# Pulley System | Options and Modeling

### Tips & Tricks

This article describes the basic principles and modeling approaches of pulley systems in RFEM.

#### Origin

Cranes were already used more than 2,500 years ago on construction sites. Over time, cranes have been further developed. In order to move large loads without motors, both lever rules and force increases using several cable lines and pulleys were used. These simple but ingenious basic principles are still used today.

#### What is a Block and Tackle Pulley System?

A block and tackle pulley system is a mixed structure consisting of a cable and at least one pulley and is used to lift loads. By using several pulleys, the force required to lift a weight can be reduced further and further. Some of the pulleys have a fixed position, while others are so-called loose pulleys that move during the lifting process. The advantage of increasing the force must be compensated by a longer pulley distance.

#### The Four Typical Pulley Systems

The following section describes four pulley system options with downward tension. In the model file, which you can download at the end of this article, the most realistic structure possible, including a simple schematic modeling, was created in order to better understand the behavior.

For each option, this example shows how to lift a weight of G = 100 N over a height of u = 100 mm. Where:
F ... Force required to lift the weight, corresponds to the lower left support in the RFEM model
n ... Number of supporting cable sections
Δl ... Required pulling distance to increase the weight by u

For this pulley system type, the required pulley distance is determined with Δl = n · u.

Option 1 : 1
F = G
Δl = u

Option 1 : 2
F = 0.5 · G
Δl = 2 · u

Option 1 : 3
F = 1/3 · G
Δl = 3 · u

Option 1 : 4
F = 1/4 · G
Δl = 4 · u

#### RFEM Modeling

During the modeling, you have to enter the cable as a continuous polyline with at least three nodes. Thus, the program "knows" that it is an element as an entire cable. Then, you can assign the "Cable on Pulleys" member type to this polyline. At least one end of the cable must have an immovable support or a member so that the applied tensile load can be transferred. Since the tensile force should be constant in a "Cable on Pulleys", the elements connected during the modeling process do not need any further definition. The adjacent elements or nodal supports receive deflection forces if there is buckling on the cables.

When modeling, rigid members were applied in such a way that the slab force can be displayed on a support. Additional stabilizing supports were arranged on the loose pulleys to counteract the instability.

The required pulling distance was applied by means of an imposed nodal deformation.

#### Reference

 [1] Manual RFEM. (2018). Tiefenbach: Dlubal Software.