Future Pipe Industries

WAVISTRONG

ENGINEERING GUIDE

WAVISTRONG FIBERSTRONG WAVIFLOAT FIBERMAR

Epoxy Pipe Systems

Title:Engineering Guide forWavistrong filament woundepoxy pipe systems

Date issued: 01-11-1997

Replaces issue of:01-04-1995

REP 348/Rev 1/1197

WavistrongEngineering 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 fibrereinforced 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, amendand update any products, systems and services described in this brochure. We accept no responsibilityfor 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 meanswithout written permission from the publisher.

Table of ContentsSection Page

I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

II. Wavistrong information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3II.1. General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3II.2. Serial identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3II.3. Winding angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4II.4. Joining systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4II.4.1. Tensile resistant joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4II.4.2. Non-tensile resistant joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5II.5. System data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5II.5.1. Pipes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5II.5.2. Fittings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11II.5.3. Combined stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12II.6. Head loss in pipes and fittings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18II.6.1. Wavistrong pipes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18II.6.2. Wavistrong fittings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18II.7. Wavistrong pipe properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23II.8. Bending radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25II.9. Fluid (water) hammer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29II.10. Stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33II.11. Buckling pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37II.12. Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

III. Wavistrong above ground pipe systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42III.1. Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42III.2. Supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42III.3. Clamps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42III.4. Support distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43III.4.1. Single span length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43III.4.2. Continuous span length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45III.5. Corrected support distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47III.6. Anchor points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52III.7. Anchor loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

IV. Wavistrong underground pipe systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56IV.1. Design and joining systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56IV.2. Anchor points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56IV.3. Calculation of underground pipe systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56IV.3.1. Pipe deflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57IV.3.2. Deflection lag factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58IV.3.3. Deflection coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58IV.3.4. Vertical soil load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59IV.3.5. Live load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59IV.3.5.1. Live load coefficient single wheel load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60IV.3.5.2. Live load coefficient two passing trucks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60IV.3.6. Pipe stiffness factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61IV.3.7. Modulus of soil reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61IV.4. Resulting hoop stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62IV.5. Allowable combined stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

I

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. IntroductionThis Wavistrong Engineering Guide provides information for the design, specification and installationof Wavistrong glass fibre reinforced epoxy pipe systems in the diameter range from 25 mm up to andincluding 1200 mm, for above ground and underground applications. For detailed specification, installationinformation and standard products reference is made to the Wavistrong System Specifications, the WavistrongInstallation Manual and the Wavistrong Product List. Beyond others, this information can be obtainedby 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 haveto be combined to an equivalent stress and compared with the allowable value of this stress. The allowableequivalent 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 calculationof 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 specificunderground 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 computerizedflexibility programs.Although our Engineering Department is able to support the pipe system design with individual calculationsas 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 asfittings. All elements of the system are designed such that the performance requirements of the pipeline is validfor each element of the Wavistrong system. The choice for one of the possible joining systems will be considered in design stage. Together with ourengineers we can advise an optimal solution.Because of its benefits, the possibility of using prefabricated pipeline sections (spools), should be consideredin 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 answeredto come to a successful operating pipeline. Besides technical discussions these questions are answered in our technical literature. The different subjectsfor 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 informyou 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. Heft4-7-12.

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 cycloaliphatic 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 lowconcentrations of acids, neutral or near-neutral salts, solvents and caustics, both under internal and externalloads at temperatures up to 110C.The helically wound continuous glass fibres of the reinforced (structural) wall of the pipes and the fittingsare 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 resinC

stands for electrical conductive epoxy resin

2. Type of application: S stands for standardW

stands for potable water

3. Type of joint: T stands for tensile resistantN

stands for non-tensile resistant

B. Pressure class

This figure indicates the maximum allowable internal pressure (bar) that the product can resist fora 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: Epoxy resinStandard applicationTensile resistant joining systemNominal pressure 20 bar.

Note: 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.

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PSS200365Polygon

II.3. Winding angle

Depending on the loading of the system and the pressure class, the continuous glass fibre reinforcementis helically wound under a predetermined angle with the axis of the pipe. For the different systems thewinding angle () is given in table II-a.

Table II-a. Winding angle (degrees)

SeriesPressure class (bar)

8 10 12.5 16 20 25 32 EST 63 55 55 55 55 55 ESN 73 63 63 63 63

For some applications it can be of advantage to use a different winding angle () in order to obtainspecific 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.

Fig. II.1. CJ

II.4.1. Tensile resistant joints

A. Adhesive bonded joint (CJ)

The Wavistrong adhesive bonded joint is a rigid typeof joining. The adhesive is a two component epoxy resinsystem, packed in separate containers. The joint consistsof a slightly conical socket end and a cylindrical spigotend.

B. Rubber seal lock joint (RSLJ)

Fig. II.2. RSLJ

This type of joint consists of an integral filament woundsocket end and a machined spigot end. The O-ring sealis positioned on the spigot end. The locking device isinserted through an opening in the socket end. It fits ina circumferential groove on the inner side of the socketend and rests against a shoulder on the spigot end. TheWavistrong rubber seal lock joint allows for some axialmovement as well as a certain angular deflection (tableIII-g., page 55).

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C. Laminated joint (LJ)

Fig. II.3. LJ

Generally these joints will only be used for diametersover 400 mm. The preparation of this rigid joint requiresgood craftsmanship; it is recommended that Future PipeIndustries provides assistance during installation.

D. Flanged joint (FJ)

To enable connections with steel piping and to allow foreasy assembling and disassembling of process lines,

Fig. II.4. FJ

Wavistrong pipes and fittings can be supplied withflanges, drilled in accordance with ANSI, DIN or otherspecifications. Special requirements can be met uponrequest.

Glass fibre reinforced epoxy flanges are always flat facedand in view of this, matching flanges should also be flatfaced. The flanged joint is completed by using a gasket.

II.4.2. Non-tensile resistant joints

A. Rubber seal joint (RSJ)

Fig. II.5. RSJ

The socket end of this joint is an integral filament woundpart of the pipe. The spigot end is a machined part onwhich the O-ring seal is positioned. This flexible jointallows for axial movement of the spigot in the socketand some angular deflection (table III-g., page 55).

B. Mechanical coupler (MC)

The mechanical coupler normally consists of a metal casing and a rubber seal. These couplers are availablein 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. Forthe determination of this behaviour, or in case these data cannot be used and separate calculations arerequired, the pipe data from table II-b. through II-d. (page 9 and 10) and fig. II.6. through II.8. (page 13through 17) provide the necessary information. Table II-b. through II-d. give the following pipe data forthe series EST and ESN:

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A. Minimum reinforced wall thickness (TE)

The minimum reinforced wall thickness is calculated with the ISO-formula:

(Eq. II.1.)

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

Note: TW = total wall thickness (mm)

TW = TE + TL + TC Where:TL = liner thickness = 0.5 mmTC = topcoat thickness = 0.3 mm

For production technical reasons the real wall thickness may be greater than the theoretically calculated minimumvalue.

B. Mass of the pipe (GB)

The mass of the pipe is calculated as follows:

(Eq. II.2.)

Where: GB = linear mass of the pipe (kg/m)OD = outer diameter (mm)ID = inner diameter (mm)SL = specific gravity of the laminate (table II-l., page 24) (kg/m3)

Note: OD = ID + 2 * TW

C. Structural wall area (A)

The structural wall area is calculated from:

(Eq. II.3.)

Where: A = structural wall area (mm2)DO = structural outer diameter (mm)DI = structural inner diameter (mm)

Note: DO = ID + 2 * (TL + TE)DI = ID + 2 * TL

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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 (mm4)DO = structural outer diameter (mm)DI = structural inner diameter (mm)

E. Radius of inertia (IR)

The radius of inertia is calculated from the following equation:

(Eq. II.5.)

Where: IR = radius of inertia (mm)IZ = linear moment of inertia (Eq. II.4.) (mm4)A = structural wall area (Eq. II.3.) (mm2)

F. Bore area (AB)

The bore area of the pipe is:

(Eq. II.6.)

Where: AB = bore area (mm2)ID = inner diameter (mm)

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G. Moment of resistance to bending (WB)

For the calculation of the moment of resistance to bending the following formula is used:

(Eq. II.7.)

Where: WB = moment of resistance to bending (mm3)DO = structural outer diameter (mm)DI = structural inner diameter (mm)

Note:

Where:WW = moment of resistance to torsion (mm3)

H. Mass of the pipe content (GV)

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 (kg/m)ID = inner diameter (mm)SV = specific gravity of the fluid (kg/m3)

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Table II-b. Pipe data for series EST

Series InnerdiameterReinforced

wall thickness

Linearmass ofthe pipe

Structural wallarea

Linear mo-ment of inertia

Radius ofinertia Bore area

Moment ofresistance to

bendingID TE GB A IZ IR AB WB

(mm) (mm) (kg/m) *102 (mm2) *104 (mm4) *10 (mm) *102 (mm2) *103 (mm3)EST 8 350 2.8 7.4 31.1 4869.9 12.5 962.1 273.1

400 3.2 9.4 40.6 8299.0 14.3 1256.6 407.4 450 3.6 11.6 51.4 13282.4 16.1 1590.4 579.8 500 4.0 14.1 63.5 20231.2 17.9 1963.5 794.9 600 4.8 19.7 91.4 41909.9 21.4 2827.4 1372.7 700 5.6 26.3 124.3 77588.3 25.0 3848.5 2178.8 750 6.0 29.9 142.7 102217.7 26.8 4417.9 2679.4 800 6.5 34.3 164.9 134409.2 28.6 5026.5 3302.4 900 7.3 42.8 208.3 214831.9 32.1 6361.7 4692.7

1000 8.1 52.2 256.8 326870.3 35.7 7854.0 6426.9 1200 9.7 73.9 368.9 676034.9 42.8 11309.7 11078.9

EST 12.5 250 2.5 4.9 19.9 1599.5 9.0 490.9 125.0 300 3.0 6.7 28.7 3310.1 10.7 706.9 215.6 350 3.5 8.9 39.0 6123.8 12.5 962.1 342.1 400 4.0 11.3 50.9 10435.8 14.3 1256.6 510.3 450 4.5 14.0 64.4 16702.4 16.1 1590.4 726.2 500 5.1 17.3 81.1 25964.7 17.9 1963.5 1015.8 600 6.1 24.3 116.3 53606.1 21.5 2827.4 1748.4 700 7.1 32.5 157.9 99002.4 25.0 3848.5 2768.5 750 7.6 37.0 181.1 130303.3 26.8 4417.9 3401.3 800 8.1 41.8 205.9 168498.1 28.6 5026.5 4123.8 900 9.1 52.4 260.2 269409.0 32.2 6361.7 5861.8

