Wavistrong products means a construction with pipes as well as fittings. All elements of the system are designed such that the performance requirements of the pipeline is valid for each element of the Wavistrong system. The choice for one of the possible joining systems will be considered in design stage. Together with our engineers we can advise an optimal solution. Because of its benefits, the possibility of using prefabricated pipeline sections (spools), should be considered in design stage of the piping system. The advantage of using spools can be found in the reduced amount of joints to be made in the field, the shorter assembly dimensions, the narrow tolerances and the shortest installation time. With the knowledge of the system requirements for a pipeline system several questions have to be answered to come to a successful operating pipeline. Besides technical discussions these questions are answered in our technical literature. The different subjects for discussion referring to the relevant information are given in the following diagram (fig. I.1., page 2). If product information is not covered by this guide, our engineers will be pleased to assist and inform you about typical design possibilities and latest improvements of Wavistrong.

"Zur Beanspruchung und Verformung von GfK Mehrschichten Verbunden", A. Puck, Kunststoffe-57, Teil 1-II, 1967. Heft 4-7-12.

1

Fig. I.1. Product information

2

II. Wavistrong information II.1. General

Wavistrong piping systems are manufactured from glass fibres, impregnated with an aromatic- or cyclo aliphatic amine cured epoxy resin. This thermosetting resin system possesses superior corrosion resistance, together with excellent mechanical, physical and thermal properties. The glass fibre reinforced epoxy resin piping system resists the corrosive effects of mixtures of low concentrations of acids, neutral or near-neutral salts, solvents and caustics, both under internal and external loads at temperatures up to 110°C. The helically wound continuous glass fibres of the reinforced (structural) wall of the pipes and the fittings are protected on the inner side by the resin-rich reinforced liner and on the outer side by the resin topcoat.

II.2. Serial identification

The serial identification consists of two parts, namely:

A. Type identification The type of product is identified by three alphabetic characters 1. Type of matrix:

E stands for epoxy resin C stands for electrical conductive epoxy resin

2. Type of application: S stands for standard W stands for potable water 3. Type of joint:

T stands for tensile resistant N stands for non-tensile resistant

B. Pressure class This figure indicates the maximum allowable internal pressure (bar) that the product can resist for a life time of 50 years, with a service (design) factor (Sf) of 0.5, which implies a safety factor of 2. Example: Serie EST 20 means:

Note:

E poxy resin S tandard application T ensile resistant joining system Nominal pressure 20 bar.

The data in this Engineering Guide for series EST are also valid for series EWT and CST. The data in this Engineering Guide for series ESN are also valid for series EWN and CSN.

For the design of the pipe it has been assumed that for the tensile resistant types of joints (identification T) the ratio R =

= 0.5, and for non-tensile resistant types of joints (identification N) the

ratio R = 0.25.

3

II.3. Winding angle

Depending on the loading of the system and the pressure class, the continuous glass fibre reinforcement is helically wound under a predetermined angle with the axis of the pipe. For the different systems the winding angle (ω ) is given in table II-a. Table II-a. Winding angle ω (degrees) Pressure class (bar) Series EST

8

10

63°

ESN

12.5

16

20

25

32

55°

55°

55°

55°

55°

63°

63°

63°

63°

73°

For some applications it can be of advantage to use a different winding angle (ω ) in order to obtain specific product characteristics.

II.4. Joining systems

The Wavistrong joining systems can be divided into two major groups: A.

Tensile resistant type of joints. These joints can take the full axial load due to internal pressure.

B.

Non-tensile resistant type of joints. The axial forces in the system have to be taken by external provisions on the pipeline.

II.4.1. Tensile resistant joints

A. Adhesive bonded joint (CJ) The Wavistrong adhesive bonded joint is a rigid type of joining. The adhesive is a two component epoxy resin system, packed in separate containers. The joint consists of a slightly conical socket end and a cylindrical spigot end.

Fig. II.1. CJ

B. Rubber seal lock joint (RSLJ) This type of joint consists of an integral filament wound socket end and a machined spigot end. The O-ring seal is positioned on the spigot end. The locking device is inserted through an opening in the socket end. It fits in a circumferential groove on the inner side of the socket end and rests against a shoulder on the spigot end. The Wavistrong rubber seal lock joint allows for some axial movement as well as a certain angular deflection (table III-g., page 55).

4

Fig. II.2. RSLJ

C. Laminated joint (LJ) Generally these joints will only be used for diameters over 400 mm. The preparation of this rigid joint requires good craftsmanship; it is recommended that Future Pipe Industries provides assistance during installation.

D. Flanged joint (FJ)

Fig. II.3. LJ

To enable connections with steel piping and to allow for easy assembling and disassembling of process lines, Wavistrong pipes and fittings can be supplied with flanges, drilled in accordance with ANSI, DIN or other specifications. Special requirements can be met upon request. Glass fibre reinforced epoxy flanges are always flat faced and in view of this, matching flanges should also be flat faced. The flanged joint is completed by using a gasket. Fig. II.4. FJ II.4.2. Non-tensile resistant joints

A. Rubber seal joint (RSJ) The socket end of this joint is an integral filament wound part of the pipe. The spigot end is a machined part on which the O-ring seal is positioned. This flexible joint allows for axial movement of the spigot in the socket and some angular deflection (table III-g., page 55). Fig. II.5. RSJ

B. Mechanical coupler (MC)

The mechanical coupler normally consists of a metal casing and a rubber seal. These couplers are available in different types and are mostly non-thrust resistant. In those joints the sealing is obtained on the (machined) surface of plain-ended pipes. The maximum allowable pressure depends on the type of coupler.

II.5. System data II.5.1. Pipes

In sections III. and IV. tables for the mechanical behaviour of the standard pipe series are listed. For the determination of this behaviour, or in case these data cannot be used and separate calculations are required, the pipe data from table II-b. through II-d. (page 9 and 10) and fig. II.6. through II.8. (page 13 through 17) provide the necessary information. Table II-b. through II-d. give the following pipe data for the series EST and ESN:

5

A. Minimum reinforced wall thickness (T E) The minimum reinforced wall thickness is calculated with the ISO-formula:

(Eq. II.1.)

Where: TE = minimum reinforced wall thickness ID = inner diameter SH = allowable hoop stress (HDS)(table II-h., page 23) PN = nominal pressure Note: TW

(mm) (mm) (N/mm²) (Mpa)

= total wall thickness (mm)

TW

= TE + TL + TC Where: TL = liner thickness = 0.5 mm TC = topcoat thickness = 0.3 mm For production technical reasons the real wall thickness may be greater than the theoretically calculated minimum value.

B. Mass of the pipe (G B) The mass of the pipe is calculated as follows:

(Eq. II.2.)

Where: GB = linear mass of the pipe OD = outer diameter ID = inner diameter SL = specific gravity of the laminate (table II-l., page 24) Note: OD

(kg/m) (mm) (mm) (kg/m3)

= ID + 2 * TW

C. Structural wall area (A) The structural wall area is calculated from:

(Eq. II.3.)

Where: A = structural wall area DO = structural outer diameter DI = structural inner diameter Note: DO DI

(mm2) (mm) (mm)

= ID + 2 * (TL + TE) = ID + 2 * TL

6

D. Linear moment of inertia (IZ) The linear moment of inertia is obtained from the following formula:

(Eq. II.4.)

Where: IZ = linear moment of inertia DO = structural outer diameter DI = structural inner diameter

(mm4) (mm) (mm)

E. Radius of inertia (IR) The radius of inertia is calculated from the following equation:

(Eq. II.5.)

Where: IR = radius of inertia IZ = linear moment of inertia (Eq. II.4.) A = structural wall area (Eq. II.3.)

(mm) (mm4) (mm2)

F. Bore area (A B) The bore area of the pipe is:

(Eq. II.6.)

Where: AB = bore area ID = inner diameter

(mm2) (mm)

7

G. Moment of resistance to bending (W B) For the calculation of the moment of resistance to bending the following formula is used:

(Eq. II.7.)

Where: W B = moment of resistance to bending DO = structural outer diameter DI = structural inner diameter

(mm3) (mm) (mm)

Note:

Where: 3 WW = moment of resistance to torsion (mm )

H. Mass of the pipe content (G V) The values in table II-d. (page 10) have been calculated with the following equation:

(Eq. II.8.)

Where: GV = linear mass of the pipe content ID = inner diameter SV = specific gravity of the fluid

(kg/m) (mm) (kg/m3)

8

Table II-b. Pipe data for series EST Series

Inner diameter ID

EST 8

EST 12.5

EST 16

EST 20

EST 25

EST 32

(mm) 350 400 450 500 600 700 750 800 900 1000 1200 250 300 350 400 450 500 600 700 750 800 900 1000 200 250 300 350 400 450 500 600 700 750 800 150 200 250 300 350 400 450 500 600 100 150 200 250 300 350 400 450 500 600 25 40 50 80 100 150 200 250 300

Reinforced wall thickness TE (mm) 2.8 3.2 3.6 4.0 4.8 5.6 6.0 6.5 7.3 8.1 9.7 2.5 3.0 3.5 4.0 4.5 5.1 6.1 7.1 7.6 8.1 9.1 10.1 2.5 3.2 3.8 4.4 5.1 5.7 6.3 7.6 8.9 9.5 10.1 2.4 3.3 4.1 4.9 5.7 6.5 7.3 8.1 9.8 2.4 3.1 4.1 5.1 6.1 7.1 8.2 9.2 10.2 12.2 1.8 1.8 1.8 2.4 2.6 3.8 5.1 6.4 7.7

Linear mass of the pipe

Structural wall Linear moarea ment of inertia

GB (kg/m) 7.4 9.4 11.6 14.1 19.7 26.3 29.9 34.3 42.8 52.2 73.9 4.9 6.7 8.9 11.3 14.0 17.3 24.3 32.5 37.0 41.8 52.4 64.0 3.9 5.9 8.1 10.7 13.9 17.2 20.9 29.7 40.0 45.5 51.4 2.8 4.9 7.3 10.1 13.5 17.3 21.6 26.3 37.6 1.9 3.5 5.8 8.8 12.3 16.4 21.4 26.7 32.7 46.3 0.4 0.6 0.8 1.5 2.0 4.1 7.1 10.8 15.2

A 2

IZ 2

*10 (mm ) 31.1 40.6 51.4 63.5 91.4 124.3 142.7 164.9 208.3 256.8 368.9 19.9 28.7 39.0 50.9 64.4 81.1 116.3 157.9 181.1 205.9 260.2 320.8 16.0 25.6 36.4 49.1 65.1 81.8 100.4 145.3 198.5 227.0 257.4 11.6 21.2 32.9 47.1 63.9 83.2 105.1 129.6 188.1 7.8 15.0 26.4 41.0 58.9 79.9 105.4 133.0 163.8 235.0 1.6 2.4 3.0 6.3 8.5 18.5 33.0 51.8 74.7

9

4

4

*10 (mm ) 4869.9 8299.0 13282.4 20231.2 41909.9 77588.3 102217.7 134409.2 214831.9 326870.3 676034.9 1599.5 3310.1 6123.8 10435.8 16702.4 25964.7 53606.1 99002.4 130303.3 168498.1 269409.0 410021.8 827.5 2064.5 4226.3 7757.7 13415.2 21325.3 32304.4 67287.9 125057.5 164115.2 211676.1 340.3 1105.3 2673.5 5509.4 10161.4 17276.9 27602.1 41982.1 87719.2 104.2 445.7 1389.7 3365.4 6940.7 12808.6 22072.7 35225.8 53531.0 110509.1 1.5 5.6 10.4 54.7 113.6 553.9 1754.4 4288.8 8900.8

Radius of inertia

Bore area

IR

AB

*10 (mm) 12.5 14.3 16.1 17.9 21.4 25.0 26.8 28.6 32.1 35.7 42.8 9.0 10.7 12.5 14.3 16.1 17.9 21.5 25.0 26.8 28.6 32.2 35.7 7.2 9.0 10.8 12.6 14.4 16.1 17.9 21.5 25.1 26.9 28.7 5.4 7.2 9.0 10.8 12.6 14.4 16.2 18.0 21.6 3.7 5.4 7.3 9.1 10.9 12.7 14.5 16.3 18.1 21.7 1.0 1.5 1.9 2.9 3.7 5.5 7.3 9.1 10.9

*10 (mm ) 962.1 1256.6 1590.4 1963.5 2827.4 3848.5 4417.9 5026.5 6361.7 7854.0 11309.7 490.9 706.9 962.1 1256.6 1590.4 1963.5 2827.4 3848.5 4417.9 5026.5 6361.7 7854.0 314.2 490.9 706.9 962.1 1256.6 1590.4 1963.5 2827.4 3848.5 4417.9 5026.5 176.7 314.2 490.9 706.9 962.1 1256.6 1590.4 1963.5 2827.4 78.5 176.7 314.2 490.9 706.9 962.1 1256.6 1590.4 1963.5 2827.4 4.9 12.6 19.6 50.3 78.5 176.7 314.2 490.9 706.9

2

Moment of resistance to bending WB

2

3

3

*10 (mm ) 273.1 407.4 579.8 794.9 1372.7 2178.8 2679.4 3302.4 4692.7 6426.9 11078.9 125.0 215.6 342.1 510.3 726.2 1015.8 1748.4 2768.5 3401.3 4123.8 5861.8 8030.2 80.3 160.4 273.9 431.2 652.5 922.4 1258.0 2184.0 3479.6 4262.7 5155.3 43.7 106.5 206.3 354.5 560.8 834.6 1185.7 1623.4 2826.9 19.7 56.7 132.9 257.7 443.2 701.5 1057.6 1500.9 2053.4 3534.0 1.0 2.5 3.8 12.8 21.4 69.8 166.1 325.2 562.6

Table II-c. Pipe data for series ESN Series

Inner diameter ID

ESN 10

ESN 16

ESN 20

ESN 25

ESN 32

(mm) 450 500 600 700 750 800 900 1000 1200 350 400 450 500 600 700 750 800 200 250 300 350 400 450 500 600 200 250 300 350 400 450 500 600 80 100 150 200 250 300

Reinforced wall thickness TE (mm) 3.3 3.6 4.3 5.1 5.4 5.8 6.5 7.2 8.6 2.8 3.2 3.6 4.0 4.8 5.6 6.0 6.5 2.4 2.5 3.0 3.5 4.0 4.5 5.1 6.1 2.5 3.2 3.8 4.4 5.1 5.7 6.3 7.6 2.4 2.4 2.4 3.3 4.1 4.9

Linear mass of the pipe

Structural wall area

GB (kg/m) 10.8 12.9 17.9 24.2 27.2 30.9 38.5 46.9 66.1 7.4 9.4 11.6 14.1 19.7 26.3 29.9 34.3 3.8 4.9 6.7 8.9 11.3 14.0 17.3 24.3 3.9 5.9 8.1 10.7 13.9 17.2 20.9 29.7 1.5 1.9 2.8 4.9 7.3 10.1

Linear moment of inertia

A 2

Radius of inertia

IZ 2

4

*10 (mm ) 47.1 57.1 81.8 113.1 128.3 147.0 185.3 228.0 326.8 31.1 40.6 51.4 63.5 91.4 124.3 142.7 164.9 15.3 19.9 28.7 39.0 50.9 64.4 81.1 116.3 16.0 25.6 36.4 49.1 65.1 81.8 100.4 145.3 6.3 7.8 11.6 21.2 32.9 47.1

4

*10 (mm ) 12151.4 18164.6 37450.9 70510.1 91776.3 119621.2 190781.1 289770.8 597730.8 4869.9 8299.0 13282.4 20231.2 41909.9 77588.3 102217.7 134409.2 793.2 1599.5 3310.1 6123.8 10435.8 16702.4 25964.7 53606.1 827.5 2064.5 4226.3 7757.7 13415.2 21325.3 32304.4 67287.9 54.7 104.2 340.3 1105.3 2673.5 5509.4

Bore area

IR

AB

*10 (mm) 16.1 17.8 21.4 25.0 26.7 28.5 32.1 35.6 42.8 12.5 14.3 16.1 17.9 21.4 25.0 26.8 28.6 7.2 9.0 10.7 12.5 14.3 16.1 17.9 21.5 7.2 9.0 10.8 12.6 14.4 16.1 17.9 21.5 2.9 3.7 5.4 7.2 9.0 10.8

*10 (mm ) 1590.4 1963.5 2827.4 3848.5 4417.9 5026.5 6361.7 7854.0 11309.7 962.1 1256.6 1590.4 1963.5 2827.4 3848.5 4417.9 5026.5 314.2 490.9 706.9 962.1 1256.6 1590.4 1963.5 2827.4 314.2 490.9 706.9 962.1 1256.6 1590.4 1963.5 2827.4 50.3 78.5 176.7 314.2 490.9 706.9

2

WB 2

Table II-d. Linear mass of the pipe content G V (kg/m) 3

ID 25 40 50 80 100 150 200 250 300 350 400 450 500 600 700 750 800 900 1000 1200

Specific gravity of the fluid SV (kg/m ) 800 0.4 1.0 1.6 4.0 6.3 14.1 25.1 39.3 56.5 77.0 100.5 127.2 157.1 226.2 307.9 353.4 402.1 508.9 628.3 904.8

1000 0.5 1.3 2.0 5.0 7.9 17.7 31.4 49.1 70.7 96.2 125.7 159.0 196.3 282.7 384.8 441.8 502.7 636.2 785.4 1131.0

1200 0.6 1.5 2.4 6.0 9.4 21.2 37.7 58.9 84.8 115.5 150.8 190.9 235.6 339.3 461.8 530.1 603.2 763.4 942.5 1357.2

1400 0.7 1.8 2.7 7.0 11.0 24.7 44.0 68.7 99.0 134.7 175.9 222.7 274.9 395.8 538.8 618.5 703.7 890.6 1099.6 1583.4

10

1600 0.8 2.0 3.1 8.0 12.6 28.3 50.3 78.5 113.1 153.9 201.1 254.5 314.2 452.4 615.8 706.9 804.2 1017.9 1256.6 1809.6

1800 0.9 2.3 3.5 9.0 14.1 31.8 56.5 88.4 127.2 173.2 226.2 286.3 353.4 508.9 692.7 795.2 904.8 1145.1 1413.7 2035.8

Moment of resistance to bending

2000 1.0 2.5 3.9 10.1 15.7 35.3 62.8 98.2 141.4 192.4 251.3 318.1 392.7 565.5 769.7 883.6 1005.3 1272.3 1570.8 2261.9

3

3

*10 (mm ) 531.1 714.9 1228.7 1982.8 2409.5 2944.2 4174.6 5707.5 9813.3 273.1 407.4 579.8 794.9 1372.7 2178.8 2679.4 3302.4 77.1 125.0 215.6 342.1 510.3 726.2 1015.8 1748.4 80.3 160.4 273.9 431.2 652.5 922.4 1258.0 2184.0 12.8 19.7 43.7 106.5 206.3 354.5

II.5.2. Fittings

The minimum reinforced wall thickness (TE) of fittings is related to the minimum reinforced wall thickness (TE) of pipes by the ratio allowable hoop stress (SH) of pipes divided by the allowable hoop stress (SH) of fittings. The allowable hoop stress (SH) for pipes is given in table II-h.(page 23), being the Hydrostatic Design Stress (HDS). For fittings the allowable hoop stress is as follows: - tee/lateral/reducer: - elbow/double socket: Note:

SH = 32 N/mm² S H = 40 N/mm²

Fittings are only available in the series EST, EWT and CST. A non-tensile resistant pipe system is a combination of non-tensile resistant pipes with tensile resistant fittings.

