Experimental study on natural droop of materials with transverse stress

Abstract

In this study, it is found that the catenary structure of materials with transverse stress is deviated from the hyperbolic cosine function derived by Euler equation. In our experiments, we verify the principle of minimum potential energy and find that the natural suspension potential energy is not necessarily the minimum for non-ideal suspension iron ropes with transverse stress (such as high-voltage ropes or suspension bridges).In other words, the variable of the principle of least action in the suspension line is not necessarily the gravitational potential energy only, but may also be the sum of gravitational potential energy and elastic potential energy in materials with high horizontal stress. Finally, the phenomenological proof of the minimum potential energy of the catenary is given through calculation and drawing.