Determining the hanger force of the suspension bridge with short extended spans: An analytical algorithm

Single-main-span suspension bridges with short extended spans usually combine significant stiffness with high economic efficiency, making them lucrative as railway bridges. However, short extended spans induce negative side hanger forces according to the conventional continuous multiple-rigid-support beam method (CMRSBM). Therefore, the support reaction of the rigid support cannot be directly used as a hanger force, thus necessitating a new solving method for hanger force assessment. This study proposes a calculation method for hanger force optimization considering the live load effect for a single-main-span suspension bridge with short extended spans. Under the combined action of dead and live loads, we optimize the hanger force to utilize the main beam material economically. It is noteworthy that the optimized hanger forces are not equal to those obtained by the CMRSBM. Therefore, the bending strain energy of the main beam is no longer the minimal, and the corresponding geometry of the main beam under the dead load differs from that at the completed bridge state. We incorporate specified hanger forces into the finite element method (FEM) to facilitate further calculation of the suspension bridge after hanger force optimization. Thus, the main beam deformation and the processing geometry of the main beam during manufacture are then estimated. The proposed method is verified by applying it to an exemplary suspension bridge. It is found that the optimized hanger forces are uniform. Under the action of dead and live loads, there are two flat bending moment envelopes for the entire main beam: one in the upper and one in the bottom. This indicates an efficient use of the material, which agrees with the initial goal. The main beam displacement manifests itself as the downwarping of the extended spans and arching of the main span. Therefore, the main beam should be pre-arched or pre-deflected during manufacturee.

Automated summary

This study proposes a calculation method for hanger force optimization considering the live load effect for a single-main-span suspension bridge with short extended spans. The optimized hanger forces are uniform and result in two flat bending moment envelopes for the entire main beam, indicating an efficient use of material. The main beam displacement manifests as the downwarping of the extended spans and arching of the main span.