INDEXPART

VPART

IVPART

IIIPART

IIPART

I

INSTALLATIONPRACTICES

FORCABLE

RACEWAY SYSTEMS

Ramsey, New Jersey 07446THE OKONITE COMPANY

MOVE YOUR POINTER OVER EDGE OF TABSAND CLICK ON TAB TO GO TO SECTION

Review Eng.

Status Code1. Reviewed and accepted as final certificated document. Manufature may proceed.2. Reviewed and accepted as noted. Submit certified dwgs. Manufature may proceed.3. Reviewed and returned. Correct and resubmit. Manufacture shall NOT roceed.4. Review not requiered. For information only. Manufature may proceed.

Reviewed for general dimensions only. This review does not relieve the Vendor from full Responsibility for the adequacy correctness, accuracy and completeness of calculat ions, details and dimensions. By reviewing thesedocument Aker Solutions does not accept liability for their completeness or accuracy

ANTAMINA EXPANSION PROGRAM

Status Code : Date

Part of the Aker group

Purchase Order Nr Aker Solutions Rev NrSequential Nr.Doc. Type

E50204 X009 010 1

4 06-09-11Digitally signed by mmamanit Date: 2011.09.06 08:34:43 -05'00'

How to navigate this manual

Page back or page forward.

Undoes a change of page or view, or redoesa change (Go Back/Go Forward).

Go to the cover page.

Go to the indicated topic.

Gotothenextpage.

Gotothepreviouspage.

text

INTRODUCTIONThe Okonite Installation Practices Manual has been developed toaid in the proper design and installation of cable raceway systems.In determining the best possible design and installation, manyparameters must be considered and weighed against each other.These parameters and installation techniques are explainedwithin this manual. A raceway system should be designed with aknowledge of proper installation techniques so as not to create asituation which would cause these techniques to be disregarded.A system designed without regard for the installation methodsmay be virtually impossible to install.The manual is divided into five parts: Part I explains therecommended procedures which should be pursued whendetermining the correct conduit or duct size for a given cable orgroup of cables. Tables are included as a handy aid which shouldeliminate some routine calculations.

Part II described the limitations and pertinent formulas required todesign an allowable pull for a cable raceway system. Pullingdevices and cable pulling parameters are explained along withtheir limitations which must not be exceeded when a properlydesigned system is desired. Again, tables are included for ease ofcalculation. Pulling precautions are listed so that the designer isalerted to these limitations during design.Several examples of typical duct pulls are included in Part III.Examples include horizontal as well as vertical runs. Eachexample is calculated in two different pulling directions. In someexamples, large differences in tension are demonstrateddepending upon the direction chosen.Part IV describes in greater detail the choices and considerationsto be made when a cable raceway system is designed. Conduitbends, risers, junction boxes, manholes, condulets and cabletrays are among those topics examined. Both the cable designerand installer should be aware of options and potential problemareas when the best possible, most economical cable racewaysystem is desired.

i

INSTALLATION PRACTICES

Installation methods and procedures are described in Part V.Correct procedures for conduit installation including feeding andpulling cables are included. Precautions and prohibitions arestated to make the installation as problem-free as possible.

ii

INSTALLATION PRACTICES

Introduction . . . . . . . . . . . . . . . . . . . . . . i

PART IMETHODS FOR DETERMININGCONDUIT SIZES . . . . . . . . . . . . . . . . . . . . 1-2

PART IIDESIGNS LIMITS AND FORMULAE . . . . . . . . . . 3-13

Pulling Eyes and Bolts . . . . . . . . . . . . . . . . . 3Basket Grip . . . . . . . . . . . . . . . . . . . . . . . 3Other Pulling Devices . . . . . . . . . . . . . . . . . . 4Sidewall Pressure . . . . . . . . . . . . . . . . . . . . 4Minimum Bending Radii for Installation . . . . . . . . . 5Jam Ratio (Three Single Conductors) . . . . . . . . . . 6Pulling Tension Calculations . . . . . . . . . . . . . . 7Pulling Precautions . . . . . . . . . . . . . . . . . . . 9Installing Cable in Tray . . . . . . . . . . . . . . . . 10

PART IIIEXAMPLE CALCULATIONS . . . . . . . . . . . . . . 15-32

Cable Construction . . . . . . . . . . . . . . . . . . 15Calculation Examples . . . . . . . . . . . . . . . . . 17

PART IVSYSTEM CONSIDERATIONS . . . . . . . . . . . . . 33-42

Introduction . . . . . . . . . . . . . . . . . . . . . . 33Cable in Conduit . . . . . . . . . . . . . . . . . . . 33Sizing of Conduit-Jam Ratio . . . . . . . . . . . . . 34Layout and Calculations . . . . . . . . . . . . . . . . 35Conduit Bends-Minimum Radii . . . . . . . . . . . . 35Junction Boxes . . . . . . . . . . . . . . . . . . . . 35Standard Condulets . . . . . . . . . . . . . . . . . . 35Unsupported Cable in VerticalConduit Risers . . . . . . . . . . . . . . . . . . . . 36

INDEX

Manholes . . . . . . . . . . . . . . . . . . . . . . . 36Splicing Cable in Manholes . . . . . . . . . . . . . . 38Cable Terminations in Enclosures . . . . . . . . . . 38Cables in Trays and Ladders . . . . . . . . . . . . . 39Cable Tray Bends . . . . . . . . . . . . . . . . . . . 39Fastening of Cable in Trays . . . . . . . . . . . . . . 39Cable Failures . . . . . . . . . . . . . . . . . . . . . 40Installers as Designers . . . . . . . . . . . . . . . . 40

PART VINSTALLATION . . . . . . . . . . . . . . . . . . . . . 43-47

Conduit Installation . . . . . . . . . . . . . . . . . . 43Pulling Equipment . . . . . . . . . . . . . . . . . . . 43Cable in Storage . . . . . . . . . . . . . . . . . . . 44Setting Up for a Pull . . . . . . . . . . . . . . . . . . 44Cable Pulling Devices . . . . . . . . . . . . . . . . . 45Pulling the Cable . . . . . . . . . . . . . . . . . . . 45Condulets . . . . . . . . . . . . . . . . . . . . . . . 46Splicing and Terminating . . . . . . . . . . . . . . . 47Installing Cable in Tray . . . . . . . . . . . . . . . . 47Specific Prohibitions . . . . . . . . . . . . . . . . . . 47Appendix 1 . . . . . . . . . . . . . . . . . . . . . . 49Appendix 2 . . . . . . . . . . . . . . . . . . . . . . 51

METHODS for DETERMININGCONDUIT SIZESConduits or ducts should be of adequate size as determined bythe maximum recommended percentage fill of conduit area. Thefollowing tables express the limitations as specified by theNational Electrical Code.For groups or combinations of cables, the National Electrical Coderequires that the conduit or duct be of such size that the sum of thecross-sectional areas of the individual cables will not be more thanthe percentage of the interior cross-sectional area of the conduitor duct as shown in the following tables:

Table 1Maximum Cable Cross-Sectional Areas as aPercentage of Internal Conduit or Duct Area

Number of Cables

1 2 3 or More

Cables (not lead-covered) 53 31 40

Table 2Dimensions of Conduit

NominalConduit Inches

Internal DiameterInches

AreaSquare Inches

1/23/4

11 1/41 1/22

0.6220.8241.0491.3861.6102.067

0.3005.30.861.502.043.36

2 1/233 1/24

2.4693.0683.5484.026

4.797.389.90

12.72

56

5.0476.065

20.0028.89

1

PART I

Table 3Maximum Allowable Diameter (in inches) ofIndividual Cables in Given Size of Conduit

Non-Metallic Jacket Cable (Lead Covered Not Included) All Cables of Same Outside Diameter

NominalSize

Conduit

Number of Cables Having Same O.D.

1 2 3 4

1/23/4

11 1/4

0.4530.6000.7631.010

0.2440.3240.4120.542

0.2270.3010.3830.504

0.1970.2600.3320.436

1 1/222 1/23

1.1731.5051.7972.234

0.6330.8120.9701.206

0.5880.7540.9011.128

0.5090.6530.7800.970

3 1/2456

2.5832.9303.6754.416

1.3951.5831.9852.385

1.2961.4701.8442.215

1.1211.2731.5951.916

For quick selection of correct conduit size (three single ormulticonductor cables) refer to Appendix 2.

2

DESIGN LIMITSAND FORMULAE

Pulling Tension Limits1. Pulling Eyes & BoltsThe maximum pulling tension on copper conductors or for 3/4hard or full hard aluminum shall not exceed .008 times the circularmil (CM) area when pulled with a pulling eye attached to eachconductor. The maximum tension on soft aluminum conductorsshall not exceed .004 times the CM area with a pulling eyeattached to each conductor.Eq. 1: Tm

= .008 x n x CM for copper or 3/4 hard orhard aluminum

Tm

= .004 x n x CM for 1/2 hard end soft aluminumconductors

NOTE: In pulling three single conductors of equal size that are nottriplexed, a value of n equal to 2, rather than 3, should beused since two of the conductors may sustain the totalpulling tension. When more than three single conductorsof equal size are pulled in parallel, the maximum tensionshould be limited to 60% of value determined by theequation, with n representing the total number ofconductors.When pulling conductors of different sizes, consultmanufacturer.When pulling using a pulling eye, the maximum tensionfor a 1/C cable should not exceed 6000 lbs. The maximumtension for 2 or more conductors shall not exceed 10000lbs.

