A new method for calculating the terminal force and sag of a cable structure is proposed, which does not require iteration in the absence of prestressing.
Based on the case of small inclinations, theoretical derivation is conducted by substituting a parabolic curve for a catenary, and it is considered that in the case of small inclinations, the error between the parabola and the catenary is extremely low, which can meet the required accuracy. This is later validated through simulation using finite element software.
The results indicate that the method presented in this paper meets the accuracy requirements over a wide range, and it can yield results without iteration under low prestress conditions. Furthermore, in the presence of prestress, the iteration speed shows significant improvement compared to finite element software.
Others mainly iterate and improve the catenary based on the finite element method, while I am the first to propose rethinking it from the parabola direction.