Table II-e. Available standard Wavistrong systems. Pressure class (bar)

Inner diameter (mm) 25-50

80

100

150

200

250-300

350-400 1 2

8 10 1 2 1 2 3 1 2 3 1 2 3 1 2 3

12.5 16

20 1 2 3 1 2 3

25 1

1 2 3

32

Note:

1 2 3 4 5

= = = = =

CJ RSLJ RSJ LJ FJ

= = = = =

1 2 3 1 2 3 1 2 3

1 2 3 1 2 3 1 2 3 1 2 3

1 2 1 2 3 1 2 3 1 2 3

Adhesive bonded Joint Rubber Seal Lock Joint Rubber Seal Joint Laminated Joint Flanged Joint

Mechanical couplers on request. = See higher pressure class Other systems are available on request.

Available for all diameter/pressure class combinations marked with 1, 2 or 3.

11

450-600

700-800

900-1000

1200

2 2 3

2 2 3

2 2 3

2

2

2

2

2 3

2 3

2 3 2 3

II.5.3. Combined stresses

Fig. II.6. through II.8. (page 13 through 17) give the allowable axial (longitudinal) and hoop (circumferential) stress for pipes and fittings. Fig. II.6-a. through II.6-c. give the allowable axial stress and hoop stress for pipes, wound under winding angles of 55°, 63° or 73°, in combination with shear stress (τ). The equivalent stress (Seq), calculated with the use of the continuum theory and related to the Hydrostatic Design Stress (HDS), for the different pipes = 19.3 N/mm². For this case the service (design) factor referred to in ASTM D 2992, (Sf) = 0.5. The maximum equivalent stress (S eq(max)) for combined stresses in the pipe wall, due to the hydrostatic load plus external mechanical loads = 24.5 N/mm². For combined stress situations the maximum service (design) factor (Sf) = 0.67. In fig. II.7. and II.8. (page 16 and 17) the allowable axial stress and hoop stress for elbows and tees is given. For elbows the equivalent stress (Seq), related to the hydrostatic design stress (HDS), will be 12.3 N/mm². For tees this value will be 9.8 N/mm². The service (design) factor as mentioned in ASTM D 2992 will be (Sf) = 0.5. For combined stresses in the fittings the maximum equivalent stress (S eq(max)) will be 15.3 N/mm² and 12.3 N/mm² for respectively elbows and tees. The service (design) factor in combined stress situations will be (Sf) = 0.67. For examples of the use of fig. II.6. through II.8., see Appendix V.

"Zur Beanspruchung und Verformung von GfK Mehrschichten Verbunden", A. Puck, Kunststoffe-57, Teil 1-II, 1967. Heft 4-7-12.

12

Fig. II.6-a. Pipes, winding angle ω = 55°

13

Fig. II.6-b. Pipes, winding angle ω = 63°

14

Fig. II.6-c. Pipes, winding angle ω = 73°

15

Fig. II.7. Elbows

16

Fig. II.8. Tees

17

II.6. Head loss in pipes and fittings

II.6.1. Wavistrong pipes

Wavistrong pipe systems have a relatively low head loss due to their smooth inner surface. The head losses have been determined by using the Darcy Weisbach formula. The friction coefficients for the pipeline system are determined by the Colebrook-White method with a wall roughness k = 0.05 mm, including head loss over the joints. This approximates a Hazen-Williams coefficient of 150. For the pipes and fittings as such the wall roughness k = 0.01 to 0.02 mm. Head loss flow charts for pipes are shown in fig. II.9. and II.10. (page 21 and 22). These figures give the head loss for the pipeline system in metre water column per metre pipe length for water at 10°C. At higher operating temperatures the kinematic viscosity of water decreases, resulting in lower head losses.

II.6.2. Wavistrong fittings

The head loss in fittings can be calculated from the following formula:

(Eq. II.9.)

Where: ∆Hfitting ζ SV v

= = = =

head loss in the fitting friction coefficient specific gravity of the fluid flow velocity

(N/m²) (-) (kg/m3) (m/s)

The friction coefficient (ζ ) for elbows and tees is given in table II-f. and II-g. (page 18 and 20). The head loss in fittings can be expressed in an equivalent pipe length (LEQ) when using the head loss of pipes from fig. II.9. and II.10. (page 21 and 22).

(Eq. II.10.)

Where: LEQ ∆Hfitting ∆Hpipe g

= = = =

equivalent pipe length head loss in the fitting head loss in the pipe (fig. II.9. and II.10., page 21 and 22) acceleration due to gravity

18

(m) (N/m²) (m.w.c./m) (m/s²)

Table II-f. Friction coefficient ζ (-) for elbows

α

22°30' 45° 90° Note:

0.07 0.24

0.11 0.16

Elbows ID ≥ 450 mm are mitered. For all standard elbows the radius R = 1.5 * ID

19

0.30

Table II-g. Friction coefficient ζ (-) for tees and laterals Flow separation

ζ

Flow combination

Flow combination

Flow separation

ζd

ζ

ζd

ζ

ζd

ζ

ζd

0

1 0.58 0.35

0.04 0.25 0

0.95 1.30 1

0.04 0.20 0

-1.20 -0.70 -1.00

0.04 0 0

0.90 1.00 2.00

0.04 0 0

-0.92 -1.00 -1.00

0.2

1 0.58 0.35

-0.08 -0.20 0

0.88 1.55 3.00

0.17 0.45 0

-0.40 0.20 2.00

-0.06 -0.15 -0.10

0.68 0.45 2.00

0.17 0.10 0

-0.38 -0.10 2.00

0.4

1 0.58 0.35

-0.05 -0.10 0

0.89 2.40 9.00

0.30 0.75 0

0.08 1.30 12.00

-0.04 0 0

0.50 0.60 6.00

0.19 -0.15 -1.10

0 0.75 9.00

0.6

1 0.58 0.35

0.07 0 0

0.95 4.25 19.00

0.41 1.00 0

0.47 2.80 29.00

0.07 0.15 0.10

0.38 1.30 14.00

0.09 -0.60 -2.90

0.22 2.15 20.00

0.8

1 0.58 0.35

0.21 0.25 0

1.10 7.10 33.00

0.51 1.25 0

0.72 4.80

0.20 0.25 0.20

0.35 2.80 27.00

-0.17 -1.50 -5.70

0.37 3.75 35.00

1

1 0.58 0.35

0.35 0.30 0

1.28

0.60 1.50 0

0.91 7.25

0.33 0.35 0.40

0.48 4.90 44.00

-0.54 -2.90 -9.60

0.37 5.40 54.00

ζ ζd (flow separation)

= friction coefficient for pressure loss of

relative to

= friction coefficient for pressure loss of

ζd (flow combination)

= friction coefficient for pressure loss of

Φ

= flow in the run

Φd

= flow in the branch

20

.

relative to

relative to

.

.

Fig. II.9. Head loss flow chart ID 25 mm through 300 mm

21

Fig. II.10. Head loss flow chart ID 300 mm through 1200 mm

22

II.7. Wavistrong pipe properties

Tables II-h. through II-l. (page 23 and 24) detail the minimum properties, obtained when testing Wavistrong in accordance with the indicated test methods. Unless otherwise stated, all properties refer to the reinforced wall and are valid for temperatures at 20°C. For higher temperatures the correction factors for the E-moduli of table II-k. (page 24) should be applied.

Table II-h. Hydrostatic properties Winding angle (ω ) Property

Test method

55°

63°

73°

650

500

-

N/mm²

Bi-axial: (R = 0.5) Ultimate hoop stress (rupture) Ultimate hoop stress (weeping)

ASTM D 1599

250

200

-

N/mm²

Ultimate Elastic Wall Stress (UEWS)

Future Pipe Industries

160

140

-

N/mm²

Hydrostatic Design Basis HDB (50 years)

ASTM D 2992 B

125

100

-

N/mm²

Hydrostatic Design Stress HDS (50 years)

ASTM D 2992 B

63

50

-

N/mm²

1000

800

N/mm²

450

370

N/mm²

200

160

N/mm²

100

80

N/mm²

Uni-axial: (R = 0.25) Ultimate hoop stress (rupture)

-

Ultimate hoop stress (weeping)

ASTM D 1599

Hydrostatic Design Basis HDB (50 years)

ASTM D 2992 B

Hydrostatic Design Stress HDS (50 years)

ASTM D 2992 B

Minimum service (design) factor Sf = 0.5.

23

-

-

-

Table II-j. Mechanical properties Winding angle (ω ) Property

Test method

Axial tensile stress Axial tensile modulus

EX

Hoop tensile stress Hoop tensile modulus

55°

63°

73°

ASTM D 2105 ASTM D 2105

75 12000

55 11500

40 11500

N/mm² N/mm²

ASTM D 2290 ASTM D 2290

210 20500

260 27500

400 37000

N/mm² N/mm²

11500

9500

7000

N/mm²

Shear modulus

ES

Axial bending stress Axial bending modulus

EX

ASTM D 2925

80 12000

65 11500

50 11500

N/mm² N/mm²

Hoop bending stress Hoop bending modulus

EH

ASTM D 2412 ASTM D 2412

90 20500

120 27500

160 37000

N/mm² N/mm²

Poisson ratio axial/hoop Poisson ratio hoop/axial

NXY NYX

0.65 0.38

0.62 0.26

0.47 0.15

-

Table II-k. Temperature correction factor R E (-) for moduli of elasticity Correction factor RE (-) RE-Axial

Winding Angle

Temperature (°C)

RE-Hoop

(ω )

20

40

60

80

100

110

RE4 RE5 RE6

55° 63° 73° 55° 63° 73°

1 1 1 1 1 1

0.92 0.92 0.92 0.95 0.97 0.99

0.82 0.82 0.82 0.90 0.94 0.98

0.72 0.72 0.72 0.83 0.90 0.97

0.60 0.60 0.60 0.75 0.85 0.95

0.53 0.53 0.53 0.70 0.82 0.94

RE1 RE2 RE3

Table II-l. Physical properties Property Coefficient of linear thermal expansion Thermal conductivity Specific heat Glass content (by mass) Glass content (by volume) Specific gravity of the laminate Barcol hardness Surface resistance (Series C..)

Test method ϒL

ASTM D 696

ASTM D 2584 ASTM D 2584 SL ASTM D 2583 ASTM D 257

-5

2 * 10 0.29 921 70 ± 5 52 ± 7 1850 35 6 < 10 * 10

The first index gives the direction of the contraction, the second index gives the load direction.

24

mm/mm.°C W/m.K J/kg.K % % 3 kg/m Ω /m

II.8. Bending radius

The minimum allowable bending radius (Rb) for a pipe, installed at 20°C, is given in table II-n. and II-o. (page 27 and 28). The allowable radius depends on the operating temperature (T) and -pressure (P). For elevated operating temperatures, the indicated values of table II-n. and II-o. have to be corrected with the temperature correction factor (RE) from the table II-k. (page 24). The minimum allowable bending radius (Rb) has been calculated with the following formula:

(Eq. II.11.)

Where: Rb = bending radius RE = temperature correction factor (table II-k., page 24) EX = axial bending modulus (table II-j., page 24) DI = structural inner diameter SA = remaining axial stress

(m) (-) (N/mm²) (mm) (N/mm²)

The value of SA is defined as follows: (Eq. II.12.) Where: SA = remaining axial stress SXT = allowable axial stress SX = actual axial stress due to internal pressure

(N/mm²) (N/mm²) (N/mm²)

For bi-axial loaded systems:

(Eq. II.13.)

For uni-axial loaded systems:

(Eq. II.14.)

Where: SX = actual axial stress due to internal pressure P = operating pressure ID = inner diameter TE = minimum reinforced wall thickness (table II-b. and II-c., page 9 and 10)

25

(N/mm²) (Mpa) (mm) (mm)

The allowable axial stress (SXT) depends on the type of loading (R) and the winding angle (ω ) and is given in table II-m.

Table II-m. Allowable axial stress S XT (N/mm²) Winding angle (ω ) R (-)

55°

63°

73°

0.25 0.50

40

32 32

25 -

The values of table II-n. and II-o. (page 27 and 28) are only valid for the pipes of the indicated series. For available standard pipe systems, see table II-e., page 11.

26

Table II-n. Bending radius R b (m) at 20°C for series EST ID Series

(mm)

EST 8

350 400 450 500 600 700 750 800 900 1000 1200 250 300 350 400 450 500 600 700 750 800 900 1000 200 250 300 350 400 450 500 600 700 750 800 150 200 250 300 350 400 450 500 600 100 150 200 250 300 350 400 450 500 600 25 40 50 80 100 150 200 250 300

EST 12.5

EST 16

EST 20

EST 25

EST 32

Operating pressure (P) 1 * PN 297 339 381 424 508 593 635 641 725 810 978 178 214 250 285 321 332 403 474 509 545 616 687 159 180 225 271 292 337 383 450 517 562 607 110 131 167 203 239 276 312 348 406 45 99 136 172 209 246 271 307 344 417 6 11 18 39 72 119 154 189 225

0.8 * PN

0.6 * PN

170 195 219 243 292 340 365 379 428 476 573 102 122 143 163 183 197 238 279 299 319 360 400 86 103 125 148 165 188 210 250 290 313 335 62 79 99 120 140 161 181 202 239 32 59 80 100 121 142 159 180 201 242 5 10 14 27 41 64 85 105 125

120 137 154 171 205 239 256 269 303 337 405 72 86 100 114 128 140 169 197 211 226 254 283 59 72 87 102 115 130 145 173 201 217 232 43 56 70 85 99 113 128 142 169 25 42 57 71 85 100 113 127 142 170 5 9 12 21 29 44 58 73 87

27

0.4 * PN 92 105 118 131 158 184 197 209 235 261 314 55 66 77 88 99 109 131 153 164 175 196 218 45 55 66 78 88 99 111 133 154 166 177 33 44 55 66 77 88 99 109 131 21 33 44 55 66 77 87 98 109 131 4 8 10 17 22 33 44 55 66

0.2 * PN 75 86 96 107 128 150 160 170 192 213 256 45 54 63 71 80 89 107 125 133 142 160 178 36 45 54 63 72 81 90 107 125 134 143 27 36 45 53 62 71 80 89 107 17 27 36 45 54 62 71 80 89 107 4 7 9 14 18 27 36 45 54

0 * PN 63 72 81 90 108 126 135 144 162 180 216 38 45 53 60 68 75 90 105 113 120 135 150 30 38 45 53 60 68 75 90 105 113 120 23 30 38 45 53 60 68 75 90 15 23 30 38 45 53 60 68 75 90 4 6 8 12 15 23 30 38 45

Table II-o. Bending radius R b (m) at 20°C for series ESN ID Series

(mm)

ESN 10

450 500 600 700 750 800 900 1000 1200 350 400 450 500 600 700 750 800 200 250 300 350 400 450 500 600 200 250 300 350 400 450 500 600 80 100 150 200 250 300

ESN 16

ESN 20

ESN 25

ESN 32

Operating pressure (P) 1 * PN 331 383 465 522 575 603 685 766 929 297 339 381 424 508 593 635 641 106 214 256 299 342 384 398 483 173 198 247 296 321 370 418 493 25 39 132 157 200 243

0.8 * PN

0.6 * PN

230 262 316 361 392 415 469 523 631 170 195 219 243 292 340 365 379 76 122 147 171 195 220 236 285 98 118 144 170 190 216 242 288 22 32 74 94 119 143

176 199 239 275 298 316 356 397 478 120 137 154 171 205 239 256 269 60 86 103 120 137 154 168 202 69 84 102 119 135 152 170 203 20 27 52 67 84 101

28

0.4 * PN 143 160 192 223 240 255 287 320 384 92 105 118 131 158 184 197 209 49 66 79 92 105 118 130 157 53 65 79 92 104 118 131 157 18 23 40 52 65 79

0.2 * PN 120 134 161 187 201 214 241 268 321 75 86 96 107 128 150 160 170 42 54 64 75 86 96 107 128 43 53 64 75 85 96 107 128 16 20 32 43 53 64

0 * PN 104 115 138 161 173 184 207 230 276 63 72 81 90 108 126 135 144 36 45 54 63 72 81 90 108 36 45 54 63 72 81 90 108 15 18 27 36 45 54

II.9. Fluid (water) hammer

Fluid (water) hammer can be defined as the occurrence of pressure changes in closed piping systems, caused by changes in the flow velocity. Therefore, fluid (water) hammer can occur in all kinds of piping systems for the transportation of liquids. The greater and faster the velocity changes are, the greater the pressure changes will be. The relation between change of velocity and pressure can be derived from the formula of Joukowsky :

(Eq. II.15.)

Where: ∆P = pressure change c = wave velocity g = acceleration due to gravity ∆v = change in flow velocity

(m.w.c) (m/s) (m/s2) (m/s)

In accordance with ANSI/AWWA C950-88 a transient pressure increase of 1.4 times the design pressure is allowable, which is also valid for the Wavistrong piping system. The wave velocity (c) depends on the type of fluid, pipe dimensions and the E-modulus. The wave velocity can be calculated with the aid of the Talbot equation:

(Eq. II.16.)

Where: c = wave velocity SV = specific gravity of the fluid KV = compression modulus of the fluid ID = inner diameter TE = minimum reinforced wall thickness (table II-b. and II-c., page 9 and 10) EV = volumetric E-modulus f = constant

(m/s) (kg/m3) (N/mm2) (mm) (mm) (N/mm2) (-)

This calculation method is only valid for straight pipeline sections with different types of joints. On request, system calculations can be made by a third party.

29

For isotropic materials, the volumetric E-modulus is equal to the E-modulus. For an-isotropic materials, where the material characteristics are dependent on the winding angle ( ω ), the volumetric E-modulus (EV) is calculated from the following equation:

(Eq. II.17.)

Where: EV = volumetric E-modulus EX = axial bending modulus EH = hoop bending modulus NXY = Poisson ratio axial/hoop NYX = Poisson ratio hoop/axial

"

(N/mm2) (N/mm2) (N/mm2) (-) (-)

(table II-j., page 24) " " " " "

For the three winding angles ( ω ) of the Wavistrong pipes the volumetric E-modulus (EV) is given in table II-p.

Table II-p. Volumetric E-modulus E V (N/mm²) Winding angle (ω )

55°

63°

73°

EV

22775

24515

26965

The constant (f) in the Talbot equation depends on the type of anchoring of the system: A. The pipeline may be anchored up-stream; in this case the system is loaded bi-axially. This can be achieved in a tensile resistant piping system.

(Eq. II.18.)

B. The pipeline may be anchored completely to prevent axial displacements. This may occur in tensile resistant and non-tensile resistant piping systems. (Eq. II.19.) C. The pipeline may be installed with expansion joints so that there will be no axial stresses. This will happen in case of non-tensile resistant pipelines. (Eq. II.20.)

30

The constant (f) is given in table II-q. for the three winding angles (ω ).

Table II-q. Constant f (-) Winding angle (ω ) Constant f1 f2 f3

55° 1.1265 0.753 0.81

63°

73°

1.1694 0.8388 0.87

1.2148 0.9295 0.925

The values of the wave velocity (c) (c1 through c3) are related to the type of anchoring of the pipeline system (constant f1 through f3). For the two systems EST and ESN these values are listed in table II-r. (page 32).

