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 Contents

Section Page

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

II. Wavistr ong 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. Wavistr ong 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. Introduction

This 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 110°C.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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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 (ω) is given in table II-a.

Table II-a. Winding angle ω (degrees)

Series

Pressure 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 (ω) 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 (T E)

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/mm²)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 (G B)

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 (I Z)

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 (I R)

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 (A B)

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 (W B)

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

8

Table II-b. Pipe data for series EST

Series Innerdiameter

Reinforcedwall

thickness

Linearmass ofthe pipe

Structural wallarea

Linear mo-ment of inertia

Radius ofinertia Bore area

Moment ofresistance to

bending

ID 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 Innerdiameter

Reinforcedwall

thicknessLinear 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 G V (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/mm²- elbow/double socket: SH = 40 N/mm²

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 23

23

23

12.5 12

12 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 (τ).

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/mm². 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/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 isgiven. For elbows the equivalent stress (Seq), related to the hydrostatic design stress (HDS), will be 12.3N/mm². For tees this value will be 9.8 N/mm². 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/mm² and12.3 N/mm² 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 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. Wavistr ong 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 10°C. At higher operating temperatures the kinematic viscosity of water decreases, resulting in lower head losses.

II.6.2. Wavistr ong fittings

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

(Eq. II.9.)

Where:∆Hfitting = head loss in the fitting (N/m²)ζ = friction coefficient (-)SV = specific gravity of the fluid (kg/m3)v = flow velocity (m/s)

The friction coefficient (ζ) 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/m²)∆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/s²)

18

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

α

22°30' 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 ζ (-) for tees and laterals

Flow separation Flow combination Flow separationFlowcombination

ζ ζd ζ ζd ζ ζd ζ ζd

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

ζ = friction coefficient for pressure loss of relative to .

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

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

Φ = flow in the run

Φd = 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 thr ough 1200 mm

22

II.7. Wavistr ong 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 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

Property Test method

Winding angle (ω)

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/mm²

N/mm²

N/mm²

N/mm²

N/mm²

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/mm²

N/mm²

N/mm²

N/mm²

Minimum service (design) factor Sf = 0.5.

23

Table II-j. Mechanical properties

Property Test method

Winding angle (ω)

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

NXY

NYX

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/mm²N/mm²

N/mm²N/mm²

N/mm²

N/mm²N/mm²

N/mm²N/mm²

--

Table II-k. Temperature correction factor R E (-) for m oduli of elasticity

Correction factorRE (-)

WindingAngle

Temperature(°C)

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

RE1

RE2

RE3

RE4

RE5

RE6

55°63°73°55°63°73°

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 method

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

ϒL

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

- Ω/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 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 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/mm²)DI = structural inner diameter (mm)SA = remaining axial stress (N/mm²)

The value of SA is defined as follows:

(Eq. II.12.)

Where:SA = remaining axial stress (N/mm²)SXT = allowable axial stress (N/mm²)SX = actual axial stress due to internal pressure (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 (N/mm²)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 (ω) and is givenin table II-m.

Table II-m. Allowable axial stress S XT (N/mm²)

R(-)

Winding angle (ω)

55° 63° 73°

0.250.50

-40

3232

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 R b (m) at 20°C for series EST

SeriesID

(mm)

Operating pressure (P)

1 * PN 0.8 * PN 0.6 * PN 0.4 * PN 0.2 * PN 0 * PN

EST 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 R b (m) at 20°C for series ESN

SeriesID

(mm)

Operating pressure (P)

1 * PN 0.8 * PN 0.6 * PN 0.4 * PN 0.2 * PN 0 * PN

ESN 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 (ω),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 (ω) of the Wavistrong pipes the volumetric E-modulus (EV) is given in tableII-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 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 (ω).

Table II-q. Constant f (-)

Constant

Winding angle (ω)

55° 63° 73°

f1f2f3

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 c3

EST 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)α = creep factor (-)β = ageing factor (-)STIS = Specific Tangential Initial Stiffness (Eq. II.21.) (N/m2)

For the glass fibre reinforced epoxy Wavistrong pipes α * β = 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 20°C are listed. At temperaturesin excess of 20°C 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 20°C.

Series EST Series ESN

Series ID(mm)

STIS(N/m²)

SF(in²lb/in)

PS(psi) Series ID

(mm)STIS

(N/m²)SF

(in²lb/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 20°C. 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 20°C 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 P B (bar) at 20°C, series EST

Series ID(mm)

Pipe length L (m) between stiff ends1 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 P B (bar) at 20°C, series ESN

Series ID(mm)

Pipe length L (m) between stiff ends1 2 2.5 3 3.3 5 6 10

ESN 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

Series

EST ESN EST EST ESN EST ESN EST ESN EST ESN

PN (bar) 8 10 12.5 16 20 25 32

Code 11FU1- 11FX2- 11FW1- 11FW1- 11FY2- 11FW1- 11FY2- 11FW1- 11FY2- 11FW1- 11FY2-

ID

25 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 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 (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. Conti nuous 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 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 (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 s upport 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 (R S)

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 (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 (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 R S (-)

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 R T (-)

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 0.28

40 0.81 0.69 0.60 0.54 0.49 0.45 0.42 0.40 0.38 0.36

50 0.85 0.73 0.65 0.59 0.54 0.50 0.47 0.44 0.42 0.40

80 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 0.54

150 0.92 0.85 0.80 0.75 0.72 0.68 0.66 0.63 0.61 0.59

200 0.94 0.89 0.84 0.81 0.77 0.75 0.72 0.70 0.68 0.66

250 0.95 0.91 0.87 0.84 0.81 0.79 0.76 0.74 0.72 0.70

300 0.96 0.92 0.89 0.87 0.84 0.82 0.80 0.78 0.76 0.74

350 0.96 0.93 0.91 0.88 0.86 0.84 0.82 0.80 0.79 0.77

400 0.97 0.94 0.92 0.89 0.87 0.85 0.83 0.82 0.80 0.79

450 0.97 0.95 0.92 0.90 0.88 0.87 0.85 0.83 0.82 0.80

500 0.97 0.95 0.93 0.91 0.90 0.88 0.86 0.85 0.83 0.82

600 0.98 0.96 0.94 0.93 0.91 0.90 0.88 0.87 0.86 0.85

700 0.99 0.98 0.97 0.96 0.95 0.94 0.93 0.92 0.91 0.91

750 0.99 0.98 0.97 0.96 0.95 0.94 0.94 0.93 0.92 0.91

800 0.99 0.98 0.97 0.96 0.95 0.95 0.94 0.93 0.93 0.92

900 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 0.94

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 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

EST 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 * P N (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 LC

EST 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 * P N (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 LC

EST 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 (γL) 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 = 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 (N)OD = outer diameter (mm)ID = inner diameter (mm)EX = axial tensile modulus (table II-j., page 24) (N/mm2)γL = coefficient of linear thermal expansion (table II-l., page 24) (mm/mm.°C)∆T = temperature change (°C)

Where temperature differences (∆T) are greater than 10°C, the anchor load (PA) shown in table III-f. (page54) should be multiplied by a factor indicating the difference between the highest actual temperature and20°C, 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 P A (N) for series EST at 20°C and ∆T = 10°C

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 deflection

RSLJ RSJ RSLJ RSJ

80 2.5 32.5 1°30' 3°

100 3 33 1°30' 3°

150 6 36 1°30' 3°

200 8 38 (58) 1°30' 3°

250 9 39 (59) 1°30' 3°

300 10 40 (60) 1°30' 3°

350 11 61 1°30' 3°

400 13 63 1°30' 3°

450 14 64 1°30' 3°

500 16 66 1°30' 3°

600 19 69 1°30' 2°

700 16 66 1° 2°

750 17 67 1° 2°

800 19 69 1° 2°

900 21 71 1° 2°

1000 23 73 1° 2°

1200 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.

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 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.

56

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.

