Claus Mattheck’s 'method of tensile triangles' - learning from Trees

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Claus Mattheck has developed a system known as the "method of tensile triangles" for optimizing a notch shape within a few minutes using only a protractor. This allows even the smallest entrepreneurs and workmen to create shape-optimized building parts. A notch is bridged by an imaginary rope, which in the case of a 90° corner forms a 45° angle to the legs of the component. In the center of the imaginary rope, a new rope is attached at half the angle of the first and this process is repeated several times. The remaining nicks, except for the lowest 45° nick, are smoothed out and the area between the building part and the ropes is filled, just like the buttress root of a tree.

“We are learning from trees“, said Prof. Claus Mattheck, head of the Department of Biomechanics at the Institute for Material Research at the Karlsruhe Research Centre. Mattheck summarised their research by saying, “During many millions of years of evolution, trees have learned to adapt their shape to external influences such as wind pressure or slopes. Each tree will grow in such a way as to achieve an even disposition. Through the strategic growth of wood at the point of greatest mechanical load, for example at crotches, the tree is able to relieve any notch stress and can achieve this without wasting any material".

Mattheck’s method of visual tree assessment (VTA) was initially sneered at and rejected by experts. The unconventional thinker was met with suspicion. However, VTA has now become accepted. Mattheck has publicly and under oath even been requested to give his expert opinion in numerous cases of damage claims caused by “fatigue fracture of mechanical components“ as well as in cases of “mechanics and fracture behavior of trees and the phenomenon of the deterioration of wood by fungi“.