31

Table II-r. Wave velocity c1, c2 and c3 (m/s) for series EST and ESN Series EST 8

EST 12.5

EST 16

EST 20

EST 25

EST 32

Note:

ID (mm) 350 400 450 500 600 700 750 800 900 1000 1200 250 300 350 400 450 500 600 700 750 800 900 1000 200 250 300 350 400 450 500 600 700 750 800 150 200 250 300 350 400 450 500 600 100 150 200 250 300 350 400 450 500 600 25 40 50 80 100 150 200 250 300

c1 394 394 394 394 394 394 394 397 396 396 396 429 429 429 429 429 433 432 432 432 431 431 431 474 479 477 476 479 477 476 477 478 477 476 529 536 534 533 533 532 532 531 533 626 589 587 586 585 585 587 586 586 585 923 794 733 684 647 640 642 643 643

c2

Series

458 458 458 458 458 458 458 461 461 461 460 513 513 513 513 513 518 517 517 516 516 516 516 565 571 568 566 570 568 567 568 569 568 567 626 634 632 631 630 630 629 629 631 732 692 690 689 688 687 690 689 689 688 1028 904 843 793 754 747 749 750 750

ESN 10

ESN 16

ESN 20

ESN 25

ESN 32

values of table II-r. are valid for the following conditions: KV = 2050 N/mm SV = 1000 kg/m

2

3

32

ID (mm) 450 500 600 700 750 800 900 1000 1200 350 400 500 600 700 750 800 200 250 300 350 400 450 500 600 200 250 300 350 400 450 500 600 80 100 150 200 250 300

c2 388 385 434 438 435 437 436 435 434 458 458 458 458 458 458 461 547 506 506 506 506 506 510 509 557 562 560 558 562 560 559 560 784 723 617 625 623 622

c3 439 435 435 439 436 438 437 436 435 451 451 451 451 451 451 454 539 498 498 498 498 498 502 501 548 554 551 550 553 551 550 551 774 713 608 616 614 613

II.10. Stiffness

An investigation of standards concerning the stiffness of flexible pipes shows that there are different opinions on the interpretation of pipe stiffness. The following identifications illustrate this point.

A. Specific Tangential Initial Stiffness (STIS) The STIS is described in NEN 7037 and is calculated with the following formula:

(Eq. II.21.) Where: STIS EH TE ID

= = = =

Specific Tangential Initial Stiffness (N/m2) hoop bending modulus (table II-j., page 24) (N/m2) minimum reinforced wall thickness (table II-b. and II-c., page 9 and 10) (mm) inner diameter (mm)

B. Specific Tangential End Stiffness (STES) The STES will be derived from the STIS and gives information on the regression of the stiffness in relation to the life time (50 years). The determination of the STES is described in NEN 7037. (Eq. II.22.) Where: STES α β STIS

= = = =

Specific Tangential End Stiffness creep factor ageing factor Specific Tangential Initial Stiffness (Eq. II.21.)

For the glass fibre reinforced epoxy Wavistrong pipes α * β = 0.9.

33

(N/m2) (-) (-) (N/m2)

C. Stiffness Factor (SF) Another identification of the stiffness is described in ASTM D 2412 and is called the Stiffness Factor (SF):

(Eq. II.23.)

Where: SF = Stiffness Factor EH = hoop bending modulus (table II-j., page 24) TE = minimum reinforced wall thickness (table II-b. and II-c., page 9 and 10)

(in2.lb/in) (psi) (in)

The Stiffness Factor (SF) can also be calculated from the STIS-value by using the following formula: (Eq. II.24.) Where: SF STIS ID TE

= = = =

Stiffness Factor (in2.lb/in) Specific Tangential Initial Stiffness (Eq. II.21.) (N/m2) inner diameter (m) minimum reinforced wall thickness (table II-b. and II-c., page 9 and 10) (m)

There is also a relation between the Stiffness Factor (SF) and the Pipe Stiffness (PS): (Eq. II.25.) Where: SF = Stiffness Factor rm = mean pipe radius PS = Pipe Stiffness (Eq. II.26.)

(in2.lb/in) (in) (psi)

34

D. Pipe Stiffness (PS) The Pipe Stiffness (PS) is described in ASTM D 2412 and can be calculated as follows:

(Eq. II.26.)

Where: PS EH TE ID

= = = =

Pipe Stiffness hoop bending modulus (table II-j., page 24) minimum reinforced wall thickness (table II-b. and II-c., page 9 and 10) inner diameter

(psi) (psi) (in) (in)

The Pipe Stiffness (PS) can also be calculated from the STIS-value by the following formula: (Eq. II.27.) Where: PS = Pipe Stiffness STIS = Specific Tangential Initial Stiffness (Eq. II.21.)

(psi) (N/m2)

In table II-s. (page 36) the different stiffness values at a temperature of 20°C are listed. At temperatures in excess of 20°C the reduction factors (RE) for the moduli of elasticity should be applied (table II-k., page 24).

35

Table II-s. Stiffness for series EST and ESN at 20°C.

Series EST 8

EST 12.5

EST 16

EST 20

EST 25

EST 32

ID (mm) 350 400 450 500 600 700 750 800 900 1000 1200 250 300 350 400 450 500 600 700 750 800 900 1000 200 250 300 350 400 450 500 600 700 750 800 150 200 250 300 350 400 450 500 600 100 150 200 250 300 350 400 450 500 600 25 40 50 80 100 150 200 250 300

Series EST STIS SF (N/m²) (in²lb/in) 1150 450 1150 660 1150 950 1150 1300 1150 2240 1150 3560 1150 4380 1200 5570 1190 7890 1190 10780 1180 18510 1660 240 1660 410 1660 650 1660 970 1660 1380 1760 2010 1740 3430 1730 5410 1720 6640 1720 8030 1710 11390 1710 15570 3210 240 3450 500 3340 830 3270 1290 3410 2010 3340 2800 3290 3780 3340 6640 3380 10660 3340 12960 3310 15570 6670 210 7310 540 7180 1040 7090 1780 7030 2800 6980 4150 6950 5880 6920 8030 7090 14230 21990 210 14180 450 13850 1040 13650 2010 13520 3430 13430 5410 13850 8330 13740 11770 13650 16040 13520 27450 517590 90 136410 90 71680 90 42210 210 27800 270 25770 830 26270 2010 26570 3960 26770 6900

PS (psi)

Series

9 9 9 9 9 9 9 9 9 9 9 13 13 13 13 13 14 14 13 13 13 13 13 25 27 26 25 27 26 26 26 26 26 26 52 57 56 55 55 54 54 54 55 171 110 108 106 105 105 108 107 106 105 4029 1062 558 329 216 201 204 207 208

ESN 10

ESN 16

ESN 20

ESN 25

ESN 32

36

ID (mm) 450 500 600 700 750 800 900 1000 1200 350 400 500 600 700 750 800 200 250 300 350 400 450 500 600 200 250 300 350 400 450 500 600 80 100 150 200 250 300

Series ESN STIS SF (N/m²) (in²lb/in) 1190 980 1130 1270 1110 2170 1170 3620 1130 4300 1150 5320 1140 7490 1130 10180 1110 17350 1150 450 1150 660 1150 1300 1150 2240 1150 3560 1150 4380 1200 5570 3820 280 2220 320 2220 550 2220 870 2220 1300 2220 1850 2360 2690 2340 4600 4310 320 4630 660 4480 1110 4390 1730 4570 2690 4480 3760 4420 5070 4480 8900 56620 280 29500 280 8950 280 9800 730 9630 1400 9510 2390

PS (psi) 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 30 17 17 17 17 17 18 18 34 36 35 34 36 35 34 35 441 230 70 76 75 74

II.11. Buckling pressure

For the calculation of the allowable buckling pressure (PB) for the Wavistrong series, the formula for thin wall pipes (mean radius/wall thickness > 10) has to be used. Besides, the allowable buckling pressure (PB) depends on the diameter/pipe length ratio. In case of integral joints, the pipe ends are much stiffer than the pipe-body itself. The pipe length (L) is the measurement between the stiff ends. The allowable buckling pressure (P B) is determined by the stability of the product. The transition from a stable into an unstable condition will take place very abruptly, so an extra safety in the form of a service factor (SF) is applied. Due to the unstable situation the allowable buckling pressure (PB) has also been made dependent on the type of loading, which can be static or cyclic. In some cases the allowable buckling pressure (P B) depends on the length between the stiff ends. Some extra external pressure allowance can be created by the application of stiffening rings. For the standard lengths of 6 and 10 metres two or one, respectively three, two or one stiffening rings can be used. The allowable external pressures for pipes are listed in table II-t. and II-u. (page 39 and 40). The tabled values are valid for an operating temperature (T) of 20°C. For higher temperatures the correction factors (RE) from table II-k. (page 24) should be applied. The listed values have been calculated for a static buckling pressure. The length, mentioned in the table depends on the standard length of the pipe and the application of a number of stiffening rings. Standard pipe lengths are mentioned in the Wavistrong Product List.

The values in table II-t. and II-u. (page 39 and 40) for pipes with stiff ends, are calculated using the following equations :

Buckling pressure (PB) = external pressure (PE) - internal pressure (PI) Full vacuum means: PE - PI = 1 bar. Roark/Young, Formulas for stress and strain, McGraw-Hill, fifth edition.

37

If:

(Eq. II.28.)

Then:

(Eq. II.29.)

Else:

(Eq. II.30.) Where: TE = minimum reinforced wall thickness (table II-b. and II-c., page 9 and 10) ID = inner diameter L = length between stiff pipe ends NXY = Poisson ratio axial/hoop (table II-j., page 24) NYX = Poisson ratio hoop/axial (table II-j., page 24) rm = mean pipe radius EH = hoop bending modulus (table II-j., page 24) SF = service factor (SF = 0.75) Sb = load-dependent safety factor static loading: Sb = 1 cyclic loading: Sb = 2 PB = buckling pressure

(mm) (mm) (mm) (-) (-) (mm) (N/mm2) (-) (-)

(bar)

At temperatures above 20°C the value (R E) of table II-k. (page 24) should be applied as follows: PBT = PB * RE4 (RE5 or RE6)

(Eq. II.31.)

Where: PBT = buckling pressure at elevated temperature PB = buckling pressure (table II-t. and II-u., page 39 and 40) RE4, RE5, RE6 = temperature correction factors for E-modulus for winding angles of respectively 55°, 63° or 73° (table II-k., page 24)

For plain end pipes without stiff ends, use equation II.29. only!

38

(bar) (bar) (-)

Table II-t. Allowable static buckling pressure P B (bar) at 20°C, series EST Series EST 8

EST 12.5

EST 16

EST 20

EST 25

EST 32

ID (mm) 350 400 450 500 600 700 750 800 900 1000 1200 250 300 350 400 450 500 600 700 750 800 900 1000 200 250 300 350 400 450 500 600 700 750 800 150 200 250 300 350 400 450 500 600 100 150 200 250 300 350 400 450 500 600 25 40 50 80 100 150 200 250 300

1 1.1 1.2 1.4 1.5 1.8 2.1 2.3 2.5 2.8 3.1 3.7 1.1 1.3 1.5 1.7 1.9 2.2 2.7 3.1 3.3 3.5 4.0 4.4 1.5 2.0 2.3 2.6 3.1 3.5 3.8 4.6 5.4 5.8 6.1 2.0 2.9 3.6 4.3 5.0 5.7 6.4 7.1 8.6 5.1 3.8 5.0 6.2 7.4 8.6 10.1 11.3 12.5 14.9 110.8 30.4 16.2 9.7 6.5 6.3 8.6 10.9 13.2

2 0.5 0.6 0.7 0.8 0.9 1.1 1.1 1.3 1.4 1.6 1.9 0.5 0.6 0.7 0.9 1.0 1.1 1.3 1.5 1.7 1.8 2.0 2.2 0.8 1.0 1.1 1.3 1.6 1.7 1.9 2.3 2.7 2.9 3.0 1.6 1.7 1.8 2.2 2.5 2.8 3.2 3.5 4.3 5.1 3.3 3.3 3.2 3.7 4.3 5.0 5.6 6.2 7.4 110.8 30.4 16.2 9.7 6.5 6.0 6.2 6.3 6.3

Pipe length L (m) between stiff ends 2.5 3 3.3 5 0.4 0.4 0.3 0.2 0.5 0.4 0.4 0.2 0.5 0.5 0.4 0.3 0.6 0.5 0.5 0.3 0.7 0.6 0.6 0.4 0.8 0.7 0.6 0.4 0.9 0.8 0.7 0.5 1.0 0.8 0.8 0.5 1.1 0.9 0.9 0.6 1.3 1.0 0.9 0.6 1.5 1.2 1.1 0.7 0.4 0.4 0.4 0.4 0.5 0.4 0.4 0.4 0.6 0.5 0.5 0.4 0.7 0.6 0.5 0.4 0.8 0.6 0.6 0.4 0.9 0.7 0.7 0.4 1.1 0.9 0.8 0.5 1.2 1.0 0.9 0.6 1.3 1.1 1.0 0.7 1.4 1.2 1.1 0.7 1.6 1.3 1.2 0.8 1.8 1.5 1.3 0.9 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.9 0.8 0.8 0.8 1.1 0.9 0.8 0.8 1.2 1.0 0.9 0.8 1.4 1.2 1.0 0.8 1.5 1.3 1.1 0.8 1.8 1.5 1.4 0.9 2.2 1.8 1.6 1.1 2.3 1.9 1.7 1.2 2.4 2.0 1.8 1.2 1.6 1.6 1.6 1.6 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 2.0 1.7 1.7 1.7 2.3 1.9 1.7 1.7 2.5 2.1 1.9 1.7 2.8 2.4 2.1 1.6 3.5 2.9 2.6 1.7 5.1 5.1 5.1 5.1 3.3 3.3 3.3 3.3 3.3 3.3 3.3 3.3 3.2 3.2 3.2 3.2 3.2 3.2 3.2 3.2 3.4 3.2 3.2 3.2 4.0 3.3 3.3 3.3 4.5 3.8 3.4 3.3 5.0 4.2 3.8 3.2 5.9 5.0 4.5 3.2 110.8 110.8 -.-.30.4 30.4 -.-.16.2 16.2 -.-.9.7 9.7 9.7 9.7 6.5 6.5 6.5 6.5 6.0 6.0 6.0 6.0 6.2 6.2 6.2 6.2 6.3 6.3 6.3 6.3 6.3 6.3 6.3 6.3

For plain end pipes without stiff ends, use equation II.29. only!

39

6 0.2 0.2 0.2 0.3 0.3 0.4 0.4 0.4 0.5 0.5 0.6 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.5 0.6 0.6 0.7 0.7 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.9 1.0 1.0 1.6 1.7 1.7 1.7 1.7 1.7 1.7 1.6 1.7 5.1 3.3 3.3 3.2 3.2 3.2 3.3 3.3 3.2 3.2 -.-.-.9.7 6.5 6.0 6.2 6.3 6.3

10 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.3 0.3 0.3 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 -.1.7 1.7 1.7 1.7 1.7 1.7 1.6 1.7 -.-.3.3 3.2 3.2 3.2 3.3 3.3 3.2 3.2 -.-.-.-.-.-.6.2 6.3 6.3

Table II-u. Allowable static buckling pressure P B (bar) at 20°C, series ESN Series ESN 10

ESN 16

ESN 20

ESN 25

ESN 32

ID (mm) 450 500 600 700 750 800 900 1000 1200 350 400 450 500 600 700 750 800 200 250 300 350 400 450 500 600 200 250 300 350 400 450 500 600 80 100 150 200 250 300

1 1.4 1.5 1.7 2.1 2.2 2.4 2.6 2.9 3.4 1.1 1.2 1.4 1.5 1.8 2.1 2.3 2.5 1.7 1.3 1.6 1.8 2.1 2.4 2.8 3.3 1.8 2.4 2.8 3.3 3.9 4.3 4.7 5.7 11.7 6.1 2.5 3.6 4.5 5.3

2 0.7 0.7 0.9 1.0 1.1 1.2 1.3 1.5 1.7 0.5 0.6 0.7 0.8 0.9 1.1 1.1 1.3 0.8 0.7 0.8 0.9 1.1 1.2 1.4 1.6 0.9 1.2 1.4 1.6 1.9 2.1 2.3 2.8 11.7 6.1 1.9 2.1 2.2 2.7

Pipe length L (m) between stiff ends 2.5 3 3.3 5 0.5 0.5 0.4 0.3 0.6 0.5 0.4 0.3 0.7 0.6 0.5 0.3 0.8 0.7 0.6 0.4 0.9 0.7 0.7 0.4 0.9 0.8 0.7 0.5 1.1 0.9 0.8 0.5 1.2 1.0 0.9 0.6 1.4 1.1 1.0 0.7 0.4 0.4 0.3 0.2 0.5 0.4 0.4 0.2 0.5 0.5 0.4 0.3 0.6 0.5 0.5 0.3 0.7 0.6 0.6 0.4 0.8 0.7 0.6 0.4 0.9 0.8 0.7 0.5 1.0 0.8 0.8 0.5 0.8 0.8 0.8 0.8 0.5 0.5 0.5 0.5 0.6 0.5 0.5 0.5 0.7 0.6 0.6 0.5 0.8 0.7 0.6 0.5 0.9 0.8 0.7 0.5 1.1 0.9 0.8 0.6 1.3 1.1 1.0 0.7 0.9 0.9 0.9 0.9 1.0 1.0 1.0 1.0 1.1 1.0 1.0 1.0 1.3 1.1 1.0 0.9 1.5 1.3 1.2 1.0 1.7 1.4 1.3 1.0 1.9 1.6 1.4 0.9 2.3 1.9 1.7 1.1 11.7 11.7 11.7 11.7 6.1 6.1 6.1 6.1 1.9 1.9 1.9 1.9 2.1 2.1 2.1 2.1 2.0 2.0 2.0 2.0 2.1 2.0 2.0 2.0

For plain end pipes without stiff ends, use equation II.29. only!

40

6 0.2 0.2 0.3 0.3 0.4 0.4 0.4 0.5 0.6 0.2 0.2 0.2 0.3 0.3 0.4 0.4 0.4 0.8 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.9 1.0 1.0 0.9 1.0 1.0 0.9 1.0 11.7 6.1 1.9 2.1 2.0 2.0

10 0.2 0.2 0.2 0.2 0.2 0.2 0.3 0.3 0.3 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.3 0.8 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.9 1.0 1.0 0.9 1.0 1.0 0.9 1.0 -.-.-.2.1 2.0 2.0

II.12. Classification

The Wavistrong pipes can be classified in accordance with ASTM D 2310, indicating type, grade and Hydrostatic Design Basis (HDB). The classification for all pipes in the series EST 12.5 through EST 32 in accordance with this specification is 11FW1. The classification for all pipes in the series EST 8 is 11FU1. For the non-tensile resistant pipes in the series ESN 16 through ESN 32 the classification code in accordance with ASTM D 2310 is 11FY2. For pipes in the series ESN 10 the classification will be 11FX2. The complete pipe designation code in accordance with ASTM D 2996, also identifying the cell classification designations of short term rupture strength, longitudinal tensile strength, longitudinal tensile modulus (EX) and apparent Stiffness Factor (SF) is presented in table II-v.