57

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

Degree of compactionAdditional deflection

(%)

DumpedSlight

ModerateHigh

+ 2+ 2+ 1

+ 0.5

Note: The actual deflection measured at a particular point along a single pipeline may vary ± 2% from the average deflectionfor 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 lagfactor (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

Equivalent bedding angle

(degrees)

Deflectioncoefficient

Kx

(-)

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

180 0.083

120 0.090

90 0.096Shaped bottom, moderately compacted, with backfill material placed at the sides of the pipe; 85- 95 % Proctor densityCoarse grained, shaped bedding, with slightly compacted backfill material placed at the sides ofthe pipe; 40 - 70 % relative density

60 0.103

30 0.108Flat bottom with loose backfill material placed at the sides of the pipe (not recommended);< 35% Proctor density; < 40% relative density

0 0.110

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

58

IV.3.4. Vertical soil load

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

(Eq. IV.3.)

Where:Wc = vertical soil load (lb/in)γs = specific mass of the soil (lb/ft3)H = burial depth to top of the pipe (ft)OD = outer diameter (II.5.1.B, page ?) (in)

Considerations should be given to pipe installed under unusual conditions, such as in unstable soils orsoils 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 (lb/in)CL = live load coefficient (single wheel load) (-)CL(T) = live load coefficient (two passing trucks) (-)PW = wheel load (table IV-c.) (lb)If = impact factor (-)

(Eq. IV.5.)

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

In abscence of specific soil information, the unit weight for soil may be assumed to be 120 lb/ft3 (= ± 2000 kg/m3)

59

Table IV-c. Wheel load (P W)

IndicationWheel load

(tons) (lb)

VOSB 30VOSB 45VOSB 60

57.510

11,00016,50022,000

H20-S16 7.2 16,000

LKW 12SKW 30SKW 60

45

10

9,00011,00022,000

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 (ft)ro = outer pipe radius (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 (ft)H = burial depth to top of pipe (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 momentof inertia of the pipewall per unit length of pipe.

(Eq. IV.8.)

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

(II.5.1.A, page 6)

IV.3.7. Modulus of soil r eaction

The modulus of the soil reaction (E') depends on the type of backfilling. Recommended values of E' forvarious soil and compaction conditions are shown in the table IV-d. The listed values are derived fromASTM D 2487.

Table IV-d. Modulus of soil r eaction (E')

Soil types backfill material

E' for degree of compaction of bedding psi (N/mm²)

Dumped Slight Moderate High

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.

50(0.34)

200(1.4)

400(2.8)

1000(6.9)

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 morethan 12% fines.

100(0.69)

400(2.8)

1000(6.9)

2000(13.8)

Coarse-grained soils with little or no fines. GW, GP, SW, SP , con-taining less than 12% fines.

200(1.4)

1000(6.9)

2000(13.8)

3000(20.7)

Crushed rock1000(6.9)

3000(20.7)

Classification of soils for engineering purposes according to ASTM D 2487 (table IV-e., page 62).

Slight = < 85 % Proctor / < 40 % relative densityModerate = 85-95 % Proctor / 40-70 % relative densityHigh = > 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

GroupSymbol

Group name

GW

GP

GM

GC

SW

SP

SM

SC

ML

CL

MH

CH

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

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

Silty gravels, poorly graded gravel-sand-silt mixtures

Clayey gravels, poorly graded gravel-sand-clay mixtures

Well graded sands, gravelly sands, little or no fines

Poorly graded sands, gravelly sands, little or no fines

Silty sands, poorly graded sand-silt mixtures

Clayey sands, poorly graded sand-clay mixtures

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

Inorganic clays of low to medium plasticity

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

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 shallmeet the following equation:

(Eq. IV.9.)

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

According to ASTM D 2487

62

σc is calculated as follows:

(Eq. IV.10.)

Where:σc = resulting hoop stress (psi)P = operating pressure (psi)D = mean pipe diameter (in)TE = minimum reinforced wall thickness

(table II-b. and II-c., page 9 and 10) (in)Df = shape factor (table IV-f.) (-)EH = hoop bending modulus (table II-j., page 24) (psi)RC = rerounding coefficient (-)∆y = predicted vertical pipe deflection (in)TT = nett total wall thickness (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

9183672

5.54.53.83.3

7.05.54.53.8

6.05.04.03.5

8.06.55.54.5

63

IV.5. Allowable combined stress

The combination of the axial stress due to internal pressure (SX) and the circumferential stresses dueto internal pressure (Sy) and vertical deflection of the pipe (σC), should not exceed the acceptablestress levels as shown in the fig. II-6. (page 13 through 15). The occurring axial stress has a greatinfluence on the allowable hoop stress. Non-tensile resistant pipes (series ESN) allow for high hoopstress. 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 asfollows:

A. Tensile resistant system (series EST):

(Eq. IV.12.)

Where:Sx = actual axial stress due to internal pressure (N/mm2)Sy = actual hoop stress due to internal pressure (N/mm2)

(ISO formula) (Eq. IV.13.)

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

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

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

(Eq. IV.14.)

Where:Sx = actual axial stress due to internal pressure (N/mm²)Nyx = Poisson ratio hoop/axial (table II-j., page 24) (-)Sy = actual hoop stress due to internal pressure (Eq. IV.13.) (N/mm²)

From the calculated values (table IV-j. through IV-m., page 66 through 69) one may conclude that thedeflection of the pipe decreases with increasing care of installation and modulus of soil reaction (E'). Stressesand 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 bythe soil loads; at shallow depths (< 1 m) wheel loads (PW) have a predominant influence on the deformationof the pipe. The table IV-j. through IV-m. (page 66 through 69) show that in some cases, the required pressure classcan 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 resultsin a higher pipe stiffness (PS) as well as a higher allowable circumferential stress (SH).

64

In the following table IV-j. through IV-m. (page 66 through 69) the results of calculations for the standardWavistrong product range are shown. These calculations at nominal pressure (PN) for the series ESTand 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) kg/m3 (pcf)

degree of compaction moderate (-)

modulus of soil reaction E' 6.9 (1000) N/mm² (psi)

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 1600 (100) kg/m3 (pcf)

degree of compaction moderate (-)

modulus of soil reaction E' 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 (σC) > 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, separatecalculations 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: Specific mass soil: 2000kg/m3 125 pcf Bedding angle: 90 °E' (ground) : 6.9 N/mm² 1000 psi Defl.lag factor: 1.5(-)

Wheel load (tons) 0 5 7.5 10 Burialdepth (m) 0.5 1 2.5 5 0.5 1 2.5 5 0.5 1 2.5 5 0.5 1 2.5 5

EST 8 350 0.4 0.9 2.2 4.3 2.8 1.7 2.3 4.3 4.0 2.0 2.4 4.4 -.- 2.4 2.4 4.4 400 0.4 0.9 2.2 4.3 2.8 1.6 2.3 4.3 4.0 2.0 2.4 4.4 -.- 2.4 2.4 4.4 450 0.4 0.9 2.2 4.3 2.7 1.6 2.3 4.3 3.9 2.0 2.4 4.4 5.0 2.4 2.4 4.4 500 0.4 0.9 2.2 4.3 2.7 1.6 2.3 4.3 3.8 2.0 2.4 4.4 4.9 2.4 2.4 4.4 600 0.4 0.9 2.2 4.3 2.5 1.6 2.3 4.3 3.6 2.0 2.4 4.4 4.6 2.4 2.4 4.4 700 0.4 0.9 2.2 4.3 2.4 1.6 2.3 4.3 3.4 2.0 2.4 4.4 4.4 2.3 2.4 4.4 750 0.4 0.9 2.2 4.3 2.3 1.6 2.3 4.3 3.3 2.0 2.4 4.4 4.2 2.3 2.4 4.4 800 0.4 0.9 2.2 4.3 2.3 1.6 2.3 4.3 3.2 1.9 2.4 4.4 4.1 2.3 2.4 4.4 900 0.4 0.9 2.2 4.3 2.2 1.6 2.3 4.3 3.0 1.9 2.4 4.4 3.9 2.2 2.4 4.4

1000 0.4 0.9 2.2 4.3 2.0 1.5 2.3 4.3 2.8 1.9 2.4 4.4 3.7 2.2 2.4 4.4 1200 0.4 0.9 2.2 4.3 1.9 1.5 2.3 4.3 2.6 1.8 2.4 4.4 3.3 2.1 2.4 4.4

