Analytical Solution for Longitudinal Anti-Push Stiffness of the Middle Tower of Cross-Cable Multi-Tower Cable-Stayed Bridge

The Queensferry Crossing in Scotland is the first multi-tower cable-stayed bridge with crossed cables in the world. This means that the conceptual design of a cross-cable multi-tower cable-stayed bridge has become a reality. In this paper, the cross-cable action mechanism is studied deeply. Suppose that the small displacement amount at the top of the side tower is ignored. The deformation coordination principle is used twice to analyze the relationship between the horizontal external force and the top displacement amount of the middle tower. Thus, derive the formula for estimating the anti-push stiffness of cross cables to the middle tower of the multi-tower cable-stayed bridge under the influence of the stiffness of the tower and beam. A numerical example is given to verify this. The research results show that the error between the analytical solution and the finite element solution is less than 8%, which meets the conceptual design requirements of cross-cable multi-tower cable-stayed bridges. The cross cables can reduce the deflection of the main beam and improve the stiffness of the bridge. After setting 10 pairs of cross cables, the displacement amount of the middle tower decreases by as high as 51%. The stiffness of the multi-tower cable-stayed bridge increases with an increase in the number of cross cables, but the increasing trend of stiffness gradually slows down. Increasing the stiffness of the tower or beam can improve the structural stiffness to a certain extent, but the effect is much less potent than that of the cross cable in the middle span.