Culmann method

Graphical determination of the sliding surface inclination according to Cullmann in foundation engineering

The Culmann method (often also called four -force method ) is a drawing method for solving static problems.

The name goes back to the Palatinate civil engineer Karl Culmann (1821–1881). He had made it his life's work to develop drawing processes in order to be able to determine the dimensions of beams in trusses . In order to be able to use the Culmann method, four forces are required, the directions of which are known, and at least the size of one of these forces must be known. The Culmann method is based on the three-force method , but serves to expand and simplify it.

In the following example some things become clearer.

example

In the example we determine the forces that act on a “roof elevator”. This is possible because only three forces ( , , ) (the directions of which are known) must be identified and the fourth force ( ) is fully known. ${\ displaystyle F_ {Z}}$ ${\ displaystyle F_ {A}}$ ${\ displaystyle F_ {B}}$ ${\ displaystyle F_ {g}}$	First step: Draw the forces in the overall system.
First the assembly must be released. You can already determine a lot through this. The carrying carriage is pulled up with a rope, the carriage with 2 wheels is connected to the supporting frame. As a result, we already know all directions of the forces, so the Culmann method can be used. To explain: Forces in wheels always act perpendicular to the ground (if 70 °, the forces and at an angle of -20 ° relative to the ground would be assumed). The force in the rope can only act in the direction of the rope, i. H. ~ 70 ° relative to the ground. ${\ displaystyle \ alpha}$ ${\ displaystyle F_ {A}}$ ${\ displaystyle F_ {B}}$	Second step: Detachment from the overall system, drawing in the power plan, extending the lines of action.
As with the three-force method, two forces can be replaced by a resulting force. Now, however, there is also the fact that the forces must cancel each other out (add up to zero). Thus, with four forces, the resulting forces must be vectorially on the same line of action , but act in opposite directions. In this example, the resulting Culmann line must go through points I and II (intersection of the respective pairs of forces).	Third step: Push two forces together into a common point of action along the line of action, the points of action are connected by the Culmann line.
After the Culmann straight line has been determined on one side, it can be transferred to the other side and the two remaining forces can be determined by parallel displacement.	Fourth step: The two remaining forces are determined by respective parallel displacements.

The easy way

The Culmann line can also be determined more easily in the force plan.

You can also immediately move the Culmann straight line from the site plan (left) into the force plan and thus determine the force corner.