EST 12.5 250 0.4 0.9 2.2 4.3 2.9 1.6 2.3 4.3 4.1 2.0 2.3 4.3 -.- 2.4 2.4 4.3 300 0.4 0.9 2.2 4.3 2.9 1.6 2.3 4.3 4.1 2.0 2.3 4.3 -.- 2.4 2.4 4.3 350 0.4 0.9 2.2 4.3 2.8 1.6 2.3 4.3 4.0 2.0 2.3 4.3 -.- 2.4 2.4 4.3 400 0.4 0.9 2.2 4.3 2.7 1.6 2.3 4.3 3.9 2.0 2.3 4.3 -.- 2.4 2.4 4.3 450 0.4 0.9 2.2 4.3 2.7 1.6 2.3 4.3 3.8 2.0 2.3 4.3 4.9 2.4 2.4 4.3 500 0.4 0.9 2.2 4.3 2.6 1.6 2.3 4.3 3.7 2.0 2.3 4.3 4.8 2.4 2.4 4.3 600 0.4 0.9 2.2 4.3 2.5 1.6 2.3 4.3 3.5 2.0 2.3 4.3 4.6 2.3 2.4 4.3 700 0.4 0.9 2.2 4.3 2.4 1.6 2.3 4.3 3.3 1.9 2.3 4.3 4.3 2.3 2.4 4.3 750 0.4 0.9 2.2 4.3 2.3 1.6 2.3 4.3 3.2 1.9 2.3 4.3 4.2 2.3 2.4 4.3 800 0.4 0.9 2.2 4.3 2.2 1.6 2.3 4.3 3.2 1.9 2.3 4.3 4.1 2.3 2.4 4.3 900 0.4 0.9 2.2 4.3 2.1 1.5 2.3 4.3 3.0 1.9 2.3 4.3 3.8 2.2 2.4 4.3

1000 0.4 0.9 2.2 4.3 2.0 1.5 2.3 4.3 2.8 1.9 2.3 4.3 3.6 2.2 2.4 4.3 EST 16 200 0.4 0.8 2.1 4.2 2.8 1.6 2.2 4.2 4.1 2.0 2.3 4.3 -.- 2.3 2.3 4.3

250 0.4 0.8 2.1 4.2 2.8 1.6 2.2 4.2 4.0 2.0 2.3 4.2 -.- 2.3 2.3 4.3 300 0.4 0.8 2.1 4.2 2.8 1.6 2.2 4.2 3.9 2.0 2.3 4.3 -.- 2.3 2.3 4.3 350 0.4 0.8 2.1 4.2 2.7 1.6 2.2 4.2 3.9 2.0 2.3 4.3 5.0 2.3 2.3 4.3 400 0.4 0.8 2.1 4.2 2.6 1.6 2.2 4.2 3.8 1.9 2.3 4.2 4.9 2.3 2.3 4.3 450 0.4 0.8 2.1 4.2 2.6 1.6 2.2 4.2 3.7 1.9 2.3 4.3 4.8 2.3 2.3 4.3 500 0.4 0.8 2.1 4.2 2.5 1.6 2.2 4.2 3.6 1.9 2.3 4.3 4.7 2.3 2.3 4.3 600 0.4 0.8 2.1 4.2 2.4 1.5 2.2 4.2 3.4 1.9 2.3 4.3 4.4 2.3 2.3 4.3 700 0.4 0.8 2.1 4.2 2.3 1.5 2.2 4.2 3.2 1.9 2.3 4.2 4.2 2.2 2.3 4.3 750 0.4 0.8 2.1 4.2 2.2 1.5 2.2 4.2 3.1 1.9 2.3 4.3 4.0 2.2 2.3 4.3 800 0.4 0.8 2.1 4.2 2.2 1.5 2.2 4.2 3.0 1.9 2.3 4.3 3.9 2.2 2.3 4.3

EST 20 150 0.4 0.8 2.0 4.1 2.7 1.5 2.1 4.1 3.8 1.8 2.1 4.1 5.0 2.2 2.2 4.1 200 0.4 0.8 2.0 4.0 2.6 1.5 2.1 4.1 3.7 1.8 2.1 4.1 4.9 2.2 2.1 4.1 250 0.4 0.8 2.0 4.0 2.6 1.5 2.1 4.1 3.7 1.8 2.1 4.1 4.8 2.2 2.2 4.1 300 0.4 0.8 2.0 4.0 2.6 1.5 2.1 4.1 3.6 1.8 2.1 4.1 4.7 2.2 2.2 4.1 350 0.4 0.8 2.0 4.1 2.5 1.5 2.1 4.1 3.6 1.8 2.1 4.1 4.6 2.2 2.2 4.1 400 0.4 0.8 2.0 4.1 2.5 1.5 2.1 4.1 3.5 1.8 2.1 4.1 4.5 2.1 2.2 4.1 450 0.4 0.8 2.0 4.1 2.4 1.5 2.1 4.1 3.4 1.8 2.1 4.1 4.4 2.1 2.2 4.1 500 0.4 0.8 2.0 4.1 2.4 1.5 2.1 4.1 3.3 1.8 2.1 4.1 4.3 2.1 2.2 4.1 600 0.4 0.8 2.0 4.0 2.2 1.4 2.1 4.1 3.2 1.8 2.1 4.1 4.1 2.1 2.2 4.1

EST 25 100 0.3 0.6 1.5 3.5 2.1 1.2 1.6 3.5 3.0 1.4 1.7 3.5 3.9 1.7 1.7 3.5 150 0.3 0.7 1.7 3.8 2.3 1.3 1.8 3.8 3.3 1.6 1.9 3.8 4.3 1.9 1.9 3.8 200 0.3 0.7 1.7 3.8 2.3 1.3 1.8 3.8 3.3 1.6 1.9 3.8 4.3 1.9 1.9 3.8 250 0.3 0.7 1.7 3.8 2.3 1.3 1.8 3.8 3.3 1.6 1.9 3.8 4.3 1.9 1.9 3.8 300 0.4 0.7 1.8 3.8 2.3 1.3 1.8 3.8 3.2 1.6 1.9 3.8 4.2 1.9 1.9 3.8 350 0.4 0.7 1.8 3.8 2.2 1.3 1.8 3.8 3.2 1.6 1.9 3.8 4.1 1.9 1.9 3.8 400 0.3 0.7 1.7 3.8 2.2 1.3 1.8 3.8 3.1 1.6 1.9 3.8 4.0 1.9 1.9 3.8 450 0.3 0.7 1.7 3.8 2.1 1.3 1.8 3.8 3.0 1.6 1.9 3.8 3.9 1.9 1.9 3.8 500 0.3 0.7 1.7 3.8 2.1 1.3 1.8 3.8 2.9 1.6 1.9 3.8 3.8 1.9 1.9 3.8 600 0.3 0.7 1.7 3.8 2.0 1.3 1.8 3.8 2.8 1.6 1.9 3.8 3.6 1.9 1.9 3.8

EST 32 25 0.0 0.1 0.2 1.4 0.3 0.2 0.2 1.4 0.4 0.2 0.2 1.4 0.5 0.2 0.2 1.4 40 0.1 0.2 0.6 2.1 0.8 0.4 0.6 2.1 1.1 0.6 0.6 2.1 1.5 0.7 0.7 2.1 50 0.2 0.4 0.9 2.6 1.2 0.7 1.0 2.6 1.8 0.8 1.0 2.6 2.3 1.0 1.0 2.6 80 0.2 0.5 1.2 3.0 1.6 0.9 1.3 3.1 2.3 1.1 1.3 3.1 3.0 1.3 1.3 3.1

100 0.3 0.6 1.4 3.4 1.9 1.1 1.5 3.4 2.7 1.3 1.5 3.4 3.6 1.6 1.6 3.4 150 0.3 0.6 1.5 3.4 2.0 1.1 1.5 3.4 2.8 1.4 1.6 3.4 3.6 1.6 1.6 3.4 200 0.3 0.6 1.4 3.4 1.9 1.1 1.5 3.4 2.7 1.3 1.5 3.4 3.6 1.6 1.6 3.4 250 0.3 0.6 1.4 3.4 1.9 1.1 1.5 3.4 2.7 1.3 1.5 3.4 3.5 1.6 1.6 3.4 300 0.3 0.6 1.4 3.4 1.8 1.1 1.5 3.4 2.6 1.3 1.5 3.4 3.4 1.6 1.6 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: Specific mass soil: 2000 kg/m3 125 pcf Bedding angle: 90 °E' (ground) : 6.9 N/mm² 1000 psi Defl.lag factor: 1.5(-)