2. Basket GripThe maximum tension on copper or aluminum conductors shallnot exceed 1000 lbs. per grip or the value calculated by Eq. 1above, whichever is smaller. The limit applies to a singleconductor cable, a multiconductor cable with common overalljacket, two or more twisted cables, or paralleled cables with onebasket grip applied to the single cable or to the group.NOTE: Same as note under Pulling Eye.

3

PART II

3. Other Pulling DevicesFor pulling limitations using devices other than pulling eyes andbasket grips, the manufacturer of these devices should beconsulted. However, the limitations of Equations 1 and 2 aboveshould not be exceeded.4. Sidewall Pressure(a) The sidewall pressure (P) in general is defined as the tension

out of a bend expressed in pounds divided by the inside radiusof the bend expressed in feet. Equation 2a and 2b are for theworst case cable.

Eq. 2: P =Tro (One Single Cable)

2a: P =(3c - 2)

3Tro (Three Single Cables -Cradle Configuration)

2b: P =cT2ro (Triangular Configuration)

P = Sidewall pressure, lbs per foot of radiusTo

= Tension (leaving the bend), poundsc = Weight correction factor (Eq. 5 and 6)r = Inside radius of conduit in feet (Table 4).

Table 4Rigid Conduit and Elbow Data

Conduit

Size

Area in

Sq. In.

Conduit ID

in inches

Elbow Centerline Radius in Inches

Std. 12 15 18 24 30 36 42 48

Inside Radius - feet

1/2

3/4

1

1 1/4

1 1/2

2

2 1/2

3

3 1/2

4

5

6

0.30

0.53

0.86

1.50

2.04

3.36

4.79

7.38

9.90

12.72

20.00

28.89

0.622

0.824

1.049

1.380

1.610

2.067

2.469

3.068

3.548

4.026

5.047

6.065

0.33

0.34

0.44

0.55

0.62

0.71

0.77

0.96

1.10

1.17

1.79

2.25

0.96

0.94

0.93

0.91

1.21

1.19

1.18

1.16

1.15

1.46

1.44

1.43

1.41

1.40

1.37

1.35

1.96

1.94

1.93

1.91

1.90

1.87

1.85

1.82

2.46

2.44

2.43

2.41

2.40

2.37

2.35

2.33

2.29

2.96

2.94

2.93

2.91

2.90

2.87

2.85

2.83

2.79

2.75

3.46

3.44

3.43

3.41

3.40

3.37

3.35

3.33

3.29

3.25

3.96

3.94

3.93

3.91

3.90

3.87

3.85

3.83

3.79

3.75

(b) The maximum sidewall pressure that modern cables canwithstand without causing incipient damage is based on thenumber of cable pulled together and the size of the conductors.These recommended limits are tabulated in Table 5.

4

Table 5Maximum Sidewall Pressure - PMAX

(lbs per ft. of radius)Power Cables Conductor Size

< 8AWG > 8AWGOne Single CableTwo or More (parallel or plex)

300500

5001000

Multiconductor Power & Control Cable All SizesOne CableTwo or More Cables

5001000

Instrument Cable

Single PairMultipair

300500

NOTE: PMAX limits given in Table 5 are for use with equation 2only. If equations 2a or 2b are used the recommendedmaximum sidewall pressure limitation is 500 pounds perfoot of radius.

5. Minimum Bending Radii for Installation(a) Provided the maximum sidewall pressures have not been

exceeded, the following shall be the minimum bending radiifor installation and training of cable.

Table 6Cables Without Metallic Shielding or Armor*

Thickness of

Conductor

Insulation

Overall Diameter of Cable - Inches

1.000

and less

1.001 to

2.001

2.001

and over

inch Minimum Bending Radius as a Multiple of Cable Diameter

0.169 and less

0.170 - .310

0.311 and over

4

5

5

6

7

6

7

8

*For 5 and 8 kV non shielded cables the minimum bending radius multiplier is 8 per NEC

300-34.

5

Table 7Cables With Metallic Shielding or Armor

Power Control

Minimum Bending Radius as a Multiple of Cable Diameter

Armored, flat tape or wire type . . . . . . . . . . . . . . 12 12Armored, smooth aluminum sheath, up to0.75 inches cable diameter. . . . . . . . . . . . . . . . 10* 10*0.76 to 1.5 inches cable diameter . . . . . . . . . . . . 12 12over 1.5 inches cable diameter . . . . . . . . . . . . . . 15 15

Armored, corrugated sheath orinterlocked type . . . . . . . . . . . . . . . . . . . . . . 7 7with shielded single conductor . . . . . . . . . . . . . . 12 12with shielded multi-conductor . . . . . . . . . . . . . . . 7 7

Non-armored, flat or corrugatedtape shielded single conductor . . . . . . . . . . . . . . 12 12tape shielded multi-conductor . . . . . . . . . . . . . . . 7 7LCS with PVC jacket . . . . . . . . . . . . . . . . . . . 15 15

Non-armored, flat strap shielded . . . . . . . . . . . . . . 8 Non-armored, wire shielded . . . . . . . . . . . . . . . . 8

*with shielded conductors 12LCS = longitudinally applied corrugated shield

6. Jam Ratio (Three Single Conductors)Jam Ratio is defined for three single conductors of equal diameteras the ratio of the conduit ID to the single conductor cable OD. Thereason for concern with the jam ratio is that damage could occur toone or more of the conductors due to their jamming (wedging) inthe pipe. Jamming is not likely to occur when D/d > 3.2 andnormally does not occur when D/d < 2.8. A 40% conduit fill gives ajam ratio of 2.74. The critical range of the ratio of the conduitdiameter to the cable diameter to avoid is 2.8 to 3.2.

Eq. 3: J.R. =Conduit IDCable OD (See Table 4 for conduit ID)

6

7. Pulling Tension Calculations(a) Straight Section For a straight section, the pulling tension is

equal to the length of the straight run multiplied by the weightper foot of the cable, the coefficient of friction, and the weightcorrection factor.

Eq. 4: T = L w f cT = Total Pulling Tension of Straight Run in lbs.L = Length of Straight Run in feet.w = Weight of Cable in lbs. per ft.f = Coefficient of Frictionc = Weight Correction FactorCoefficient of friction

Dry cable or ducts: 0.5Well lubricated cable or ducts: 0.35

Weight correction factor This takes into account the added frictional forces that existbetween triangular or cradle arranged cables resulting in a greaterpulling tension than when pulling a single cable.Values of c: (For Three Single Conductors same diameter

& weight)

Eq.5: Cradled: c=1 + 4/3d

D - d

2

Eq. 6: Triangular: c=1

1-d

D d

2

D = Conduit I.D.d = Single conductor cable O.D.

7

Weight Correction Factors3 Single Conductors in Duct

8

22

PER

CENT

FILL

(%)

WEIGHT CORRECTION FACTOR (c)

DUC

TD

IAM

ETER

SIN

GLE

CON

DUC

TOR

DIA

MET

ER

3.7

3.6

3.5

3.4

3.3

3.2

3.130

25

35

40

45

48

1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

3.0

2.9

2.8

2.7

2.6

2.5

D d

JAM RATIOCRITICAL AREA

For 40% fill and less, cables are likely to be in cradledconfiguration.Triplexed cables assure the triangular configuration.(b) Tension Out of a Horizontal BendEq. 7: To

= Tin

e cfa

To

= Tension out of bendTin

=Tension coming into bendc = weight correction factor (see above)f = Coefficient of friction (see above)a = angle of change of direction in radians

produced by the bendThis is a simplified equation which ignores the weight ofthe cable. It is very accurate where the incoming tensionat a bend is equal to or greater than 10 times the productof cable weight per foot times the bend radius expressedin feet.

Eq. 8: Tin

< 10 w r (terms are all defined above)If Tin is less than 10wr, the following equation should beused for precise calculations. (These cases occur wherelight tensions enter large radii bends.)

Eq. 9: To

= Tin

e + ecfa -cfa

2

T wr

e - e

2incfa -cfa

2

2

In general, factory bends, both standard and sweepelbows, will not require use of equation 9.

8. Pulling Precautions(a) The direction of pulling cable can make a very substantial

difference in pulling tensions and sidewall pressuresdepending on the exact configuration of conduit and bends.

(b) The limitation of four (4) ninety degree bends or equivalent perthe National Electrical Code cannot be completely relied uponto guarantee safe maximum pulling tensions and sidewallpressures. Pulling tensions should be calculated in bothdirections to verify that pulling limitations have not beenexceeded.

9

(c) The minimum allowable bending radius will be determined bythe largest radius required to meet either the minimum trainingvalue or minimum allowable radius due to sidewall pressureduring or after installation.

(d) The effect of sidewall pressure must be considered whencables are hanging down vertically around a conduit bend.Supporting the cable around tight radius bends, such ascondulets, should be avoided. Considerable pressure can beexerted by the total weight of the cable in the vertical portionand sidewall pressures in this region should be limited to 120lbs./ft. of bend radius under static loading.

(e) Although rather complex formulas have been developed forbends in a vertical plane, little accuracy is sacrificed in usingequations 7 or 9 for calculating tensions out of these bends.

9. Installing Cable in TrayAs indicated in Part IV, SYSTEM CONSIDERATIONS, similardesign limits for maximum allowable pulling tensions, sidewallpressures, and minimum allowable bending radii apply to cablesinstalled in cable tray as described for cables installed in conduits.Based on field data, a simplified method for calculating pullingtensions and sidewall pressures may be used for cables to beinstalled in tray if the following assumptions are satisfied.1. Rollers are mounted over the tray and supported by the

shoulders of the tray, properly spaced to prevent the cablefrom touching the bottom of the tray.