Table II-v. Designation code Series EST

ESN

PN (bar)

8

10

Code

11FU1-

11FX2-

EST

EST

12.5

ESN

EST

11FY2-

11FW1-

16

11FW1- 11FW1-

ESN

EST

11FY2-

11FW1-

20

ESN

EST

25

ESN 32

11FY2-

11FW1- 11FY2-

ID 25 40

2111 2111

50 80 100

2111 2112 2114

5112 5116

5112

2115 2116

5116 5116

2112

150 200

2112

2112

2112 2112

5112

2112 2113

250

2112

2112

300

2112

2112

2113

5112

2115

5112

2116

5116

2114

5112

2116

5113

2116

2112 2112

2113 2115

5116

5112 5112

2116 2116

5112 5113

2116 2116

5114 5116

2116 2116 2116

5114 5116 5116

2116 2116 2116

5116 5116 5116

350 400

2112 2112

450 500 600

2112 2113 2115

4012 4013 4015

2113 2116 2116

2116 2116 2116

5112 5113 5115

700 750 800

2116 2116 2116

4016 4016 4016

2116 2116 2116

2116 2116 2116

5116 5116 5116

900 1000 1200

2116 2116 2116

4016 4016 4016

2116 2116

41

III. Wavistrong above ground pipe systems III.1. Design

In nearly all above ground applications thrust resistant types of joints are used (adhesive bonded joint, rubber seal lock joint, laminated joint or flanged joint). In case of well supported and anchored pipelines non-thrust resistant systems can be used (rubber seal joint or mechanically joined systems). In II.4. (page 4) a brief review of the various types of joints is given.

III.2. Supports

Above ground pipeline systems are installed on supports. At least one support per standard pipe length should be used if the joining is a flanged joint or rubber seal (lock) joint system (fig. III.1.). In case mechanical couplers are used, Future Pipe Industries engineers are pleased to inform you about the supporting. If one of the other tensile resistant joints is used, the support distance may never exceed the values listed in table III-c. through III-e. (page 49 through 51), taking into account Eq.III.11., page 47. Whether the support system is new or old, take care that the couplers do not interfere with the supports; the support should not be located at the pipe joint (fig. III.1.).

Fig. III.1. III.3. Clamps

For the supporting of Wavistrong pipe systems several types of clamps can be used. Point- and line loading must be avoided and therefore flat strips should be used (fig. III.2. a and b, page 43). The width of the clamps should be in accordance with applicable standards. The inside of the clamp must be provided with a protective rubber or thermoplastic layer. Guides enabling the pipe system to move freely in longitudinal direction should have a low friction inner surface to allow for this movement. In this case a protective layer of PTFE, PE or equivalent is required.

42

For the design of clamps, detailed drawings are available on request.

Fig. III.2.a Single clamp

Fig. III.2.b Double clamp

III.4. Support distance

Table III-c. through III-e. (page 49 through 51) show the maximum support distance (L') for the different pipe series (pipe series number = nominal pressure PN), at various operating pressures (P) and temperatures (T). The calculations have been made for water filled pipes where the specific gravity SV = 1000 kg/m3. These tables enable the selection of a pipe system for a given support distance or the determination of the maximum allowable distance between the supports for a given pipe system (mind the remarks in III.2., page 42). The support distance depends on one of the following two criteria: A. The axial stress, B. The allowable sag, which has been set on 5 ‰ of the span length. If A. is the determining factor, the support distance will change with an increasing pressure. If B. is the determining factor, the support distance will change with an increasing temperature.

The span length can be divided in: - Single span length (LS) as described in III.4.1., - Continuous span length (LC) as described in III.4.2., page 45.

III.4.1. Single span length

The single span length (LS) is the length between two supports of one single pipe or a string of flexible jointed pipes (fig. III.3.). The single span length (LS) should be used in each of the following situations (fig. III.5., page 47):

43

Fig. III.3.

-

For pipe systems where the joint is not designed to transmit bending forces; this is the case for mechanical couplers, flanged joints and the rubber seal (lock) joint, Twice on each side of any change of direction, Twice on both sides of an anchored valve or pump, Twice on both sides of an expansion joint or expansion loop.

The single span length (LS) is calculated from the following formulas: A. Based on the axial stress:

(Eq. III.1.)

Where: LS1 = single span length based on axial stress W B = moment of resistance to bending (table II-b. and II-c., page 9 and 10) SA = remaining axial stress QP = linear weight of the filled pipe (Eq. III.5.)

(mm) (mm3) (N/mm2) (N/mm)

The value of SA depends on the actual stress due to internal pressure: (Eq. III.2.) Where: SA = remaining axial stress SXT = allowable axial stress (table II-m., page 26) SX = actual axial stress due to internal pressure

(N/mm2) (N/mm 2) (N/mm2)

For bi-axial loaded systems:

(Eq. III.3.)

For uni-axial loaded systems:

(Eq. III.4.)

Where: SX = actual axial stress due to internal pressure P = operating pressure ID = inner diameter TE = minimum reinforced wall thickness (table II-b. and II-c., page 9 and 10)

44

(N/mm2) (Mpa) (mm) (mm)

The value of QP depends on the type of fluid that is transported:

(Eq. III.5.)

Where: QP = linear weight of the filled pipe GB = linear mass of the pipe (table II-b. and II-c., page 9 and 10) GV = linear mass of the pipe content (table II-d., page 10) g = acceleration due to gravity

(N/mm) (kg/m) (kg/m) (m/s2)

B. Based on the allowable sag:

(Eq. III.6.)

Where: LS2 = single span length based on the allowable sag EXT = axial bending modulus at elevated temperature IZ = linear moment of inertia (table II-b. and II-c., page 9 and 10) QP = linear weight of the filled pipe (Eq. III.5.)

(mm) (N/mm2) (mm 4) (N/mm)

At temperatures in excess of 20°C the correction factors for the E-moduli (RE) of table II-k. (page 24) should be applied as follows: (Eq. III.7.) Where: EXT = axial bending modulus at elevated temperature EX = axial bending modulus (table II-j., page 24) RE1, RE2 or RE3 = temperature correction factors for winding angles of respectively 55°, 63° or 73°. (table II-k., page 24)

The single span length (LS) will be the lowest value of LS1 and LS2.

III.4.2. Continuous span length

The continuous span length (LC) is the length between two supports of a string of rigid jointed pipes (fig. III.4.).

Fig. III.4.

45

(N/mm2) (N/mm2) (-)

The continuous span length (LC) may be used for pipe systems where the joint is rigid and capable to transmit bending forces. This continuous span length (LC) can be used for adhesive bonded and laminated pipe systems. The continuous span length (LC) is calculated from the following formulas:

A. Based on the axial stress:

(Eq. III.8.)

Where: LC1 = continuous span length based on axial stress W B = moment of resistance to bending (table II-b. and II-c., page 9 and 10) SA = remaining axial stress (Eq. III.2.) QP = linear weight of the filled pipe (Eq. III.5.)

(mm) (mm3) (N/mm2) (N/mm)

From above it can be found that: LC1 = 1.225 * LS1

B. Based on the allowable sag:

(Eq. III.9.)

Where: LC2 = continuous span length based on the allowable sag EXT = axial bending modulus at elevated temperature IZ = linear moment of inertia (table II-b. and II-c., page 9 and 10) QP = linear weight of the filled pipe (Eq. III.5.)

(mm) (N/mm2) (mm 4) (N/mm)

From above it can be found that: LC2 = 1.71 * LS2 At temperatures in excess of 20°C the correction factors for the E-moduli (RE) of table II-k. (page 24) should be applied as follows: (Eq. III.10.) Where: EXT = axial bending modulus at elevated temperature EX = axial bending modulus (table II-j., page 24) RE1, RE2 or RE3 = temperature correction factors for winding angles of respectively 55°, 63° or 73°. (table II-k., page 24)

46

(N/mm2) (N/mm2)

(-)

The continuous span length (LC) will be the lowest value of LC1 and LC2.

Fig. III.5. Example of single span length (LS) and continuous span length (LC) (III.4.1. and III.4.2., page 43 through 47).

III.5. Corrected support distance

Depending on the application, the values of table III-c. through III-e. (page 49 through 51) have to be multiplied with one or more of the following correction factors:

A. Specific gravity correction factor (R S) Above ground pipelines used for the transportation of fluids with a specific gravity (SV) other than 1000 kg/m3 should be supported at a span length adapted with the correction factor (RS) as listed in table III-a. (page 48)

B. Temperature change correction factor (R T) When temperature changes occur in a straight pipeline between fixed points, a correction factor (RT) as shown in table III-b. (page 48) must be applied. The final support distance (LF) can be derived from the following equation: (Eq. III.11.) Where: LF = final support distance L' = support distance at operating temperature (T) and -pressure (P) (table III-c. through III-e. (page 49 through 51)) RS = specific gravity correction factor (table III-a., page 48) RT = temperature change correction factor (table III-b., page 48)

47

(m) (m) (-) (-)

Table III-a. Specific gravity correction factor R S (-) 3

Specific gravity of the fluid SV (kg/m ) RS

0

600

800

900

1000

1100

1250

1.55

1.25

1.07

1.03

1.0

0.95

0.90

Table III-b. Temperature change correction factor R T (-) Temperature change ∆ T (°C) ID (mm) 25 40

10

20

30

40

50

60

70

80

90

100

0.73 0.81

0.58 0.69

0.49 0.60

0.44 0.54

0.39 0.49

0.36 0.45

0.34 0.42

0.32 0.40

0.30 0.38

0.28 0.36

50 80 100

0.85 0.90 0.92

0.73 0.81 0.85

0.65 0.74 0.79

0.59 0.69 0.74

0.54 0.64 0.69

0.50 0.60 0.66

0.47 0.57 0.62

0.44 0.54 0.59

0.42 0.51 0.57

0.40 0.49 0.54

150 200

0.92 0.94

0.85 0.89

0.80 0.84

0.75 0.81

0.72 0.77

0.68 0.75

0.66 0.72

0.63 0.70

0.61 0.68

0.59 0.66

250

0.95

0.91

0.87

0.84

0.81

0.79

0.76

0.74

0.72

0.70

300 350 400

0.96 0.96 0.97

0.92 0.93 0.94

0.89 0.91 0.92

0.87 0.88 0.89

0.84 0.86 0.87

0.82 0.84 0.85

0.80 0.82 0.83

0.78 0.80 0.82

0.76 0.79 0.80

0.74 0.77 0.79

450 500 600

0.97 0.97 0.98

0.95 0.95 0.96

0.92 0.93 0.94

0.90 0.91 0.93

0.88 0.90 0.91

0.87 0.88 0.90

0.85 0.86 0.88

0.83 0.85 0.87

0.82 0.83 0.86

0.80 0.82 0.85

700 750 800

0.99 0.99 0.99

0.98 0.98 0.98

0.97 0.97 0.97

0.96 0.96 0.96

0.95 0.95 0.95

0.94 0.94 0.95

0.93 0.94 0.94

0.92 0.93 0.93

0.91 0.92 0.93

0.91 0.91 0.92

900 1000

0.99 0.99

0.98 0.98

0.98 0.98

0.97 0.97

0.96 0.97

0.96 0.96

0.95 0.96

0.94 0.95

0.94 0.94

0.93 0.94

1200

0.99

0.99

0.98

0.98

0.97

0.97

0.96

0.96

0.95

0.95

48

Table III-c. Support distance L' (m) for series EST, P = 1 * P N (bar). Series

EST 8

EST 12.5

EST 16

EST 20

EST 25

EST 32

ID

T = 20° C

(mm)

LS

350 400 450 500 600 700 750 800 900 1000 1200 250 300 350 400 450 500 600 700 750 800 900 1000 200 250 300 350 400 450 500 600 700 750 800 150 200 250 300 350 400 450 500 600 100 150 200 250 300 350 400 450 500 600 25 40 50 80 100 150 200 250 300

4.0 4.2 4.5 4.7 5.2 5.6 5.8 6.2 6.6 6.9 7.5 4.0 4.4 4.7 5.1 5.4 5.9 6.4 6.9 7.2 7.4 7.8 8.2 3.8 4.5 4.8 5.1 5.6 5.9 6.1 6.8 7.4 7.6 7.8 3.8 4.7 5.2 5.6 6.1 6.5 6.8 7.2 8.0 3.7 4.5 5.1 5.6 6.1 6.6 7.2 7.6 8.0 8.7 2.0 2.4 2.6 3.4 3.8 4.5 5.3 5.9 6.6

LC 4.9 5.2 5.5 5.8 6.4 6.9 7.1 7.6 8.0 8.5 9.2 4.9 5.4 5.8 6.2 6.6 7.3 7.9 8.5 8.8 9.0 9.6 10.1 4.6 5.5 5.8 6.2 6.9 7.2 7.5 8.3 9.0 9.3 9.5 4.6 5.7 6.4 6.9 7.4 7.9 8.4 8.8 9.8 5.7 5.5 6.2 6.9 7.5 8.1 8.8 9.3 9.8 10.7 3.4 4.1 4.5 5.5 4.7 6.4 6.4 7.3 8.0

T = 40° C

T = 60° C

T = 80° C

T = 100° C

T = 110° C

LS

LC

LS

LC

LS

LC

LS

LC

LS

LC

4.0 4.2 4.5 4.7 5.2 5.6 5.8 6.2 6.6 6.9 7.5 4.0 4.4 4.7 5.1 5.4 5.9 6.4 6.9 7.2 7.4 7.8 8.2 3.8 4.5 4.8 5.1 5.6 5.9 6.1 6.8 7.4 7.6 7.8 3.8 4.7 5.2 5.6 6.1 6.5 6.8 7.2 8.0 3.6 4.5 5.1 5.6 6.1 6.6 7.2 7.6 8.0 8.7 1.9 2.3 2.5 3.3 3.7 5.3 5.3 5.9 6.6

4.9 5.2 5.5 5.8 6.4 6.9 7.1 7.6 8.0 8.5 9.2 4.9 5.4 5.8 6.2 6.6 7.3 7.9 8.5 8.8 9.0 9.6 10.1 4.6 5.5 5.8 6.2 6.9 7.2 7.5 8.3 9.0 9.3 9.5 4.6 5.7 6.4 6.9 7.4 7.9 8.4 8.8 9.8 5.7 5.5 6.2 6.9 7.5 8.1 8.8 9.3 9.8 10.7 3.3 4.0 4.3 5.5 4.7 6.4 6.4 7.3 8.0

4.0 4.2 4.5 4.7 5.2 5.6 5.8 6.2 6.6 6.9 7.5 4.0 4.4 4.7 5.1 5.4 5.9 6.4 6.9 7.2 7.4 7.8 8.2 3.8 4.5 4.8 5.1 5.6 5.9 6.1 6.8 7.4 7.6 7.8 3.8 4.7 5.2 5.6 6.1 6.5 6.8 7.2 8.0 3.5 4.3 5.1 5.6 6.1 6.6 7.2 7.6 8.0 8.7 1.9 2.2 2.4 3.2 3.5 5.3 5.3 5.9 6.6

4.9 5.2 5.5 5.8 6.4 6.9 7.1 7.6 8.0 8.5 9.2 4.9 5.4 5.8 6.2 6.6 7.3 7.9 8.5 8.8 9.0 9.6 10.1 4.6 5.5 5.8 6.2 6.9 7.2 7.5 8.3 9.0 9.3 9.5 4.6 5.7 6.4 6.9 7.4 7.9 8.4 8.8 9.8 5.7 5.5 6.2 6.9 7.5 8.1 8.8 9.3 9.8 10.7 3.2 3.8 4.2 5.4 4.7 6.4 6.4 7.3 8.0

4.0 4.2 4.5 4.7 5.2 5.6 5.8 6.2 6.6 6.9 7.5 4.0 4.4 4.7 5.1 5.4 5.9 6.4 6.9 7.2 7.4 7.8 8.2 3.8 4.5 4.8 5.1 5.6 5.9 6.1 6.8 7.4 7.6 7.8 3.8 4.7 5.2 5.6 6.1 6.5 6.8 7.2 8.0 3.3 4.1 5.0 5.6 6.1 6.6 7.2 7.6 8.0 8.7 1.8 2.1 2.3 3.0 3.4 5.3 5.3 5.9 6.6

4.9 5.2 5.5 5.8 6.4 6.9 7.1 7.6 8.0 8.5 9.2 4.9 5.4 5.8 6.2 6.6 7.3 7.9 8.5 8.8 9.0 9.6 10.1 4.6 5.5 5.8 6.2 6.9 7.2 7.5 8.3 9.0 9.3 9.5 4.6 5.7 6.4 6.9 7.4 7.9 8.4 8.8 9.8 5.7 5.5 6.2 6.9 7.5 8.1 8.8 9.3 9.8 10.7 3.1 3.7 4.0 5.2 4.7 6.4 6.4 7.3 8.0

4.0 4.2 4.5 4.7 5.2 5.6 5.8 6.2 6.6 6.9 7.5 4.0 4.4 4.7 5.1 5.4 5.9 6.4 6.9 7.2 7.4 7.8 8.2 3.8 4.5 4.8 5.1 5.6 5.9 6.1 6.8 7.4 7.6 7.8 3.6 4.4 5.1 5.6 6.1 6.5 6.8 7.2 8.0 3.1 3.9 4.7 5.5 6.1 6.6 7.2 7.6 8.0 8.7 1.7 2.0 2.2 2.9 3.2 5.0 5.0 5.9 6.6

4.9 5.2 5.5 5.8 6.4 6.9 7.1 7.6 8.0 8.5 9.2 4.9 5.4 5.8 6.2 6.6 7.3 7.9 8.5 8.8 9.0 9.6 10.1 4.6 5.5 5.8 6.2 6.9 7.2 7.5 8.3 9.0 9.3 9.5 4.6 5.7 6.4 6.9 7.4 7.9 8.4 8.8 9.8 5.3 5.5 6.2 6.9 7.5 8.1 8.8 9.3 9.8 10.7 2.9 3.5 3.8 4.9 4.7 6.4 6.4 7.3 8.0

4.0 4.2 4.5 4.7 5.2 5.6 5.8 6.2 6.6 6.9 7.5 4.0 4.4 4.7 5.1 5.4 5.9 6.4 6.9 7.2 7.4 7.8 8.2 3.8 4.5 4.8 5.1 5.6 5.9 6.1 6.8 7.4 7.6 7.8 3.5 4.2 4.9 5.5 6.1 6.5 6.8 7.2 8.0 3.0 3.7 4.5 5.3 5.9 6.6 7.2 7.6 8.0 8.7 1.6 1.9 2.1 2.7 3.1 4.8 4.8 5.6 6.4

4.9 5.2 5.5 5.8 6.4 6.9 7.1 7.6 8.0 8.5 9.2 4.9 5.4 5.8 6.2 6.6 7.3 7.9 8.5 8.8 9.0 9.6 10.1 4.6 5.5 5.8 6.2 6.9 7.2 7.5 8.3 9.0 9.3 9.5 4.6 5.7 6.4 6.9 7.4 7.9 8.4 8.8 9.8 5.1 5.5 6.2 6.9 7.5 8.1 8.8 9.3 9.8 10.7 2.8 3.3 3.6 4.7 4.7 6.4 6.4 7.3 8.0

L S = Single span length L C = Continuous span length

49

Table III-d. Support distance L' (m) for series EST, P = 0.75 * P N (bar). Series

EST 8

EST 12.5

EST 16

EST 20

EST 25

EST 32

ID

T = 20° C

T = 40° C

T = 60° C

T = 80° C

T = 100° C

T = 110° C

(mm)

LS

LC

LS

LC

LS

LC

LS

LC

LS

LC

LS

LC

350 400 450 500 600 700 750 800 900 1000 1200 250 300 350 400 450 500 600 700 750 800 900 1000 200 250 300 350 400 450 500 600 700 750 800 150 200 250 300 350 400 450 500 600 100 150 200 250 300 350 400 450 500 600 25 40 50 80 100 150 200 250 300

