# Cable Tray Pulling Tension Calculator

by Gerald Newton
January 17, 2000

The Calculator uses Standard Equations based on  Industry Practices.

For finding tension at sheave using a tension meter go to:
How to measure tension at a sheave.

 Cable Tension Pull Calculator for Straight Pulls (Read reference material below for explanations.) by electrician2.com Select  Material  Copper Aluminum Select  Size  18 AWG 16 AWG 14 AWG 12 AWG 10 AWG 8 AWG 6 AWG 4 AWG 3 AWG 2 AWG 1 AWG 1/0 AWG 2/0 AWG 3/0 AWG 4/0 AWG 250 kcmil 300 kcmil 350 kcmil 400 kcmil 500 kcmil 600 kcmil 700 kcmil 750 kcmil 800 kcmil 900 kcmil 1000 kcmil 1250 kcmil 1500 kcmil 1750 kcmil 2000 kcmil Coefficient  of Friction  .0001 .10 .11 .12 .13 .14 .15.16 .17 .18 .19 .20 .21 .22 .23 .24 .25 .26.27 .28 .29 .30 .31 .32 .33 .34 .35 .36 .37 .38 .39 .40 .41 .42 .43 .44 .45 .46 .47 .48 .49 .50 .51 .52 .53 .54 .55 .56 .57 .58 .59 .60 .61 .62 .63 .64 .65 .66 .67 .68 .69 .70 .71.72 .73 .74 .75 .76 .77 .78 .79 .80 .81 .82 .83.84 .85 .86 .87 .88 .89 .90 .91 .92 .93 .94 .95 .96 .97 .98 .99 1.00 Weight  Multiplier  1.0001 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.18 1.191.20 1.21 1.22 1.23 1.24 1.25 1.26 1.27 1.28 1.29 1.30 1.31 1.32 1.33 1.34 1.35 1.36 1.37 1.381.39 1.40 1.41 1.42 1.43 1.44 1.45 1.46 1.47 1.48 1.49 1.50 1.51 1.52 1.53 1.54 1.55 1.56 1.57 1.58 1.59 1.60 1.61 1.62 1.63 1.64 1.65 1.66 1.67 1.68 1.69 1.70 1.71 1.72 1.73 1.74 1.75 1.76 1.77 1.78 1.79 1.80 1.81 1.82 1.83 1.84 1.85 1.86 1.87 1.88 1.89 1.91 1.921.93 1.94 1.95 1.96 1.97 1.98 1.99 2.00 Number of  Conductors  1 2 3 4 5 6 7 8 91011 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 6061 62 63 64 65 66 67 68 69 70 71 72 7374 75 76 77 78 79 80 8182 83 84 85 86 87 88 89 90 91 92 9394 95 96 97 98 99 100 Enter  Length in Feet Add/Sub  weight  Add Subtract degrees of  incline  0 1 2 3 4 5 6 7 8 91011 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 6263 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 incline  up/down  Up Down Circular  mil area Total Weight of  one foot of wire(s) Maximum Pulling  Tension in Pounds Maximum  Pulling  Length in Feet Reel  Tension  in Lbs. Pulling  Tension in  Lbs. ****************  **************** Cable Tension Pull Calculator for Sheave and Sidewall Pressure (uses weight from above) Enter tension  into  sheave Enter sheave Lb  Adder  50 75 100 125 150 175 200 225 250275300 Enter diameter  of  sheave in inches  1 2 3 4 5 6 7 8 91011 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 4142 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 6061 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 939495 96 97 98 99 100 Enter sidewall  pressure  multiplier (see the table below) 300 500 1000 Tension  out of sheave Sidewall  Pressure in Lbs. Maximum allowed  Sidewall Pressure  in Lbs. ****************  **************** Roller Spacing Estimator Uses weight from above.  Values must be entered in top calculator first. Enter height  to top roller  in feet Enter tension  for roller  section Distance  between rollers  in feet

 Pulling  with rollers all directions 0.15

 For Horizontal pulls 0 degrees For Straight up 90 degrees up For Straight down 90 degrees down For inclined angles X from  horizontal X degrees up For angles X down from horizontal (declination) X degrees down

