Qualification of the Ernst formula for modeling the sag effect of super-long stay cables in the long-span railway cable-stayed bridges

Abstract

It is believed that the cable sag effect becomes more substantial with ever-increasing main span of the railway cable-stayed bridges, which have much heavier stay cables and larger live-to-dead load ratio than the highway cable-stayed bridges. The qualification of the Ernst formula to simulate the sag effect of super-long stay cables should be examined for design use. An explicit secant modulus formula has been proposed to conveniently assess the reliability of the Ernst formula. A finite element model for a railway cable-stayed bridge with the main span of 1316 m is established based on ANSYS software package, in which the stay cable has been consecutively modeled by the Ernst formula, the explicit secant modulus formula, and the multi-straight bar element model. The induced stresses and displacements in the cable, main girder and pylon obtained based on those cable models are compared to demonstrate their validity in dealing with the sag effect of railway cable-stayed bridge. The comparisons show that the relative error of the explicit secant modulus formula is less than 1 % against the benchmark solutions given by the multi-straight bar approach. The relative error of the stretching stiffness of stay cable obtained by the Ernst formula is within 8 %, and that of the displacements and internal forces in the girder and pylon is not more than 5 %. Due to its soften property, the Ernst formula is slightly conservative for structural analysis of the long-span railway cable-stayed bridges.