1000 10.1 64.0 320.8 410021.8 35.7 7854.0 8030.2 EST 16 200 2.5 3.9 16.0 827.5 7.2 314.2 80.3

250 3.2 5.9 25.6 2064.5 9.0 490.9 160.4 300 3.8 8.1 36.4 4226.3 10.8 706.9 273.9 350 4.4 10.7 49.1 7757.7 12.6 962.1 431.2 400 5.1 13.9 65.1 13415.2 14.4 1256.6 652.5 450 5.7 17.2 81.8 21325.3 16.1 1590.4 922.4 500 6.3 20.9 100.4 32304.4 17.9 1963.5 1258.0 600 7.6 29.7 145.3 67287.9 21.5 2827.4 2184.0 700 8.9 40.0 198.5 125057.5 25.1 3848.5 3479.6 750 9.5 45.5 227.0 164115.2 26.9 4417.9 4262.7 800 10.1 51.4 257.4 211676.1 28.7 5026.5 5155.3

EST 20 150 2.4 2.8 11.6 340.3 5.4 176.7 43.7 200 3.3 4.9 21.2 1105.3 7.2 314.2 106.5 250 4.1 7.3 32.9 2673.5 9.0 490.9 206.3 300 4.9 10.1 47.1 5509.4 10.8 706.9 354.5 350 5.7 13.5 63.9 10161.4 12.6 962.1 560.8 400 6.5 17.3 83.2 17276.9 14.4 1256.6 834.6 450 7.3 21.6 105.1 27602.1 16.2 1590.4 1185.7 500 8.1 26.3 129.6 41982.1 18.0 1963.5 1623.4 600 9.8 37.6 188.1 87719.2 21.6 2827.4 2826.9

EST 25 100 2.4 1.9 7.8 104.2 3.7 78.5 19.7 150 3.1 3.5 15.0 445.7 5.4 176.7 56.7 200 4.1 5.8 26.4 1389.7 7.3 314.2 132.9 250 5.1 8.8 41.0 3365.4 9.1 490.9 257.7 300 6.1 12.3 58.9 6940.7 10.9 706.9 443.2 350 7.1 16.4 79.9 12808.6 12.7 962.1 701.5 400 8.2 21.4 105.4 22072.7 14.5 1256.6 1057.6 450 9.2 26.7 133.0 35225.8 16.3 1590.4 1500.9 500 10.2 32.7 163.8 53531.0 18.1 1963.5 2053.4 600 12.2 46.3 235.0 110509.1 21.7 2827.4 3534.0

EST 32 25 1.8 0.4 1.6 1.5 1.0 4.9 1.0 40 1.8 0.6 2.4 5.6 1.5 12.6 2.5 50 1.8 0.8 3.0 10.4 1.9 19.6 3.8 80 2.4 1.5 6.3 54.7 2.9 50.3 12.8

100 2.6 2.0 8.5 113.6 3.7 78.5 21.4 150 3.8 4.1 18.5 553.9 5.5 176.7 69.8 200 5.1 7.1 33.0 1754.4 7.3 314.2 166.1 250 6.4 10.8 51.8 4288.8 9.1 490.9 325.2 300 7.7 15.2 74.7 8900.8 10.9 706.9 562.6

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Table II-c. Pipe data for series ESN

Series InnerdiameterReinforced

wall thickness

Linear massof the pipe

Structural wallarea

Linear moment of

inertiaRadius of

inertia Bore areaMoment of

resistance tobending

ID TE GB A IZ IR AB WB(mm) (mm) (kg/m) *102 (mm2) *104 (mm4) *10 (mm) *102(mm2) *103 (mm3)

ESN 10 450 3.3 10.8 47.1 12151.4 16.1 1590.4 531.1 500 3.6 12.9 57.1 18164.6 17.8 1963.5 714.9 600 4.3 17.9 81.8 37450.9 21.4 2827.4 1228.7 700 5.1 24.2 113.1 70510.1 25.0 3848.5 1982.8 750 5.4 27.2 128.3 91776.3 26.7 4417.9 2409.5 800 5.8 30.9 147.0 119621.2 28.5 5026.5 2944.2 900 6.5 38.5 185.3 190781.1 32.1 6361.7 4174.6

1000 7.2 46.9 228.0 289770.8 35.6 7854.0 5707.5 1200 8.6 66.1 326.8 597730.8 42.8 11309.7 9813.3

ESN 16 350 2.8 7.4 31.1 4869.9 12.5 962.1 273.1 400 3.2 9.4 40.6 8299.0 14.3 1256.6 407.4 450 3.6 11.6 51.4 13282.4 16.1 1590.4 579.8 500 4.0 14.1 63.5 20231.2 17.9 1963.5 794.9 600 4.8 19.7 91.4 41909.9 21.4 2827.4 1372.7 700 5.6 26.3 124.3 77588.3 25.0 3848.5 2178.8 750 6.0 29.9 142.7 102217.7 26.8 4417.9 2679.4 800 6.5 34.3 164.9 134409.2 28.6 5026.5 3302.4

ESN 20 200 2.4 3.8 15.3 793.2 7.2 314.2 77.1 250 2.5 4.9 19.9 1599.5 9.0 490.9 125.0 300 3.0 6.7 28.7 3310.1 10.7 706.9 215.6 350 3.5 8.9 39.0 6123.8 12.5 962.1 342.1 400 4.0 11.3 50.9 10435.8 14.3 1256.6 510.3 450 4.5 14.0 64.4 16702.4 16.1 1590.4 726.2 500 5.1 17.3 81.1 25964.7 17.9 1963.5 1015.8 600 6.1 24.3 116.3 53606.1 21.5 2827.4 1748.4

ESN 25 200 2.5 3.9 16.0 827.5 7.2 314.2 80.3 250 3.2 5.9 25.6 2064.5 9.0 490.9 160.4 300 3.8 8.1 36.4 4226.3 10.8 706.9 273.9 350 4.4 10.7 49.1 7757.7 12.6 962.1 431.2 400 5.1 13.9 65.1 13415.2 14.4 1256.6 652.5 450 5.7 17.2 81.8 21325.3 16.1 1590.4 922.4 500 6.3 20.9 100.4 32304.4 17.9 1963.5 1258.0 600 7.6 29.7 145.3 67287.9 21.5 2827.4 2184.0

ESN 32 80 2.4 1.5 6.3 54.7 2.9 50.3 12.8 100 2.4 1.9 7.8 104.2 3.7 78.5 19.7 150 2.4 2.8 11.6 340.3 5.4 176.7 43.7 200 3.3 4.9 21.2 1105.3 7.2 314.2 106.5 250 4.1 7.3 32.9 2673.5 9.0 490.9 206.3 300 4.9 10.1 47.1 5509.4 10.8 706.9 354.5

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

ID Specific gravity of the fluid SV (kg/m3) 800 1000 1200 1400 1600 1800 2000

25 0.4 0.5 0.6 0.7 0.8 0.9 1.0 40 1.0 1.3 1.5 1.8 2.0 2.3 2.5 50 1.6 2.0 2.4 2.7 3.1 3.5 3.9 80 4.0 5.0 6.0 7.0 8.0 9.0 10.1

100 6.3 7.9 9.4 11.0 12.6 14.1 15.7 150 14.1 17.7 21.2 24.7 28.3 31.8 35.3 200 25.1 31.4 37.7 44.0 50.3 56.5 62.8 250 39.3 49.1 58.9 68.7 78.5 88.4 98.2 300 56.5 70.7 84.8 99.0 113.1 127.2 141.4 350 77.0 96.2 115.5 134.7 153.9 173.2 192.4 400 100.5 125.7 150.8 175.9 201.1 226.2 251.3 450 127.2 159.0 190.9 222.7 254.5 286.3 318.1 500 157.1 196.3 235.6 274.9 314.2 353.4 392.7 600 226.2 282.7 339.3 395.8 452.4 508.9 565.5 700 307.9 384.8 461.8 538.8 615.8 692.7 769.7 750 353.4 441.8 530.1 618.5 706.9 795.2 883.6 800 402.1 502.7 603.2 703.7 804.2 904.8 1005.3 900 508.9 636.2 763.4 890.6 1017.9 1145.1 1272.3

1000 628.3 785.4 942.5 1099.6 1256.6 1413.7 1570.8 1200 904.8 1131.0 1357.2 1583.4 1809.6 2035.8 2261.9

10

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 DesignStress (HDS). For fittings the allowable hoop stress is as follows:

- tee/lateral/reducer: SH = 32 N/mm- elbow/double socket: SH = 40 N/mm

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

Table II-e. Available standard Wavistrong systems.

Pressureclass(bar)

Inner diameter (mm)25-50 80 100 150 200 250-300 350-400 450-600 700-800 900-1000 1200

8 12 2 2 2 2

10 2323

23

12.5 1212 2 2 2

16123

123

123

23

23

20123

123

123

123

23

25123

123

123

123

123

23

321 1

23

123

123

123

123

Note: 1 = CJ = Adhesive bonded Joint2 = RSLJ = Rubber Seal Lock Joint3 = RSJ = Rubber Seal Joint4 = LJ = Laminated Joint5 = FJ = 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

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 windingangles of 55, 63 or 73, in combination with shear stress ().

The equivalent stress (Seq), calculated with the use of the continuum theory and related to the HydrostaticDesign Stress (HDS), for the different pipes = 19.3 N/mm. For this case the service (design) factor referredto in ASTM D 2992, (Sf) = 0.5. The maximum equivalent stress (Seq(max)) for combined stresses in the pipe wall, due to the hydrostaticload plus external mechanical loads = 24.5 N/mm. 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 isgiven. For elbows the equivalent stress (Seq), related to the hydrostatic design stress (HDS), will be 12.3N/mm. For tees this value will be 9.8 N/mm. The service (design) factor as mentioned in ASTM D 2992will be (Sf) = 0.5.For combined stresses in the fittings the maximum equivalent stress (Seq(max)) will be 15.3 N/mm and12.3 N/mm for respectively elbows and tees. The service (design) factor in combined stress situationswill 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. Heft4-7-12.

12

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

13

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

14

Fig. II.6-c. Pipes, winding angle = 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 headlosses have been determined by using the Darcy Weisbach formula.

The friction coefficients for the pipeline system are determined by the Colebrook-White method with awall 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 roughnessk = 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 givethe head loss for the pipeline system in metre water column per metre pipe length for water at 10C. 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 = head loss in the fitting (N/m) = friction coefficient (-)SV = specific gravity of the fluid (kg/m3)v = flow velocity (m/s)

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

(Eq. II.10.)