 For larger wires add 1.09, the default.  This approximately compensates for the weight of the insulation. If weight of 1 ft of wire(s) or cable(s)  is known use the multiplier that gives the nearest weight per foot for all the wires or cables the same as known value.  The default weight with multiplier set to 1.00 is 0.321 Lbs per cubic inch of copper and 0.10 Lbs. per cubic inch of Aluminum.  The cubic inch per foot calculation is found from  the circular mil area for the selected size of conductor.  The weight and not the circular mil area is used in subsequent calculations for Pulling Tension.   For other weights that are lighter, for instance fiber optic cables, use a negative multiplier.  The weight multiplier uses the size of conductors as a reference only.   This way the calculator can be used for calculating Pulling Tension for communications and fiber optic cables.  The Maximum Pulling Tension is calculated  as 0.008 times the circular mil area for copper and 0.006 times the circular mil area for aluminum.   The Maximum Pull Tension and Maximum Pulling Length are not adjustable and would not be correct for fiber optic cables, but the Pulling Tension based on weight and coefficient of friction would be correct, likewise for the curvature calculator.

 Power Cables Cable Type Less than 8 AWG Greater than No. 8 AWG One Single Cable 300 500 Two or More (parallel or plex) 500 1000 Multi Conductor Power and Control Cable One Cable 500 Two or more Cables 1000 Instrument Cable Single Pair 300 Multipair 500

## Example 1 Given:
L1 = 300 ft.
L2 = 200 ft.
H1 = 30 ft.
H2 = 30 ft.
H3 = 60 ft.
T1 is tension out of first sheave.
T2 is tension out of second Sheave.
T3 is tension out of third sheave.
T4 is total tension at end of pull.

Cable is 3/c 500 kcmil copper 15 Kv Type MC corrugated approved for cable tray installation.
Cable O.D. is 3.60 inches.
Net weight per foot is 8.67 Lb.
Minimum Bending Radius is equal to 7xOD = 25.2 inches.
see NEC Section 334-11(b)
Maximum Sidewall Pressure is 1000 per foot of bend radius for three conductor cable.
See table below.
With a radius of 3 feet for a sheave the maximum pulling tension is 3000 Lbs.
Rollers are 1 foot above tray.

Using Given Conditions to find total pulling tension at T4 and number and spacing of rollers between T1 and T2 and between T3 and T4.

Step 1
Set add multiplier to 1.91 to get 8.67 Lb/Ft  for conductor weight
for 3 1/C  500 kcmil
Calculate pull tension off reel and first 30 feet. using top calculator
Coefficient of Friction = 0.15
Length = 30 feet
degrees of incline = 90
incline up/down = up
Calculated pull tension = 260 Lbs.
Calculated pull tension off reel is 217 Lbs.

Step 2
Calculate pull tension  at T1 using bottom calculator
Tension into sheave is 260 + 217
(Adder is the estimated force required to bend the cable around the sheave)
diameter of sheave is 72 inches
(Remember the larger the sheave diameter the less the sidewall pressure)
Calculated pull tension = 602 Lbs.

Step 3
Calculate pull tension into T2 using top calculator
Coefficient of Friction = 0.15
Length in feet = 300 ft.
Angle of Bend = 0 degrees
Total Calculated pull tension = 390 Lbs.
Total tension into T2 sheave is 390 + 602 = 992 Lbs.

Find Spacing for rollers between T1 and T2
using roller spacing estimator:
Height to top of roller = 1 ft.
Tension for roller section = 992 Lbs.
Calculated spacing = 30.25 ft.
300/30 = 10 rollers

Step 4
Calculate pull tension out of T2 Sheave using bottom calculator
Tension into T2 sheave is 992 Lbs.
Diameter of Sheave is 72 inches.
Calculated Pull Tension = 1117

Step 5
Calculate pull tension into T3 using top calculator
Coefficient of Friction = 0.15
Length in feet = 30 ft.
Angle of Bend = 90 degrees up
Total Calculated pull tension = 269 Lbs.
Total tension into T2 sheave is 260 + 1117 = 1377 Lbs.

Step 6
Calculate pull tension out of T3 Sheave using bottom calculator
Tension into T2 sheave is 1377 Lbs.
Diameter of Sheave is 72 inches.
Calculated Pull Tension = 1502

Step 7
Calculate pull tension at T4 using top calculator
Coefficient of Friction = 0.15
Length in feet = 200 ft.
Angle of Bend = 0 degrees up
Total Calculated pull tension = 260 Lbs.
Total tension at T4  is 260 + 1502 = 1762 Lbs.