Wheel load (tons) 0 5 7.5 10 Burialdepth (m) 0.5 1 2.5 5 0.5 1 2.5 5 0.5 1 2.5 5 0.5 1 2.5 5

ESN 10 450 0.4 0.9 2.2 4.3 2.7 1.6 2.3 4.3 3.9 2.0 2.4 4.4 5.0 2.4 2.4 4.4 500 0.4 0.9 2.2 4.3 2.6 1.6 2.3 4.4 3.6 2.0 2.4 4.4 4.7 2.4 2.4 4.4 600 0.4 0.9 2.2 4.3 2.4 1.6 2.3 4.4 3.4 2.0 2.4 4.4 4.4 2.3 2.4 4.4 700 0.4 0.9 2.2 4.3 2.3 1.6 2.3 4.4 3.3 2.0 2.4 4.4 4.3 2.3 2.4 4.4 750 0.4 0.9 2.2 4.3 2.3 1.6 2.3 4.4 3.2 1.9 2.4 4.4 4.1 2.3 2.4 4.4 800 0.4 0.9 2.2 4.3 2.2 1.6 2.3 4.4 3.0 1.9 2.4 4.4 3.9 2.3 2.4 4.4 900 0.4 0.9 2.2 4.3 2.1 1.6 2.3 4.4 2.9 1.9 2.4 4.4 3.7 2.2 2.4 4.4

1000 0.4 0.9 2.2 4.3 1.9 1.5 2.3 4.4 2.6 1.8 2.4 4.4 3.3 2.2 2.4 4.4 1200 0.2 0.5 1.2 3.0 1.5 0.9 1.2 3.0 2.1 1.1 1.3 3.0 2.7 1.3 1.3 3.0

ESN 16 350 0.4 0.9 2.2 4.3 2.8 1.7 2.3 4.4 4.0 2.0 2.4 4.4 -.- 2.4 2.4 4.4 400 0.4 0.9 2.2 4.3 2.7 1.7 2.3 4.4 3.9 2.0 2.4 4.4 5.0 2.4 2.4 4.4 450 0.4 0.9 2.2 4.3 2.7 1.6 2.3 4.4 3.8 2.0 2.4 4.4 4.9 2.4 2.4 4.4 500 0.4 0.9 2.2 4.3 2.6 1.6 2.3 4.4 3.6 2.0 2.4 4.4 4.7 2.4 2.4 4.4 600 0.4 0.9 2.2 4.3 2.4 1.6 2.3 4.4 3.4 2.0 2.4 4.4 4.4 2.3 2.4 4.4 700 0.4 0.9 2.2 4.3 2.3 1.6 2.3 4.4 3.3 2.0 2.4 4.4 4.3 2.3 2.4 4.4 750 0.4 0.9 2.2 4.3 2.3 1.6 2.3 4.4 3.2 1.9 2.4 4.4 4.1 2.3 2.4 4.4 800 0.2 0.4 0.9 2.6 1.2 0.7 0.9 2.6 1.7 0.8 1.0 2.6 2.2 1.0 1.0 2.6

ESN 20 200 0.4 0.9 2.2 4.3 2.9 1.6 2.3 4.3 4.1 2.0 2.3 4.3 -.- 2.4 2.4 4.3 250 0.4 0.9 2.2 4.3 2.9 1.7 2.3 4.3 4.1 2.0 2.4 4.3 -.- 2.4 2.4 4.4 300 0.4 0.9 2.2 4.3 2.8 1.6 2.3 4.3 4.0 2.0 2.4 4.3 -.- 2.4 2.4 4.4 350 0.4 0.9 2.2 4.3 2.8 1.6 2.3 4.3 3.9 2.0 2.3 4.3 -.- 2.4 2.4 4.3 400 0.4 0.9 2.2 4.3 2.7 1.6 2.3 4.3 3.8 2.0 2.3 4.3 5.0 2.4 2.4 4.3 450 0.4 0.9 2.2 4.3 2.6 1.6 2.3 4.3 3.7 2.0 2.3 4.3 4.8 2.4 2.4 4.3 500 0.4 0.9 2.2 4.3 2.5 1.6 2.3 4.3 3.6 2.0 2.4 4.3 4.6 2.3 2.4 4.4 600 0.2 0.4 1.0 2.7 1.3 0.7 1.0 2.7 1.9 0.9 1.1 2.7 2.4 1.1 1.1 2.7

ESN 25 200 0.4 0.9 2.2 4.3 2.9 1.6 2.3 4.3 4.1 2.0 2.3 4.3 -.- 2.4 2.4 4.3 250 0.4 0.9 2.1 4.2 2.8 1.6 2.2 4.3 4.0 2.0 2.3 4.3 -.- 2.4 2.3 4.3 300 0.4 0.9 2.1 4.2 2.7 1.6 2.2 4.3 3.9 2.0 2.3 4.3 5.0 2.3 2.3 4.3 350 0.4 0.8 2.1 4.2 2.7 1.6 2.2 4.3 3.8 2.0 2.3 4.3 4.9 2.3 2.3 4.3 400 0.4 0.8 2.1 4.2 2.6 1.6 2.2 4.2 3.7 1.9 2.3 4.3 4.8 2.3 2.3 4.3 450 0.4 0.8 2.1 4.2 2.5 1.6 2.2 4.2 3.6 1.9 2.3 4.2 4.7 2.3 2.3 4.3 500 0.4 0.9 2.1 4.3 2.5 1.6 2.2 4.3 3.5 1.9 2.3 4.3 4.5 2.3 2.3 4.3 600 0.0 0.0 0.1 1.1 0.1 0.1 0.1 1.1 0.1 0.1 0.1 1.1 0.2 0.1 0.1 1.1

ESN 32 80 0.3 0.6 1.4 3.3 1.9 1.0 1.5 3.3 2.7 1.3 1.5 3.3 3.5 1.5 1.5 3.3 100 0.4 0.8 1.9 4.0 2.6 1.4 2.0 4.0 3.7 1.8 2.0 4.0 4.8 2.1 2.1 4.0 150 0.4 0.8 2.1 4.2 2.8 1.6 2.2 4.2 4.0 1.9 2.2 4.2 -.- 2.3 2.3 4.2 200 0.4 0.8 2.0 4.1 2.7 1.5 2.1 4.2 3.9 1.9 2.2 4.2 5.0 2.3 2.2 4.2 250 0.4 0.8 2.0 4.1 2.6 1.5 2.1 4.1 3.7 1.9 2.2 4.1 4.9 2.2 2.2 4.1 300 0.4 0.9 2.2 4.3 2.5 1.6 2.3 4.3 3.6 2.0 2.4 4.4 4.6 2.4 2.4 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: Specific mass soil: 1600 kg/m3 100 pcf Bedding angle: 120 °E' (ground) : 4.8 N/mm² 700 psi Defl.lag factor: 1.5(-)

Wheel load (tons) 0 5 7.5 10 Burialdepth (m) 0.5 1 2.5 5 0.5 1 2.5 5 0.5 1 2.5 5 0.5 1 2.5 5

EST 8 350 0.5 0.9 2.3 4.5 3.6 2.0 2.5 4.6 -.- 2.5 2.5 4.6 -.- 3.0 2.6 4.6 400 0.5 0.9 2.3 4.5 3.6 1.9 2.5 4.6 -.- 2.5 2.5 4.6 -.- 3.0 2.6 4.6 450 0.5 0.9 2.3 4.5 3.5 1.9 2.5 4.6 5.0 2.4 2.5 4.6 -.- 2.9 2.6 4.6 500 0.5 0.9 2.3 4.5 3.4 1.9 2.5 4.6 4.9 2.4 2.5 4.6 -.- 2.9 2.6 4.6 600 0.5 0.9 2.3 4.5 3.2 1.9 2.5 4.6 4.6 2.4 2.5 4.6 -.- 2.9 2.6 4.6 700 0.5 0.9 2.3 4.5 3.1 1.9 2.5 4.6 4.4 2.4 2.5 4.6 -.- 2.8 2.6 4.6 750 0.5 0.9 2.3 4.5 3.0 1.9 2.5 4.6 4.2 2.4 2.5 4.6 -.- 2.8 2.6 4.6 800 0.5 0.9 2.3 4.5 2.9 1.9 2.5 4.6 4.1 2.3 2.5 4.6 -.- 2.8 2.6 4.6 900 0.5 0.9 2.3 4.5 2.7 1.8 2.5 4.6 3.9 2.3 2.5 4.6 5.0 2.7 2.6 4.6

