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# Forces and Tensions in Ropes due to Angle

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The increased force or tension in a rope or cable due to angles:

Increased Force or Tension in a Rope or Cable due to Angles
Rope Angle with Load (degrees)Increased Force or Tension Factor
- θ -
- α -
- β -
0 90 1.00
5 85 1.00
10 80 1.02
15 75 1.04
20 70 1.07
25 65 1.10
30 60 1.16
35 55 1.22
40 50 1.31
45 45 1.41
50 40 1.56
55 35 1.74
60 30 2.00
65 25 2.37
70 20 2.92
75 15 3.86
80 10 5.76
85 5 11.5

As we can see from the table above - with

α angle = 60 degrees

and

β angle = 30 degrees

the force or tension F in the rope is doubled.

The force acting in the rope can be calculated as

Frope = θ F                 (1)

where

Frope = force acting in the rope (N, lb)

θ = increased force or tension factor from the table above

F = load (N, lb)

The force acting in the horizontal beam can be calculated as

Fbeam = (Frope2 + F2)1/2                           (2)

The angle α can be calculated as

α = tan-1(h / d)                 (3)

where

α = angle (degrees)

h = vertical distance between horizontal beam and rope (m, ft)

d = length of horizontal beam (m, ft)

The angle β can be calculated as

β = tan-1(d / h)                 (4)

where

β = angle (degrees)

### Example - Increased Force in a Rope due to Angle

The maximum force in the rope in the figure above can be estimated by firs calculate the angles:

α = tan-1(3.1 / 4.3)

= 35.8 o

β = tan-1(4.3 / 3.1)

= 54.2 o

From the table above the tension factor is approximately 1.22 and the force in the rope can be calculated as

Frope = (500 kN) 1.22

= 610 kN

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