Where:LEQ = equivalent pipe length (m)Hfitting = head loss in the fitting (N/m)Hpipe = head loss in the pipe (fig. II.9. and II.10., page 21 and 22) (m.w.c./m)g = acceleration due to gravity (m/s)

18

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

2230' 45 90

0.11 0.16

0.07 0.24

0.30

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

19

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

Flow separation Flow combination Flow separation Flowcombination

d d d d

0

0.2

0.4

0.6

0.8

1

1 0.58 0.35

1 0.58 0.35

1 0.58 0.35

1 0.58 0.35

1 0.58 0.35

1 0.58 0.35

0.04 0.25

0

-0.08-0.20

0

-0.05-0.10

0

0.07 0 0

0.21 0.25

0

0.35 0.30

0

0.95 1.30

1

0.88 1.55 3.00

0.89 2.40 9.00

0.95 4.2519.00

1.10 7.1033.00

1.28

0.04 0.20

0

0.17 0.45

0

0.30 0.75

0

0.41 1.00

0

0.51 1.25

0

0.60 1.50

0

-1.20-0.70-1.00

-0.40 0.20 2.00

0.08 1.3012.00

0.47 2.8029.00

0.72 4.80

0.91 7.25

0.04 0 0

-0.06-0.15-0.10

-0.04 0 0

0.07 0.15 0.10

0.20 0.25 0.20

0.33 0.35 0.40

0.90 1.00 2.00

0.68 0.45 2.00

0.50 0.60 6.00

0.38 1.3014.00

0.35 2.8027.00

0.48 4.9044.00

0.04 0 0

0.17 0.10

0

0.19-0.15-1.10

0.09-0.60-2.90

-0.17-1.50-5.70

-0.54-2.90 -9.60

-0.92-1.00-1.00

-0.38-0.10 2.00

0 0.75 9.00

0.22 2.1520.00

0.37 3.7535.00

0.37 5.4054.00

= friction coefficient for pressure loss of relative to .

d (flow separation) = friction coefficient for pressure loss of relative to .

d (flow combination) = friction coefficient for pressure loss of relative to .

= flow in the run

d = flow in the branch

20

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 Wavistrongin accordance with the indicated test methods. Unless otherwise stated, all properties refer to the reinforced wall and are valid for temperatures at 20C.For higher temperatures the correction factors for the E-moduli of table II-k. (page 24) should be applied.

Table II-h. Hydrostatic properties

Property Test method

Winding angle ()55 63 73

Bi-axial: (R = 0.5)

Ultimate hoop stress (rupture)

Ultimate hoop stress (weeping)

Ultimate Elastic Wall Stress (UEWS)

Hydrostatic Design Basis HDB (50 years)

Hydrostatic Design Stress HDS (50 years)

ASTM D 1599

Future Pipe Industries

ASTM D 2992 B

ASTM D 2992 B

650

250

160

125

63

500

200

140

100

50

-

-

-

-

-

N/mm

N/mm

N/mm

N/mm

N/mm

Uni-axial: (R = 0.25)

Ultimate hoop stress (rupture)

Ultimate hoop stress (weeping)

Hydrostatic Design Basis HDB (50 years)

Hydrostatic Design Stress HDS (50 years)

ASTM D 1599

ASTM D 2992 B

ASTM D 2992 B

-

-

-

-

1000

450

200

100

800

370

160

80

N/mm

N/mm

N/mm

N/mm

Minimum service (design) factor Sf = 0.5.

23

Table II-j. Mechanical properties

Property Test methodWinding angle ()

55 63 73

Axial tensile stressAxial tensile modulus

Hoop tensile stressHoop tensile modulus

Shear modulus

Axial bending stressAxial bending modulus

Hoop bending stressHoop bending modulus

Poisson ratio axial/hoop Poisson ratio hoop/axial

EX

ES

EX

EH

NXYNYX

ASTM D 2105ASTM D 2105

ASTM D 2290ASTM D 2290

ASTM D 2925

ASTM D 2412ASTM D 2412

7512000

21020500

11500

8012000

9020500

0.650.38

5511500

26027500

9500

6511500

12027500

0.620.26

4011500

40037000

7000

5011500

16037000

0.470.15

N/mmN/mm

N/mmN/mm

N/mm

N/mmN/mm

N/mmN/mm

-

-

Table II-k. Temperature correction factor RE (-) for moduli of elasticity

Correction factorRE (-)

WindingAngle

Temperature(C)

RE-Axial RE-Hoop () 20 40 60 80 100 110RE1RE2RE3

RE4RE5RE6

556373556373

111111

0.920.920.920.950.970.99

0.820.820.820.900.940.98

0.720.720.720.830.900.97

0.600.600.600.750.850.95

0.530.530.530.700.820.94

Table II-l. Physical properties

Property Test methodCoefficient of linear thermal expansion Thermal conductivitySpecific heatGlass content (by mass)Glass content (by volume)Specific gravity of the laminateBarcol hardnessSurface resistance (Series C..)

L

SL

ASTM D 696

ASTM D 2584ASTM D 2584

ASTM D 2583ASTM D 257

2 * 10-5 0.29 921 70 5 52 7 1850 35

< 10 * 10 6

mm/mm.C W/m.K J/kg.K % % kg/m3 -

/m

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

24

II.8. Bending radius

The minimum allowable bending radius (Rb) for a pipe, installed at 20C, 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 operatingtemperatures, the indicated values of table II-n. and II-o. have to be corrected with the temperature correctionfactor (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 (m)RE = temperature correction factor (table II-k., page 24) (-)EX = axial bending modulus (table II-j., page 24) (N/mm)DI = structural inner diameter (mm)SA = remaining axial stress (N/mm)

The value of SA is defined as follows:

(Eq. II.12.)

Where:SA = remaining axial stress (N/mm)SXT = allowable axial stress (N/mm)SX = actual axial stress due to internal pressure (N/mm)

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 (N/mm)P = operating pressure (Mpa)ID = inner diameter (mm)TE = minimum reinforced wall thickness (mm)

(table II-b. and II-c., page 9 and 10)

25

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

Table II-m. Allowable axial stress SXT (N/mm)

R(-)

Winding angle ()55 63 73

0.250.50

-

403232

25-

The values of table II-n. and II-o. (page 27 and 28) are only valid for the pipes of the indicatedseries.

For available standard pipe systems, see table II-e., page 11.

26

Table II-n. Bending radius Rb (m) at 20C for series EST

SeriesID

(mm)Operating pressure (P)

1 * PN 0.8 * PN 0.6 * PN 0.4 * PN 0.2 * PN 0 * PNEST 8 350 297 170 120 92 75 63

400 339 195 137 105 86 72 450 381 219 154 118 96 81 500 424 243 171 131 107 90 600 508 292 205 158 128 108 700 593 340 239 184 150 126 750 635 365 256 197 160 135 800 641 379 269 209 170 144 900 725 428 303 235 192 162

1000 810 476 337 261 213 180 1200 978 573 405 314 256 216

EST 12.5 250 178 102 72 55 45 38 300 214 122 86 66 54 45 350 250 143 100 77 63 53 400 285 163 114 88 71 60 450 321 183 128 99 80 68 500 332 197 140 109 89 75 600 403 238 169 131 107 90 700 474 279 197 153 125 105 750 509 299 211 164 133 113 800 545 319 226 175 142 120 900 616 360 254 196 160 135

1000 687 400 283 218 178 150 EST 16 200 159 86 59 45 36 30

250 180 103 72 55 45 38 300 225 125 87 66 54 45 350 271 148 102 78 63 53 400 292 165 115 88 72 60 450 337 188 130 99 81 68 500 383 210 145 111 90 75 600 450 250 173 133 107 90 700 517 290 201 154 125 105 750 562 313 217 166 134 113 800 607 335 232 177 143 120

EST 20 150 110 62 43 33 27 23 200 131 79 56 44 36 30 250 167 99 70 55 45 38 300 203 120 85 66 53 45 350 239 140 99 77 62 53 400 276 161 113 88 71 60 450 312 181 128 99 80 68 500 348 202 142 109 89 75 600 406 239 169 131 107 90

EST 25 100 45 32 25 21 17 15 150 99 59 42 33 27 23 200 136 80 57 44 36 30 250 172 100 71 55 45 38 300 209 121 85 66 54 45 350 246 142 100 77 62 53 400 271 159 113 87 71 60 450 307 180 127 98 80 68 500 344 201 142 109 89 75 600 417 242 170 131 107 90

EST 32 25 6 5 5 4 4 4 40 11 10 9 8 7 6 50 18 14 12 10 9 8 80 39 27 21 17 14 12

100 72 41 29 22 18 15 150 119 64 44 33 27 23 200 154 85 58 44 36 30 250 189 105 73 55 45 38 300 225 125 87 66 54 45

27

Table II-o. Bending radius Rb (m) at 20C for series ESN

SeriesID

(mm)Operating pressure (P)

1 * PN 0.8 * PN 0.6 * PN 0.4 * PN 0.2 * PN 0 * PNESN 10 450 331 230 176 143 120 104

500 383 262 199 160 134 115 600 465 316 239 192 161 138 700 522 361 275 223 187 161 750 575 392 298 240 201 173 800 603 415 316 255 214 184 900 685 469 356 287 241 207

1000 766 523 397 320 268 230 1200 929 631 478 384 321 276

ESN 16 350 297 170 120 92 75 63 400 339 195 137 105 86 72 450 381 219 154 118 96 81 500 424 243 171 131 107 90 600 508 292 205 158 128 108 700 593 340 239 184 150 126 750 635 365 256 197 160 135 800 641 379 269 209 170 144

ESN 20 200 106 76 60 49 42 36 250 214 122 86 66 54 45 300 256 147 103 79 64 54 350 299 171 120 92 75 63 400 342 195 137 105 86 72 450 384 220 154 118 96 81 500 398 236 168 130 107 90 600 483 285 202 157 128 108

ESN 25 200 173 98 69 53 43 36 250 198 118 84 65 53 45 300 247 144 102 79 64 54 350 296 170 119 92 75 63 400 321 190 135 104 85 72 450 370 216 152 118 96 81 500 418 242 170 131 107 90 600 493 288 203 157 128 108

ESN 32 80 25 22 20 18 16 15 100 39 32 27 23 20 18 150 132 74 52 40 32 27 200 157 94 67 52 43 36 250 200 119 84 65 53 45 300 243 143 101 79 64 54

28

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 relationbetween change of velocity and pressure can be derived from the formula of Joukowsky :

(Eq. II.15.)

Where:P = pressure change (m.w.c)c = wave velocity (m/s)g = acceleration due to gravity (m/s2)v = change in flow velocity (m/s)

In accordance with ANSI/AWWA C950-88 a transient pressure increase of 1.4 times the design pressureis 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 velocitycan be calculated with the aid of the Talbot equation:

(Eq. II.16.)

