Shackles are a primary means of connecting the parts of rigging systems on vessels and industrial cranes. In its simplest form, a shackle is a U-shaped piece of metal secured by a clevis pin, screw or bolt at its opening. Shackles range in size from this extraordinarily large forged wide-body shackle capable of managing a working load of 2500 metric tons to these amethyst and gold shackle earrings, whose lifting capacity may not exceed one’s spirits.

Today we are concerned with determining what size shackle would be required to lift a specified weight of cargo when the cargo boom is at a specified angle to the horizontal. Two calculations and a vector diagram are used in the solution to this problem.

The problem is this:

You are lifting a 3-ton weight with a single whip rove on a swinging boom set at an angle 20° to the horizontal. Use the formula for the size of a shackle with a safe working load and determine the minimum size shackle that should be used to secure the head block to the boom. |

A. 1-3/8″ |

B. 1-1/2″ |

C. 1-5/8″ |

D. 1-3/4″ |

Answer: A |

The single whip uses a single sheave and has a mechanical advantage of one. If friction were not an issue, then applying 3-tons of force would lift a 3-ton cargo suspended at “w.” But friction is a factor, so applying the industry standard of an additional 10% of the weight for each sheave, the force necessary to lift this cargo in this configuration would be 3.3 tons (3 + (.10 x 3) = 3.3).

However in the problem, this single whip hangs on the end of a boom angled at 20° to the horizontal. In addition to the vertical and frictional forces, an angular stress has been added. To determine the total force required to lift the weight in this arrangement, we recommend using a vector diagram.

Vectors are lines describing two values. Here the length of the vector will represent a weight or stress. The direction of the vector describes the direction in which the force of that weight is applied. Attaching one vector to the head of another creates two sides of a potential triangle. The third side of that triangle will give the total force necessary to make the lift.

Steps:

- From the center, draw a line in the direction of 70° (the boom is set at 20° above the horizontal). End it anywhere along the line and label that end “B.”
- From “B,” drop a vertical of 3 units. Label the end of this line “A.” This vector represents the weight of the cargo.
- Parallel the boom direction to the end of the line just drawn and extend it back towards the center the length of the stress on the hauling part, in this case, 3.3 tons. Label that endpoint “C.”
- Line CB closes the triangle. The distance from “C” to “B” represents the total stress to apply. In this case, the necessary force is roughly 5.1 tons.

The formula used to find the **Safe Working Load (SWL)** of shackles is **Diameter of shackle ^{2} x 3.**

As determined by the vector diagram, the SWL in this example is 5.1 tons. Dividing 5.1 by 3 gives 1.7. The square root of 1.7 is 1.30″. The proper size shackle will be the one just larger than 1.3″, in this case, the 1-3/8″ shackle. 1-3/8″ is equivalent to 1.375″.

Here are a few more problems along with the vectored solutions.

You are lifting a 3-ton weight with a single whip rove on a swinging boom set at an angle of 60° to the horizontal. Use the formula for the size of a shackle with a safe working load and determine the minimum size shackle that should be used to secure the head block to the boom. |

A. 1-1/8″ |

B. 1-1/2″ |

C. 1-3/4″ |

D. 2″ |

Answer: B |

You are lifting a 5-ton weight with a single whip rove on a swinging boom set at an angle of 20° to the horizontal. Use the formula for the size of a shackle with a safe working load and determine the minimum size shackle that should be used to secure the head block to the boom. |

A. 1-3/8″ |

B. 1-1/2″ |

C. 1-3/4″ |

D/ 1-7/8″ |

Answer: C |

You are lifting a 5-ton weight with a single whip rove on a swinging boom set at an angle of 60° to the horizontal. Use the formula for the size of a shackle with a safe working load and determine the minimum size shackle that should be used to secure the head block to the boom? |

A. 1″ |

B. 1-3/8″ |

C. 1-1/2″ |

D. 1-7/8″ |

Answer: D |

Finally, it is not necessary to apply a safety factor to the breaking strength of a shackle to determine its safe working load. The safety factor has been incorporated into the formula.

Shackles also have more unsavory applications.