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	Select Size	Coefficient of Friction
Weight Multiplier	Number of Conductors	Enter Length in Feet
Add/Sub weight	degrees of incline	incline 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	Enter diameter of sheave in inches
Enter sidewall pressure multiplier (see the table below)

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

**Recommended Coefficient of Friction**
Pulling with rollers all directions	0.15

**Angles of Inclination**
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

**Recommended Adder/Subtractor**
**weight multiplier**
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.

**Sidewall Pressure Multipliers**
(Lbs per sheave radius in feet)
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
Sheave adder = 125 Lbs.
(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.
Sheave adder is 125 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.
Sheave adder is 125 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

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.
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

With pulling eye attached to copper conductors, the maximum pulling strain in pounds should not exceed 0.008 times cir-mil area.
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

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

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.
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

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.
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

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:

Allowable tensions on conductor.
Allowable tensions on pulling device.
Allowable sidewall pressure.

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.