2. The rollers or sheaves are free turning with a low coefficient offriction.

3. Where the tray changes direction sheaves are employed withradii sufficiently large to satisfy maximum allowable sidewallpressure limits and minimum bending radii requirements.

(a) If these conditions are met the pulling tension for horizontalsections of tray can be calculated as follows:

T = LwfL = total length of runw = weight of cable per foot (all conductors)f = coefficient of friction = 0.15

10

NOTE: Field data indicates that an effective coefficient of 0.15 willaccount for the low rolling friction coefficients of welldesigned and lubricated rollers and sheaves in goodoperating condition.This equation will not account for tension developed whenthe cable changes elevation, as in a vertical section, norwill it account for the tension that may be developed inpulling cable from a reel. These tensions must becalculated separately.

For changes in elevation the methods illustrated in Part III,EXAMPLE CALCULATIONS, may be used. For pulling on a slopethe coefficient, f, of 0.15 applies if the conditions outlined in (1)through (3) are satisfied. For vertical sections the weight of thecable, w, applies.(b) Tension at Cable Reel:

Since cable trays are elevated above floor level, it is commonpractice to mount the cable reel or reels at floor level and feedthe cable up to and on the cable tray in making an installation.Unless cable slack is provided at the reel either by manpoweror by a drive mechanism, tension will be developed in thecable as it is removed from the reel. This tension should betaken into account in calculating the total tension developedduring installation. The following equation is recommended:

Tr = 25 wTr = tension in cable at reelw = weight of cable per foot (all conductors)

This equation is based on the tension required to pull 50 feetof cable in a straight, horizontal section of conduit assumingan effective coefficient of friction (basic coefficient of friction (f)multiplied by the weight correction factor (c) of 0.5).

(c) Tension in Vertical Section:If cable reel is mounted at floor level directly below the startingpoint of the cable tray installation, the tension developedbetween reel and tray must be included in the calculations andis given by the following:

11

Tw = wLTw = tension due to cable weightw = weight of cable per foot (all conductors)L = length of cable between reel and tray

If the cable reel is mounted above floor level, as on the bed ofa truck, this component of tension can be reduced. In somecases the cable may be mounted below the tray but at somedistance from the starting point of the pull. Theoretically amore sophisticated method could be employed to calculatethis component of tension. However, the complexity of theprocedure and the uncertainty of parameters does not warrantsuch an approach. It is recommended that the tension becalculated as though the cable were in a vertical configuration,with the height taken as the vertical distance between cablereel and tray.

(d) Spacing of Rollers:The maximum required spacing of rollers along the cable trayroute will vary with the cable weight, the tension in the cable,the cable construction, and the height of the rollers above thetray bottom. Near the end of the pull, where the tension isapproaching the maximum value, the spacing can be greaterthan at the beginning of the pull, where the tension is aminimum.If vertical clearance permits, roller mounting brackets can befashioned to provide considerable sag clearance betweencable and tray, thus extending maximum allowable spacingbetween rollers.If one assumes a perfectly flexible cable construction, thefollowing expression can be used as an approximation indetermining the spacing interval:

s =8hTw

s = distance between rollers in feeth = height of top of roller above tray bottom in feetT = tension in poundsw = weight of cable per foot

12

NOTE: The height should be taken as the distance from the topsurface of the roller on which the cable bears to the uppersurface of the tray bottom.This equation will give a conservative result, particularly forarmored cable, assuming the value of T is correctlycalculated.In general it is not practical to establish a large number ofdifferent spacings along the tray route. It is recommended thata maximum number of three different intervals be used andthen only for the longer runs. It is also recommended thatsurplus rollers be available should the calculated spacingprove to be excessive.Whenever possible, a length of cable should be used todetermine maximum spacing permissible in the absence oftension. This will serve as a check against the equation, andprovide a means for adjusting the calculation of the totalnumber of rollers required.

(e) Bends in Cable TrayUnlike cables pulled around bends in conduit or duct, bendsaround free turning sheaves are not treated as tensionmultipliers. A multiplying affect does not occur since thesurface of the sheave(s) turns with the cable. The coefficientof friction (f) for a free turning, well lubricated sheave isassumed to approach zero. Therefore, ecfa is essential unity.Although no multiplying affect is assumed at bends in trayinstallations, an increase in tension is sometimes necessaryto account for the force required to bend the cable around thesheave.This tension adder is usually necessary for heavy, less flexiblecable. Experience has indicated that a 100 to 150 poundadder is typical for a 3/C 15 kV 500 kcmil copper conductor,metallic sheathed cable. For longer pulls having severalbends, this adder could become significant especially withrespect to sidewall pressure limitations.

13

EXAMPLECALCULATIONSIn the following examples it is assumed that rigid conduit is to beinstalled above grade.Basic coefficient of friction, f, is assumed to be .35 (for one cable instraight section of lubricated conduit).Maximum sidewall pressure due to static loading after installationis 120 lbs. per foot of bend radius for the worst case cable.

All bends equal /2 radians.Cable ConstructionOne conductor cable, 500 kcmil copper, .065 insulation, .065jacket.Net weight per foot = 1.83 lbs.OD = overall diameter = 1.10 inches = dMaximum pulling tension using pulling eye: .008 x 500,000 cmils =4000 lbs./cond. For three conductors: 4000 x 2 = 8000 lbs.If basket grips are used, the max. pulling tension is 1000 lbs./conductor for each of 2 conductors. See note on Pg. 3 whenpulling more than one conductor.

NOTE: The maximum allowable pulling tension duringinstallation may be limited by the values given for pullingeye or basket grip. However, the maximum tension maybe limited by the sidewall pressures developed in pullingcable around a bend. It is the lowest value of tension thatwill control.

If 3 nominal conduit size is used:actual ID = 3.068 = DAdd 5% for flattening at bends = 3.221 = DPercentage fill = 38.6%Jam Ratio in conduit = 2.789Jam Ratio in bend = D/d = 3.221/1.10 = 2.93

NOTE: Jam ratio is in the danger area. Use 3 12 conduit iffield bending is contemplated. Where triplexed cable isused jamming is not a problem.

15

PART III

3 12 Conduit:Actual ID = 3.548 = DAdd 5% for flattening at bends = 3.715 = DPercentage fill = 28.8% based on actual IDJam ratio in conduit = 3.548/1.10 = 3.225Jam ratio at bend = 3.725/1.10 = 3.386

NOTE: Both jam ratios are acceptable. 3 12 conduit will be utilizedin the following examples.

Minimum training radius (without static loading) for nonshieldedcable = 5 x OD = 5.50. (See Table 6).If tape shielded cable were being installed, the minimum trainingradius must be verified. (See Table 7).Minimum training radius (without static loading) for tape shieldedcable = 12 x OD = 12 x 1.10 = 13.2 or 1.1.A standard 3 12 factory elbow with an inside radius of 1.10 willsatisfy the minimum training radius requirements.NOTE: It may not satisfy either the static loading requirement or

the minimum allowable radius due to sidewall pressureduring installation. In all cases the largest radius willcontrol.

Weight correction factor c: When all three cables ride on theconduit wall during installation, it is termed a cradledconfiguration. When only two cables ride on the wall of the conduitand the third cable resides on the other two, the arrangement isdescribed as a triangular configuration. For large jam ratios, it islikely that the cables will move in a cradled configuration. In eitherconfiguration the pulling tension required will be greater than thesum of the weights when moving in a straight section of conduit,and greater than the tension out of a bend divided by the radius ofthe bend (T/R) when negotiating a change of direction.Furthermore, the pulling tension is not equally distributed amongthe three cables; and, therefore, the weight correction factor mustbe used not only to calculate increased pulling tension due to thisfact, but also to take into account the sidewall pressure on theworst case cable. For cradled configurations the middle cable isthe worst case. For triangular configurations it is actually twocables, the pair making contact with the conduit.

16

In these examples a cradled configuration is assumed:

c = 1 +43

dD - d = 1 +

43

1.13.548 - 1.1 = 1.262 2

9

Calculation ExamplesExample 1: One conductor - Figure 1Case A Pulling from A to D

Maximum Tension will occur at T4

when Pulling from A to DT1

= 0 (Assumed)T2

= L1

W f = 550 x 1.83 x .35 = 352.3T3

= T2

efa = 352.3 e.35 p/2T3

= 610.5Minimum Bend Radius r

P = T/r and r =TP

r =T

5003

=

610.5500

r = 1.22 ft. Inside radius minimum based on sidewallpressure.

Use 18 Sweep Radius (See Table 4.)To verify use of the short form tension multiplier at a bend, we testwith Eq.8:Test Is: T2

> 10 wr?w = 1.83 #/ft.r = 1.35 ft. (See Table 4)Is T2

> 10 x 1.83 x 1.35Is T2

> 24.7

Since T2

= 352.3 it is greater than 24.7 then the short form equationcan therefore be used.

T4

= T3

+ L2

W f = 610.5 + 250 x 1.83 x .35T4

= 770.6 lbs.One basket grip or pulling eye can be used.

17

Case B Pulling from D to AT4

= 0 (Assumed)T3

= 250 x 1.83 x .35T3

= 160.13 lbs.T2

= T3

efa = 160.13 x efa = 160.13 x e.35 p/2T2

= 277.48 lbs.

