Modified catenary equation considering bending nonlinear effect and its influence on the catenary sag
The existing catenary theory is typically based on the assumption that the structure is completely flexible,without considering the impact of bending effects on the configuration of the catenary.The bending effect caused by the flexural rigidity of the cross-section can affect the configuration of the catenary.The large slope of the catenary induces nonlinear effects that influence the bending effect,further affecting the configuration of the catenary.The cross-sectional structure of flexible beams has a certain flexural rigidity,and the flexible beam theory takes into account the effect of bending on the configuration of flexible beams in calculations.Currently,research has not effectively combined catenary theory with flexible beam theory.This paper combines classic catenary theory with flexible beam theory and through in-depth theoretical analysis,derives a modified catenary equation that includes bending nonlinear effects.The study finds that in cases where the structure has a relatively small length-to-diameter ratio,low mid-span cross-sectional stress,and is subjected to significant downward loads,the impact of bending nonlinear effects is significant.This effect leads to a reduction in the sag of the structure.Finite element simulation software was used to calculate various catenaries under different conditions.The results show that the finite element simulation results are consistent with the theoretically derived formula,effectively proving the reliability of the theoretical derivation.
revised catenary equationbending nonlinear effectsbending stiffnessflexible beamcatenary sag
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