Where:c

= wave velocity (m/s)SV = specific gravity of the fluid (kg/m3)KV = compression modulus of the fluid (N/mm2)ID = inner diameter (mm)TE = minimum reinforced wall thickness (table II-b. and II-c., page 9 and 10) (mm)EV = volumetric E-modulus (N/mm2)f = constant (-)

This calculation method is only valid for straight pipeline sections with different types of joints. On request, system calculationscan 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 (),the volumetric E-modulus (EV) is calculated from the following equation:

(Eq. II.17.)

Where:EV = volumetric E-modulus (N/mm2)EX = axial bending modulus (table II-j., page 24) (N/mm2)EH = hoop bending modulus " " (N/mm2)NXY = Poisson ratio axial/hoop " " (-)NYX = Poisson ratio hoop/axial " " (-)

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

Table II-p. Volumetric E-modulus EV (N/mm)

Winding angle () 55 63 73EV 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 beachieved in a tensile resistant piping system.

(Eq. II.18.)

B. The pipeline may be anchored completely to prevent axial displacements. This may occur in tensileresistant 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 willhappen 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 ().

Table II-q. Constant f (-)

ConstantWinding angle ()

55 63 73f1f2f3

1.1265 0.753 0.81

1.16940.83880.87

1.21480.92950.925

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

31

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

Series ID(mm) c1 c2 Series ID(mm) c2 c3EST 8 350 394 458 ESN 10 450 388 439

400 394 458 500 385 435 450 394 458 600 434 435 500 394 458 700 438 439 600 394 458 750 435 436 700 394 458 800 437 438 750 394 458 900 436 437 800 397 461 1000 435 436 900 396 461 1200 434 435

1000 396 461 ESN 16 350 458 451 1200 396 460 400 458 451

EST 12.5 250 429 513 500 458 451 300 429 513 600 458 451 350 429 513 700 458 451 400 429 513 750 458 451 450 429 513 800 461 454 500 433 518 ESN 20 200 547 539 600 432 517 250 506 498 700 432 517 300 506 498 750 432 516 350 506 498 800 431 516 400 506 498 900 431 516 450 506 498

1000 431 516 500 510 502 EST 16 200 474 565 600 509 501

250 479 571 ESN 25 200 557 548 300 477 568 250 562 554 350 476 566 300 560 551 400 479 570 350 558 550 450 477 568 400 562 553 500 476 567 450 560 551 600 477 568 500 559 550 700 478 569 600 560 551 750 477 568 ESN 32 80 784 774 800 476 567 100 723 713

EST 20 150 529 626 150 617 608 200 536 634 200 625 616 250 534 632 250 623 614 300 533 631 300 622 613 350 533 630 400 532 630 450 532 629 500 531 629 600 533 631

EST 25 100 626 732 150 589 692 200 587 690 250 586 689 300 585 688 350 585 687 400 587 690 450 586 689 500 586 689 600 585 688

EST 32 25 923 1028 40 794 904 50 733 843 80 684 793

100 647 754 150 640 747 200 642 749 250 643 750 300 643 750

Note: values of table II-r. are valid for the following conditions:

KV = 2050 N/mm2

SV = 1000 kg/m3

32

II.10. Stiffness

An investigation of standards concerning the stiffness of flexible pipes shows that there are differentopinions 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 = Specific Tangential Initial Stiffness (N/m2)EH = hoop bending modulus (table II-j., page 24) (N/m2)TE = minimum reinforced wall thickness (table II-b. and II-c., page 9 and 10) (mm)ID = 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 inrelation to the life time (50 years). The determination of the STES is described in NEN 7037.

(Eq. II.22.)Where:STES = Specific Tangential End Stiffness (N/m2) = creep factor (-) = ageing factor (-)STIS = Specific Tangential Initial Stiffness (Eq. II.21.) (N/m2)

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

33

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 (in2.lb/in)EH = hoop bending modulus (table II-j., page 24) (psi)TE = minimum reinforced wall thickness (table II-b. and II-c., page 9 and 10) (in)

The Stiffness Factor (SF) can also be calculated from the STIS-value by using the following formula:

(Eq. II.24.)

Where:SF = Stiffness Factor (in2.lb/in)STIS = Specific Tangential Initial Stiffness (Eq. II.21.) (N/m2)ID = inner diameter (m)TE = 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 (in2.lb/in)rm = mean pipe radius (in)PS = Pipe Stiffness (Eq. II.26.) (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 = Pipe Stiffness (psi)EH = hoop bending modulus (table II-j., page 24) (psi)TE = minimum reinforced wall thickness (table II-b. and II-c., page 9 and 10) (in)ID = inner diameter (in)

The Pipe Stiffness (PS) can also be calculated from the STIS-value by the following formula:

(Eq. II.27.)

Where:PS = Pipe Stiffness (psi)STIS = Specific Tangential Initial Stiffness (Eq. II.21.) (N/m2)

In table II-s. (page 36) the different stiffness values at a temperature of 20C are listed. At temperaturesin excess of 20C the reduction factors (RE) for the moduli of elasticity should be applied (table II-k., page24).

35

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

Series EST Series ESNSeries ID(mm) STIS(N/m) SF(inlb/in) PS(psi) Series ID(mm) STIS(N/m) SF(inlb/in) PS(psi)EST 8 350 1150 450 9 ESN 10 450 1190 980 9

400 1150 660 9 500 1130 1270 9 450 1150 950 9 600 1110 2170 9 500 1150 1300 9 700 1170 3620 9 600 1150 2240 9 750 1130 4300 9 700 1150 3560 9 800 1150 5320 9 750 1150 4380 9 900 1140 7490 9 800 1200 5570 9 1000 1130 10180 9 900 1190 7890 9 1200 1110 17350 9

1000 1190 10780 9 ESN 16 350 1150 450 9 1200 1180 18510 9 400 1150 660 9

EST 12.5 250 1660 240 13 500 1150 1300 9 300 1660 410 13 600 1150 2240 9 350 1660 650 13 700 1150 3560 9 400 1660 970 13 750 1150 4380 9 450 1660 1380 13 800 1200 5570 9 500 1760 2010 14 ESN 20 200 3820 280 30 600 1740 3430 14 250 2220 320 17 700 1730 5410 13 300 2220 550 17 750 1720 6640 13 350 2220 870 17 800 1720 8030 13 400 2220 1300 17 900 1710 11390 13 450 2220 1850 17

1000 1710 15570 13 500 2360 2690 18 EST 16 200 3210 240 25 600 2340 4600 18

250 3450 500 27 ESN 25 200 4310 320 34 300 3340 830 26 250 4630 660 36 350 3270 1290 25 300 4480 1110 35 400 3410 2010 27 350 4390 1730 34 450 3340 2800 26 400 4570 2690 36 500 3290 3780 26 450 4480 3760 35 600 3340 6640 26 500 4420 5070 34 700 3380 10660 26 600 4480 8900 35 750 3340 12960 26 ESN 32 80 56620 280 441 800 3310 15570 26 100 29500 280 230

EST 20 150 6670 210 52 150 8950 280 70 200 7310 540 57 200 9800 730 76 250 7180 1040 56 250 9630 1400 75 300 7090 1780 55 300 9510 2390 74 350 7030 2800 55 400 6980 4150 54 450 6950 5880 54 500 6920 8030 54 600 7090 14230 55

EST 25 100 21990 210 171 150 14180 450 110 200 13850 1040 108 250 13650 2010 106 300 13520 3430 105 350 13430 5410 105 400 13850 8330 108 450 13740 11770 107 500 13650 16040 106 600 13520 27450 105

EST 32 25 517590 90 4029 40 136410 90 1062 50 71680 90 558 80 42210 210 329

100 27800 270 216 150 25770 830 201 200 26270 2010 204 250 26570 3960 207 300 26770 6900 208

36

II.11. Buckling pressure

For the calculation of the allowable buckling pressure (PB) for the Wavistrong series, the formula forthin wall pipes (mean radius/wall thickness > 10) has to be used. Besides, the allowable bucklingpressure (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 (PB) is determined by the stability of the product. The transition froma stable into an unstable condition will take place very abruptly, so an extra safety in the form of aservice factor (SF) is applied.Due to the unstable situation the allowable buckling pressure (PB) has also been made dependent onthe type of loading, which can be static or cyclic.

In some cases the allowable buckling pressure (PB) depends on the length between the stiff ends.Some extra external pressure allowance can be created by the application of stiffening rings. For thestandard lengths of 6 and 10 metres two or one, respectively three, two or one stiffening rings canbe used.

The allowable external pressures for pipes are listed in table II-t. and II-u. (page 39 and 40). Thetabled values are valid for an operating temperature (T) of 20C. For higher temperatures thecorrection 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 thetable 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 thefollowing 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) (mm)ID = inner diameter (mm)L = length between stiff pipe ends (mm)NXY = Poisson ratio axial/hoop (table II-j., page 24) (-)NYX = Poisson ratio hoop/axial (table II-j., page 24) (-)rm = mean pipe radius (mm)EH = hoop bending modulus (table II-j., page 24) (N/mm2)SF = service factor (SF = 0.75) (-)Sb = load-dependent safety factor (-)

static loading: Sb = 1 cyclic loading: Sb = 2

PB = buckling pressure (bar)

At temperatures above 20C the value (RE) 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 (bar)PB = buckling pressure (table II-t. and II-u., page 39 and 40) (bar)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

Table II-t. Allowable static buckling pressure PB (bar) at 20C, series EST

Series ID(mm)Pipe length L (m) between stiff ends

1 2 2.5 3 3.3 5 6 10 EST 8 350 1.1 0.5 0.4 0.4 0.3 0.2 0.2 0.2

400 1.2 0.6 0.5 0.4 0.4 0.2 0.2 0.2 450 1.4 0.7 0.5 0.5 0.4 0.3 0.2 0.2 500 1.5 0.8 0.6 0.5 0.5 0.3 0.3 0.2 600 1.8 0.9 0.7 0.6 0.6 0.4 0.3 0.2 700 2.1 1.1 0.8 0.7 0.6 0.4 0.4 0.2 750 2.3 1.1 0.9 0.8 0.7 0.5 0.4 0.2 800 2.5 1.3 1.0 0.8 0.8 0.5 0.4 0.3 900 2.8 1.4 1.1 0.9 0.9 0.6 0.5 0.3

1000 3.1 1.6 1.3 1.0 0.9 0.6 0.5 0.3 1200 3.7 1.9 1.5 1.2 1.1 0.7 0.6 0.4

EST 12.5 250 1.1 0.5 0.4 0.4 0.4 0.4 0.4 0.4 300 1.3 0.6 0.5 0.4 0.4 0.4 0.4 0.4 350 1.5 0.7 0.6 0.5 0.5 0.4 0.4 0.4 400 1.7 0.9 0.7 0.6 0.5 0.4 0.4 0.4 450 1.9 1.0 0.8 0.6 0.6 0.4 0.4 0.4 500 2.2 1.1 0.9 0.7 0.7 0.4 0.4 0.4 600 2.7 1.3 1.1 0.9 0.8 0.5 0.4 0.4 700 3.1 1.5 1.2 1.0 0.9 0.6 0.5 0.4 750 3.3 1.7 1.3 1.1 1.0 0.7 0.6 0.4 800 3.5 1.8 1.4 1.2 1.1 0.7 0.6 0.4 900 4.0 2.0 1.6 1.3 1.2 0.8 0.7 0.4