5.4 5.8 6.1 6.5 7.1 7.7 7.9 8.4 8.8 9.3 10.2 5.2 5.9 6.5 7.0 7.5 8.1 8.8 9.5 9.8 10.1 10.7 11.3 4.8 5.6 6.3 7.0 7.7 8.3 8.7 9.6 10.4 10.7 11.0 4.3 5.2 6.1 6.8 7.6 8.3 9.0 9.6 10.9 3.7 4.6 5.6 6.5 7.3 8.1 8.9 9.6 10.3 11.6 2.0 2.4 2.6 3.4 3.8 4.9 6.0 7.0 7.9

6.6 7.1 7.5 7.9 8.7 9.4 9.7 10.2 10.8 11.4 12.5 6.8 7.5 8.1 8.6 9.2 9.9 10.8 11.6 12.0 12.4 13.1 13.8 6.6 7.6 8.3 8.8 9.6 10.1 10.6 11.7 12.7 13.1 13.5 6.5 7.8 8.7 9.5 10.2 10.9 11.5 12.1 13.4 6.3 7.4 8.5 9.5 10.4 11.2 12.1 12.8 13.5 14.7 3.4 4.1 4.5 5.8 6.5 7.9 9.2 10.3 11.3

5.4 5.8 6.1 6.5 7.1 7.7 7.9 8.4 8.8 9.3 10.2 5.0 5.7 6.3 6.9 7.5 8.1 8.8 9.5 9.8 10.1 10.7 11.3 4.7 5.5 6.1 6.8 7.5 8.1 8.6 9.6 10.4 10.7 11.0 4.2 5.1 5.9 6.7 7.4 8.1 8.7 9.3 10.6 3.6 4.5 5.4 6.3 7.1 7.9 8.7 9.4 10.0 11.3 1.9 2.3 2.5 3.3 3.7 4.8 5.8 6.8 7.7

6.6 7.1 7.5 7.9 8.7 9.4 9.7 10.2 10.8 11.4 12.5 6.8 7.5 8.1 8.6 9.2 9.9 10.8 11.6 12.0 12.4 13.1 13.8 6.6 7.6 8.3 8.8 9.6 10.1 10.6 11.7 12.7 13.1 13.5 6.5 7.8 8.7 9.5 10.2 10.9 11.5 12.1 13.4 6.1 7.4 8.5 9.5 10.4 11.2 12.1 12.8 13.5 14.7 3.3 4.0 4.3 5.6 6.3 7.9 9.2 10.3 11.3

5.4 5.8 6.1 6.5 7.1 7.7 7.9 8.4 8.8 9.3 10.2 4.9 5.5 6.1 6.6 7.2 7.8 8.8 9.5 9.8 10.1 10.7 11.3 4.5 5.3 5.9 6.5 7.2 7.8 8.3 9.4 10.4 10.7 11.0 4.0 4.9 5.7 6.4 7.1 7.8 8.4 9.0 10.2 3.5 4.3 5.2 6.1 6.9 7.6 8.3 9.0 9.7 10.9 1.9 2.2 2.4 3.2 3.5 4.6 5.6 6.5 7.4

6.6 7.1 7.5 7.9 8.7 9.4 9.7 10.2 10.8 11.4 12.5 6.8 7.5 8.1 8.6 9.2 9.9 10.8 11.6 12.0 12.4 13.1 13.8 6.6 7.6 8.3 8.8 9.6 10.1 10.6 11.7 12.7 13.1 13.5 6.5 7.8 8.7 9.5 10.2 10.9 11.5 12.1 13.4 5.9 7.4 8.5 9.5 10.4 11.2 12.1 12.8 13.5 14.7 3.2 3.8 4.2 5.4 6.0 7.9 9.2 10.3 11.3

5.3 5.8 6.1 6.5 7.1 7.7 7.9 8.4 8.8 9.3 10.2 4.6 5.3 5.8 6.4 6.9 7.4 8.4 9.3 9.7 10.1 10.7 11.3 4.3 5.0 5.7 6.3 6.9 7.4 8.0 9.0 10.0 10.4 10.9 3.8 4.7 5.4 6.1 6.8 7.4 8.0 8.6 9.7 3.3 4.1 5.0 5.8 6.6 7.3 8.0 8.6 9.2 10.4 1.8 2.1 2.3 3.0 3.4 4.4 5.4 6.2 7.1

6.6 7.1 7.5 7.9 8.7 9.4 9.7 10.2 10.8 11.4 12.5 6.8 7.5 8.1 8.6 9.2 9.9 10.8 11.6 12.0 12.4 13.1 13.8 6.6 7.6 8.3 8.8 9.6 10.1 10.6 11.7 12.7 13.1 13.5 6.5 7.8 8.7 9.5 10.2 10.9 11.5 12.1 13.4 5.7 7.1 8.5 9.5 10.4 11.2 12.1 12.8 13.5 14.7 3.1 3.7 4.0 5.2 5.8 7.5 9.2 10.3 11.3

5.0 5.5 5.9 6.4 7.1 7.7 7.9 8.4 8.8 9.3 10.2 4.4 4.9 5.5 6.0 6.5 7.0 7.9 8.7 9.2 9.6 10.3 11.1 4.0 4.7 5.3 5.9 6.5 7.0 7.5 8.5 9.4 9.8 10.3 3.6 4.4 5.1 5.8 6.4 7.0 7.6 8.1 9.2 3.1 3.9 4.7 5.5 6.2 6.8 7.5 8.1 8.7 9.8 1.7 2.0 2.2 2.9 3.2 4.2 5.0 5.9 6.6

6.6 7.1 7.5 7.9 8.7 9.4 9.7 10.2 10.8 11.4 12.5 6.8 7.5 8.1 8.6 9.2 9.9 10.8 11.6 12.0 12.4 13.1 13.8 6.6 7.6 8.3 8.8 9.6 10.1 10.6 11.7 12.7 13.1 13.5 6.2 7.5 8.7 9.5 10.2 10.9 11.5 12.1 13.4 5.3 6.7 8.1 9.4 10.4 11.2 12.1 12.8 13.5 14.7 2.9 3.5 3.8 4.9 5.5 7.1 8.6 10.0 11.3

4.8 5.3 5.7 6.1 6.9 7.7 7.9 8.4 8.8 9.3 10.2 4.2 4.7 5.3 5.7 6.2 6.7 7.6 8.4 8.8 9.2 9.9 10.6 3.9 4.5 5.1 5.7 6.2 6.7 7.2 8.1 9.0 9.4 9.8 3.5 4.2 4.9 5.5 6.1 6.7 7.2 7.8 8.8 3.0 3.7 4.5 5.3 5.9 6.6 7.2 7.8 8.4 9.4 1.6 1.9 2.1 2.7 3.1 4.0 4.8 5.6 6.4

6.6 7.1 7.5 7.9 8.7 9.4 9.7 10.2 10.8 11.4 12.5 6.8 7.5 8.1 8.6 9.2 9.9 10.8 11.6 12.0 12.4 13.1 13.8 6.6 7.6 8.3 8.8 9.6 10.1 10.6 11.7 12.7 13.1 13.5 5.9 7.2 8.4 9.5 10.2 10.9 11.5 12.1 13.4 5.1 6.4 7.7 9.0 10.1 11.2 12.1 12.8 13.5 14.7 2.8 3.3 3.6 4.7 5.2 6.8 8.3 9.6 10.9

L S = Single span length L C = Continuous span length

50

Table III-e. Support distance L' (m) for series EST, P = 0.5 * P N (bar). Series

EST 8

EST 12.5

EST 16

EST 20

EST 25

EST 32

ID

T = 20° C

(mm)

LS

350 400 450 500 600 700 750 800 900 1000 1200 250 300 350 400 450 500 600 700 750 800 900 1000 200 250 300 350 400 450 500 600 700 750 800 150 200 250 300 350 400 450 500 600 100 150 200 250 300 350 400 450 500 600 25 40 50 80 100 150 200 250 300

6.0 6.5 7.1 7.6 8.5 9.3 9.6 10.0 10.6 11.2 12.3 5.2 5.9 6.5 7.1 7.7 8.3 9.4 10.4 10.9 11.3 12.3 13.1 4.8 5.6 6.3 7.0 7.7 8.3 8.9 10.0 11.1 11.7 12.2 4.3 5.2 6.1 6.8 7.6 8.3 9.0 9.6 10.9 3.7 4.6 5.6 6.5 7.3 8.1 8.9 9.6 10.3 11.6 2.0 2.4 2.6 3.4 3.8 4.9 6.0 7.0 7.9

T = 40° C

T = 60° C

T = 80° C

T = 100° C

T = 110° C

LC

LS

LC

LS

LC

LS

LC

LS

LC

LS

LC

8.0 8.6 9.1 9.6 10.5 11.4 11.8 12.3 13.0 13.7 15.0 8.3 9.1 9.8 10.5 11.2 11.9 13.1 14.1 14.6 15.0 15.9 16.8 8.1 9.3 10.1 10.9 11.7 12.4 13.0 14.3 15.5 16.0 16.5 7.3 8.9 10.4 11.5 12.4 13.2 14.0 14.7 16.3 6.3 7.9 9.6 11.1 12.5 13.6 14.7 15.5 16.4 17.9 3.4 4.1 4.5 5.8 6.5 8.4 10.2 11.9 13.5

5.8 6.3 6.9 7.4 8.3 9.2 9.6 10.0 10.6 11.2 12.3 5.0 5.7 6.3 6.9 7.5 8.1 9.1 10.1 10.6 11.0 11.9 12.8 4.7 5.5 6.1 6.8 7.5 8.1 8.6 9.8 10.8 11.3 11.8 4.2 5.1 5.9 6.7 7.4 8.1 8.7 9.3 10.6 3.6 4.5 5.4 6.3 7.1 7.9 8.7 9.4 10.0 11.3 1.9 2.3 2.5 3.3 3.7 4.8 5.8 6.8 7.7

8.0 8.6 9.1 9.6 10.5 11.4 11.8 12.3 13.0 13.7 15.0 8.3 9.1 9.8 10.5 11.2 11.9 13.1 14.1 14.6 15.0 15.9 16.8 8.0 9.3 10.1 10.9 11.7 12.4 13.0 14.3 15.5 16.0 16.5 7.1 8.7 10.1 11.4 12.4 13.2 14.0 14.7 16.3 6.1 7.7 9.3 10.8 12.2 13.5 14.7 15.5 16.4 17.9 3.3 4.0 4.3 5.6 6.3 8.2 10.0 11.6 13.1

5.6 6.1 6.6 7.1 8.0 8.9 9.3 9.7 10.5 11.2 12.3 4.9 5.5 6.1 6.6 7.2 7.8 8.8 9.7 10.2 10.6 11.5 12.3 4.5 5.3 5.9 6.5 7.2 7.8 8.3 9.4 10.4 10.9 11.4 4.0 4.9 5.7 6.4 7.1 7.8 8.4 9.0 10.2 3.5 4.3 5.2 6.1 6.9 7.6 8.3 9.0 9.7 10.9 1.9 2.2 2.4 3.2 3.5 4.6 5.6 6.5 7.4

8.0 8.6 9.1 9.6 10.5 11.4 11.8 12.3 13.0 13.7 15.0 8.3 9.1 9.8 10.5 11.2 11.9 13.1 14.1 14.6 15.0 15.9 16.8 7.7 9.0 10.1 10.9 11.7 12.4 13.0 14.3 15.5 16.0 16.5 6.8 8.4 9.7 11.0 12.1 13.2 14.0 14.7 16.3 5.9 7.4 9.0 10.4 11.7 13.0 14.3 15.4 16.4 17.9 3.2 3.8 4.2 5.4 6.0 7.9 9.6 11.1 12.6

5.3 5.8 6.3 6.8 7.7 8.5 8.9 9.3 10.1 10.8 12.2 4.6 5.3 5.8 6.4 6.9 7.4 8.4 9.3 9.7 10.2 11.0 11.8 4.3 5.0 5.7 6.3 6.9 7.4 8.0 9.0 10.0 10.4 10.9 3.8 4.7 5.4 6.1 6.8 7.4 8.0 8.6 9.7 3.3 4.1 5.0 5.8 6.6 7.3 8.0 8.6 9.2 10.4 1.8 2.1 2.3 3.0 3.4 4.4 5.4 6.2 7.1

8.0 8.6 9.1 9.6 10.5 11.4 11.8 12.3 13.0 13.7 15.0 7.9 9.0 9.8 10.5 11.2 11.9 13.1 14.1 14.6 15.0 15.9 16.8 7.3 8.6 9.7 10.7 11.7 12.4 13.0 14.3 15.5 16.0 16.5 6.5 8.0 9.3 10.5 11.6 12.7 13.7 14.7 16.3 5.7 7.1 8.6 9.9 11.2 12.4 13.6 14.8 15.8 17.8 3.1 3.7 4.0 5.2 5.8 7.5 9.2 10.7 12.1

5.0 5.5 5.9 6.4 7.2 8.0 8.4 8.8 9.5 10.2 11.5 4.4 4.9 5.5 6.0 6.5 7.0 7.9 8.7 9.2 9.6 10.3 11.1 4.0 4.7 5.3 5.9 6.5 7.0 7.5 8.5 9.4 9.8 10.3 3.6 4.4 5.1 5.8 6.4 7.0 7.6 8.1 9.2 3.1 3.9 4.7 5.5 6.2 6.8 7.5 8.1 8.7 9.8 1.7 2.0 2.2 2.9 3.2 4.2 5.0 5.9 6.6

8.0 8.6 9.1 9.6 10.5 11.4 11.8 12.3 13.0 13.7 15.0 7.5 8.4 9.4 10.2 11.1 11.9 13.1 14.1 14.6 15.0 15.9 16.8 6.9 8.1 9.1 10.1 11.1 11.9 12.8 14.3 15.5 16.0 16.5 6.2 7.5 8.7 9.9 10.9 11.9 12.9 13.9 15.7 5.3 6.7 8.1 9.4 10.6 11.7 12.8 13.9 14.9 16.8 2.9 3.5 3.8 4.9 5.5 7.1 8.6 10.0 11.3

4.8 5.3 5.7 6.1 6.9 7.7 8.0 8.4 9.1 9.8 11.0 4.2 4.7 5.3 5.7 6.2 6.7 7.6 8.4 8.8 9.2 9.9 10.6 3.9 4.5 5.1 5.7 6.2 6.7 7.2 8.1 9.0 9.4 9.8 3.5 4.2 4.9 5.5 6.1 6.7 7.2 7.8 8.8 3.0 3.7 4.5 5.3 5.9 6.6 7.2 7.8 8.4 9.4 1.6 1.9 2.1 2.7 3.1 4.0 4.8 5.6 6.4

8.0 8.6 9.1 9.6 10.5 11.4 11.8 12.3 13.0 13.7 15.0 7.2 8.1 9.0 9.8 10.6 11.5 13.0 14.1 14.6 15.0 15.9 16.8 6.6 7.8 8.7 9.7 10.6 11.5 12.3 13.9 15.4 16.0 16.5 5.9 7.2 8.4 9.5 10.5 11.5 12.4 13.3 15.1 5.1 6.4 7.7 9.0 10.1 11.2 12.3 13.3 14.3 16.1 2.8 3.3 3.6 4.7 5.2 6.8 8.3 9.6 10.9

L S = Single span length L C = Continuous span length

51

III.6. Anchor points

Anchor points are used to fix a certain point of the pipeline system. The expansion of the pipeline system is directed from a fixed point towards the supports next to the anchor point. The pipe should be able to move within these pipe supports. Anchor points can be created as follows:

A. Adhesive bonded saddle Adhesive bonded saddles can be fixed on the bottom of the pipe on each side of a pipe clamp.

Fig. III.6. B. Laminate build-ups On each side of a pipe clamp a laminate can be wrapped.

Fig III.7. III.7. Anchor loads

Although Wavistrong pipes have a higher coefficient of linear thermal expansion (γL) than steel pipes, their far lower axial E-modulus results in comparatively low expansion forces at the anchor points when the pipeline is subjected to temperature changes (∆T).

52

In table III-f. (page 54) the anchor loads (PA) for series EST at a temperature change ∆T = 10°C are listed. The E-modulus of 20°C has been used in the following formula for the determination of this load:

(Eq. III.12.)

Where: PA = anchor load OD = outer diameter ID = inner diameter EX = axial tensile modulus (table II-j., page 24) γL = coefficient of linear thermal expansion (table II-l., page 24) ∆T = temperature change

(N) (mm) (mm) (N/mm2) (mm/mm.°C) (°C)

Where temperature differences (∆T) are greater than 10°C, the anchor load (PA) shown in table III-f. (page 54) should be multiplied by a factor indicating the difference between the highest actual temperature and 20°C, resulting in the following equation. Also, the temperature correction factor (R E) from table II-k. (page 24), corresponding to the highest actual temperature, must be applied:

(Eq. III.13.)

Where: PAT = anchor load at elevated temperature PA = anchor load (Eq. III.12.) ∆T = temperature change RE = temperature correction factor (table II-k., page 24)

(N) (N) (°C) (-)

As a rule no expansion loops or compensators are required. The distance between the supports should be reduced when there is a risk of axial buckling due to increasing axial stresses (III.5., page 47). However, when the expansion forces on the anchor points are considered to be excessively high, compensation of the load can be found by using compensators or expansion loops; the Future Pipe Industries engineers can advise you.

53

Table III-f. Anchor load P A (N) for series EST at 20°C and ∆T = 10°C

Series EST ID (mm)

8

16

20

25

32

25 40

541 835

50 80 100 150 200 250

Note:

12.5

2490

1031 2007 2651

6302

5058 7660

3696 6309 9417

4525 7570 11384

5362 9159 13963 19771

300 350

9198

8704 11487

10564 13926

13138 17472

15966 21318

400

11677

14650

18056

22418

27754

450 500 600

14447 17508 24505

18194 22505 31574

22373 27146 38533

27977 34149 48800

34683 42381 60085

700 750 800

32667 37185 42583

42166 48033 54281

51905 59045 66643

900

53149

67919

1000 1200

64881 91840

83080

The rubber seal (lock) joint can accommodate expansion due to a free end play. This end play ability can be used to advantage, provided that during installation of the joint, allowance is made for possible expansion. In table III-g. (page 55) the available end play in the joint (at an angular deflection = 0°) is given. The rubber seal (lock) joints have an angular deflection capability, dependent on the diameter. This angular deflection is also listed in table III-g.

54

Table III-g. End play and angular deflection of the RSLJ and RSJ

End play (mm)

Note:

Angular deflection

ID (mm)

RSLJ

RSJ

RSLJ

RSJ

80 100

2.5 3

32.5 33

1°30' 1°30'

3° 3°

150

6

36

1°30'

3°

200 250

8 9

38 (58) 39 (59)

1°30' 1°30'

3° 3°

300 350 400

10 11 13

40 (60) 61 63

1°30' 1°30' 1°30'

3° 3° 3°

450 500 600

14 16 19

64 66 69

1°30' 1°30' 1°30'

3° 3° 2°

700 750 800

16 17 19

66 67 69

1° 1° 1°

2° 2° 2°

900 1000 1200

21 23 27

71 73 77

1° 1° 1°

2° 2° 1°

The end play is required to accommodate soil settlement, Poisson contraction and temperature changes and can therefore not be used for installation adjustments.

