By Patrick Baumann

Life in nature has 3.8 billion years of research, development and testing experience. That means chances are very high that the structures we find in nature exhibit optimal shapes what means maximum strength with the least amount of material. Prof. Dr. Claus Mattheck analyzed these structures and developed the striking simple method of the tension triangle.

Release peak stress in notches for extended durability

Nature as model

How do I release tension peaks in a notch in a simple way?

Nowadays you are able to optimize structures with FEA software tools and minimize notch tensions with automated algorithms (CAO). This software continuously becomes more user friendly and efficient but the method of the tension triangle is still unbeatable when it comes down to effort and output.

The genius thing about the method of the tension triangle is that you only need a ruler and a pair of compasses and the knowledge of the direction of the applied force to design an almost perfect notch shape. You reach comparable results as with the much more resource consuming CAO software (Computer Aided Optimization).

Method of the tension triangle, how is it done?

fig. 1: design of the tension triangle [drawing c. mattheck]

In the figure above you see the direction of the force (red arrows) and the sharp notch in blue. With a symmetrical triangle of 45° you can release the stress in the sharp notch. This creates two additional notches (A, B) of which notch A is harmless because it is in the same direction as the flow of the force into the material. We have to disarm notch B, though. Again we design a symmetrical triangle according in figure 1 over notch B. Again there are two additional notches created of which the upper one can be improved. A third triangle has still a reasonable effect.

In principle this procedure can be continued infinitely. But the analysis shows that 3 triangles are enough for a very effective tension release.

fig. 2: rounding of the edges [drawing Wissner]

This basic design of the triangles can be rounded with maximal tangential radiuses for maximal effect and elegant appearance.

With this approach you can improve structures very effectively and design the strongest structures with the least amount of material. That is the secret of light weight design.

The nature of lightweight design