1000 0.5 0.9 2.3 4.5 2.6 1.8 2.5 4.6 3.7 2.3 2.5 4.6 4.7 2.7 2.6 4.6 1200 0.5 0.9 2.3 4.5 2.3 1.8 2.5 4.6 3.3 2.2 2.5 4.6 4.2 2.6 2.6 4.6

EST 12.5 250 0.5 0.9 2.3 4.5 3.7 1.9 2.4 4.5 -.- 2.5 2.5 4.5 -.- 3.0 2.6 4.6 300 0.5 0.9 2.3 4.5 3.7 1.9 2.4 4.5 -.- 2.4 2.5 4.5 -.- 2.9 2.6 4.6 350 0.5 0.9 2.3 4.5 3.6 1.9 2.4 4.5 -.- 2.4 2.5 4.5 -.- 2.9 2.6 4.6 400 0.5 0.9 2.3 4.5 3.5 1.9 2.4 4.5 5.0 2.4 2.5 4.5 -.- 2.9 2.6 4.6 450 0.5 0.9 2.3 4.5 3.4 1.9 2.4 4.5 4.9 2.4 2.5 4.5 -.- 2.9 2.6 4.6 500 0.5 0.9 2.3 4.5 3.3 1.9 2.4 4.5 4.8 2.4 2.5 4.5 -.- 2.9 2.6 4.5 600 0.5 0.9 2.3 4.5 3.2 1.9 2.4 4.5 4.5 2.4 2.5 4.5 -.- 2.8 2.6 4.5 700 0.5 0.9 2.3 4.5 3.0 1.9 2.4 4.5 4.3 2.3 2.5 4.5 -.- 2.8 2.6 4.5 750 0.5 0.9 2.3 4.5 2.9 1.8 2.4 4.5 4.2 2.3 2.5 4.5 -.- 2.8 2.6 4.5 800 0.5 0.9 2.3 4.5 2.8 1.8 2.4 4.5 4.0 2.3 2.5 4.5 -.- 2.8 2.6 4.5 900 0.5 0.9 2.3 4.5 2.7 1.8 2.4 4.5 3.8 2.3 2.5 4.5 4.9 2.7 2.6 4.5

1000 0.5 0.9 2.3 4.5 2.5 1.8 2.4 4.5 3.6 2.2 2.5 4.5 4.6 2.6 2.6 4.5 EST 16 200 0.4 0.9 2.2 4.4 3.6 1.9 2.3 4.4 -.- 2.3 2.4 4.4 -.- 2.8 2.5 4.4

250 0.4 0.9 2.2 4.4 3.5 1.8 2.3 4.4 -.- 2.3 2.4 4.4 -.- 2.8 2.5 4.4 300 0.4 0.9 2.2 4.4 3.5 1.8 2.3 4.4 5.0 2.3 2.4 4.4 -.- 2.8 2.5 4.4 350 0.4 0.9 2.2 4.4 3.4 1.8 2.3 4.4 4.9 2.3 2.4 4.4 -.- 2.8 2.5 4.4 400 0.4 0.9 2.2 4.4 3.3 1.8 2.3 4.4 4.8 2.3 2.4 4.4 -.- 2.8 2.5 4.4 450 0.4 0.9 2.2 4.4 3.3 1.8 2.3 4.4 4.7 2.3 2.4 4.4 -.- 2.8 2.5 4.4 500 0.4 0.9 2.2 4.4 3.2 1.8 2.3 4.4 4.6 2.3 2.4 4.4 -.- 2.8 2.5 4.4 600 0.4 0.9 2.2 4.4 3.0 1.8 2.3 4.4 4.3 2.3 2.4 4.4 -.- 2.7 2.5 4.4 700 0.4 0.9 2.2 4.4 2.9 1.8 2.3 4.4 4.1 2.2 2.4 4.4 -.- 2.7 2.5 4.4 750 0.4 0.9 2.2 4.4 2.8 1.8 2.3 4.4 4.0 2.2 2.4 4.4 -.- 2.6 2.5 4.4 800 0.4 0.9 2.2 4.4 2.7 1.8 2.3 4.4 3.8 2.2 2.4 4.4 5.0 2.6 2.5 4.4

EST 20 150 0.4 0.8 2.0 4.2 3.3 1.7 2.1 4.2 4.8 2.1 2.2 4.2 -.- 2.6 2.3 4.2 200 0.4 0.8 2.0 4.1 3.2 1.7 2.1 4.1 4.6 2.1 2.2 4.1 -.- 2.5 2.2 4.2 250 0.4 0.8 2.0 4.1 3.2 1.7 2.1 4.1 4.6 2.1 2.2 4.2 -.- 2.5 2.2 4.2 300 0.4 0.8 2.0 4.1 3.1 1.7 2.1 4.1 4.5 2.1 2.2 4.2 -.- 2.5 2.2 4.2 350 0.4 0.8 2.0 4.1 3.1 1.7 2.1 4.2 4.4 2.1 2.2 4.2 -.- 2.5 2.2 4.2 400 0.4 0.8 2.0 4.1 3.0 1.7 2.1 4.2 4.3 2.1 2.2 4.2 -.- 2.5 2.2 4.2 450 0.4 0.8 2.0 4.1 3.0 1.6 2.1 4.2 4.2 2.1 2.2 4.2 -.- 2.5 2.2 4.2 500 0.4 0.8 2.0 4.1 2.9 1.6 2.1 4.2 4.1 2.1 2.2 4.2 -.- 2.5 2.2 4.2 600 0.4 0.8 2.0 4.1 2.7 1.6 2.1 4.1 3.9 2.0 2.2 4.2 -.- 2.4 2.2 4.2

EST 25 100 0.3 0.6 1.4 3.4 2.4 1.2 1.5 3.4 3.4 1.5 1.6 3.4 4.5 1.9 1.6 3.5 150 0.3 0.7 1.7 3.7 2.8 1.4 1.8 3.8 4.0 1.8 1.8 3.8 -.- 2.2 1.9 3.8 200 0.3 0.7 1.7 3.8 2.7 1.4 1.8 3.8 4.0 1.8 1.8 3.8 -.- 2.2 1.9 3.8 250 0.3 0.7 1.7 3.8 2.7 1.4 1.8 3.8 3.9 1.8 1.9 3.8 -.- 2.2 1.9 3.8 300 0.3 0.7 1.7 3.8 2.7 1.4 1.8 3.8 3.8 1.8 1.9 3.8 5.0 2.2 1.9 3.8 350 0.3 0.7 1.7 3.8 2.6 1.4 1.8 3.8 3.8 1.8 1.9 3.8 4.9 2.2 1.9 3.8 400 0.3 0.7 1.7 3.7 2.6 1.4 1.8 3.8 3.7 1.8 1.8 3.8 4.8 2.1 1.9 3.8 450 0.3 0.7 1.7 3.8 2.5 1.4 1.8 3.8 3.6 1.8 1.8 3.8 4.7 2.1 1.9 3.8 500 0.3 0.7 1.7 3.8 2.4 1.4 1.8 3.8 3.5 1.8 1.9 3.8 4.6 2.1 1.9 3.8 600 0.3 0.7 1.7 3.8 2.3 1.4 1.8 3.8 3.3 1.7 1.9 3.8 4.3 2.1 1.9 3.8

EST 32 25 0.0 0.1 0.2 1.3 0.3 0.1 0.2 1.3 0.4 0.2 0.2 1.3 0.5 0.2 0.2 1.3 40 0.1 0.2 0.5 1.9 0.8 0.4 0.5 1.9 1.1 0.5 0.5 1.9 1.5 0.6 0.5 1.9 50 0.2 0.3 0.8 2.4 1.3 0.6 0.8 2.4 1.8 0.8 0.8 2.4 2.4 1.0 0.9 2.4 80 0.2 0.4 1.1 2.9 1.7 0.9 1.1 2.9 2.5 1.1 1.2 2.9 3.3 1.4 1.2 2.9