Values between brackets are valid for pipes with standard length L O = 10 m.

55

IV. Wavistrong underground pipe systems IV.1. Design and joining systems

When using the Wavistrong pipe systems for underground applications, several types of joints can be used (II.4., page 4). In contrast to above ground pipelines, these joints can be unrestrained (ratio axial stress/hoop stress (R) = 0.25). Only at directional changes and depending on the pressure, diameter and soil conditions, some lengths of pipe should be installed with tensile resistant couplers. Alternatively an external axial restraint, e.g. a concrete anchor block can be used.

IV.2. Anchor points

Buried Wavistrong non-tensile resistant pipe systems can be anchored at turns and branches by means of thrust blocks. This not only alleviates the need for expansion details, it also eliminates underground movement of the pipe system. However, in most circumstances the use of restrained couplers (e.g. rubber seal lock joint or adhesive bonded joint) over a certain distance, starting from the fitting, may offer a better solution. For this purpose, the fictive anchor length (L A) must be determined. The fictive anchor length (LA) can be calculated from the following formula:

(Eq. IV.1.) Where: LA = fictive anchor length P = operating pressure ID = inner diameter FW = frictional force between soil and pipe OD = outer diameter (II.5.1.B, page ?)

(m) (Mpa) (mm) (N/mm 2) (mm)

The value of FW can be obtained from the soil mechanics report. If not, the following values may provide a rough indication: - soft clay and peaty soils - sandy clay and sand

: :

0.001 ≤ FW ≤ 0.003 (N/mm2) 0.003 ≤ FW ≤ 0.010 (N/mm2)

IV.3. Calculation of underground pipe systems

Calculations, as described in this paragraph are in line with ANSI/AWWA C950-88. Based on specific material data (and many years of experience) a number of deviations are stated in the text. As in ANSI/AWWA C950-88, Anglo-Saxon units are used. The stresses in the wall of a flexible buried pipe not only depend on the internal pressure, but are also a result of the deflection due to external loads. The stress resulting from the deflection depends on the interaction between the soil and the pipe, which is among others determined by the installation method.

56

IV.3.1. Pipe deflection

The vertical deflection of an underground pipe is a function of the installation parameters, the vertical load on the pipe, the pipe stiffness and the soil characteristics. When installed underground, a flexible pipe deflects, which means a decrease of the vertical diameter. Many theories are used to predict this deflection; however, in actual field conditions, pipe deflections may vary from the calculated values because theories cannot anticipate all the parameters associated with a given installation. These variations include the inherent variability of native ground conditions and variations in methods, materials, and equipment used to install a buried pipe. A prediction is made using the following formula:

(Eq IV.2.)

Where: ∆y = predicted vertical pipe deflection Dl = deflection lag factor W c = vertical soil load W L = live load Kx = deflection coefficient (table IV-b., page 58) rm = mean pipe radius EI = stiffness factor E' = modulus of soil reaction (table IV-d., page 61)

(in) (-) (lb/in) (lb/in) (-) (in) (in2.lb/in) (psi)

Two procedures are available to obtain an estimated average deflection, in order to obtain a 95% probability that the actual deflection will be less than the calculated value.

Procedure A:

This procedure is used if the burial depth (H) is less than or equal to 16 ft (± 4.9 m). Procedure A uses a modulus of soil reaction (E') equal to 0.75 times the value obtained from table IV-d. (page 61).

Procedure B:

This procedure is used if the burial depth (H) is greater than 16 ft (± 4.9 m). Procedure B uses a modulus of soil reaction (E') equal to the value obtained from table IV-d. (page 61), and adds the percentage deflection, given in table IV-a. (page 58) to the value obtained from Eq. IV.2.

57

Table IV-a. Additional deflection dependent on the degree of compaction

Note:

Degree of compaction

Additional deflection (%)

Dumped Slight Moderate High

+2 +2 +1 + 0.5

The actual deflection measured at a particular point along a single pipeline may vary ± 2% from the average deflection for the entire pipeline due to variations from specific conditions in the soil and in the compaction procedures used.

IV.3.2. Deflection lag factor

After the soil has been initially loaded, it continues to deform (consolidate) with time. The deflection lag factor (Dl) converts the immediate deflection of the pipe to the deflection of the pipe after many years. For plastic pipes a value of Dl = 1.5 to 2 is recommended by ANSI/AWWA C950-88.

IV.3.3. Deflection coefficient

The deflection coefficient (Kx) reflects the degree of support provided by the soil at the bottom of the pipe. Table IV-b. gives the recommended values for different types of installation.

Table IV-b. Deflection coefficient (K X) as function of type of installation

Type of installation Shaped bottom with tampered backfill material placed at the sides of the pipe; ≥ 95 % Proctor density Compacted coarse-grained, shaped bedding with backfill material placed at the sides of the pipe; 70 - 100 % relative density

Shaped bottom, moderately compacted, with backfill material placed at the sides of the pipe; 85 - 95 % Proctor density Coarse grained, shaped bedding, with slightly compacted backfill material placed at the sides of the pipe; 40 - 70 % relative density Flat bottom with loose backfill material placed at the sides of the pipe (not recommended); < 35% Proctor density; < 40% relative density

At least one lift of backfill material should be placed and compacted at the sides of the pipe.

58

Equivalent bedding angle (degrees)

Deflection coefficient Kx (-)

180

0.083

120

0.090

90

0.096

60

0.103

30

0.108

0

0.110

IV.3.4. Vertical soil load

The vertical soil load (Wc) on the pipe may be considered as the mass of the rectangular prism of soil directly above the pipe, according to the following equation:

(Eq. IV.3.)

Where: W c = vertical soil load γs = specific mass of the soil H = burial depth to top of the pipe OD = outer diameter (II.5.1.B, page ?)

(lb/in) (lb/ft3) (ft) (in)

Considerations should be given to pipe installed under unusual conditions, such as in unstable soils or soils with high groundwater tables.

IV.3.5. Live load

The live load (WL) will be calculated according to the following equation:

or

(Eq. IV.4.)

Where: WL = live load CL = live load coefficient (single wheel load) CL(T) = live load coefficient (two passing trucks) PW = wheel load (table IV-c.) If = impact factor

(lb/in) (-) (-) (lb) (-) (Eq. IV.5.)

Where: H = burial depth to top of pipe (0 ≤ If ≤ 0.50)

In abscence of specific soil information, the unit weight for soil may be assumed to be 3 3 120 lb/ft (= ± 2000 kg/m )

59

(ft)

Table IV-c. Wheel load (P W ) Wheel load Indication

(tons)

(lb)

VOSB 30 VOSB 45 VOSB 60

5 7.5 10

11,000 16,500 22,000

H20-S16

7.2

16,000

LKW 12 SKW 30 SKW 60

4 5 10

9,000 11,000 22,000

IV.3.5.1. Live load coefficient single wheel load

The live load coefficient (CL) for a single wheel load will be determined with the following equation :

(Eq. IV.6.)

Where: CL = live load coefficient (single wheel load) H = burial depth to top of pipe ro = outer pipe radius

(-) (ft) (ft)

ARCSIN must be in radians.

IV.3.5.2. Live load coefficient two passing trucks

The live load coefficient (CL(T)) for two passing trucks will be determined with the following equation:

(Eq. IV.7.)

Where: CL(T) = live load coefficient (two passing trucks) D = mean pipe diameter H = burial depth to top of pipe

(-) (ft) (ft)

COS and TAN must be in radians

This equation (Eq. IV.6.) is based on the Boussinesq formula for a point load at the surface of a semi-infinite elastic soil.

60

IV.3.6. Stiffness factor

The stiffness factor (EI) is the product of the hoop bending modulus (EH) of the pipewall and the moment of inertia of the pipewall per unit length of pipe.

(Eq. IV.8.)

Where: EH = hoop bending modulus (table II-j., page 24) TT = nett total wall thickness

(psi) (in)

(II.5.1.A, page 6)

IV.3.7. Modulus of soil reaction

The modulus of the soil reaction (E') depends on the type of backfilling. Recommended values of E' for various soil and compaction conditions are shown in the table IV-d. The listed values are derived from ASTM D 2487. Table IV-d. Modulus of soil reaction (E') E' for degree of compaction of bedding psi (N/mm²) Dumped Slight Moderate High

Soil types backfill material Fine-grained soils LL < 50. Soils with medium to no plasticity CL, ML, ML-CL, CL-CH, ML-MH, with less than 25% coarse-grained particles. Fine-grained soils LL < 50. Soils with medium to no plasticity CL, ML, ML-CL, CL-CH, ML-MH, with more than 25% coarse-grained particles. Coarse-grained soils with fines GM, GC, SM, SC , containing more than 12% fines. Coarse-grained soils with little or no fines. GW, GP, SW, SP , containing less than 12% fines. Crushed rock

50 (0.34)

200 (1.4)

400 (2.8)

1000 (6.9)

100 (0.69)

400 (2.8)

1000 (6.9)

2000 (13.8)

200 (1.4) 1000 (6.9)

1000 (6.9)

2000 (13.8) 3000 (20.7)

3000 (20.7)

Classification of soils for engineering purposes according to ASTM D 2487 (table IV-e., page 62). Slight = < 85 % Proctor / < 40 % relative density Moderate = 85-95 % Proctor / 40-70 % relative density High = > 95 % Proctor / > 70 % relative density LL = Liquid Limit Or any borderline soil beginning with one of these symbols (i.e. GM-GC, GC-SC).

61

Table IV-e. Soil classification Group Symbol

Group name

GW

Well graded gravels, gravel-sand mixtures, little or no fines

GP

Poorly graded gravels, gravel-sand mixtures, little or no fines

GM

Silty gravels, poorly graded gravel-sand-silt mixtures

GC

Clayey gravels, poorly graded gravel-sand-clay mixtures

SW

Well graded sands, gravelly sands, little or no fines

SP

Poorly graded sands, gravelly sands, little or no fines

SM

Silty sands, poorly graded sand-silt mixtures

SC

Clayey sands, poorly graded sand-clay mixtures

ML

Inorganic silts and very fine sand, silty or clayey fine sands

CL

Inorganic clays of low to medium plasticity

MH

Inorganic silts, micaceous or diatomaceous fine sandy or silty soils, elastic silts

CH

Inorganic clays of high plasticity, fat clays

IV.4. Resulting hoop stress

The maximum hoop stress resulting from the combined effects of internal pressure and deflection shall meet the following equation:

(Eq. IV.9.)

Where: σc = resulting hoop stress HDB = Hydrostatic Design Basis (table II-h., page 23) FS = design factor (1.5)

According to ASTM D 2487

62

(psi) (psi) (-)

σ c is calculated as follows:

(Eq. IV.10.)

Where: σ c = resulting hoop stress P = operating pressure D = mean pipe diameter TE = minimum reinforced wall thickness (table II-b. and II-c., page 9 and 10) Df = shape factor (table IV-f.) EH = hoop bending modulus (table II-j., page 24) RC = rerounding coefficient ∆y = predicted vertical pipe deflection TT = nett total wall thickness

(psi) (psi) (in) (in) (-) (psi) (-) (in) (in)

(II.5.1.A., page 6) If:

Then:

Else:

(Eq. IV.11.)

Where: P = operating pressure

(psi)

Table IV-f. Shape factor Pipe-zone backfill material and compaction Gravel

Sand

Pipe Stiffness (psi)

dumped to slight

moderate to high

dumped to slight

moderate to high

9 18 36 72

5.5 4.5 3.8 3.3

7.0 5.5 4.5 3.8

6.0 5.0 4.0 3.5

8.0 6.5 5.5 4.5

63

IV.5. Allowable combined stress

The combination of the axial stress due to internal pressure (SX) and the circumferential stresses due to internal pressure (Sy) and vertical deflection of the pipe (σ C), should not exceed the acceptable stress levels as shown in the fig. II-6. (page 13 through 15). The occurring axial stress has a great influence on the allowable hoop stress. Non-tensile resistant pipes (series ESN) allow for high hoop stress. It is beneficial to use this type of pipe for underground applications. The occurring axial stress for tensile resistant and the non-tensile resistant pipes is calculated as follows:

A. Tensile resistant system (series EST):

(Eq. IV.12.)

Where: Sx = actual axial stress due to internal pressure Sy = actual hoop stress due to internal pressure

(ISO formula)

(N/mm2) (N/mm 2)

(Eq. IV.13.)

Where: P = operating pressure ID = inner diameter TE = minimum reinforced wall thickness (table II-b. and II-c., page 9 and 10)

(Mpa) (mm) (mm)

B. Non-tensile resistant system (series ESN):

(Eq. IV.14.) Where: Sx = actual axial stress due to internal pressure Nyx = Poisson ratio hoop/axial (table II-j., page 24) Sy = actual hoop stress due to internal pressure (Eq. IV.13.)

(N/mm²) (-) (N/mm²)

From the calculated values (table IV-j. through IV-m., page 66 through 69) one may conclude that the deflection of the pipe decreases with increasing care of installation and modulus of soil reaction (E'). Stresses and deflections of the pipe system at burial depths varying from 1 to 5 metres are acceptable. If the pipe system is installed with a depth of cover over 2.5 metres, the deflection is mainly caused by the soil loads; at shallow depths (< 1 m) wheel loads (PW) have a predominant influence on the deformation of the pipe. The table IV-j. through IV-m. (page 66 through 69) show that in some cases, the required pressure class can be reduced when using series ESN instead of EST. This is the result of the design of series ESN, where a steeper winding angle is used compared with series EST. This steeper winding angle results in a higher pipe stiffness (PS) as well as a higher allowable circumferential stress (S H).

64

In the following table IV-j. through IV-m. (page 66 through 69) the results of calculations for the standard Wavistrong product range are shown. These calculations at nominal pressure (PN) for the series EST and ESN give the deflection (∆y) for various burial depths (H) and different wheel loads (PW). The values in table IV-j through IV-m. are determined for two different soil conditions: Table IV-g. Input conditions for table IV-j. and IV-k. (page 66 and 67).

coarse grained soils with fines

γs

2000 (125) moderate

(-)

E'

6.9 (1000)

N/mm² (psi)

degree of compaction modulus of soil reaction

3

kg/m (pcf)

bedding angle

α

90

°

deflection coefficient

KX

0.096

(-)

deflection lag factor

Dl

1.5

(-)

Table IV-h. Input conditions for table IV-l. and IV-m. (page 68 and 69)

fine grained soil with medium or no plasticity

γs

degree of compaction modulus of soil reaction

E'

1600 (100)

3

kg/m (pcf)

moderate

(-)

4.8 (700)

N/mm² (psi)

bedding angle

α

120

°

deflection coefficient

KX

0.090

(-)

deflection lag factor

Dl

1.5

(-)

Criteria for rejection ("--") in the table IV-j. through IV-m. are: -

resulting hoop stress (σ C)

> maximum hoop stress (HDB/FS) (Eq.IV.9.)

-

predicted vertical pipe deflection (∆y)

> 5%

In case the conditions in the field differ from those used for the following listed calculations, separate calculations can be made on request.

65

Table IV-j. Vertical deflection ∆y (%) at P N for buried series EST at 20°C Calculations in line with ANSI/AWWA C950-88. Burial conditions: Wheel load (tons) Burial (m) depth EST 8 350 400 450 500 600 700 750 800 900 1000 1200 EST 12.5 250 300 350 400 450 500 600 700 750 800 900 1000 EST 16 200 250 300 350 400 450 500 600 700 750 800 EST 20 150 200 250 300 350 400 450 500 600 EST 25 100 150 200 250 300 350 400 450 500 600 EST 32 25 40 50 80 100 150 200 250 300

Specific mass soil: : E' (ground)

2000kg/m3 6.9 N/mm²

0

125 pcf 1000 psi

Bedding angle: Defl.lag factor:

5

90 ° 1.5(-)

7.5

10

0.5

1

2.5

5

0.5

1

2.5

5

0.5

1

2.5

5

0.5

1

2.5

5

0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.3 0.3 0.3 0.3 0.4 0.4 0.3 0.3 0.3 0.3 0.0 0.1 0.2 0.2 0.3 0.3 0.3 0.3 0.3

0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.6 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.1 0.2 0.4 0.5 0.6 0.6 0.6 0.6 0.6

2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.1 2.1 2.1 2.1 2.1 2.1 2.1 2.1 2.1 2.1 2.1 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 1.5 1.7 1.7 1.7 1.8 1.8 1.7 1.7 1.7 1.7 0.2 0.6 0.9 1.2 1.4 1.5 1.4 1.4 1.4

4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.2 4.2 4.2 4.2 4.2 4.2 4.2 4.2 4.2 4.2 4.2 4.1 4.0 4.0 4.0 4.1 4.1 4.1 4.1 4.0 3.5 3.8 3.8 3.8 3.8 3.8 3.8 3.8 3.8 3.8 1.4 2.1 2.6 3.0 3.4 3.4 3.4 3.4 3.4

2.8 2.8 2.7 2.7 2.5 2.4 2.3 2.3 2.2 2.0 1.9 2.9 2.9 2.8 2.7 2.7 2.6 2.5 2.4 2.3 2.2 2.1 2.0 2.8 2.8 2.8 2.7 2.6 2.6 2.5 2.4 2.3 2.2 2.2 2.7 2.6 2.6 2.6 2.5 2.5 2.4 2.4 2.2 2.1 2.3 2.3 2.3 2.3 2.2 2.2 2.1 2.1 2.0 0.3 0.8 1.2 1.6 1.9 2.0 1.9 1.9 1.8

1.7 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.5 1.5 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.5 1.5 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.4 1.2 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 0.2 0.4 0.7 0.9 1.1 1.1 1.1 1.1 1.1

2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.1 2.1 2.1 2.1 2.1 2.1 2.1 2.1 2.1 1.6 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 0.2 0.6 1.0 1.3 1.5 1.5 1.5 1.5 1.5

4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.2 4.2 4.2 4.2 4.2 4.2 4.2 4.2 4.2 4.2 4.2 4.1 4.1 4.1 4.1 4.1 4.1 4.1 4.1 4.1 3.5 3.8 3.8 3.8 3.8 3.8 3.8 3.8 3.8 3.8 1.4 2.1 2.6 3.1 3.4 3.4 3.4 3.4 3.4

4.0 4.0 3.9 3.8 3.6 3.4 3.3 3.2 3.0 2.8 2.6 4.1 4.1 4.0 3.9 3.8 3.7 3.5 3.3 3.2 3.2 3.0 2.8 4.1 4.0 3.9 3.9 3.8 3.7 3.6 3.4 3.2 3.1 3.0 3.8 3.7 3.7 3.6 3.6 3.5 3.4 3.3 3.2 3.0 3.3 3.3 3.3 3.2 3.2 3.1 3.0 2.9 2.8 0.4 1.1 1.8 2.3 2.7 2.8 2.7 2.7 2.6

2.0 2.0 2.0 2.0 2.0 2.0 2.0 1.9 1.9 1.9 1.8 2.0 2.0 2.0 2.0 2.0 2.0 2.0 1.9 1.9 1.9 1.9 1.9 2.0 2.0 2.0 2.0 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.4 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 0.2 0.6 0.8 1.1 1.3 1.4 1.3 1.3 1.3

2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.1 2.1 2.1 2.1 2.1 2.1 2.1 2.1 2.1 1.7 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 0.2 0.6 1.0 1.3 1.5 1.6 1.5 1.5 1.5

4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.2 4.3 4.3 4.2 4.3 4.3 4.3 4.2 4.3 4.3 4.1 4.1 4.1 4.1 4.1 4.1 4.1 4.1 4.1 3.5 3.8 3.8 3.8 3.8 3.8 3.8 3.8 3.8 3.8 1.4 2.1 2.6 3.1 3.4 3.4 3.4 3.4 3.4

-.-.5.0 4.9 4.6 4.4 4.2 4.1 3.9 3.7 3.3 -.-.-.-.4.9 4.8 4.6 4.3 4.2 4.1 3.8 3.6 -.-.-.5.0 4.9 4.8 4.7 4.4 4.2 4.0 3.9 5.0 4.9 4.8 4.7 4.6 4.5 4.4 4.3 4.1 3.9 4.3 4.3 4.3 4.2 4.1 4.0 3.9 3.8 3.6 0.5 1.5 2.3 3.0 3.6 3.6 3.6 3.5 3.4

2.4 2.4 2.4 2.4 2.4 2.3 2.3 2.3 2.2 2.2 2.1 2.4 2.4 2.4 2.4 2.4 2.4 2.3 2.3 2.3 2.3 2.2 2.2 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.1 2.1 2.1 2.1 1.7 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 0.2 0.7 1.0 1.3 1.6 1.6 1.6 1.6 1.6

2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.2 2.1 2.2 2.2 2.2 2.2 2.2 2.2 2.2 1.7 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 0.2 0.7 1.0 1.3 1.6 1.6 1.6 1.6 1.6

4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.1 4.1 4.1 4.1 4.1 4.1 4.1 4.1 4.1 3.5 3.8 3.8 3.8 3.8 3.8 3.8 3.8 3.8 3.8 1.4 2.1 2.6 3.1 3.4 3.4 3.4 3.4 3.4

For different soil conditions, separate calculations can be made on request.