Minimum Bend Radius based of Sidewall Pressure:r =

T500 =

277.48500 = .55 ft.2

Standard 3 12 elbow is acceptable.Test: Is T3

> 10 Wr?160> 10 x 1.83 x 1.10160> 20.13T1

= 277.48 + 550 x 1.83 x .35T1

= 629.8 lbs.

Pulling eye or basket grip may be used.COMMENTS: Case B is the preferred direction since it produces

lower maximum tension and permits utilization of astandard factory elbow.

18

FIGURE 1 - HORIZONTAL PLANE

DIRECTION OF PULL

CASE A

T4

L1T1

D

CR

A B

L2

T3

T2

CASE B

250

500

2 (90)

Example 2: Three Cables - Figure 1Case A Pulling from A to D

T1 = 0 (Assumed)T2 = L1 N W c fLet cf=f=1.269 x .35 = .444T2 = 0.550 x 3 x 1.83 x .444 = 1341 lbs.T3 = T2 efa = 1341 x e .444 /2 = 2693 lbs.

Minimum bend requirement based on sidewall pressure:r = T3/1000 = 2692.9/1000 = 2.7 ft.A 36 radius is required.Test: Is T2

> 10 W r ?1219> 10 x 5.49 x 2.851219> 156.5T4

= T3

+ L2

Wf = 2937.6 + 250 x 3 x 1.83 x .444T4

= 3302.3 lbs.Case B Pulling from D to A

T4 = 0 (Assumed)T3 = 250 x 3 x 1.83 x .444 = 609.4T2 = 609.4 x e .444 /2 = 1224 lbs.

Minimum radius requirment based on sidewall pressure:

rmin =12241000

=1.22

A 18 sweep radius is required.Test: Is T3

> 10 W r?609> 10 x 5.49 x 1.35609> 74.1T1

= 1224 + 550 x 3 x 1.83 x .444 = 2565Pulling eye is required.COMMENTS: Case B is the preferred direction since it produces

lower maximum tension.

19

= Angle of SlopeW = Weight of BlockN = Normal Force of Slope = W cos

Normal Force Produces A FrictionForce Resisting Motion = Wf cos

NOTE: W & f in this illustration represent L N W & f inExample 3 respectively.

C = Downward Force Parallel to Slope = W sin NOTE: This force will increase the tension pulling up the slope and

decrease it pulling downward.Tup

= W (f cos + sin )Tdown

= W (f cos -sin )

20

CW

W

N

PULLING TENSION ON A SLOPEFigure 2A

FIGURE 2- VERTICAL PLANE

T1L1 R1

R2 L3

T6T5

T4

T3T2

DIRECTION OF PULL

CASE ACASE B

100 100

L 2

50

6 (30)

Example 3: Three Cables - Figure 2L2

=

50Sin =

500.5 = 100 ft.

Where =

6 and Sin

6 = 0.5

Case AT1

= 0 (Assumed)T2

= L1

W fwhere f = cf = 1.269 x .35 = .444T2

= 100 x 3 x 1.83 x .444T2

= 243.76 lbs.T3

= T2

efa = 243.76 e .444 p/6T3

= 307.56 lbs.Minimum bend radius at R1

based on sidewall pressure duringinstallation:

rmin

=

T10003

=

307.561000 = .31

Minimum bend requirements:Standard 3 12 elbow is acceptable.

Test: Is T2

>10 W r ?244> 10 x 5.49 x 1.10244> 60.39T4

= T3

+ L2

W (f cos + sin )

= 307.56 + 100 x 3 x 1.83 .444 x3

2 + .5

T4

= 793.16 lbs.See Figure 2A for calculating tension developed on a slope

T5

= 793.16 e.444 p/6T5

= 1000.75

21

Minimum bend at R2

based on sidewall pressure:

rmin

=

T1000 =

1000.751000 = 1.0' minimum5

A standard 3 12 elbow is acceptable.Test: Is T4

> 10 W r ?793> 10 x 5.49 x 1.1793> 60.39

At R2 the sidewall pressure from static loading must beconsidered. If sin is greater than f cos the cables will tend toslide downward therefore a permanent static loading exists and aminimum training radius based on a maximum sidewall pressurelimited to 120 lbs. per foot of bend radius for the worst cable mustbe satisfied.

f cos = .444 cos 30 = .385sin = .5

Static Loading = (.5 - .385) 100 x 3 x 1.83 = 63.14 lbs.

Minimum r =3 x 1.269 - 2

3 x 120

63.14 = .317 ft.

Sidewall pressure during installation will control. The standard3 12 elbow is acceptable.

T6 = T5 + L3 W f = 1000.75 + 100 x 5.49 x .444T6 = 1244.51 lbs.

Use a pulling eye or 3 basket grips, one per cable.Case B

T6 = 0 (Assumed)T5 = 100 x 5.49 x .444T5 = 243.76 lbs.T4 = 243.76 x e .444 /6 = 307.56

Minimum bend radius at R2 based on sidewall pressure:rmin =

307.561000

= .31 ft. minimum

Standard 3 12 elbow is adequate.

22

Test: Is T5

> 10 W r ?244> 10 x 5.49 x 1.10244> 60.39T3

= T4

+ L2

W (f cos - sin )

= 307.56 + 100 X 3 X 1.83 .444 x3

2 -.5

T3

= 244.16Note that the tension has been reduced in this case. This is notalways so, depending on the values of f and .

T2

= 244.16 x e .444 p/6T2

= 308.06Minimum bend radius at R1

based on sidewall pressure:

rmin

=

308.061000 = .31 ft.

Standard 3 12 elbow is acceptable.Test: Is T3

> 10 W r ?244> 10 x 5.49 x 1.10244> 60.39T1

= 308.06 + (100 x 5.49 x .444)T1

= 551.82 lbs.

One basket grip or pulling eye can be used.

23

FIGURE 3- VERTICAL PLANE

L1T1 T2

R2

R1

L2

T4

L3

T3

T6T5DIRECTION OF PULL

CASE ACASE B

50

50

400

2 (90)

2 (90)

Example 4: Figure 3Case A

T1

= 0 (Assumed)T2

= L1 Wf = 400 x 3 x 1.83 x .444T2

= 975.02 lbsT3

= T2

efa=

975.02 x e .444 p/2T3

= 1958.81Minimum bend radius at R1

based on sidewall pressure:

rmin

=

1958.811000

rmin

= 1.96 ft.A 30 sweep elbow is required.Test: Is T2

> 10 W r ?975> 10 x 5.49 x 2.35975> 129.02T4

= T3

+ L2

W = 1958.81 + 50 x 5.49T4

= 2233.31NOTE: In the vertical section the full cable weight is used.

T5

= T4

efa = 2233.31 e .444 (p/2)T5

= 4486.72Minimum bend radius at R2

based on the sidewall pressure:

rmin

=

4486.721000

= 4.49 ft.

Test: Is T4 > 10 W r ?2233> 10 x 5.49 x 4.492233> 246.5

This requires a special sweep. It must be determined whether thissweep can be accomplished in the field with a standard 10conduit length.

S = rwhere: s = arc length in feet

24

r = radius of bend in feet = angle of bend in radians

If a 1 straight section on both ends of a 10 conduit is sufficient forthe bending machine S = 8.

r =S90 =

8/ 2 = 5.09 ft.

This would satisfy the minimum radius at R2.If an 18 machine clearance is required at both ends

S = 7 andr =

7/ 2 = 4.46 ft.

This would not satisfy the requirements at R2.T6

= T5

+ L3

W f= 4486.72 + 50 x 5.49 x .444

T6

= 4608.6 lbs.If the minimum radius of R2 is satisfied, the cable must be pulledusing a pulling eye. Assuming the cable is installed it is nownecessary to determine if the forces are in equilibrium.Friction Force in L3

= 50 X 5.49 X .444 = 121.88 lbs.Force required to pull downward around R2

:= 121.88 e .444 p/2 = 244.86 lbs.

Cable weight in vertical section L2

:= L2

W = 50 x 5.49 = 274.50 lbs.Net downward force = 274.50 - 244.86 = 29.64 lbs.

Based on effective coefficient of friction (f) of .444 the forces arenot in equilibrium. Although the static coefficient of friction will behigher than .444 and the net downward force as calculated -29.64lbs. is not substantial, the cable should be secured at the uppertermination by means of basket grips. For such application themaximum load is 400 pounds per cable with one grip attached toeach cable. Two layers of half lapped tape should be wrappedover the cable jacket to serve as a bedding for the grips, sufficientin length to extend 6 beyond the ends of the grips.The static load at R2 must also be examined based on a sidewallpressure limit of 120 pounds per foot of bend radius for the worstcase cable.

25

Cable weight in vertical section L2

= 274.50 lbs.

rmin

=

3 c - 23 x P

T=3 x 1.269 - 2

3 x 120

274.5

rmin

= 1.38This is a smaller value than that found for the sidewall pressureduring installation. The minimum allowable radius is 4.49 ft.Case B

T6

= 0 (Assumed)T5

= 50 x 5.49 x .444T5

= 121.88 lbs.T4

= 121.88 e .444 p/2T4

= 244.86 lbs.Minimum bend radius at R2

:

rmin

=

244.861000 = .24 ft.

rmin

= .24 ft. based on sidewall pressure duringinstallation.

The minimum allowable radius is determined by static loading andis 1.38. See case A. A 24 factory sweep radius may be used.Test: Is T5 > 10 W r ?