100 0.3 0.5 1.3 3.2 2.2 1.1 1.4 3.2 3.1 1.4 1.4 3.2 4.0 1.7 1.5 3.3 150 0.3 0.5 1.3 3.3 2.2 1.1 1.4 3.3 3.2 1.4 1.5 3.3 4.1 1.7 1.5 3.3 200 0.3 0.5 1.3 3.3 2.2 1.1 1.4 3.3 3.1 1.4 1.5 3.3 4.0 1.7 1.5 3.3 250 0.3 0.5 1.3 3.2 2.1 1.1 1.4 3.3 3.0 1.4 1.4 3.3 4.0 1.7 1.5 3.3 300 0.3 0.5 1.3 3.2 2.1 1.1 1.4 3.3 3.0 1.4 1.4 3.3 3.9 1.7 1.5 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: Specific mass soil: 1600 kg/m3 100 pcf Bedding angle: 120 °E' (ground) : 4.8 N/mm² 700 psi Defl.lag factor: 1.5(-)

Wheel load (tons) 0 5 7.5 10 Burialdepth (m) 0.5 1 2.5 5 0.5 1 2.5 5 0.5 1 2.5 5 0.5 1 2.5 5

ESN 10 450 0.5 0.9 2.3 4.5 3.5 1.9 2.5 4.6 5.0 2.4 2.5 4.6 -.- 2.9 2.6 4.6 500 0.5 0.9 2.4 4.6 3.3 1.9 2.5 4.6 4.7 2.4 2.6 4.6 -.- 2.9 2.7 4.6 600 0.5 0.9 2.4 4.6 3.1 1.9 2.5 4.6 4.4 2.4 2.6 4.6 -.- 2.9 2.6 4.6 700 0.5 0.9 2.3 4.5 3.0 1.9 2.5 4.6 4.3 2.4 2.6 4.6 -.- 2.8 2.6 4.6 750 0.5 0.9 2.3 4.5 2.9 1.9 2.5 4.6 4.1 2.3 2.6 4.6 -.- 2.8 2.6 4.6 800 0.5 0.9 2.4 4.6 2.8 1.9 2.5 4.6 3.9 2.3 2.6 4.6 -.- 2.8 2.6 4.6 900 0.5 0.9 2.4 4.6 2.6 1.8 2.5 4.6 3.7 2.3 2.6 4.6 4.8 2.7 2.6 4.6

1000 0.5 0.9 2.4 4.6 2.4 1.8 2.5 4.6 3.3 2.2 2.6 4.6 4.3 2.6 2.6 4.6 1200 0.2 0.4 1.0 2.8 1.6 0.9 1.1 2.8 2.3 1.1 1.1 2.8 3.0 1.3 1.2 2.8

ESN 16 350 0.5 0.9 2.4 4.6 3.6 2.0 2.5 4.6 -.- 2.5 2.6 4.6 -.- 3.0 2.6 4.6 400 0.5 0.9 2.4 4.6 3.5 2.0 2.5 4.6 -.- 2.5 2.6 4.6 -.- 3.0 2.6 4.6 450 0.5 0.9 2.4 4.6 3.4 2.0 2.5 4.6 4.9 2.5 2.6 4.6 -.- 3.0 2.6 4.6 500 0.5 0.9 2.4 4.6 3.3 1.9 2.5 4.6 4.7 2.4 2.6 4.6 -.- 2.9 2.7 4.6 600 0.5 0.9 2.4 4.6 3.1 1.9 2.5 4.6 4.4 2.4 2.6 4.6 -.- 2.9 2.6 4.6 700 0.5 0.9 2.3 4.5 3.0 1.9 2.5 4.6 4.3 2.4 2.6 4.6 -.- 2.8 2.6 4.6 750 0.5 0.9 2.3 4.5 2.9 1.9 2.5 4.6 4.1 2.3 2.6 4.6 -.- 2.8 2.6 4.6 800 0.2 0.3 0.8 2.4 1.2 0.6 0.8 2.4 1.7 0.8 0.8 2.4 2.3 1.0 0.8 2.4

ESN 20 200 0.5 0.9 2.3 4.5 3.7 1.9 2.4 4.5 -.- 2.4 2.5 4.5 -.- 2.9 2.6 4.5 250 0.5 0.9 2.3 4.5 3.7 2.0 2.5 4.5 -.- 2.5 2.5 4.6 -.- 3.0 2.6 4.6 300 0.5 0.9 2.3 4.5 3.6 1.9 2.5 4.5 -.- 2.4 2.5 4.6 -.- 3.0 2.6 4.6 350 0.5 0.9 2.3 4.5 3.5 1.9 2.5 4.5 -.- 2.4 2.5 4.5 -.- 2.9 2.6 4.6 400 0.5 0.9 2.3 4.5 3.4 1.9 2.4 4.5 4.9 2.4 2.5 4.5 -.- 2.9 2.6 4.6 450 0.5 0.9 2.3 4.5 3.4 1.9 2.4 4.5 4.8 2.4 2.5 4.5 -.- 2.9 2.6 4.6 500 0.5 0.9 2.3 4.5 3.2 1.9 2.5 4.5 4.6 2.4 2.5 4.6 -.- 2.9 2.6 4.6 600 0.2 0.3 0.8 2.5 1.4 0.7 0.9 2.5 2.0 0.9 0.9 2.5 2.6 1.1 1.0 2.5

ESN 25 200 0.5 0.9 2.3 4.5 3.7 1.9 2.4 4.5 -.- 2.4 2.5 4.5 -.- 2.9 2.5 4.5 250 0.4 0.9 2.2 4.4 3.5 1.9 2.4 4.4 -.- 2.4 2.4 4.5 -.- 2.9 2.5 4.5 300 0.4 0.9 2.2 4.4 3.5 1.9 2.4 4.4 5.0 2.3 2.4 4.4 -.- 2.8 2.5 4.5 350 0.4 0.9 2.2 4.4 3.4 1.8 2.4 4.4 4.8 2.3 2.4 4.4 -.- 2.8 2.5 4.5 400 0.4 0.9 2.2 4.4 3.3 1.8 2.3 4.4 4.7 2.3 2.4 4.4 -.- 2.8 2.5 4.4 450 0.4 0.9 2.2 4.4 3.2 1.8 2.3 4.4 4.6 2.3 2.4 4.4 -.- 2.8 2.5 4.4 500 0.4 0.9 2.2 4.4 3.1 1.8 2.4 4.5 4.4 2.3 2.4 4.5 -.- 2.8 2.5 4.5 600 0.0 0.0 0.1 1.1 0.1 0.0 0.1 1.1 0.1 0.1 0.1 1.1 0.2 0.1 0.1 1.1

ESN 32 80 0.3 0.5 1.3 3.2 2.1 1.1 1.3 3.2 3.0 1.3 1.4 3.2 3.9 1.6 1.4 3.2 100 0.4 0.8 1.9 4.0 3.1 1.6 2.0 4.0 4.5 2.0 2.1 4.0 -.- 2.4 2.1 4.1 150 0.4 0.9 2.2 4.3 3.5 1.8 2.3 4.4 -.- 2.3 2.4 4.4 -.- 2.8 2.4 4.4 200 0.4 0.8 2.1 4.3 3.4 1.8 2.2 4.3 4.8 2.2 2.3 4.3 -.- 2.7 2.3 4.3 250 0.4 0.8 2.1 4.2 3.3 1.7 2.2 4.2 4.7 2.2 2.2 4.3 -.- 2.6 2.3 4.3 300 0.5 0.9 2.3 4.5 3.2 1.9 2.5 4.6 4.6 2.4 2.5 4.6 -.- 2.9 2.6 4.6

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

69

Appendix I : List of symbols

A = structural wall area (mm2)AB = bore area (mm2)

c = wave velocity (m/s)CL = live-load coefficient (single wheel load) (-)CL(T) = live-load coefficient (two passing trucks) (-)

D = mean pipe diameter (m), (in), (ft)Df = shape factor (-)DI = structural inner diameter (mm), (in)Dl = deflection lag factor (-)DO = structural outer diameter (mm), (in)