Find Spacing for rollers between T3 and T4
using roller spacing estimator:
Height to top of roller = 1 ft.
Tension for roller section = 1762 Lbs.
Calculated spacing = 40.33 ft.
200/40 = 5 rollers

## Bending Radii and Pulling Tensions

Power Cables Without Metallic Shielding
The minimum bending radii for both single and multiple-conductor cable with or without lead sheath and without metallic shielding are as follows:

 Minimum Bending Radius as a Multiple of Cable Diameter

 Thickness of Conductor Insulation in Mils Overall Diameter of Cable Diameter in Inches

 1,000 and Less 1,001 to 2,000 2,001 and Over

 155 and less 170-310 325 and over 4 5 - 5 6 7 6 7 8

Power Cables With Metallic Shielding

1. For Tape Shielded Cables, the minimum bending radius for all cables with metallic shielding tapes is twelve times the overall diameter of the completed cable.
2. For Wire Shielded Cables, the minimum bending radius for all cables with wire shielding is eight times the overall diameter of the completed cable.

The following recommendations are based on a study sponsored by ICEA. These recommendations may be modified if experience and more exact information so indicate.

### A. Maximum Pulling Tension On Cable

1. With pulling eye attached to copper conductors, the maximum pulling strain in pounds should not exceed 0.008 times cir-mil area.
2. With pulling attached to aluminum conductors, the maximum pulling strain in pounds should not exceed 0.006 times cir-mil area.
• TM =0.008 x n x CM, for copper  Done in Calculator
TM =0.006 x n x CM, for aluminum Done in Calculator
where
TM = max. tension, lb.
n = number of conductors
CM = cir-mil area of each conductor
3. With cable grip over lead sheath, the maximum pulling strain in pounds should not exceed 1500 lb./sq. inch of lead sheath cross-sectional area for commercial lead
• TM=4712 x t x (D-t), where
t = sheath thickness, inches
D = overall diameter of cable, inches
4. With cable grip over non-loaded cable, the maximum pulling strain should not exceed 1000 lb. and may not exceed the maximum tension based on 0.008 or 0.006 x total conductor area.
5. Where more than three conductors are pulled together, reduce the pulling tension 20%. Done in Calculator

### B. Maximum Permissible Pulling Length

LM = TM/(C x W)  Done in Calculator

where
LM = pulling length, feet (straight section)
TM = maximum tension, lb.
W = weight of cable per foot, lb.
C = coefficient of friction (usually 0.15 when rollers are used)

### C. Reel Back Tension

Tr = 25 * W  Done in Calculator

where
Tr = Tension in pounds at reel
W = weight of cable per foot, lb.

### D. Pulling Tension Requirements in Tray

1. For straight tray sections, the pulling tension in pounds equals the length of tray multiplied by the weight per foot of cable and the coefficient of friction.
2. For straight sections, the following formula applies:
• Tout= f x W x L + Tin in pounds
where
Tout = tension for straight section at pulling end, lb.
f = coefficient of friction (usually 0.15 for rollers)
W = weight of one foot of cable(s)
L = Length in feet
Tin = pounds of tension in.

For inclination (pulling up) the following formula applies:
ø = angle of inclination (up) or declination (down)

T out = W L (sin ø + f cos ø ) + Tin pounds
Done in Calculator

For declinations (pulling down) the following formula applies:

T out = - W L (sin ø - f cos ø ) + Tin pounds
Done in Calculator

3. The maximum pulling tension in pounds shall not exceed the sidewall pressure multiplier  times the radius of the sheave expressed in feet.  Done in Calculator

### E. Sidewall Pressure

Sidewall Pressure = T / R Done in Calculator
Where
T = Pulling Tension out of bend
R = Radius of sheave in feet
F. Roller Spacing Estimator

To estimate Roller Spacing the following can be used.

s = SQRT ( (8 x h x t) / W) )  Done in Calculator

s - distance between rollers in feet.

h= height of top roller above tray bottom in feet

t = tension in pounds for the section where rollers are being installed

W = total weight in pounds for cable(s) for one foot.

### G. Pulling Tensions Must Not Exceed The Smaller of These Values:

1. Allowable tensions on conductor.
2. Allowable tensions on pulling device.
3. Allowable sidewall pressure.

4.

Pulling Eye: T (Cu) = Number conductors x circular mills x .008 for copper
Pulling Eye: T (Al) = Number conductors x circular mills x .006 for aluminum

Basket-Grip: T = 1000 lbs. per grip

Sidewall Pressure: P = (300, 500 or 1000) pounds x radius of curve in feet depending on type and size of cable.