122> 10 x 5.49 x 1.85122> 101.57T3

= T4

minus vertical load = 244.86 274.50T3

= -29.64 lbs.During installation it will be necessary to brake the reel. Assumethe reel is braked sufficiently to provide the equivalent of 50 feet ofhorizontal pulling tension, and assume that this net positivetension is developed at the bottom of the vertical section enteringR1 at T3.

T3

= L W f = 50 x 3 x 1.83 x .444T3

= 121.88 lbsT2

= T3

efa = 121.88 e .444 p/2T2

= 244.86Minimum bending radius at R1

based on sidewall pressure:

rmin =244.861000 = .245 ft.

26

Standard 3 12 elbow is acceptableTest: Is T3

> 10 W r ?122> 10 x 5.49 x 1.10122> 60.39T1

= 244.86 + 400 ft. x 5.49 x .444T1

= 1219.9 lbs.A pulling eye or basket grips may be used. Once the cable isinstalled, the static loading and supports at the upper end will bethe same as in Case A.

Example 5: Figure 4Case A

T1

= 0 (Assumed)T2

= L1

Wf = 5 x 5.49 x .444T2

= 12.2 lbs.T3

= T2

e fa = 12.20 e .444 p/2 = 24.51For this example, involving several short sections, it is convenientto confirm use of the short form equation, e fa, by solving for theminimum incoming tension to satisfy Tin> 10 W r assuming R1 =1.10; the inside of a standard 3 12 conduit elbow.Test: Is T> 10 x 5.49 x 1.10

Tmin

= 60.39 lbs.

27

FIGURE 4- HORIZONTAL PLANE

ALL BENDS

R4

R3R2

R1

L2T4

T9

L4

L5

L3

T3

T8

T6T5T7

T10

T1T2

L1

DIRECTION OF PULL

CASE ACASE B

200

2 (90)

5

5

5

5

Since the tension at T2

is only 12.2 lbs. the complete equation isrequired for a rigorous solution.

T3

= T2

e + e

2

f'a - f'a

+ T + (Wr)2

2

2

e - e

2

fa - fa

e fa = e .444 p/2 = 2.009e -fa = 1/e fa = .498(Wr)2 = (5.49 x 1.1)2 36.47T3

= 12.22.01 + .50

2

+ (12.2) + 36.472 2.01 - .502

T3

= 25.59This compares with a value of 24.51 based on the simplifiedequation.Even though some error is introduced by use of the short form itmay be concluded that for short radius bends and relatively lightweights of cable, the error is negligible. However, for low incomingtensions and very large bend radii the complete equation shouldbe used.In calculations for determining minimum bend radii to limit sidewallpressure it is often convenient to determine the maximumallowable tension out of the standard factory bend radius.From equation 2: To = P rfor 3 12 conduit r = 1.1

P Max = 1000 from Table 5and To = 1000 (1.1) = 11003 12 standard elbow is acceptable.

T4 = T3 + L2 W f = 24.51 + 12.2Note that each 5 foot straight section accumulates 12.2pounds tension.T4 = 36.71 lbsT5 = T4 e fa = 36.71 e .444 /2 = 73.75 lbs.

3 12 standard elbow is acceptable.T6 = T5 + L3 W f = 73.75 + 12.20T6 = 85.95 lbsT7 = T6 e fa = 85.95 e .444 /2T7 = 172.67 lbs.

28

3 12 standard elbow is acceptable.T8 = T7 + L4 W f = 172.67 + 12.20T8 = 184.87 lbs.T9 = T8 e fa = 184.87 e .444 /2 = 371.4 lbs.

3 12 standard elbow is acceptable.T10 = T9 + L5 W f = 371.4 + 200 x 3 x 1.83 x .444T10 = 858.91

Cable may be installed with one basket grip or pulling eye.Case B

T10 = 0 (Assumed)T9 = L5 W f = 200 x 3 x 1.83 x .444 = 487.51T8 = 487.51 e .444 /2 = 979.41 lbs.

3 12 standard elbow is acceptable.T7 = 979.41 + 12.2 = 991.61 lbs.T6 = 991.61 e .444 /2 = 1992.14R3 =

1992.141000 = 1.99 ft. minimum

A 30 sweep radius is requiredTest: Is T7

> 10 W r ?1992> 10 x 5.49 x 2.351992> 129.0

T5

= 1992.14 + 12.2 = 2004.34T4

= 2004.34 e .444 p/2 = 4026.72R2

=

4026.721000 = 4.03 ft. minimum

A special sweep radius is required.Test: Is T5

> 10 W r?2004> 10 x 5.49 x 4.032004> 221.2T3

= 4026.72 + 12.2 = 4038.92T2

= 4038.92 e .444 p/2 = 8114.19R1

=

8114.191000 = 8.11 ft. minimum

29

These last bends would require a special sweep of extendedconduit length and strongly suggests that installing the cable inthis direction in one length is not feasible.Test: Is T3

> 10 W r ?4039> 10 x 5.49 x 8.114039> 445.2

In addition to a monumental bend radius requirement themaximum allowable pulling tension of 8000 pounds is exceeded.

T1 = 8114.19 + 12.2 = 8126.39 lbs.Example 5 illustrates two interesting and significant points:1. The direction of pulling cable can make a very substantial

difference in pulling tensions and sidewall pressures,depending on the exact configuration of conduit and bends.

2. Case B illustrates that the limitation of four (4) ninety degreebends or equivalent per NEC cannot be relied upon to assurelimiting pulling tensions and sidewall pressures to safe values.If the cable is pulled in the Case A direction, several additionalbends can be added, assuming 5 foot straight sectionsbetween bends, without posing insurmountable problems. Forcase A the limitation of four ninety degree bends is undulyrestrictive. For Case B it is far too generous.

For the five examples given it should be observed that incomingtension at the feed end has been assumed to be zero. Thecalculations indicate that this is highly desirable to hold theincoming pulling tensions to minimum values. If calculations aremade on this assumption, then the installation procedure mustassure this condition.In all the examples the pulls have been completed out of a straightsection of conduit. In the practical case, however, a ninety degreebend is frequently encountered at the end of the pull. As hasalready been shown, in some detail, each change of direction in aconduit run acts as a multiplier of the incoming tension at thatpoint. Consider the effect of a ninety degree bend at the pullingend of Case B, Example 5. The multiplying effects of this bend is2.009, and with an incoming tension of 8126.39 calculated for T1,the tension out of such an additional bend would be 16,325.92pounds. Avoid the nineties at the ends of the pulls whereverpossible.

30

Example 6: Cable in Tray See Fig. 5Given a 3/C - 500 kcmil copper 15kV - 133% Level armored cable(Type MV-105 or MC approved for cable tray use per NEC)Approximate OD = 3.60 inNet Weight per Foot = 8.67 lb.Minimum Bend Radius: 7 x OD (during installation) or larger tosatisfy the maximum allowable sidewall pressure limit. OD = 7 x3.6 in. = 25.2Effective Cable Weight: wf = 8.67 x .15 = 1.30 lb. MaximumSidewall Pressure: 1000 lb. per foot of bend radius for threeconductor cable. With a radius of 3 ft. for all sheaves the maximumpulling tension is 3000 lbs.

A precise calculation of the effective distance h between cablereel and sheave shown in Fig. 5 could be made at the start of thepull, if reel and sheave dimensions, A-frame or reel jack details areknown, and if the mounting height of rollers on the cable tray isestablished. Even so the actual height will change as successivelayers are removed from the reel. In general it is sufficiently

31

T1

T3T4

T3

NTS

DIRECTION OF PULLCASE ACASE B

300 200

30 ft.

h30 ft.

FIGURE 5 - VERTICAL PLANE

accurate to treat the cable tray elevation above the floor as h,unless the cable reel is elevated above normal floor mountingheight.The following calculations assume that properly sized sheavesare installed securely in place to accommodate changes indirection along the cable tray route.Case A

Tr

= 25w = 25 x 8.67 lb. = 217 lb.This assumes that cable is removed from the reel undertension from the pulling end.

Ta

= 125 lbs. Assumed tension adder for bends.Tw

= wt/ft of cable times heightT1

= Tr

+ Tw

+ Ta

= 217 + 30 x 8.67 + 125 = 602 lb.T2

= T1

+ 300 x 1.3 + Ta

= 602 x + 390 + 125 = 1117 lb.T3

= T2

+ Tw

+ Ta

= 1117 + 30 x 8.67 + 125 = 1502 lb.T4

= T3

+ 200 x 1.3 = 1502 + 260 = 1762Use pulling eye on conductors and install basket grip over metalsheath securely attached to pulling line.Case B

Tr

= 25w = 217 lb.T4

= Tr

+ Tw

+ Ta

= 217 + 60 x 8.67 + 125 = 862 lb.T3

= T4

= 200 x 1.3 + 125 = 1247 lb.T2

= T3

- Tw

+ Ta

= 1247 - 30 x 8.67 + 125 = 1112 lb.T1

= T2

+ 300 x 1.3 = 1502 lb.Use pulling eyes on conductors and install basket grip over metalsheath securely attached to pulling line.Difference in tension = 1762 - 1502 = 260 lb.Even though the bends are not treated as tension multipliers thedirection of pull affects the total tension. In Case A the cable israised 60 ft. vertically. In Case B the cable is raised a net height ofonly 30 ft. with respect to pulling tension.Theoretically the distance around the sheaves should be includedin the computation. However, in the practical case the totaldistance involved in relatively short, and adds little to the totaltension.

