Estimation Formula for Longitudinal Restraint Stiffness of the Middle Tower of Multi-tower Cable-stayed Bridge With Crossed Cables by Considering the Effect of Tower and Beam

With the construction of Queensferry bridge in Scotland, the multi-tower cable-stayed bridges with crossed cables have entered the field of bridge engineers. In order to explore the action mechanism of crossed cables, considering the effect of tower and beam and ignoring the small level displacement of the side tower, based on the principle of deformation coordination, an analytic formula for calculating the longitudinal restraint stiffness of the middle tower of multi-tower cable-stayed bridge with crossed cables was deduced, and a numerical example was carried out. The results show that the error between the formula and finite element is within 8%, and it can meet the requirements of the conceptual design of cable-stayed bridge. Crossed cables can make the beam deflection decrease, thus increasing the overall stiffness of the cable-stayed bridge. The overall stiffness of multi-tower cable-stayed bridge rises as the number of crossed cables increasing.The displacement of middle tower reduction is up to 51% after 10 pairs of crossed cables are set, while the stiffness increase gradually slows down. The change of the stiffness of the tower's effect on longitudinal restraint stiffness of the middle tower for multi-tower cable-stayed bridge is greater than that of the main beam, but the crossed cables play more important roles in increasing the stiffness of the structure.