E' = modulus of soil reaction (psi)EH = hoop bending modulus (N/mm2), (N/m2), (psi)EI = stiffness factor (in2.lb/in)ES = shear modulus (N/mm²)EV = volumetric E-modulus (N/mm2)EX = axial bending (tensile) modulus (N/mm2)EXT = axial bending (tensile) modulus at elevated temperature (N/mm2)

f = constant (-)FS = design factor (-)FW = frictional force between soil and pipe (N/mm2)

g = acceleration due to gravity (m/s2)GB = linear mass of the pipe (kg/m)GV = lenear mass of the pipe content (kg/m)

H = burial depth to top of the pipe (ft)HDB = Hydrostatic Design Basis (N/mm2), (psi)HDS = Hydrostatic Design Stress (N/mm2), (psi)

ID = inner diameter (mm), (m), (in)If = impact factor (-)IR = radius of inertia (mm)IZ = linear moment of inertia (mm4)

k = wall roughness (mm)KV = compression modulus of the fluid (N/mm2)KX = deflection coefficient (-)

L = length between stiff pipe ends (mm)L' = support distance at operating temperature and -pressure (m)LA = fictive anchor length (m)LC = continuous span length (mm), (m)LC1 = continuous span length based on axial stress (mm)LC2 = continuous span length based on the allowable sag (mm)LEQ = equivalent pipe length (m)LF = final support distance (m)LO = standard length (m)

70

LS = single span length (mm), (m)LS1 = single span length based on axial stress (mm)LS2 = single span length based on allowable sag (mm)

NXY = Poisson ratio axial/hoop (-)NYX = Poisson ratio hoop/axial (-)

OD = outer diameter (mm), (in)

P = operating pressure (Mpa), (psi)PA = anchor load (N)PAT = anchor load at elevated temperature (N)PB = buckling pressure (bar)PBT = buckling pressure at elevated temperature (bar)PN = nominal pressure (bar), (Mpa)PS = Pipe Stiffness (psi)PW = wheel load (lb)

QP = linear weight of the filled pipe (N/mm)

R = ratio axial stress/hoop stress, elbow radius (-), (mm)Rb = bending radius (m), (in)Rc = rerounding coefficient (-)RE = temperature correction factor (-)rm = mean pipe radius (mm), (in)ro = outer pipe radius (ft)RS = specific gravity correction factor (-)RT = temperature change correction factor (-)

SA = remaining axial stress (N/mm2)Sb = load-dependent safety factor (-)Seq = equivalent stress (N/mm2)Seq(max) = maximum equivalent stress (N/mm²)SF = Stiffness Factor (in2.lb/in)SF = service factor (-)Sf = service (design) factor (-)SH = allowable hoop stress (N/mm2)SL = specific gravity of the laminate (kg/m3)STES = Specific Tangential End Stiffness (N/m2)STIS = Specific Tangential Initial Stiffness (N/m2)SV = specific gravity of the fluid (kg/m3)SX = actual axial stress due to internal pressure (N/mm2)SXT = allowable axial stress (N/mm2)SY = actual hoop stress due to internal pressure (N/mm2)

T = operating temperature (°C)TC = topcoat thickness (mm)TE = minimum reinforced wall thickness (mm), (m), (in)TL = liner thickness (mm)TT = nett total wall thickness (in)TW = total wall thickness (mm), (in)

UEWS = Ultimate Elastic Wall Stress (N/mm2)

v = flow velocity (m/s)

71

WB = moment of resistance to bending (mm3)WC = vertical soil load (lb/in)WL = live load (lb/in)WW = moment of resistance to torsion (mm3)

α = creep factor (-)α = bedding angle (°)

β = ageing factor (-)

γS = specific mass of soil (kg/m3), (lb/ft3)

∆Hfitting = head loss in the fitting (N/m2)∆Hpipe = head loss in the pipe (m.w.c./m.)∆P = pressure change (N/m2), (m.w.c.)∆T = temperature change (°C)∆y = predicted vertical pipe deflection (in)∆v = change in flow velocity (m/s)

ζ = friction coefficient (-)

σC = resulting hoop stress (psi)

τ = shear stress (N/mm2)

ω = winding angle (°)

ϒL = coefficient of linear thermal expansion (mm/mm°C)

72

Appendix II: Conversion tablesConversion figures for anglo-saxon units into metric units

Length (SI = m)1 inch = 0.02540 m1 foot = 12 inch = 0.30480 m1 yard = 3 feet = 0.91440 m1 mile = 1760 yards = 1.609 * 103 m1 seamile = 1.852 * 103 m

Area (SI = m 2)1 square inch = 6.4516*10-4 m2

1 square foot = 144 square inch = 9.2903*10-2 m2

1 square yard = 9 square feet = 0.8361 m1 acre = 4840 square yards = 4,046.85 m2

1 square mile = 640 acres = 2.58998*106 m2

1 circular inch= square inch = 5.0671*10-4 m2 π4

Volume (SI = m 3)1 cubic inch = 16.387*10-6 m3

1 cubic foot= 1728 cubic inch = 28.317*10-3 m3

1 cubic yard= 27 cubic feet = 0.76455 m3

1 imperial gallon = 4.5461*10-3 m3

1 US gallon = 3.7854*10-3 m3

1 US barrel (petrol) = 0.158762 m3

1 barrel (imperial) = 0.163656 m3

Mass (SI = kg)1 grain = 0.0648*10-3 kg1 ounce = 437.5 grains = 0.0283495 kg1 pound = 16 ounces = 0.4535924 kg1 US long ton= 2240 pound = 1,016.05 kg1 US short ton= 2000 pound = 907.185 kg1 hundred weight (imp.) = 50.80235 kg1 hundred weight (US) = 45.3592 kg

Mass per length (SI = kg/m)1 pound per inch = 17.858 kg/m1 pound per foot = 1.488 kg/m1 pound per yard = 0.4961 kg/m

Mass per area (SI = kg/m 2)1 pound per square inch = 0.0703*104 kg/m2

1 pound per square foot = 4.8825 kg/m2

1 pound per square yard = 0.5425 kg/m2

Density (SI = kg/m 3)1 grain per cubic foot = 2.288*10-3 kg/m3

1 pound per cubic foot = 16.0256 kg/m3

1 grain per gallon (US) = 1.711 kg/m3

1 pound per gallon (US) = 119.8 kg/m3

Pressure (SI = Pa = 1 N/m 2 = 10-5 bar)1 pound per square inch = 6.8948*103 N/m2

1 pound per square foot = 47.876 N/m2

1 pound per square yard = 5.3201 N/m2

1 long ton per sq. inch (imp) = 1.0725*105 N/m2

1 long ton per sq. foot (imp) = 1.5444*107 N/m2

1 short ton per sq. inch (US) = 1.3789*107 N/m2

1 grain per square inch = 0.9850*102 N/m2

1 ounce per square inch = 4.3092*102 N/m2

1 ounce per square foot = 2.9925 N/m2

1 ounce per square yard = 0.3313 N/m2

1 inch head of water = 249.089 N/m2

1 inch head of mercury = 3.3864*103 N/m2

1 foot head of water = 2.9879*102 N/m2

Power (SI = W)1 foot pounds per second = 1.35582 W1 foot pounds per minute = 2.25 * 10-2 W1 British thermal unit per sec. = 1.0549*10-3 W1 centigrade thermal unit p. sec. = 1.8987*10-3 W1 horsepower (Hp) = 7.457 *10-4 W

Work (SI = Nm = J)1 foot pound = 1.3558 J1 yard pound = 4.0675 J1 foot ton (US) = 2.7164*103 J1 foot ton (imp.) = 3.0371*103 J1 HPh = 2.6815*106 J1 Btu = 1.0555*103 J1 Ctu = 1.8991*103 J

Acceleration (SI = m/s 2)

feet per second squared = 0.3048 m/s2

Flow rate1 cubic feet per hour = 0.02679 m3/h1 gallon per minute = 227.1 dm3/h

Mass basePounds per hour = 0.01088 tons per dayMT/D = 0.4536 kg/h

Force (SI = N)pounds force = 4.4482 N

HeatBtu per pound = 2.326 kJ/kgBtu per hour = 0.2931 WBtu / hr.ft2°F = 5.678 W/m2.°CBtu / lb.°F = 4.187 KJ/kg.°CBtu / hr.ft2 = 3.155 W/m2

