Forces and Tensions in Ropes due to Angle
Reduced load capacities in ropes, cables or lines  due to acting angle.
The 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
F_{rope} = θ F (1)
where
F_{rope} = 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
F_{beam} = (F_{rope}^{2} + F^{2})^{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
F_{rope} = (500 kN) 1.22
= 610 kN
Rope Force and Tension Calculator
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