66

Table IV-k. Vertical deflection ∆y (%) at P N for buried series ESN at 20°C Calculations in line with ANSI/AWWA C950-88. Burial conditions: Wheel load (tons) Burial (m) depth ESN 10 450 500 600 700 750 800 900 1000 1200 ESN 16 350 400 450 500 600 700 750 800 ESN 20 200 250 300 350 400 450 500 600 ESN 25 200 250 300 350 400 450 500 600 ESN 32 80 100 150 200 250 300

Specific mass soil: : E' (ground)

2000 kg/m3 6.9 N/mm²

0

125 pcf 1000 psi

Bedding angle: Defl.lag factor:

5

90 ° 1.5(-)

7.5

10

0.5

1

2.5

5

0.5

1

2.5

5

0.5

1

2.5

5

0.5

1

2.5

5

0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.2 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.2 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.2 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.0 0.3 0.4 0.4 0.4 0.4 0.4

0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.5 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.4 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.4 0.9 0.9 0.9 0.8 0.8 0.8 0.9 0.0 0.6 0.8 0.8 0.8 0.8 0.9

2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 1.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 0.9 2.2 2.2 2.2 2.2 2.2 2.2 2.2 1.0 2.2 2.1 2.1 2.1 2.1 2.1 2.1 0.1 1.4 1.9 2.1 2.0 2.0 2.2

4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 3.0 4.3 4.3 4.3 4.3 4.3 4.3 4.3 2.6 4.3 4.3 4.3 4.3 4.3 4.3 4.3 2.7 4.3 4.2 4.2 4.2 4.2 4.2 4.3 1.1 3.3 4.0 4.2 4.1 4.1 4.3

2.7 2.6 2.4 2.3 2.3 2.2 2.1 1.9 1.5 2.8 2.7 2.7 2.6 2.4 2.3 2.3 1.2 2.9 2.9 2.8 2.8 2.7 2.6 2.5 1.3 2.9 2.8 2.7 2.7 2.6 2.5 2.5 0.1 1.9 2.6 2.8 2.7 2.6 2.5

1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.5 0.9 1.7 1.7 1.6 1.6 1.6 1.6 1.6 0.7 1.6 1.7 1.6 1.6 1.6 1.6 1.6 0.7 1.6 1.6 1.6 1.6 1.6 1.6 1.6 0.1 1.0 1.4 1.6 1.5 1.5 1.6

2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 1.2 2.3 2.3 2.3 2.3 2.3 2.3 2.3 0.9 2.3 2.3 2.3 2.3 2.3 2.3 2.3 1.0 2.3 2.2 2.2 2.2 2.2 2.2 2.2 0.1 1.5 2.0 2.2 2.1 2.1 2.3

4.3 4.4 4.4 4.4 4.4 4.4 4.4 4.4 3.0 4.4 4.4 4.4 4.4 4.4 4.4 4.4 2.6 4.3 4.3 4.3 4.3 4.3 4.3 4.3 2.7 4.3 4.3 4.3 4.3 4.2 4.2 4.3 1.1 3.3 4.0 4.2 4.2 4.1 4.3

3.9 3.6 3.4 3.3 3.2 3.0 2.9 2.6 2.1 4.0 3.9 3.8 3.6 3.4 3.3 3.2 1.7 4.1 4.1 4.0 3.9 3.8 3.7 3.6 1.9 4.1 4.0 3.9 3.8 3.7 3.6 3.5 0.1 2.7 3.7 4.0 3.9 3.7 3.6

2.0 2.0 2.0 2.0 1.9 1.9 1.9 1.8 1.1 2.0 2.0 2.0 2.0 2.0 2.0 1.9 0.8 2.0 2.0 2.0 2.0 2.0 2.0 2.0 0.9 2.0 2.0 2.0 2.0 1.9 1.9 1.9 0.1 1.3 1.8 1.9 1.9 1.9 2.0

2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 1.3 2.4 2.4 2.4 2.4 2.4 2.4 2.4 1.0 2.3 2.4 2.4 2.3 2.3 2.3 2.4 1.1 2.3 2.3 2.3 2.3 2.3 2.3 2.3 0.1 1.5 2.0 2.2 2.2 2.2 2.4

4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.4 3.0 4.4 4.4 4.4 4.4 4.4 4.4 4.4 2.6 4.3 4.3 4.3 4.3 4.3 4.3 4.3 2.7 4.3 4.3 4.3 4.3 4.3 4.2 4.3 1.1 3.3 4.0 4.2 4.2 4.1 4.4

5.0 4.7 4.4 4.3 4.1 3.9 3.7 3.3 2.7 -.5.0 4.9 4.7 4.4 4.3 4.1 2.2 -.-.-.-.5.0 4.8 4.6 2.4 -.-.5.0 4.9 4.8 4.7 4.5 0.2 3.5 4.8 -.5.0 4.9 4.6

2.4 2.4 2.3 2.3 2.3 2.3 2.2 2.2 1.3 2.4 2.4 2.4 2.4 2.3 2.3 2.3 1.0 2.4 2.4 2.4 2.4 2.4 2.4 2.3 1.1 2.4 2.4 2.3 2.3 2.3 2.3 2.3 0.1 1.5 2.1 2.3 2.3 2.2 2.4

2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 1.3 2.4 2.4 2.4 2.4 2.4 2.4 2.4 1.0 2.4 2.4 2.4 2.4 2.4 2.4 2.4 1.1 2.4 2.3 2.3 2.3 2.3 2.3 2.3 0.1 1.5 2.1 2.3 2.2 2.2 2.4

4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.4 3.0 4.4 4.4 4.4 4.4 4.4 4.4 4.4 2.6 4.3 4.4 4.4 4.3 4.3 4.3 4.4 2.7 4.3 4.3 4.3 4.3 4.3 4.3 4.3 1.1 3.3 4.0 4.2 4.2 4.1 4.4

For different soil conditions, separate calculations can be made on request.

67

Table IV-l. Vertical deflection ∆y (%) at P N for buried series EST at 20°C Calculations in line with ANSI/AWWA C 950-88. Burial conditions: Wheel load (tons) Burial (m) depth EST 8 350 400 450 500 600 700 750 800 900 1000 1200 EST 12.5 250 300 350 400 450 500 600 700 750 800 900 1000 EST 16 200 250 300 350 400 450 500 600 700 750 800 EST 20 150 200 250 300 350 400 450 500 600 EST 25 100 150 200 250 300 350 400 450 500 600 EST 32 25 40 50 80 100 150 200 250 300

Specific mass soil: : E' (ground)

1600 kg/m3 4.8 N/mm²

0

100 pcf 700 psi

Bedding angle: Defl.lag factor:

5

120 ° 1.5(-)

7.5

10

0.5

1

2.5

5

0.5

1

2.5

5

0.5

1

2.5

5

0.5

1

2.5

5

0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.0 0.1 0.2 0.2 0.3 0.3 0.3 0.3 0.3

0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.6 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.1 0.2 0.3 0.4 0.5 0.5 0.5 0.5 0.5

2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 1.4 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 0.2 0.5 0.8 1.1 1.3 1.3 1.3 1.3 1.3

4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.2 4.1 4.1 4.1 4.1 4.1 4.1 4.1 4.1 3.4 3.7 3.8 3.8 3.8 3.8 3.7 3.8 3.8 3.8 1.3 1.9 2.4 2.9 3.2 3.3 3.3 3.2 3.2

3.6 3.6 3.5 3.4 3.2 3.1 3.0 2.9 2.7 2.6 2.3 3.7 3.7 3.6 3.5 3.4 3.3 3.2 3.0 2.9 2.8 2.7 2.5 3.6 3.5 3.5 3.4 3.3 3.3 3.2 3.0 2.9 2.8 2.7 3.3 3.2 3.2 3.1 3.1 3.0 3.0 2.9 2.7 2.4 2.8 2.7 2.7 2.7 2.6 2.6 2.5 2.4 2.3 0.3 0.8 1.3 1.7 2.2 2.2 2.2 2.1 2.1

2.0 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.8 1.8 1.8 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.8 1.8 1.8 1.8 1.9 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.7 1.7 1.7 1.7 1.7 1.7 1.6 1.6 1.6 1.2 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 0.1 0.4 0.6 0.9 1.1 1.1 1.1 1.1 1.1

2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.1 2.1 2.1 2.1 2.1 2.1 2.1 2.1 2.1 1.5 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 0.2 0.5 0.8 1.1 1.4 1.4 1.4 1.4 1.4

4.6 4.6 4.6 4.6 4.6 4.6 4.6 4.6 4.6 4.6 4.6 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.2 4.1 4.1 4.1 4.2 4.2 4.2 4.2 4.1 3.4 3.8 3.8 3.8 3.8 3.8 3.8 3.8 3.8 3.8 1.3 1.9 2.4 2.9 3.2 3.3 3.3 3.3 3.3

-.-.5.0 4.9 4.6 4.4 4.2 4.1 3.9 3.7 3.3 -.-.-.5.0 4.9 4.8 4.5 4.3 4.2 4.0 3.8 3.6 -.-.5.0 4.9 4.8 4.7 4.6 4.3 4.1 4.0 3.8 4.8 4.6 4.6 4.5 4.4 4.3 4.2 4.1 3.9 3.4 4.0 4.0 3.9 3.8 3.8 3.7 3.6 3.5 3.3 0.4 1.1 1.8 2.5 3.1 3.2 3.1 3.0 3.0

2.5 2.5 2.4 2.4 2.4 2.4 2.4 2.3 2.3 2.3 2.2 2.5 2.4 2.4 2.4 2.4 2.4 2.4 2.3 2.3 2.3 2.3 2.2 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.2 2.2 2.2 2.1 2.1 2.1 2.1 2.1 2.1 2.1 2.1 2.0 1.5 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.7 0.2 0.5 0.8 1.1 1.4 1.4 1.4 1.4 1.4

2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 1.6 1.8 1.8 1.9 1.9 1.9 1.8 1.8 1.9 1.9 0.2 0.5 0.8 1.2 1.4 1.5 1.5 1.4 1.4

4.6 4.6 4.6 4.6 4.6 4.6 4.6 4.6 4.6 4.6 4.6 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.2 4.1 4.2 4.2 4.2 4.2 4.2 4.2 4.2 3.4 3.8 3.8 3.8 3.8 3.8 3.8 3.8 3.8 3.8 1.3 1.9 2.4 2.9 3.2 3.3 3.3 3.3 3.3

-.-.-.-.-.-.-.-.5.0 4.7 4.2 -.-.-.-.-.-.-.-.-.-.4.9 4.6 -.-.-.-.-.-.-.-.-.-.5.0 -.-.-.-.-.-.-.-.-.4.5 -.-.-.5.0 4.9 4.8 4.7 4.6 4.3 0.5 1.5 2.4 3.3 4.0 4.1 4.0 4.0 3.9

3.0 3.0 2.9 2.9 2.9 2.8 2.8 2.8 2.7 2.7 2.6 3.0 2.9 2.9 2.9 2.9 2.9 2.8 2.8 2.8 2.8 2.7 2.6 2.8 2.8 2.8 2.8 2.8 2.8 2.8 2.7 2.7 2.6 2.6 2.6 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.4 1.9 2.2 2.2 2.2 2.2 2.2 2.1 2.1 2.1 2.1 0.2 0.6 1.0 1.4 1.7 1.7 1.7 1.7 1.7

2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.3 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 1.6 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 0.2 0.5 0.9 1.2 1.5 1.5 1.5 1.5 1.5

4.6 4.6 4.6 4.6 4.6 4.6 4.6 4.6 4.6 4.6 4.6 4.6 4.6 4.6 4.6 4.6 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.2 4.2 4.2 4.2 4.2 4.2 4.2 4.2 4.2 3.5 3.8 3.8 3.8 3.8 3.8 3.8 3.8 3.8 3.8 1.3 1.9 2.4 2.9 3.3 3.3 3.3 3.3 3.3

For different soil conditions, separate calculations can be made on request.

68

Table IV-m. Vertical deflection ∆y (%) at P N for buried series ESN at 20°C Calculations in line with ANSI/AWWA C950-88. Burial conditions: Wheel load (tons) Burial (m) depth ESN 10 450 500 600 700 750 800 900 1000 1200 ESN 16 350 400 450 500 600 700 750 800 ESN 20 200 250 300 350 400 450 500 600 ESN 25 200 250 300 350 400 450 500 600 ESN 32 80 100 150 200 250 300

Specific mass soil: : E' (ground)

1600 kg/m3 4.8 N/mm²

0

100 pcf 700 psi

Bedding angle: Defl.lag factor:

5

120 ° 1.5(-)

7.5

10

0.5

1

2.5

5

0.5

1

2.5

5

0.5

1

2.5

5

0.5

1

2.5

5

0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.2 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.2 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.2 0.5 0.4 0.4 0.4 0.4 0.4 0.4 0.0 0.3 0.4 0.4 0.4 0.4 0.5

0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.4 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.3 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.3 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.0 0.5 0.8 0.9 0.8 0.8 0.9

2.3 2.4 2.4 2.3 2.3 2.4 2.4 2.4 1.0 2.4 2.4 2.4 2.4 2.4 2.3 2.3 0.8 2.3 2.3 2.3 2.3 2.3 2.3 2.3 0.8 2.3 2.2 2.2 2.2 2.2 2.2 2.2 0.1 1.3 1.9 2.2 2.1 2.1 2.3

4.5 4.6 4.6 4.5 4.5 4.6 4.6 4.6 2.8 4.6 4.6 4.6 4.6 4.6 4.5 4.5 2.4 4.5 4.5 4.5 4.5 4.5 4.5 4.5 2.5 4.5 4.4 4.4 4.4 4.4 4.4 4.4 1.1 3.2 4.0 4.3 4.3 4.2 4.5

3.5 3.3 3.1 3.0 2.9 2.8 2.6 2.4 1.6 3.6 3.5 3.4 3.3 3.1 3.0 2.9 1.2 3.7 3.7 3.6 3.5 3.4 3.4 3.2 1.4 3.7 3.5 3.5 3.4 3.3 3.2 3.1 0.1 2.1 3.1 3.5 3.4 3.3 3.2

1.9 1.9 1.9 1.9 1.9 1.9 1.8 1.8 0.9 2.0 2.0 2.0 1.9 1.9 1.9 1.9 0.6 1.9 2.0 1.9 1.9 1.9 1.9 1.9 0.7 1.9 1.9 1.9 1.8 1.8 1.8 1.8 0.0 1.1 1.6 1.8 1.8 1.7 1.9

2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 1.1 2.5 2.5 2.5 2.5 2.5 2.5 2.5 0.8 2.4 2.5 2.5 2.5 2.4 2.4 2.5 0.9 2.4 2.4 2.4 2.4 2.3 2.3 2.4 0.1 1.3 2.0 2.3 2.2 2.2 2.5

4.6 4.6 4.6 4.6 4.6 4.6 4.6 4.6 2.8 4.6 4.6 4.6 4.6 4.6 4.6 4.6 2.4 4.5 4.5 4.5 4.5 4.5 4.5 4.5 2.5 4.5 4.4 4.4 4.4 4.4 4.4 4.5 1.1 3.2 4.0 4.4 4.3 4.2 4.6

5.0 4.7 4.4 4.3 4.1 3.9 3.7 3.3 2.3 -.-.4.9 4.7 4.4 4.3 4.1 1.7 -.-.-.-.4.9 4.8 4.6 2.0 -.-.5.0 4.8 4.7 4.6 4.4 0.1 3.0 4.5 -.4.8 4.7 4.6

2.4 2.4 2.4 2.4 2.3 2.3 2.3 2.2 1.1 2.5 2.5 2.5 2.4 2.4 2.4 2.3 0.8 2.4 2.5 2.4 2.4 2.4 2.4 2.4 0.9 2.4 2.4 2.3 2.3 2.3 2.3 2.3 0.1 1.3 2.0 2.3 2.2 2.2 2.4

2.5 2.6 2.6 2.6 2.6 2.6 2.6 2.6 1.1 2.6 2.6 2.6 2.6 2.6 2.6 2.6 0.8 2.5 2.5 2.5 2.5 2.5 2.5 2.5 0.9 2.5 2.4 2.4 2.4 2.4 2.4 2.4 0.1 1.4 2.1 2.4 2.3 2.2 2.5

4.6 4.6 4.6 4.6 4.6 4.6 4.6 4.6 2.8 4.6 4.6 4.6 4.6 4.6 4.6 4.6 2.4 4.5 4.6 4.6 4.5 4.5 4.5 4.6 2.5 4.5 4.5 4.4 4.4 4.4 4.4 4.5 1.1 3.2 4.0 4.4 4.3 4.3 4.6

-.-.-.-.-.-.4.8 4.3 3.0 -.-.-.-.-.-.-.2.3 -.-.-.-.-.-.-.2.6 -.-.-.-.-.-.-.0.2 3.9 -.-.-.-.-.-

2.9 2.9 2.9 2.8 2.8 2.8 2.7 2.6 1.3 3.0 3.0 3.0 2.9 2.9 2.8 2.8 1.0 2.9 3.0 3.0 2.9 2.9 2.9 2.9 1.1 2.9 2.9 2.8 2.8 2.8 2.8 2.8 0.1 1.6 2.4 2.8 2.7 2.6 2.9

2.6 2.7 2.6 2.6 2.6 2.6 2.6 2.6 1.2 2.6 2.6 2.6 2.7 2.6 2.6 2.6 0.8 2.6 2.6 2.6 2.6 2.6 2.6 2.6 1.0 2.5 2.5 2.5 2.5 2.5 2.5 2.5 0.1 1.4 2.1 2.4 2.3 2.3 2.6

4.6 4.6 4.6 4.6 4.6 4.6 4.6 4.6 2.8 4.6 4.6 4.6 4.6 4.6 4.6 4.6 2.4 4.5 4.6 4.6 4.6 4.6 4.6 4.6 2.5 4.5 4.5 4.5 4.5 4.4 4.4 4.5 1.1 3.2 4.1 4.4 4.3 4.3 4.6

For different soil conditions, separate calculations can be made on request.