1000 4.4 2.2 1.8 1.5 1.3 0.9 0.7 0.4 EST 16 200 1.5 0.8 0.8 0.8 0.8 0.8 0.8 0.8

250 2.0 1.0 0.8 0.8 0.8 0.8 0.8 0.8 300 2.3 1.1 0.9 0.8 0.8 0.8 0.8 0.8 350 2.6 1.3 1.1 0.9 0.8 0.8 0.8 0.8 400 3.1 1.6 1.2 1.0 0.9 0.8 0.8 0.8 450 3.5 1.7 1.4 1.2 1.0 0.8 0.8 0.8 500 3.8 1.9 1.5 1.3 1.1 0.8 0.8 0.8 600 4.6 2.3 1.8 1.5 1.4 0.9 0.8 0.8 700 5.4 2.7 2.2 1.8 1.6 1.1 0.9 0.8 750 5.8 2.9 2.3 1.9 1.7 1.2 1.0 0.8 800 6.1 3.0 2.4 2.0 1.8 1.2 1.0 0.8

EST 20 150 2.0 1.6 1.6 1.6 1.6 1.6 1.6 -.-200 2.9 1.7 1.7 1.7 1.7 1.7 1.7 1.7 250 3.6 1.8 1.7 1.7 1.7 1.7 1.7 1.7 300 4.3 2.2 1.7 1.7 1.7 1.7 1.7 1.7 350 5.0 2.5 2.0 1.7 1.7 1.7 1.7 1.7 400 5.7 2.8 2.3 1.9 1.7 1.7 1.7 1.7 450 6.4 3.2 2.5 2.1 1.9 1.7 1.7 1.7 500 7.1 3.5 2.8 2.4 2.1 1.6 1.6 1.6 600 8.6 4.3 3.5 2.9 2.6 1.7 1.7 1.7

EST 25 100 5.1 5.1 5.1 5.1 5.1 5.1 5.1 -.- 150 3.8 3.3 3.3 3.3 3.3 3.3 3.3 -.- 200 5.0 3.3 3.3 3.3 3.3 3.3 3.3 3.3 250 6.2 3.2 3.2 3.2 3.2 3.2 3.2 3.2 300 7.4 3.7 3.2 3.2 3.2 3.2 3.2 3.2 350 8.6 4.3 3.4 3.2 3.2 3.2 3.2 3.2 400 10.1 5.0 4.0 3.3 3.3 3.3 3.3 3.3 450 11.3 5.6 4.5 3.8 3.4 3.3 3.3 3.3 500 12.5 6.2 5.0 4.2 3.8 3.2 3.2 3.2 600 14.9 7.4 5.9 5.0 4.5 3.2 3.2 3.2

EST 32 25 110.8 110.8 110.8 110.8 -.- -.- -.- -.- 40 30.4 30.4 30.4 30.4 -.- -.- -.- -.- 50 16.2 16.2 16.2 16.2 -.- -.- -.- -.- 80 9.7 9.7 9.7 9.7 9.7 9.7 9.7 -.-

100 6.5 6.5 6.5 6.5 6.5 6.5 6.5 -.- 150 6.3 6.0 6.0 6.0 6.0 6.0 6.0 -.- 200 8.6 6.2 6.2 6.2 6.2 6.2 6.2 6.2 250 10.9 6.3 6.3 6.3 6.3 6.3 6.3 6.3 300 13.2 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

Table II-u. Allowable static buckling pressure PB (bar) at 20C, series ESN

Series ID(mm)Pipe length L (m) between stiff ends

1 2 2.5 3 3.3 5 6 10ESN 10 450 1.4 0.7 0.5 0.5 0.4 0.3 0.2 0.2

500 1.5 0.7 0.6 0.5 0.4 0.3 0.2 0.2 600 1.7 0.9 0.7 0.6 0.5 0.3 0.3 0.2 700 2.1 1.0 0.8 0.7 0.6 0.4 0.3 0.2 750 2.2 1.1 0.9 0.7 0.7 0.4 0.4 0.2 800 2.4 1.2 0.9 0.8 0.7 0.5 0.4 0.2 900 2.6 1.3 1.1 0.9 0.8 0.5 0.4 0.3

1000 2.9 1.5 1.2 1.0 0.9 0.6 0.5 0.3 1200 3.4 1.7 1.4 1.1 1.0 0.7 0.6 0.3

ESN 16 350 1.1 0.5 0.4 0.4 0.3 0.2 0.2 0.2 400 1.2 0.6 0.5 0.4 0.4 0.2 0.2 0.2 450 1.4 0.7 0.5 0.5 0.4 0.3 0.2 0.2 500 1.5 0.8 0.6 0.5 0.5 0.3 0.3 0.2 600 1.8 0.9 0.7 0.6 0.6 0.4 0.3 0.2 700 2.1 1.1 0.8 0.7 0.6 0.4 0.4 0.2 750 2.3 1.1 0.9 0.8 0.7 0.5 0.4 0.2 800 2.5 1.3 1.0 0.8 0.8 0.5 0.4 0.3

ESN 20 200 1.7 0.8 0.8 0.8 0.8 0.8 0.8 0.8 250 1.3 0.7 0.5 0.5 0.5 0.5 0.5 0.5 300 1.6 0.8 0.6 0.5 0.5 0.5 0.5 0.5 350 1.8 0.9 0.7 0.6 0.6 0.5 0.5 0.5 400 2.1 1.1 0.8 0.7 0.6 0.5 0.5 0.5 450 2.4 1.2 0.9 0.8 0.7 0.5 0.5 0.5 500 2.8 1.4 1.1 0.9 0.8 0.6 0.5 0.5 600 3.3 1.6 1.3 1.1 1.0 0.7 0.5 0.5

ESN 25 200 1.8 0.9 0.9 0.9 0.9 0.9 0.9 0.9 250 2.4 1.2 1.0 1.0 1.0 1.0 1.0 1.0 300 2.8 1.4 1.1 1.0 1.0 1.0 1.0 1.0 350 3.3 1.6 1.3 1.1 1.0 0.9 0.9 0.9 400 3.9 1.9 1.5 1.3 1.2 1.0 1.0 1.0 450 4.3 2.1 1.7 1.4 1.3 1.0 1.0 1.0 500 4.7 2.3 1.9 1.6 1.4 0.9 0.9 0.9 600 5.7 2.8 2.3 1.9 1.7 1.1 1.0 1.0

ESN 32 80 11.7 11.7 11.7 11.7 11.7 11.7 11.7 -.-100 6.1 6.1 6.1 6.1 6.1 6.1 6.1 -.-150 2.5 1.9 1.9 1.9 1.9 1.9 1.9 -.-200 3.6 2.1 2.1 2.1 2.1 2.1 2.1 2.1250 4.5 2.2 2.0 2.0 2.0 2.0 2.0 2.0300 5.3 2.7 2.1 2.0 2.0 2.0 2.0 2.0

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

40

II.12. Classification

The Wavistrong pipes can be classified in accordance with ASTM D 2310, indicating type, grade andHydrostatic Design Basis (HDB).The classification for all pipes in the series EST 12.5 through EST 32 in accordance with this specificationis 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 accordancewith 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 classificationdesignations 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

SeriesEST ESN EST EST ESN EST ESN EST ESN EST ESN

PN (bar) 8 10 12.5 16 20 25 32Code 11FU1- 11FX2- 11FW1- 11FW1- 11FY2- 11FW1- 11FY2- 11FW1- 11FY2- 11FW1- 11FY2-

ID25 2111 40 2111 50 2111 80 2112 5112

100 2112 2114 5116 150 2112 2112 2115 5116 200 2112 2112 2112 5112 2113 5112 2116 5116 250 2112 2112 2113 5112 2115 5112 2116 5116 300 2112 2112 2114 5112 2116 5113 2116 5116 350 2112 2112 2113 5112 2116 5112 2116 5114 400 2112 2112 2115 5112 2116 5113 2116 5116 450 2112 4012 2113 2116 5112 2116 5114 2116 5116 500 2113 4013 2116 2116 5113 2116 5116 2116 5116 600 2115 4015 2116 2116 5115 2116 5116 2116 5116 700 2116 4016 2116 2116 5116 750 2116 4016 2116 2116 5116 800 2116 4016 2116 2116 5116 900 2116 4016 2116

1000 2116 4016 2116 1200 2116 4016

41

III. Wavistrong above ground pipe systems

III.1. Design

In nearly all above ground applications thrust resistant types of joints are used (adhesive bondedjoint, rubber seal lock joint, laminated joint or flanged joint).In case of well supported and anchored pipelines non-thrust resistant systems can be used (rubberseal 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 orrubber seal (lock) joint system (fig. III.1.). In case mechanical couplers are used, Future PipeIndustries 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 valueslisted 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 thesupports; 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 loadingmust 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 mustbe provided with a protective rubber or thermoplastic layer.

Guides enabling the pipe system to move freely in longitudinal direction should have a low friction innersurface 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 differentpipe 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 ofthe 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

Fig. III.3.

The single span length (LS) is the length between twosupports of one single pipe or a string of flexible jointedpipes (fig. III.3.). The single span length (LS) should beused in each of the following situations (fig. III.5., page47):

43

- For pipe systems where the joint is not designed to transmit bending forces; this is the case for mecha-nical 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 (mm)WB = moment of resistance to bending (table II-b. and II-c., page 9 and 10) (mm3)SA = remaining axial stress (N/mm2)QP = linear weight of the filled pipe (Eq. III.5.) (N/mm)

The value of SA depends on the actual stress due to internal pressure:

(Eq. III.2.)

Where:SA = remaining axial stress (N/mm2)SXT = allowable axial stress (table II-m., page 26) (N/mm2)SX = actual axial stress due to internal pressure (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 (N/mm2)P = operating pressure (Mpa)ID = inner diameter (mm)TE = minimum reinforced wall thickness (table II-b. and II-c., page 9 and 10) (mm)

44

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

(Eq. III.5.)

Where:QP = linear weight of the filled pipe (N/mm)GB = linear mass of the pipe (table II-b. and II-c., page 9 and 10) (kg/m)GV = linear mass of the pipe content (table II-d., page 10) (kg/m)g = acceleration due to gravity (m/s2)

B. Based on the allowable sag:

(Eq. III.6.)