32

SystemConsiderationsIntroductionInsulated conductors often fail because of mechanical damagedue to improper raceway and terminal design, or to improperinstallation techniques. There is an ongoing trend toward reducedinsulation thickness which makes it increasingly important toobserve established limitations on the physical treatment of thesecables. It is highly desirable to make these cables damage-proof,but that is beyond the present state of the art, particularly sincethere are a number of other criteria these cables must satisfy:Long service life under voltage stress and heat aging, flameretardance, thermal stability, dielectric strength, are some of therequirements that come to mind. This is to say nothing of thespecial requirements for nuclear power plants such as radiationresistance and performance during a Loss of Coolant Accident. Inachieving these requirements some limits are imposed on themechanical durability of the cable, and these limits must berecognized.Cable in ConduitThe maximum allowable limits of pulling tension and sidewallpressure are given in Part II. Equations are also given forcalculating the anticipated values when the cable is installed.Equation 7 of Part II demonstrates that a bend in a conduit run actsas a multiplier of incoming tension. The examples in Part IIIdemonstrate that the direction of pulling can have significantinfluence on the tensions and pressures generated.The total pulling tension in a straight section of conduit may not beshared equally by the cables. In the case of three cables intriangular configuration one cable can get a free ride. Even for thecase of cradled configuration the tensions will not be equal sincethe center cable has a higher effective coefficient of friction thanthe other two. For three cables in conduit it should be assumedthat the total tension is sustained by two of the three cables.

33

PART IV

Weight correction factor, c, (Part II - Equations 5 and 6) expressesmathematically the fact that where two or more cables rest in aconduit the sum of the normal forces developed between cablesand conduit is greater than the sum of cable weights. This factor,greater than unity, has three significant consequences: (1) itoperates to increase the effective weight of the cable in a straightpull, (2) it increases the tension generated in pulling cable arounda bend; and (3) it increases the sidewall pressure on the worstcase cable or cables.The equations of Part II clearly show that the minimum allowablebend radius will be determined by either the allowable trainingradius with or without static loading, or by maximum allowablesidewall pressure during installation, whichever of these criteriarequire the largest radius at each bend. Factory elbows, bothstandard and sweep elbows, for the various nominal conduit sizesare given in Table 4. This table shows the radius to the inside ofthe bend, the value to be used in calculating sidewall pressures.Sizing of Conduit - Jam RatioWhere three cables of equal diameter are to be installed and thesum of the three diameters are approximately equal to the insidediameter of the conduit one cable can be wedged between theother two and serious cable damage can occur. For the case ofthree cables of equal diameter it is conventional to express thejam ratio as the ratio of the inside diameter of conduit to thediameter of one cable. Expressed in this way the prospect ofjamming increased as the ratio approaches 3. Jamming is stillpossible for ratios greater than three and it is recommended thatjam ratios between 2.8 and 3.2 be avoided in the sizing of conduit.For precisely 40% Code fill the jam ratio is 2.739.Oversizing of conduit with the consequent increase of jam ratioshould be carefully analyzed to avoid the hazardous range. Forthe installation of more than three cables jamming is still possible.but experience suggests that the case of three cables representsthe greatest hazard. Obviously, the cables need not be of thesame diameter, and an analysis based on the sum of the threediameters to the inside conduit diameter is then required.

34

Jamming is not possible when the cables are triplexed by themanufacturer, providing the conduit fill limit is not exceeded.Layout and CalculationsThe layout of cable raceway system and calculations to predictpulling tensions and sidewall pressures should be regarded astwo facets of the same design process.Conduit Bends - Minimum RadiiFactory elbows may not be available to satisfy sidewall pressurelimitations. Conduit sweeps, produced in the field may berequired, but required bend radii may be prohibitively large. Analternate design should be carefully considered that contemplatesthe use of a concrete trench under switchgear, motor controlcenters, and other terminals, sufficiently wide from front to back toallow pulling the cable into the trench with sufficient cable toprovide required makeup. The back wall of such a trench can beprovided with eyes to accommodate the pulls. Where the requiredwidth of the trench is greater than the free standing equipment, asteel cover plate can be used and supports can be provided tohold the cable above the bottom of the trench. In addition toeliminating the sidewall pressure problem at the pulling end, thisdesign can offer attractive economies by elimination of elbows.Junction BoxesCare must be given to the sizing and location of junction boxes. Itmust be remembered that junction boxes are not designed to pullthrough or pull around. They are intended for junction or splicepoints. If an enclosure is to be used as a pull box, then carefulattention should be given to the box or feeding into the box. If ajunction box is installed in a run and then cable is pulled through it,it is possible that the box should have been omitted from thedesign.Standard ConduletsIn general, these enclosures should be treated with care. Exceptfor the straight through type, cable should never be pulled throughthem and minimum prescribed bending radii for installed cablemust be reviewed. Violations occur regularly in condulets.

35

Unsupported Cable in Vertical Conduit RisersInsulated cables are frequently damaged where overheadhorizontal conduit runs turn down to terminal enclosures. Ifcondulets are used for the ninety degree turns and the risers aremore than a few feet, damage can occur from the cable weight.Junction boxes and wireways can also produce the same kind ofdamage unless special cable supports are provided in theenclosures. Conduit bushings are not adequate and are notdesigned for that purpose.ManholesJudicious placement of manholes in a duct system is obviously animportant criterion for good design. Regrettably manholes areoften included in a system which are not require, and sometimesomitted where they are critically needed. The inclusion of anintermediate manhole between Point A and Point B in a duct banksystem adds substantially to the cost, complicates cableinstallation, and can produce cable damage.The chief cause for inclusion of extra manholes is failure to makepulling tension calculations during the design phase. In theinstallation phase the installer will be tempted to pull from manholeA through the intermediate manhole to manhole B, and employ asplit basket grip or line grip to acquire slack for training the cable inthe intermediate manhole. Such a procedure can damage thecable.Corresponding duct segments, in and out of the manhole, arerarely in true alignment. In pulling the cable through the manhole,failure to align the cable by means of properly sized sheaves canlead to cable damage. Recessed duct entries with flared openingin the concrete by means of bells or wooden plug can sometimealleviate this specific problem. But use of a basket grip or line toprovide slack will very frequently exceed the maximum allowable1000 pound limit, due partly to the fact that an entire section ofcable will have to be accelerated from rest, due partly to the factthat static friction is significantly higher than sliding friction, andoften due to the length of the cable section.Whenever an intermediate manhole is included in a straightsection of duct bank between two point, A and B, a decision

36

should be made at the time of design whether this is to be a splicepoint or a point for feeding the cable in both directions. The intentshould be so stated and specified for the installer.Using the intermediate manhole for a feed point poses problems.The typical manhole will have a 30 inch manhole cover with a clearopening of approximately 29 inches. With care the cable can befed through the opening from the lead off end to the reel of cable.But feeding the inner end of the cable into the manhole for pullingin another direction will require bending the cable into a radius of14 12 inches maximum. It is true that cable can be benttemporarily into a tighter radius than the limits specified forpermanent in-place training in accordance with the limits forshipment of cables on reels. See ICEA S-68-516 Part 8. In nocase, however, should this minimum bending radius be violated.And even assuming that this minimum radius can be satisfied, theinner end of the cable will have to be removed from the reel andusually this will involve dragging that portion of the cable over theground. Damage can occur during this phase of installation andsuch design should be avoided. A proper splice at theintermediate manhole is preferable to the risk of cable damage.Manholes are sometimes used for producing a turn in the directionof a duct bank, perhaps most frequently a ninety degree turn. Andjust as frequently the cable will be pulled through such a manholeand the turn negotiated by means of a sheave installed in themanhole. Recalling the size of a manhole opening and thelimitations on sidewall pressure, it is not difficult to imagine thatthis situation can represent a flagrant abuse of sidewall pressurelimitations. Given a standard sheave of 24 inch nominal diameter,the effective inside radius is approximately 912

inches. Themaximum sidewall pressures given by Table 5 in Part II for cablesheaves impose limitations that are frequently violated.Undeniably, these limits place substantial restrictions on thedesigner and the installer, but the problem should be recognizedand anticipated.In new construction it is often feasible to delay installation ofmanhole roofs until the cable has been installed. This will facilitateuse of sheaves with adequate bend radii, and simplify bothfeeding and pulling at a manhole.