Btu.ft / hr.ft2.°F = 1.731 W/m.°Cft2.hr.°F/Btu = 0.1761 m2.°C/W

Moment of inertiainch4 = 4.162 * 10-6 m4

Moment of bending (SI = Nm)1 inch pound = 0.1130 Nm1 foot pound = 1.356 Nm

Velocity (SI = m/s)1 ft/second = 0.3048 m/s1 ft/minute = 0.00508 m/s1 mile/hr = 0.44704 m/s

Conversion figures for metric into anglo-saxon units

Length1 metre = 1.094 yards

= 3.281 feet= 39.37 inches

1 kilometre = 0.621 statute mile= 0.540 nautical mile

Area1 square millimetre = 15.51 square inch 1 square metre = 1.196 square yards

= 10.76 square feet1 square kilometre = 0.3861 square mile

= 0.02471 acres

Volume1 cubic metre = 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

Mass1 kilogram = 15430 grains

= 35.27 ounces= 2.205 pounds

1 metric ton = 1.102 US short tons= 0.984 long ton

Mass per length1 kilogram per metre = 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 psi

= 0.2048 psf= 1.8433 lb/sq. yard

Density1 kilogram per cubic metre = 0.0624 pcf

= 437 grain pr cubic foot= 58.4 grain per gallon

73

Moment of inertiamillimetres4 = 2.40269 * 10-6 in4

Moment of bendingNm = 8.850 inch pounds

= 0.07375 foot pounds

Pressure1 N/m2 = 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

1 MN/m2 = 9.324long tons/ft²(eng)= 0.648long tons/in²(eng)= 0.725short tons/in²(US)

Power1 kilowatt = 738 foot pounds/sec.

= 4.428*104 ft lb/min.= 0.94799 Btu/sec.= 0.526676 Ctu/sec.= 1.340536 Horse Power

Work1 Joule = 0.73756 foot pound

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

Heat1 Kj/kg = 0.42992 Btu/pound1 W = 0.341180 Btu/hour1 W/m2.°C = 0.17612 Btu/hr.ft2.°F1 W/m2 = 0.31696 Btu/hr.ft2

1 W/m.°C = 0.5777 Btu.ft/hr.ft2.°F1 m2.°C/W = 5.6786 ft2.hr.°F/Btu1 Kj/kg.°C = 0.23883 Btu/lb.°F

Velocity1 m/s = 3.28084 ft/sec

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

Acceleration1 m/s2 = 3.28084 ft/sec²

Flow rate1 m3/hr = 37.32736 feet3/hour

= 0.00440 gallons/minute

Mass baseMT/D = 91.91176 pounds/hourkg/h = 2.20459 pounds/hour

Force1 N (Newton) = 0.22481 pounds force

Prefixes Prefix Factor Symbol giga 109 Gmega 106 Mkilo 103 kmilli 10-3 mmicro 10-6 µ

Conversion figures for metric units into SI-units

Length (SI = m)1 km = 103 m1 cm = 10-2 m1 mm = 10-3 m1 micron = 10-6 m

Area (SI = m 2)1 km2 = 106 m2

1 cm2 = 10-4 m2

1 mm2 = 10-6 m2

Volume (SI = m 3)1 dm3 = 1 litre = 10-3 m3

1 cm2 = 10-6 m3

1 mm3 = 10-9 m3

Mass (SI = kg)1 gram = 10-3 kg1 metric ton = 103 kg1 milligram = 10-6 kg

Mass per length (SI = kg/m)1 den = (1/9)*10-6kg/m1 tex = 10-6 kg/m

Mass per area1 gram/mm2 = 10-3 kg/mm2

= 103 kg/m2

Density1 gram/dm3 = 1 gram/ltr

= 10-3 kg/dm3

= 1 kg/m3

Pressure1 bar = 105 Pa = 105 N/m2

1 kgf/cm2 = 98066 Pa1 atm. = 101.325*103 Pa1 at = 98066.5 Pa 1 Torr = 133.322 Pa1 metre water column = 9.80665 * 103 Pa1 metre mercury column = 133.322 * 102 Pa

Power1 kgf.m/s = 9.80665 W1 metric horsepower = 735.499 W1 kcal/h = 1.163 W

Work1 Nm = 1 J1 kgf.m = 9.80665 J1 kWh = 3.6*106 J1 kcal = 4186.8 J1 metric horse power.hour = 2.64780 * 106 J1 erg = 1 dyn.cm = 10-7 J

Accelerationg = gravitation = 9.8067 m/s2

Velocity1 km/h = 0.2778 m/s1 m/min. = 0.0167 m/s1 knot = 0.5144 m/s

Flow rate1 litre/h = 10-3 m3/h1 m3/h = 0.2778 m3/h

Mass base1 kg/h = 24.0 MT/D

Force1 kgf = 9.80665 N1 dyn = 1 g.cm/s2 = 10-5 N

Heat1 kcal/hr = 1.163 W1 kcal = 4186.8 J1 kcal(h.m) = 1.163 W/m1 kcal(h.m2) = 1.163 W/m2

1 cal(s.cm) = 418.68 W/m

74

Appendix III: Conversion graph psi vs bar

75

Appendix IV : Conversion graph °C vs °F

76

Appendix V : Examples combined stresses

Example I:

QuestionInner diameter 400 mm, pipe series EST 20 to be used as vertical pump column. Is the maximum torquegenerated by the pump allowable?

Pump datamax operating pressure (P) 12 barpump weight 90 kNmaximum moment (MW) 8100 Nm

Pipe datapipe series EST 20inner diameter (ID) 400 mmwinding angle (ω) 55 °effective wall thickness (TE) 6.5 mmlinear mass (GB) 17.3 kg/mbore area (AB) 125660 mm2

structural wall area (A) 8320 mm2 (table II-b., page 9)moment of resistance to torsion (WW) 1669200 mm3 (Eq.II.7. incl. note, table II-b., page 9)specific gravity of pipelaminate (SL) 1850 kg/m3

mass of ID 400 mmEST 20 flange 27.5 kg (Product List)pipe length (LP) 3 mcolumn length (L) 12 mflanged pipe lenghts of 3 m each,total column length 12 m.

Calculation1) axial load due to pressure:

Fax,1 = AB * P= 125660 * 1.2 = 150792 N

2) weight of water column:Fax,2 = AB * L * 1000E-8

= 125660 * 12000 * 1000E-8 = 15079 N 3) weight of pipe EST 20:

Fax,3 = GB * L= 173 * 12 = 2076 N

4) weight of pumpFax,4 = 90000 N

5) weight of flanges: number of flanges = 2 * L/LP = 2 * 12/3 = 8

Fax,5 = 8 * 275 = 2200 N+

Total axial load (Fax,tot): 260147 N

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 / WW

= 8100000 / 1669200 = 4.9 N/mm2

Fig. V-1.

ConclusionThe 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:

QuestionInner diameter 150 mm, pipe series EST 20 to be installed horizontally on pipe supports. What is the maximumsupport distance?

Operating dataoperating pressure (P) 15 baroccuring shear stress due to torsion (τ) 15 N/mm²continuous span supportoperating temperature (T) 60 °C

Pipe dataPipe series EST 20Inner diameter (ID) 150 mmwinding angle (ω) 55 °effective wall thickness (TE) 2.4 mmlinear mass of the pipe (GB) 2.8 kg/mlinear mass of the pipe content (GV) 17.7 kg/m (table II-d., page 10;

SV = 1000 kg/m3)bore area (AB) 17670 mm2

structural wall area (A) 1160 mm2 (table II-b., page 9)moment of resistance to bending (WB) 43700 mm3 (equation II.7. including

note, table II-b., page 9)axial bending modulus (EX) 12000 N/mm2 (table II-j., page 24)linear moment of inertia (IZ) 3403000 mm4 (table II-b., page 9)

Calculation1) Hoop stress due to internal pressure

= 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

5) Axial bending modulus at 60°C (Eq. III.10.) = 12000 * 0.82 = 9840 N/mm2

6) Linear weight of the filled pipe (Eq. III.5.)

= = 0.201 N/mm

79

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 toobtain a service factor (SF) of 1.5.

80

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