Where:LS2 = single span length based on the allowable sag (mm)EXT = axial bending modulus at elevated temperature (N/mm2)IZ = linear moment of inertia (table II-b. and II-c., page 9 and 10) (mm4)QP = linear weight of the filled pipe (Eq. III.5.) (N/mm)

At temperatures in excess of 20C 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 (N/mm2)EX = axial bending modulus (table II-j., page 24) (N/mm2)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

Fig. III.4.

The continuous span length (LC) is the lengthbetween two supports of a string of rigid jointedpipes (fig. III.4.).

45

The continuous span length (LC) may be used for pipe systems where the joint is rigid and capable totransmit bending forces. This continuous span length (LC) can be used for adhesive bonded and laminatedpipe 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 (mm)WB = moment of resistance to bending (table II-b. and II-c., page 9 and 10) (mm3)SA = remaining axial stress (Eq. III.2.) (N/mm2)QP = linear weight of the filled pipe (Eq. III.5.) (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 (mm)EXT = axial bending modulus at elevated temperature (N/mm2)IZ = linear moment of inertia (table II-b. and II-c., page 9 and 10) (mm4)QP = linear weight of the filled pipe (Eq. III.5.) (N/mm)

From above it can be found that: LC2 = 1.71 * LS2

At temperatures in excess of 20C 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 (N/mm2)EX = axial bending modulus (table II-j., page 24) (N/mm2)RE1, RE2 or RE3 = temperature correction factors

for winding angles of respectively 55, 63 or 73. (table II-k., page 24) (-)

46

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 bemultiplied with one or more of the following correction factors:

A. Specific gravity correction factor (RS)

Above ground pipelines used for the transportation of fluids with a specific gravity (SV) other than1000 kg/m3 should be supported at a span length adapted with the correction factor (RS) as listedin table III-a. (page 48)

B. Temperature change correction factor (RT)

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 (m)L' = support distance at operating temperature (T) and -pressure (P)

(table III-c. through III-e. (page 49 through 51)) (m)RS = specific gravity correction factor (table III-a., page 48) (-)RT = temperature change correction factor (table III-b., page 48) (-)

47

Table III-a. Specific gravity correction factor RS (-)

Specific gravity of the fluid SV (kg/m3)0 600 800 900 1000 1100 1250

RS 1.55 1.25 1.07 1.03 1.0 0.95 0.90

Table III-b. Temperature change correction factor RT (-)

ID(mm)

Temperature change T (C)10 20 30 40 50 60 70 80 90 100

25 0.73 0.58 0.49 0.44 0.39 0.36 0.34 0.32 0.30 0.2840 0.81 0.69 0.60 0.54 0.49 0.45 0.42 0.40 0.38 0.3650 0.85 0.73 0.65 0.59 0.54 0.50 0.47 0.44 0.42 0.4080 0.90 0.81 0.74 0.69 0.64 0.60 0.57 0.54 0.51 0.49

100 0.92 0.85 0.79 0.74 0.69 0.66 0.62 0.59 0.57 0.54150 0.92 0.85 0.80 0.75 0.72 0.68 0.66 0.63 0.61 0.59200 0.94 0.89 0.84 0.81 0.77 0.75 0.72 0.70 0.68 0.66250 0.95 0.91 0.87 0.84 0.81 0.79 0.76 0.74 0.72 0.70300 0.96 0.92 0.89 0.87 0.84 0.82 0.80 0.78 0.76 0.74350 0.96 0.93 0.91 0.88 0.86 0.84 0.82 0.80 0.79 0.77400 0.97 0.94 0.92 0.89 0.87 0.85 0.83 0.82 0.80 0.79450 0.97 0.95 0.92 0.90 0.88 0.87 0.85 0.83 0.82 0.80500 0.97 0.95 0.93 0.91 0.90 0.88 0.86 0.85 0.83 0.82600 0.98 0.96 0.94 0.93 0.91 0.90 0.88 0.87 0.86 0.85700 0.99 0.98 0.97 0.96 0.95 0.94 0.93 0.92 0.91 0.91750 0.99 0.98 0.97 0.96 0.95 0.94 0.94 0.93 0.92 0.91800 0.99 0.98 0.97 0.96 0.95 0.95 0.94 0.93 0.93 0.92900 0.99 0.98 0.98 0.97 0.96 0.96 0.95 0.94 0.94 0.93

1000 0.99 0.98 0.98 0.97 0.97 0.96 0.96 0.95 0.94 0.941200 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 * PN (bar).

Series 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 LCEST 8 350 4.0 4.9 4.0 4.9 4.0 4.9 4.0 4.9 4.0 4.9 4.0 4.9

400 4.2 5.2 4.2 5.2 4.2 5.2 4.2 5.2 4.2 5.2 4.2 5.2 450 4.5 5.5 4.5 5.5 4.5 5.5 4.5 5.5 4.5 5.5 4.5 5.5 500 4.7 5.8 4.7 5.8 4.7 5.8 4.7 5.8 4.7 5.8 4.7 5.8 600 5.2 6.4 5.2 6.4 5.2 6.4 5.2 6.4 5.2 6.4 5.2 6.4 700 5.6 6.9 5.6 6.9 5.6 6.9 5.6 6.9 5.6 6.9 5.6 6.9 750 5.8 7.1 5.8 7.1 5.8 7.1 5.8 7.1 5.8 7.1 5.8 7.1 800 6.2 7.6 6.2 7.6 6.2 7.6 6.2 7.6 6.2 7.6 6.2 7.6 900 6.6 8.0 6.6 8.0 6.6 8.0 6.6 8.0 6.6 8.0 6.6 8.0

1000 6.9 8.5 6.9 8.5 6.9 8.5 6.9 8.5 6.9 8.5 6.9 8.5 1200 7.5 9.2 7.5 9.2 7.5 9.2 7.5 9.2 7.5 9.2 7.5 9.2

EST 12.5 250 4.0 4.9 4.0 4.9 4.0 4.9 4.0 4.9 4.0 4.9 4.0 4.9 300 4.4 5.4 4.4 5.4 4.4 5.4 4.4 5.4 4.4 5.4 4.4 5.4 350 4.7 5.8 4.7 5.8 4.7 5.8 4.7 5.8 4.7 5.8 4.7 5.8 400 5.1 6.2 5.1 6.2 5.1 6.2 5.1 6.2 5.1 6.2 5.1 6.2 450 5.4 6.6 5.4 6.6 5.4 6.6 5.4 6.6 5.4 6.6 5.4 6.6 500 5.9 7.3 5.9 7.3 5.9 7.3 5.9 7.3 5.9 7.3 5.9 7.3 600 6.4 7.9 6.4 7.9 6.4 7.9 6.4 7.9 6.4 7.9 6.4 7.9 700 6.9 8.5 6.9 8.5 6.9 8.5 6.9 8.5 6.9 8.5 6.9 8.5 750 7.2 8.8 7.2 8.8 7.2 8.8 7.2 8.8 7.2 8.8 7.2 8.8 800 7.4 9.0 7.4 9.0 7.4 9.0 7.4 9.0 7.4 9.0 7.4 9.0 900 7.8 9.6 7.8 9.6 7.8 9.6 7.8 9.6 7.8 9.6 7.8 9.6

1000 8.2 10.1 8.2 10.1 8.2 10.1 8.2 10.1 8.2 10.1 8.2 10.1 EST 16 200 3.8 4.6 3.8 4.6 3.8 4.6 3.8 4.6 3.8 4.6 3.8 4.6

250 4.5 5.5 4.5 5.5 4.5 5.5 4.5 5.5 4.5 5.5 4.5 5.5 300 4.8 5.8 4.8 5.8 4.8 5.8 4.8 5.8 4.8 5.8 4.8 5.8 350 5.1 6.2 5.1 6.2 5.1 6.2 5.1 6.2 5.1 6.2 5.1 6.2 400 5.6 6.9 5.6 6.9 5.6 6.9 5.6 6.9 5.6 6.9 5.6 6.9 450 5.9 7.2 5.9 7.2 5.9 7.2 5.9 7.2 5.9 7.2 5.9 7.2 500 6.1 7.5 6.1 7.5 6.1 7.5 6.1 7.5 6.1 7.5 6.1 7.5 600 6.8 8.3 6.8 8.3 6.8 8.3 6.8 8.3 6.8 8.3 6.8 8.3 700 7.4 9.0 7.4 9.0 7.4 9.0 7.4 9.0 7.4 9.0 7.4 9.0 750 7.6 9.3 7.6 9.3 7.6 9.3 7.6 9.3 7.6 9.3 7.6 9.3 800 7.8 9.5 7.8 9.5 7.8 9.5 7.8 9.5 7.8 9.5 7.8 9.5

EST 20 150 3.8 4.6 3.8 4.6 3.8 4.6 3.8 4.6 3.6 4.6 3.5 4.6 200 4.7 5.7 4.7 5.7 4.7 5.7 4.7 5.7 4.4 5.7 4.2 5.7 250 5.2 6.4 5.2 6.4 5.2 6.4 5.2 6.4 5.1 6.4 4.9 6.4 300 5.6 6.9 5.6 6.9 5.6 6.9 5.6 6.9 5.6 6.9 5.5 6.9 350 6.1 7.4 6.1 7.4 6.1 7.4 6.1 7.4 6.1 7.4 6.1 7.4 400 6.5 7.9 6.5 7.9 6.5 7.9 6.5 7.9 6.5 7.9 6.5 7.9 450 6.8 8.4 6.8 8.4 6.8 8.4 6.8 8.4 6.8 8.4 6.8 8.4 500 7.2 8.8 7.2 8.8 7.2 8.8 7.2 8.8 7.2 8.8 7.2 8.8 600 8.0 9.8 8.0 9.8 8.0 9.8 8.0 9.8 8.0 9.8 8.0 9.8

EST 25 100 3.7 5.7 3.6 5.7 3.5 5.7 3.3 5.7 3.1 5.3 3.0 5.1 150 4.5 5.5 4.5 5.5 4.3 5.5 4.1 5.5 3.9 5.5 3.7 5.5 200 5.1 6.2 5.1 6.2 5.1 6.2 5.0 6.2 4.7 6.2 4.5 6.2 250 5.6 6.9 5.6 6.9 5.6 6.9 5.6 6.9 5.5 6.9 5.3 6.9 300 6.1 7.5 6.1 7.5 6.1 7.5 6.1 7.5 6.1 7.5 5.9 7.5 350 6.6 8.1 6.6 8.1 6.6 8.1 6.6 8.1 6.6 8.1 6.6 8.1 400 7.2 8.8 7.2 8.8 7.2 8.8 7.2 8.8 7.2 8.8 7.2 8.8 450 7.6 9.3 7.6 9.3 7.6 9.3 7.6 9.3 7.6 9.3 7.6 9.3 500 8.0 9.8 8.0 9.8 8.0 9.8 8.0 9.8 8.0 9.8 8.0 9.8 600 8.7 10.7 8.7 10.7 8.7 10.7 8.7 10.7 8.7 10.7 8.7 10.7