37

As an alternative the cable can be spliced. It is far better to includesplices in accessible locations than to damage cable that mayreside in the middle of a duct run. Even if a splice is questionable,it is accessible in the manhole and can be repaired withoutdisturbing the cable in duct and without cable replacement,providing sufficient slack is provided in the manhole, and providedmanhole design offers adequate space.An alternative to using manholes for direction change of duct runsis to use sweeping bends of large radii and eliminate themanholes. When non-metallic conduit is used this is easilyaccomplished at considerable cost saving. Pulling tensions will beincreased, but sidewall pressure limitations can be satisfied withthe large bend radii, and recognizing that sidewall pressurelimitations usually control, judicious elimination of unnecessarymanholes represent sound engineering design.Splicing Cable in ManholesSplice points in a circuit should be included in the design andspecified. In these manholes, slack should be provided for theeventuality of a splice repair. Some electric utilities follow thepractice of installing a complete loop of cable per leg on one sideof a splice. Splices should be staggered horizontally and beinstalled with adequate clearance vertically to facilitate not onlythe original installation but subsequent repair or replacement,should this be necessary. These details should be designed andspecified.Cable Terminations in EnclosuresEconomics in the manufacture of switchgear, motor controlcenters, control devices and a wide variety of related equipmentdictate that their enclosures be held to tight limits. The physicalspace for the installation of such equipment may also conspire toreduce the size of such equipment. The unfortunate result is thatall too often the space provided for the termination of cablesmakes it impossible for the installer to satisfy minimum bendingradii for the training of cables into their final, installedconfiguration. The installer can hardly be held responsible forerrors of design, but this does not solve the problem.Even where physical space will permit larger enclosures thequestion of space within the enclosure for cable termination can

38

be overlooked by the designer. Consider the case of switchgearand cable run in conduits below grade. How often the spaceprovided for termination of cables simply does not permitsatisfying minimum training radii for the cables. A review of shopdrawings at the time of submittal and before manufacture cansolve such a problem by insisting on adequate vertical clearance.Cables in Trays and LaddersThe same limitations of pulling tensions and sidewall pressuresapply for cable in tray as for cable in conduit. Attention must begiven to the length of runs, the number of turns and the size ofsheaves used for pulling cable around these turns toaccommodate changes in direction. Sheaves are often used asrollers in horizontal sections and for bends either concave upwardor concave downward in connecting horizontal and verticalsections of tray. If trays are stacked vertically without sufficientclearance the installation of such rollers can be difficult if notimpossible.The use of trapeze hangers involving two vertical members for thehanger, one on each side of the tray, makes it impossible to laycable into the tray and the cable must be pulled into place. The useof catilevered supports should be given careful consideration,especially where placement of sheaves and pulling of cable isdifficult.Cable Tray BendsPulling sheaves of adequate diameter should be used in pullingcable around bends in cable tray. The minimum allowablediameters should be determined by calculation of sidewallpressures and these values compared with minimum allowabletraining radii of the cables once they are installed. See Part IITables 5, 6 & 7 and Part III. The inside radius of a cable tray bendcan violate the in-place allowable radius for a cable, even though asheave of adequate radius was used in the pulling of the cable.Fastening of Cable in TraysThe use of nylon fasteners for securing cables in cable trays hasbecome popular. Their use is acceptable providing that thetension developed in applying the fastener is not excessive.Torque limiting tools are available for use with the fasteners. Theiruse should be specified together with a provision in the

39

specifications that excessive tension with the consequentdeformation of cable will not be permitted.Cable Sheaves and Cable Sheave AssembliesAs indicated in other sections of this manual, it is often necessaryto pull around bends in cable tray or to change direction in amanhole. Excessive sidewall pressure can result in damage to thecable. Sidewall pressure can be minimized by the use of a largeradius sheave. Unfortunately, large radius sheaves are oftenimpractical since they may not fit inside a manhole or cannot berigged in congested tray runs. Even if they can fit, they are oftenunavailable. To alleviate this problem, multiple smaller sheavesare placed on a radius. This device is known as a radius-typecable sheave assembly.Precautions must be followed when using a radius type cablesheave assembly to prevent damage due to excessive sidewallpressure around the individual sheaves. Each individual sheaveshould have an inside radius of a least 114

inches. The assemblyshould consist of a least one sheave per 20 of bend. The practiceof using a three sheave assembly to make a 90 bend should beprohibited.Cable FailuresA great many cases of cable failure are directly attributable todamage caused by their installation, occurring either duringinstallation, or as a result of their in-place configuration withsubsequent cable breakdown. Very often the damage can bedirectly attributed to improper raceway design.Installers as DesignersIt is fully recognized that in many instances the installer does thedesign work; at least the routing and size of raceway, the choiceand location of junction boxes, the direction of pulling cable. Theinstaller, for example, is frequently left to his own devices to routea 4-inch feeder conduit that must be installed from point A to pointB. Often the stage of construction and the nature of the structurewill make such an installation a real challenge that can be hailedas a triumph in mechanical ingenuity when once accomplished.But the raceway serves no useful purpose if the cable cannot beinstalled without damage. All too often pulling calculations, if theyare made at all, are done after the raceway is installed, a

40

dynamometer is not used, and the cable is worried into place.Hopefully it will survive, but sometimes it does not.If the conduit installer is to route the conduit, select appropriatefittings, determine the size and location of boxes, and decide thenumber of slices required, he must be more than a good pipeman. He must also be a good cable man, conversant with thenecessary limitations imposed on its installation and the methodsfor predicting whether these limits will be exceeded when thecable is installed. He must recognize that every change ofdirection in a conduit run increases the pulling tension, and eachof these bends or offsets or saddles or swings not only increasesthe tension but also produces a sidewall pressure on the cable, atension or a pressure or both that may damage the cable.The installation of conduit in concrete and the installation ofoverhead exposed conduit represent the worst cases where manychanges in direction may occur simply to avoid obstacles.Consider the simple case of two junction boxes surface mountedon the wall of a structure at the same elevation and an exposedconduit must be installed between the boxes. Consider further thattwo vertical columns lie in the path of the conduit. In standardinstallation this will involve two bends at each box, one offset perbox, and four bends at each column. If the offsets and saddles areheld close to the boxes and columns to make the job lookaesthetic, one might expect two 45 degree bends at each box andfour 60 degree bends at each saddle. This run represents a totalangular change of direction of 540 degrees. Such an installationdoes not satisfy the National Electrical Code where a limitation offour ninety degree bends or their equivalent is specified. But asidefrom this restriction, which is not a reliable index to pulling tensionsand sidewall pressures, consider what might have been done toeliminate all bends in the run. Instead of using standard 4-inchsquare boxes, suppose that special boxes of adequate depth hadbeen used and that appropriate blocking was placed between theconduit and the wall for supporting the conduit. With such aninstallation a straight conduit run could be achieved from box tobox without offsets or saddles.This is a simple case. Many conduit installations are not so simple.But a competent installer will call for help in those situations where

41

pulling tensions and/or sidewall pressures are likely to beexcessive. He will know that the greater the change in direction(the larger the angle) the greater the increase in tension at thebend. He will also know that the smaller the radius of bend thegreater will be the sidewall pressure on the cable in that bend. Hewill, therefore, hold the bends to the minimum, and, whereunavoidable, will keep the angle of bend as small as possible andthe radius of bend as large as possible.

42

INSTALLATIONGood design of a raceway system is the first step in the properinstallation of cables. But good design alone will not guaranteethat the cable will be installed and connected without damage.Conduit InstallationAdequate reaming of metallic conduit and cleaning to removecuttings, fillings, and cutting oil are required. Field bending ofconduit must provide bends of acceptable radii without undueflattening of the conduit. Conduits should be capped prior to cableinstallation to avert the presence of dirt and rocks.Non-metallic ducts in underground installations should bemandreled and swabbed to confirm the integrity of the duct runsprior to installation. Manholes should be cleaned prior to cableinstallation and the proper location of pulling eyes in the manholeshould be confirmed.Pulling EquipmentThe installer should be familiar with all pulling equipmentnecessary for the cable pull and all safety precautions associatedwith it.

Suitable pulling equipment, confirmed to be in good workingconditions, should be on hand. Hydraulic pulling equipment withsmooth, variable speed control is recommended.The pulling line should be adequately sized to safely pull the cableinto the raceway. The pulling line should be high strength, lowstretch and abrasion resistant. Polypropylene pulling line is oftenselected for general use. Manila hemp is satisfactory although ithas a lower tensile strength than polypropylene. Ropes made ofaramid and some polyesters are also very good. Unstressed nylonis not acceptable due to its high stretch characteristics.Pulling lines under tension can sometime impart a torque on thecable which may cause cable rotation. The proper use of anadequately sized swivel joint placed between the line and thecable pulling eye/bolt should prevent this condition. A torquebalance pulling line will also help eliminate cable rotation.

43

PART V

A dynamometer to measure the pulling tensions should be used atthe pulling end of the installation and the value recorded for eachpull. Three sheave, direct-reading dynamometers are available,but many in general use are not of the direct-reading type. Themethod for translating the dynamometer reading to actual pullingtension is given in Appendix 1.Cable in StorageProper storage and handling of cable prior to installation isrequired. Many instances of cable damage occur in moving reels,especially where fork lift trucks are used. Frequently cable isdamaged when accidentally dropped from a loading dock or atruck bed.Setting Up for a PullIn this phase of the operation it is critical that the correct pullingdirection has been determined in conformance with thecalculations for pulling tensions and sidewall pressures.Moving the cable reels into proper positions requires care.Damage has often occurred in this operation, especially if a pulland cut method of operation is used for several pulls at differentlocations. Once the protective covering is removed from a reel, thecable is particularly vulnerable.For cable on reels, reel jacks or other adequate means must beutilized to support an axle to provide minimal friction. The axlemust be properly selected to carry the load with minimal deflectionin order to avoid excessive rotational friction between reel andaxle.

The operation must necessarily include proper procedures forfeeding the cable into the conduit. Manhandling the cable, one ormore journeymen per reel, may be entirely adequate to feed thecable into the raceway with zero tension at the point of feed.Often a flexible cable guide or feed in tube is used when pullingcables from above grade, into a manhole and to the undergroundduct. The guide must be appropriately sized for the cable beingpulled and the duct. A properly sized bell adapter and a ductadapter must also be used with the guide to assure the cable is notdamaged either entering or exiting the guide. Cable must be fedinto the guide with little or no back tension.

44

Consider the case of feeding three 500 kcmil cables into a surfacemounted junction box thirty feet above the floor. A feed-in tube andproperly sized sheaves will be required to do a proper job if thecable reels are set up on the floor below. Pulling the cable from thefloor into the box without proper rigging produces considerabletension in the cable at point of conduit entry and will very probablydamage the cable at that point. Pipe rollers are frequently used,but in general they are not acceptable. A single 4-inch pipe nipplerotating on a smaller nipple, used as an axle, provides a bendingradius well below the minimum training radius for these installedcable, with the rotational friction being relatively high. This is to saynothing of the sidewall pressures that would be generated duringinstallation.

