Optimization of the Main Cable Shape in Double-Cable Suspension Bridges and the Effect on Live-Load Responses

Double-cable suspension bridges (2-CSBs) usually have smaller main cable diameters and larger cable stiffness and enjoy bright engineering prospects. However, there is still a need for studies on the mechanical properties of this special type of bridge, and an insufficiency of understanding within the engineering sector has directly restricted the construction of such bridges. Based on the multisegment catenary theory, we propose an analytical algorithm for main cable shape-finding and an optimization algorithm for the main cable shape of the 2-CSB and study the effect of the hanger tension coefficient on the position of the lowest point in the main cable. An analytical algorithm for solving live load responses is established and implemented, and the live load responses of different types of 2-CSBs and a single-cable suspension bridge (1-CSB) are compared. The effect of displacement constraint imposed at the midspan where the main cables are crossed on the live load responses of the bridge is analyzed. The 2-CSB main cable shape effect on the maximum deflection of the main beam when the half-span is uniformly loaded by a live load is also explored. It was found that the hanger tension coefficient variation changes the 2-CSB main cable shape. Besides, smaller horizontal distances between the position with maximum deflection under the live load and the lowest point in the main cable were found to reduce the maximum deflection. Thus, 2-CSB’s stiffness exceeds that of 1-CSB, offering an effective pathway to reduce vertical and longitudinal displacements of the main beam under two loading conditions: (1) a uniformly distributed load imposed on the entire span, and (2) a uniformly distributed load imposed on half of the span. Moreover, imposing a displacement constraint at the midspan where the main cables are crossed in the Type B 2-CSB alters the deflection curve compared with the situation where the uniformly distributed load is imposed over the entire span. The maximum deflection of the main beam is reduced when the uniformly distributed load is imposed on half of the span. Finally, we estimate the variation range of the main cable shape in the Type A 2-CSB influenced by the hanger tension coefficient.