EST 32 25 2.0 3.4 1.9 3.3 1.9 3.2 1.8 3.1 1.7 2.9 1.6 2.8 40 2.4 4.1 2.3 4.0 2.2 3.8 2.1 3.7 2.0 3.5 1.9 3.3 50 2.6 4.5 2.5 4.3 2.4 4.2 2.3 4.0 2.2 3.8 2.1 3.6 80 3.4 5.5 3.3 5.5 3.2 5.4 3.0 5.2 2.9 4.9 2.7 4.7

100 3.8 4.7 3.7 4.7 3.5 4.7 3.4 4.7 3.2 4.7 3.1 4.7 150 4.5 6.4 5.3 6.4 5.3 6.4 5.3 6.4 5.0 6.4 4.8 6.4 200 5.3 6.4 5.3 6.4 5.3 6.4 5.3 6.4 5.0 6.4 4.8 6.4 250 5.9 7.3 5.9 7.3 5.9 7.3 5.9 7.3 5.9 7.3 5.6 7.3 300 6.6 8.0 6.6 8.0 6.6 8.0 6.6 8.0 6.6 8.0 6.4 8.0

LS = Single span lengthLC = Continuous span length

49

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

Series 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 LCEST 8 350 5.4 6.6 5.4 6.6 5.4 6.6 5.3 6.6 5.0 6.6 4.8 6.6

400 5.8 7.1 5.8 7.1 5.8 7.1 5.8 7.1 5.5 7.1 5.3 7.1 450 6.1 7.5 6.1 7.5 6.1 7.5 6.1 7.5 5.9 7.5 5.7 7.5 500 6.5 7.9 6.5 7.9 6.5 7.9 6.5 7.9 6.4 7.9 6.1 7.9 600 7.1 8.7 7.1 8.7 7.1 8.7 7.1 8.7 7.1 8.7 6.9 8.7 700 7.7 9.4 7.7 9.4 7.7 9.4 7.7 9.4 7.7 9.4 7.7 9.4 750 7.9 9.7 7.9 9.7 7.9 9.7 7.9 9.7 7.9 9.7 7.9 9.7 800 8.4 10.2 8.4 10.2 8.4 10.2 8.4 10.2 8.4 10.2 8.4 10.2 900 8.8 10.8 8.8 10.8 8.8 10.8 8.8 10.8 8.8 10.8 8.8 10.8

1000 9.3 11.4 9.3 11.4 9.3 11.4 9.3 11.4 9.3 11.4 9.3 11.4 1200 10.2 12.5 10.2 12.5 10.2 12.5 10.2 12.5 10.2 12.5 10.2 12.5

EST 12.5 250 5.2 6.8 5.0 6.8 4.9 6.8 4.6 6.8 4.4 6.8 4.2 6.8 300 5.9 7.5 5.7 7.5 5.5 7.5 5.3 7.5 4.9 7.5 4.7 7.5 350 6.5 8.1 6.3 8.1 6.1 8.1 5.8 8.1 5.5 8.1 5.3 8.1 400 7.0 8.6 6.9 8.6 6.6 8.6 6.4 8.6 6.0 8.6 5.7 8.6 450 7.5 9.2 7.5 9.2 7.2 9.2 6.9 9.2 6.5 9.2 6.2 9.2 500 8.1 9.9 8.1 9.9 7.8 9.9 7.4 9.9 7.0 9.9 6.7 9.9 600 8.8 10.8 8.8 10.8 8.8 10.8 8.4 10.8 7.9 10.8 7.6 10.8 700 9.5 11.6 9.5 11.6 9.5 11.6 9.3 11.6 8.7 11.6 8.4 11.6 750 9.8 12.0 9.8 12.0 9.8 12.0 9.7 12.0 9.2 12.0 8.8 12.0 800 10.1 12.4 10.1 12.4 10.1 12.4 10.1 12.4 9.6 12.4 9.2 12.4 900 10.7 13.1 10.7 13.1 10.7 13.1 10.7 13.1 10.3 13.1 9.9 13.1

1000 11.3 13.8 11.3 13.8 11.3 13.8 11.3 13.8 11.1 13.8 10.6 13.8 EST 16 200 4.8 6.6 4.7 6.6 4.5 6.6 4.3 6.6 4.0 6.6 3.9 6.6

250 5.6 7.6 5.5 7.6 5.3 7.6 5.0 7.6 4.7 7.6 4.5 7.6 300 6.3 8.3 6.1 8.3 5.9 8.3 5.7 8.3 5.3 8.3 5.1 8.3 350 7.0 8.8 6.8 8.8 6.5 8.8 6.3 8.8 5.9 8.8 5.7 8.8 400 7.7 9.6 7.5 9.6 7.2 9.6 6.9 9.6 6.5 9.6 6.2 9.6 450 8.3 10.1 8.1 10.1 7.8 10.1 7.4 10.1 7.0 10.1 6.7 10.1 500 8.7 10.6 8.6 10.6 8.3 10.6 8.0 10.6 7.5 10.6 7.2 10.6 600 9.6 11.7 9.6 11.7 9.4 11.7 9.0 11.7 8.5 11.7 8.1 11.7 700 10.4 12.7 10.4 12.7 10.4 12.7 10.0 12.7 9.4 12.7 9.0 12.7 750 10.7 13.1 10.7 13.1 10.7 13.1 10.4 13.1 9.8 13.1 9.4 13.1 800 11.0 13.5 11.0 13.5 11.0 13.5 10.9 13.5 10.3 13.5 9.8 13.5

EST 20 150 4.3 6.5 4.2 6.5 4.0 6.5 3.8 6.5 3.6 6.2 3.5 5.9 200 5.2 7.8 5.1 7.8 4.9 7.8 4.7 7.8 4.4 7.5 4.2 7.2 250 6.1 8.7 5.9 8.7 5.7 8.7 5.4 8.7 5.1 8.7 4.9 8.4 300 6.8 9.5 6.7 9.5 6.4 9.5 6.1 9.5 5.8 9.5 5.5 9.5 350 7.6 10.2 7.4 10.2 7.1 10.2 6.8 10.2 6.4 10.2 6.1 10.2 400 8.3 10.9 8.1 10.9 7.8 10.9 7.4 10.9 7.0 10.9 6.7 10.9 450 9.0 11.5 8.7 11.5 8.4 11.5 8.0 11.5 7.6 11.5 7.2 11.5 500 9.6 12.1 9.3 12.1 9.0 12.1 8.6 12.1 8.1 12.1 7.8 12.1 600 10.9 13.4 10.6 13.4 10.2 13.4 9.7 13.4 9.2 13.4 8.8 13.4

EST 25 100 3.7 6.3 3.6 6.1 3.5 5.9 3.3 5.7 3.1 5.3 3.0 5.1 150 4.6 7.4 4.5 7.4 4.3 7.4 4.1 7.1 3.9 6.7 3.7 6.4 200 5.6 8.5 5.4 8.5 5.2 8.5 5.0 8.5 4.7 8.1 4.5 7.7 250 6.5 9.5 6.3 9.5 6.1 9.5 5.8 9.5 5.5 9.4 5.3 9.0 300 7.3 10.4 7.1 10.4 6.9 10.4 6.6 10.4 6.2 10.4 5.9 10.1 350 8.1 11.2 7.9 11.2 7.6 11.2 7.3 11.2 6.8 11.2 6.6 11.2 400 8.9 12.1 8.7 12.1 8.3 12.1 8.0 12.1 7.5 12.1 7.2 12.1 450 9.6 12.8 9.4 12.8 9.0 12.8 8.6 12.8 8.1 12.8 7.8 12.8 500 10.3 13.5 10.0 13.5 9.7 13.5 9.2 13.5 8.7 13.5 8.4 13.5 600 11.6 14.7 11.3 14.7 10.9 14.7 10.4 14.7 9.8 14.7 9.4 14.7

EST 32 25 2.0 3.4 1.9 3.3 1.9 3.2 1.8 3.1 1.7 2.9 1.6 2.8 40 2.4 4.1 2.3 4.0 2.2 3.8 2.1 3.7 2.0 3.5 1.9 3.3 50 2.6 4.5 2.5 4.3 2.4 4.2 2.3 4.0 2.2 3.8 2.1 3.6 80 3.4 5.8 3.3 5.6 3.2 5.4 3.0 5.2 2.9 4.9 2.7 4.7

100 3.8 6.5 3.7 6.3 3.5 6.0 3.4 5.8 3.2 5.5 3.1 5.2 150 4.9 7.9 4.8 7.9 4.6 7.9 4.4 7.5 4.2 7.1 4.0 6.8 200 6.0 9.2 5.8 9.2 5.6 9.2 5.4 9.2 5.0 8.6 4.8 8.3 250 7.0 10.3 6.8 10.3 6.5 10.3 6.2 10.3 5.9 10.0 5.6 9.6 300 7.9 11.3 7.7 11.3 7.4 11.3 7.1 11.3 6.6 11.3 6.4 10.9

LS = Single span lengthLC = Continuous span length

50

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

Series 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 LCEST 8 350 6.0 8.0 5.8 8.0 5.6 8.0 5.3 8.0 5.0 8.0 4.8 8.0

400 6.5 8.6 6.3 8.6 6.1 8.6 5.8 8.6 5.5 8.6 5.3 8.6 450 7.1 9.1 6.9 9.1 6.6 9.1 6.3 9.1 5.9 9.1 5.7 9.1 500 7.6 9.6 7.4 9.6 7.1 9.6 6.8 9.6 6.4 9.6 6.1 9.6 600 8.5 10.5 8.3 10.5 8.0 10.5 7.7 10.5 7.2 10.5 6.9 10.5 700 9.3 11.4 9.2 11.4 8.9 11.4 8.5 11.4 8.0 11.4 7.7 11.4 750 9.6 11.8 9.6 11.8 9.3 11.8 8.9 11.8 8.4 11.8 8.0 11.8 800 10.0 12.3 10.0 12.3 9.7 12.3 9.3 12.3 8.8 12.3 8.4 12.3 900 10.6 13.0 10.6 13.0 10.5 13.0 10.1 13.0 9.5 13.0 9.1 13.0

1000 11.2 13.7 11.2 13.7 11.2 13.7 10.8 13.7 10.2 13.7 9.8 13.7 1200 12.3 15.0 12.3 15.0 12.3 15.0 12.2 15.0 11.5 15.0 11.0 15.0

