Simplified Calculation Method of Middle Tower Effect of Multi-tower Suspension Bridge

In accordance with the “middle tower effect” design problem of multi-tower suspension bridges, the finite element method is currently used to find the reasonable range of the longitudinal stiffness of the middle tower through trial calculations. This method has disadvantages such as complex modeling and large calculation workload. Based on the principle of stiffness distribution, a simplified analysis method of the mid-tower effect of the multi-tower suspension bridge is proposed with the coordination of unbalanced force at the tower top and tower offset as the convergence target. By this method, the mid-span deflection-span ratio parameter and the anti-slip safety factor of the main cable at the saddle under the most unfavorable vehicle live load can be quickly obtained. Relying on the Oujiang River North Estuary Bridge project, the applicability of the method is verified, and the result has a slight deviation from the finite element solution, and the calculation accuracy meets the requirements. The influence of the longitudinal stiffness of the center tower and the friction coefficient between the main cable saddle slots on the middle tower effect of multi-tower suspension bridge is studied. (1) For an 800 m main span multi-tower suspension bridge, when the longitudinal stiffness of the middle tower is greater than 4 MN.m^-1, the structure can basically satisfy the requirements of the vertical rigidity of the specification, and the deflection-span ratio is greater than 1/300; when the longitudinal rigidity of the middle tower is greater than 20 MN.m^-1, the structure can meet the design requirements of the deflection-span ratio of 1/400. (2) When the longitudinal tower stiffness of the middle tower is 4 MN.m^-1, the maximum tower deflection reaches 0.95 m; when the stiffness of the middle tower is greater than 80 MN.m^-1, the maximum tower deflection of the middle tower is less than 0.3 m, but the unbalanced force at the top of the tower is greater than 27000 kN, which is unfavorable for the anti-skid requirements of the main cable at the top of the middle tower. (3) Increasing the friction coefficient of the cable saddle from 0.15 to 0.3 can effectively reduce the limiting effect of the middle tower effect on the value of the longitudinal stiffness of the bridge tower. Finally, through the response surface analysis method, based on the independent variable parameters such as the span of the main span, the number of lanes, the friction coefficient of the saddle groove, etc., the recommended formula for the longitudinal stiffness of the middle tower is given, which provides a quick solution method and check basis for the preliminary design of the middle tower of a multi-tower suspension bridge.