Approved lubrication in ample quantity must be on hand inpreparation for the installation.Pulling equipment must be set in proper position to accommodatethe rigging of the dynamometer.For short, easy runs, pulling by hand may be satisfactory, but for arun of substantial length or one involving several changes ofdirection, proper pulling equipment is preferred. Pulling by handmoves the cable by jerks and stops, while the application of manyhands to the pulling line can damage the cable.Cable Pulling DevicesManufacturers can provide a pulling eye or pulling bolt to theleading end of the cable on the reel. These devices usually consistof a long barrel aluminum ferrule which is compressed onto theexposed conductor. A temporary seal is made over the remainingexposed conductor using tape and/or a heat shrink sleeve. Thisseal is to help prevent water from entering the cable during thepull.Once the cable has been installed, the pulling attachment is to beremoved and the cable cut end resealed.The factory applied pulling device having gone through the rigorsof installation, cannot be considered a permanent water tight seal.

45

Pulling the CableIt is important that two-way voice communication is availablebefore and during the installation.Cable should be pulled at constant velocity, not to exceed 50 feetper minute and not to be less than 15 feet per minute.At the beginning of the pull the angle formed between the twosegments of pulling line around the sheave in the dynamometermust be carefully estimated and recorded to accurately translatethe dynamometer reading to pull tension. Dynamometer readingsshould be taken periodically during the pull and recorded.If basket grips are used, sufficient slack must be pulled to removeat least one foot of cable beyond the inside end of the grip.At the feed end during the pull, care must be exercised to avoidcrossovers in the cable.Lubricant should be applied liberally and continuously during thepull.Pulling through manholes should be avoided. Whether the pull isstraight through or around a bend the cable can be damaged. Ineither case slack will be required and getting this slack after thecable is pulled from feed point to pulling point can damage thecable. If sheaves are used in manholes to change direction theymust be of proper size. Trolley assemblies consisting of severalsmall diameter sheaves mounted in an assembly given theappearance of increasing the radius of bend, but this is deceptive.Care must be taken so that the apparent overall radius of thesheave arrangement does not violate any of the criteria forminimum bending radius.When using these sheave assemblies, the maximum sidewallpressure for the apparent overall radius shall not be exceeded.Even though good quality sheaves are treated as frictionless andtension increase is not imputed to them, extreme care and goodjudgment must be exercised in their use.Once the cable is pulled, steps must be taken to protect it. Cable isfrequently damaged during this phase of the installation,particularly if it is not trained into final position and terminated or

46

spliced immediately. Consider as one example cable pulled into apull box above switchgear with sufficient slack to be installedsubsequently in riser conduits extending from the top of theswitchgear. During this period the relatively long lengths of cableare allowed to hang out the face of the box and over an edge of thebox. In order to keep the space below clear, the cable is coiled andtied below the box awaiting a more convenient time for installationin the switchgear. This practice and practices like it have causeddamage.ConduletsThe general use of standard condulets should be avoided. Thespace is limited, the bend radius is small and many cases ofdamaged cable have occurred in the use of the ninety degree turntype. Cable should never be pulled through these types, norshould substantial lengths of cable in conduit riser be supportedby the condulets.See Part II - Section 8-d for minimum training radii of installedcables under static loading. In no case should cable be hammeredinto a condulet in order to fasten the condulet cover.Splicing and TerminatingThe mechanics of good splicing and terminating techniques arespecial subjects not covered in this Guide. However, both splicingand terminating require training the cable into final position.Minimum training radii must be observed. The conduit hickey isnot a suitable tool for training cable. Special forming tools can befashioned or purchased that will produce acceptable radii withoutcable damage.Installing Cable in TrayMany of the recommendations and prohibitions offered withregard to the installation of cable in conduit apply to the installationof cable in tray. Particularly relevant are the admonitionsregarding the use of sheaves, and the temporary drooping ofcable over sharp edges. (See System Considerations)Where cable is fastened to tray, extreme care must be exercisedto avoid deforming the cable under the fasteners. If nylonfasteners are used the tension limiting tools should be used.

47

Since cable is exposed in cable tray, it is very vulnerable todamage during installation. This damage can be occasioned notonly by electrical crews but by other crafts. Protection of cableduring construction requires special attention.Specific ProhibitionsDo not pull cable into a conduit that already contains conductors.Do not attempt to remove a portion of the cables in a conduit.Do not remove cable from a conduit and then reinstall any of thatcable in conduit for permanent use.

48

DYNAMOMETER READING

To Find 1. Using a wooden stick or other rigid straight object and holding

object tangent to pulley at Point A, measure distance whereobject crosses pulling lines and let this distance equal BC,with distance B1 = C2. 1 and 2 are point of tangency betweenthe pulling line and the pulley.

2. Starting at Point B, measure the distance BC along the pullingline and mark this distance D. Thus, BD = BC.

3. Starting at Point C once again measure the distance BC alongthis side of pulling line. Thus, CE = BC.

4. With Points D and E suitably marked, measure the distancefrom D to E and record DE.

Sin =DE - BC

2 BCOnce is known, then tension can be calculated from reading.

Tension =Meter Reading

2 cos NOTE: Dynamometer must be zeroed with pulley assembly

attached or else the weight of pulley assembly must besubtracted from meter reading.

49

PULLING DEVICE

E

C

CABLE PULLD B

A

DYNAMOMETER

TENSION PULLEY

2

1

APPENDIX 1

Sin 2 Cos 0 0 2

11.5 .2 1.9617.5 .3 1.9123.6 .4 1.8330 .5 1.7336.8 .6 1.6045 .71 1.4153.1 .8 1.2058.2 .85 1.0564.2 .9 .87

Example:Assume measure BC = 40 inchesAfter marking off BD and CE equal to 40 inchesDE is measured to be 84 inches

sin =84 - 402(40) =

4480 = .55

Interpolating between .5 = 1.73 and .6 = 1.60Then .55 = 1.665 or 1.67

Assuming meter reading is 2000 lbs, thenTension =

2000167. = 1198 lbs.

50

CONDUIT SELECTION CHART -THREE SINGLE OR MULTICONDUCTOR CABLES

Based on 40% Fill and to Avoid theJam Ratio or 2.8-3.2

51

Conduit Size

1

2

3

4

1 1

1

4

1

1

2

2 2

1

2

3 3

1

2

4 5 6

Conduit I.D. 0.622 0.824 1.049 1.380 1.610 2.067 2.469 3.068 3.548 4.026 5.047 6.065

Area (sq. in.) 0.30 0.53 0.86 1.50 2.04 3.36 4.79 7.38 9.90 12.72 20.00 28.89

Cable Diameter (in.)

0.000 - 0.193 X

0.194 - 0.222 X

0.223 - 0.227 X

0.228 - 0.256 X

0.257 - 0.294 X

0.295 - 0.301 X

0.302 - 0.326 X

0.327 - 0.375 X

0.376 - 0.383 X

0.384 - 0.430 X

0.431 - 0.493 X

0.494 - 0.504 X

0.505 - 0.575 X

0.576 - 0.588 X

0.589 - 0.645 X

0.646 - 0.738 X

0.739 - 0.754 X

0.755 - 0.770 X

0.771 - 0.882 X

0.883 - 0.901 X

0.902 - 0.958 X

0.959 - 1.096 X

1.097 - 1.120 X

1.121 - 1.267 X

1.268 - 1.296 X

1.297 - 1.438 X

1.439 - 1.470 X

1.471 - 1.576 X

1.577 - 1.803 X

1.804 - 1.844 X

UNACCEPTABLESIZES

ACCEPTABLESIZES

APPENDIX 2

Navigating this manualINDEXINSTALLATION PRACTICESINTRODUCTION

PART I - METHODS for DETERMINING CONDUIT SIZES PART II - DESIGN LIMITS AND FORMULAE Pulling Eyes & BoltsBasket GripOther Pulling DevicesSidewall PressureMinimum Bending Radii for InstallationJam Ratio (Three Single Conductors)Pulling Tension CalculationsPulling PrecautionsInstalling Cable in Tray

PART III - EXAMPLE CALCULATIONS Cable ConstructionCalculation Examples

PART IV - System Considerations IntroductionCable in ConduitSizing of Conduit - Jam RatioLayout and CalculationsConduit Bends - Minimum RadiiJunction BoxesStandard ConduletsUnsupported Cable in Vertical Conduit RisersManholesSplicing Cable in ManholesCable Terminations in EnclosuresCables in Trays and LaddersCable Tray BendsFastening of Cable in TraysInstallers as Designers

PART V - INSTALLATION Conduit InstallationPulling EquipmentCable in StorageSetting Up for a PullCable Pulling DevicesPulling the CableConduletsSplicing and TerminatingInstalling Cable in TraySpecific ProhibitionsAPPENDIX 1APPENDIX 2

Previous Page:

Home:

Next Page:

PART V TAB:

PART V: INSTALLATION

PART IV TAB:

PART IV : SYSTEM CONSIDERATIONS

PART III TAB:

PART III: EXAMPLE CALCULATIONS

PART II TAB:

PART II: DESIGN LIMITS AND FORMULAE

PART I TAB:

PART I: METHODS FOR DETERMINING CONDUIT SIZES

INDEX TAB:

INDEX: INDEX AND INTRODUCTION

Previous:

next:

home: