Stress trajectories
The stress trajectories (singular: stress trajectory) are terms of beam theory and, as vectors, indicate the direction of the main stresses within a solid body loaded by forces . These main stresses deviate in their direction, especially in the area of the direct force effect, from the theoretically determined values and are broken down into tensile stresses and into compressive stresses at right angles to them . The stress trajectories represent an optimal course of the tension and compression members, since all shear stresses are missing in the direction determined by them .
The stress trajectories are determined primarily with the finite element method and with the help of stress optics . The long bones of vertebrates are a prominent example for the representation of tension trajectories: While the shaft cross-section of the bone is shaped according to the beam theory in terms of an optimal area moment of inertia , the cancellous bone near the joints depict the tension trajectors for a large number of load cases .
Another instance of the occurrence of stress trajectories is found on the surface of a thin-walled sphere . When the ball is loaded by a compressive force, the force is broken down into compressive stress along the meridians , while tensile stresses occurring at right angles occur along the circles of latitude. The effect also occurs with the hard-shelled eggs of the birds , provided that the pressure force acts on the tip of the egg as well as on its blunt end. The tension trajectories thus provide the physical explanation for the phenomenon that a raw hen's egg will not burst if you squeeze it between these two places with your thumb and forefinger .
literature
- Klaus Wunderlich, Wolfgang Gloede: Nature as a Constructor , Edition Leipzig 1977, pages 16 and 17