# Force and Tension in a Rope due to Angle

## Reduced load capacity in ropes, cables or lines - due to angle

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

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

*height (m, ft)*

* depth (m, ft)*

* load (N, lb)*

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