EST 12.5 250 5.2 8.3 5.0 8.3 4.9 8.3 4.6 7.9 4.4 7.5 4.2 7.2 300 5.9 9.1 5.7 9.1 5.5 9.1 5.3 9.0 4.9 8.4 4.7 8.1 350 6.5 9.8 6.3 9.8 6.1 9.8 5.8 9.8 5.5 9.4 5.3 9.0 400 7.1 10.5 6.9 10.5 6.6 10.5 6.4 10.5 6.0 10.2 5.7 9.8 450 7.7 11.2 7.5 11.2 7.2 11.2 6.9 11.2 6.5 11.1 6.2 10.6 500 8.3 11.9 8.1 11.9 7.8 11.9 7.4 11.9 7.0 11.9 6.7 11.5 600 9.4 13.1 9.1 13.1 8.8 13.1 8.4 13.1 7.9 13.1 7.6 13.0 700 10.4 14.1 10.1 14.1 9.7 14.1 9.3 14.1 8.7 14.1 8.4 14.1 750 10.9 14.6 10.6 14.6 10.2 14.6 9.7 14.6 9.2 14.6 8.8 14.6 800 11.3 15.0 11.0 15.0 10.6 15.0 10.2 15.0 9.6 15.0 9.2 15.0 900 12.3 15.9 11.9 15.9 11.5 15.9 11.0 15.9 10.3 15.9 9.9 15.9

1000 13.1 16.8 12.8 16.8 12.3 16.8 11.8 16.8 11.1 16.8 10.6 16.8 EST 16 200 4.8 8.1 4.7 8.0 4.5 7.7 4.3 7.3 4.0 6.9 3.9 6.6

250 5.6 9.3 5.5 9.3 5.3 9.0 5.0 8.6 4.7 8.1 4.5 7.8 300 6.3 10.1 6.1 10.1 5.9 10.1 5.7 9.7 5.3 9.1 5.1 8.7 350 7.0 10.9 6.8 10.9 6.5 10.9 6.3 10.7 5.9 10.1 5.7 9.7 400 7.7 11.7 7.5 11.7 7.2 11.7 6.9 11.7 6.5 11.1 6.2 10.6 450 8.3 12.4 8.1 12.4 7.8 12.4 7.4 12.4 7.0 11.9 6.7 11.5 500 8.9 13.0 8.6 13.0 8.3 13.0 8.0 13.0 7.5 12.8 7.2 12.3 600 10.0 14.3 9.8 14.3 9.4 14.3 9.0 14.3 8.5 14.3 8.1 13.9 700 11.1 15.5 10.8 15.5 10.4 15.5 10.0 15.5 9.4 15.5 9.0 15.4 750 11.7 16.0 11.3 16.0 10.9 16.0 10.4 16.0 9.8 16.0 9.4 16.0 800 12.2 16.5 11.8 16.5 11.4 16.5 10.9 16.5 10.3 16.5 9.8 16.5

EST 20 150 4.3 7.3 4.2 7.1 4.0 6.8 3.8 6.5 3.6 6.2 3.5 5.9 200 5.2 8.9 5.1 8.7 4.9 8.4 4.7 8.0 4.4 7.5 4.2 7.2 250 6.1 10.4 5.9 10.1 5.7 9.7 5.4 9.3 5.1 8.7 4.9 8.4 300 6.8 11.5 6.7 11.4 6.4 11.0 6.1 10.5 5.8 9.9 5.5 9.5 350 7.6 12.4 7.4 12.4 7.1 12.1 6.8 11.6 6.4 10.9 6.1 10.5 400 8.3 13.2 8.1 13.2 7.8 13.2 7.4 12.7 7.0 11.9 6.7 11.5 450 9.0 14.0 8.7 14.0 8.4 14.0 8.0 13.7 7.6 12.9 7.2 12.4 500 9.6 14.7 9.3 14.7 9.0 14.7 8.6 14.7 8.1 13.9 7.8 13.3 600 10.9 16.3 10.6 16.3 10.2 16.3 9.7 16.3 9.2 15.7 8.8 15.1

EST 25 100 3.7 6.3 3.6 6.1 3.5 5.9 3.3 5.7 3.1 5.3 3.0 5.1 150 4.6 7.9 4.5 7.7 4.3 7.4 4.1 7.1 3.9 6.7 3.7 6.4 200 5.6 9.6 5.4 9.3 5.2 9.0 5.0 8.6 4.7 8.1 4.5 7.7 250 6.5 11.1 6.3 10.8 6.1 10.4 5.8 9.9 5.5 9.4 5.3 9.0 300 7.3 12.5 7.1 12.2 6.9 11.7 6.6 11.2 6.2 10.6 5.9 10.1 350 8.1 13.6 7.9 13.5 7.6 13.0 7.3 12.4 6.8 11.7 6.6 11.2 400 8.9 14.7 8.7 14.7 8.3 14.3 8.0 13.6 7.5 12.8 7.2 12.3 450 9.6 15.5 9.4 15.5 9.0 15.4 8.6 14.8 8.1 13.9 7.8 13.3 500 10.3 16.4 10.0 16.4 9.7 16.4 9.2 15.8 8.7 14.9 8.4 14.3 600 11.6 17.9 11.3 17.9 10.9 17.9 10.4 17.8 9.8 16.8 9.4 16.1

EST 32 25 2.0 3.4 1.9 3.3 1.9 3.2 1.8 3.1 1.7 2.9 1.6 2.8 40 2.4 4.1 2.3 4.0 2.2 3.8 2.1 3.7 2.0 3.5 1.9 3.3 50 2.6 4.5 2.5 4.3 2.4 4.2 2.3 4.0 2.2 3.8 2.1 3.6 80 3.4 5.8 3.3 5.6 3.2 5.4 3.0 5.2 2.9 4.9 2.7 4.7

100 3.8 6.5 3.7 6.3 3.5 6.0 3.4 5.8 3.2 5.5 3.1 5.2 150 4.9 8.4 4.8 8.2 4.6 7.9 4.4 7.5 4.2 7.1 4.0 6.8 200 6.0 10.2 5.8 10.0 5.6 9.6 5.4 9.2 5.0 8.6 4.8 8.3 250 7.0 11.9 6.8 11.6 6.5 11.1 6.2 10.7 5.9 10.0 5.6 9.6 300 7.9 13.5 7.7 13.1 7.4 12.6 7.1 12.1 6.6 11.3 6.4 10.9

LS = Single span lengthLC = 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 systemis directed from a fixed point towards the supports next to the anchor point. The pipe should be able tomove 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 (L) than steel pipes,their far lower axial E-modulus results in comparatively low expansion forces at the anchor points whenthe 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 = 10C are listed. The E-modulus of 20C has been used in the following formula for the determination of this load:

(Eq. III.12.)

Where:PA = anchor load (N)OD = outer diameter (mm)ID = inner diameter (mm)EX = axial tensile modulus (table II-j., page 24) (N/mm2)L = coefficient of linear thermal expansion (table II-l., page 24) (mm/mm.C)T = temperature change (C)

Where temperature differences (T) are greater than 10C, the anchor load (PA) shown in table III-f. (page54) should be multiplied by a factor indicating the difference between the highest actual temperature and20C, resulting in the following equation. Also, the temperature correction factor (RE) from table II-k. (page24), corresponding to the highest actual temperature, must be applied:

(Eq. III.13.)

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

As a rule no expansion loops or compensators are required. The distance between the supports shouldbe 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 Industriesengineers can advise you.

53

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

ID(mm)

Series EST

8 12.5 16 20 25 32

25 541 40 835 50 1031 80 2007

100 2490 2651 150 3696 4525 5362 200 5058 6309 7570 9159 250 6302 7660 9417 11384 13963 300 8704 10564 13138 15966 19771 350 9198 11487 13926 17472 21318 400 11677 14650 18056 22418 27754 450 14447 18194 22373 27977 34683 500 17508 22505 27146 34149 42381 600 24505 31574 38533 48800 60085 700 32667 42166 51905 750 37185 48033 59045 800 42583 54281 66643 900 53149 67919

1000 64881 83080 1200 91840

Note: 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 isalso listed in table III-g.

54

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

ID(mm)

End play (mm) Angular deflectionRSLJ RSJ RSLJ RSJ

80 2.5 32.5 130' 3100 3 33 130' 3150 6 36 130' 3200 8 38 (58) 130' 3250 9 39 (59) 130' 3300 10 40 (60) 130' 3350 11 61 130' 3400 13 63 130' 3450 14 64 130' 3500 16 66 130' 3600 19 69 130' 2700 16 66 1 2750 17 67 1 2800 19 69 1 2900 21 71 1 2

1000 23 73 1 21200 27 77 1 1

Note: The end play is required to accommodate soil settlement, Poisson contraction and temperature changes and can thereforenot be used for installation adjustments.

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

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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 beused (II.4., page 4). In contrast to above ground pipelines, these joints can be unrestrained (ratio axialstress/hoop stress (R) = 0.25). Only at directional changes and depending on the pressure, diameterand soil conditions, some lengths of pipe should be installed with tensile resistant couplers. Alternativelyan 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 meansof thrust blocks. This not only alleviates the need for expansion details, it also eliminates undergroundmovement of the pipe system. However, in most circumstances the use of restrained couplers (e.g. rubberseal lock joint or adhesive bonded joint) over a certain distance, starting from the fitting, may offer a bettersolution.For this purpose, the fictive anchor length (LA) must be determined. The fictive anchor length (LA) canbe calculated from the following formula:

(Eq. IV.1.)

Where:LA = fictive anchor length (m)P = operating pressure (Mpa)ID = inner diameter (mm)FW = frictional force between soil and pipe (N/mm2)OD = outer diameter (II.5.1.B, page ?) (mm)

The value of FW can be obtained from the soil mechanics report. If not, the following values may providea rough indication:

- soft clay and peaty soils : 0.001 FW 0.003 (N/mm2)- sandy clay and sand : 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 specificmaterial data (and many years of experience) a number of deviations are stated in the text. As in ANSI/AWWAC950-88, Anglo-Saxon units are used.

The stresses in the wall of a flexible buried pipe not only depend on the internal pressure, but are alsoa result of the deflection due to external loads. The stress resulting from the deflection depends on theinteraction between the soil and the pipe, which is among others determined by the installation method.

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IV.3.1. Pipe deflection

The vertical deflection of an underground pipe is a function of the installation parameters, the verticalload 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 mayvary from the calculated values because theories cannot anticipate all the parameters associated witha given installation. These variations include the inherent variability of native ground conditions and variationsin 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 (in)Dl = deflection lag factor (-)Wc = vertical soil load (lb/in)WL = live load (lb/in)Kx = deflection coefficient (table IV-b., page 58) (-)rm = mean pipe radius (in)EI = stiffness factor (in2.lb/in)E' = modulus of soil reaction (table IV-d., page 61) (psi)

Two procedures are available to obtain an estimated average deflection, in order to obtain a 95% probabilitythat 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.

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

Degree of compaction Additional defle