Finding the Completed Bridge State of Suspension Bridges with Short Extended Spans Based on Specified Hanger Forces

A suspension bridge with short extended spans is a distinct and novel bridge type combining large stiffness and economic efficiency. This form of suspension bridge has been extensively built to carry trains. However, due to extended spans, hanger forces cannot be determined using the multipoint rigidly supported continuous beam method, a conventional method to determine the completed bridge state of suspension bridges without short extended spans. Addressing this problem, we propose two analytical approaches, namely, the precambering (PC) approach and the equivalent temperature load (ETL) approach. First, specified hanger forces are imposed on the three-span continuous beam, which is the main beam. The bending moment and deflection of the main beam caused by hanger forces and self-weight are solved. Next, the opposite number is taken of the y-coordinates of the node corresponding to the deflected geometric configuration of the main beam to obtain the geometric configuration of a curved beam with a predeflection (the PC approach). Another approach is to perform a reverse calculation of gradient temperature load from the estimated bending moments of each cross section of the main beam (the ETL approach). After that, the catenary theory is used to solve the geometric configuration of the main cable under the action of specified hanger forces. Finally, the initial strain of the hanger is solved. So far, we have obtained the analytical data of the entire bridge as inputs of the finite-element model, which is run only once to yield the completed bridge state. The results are satisfactory using either proposed approach. There is no need for iteration, which is otherwise tedious and time-consuming. The proposed approaches prove to have higher universality and practicability. The feasibility and accuracy of the analytical approaches are verified through an engineering example, which is a single-main-span suspension bridge with two short extended spans and a span length layout of 100 m + 1,080 m + 100 m.