69

Appendix I : List of symbols (mm2) (mm2)

A AB

= structural wall area = bore area

c CL CL(T)

= wave velocity = live-load coefficient (single wheel load) = live-load coefficient (two passing trucks)

D Df DI Dl DO

= = = = =

mean pipe diameter shape factor structural inner diameter deflection lag factor structural outer diameter

E' EH EI ES EV EX EXT

= = = = = = =

modulus of soil reaction hoop bending modulus stiffness factor shear modulus volumetric E-modulus axial bending (tensile) modulus axial bending (tensile) modulus at elevated temperature

f FS FW

= constant = design factor = frictional force between soil and pipe

g GB GV

= acceleration due to gravity = linear mass of the pipe = lenear mass of the pipe content

H HDB HDS

= burial depth to top of the pipe = Hydrostatic Design Basis = Hydrostatic Design Stress

(ft) (N/mm2), (psi) (N/mm2), (psi)

ID If IR IZ

= = = =

(mm), (m), (in) (-) (mm) (mm4)

k KV KX

= wall roughness = compression modulus of the fluid = deflection coefficient

L L' LA LC LC1 LC2 LEQ LF LO

= = = = = = = = =

(m/s) (-) (-) (m), (in), (ft) (-) (mm), (in) (-) (mm), (in) (psi) (N/mm2), (N/m2), (psi) (in2.lb/in) (N/mm²) (N/mm2) (N/mm2) (N/mm 2) (-) (-) (N/mm 2) (m/s2) (kg/m) (kg/m)

inner diameter impact factor radius of inertia linear moment of inertia

(mm) (N/mm2) (-)

length between stiff pipe ends support distance at operating temperature and -pressure fictive anchor length continuous span length continuous span length based on axial stress continuous span length based on the allowable sag equivalent pipe length final support distance standard length

70

(mm) (m) (m) (mm), (m) (mm) (mm) (m) (m) (m)

LS LS1 LS2

= single span length = single span length based on axial stress = single span length based on allowable sag

(mm), (m) (mm) (mm)

NXY NYX

= Poisson ratio axial/hoop = Poisson ratio hoop/axial

OD

= outer diameter

P PA PAT PB PBT PN PS PW

= = = = = = = =

QP

= linear weight of the filled pipe

R Rb Rc RE rm ro RS RT

= = = = = = = =

ratio axial stress/hoop stress, elbow radius bending radius rerounding coefficient temperature correction factor mean pipe radius outer pipe radius specific gravity correction factor temperature change correction factor

(-), (mm) (m), (in) (-) (-) (mm), (in) (ft) (-) (-)

SA Sb Seq Seq(max) SF SF Sf SH SL STES STIS SV SX SXT SY

= = = = = = = = = = = = = = =

remaining axial stress load-dependent safety factor equivalent stress maximum equivalent stress Stiffness Factor service factor service (design) factor allowable hoop stress specific gravity of the laminate Specific Tangential End Stiffness Specific Tangential Initial Stiffness specific gravity of the fluid actual axial stress due to internal pressure allowable axial stress actual hoop stress due to internal pressure

(N/mm2) (-) (N/mm2) (N/mm²) (in2.lb/in) (-) (-) (N/mm 2) (kg/m3) (N/m2) (N/m2) (kg/m3) (N/mm2) (N/mm2) (N/mm2)

T TC TE TL TT TW

= = = = = =

operating temperature topcoat thickness minimum reinforced wall thickness liner thickness nett total wall thickness total wall thickness

UEWS

= Ultimate Elastic Wall Stress

v

= flow velocity

(-) (-) (mm), (in)

operating pressure anchor load anchor load at elevated temperature buckling pressure buckling pressure at elevated temperature nominal pressure Pipe Stiffness wheel load

(Mpa), (psi) (N) (N) (bar) (bar) (bar), (Mpa) (psi) (lb) (N/mm)

(°C) (mm) (mm), (m), (in) (mm) (in) (mm), (in) (N/mm2) (m/s)

71

(mm3) (lb/in) (lb/in) (mm3)

WB WC WL WW

= = = =

moment of resistance to bending vertical soil load live load moment of resistance to torsion

α α

= creep factor = bedding angle

(-) (°)

β

= ageing factor

(-)

γS

= specific mass of soil

∆Hfitting ∆Hpipe ∆P ∆T ∆y ∆v

= = = = = =

ζ

= friction coefficient

σC

= resulting hoop stress

τ

= shear stress

ω

= winding angle

ϒL

= coefficient of linear thermal expansion

(kg/m3), (lb/ft3) (N/m2) (m.w.c./m.) (N/m2), (m.w.c.) (°C) (in) (m/s)

head loss in the fitting head loss in the pipe pressure change temperature change predicted vertical pipe deflection change in flow velocity

(-) (psi) (N/mm2) (°)

72

(mm/mm°C)

Appendix II: Conversion tables feet per second squared

= 0.3048

m/s2

Flow rate 1 cubic feet per hour 1 gallon per minute

= 0.02679 = 227.1

m 3/h dm 3/h

Mass base Pounds per hour MT/D

= 0.01088 tons per day = 0.4536 kg/h

Force (SI = N) pounds force

= 4.4482

N

Heat Btu per pound Btu per hour Btu / hr.ft2°F Btu / lb.°F2 Btu / hr.ft 2 Btu.ft / hr.ft .°F ft2.hr.°F/Btu

= = = = = = =

kJ/kg W 2 W/m .°C KJ/kg.°C W/m 2 W/m.°C m2.°C/W

Moment of inertia inch 4

= 4.162 * 10 -6

m4

Moment of bending (SI = Nm) 1 inch pound 1 foot pound

= 0.1130 = 1.356

Nm Nm

Velocity (SI = m/s) 1 ft/second 1 ft/minute 1 mile/hr

= 0.3048 = 0.00508 = 0.44704

m/s m/s m/s

Conversion figures for anglo-saxon units into metric units Length (SI = m) 1 inch 1 foot = 12 inch 1 yard = 3 feet 1 mile = 1760 yards 1 seamile Area (SI = m 2 ) 1 square inch 1 square foot = 144 square inch 1 square yard = 9 square feet 1 acre = 4840 square yards 1 square mile = 640 acres 1 circular inch= π square inch 4 Volume (SI = m 3 ) 1 cubic inch 1 cubic foot= 1728 cubic inch 1 cubic yard= 27 cubic feet 1 imperial gallon 1 US gallon 1 US barrel (petrol) 1 barrel (imperial)

= = = = =

0.02540 0.30480 0.91440 3 1.609 * 10 1.852 * 10 3

m m m m m

= = = = =

6.4516*10 -4 9.2903*10 -2 0.8361 4,046.85 2.58998*10 6

m 22 m m2 m m2

= 5.0671*10 -4

m2

= = = = = = =

16.387*10 -6 28.317*10 -3 0.76455 -3 4.5461*10 3.7854*10 -3 0.158762 0.163656

m 33 m m 33 m3 m3 m3 m

Mass (SI = kg) 1 grain 1 ounce = 437.5 grains 1 pound = 16 ounces 1 US long ton= 2240 pound 1 US short ton= 2000 pound 1 hundred weight (imp.) 1 hundred weight (US)

= = = = = = =

0.0648*10 -3 0.0283495 0.4535924 1,016.05 907.185 50.80235 45.3592

kg kg kg kg kg kg kg

Mass per length (SI = kg/m) 1 pound per inch 1 pound per foot 1 pound per yard

= 17.858 = 1.488 = 0.4961

kg/m kg/m kg/m

Mass per area (SI = kg/m 2 ) 1 pound per square inch 1 pound per square foot 1 pound per square yard

= 0.0703*10 4 = 4.8825 = 0.5425

kg/m 22 kg/m 2 kg/m

2.288*10 -3 16.0256 1.711 119.8

kg/m 33 kg/m 3 kg/m kg/m 3

Conversion figures for metric into anglo-saxon units Length 1 metre

1 kilometre Area 1 square millimetre 1 square metre

3

Density (SI = kg/m ) 1 grain per cubic foot 1 pound per cubic foot 1 grain per gallon (US) 1 pound per gallon (US)

= = = = 2

1 square kilometre Volume 1 cubic metre

-5

Pressure (SI = Pa = 1 N/m = 10 bar) 1 pound per square inch = 6.8948*10 3 1 pound per square foot = 47.876 1 pound per square yard = 5.3201 1 long ton per sq. inch (imp) = 1.0725*10 5 1 long ton per sq. foot (imp) = 1.5444*10 77 1 short ton per sq. inch (US) = 1.3789*10 2 1 grain per square inch = 0.9850*10 2 1 ounce per square inch = 4.3092*10 1 ounce per square foot = 2.9925 1 ounce per square yard = 0.3313 1 inch head of water = 249.089 1 inch head of mercury = 3.3864*10 32 1 foot head of water = 2.9879*10

2

N/m 2 N/m 2 N/m N/m 22 N/m 2 N/m 2 N/m 2 N/m 2 N/m 2 N/m 2 N/m N/m 22 N/m

Mass 1 kilogram

1 metric ton Mass per length 1 kilogram per metre

Power (SI = W) 1 foot pounds per second 1 foot pounds per minute 1 British thermal unit per sec. 1 centigrade thermal unit p. sec. 1 horsepower (Hp)

= = = = =

1.35582 -2 2.25 * 10 1.0549*10 -3 1.8987*10-4-3 7.457 *10

W W W W W

Work (SI = Nm = J) 1 foot pound 1 yard pound 1 foot ton (US) 1 foot ton (imp.) 1 HPh 1 Btu 1 Ctu

= = = = = = =

1.3558 4.0675 2.7164*10 3 3.0371*10 36 2.6815*10 3 1.0555*10 3 1.8991*10

J J J J J J J

2.326 0.2931 5.678 4.187 3.155 1.731 0.1761

= = = = =

1.094 3.281 39.37 0.621 0.540

yards feet inches statute mile nautical mile

= = = = =

15.51 square inch 1.196 square yards 10.76 square feet 0.3861 square mile 0.02471 acres

= = = = = = =

61.024 cubic inch 35.31 cubic feet 1.308 cubic yards 220 imperial gallon 264.2 US gallon 6.290 US barrel 6.286 imperial barrel

= = = = =

15430 grains 35.27 ounces 2.205 pounds 1.102 US short tons 0.984 long ton

= 0.056 pounds per inch = 0.672 pounds per foot = 2.016 pounds per yard

Mass per area (specific pressure) 1 kilogram per sq. metre = 0.0014 = 0.2048 = 1.8433 Density 1 kilogram per cubic metre

Acceleration (SI = m/s 2 )

73

psi psf lb/sq. yard

= 0.0624 pcf = 437 grain pr cubic foot = 58.4 grain per gallon

Moment of4 inertia millimetres Moment of bending Nm

= 8.850 inch pounds = 0.07375 foot pounds

Pressure 1 N/m 2

1 MN/m

Length (SI = m) 1 km 1 cm 1 mm 1 micron = 10 -6

= 2.40269 * 10 -6 in 4

= = = = = = = = =

2

Power 1 kilowatt

Work 1 Joule

Heat 1 Kj/kg 1W 2 1 W/m 2.°C 1 W/m 1 W/m.°C 1 m 2.°C/W 1 Kj/kg.°C Velocity 1 m/s

738 foot pounds/sec. 4.428*10 4 ft lb/min. 0.94799 Btu/sec. 0.526676 Ctu/sec. 1.340536 Horse Power

= = = = = = =

0.73756 foot pound 0.24585 yard pound 0.3681*10-3-3 ft.tons(US) 0.3293*10 -6 ft.tons(Eng) 0.3250*10 Hph 0.9474*10 -3 Btu 0.5266*10 -3 Ctu

= = = = = = =

0.42992 Btu/pound 0.341180 Btu/hour 0.17612 Btu/hr.ft22.°F 0.31696 Btu/hr.ft 2 0.5777 Btu.ft/hr.ft .°F 5.6786 ft2.hr.°F/Btu 0.23883 Btu/lb.°F

= 91.91176 pounds/hour = 2.20459 pounds/hour

Force 1 N (Newton)

= 0.22481 pounds force

Volume (SI = m ) 1 dm23 = 1 litre = 10 -3 1 cm 3 = 10 -6 1 mm = 10 -9

m 33 m3 m

Mass (SI = kg) 1 gram 1 metric ton 1 milligram

kg kg kg

= 10 -3 = 10 3-6 = 10

Mass per length (SI = kg/m)-6 1 den = (1/9)*10 kg/m kg/m 1 tex = 10 -6 Mass per area 1 gram/mm 2 Density 3 1 gram/dm

= 10 -3 = 10 3

2 kg/mm kg/m 2

=1 = 10 -3 =1

gram/ltr 3 kg/dm kg/m 3

Pressure 5 1 bar = 10 Pa = 10 5 N/m 2 1 kgf/cm 2 = 98066 Pa3 1 atm. = 101.325*10 Pa 1 at = 98066.5 Pa 1 Torr = 133.322 Pa 1 metre water column = 9.80665 * 10 3 Pa 1 metre mercury column = 133.322 * 10 2 Pa Power 1 kgf.m/s = 9.80665 W 1 metric horsepower = 735.499 W 1 kcal/h = 1.163 W Work 1 Nm =1 J 1 kgf.m = 9.80665 J 6 1 kWh = 3.6*10 J 1 kcal = 4186.8 J 1 metric horse power.hour = 2.64780 * 10 6 J J 1 erg = 1 dyn.cm = 10 -7

= 37.32736 feet3/hour = 0.00440 gallons/minute

Mass base MT/D kg/h

m 22 m m2

3

= 3.28084 ft/sec²

Flow3 rate 1 m /hr

= 10 6-4 = 10 -6 = 10

2

= 3.28084 ft/sec = 196.8504 ft/min. = 2.236936 mile/hr.

Acceleration 1 m/s 2

m m m

Area 2(SI = m ) 1 km 2 1 cm 2 1 mm

0.0001450 psi 0.0208873 psf 0.18797lb/sq. yard 0.0102 grains/sq. inch 3.0184 ounces/sq. yard 0.0023 ounces/sq. inch 9.324long tons/ft²(eng) 0.648long tons/in²(eng) 0.725short tons/in²(US)

= = = = =

= 10 3-2 = 10 = 10 -3 m

Acceleration g = gravitation

= 9.8067

m/s2

Velocity 1 km/h = 0.2778 1 m/min. = 0.0167 1 knot = 0.5144

m/s m/s m/s

Flow rate 1 litre/h 1 m 3/h

= 10 -3 = 0.2778

m 33/h m /h

Mass base 1 kg/h

= 24.0

MT/D

Prefixes Prefix

Factor

giga mega kilo milli micro

10 9 10 63 10 -3 10 10 -6

Symbol

G M k m µ

Force 1 kgf = 9.80665 N N 1 dyn = 1 g.cm/s 2 = 10 -5 Heat 1 kcal/hr = 1.163 1 kcal 1 kcal(h.m)2 1 kcal(h.m ) 1 cal(s.cm)

Conversion figures for metric units into SI-units

74

W = 4186.8 = 1.163 = 1.163 = 418.68

J W/m 2 W/m W/m

Appendix III: Conversion graph psi vs bar

75

Appendix IV : Conversion graph °C vs °F

76

Appendix V : Examples combined stresses Example I:

Question Inner diameter 400 mm, pipe series EST 20 to be used as vertical pump column. Is the maximum torque generated by the pump allowable? Pump data max operating pressure (P) pump weight maximum moment Pipe data pipe series inner diameter winding angle (ω ) effective wall thickness linear mass bore area structural wall area moment of resistance to torsion specific gravity of pipe laminate mass of ID 400 mm EST 20 flange pipe length column length flanged pipe lenghts of 3 m each, total column length 12 m.

12

bar

90 (MW) 8100

EST 20 (ID) 400 55 ° (TE) 6.5 (GB) 17.3 (AB) 125660 (A) 8320

kN Nm

mm mm kg/m mm2 mm2

(table II-b., page 9)

(W W) 1669200

mm3

(SL)

1850

kg/m3

27.5 3 12

kg m m

(Product List)

(LP) (L)

=

150792

N

=

15079

N

=

2076

N

=

90000

N

=

2200

N + N

Calculation 1) axial load due to pressure: Fax,1 = AB * P = 125660 * 1.2 2) weight of water column: Fax,2 = AB * L * 1000E-8 = 125660 * 12000 * 1000E-8 3) weight of pipe EST 20: Fax,3 = GB * L = 173 * 12 4) weight of pump Fax,4 5) weight of flanges: number of flanges = 2 * L/LP = 2 * 12/3 = 8 Fax,5 = 8 * 275 Total axial load (Fax,tot):

(Eq.II.7. incl. note, table II-b., page 9)

260147

77

Resulting axial stress (Sax): Sax = Fax,tot / A = 260147 / 8320

=

31.3

N/mm2

Actual hoop stress due to internal pressure (SY): SY = P/2 *{(ID/TE)+ 1} = 1.2/2 *{(400/6.5)+ 1}

=

37.5

N/mm2

Actual shear stress due to torsion (τ) τ = MW / W W = 8100000 / 1669200

=

4.9

N/mm2

Fig. V-1.

Conclusion The allowable shear stress at the combination of Sax = 31.3 N/mm2 and SY = 37.5 N/mm2 is τ = 20 N/mm2, which exceeds the calculated τ of 4.9 N/mm2 clearly. The torque generated by the pump is allowable.

78

Example II:

Question Inner diameter 150 mm, pipe series EST 20 to be installed horizontally on pipe supports. What is the maximum support distance? Operating data operating pressure occuring shear stress due to torsion continuous span support operating temperature Pipe data Pipe series Inner diameter (ID) winding angle effective wall thickness linear mass of the pipe linear mass of the pipe content

(P)

15

bar

(τ)

15

N/mm²

(T)

60

°C

EST 20 150 (ω ) 55 (TE) 2.4 (GB) 2.8 (G V) 17.7

mm ° mm kg/m kg/m

bore area structural wall area moment of resistance to bending

(AB) (A)

17670 1160

mm2 mm2

(W B)

43700

mm3

axial bending modulus linear moment of inertia

(EX) (I Z)

12000 3403000

N/mm2 mm4

=

47

N/mm²

2) Axial stress due to internal pressure (Eq.III.3.) =

24

N/mm²

3) Allowable axial stress (see fig. V-2.)

=

34

N/mm²

4) Allowable axial stress for support purposes = 34 - 24

=

10

N/mm²

9840

N/mm 2

0.201

N/mm

Calculation 1) Hoop stress due to internal pressure

5) Axial bending modulus at 60°C (Eq. III.10.) = 12000 * 0.82 = 6) Linear weight of the filled pipe (Eq. III.5.) =

=

79

(table II-d., page 10; SV = 1000 kg/m3) (table II-b., page 9) (equation II.7. including note, table II-b., page 9) (table II-j., page 24) (table II-b., page 9)

Continuous span length based on axial stress (LC1) = =

5108 mm

Continuous span length based on allowable sag (LC2) = =

6839 mm

Fig V-2.

Conclusion Under the described circumstances, a maximum support distance of 5.1 m. should be applied in order to obtain a service factor (S F) of 1.5.

80

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