An analytical algorithm for reasonable central tower stiffness in the three-tower suspension bridge with unequal-length main spans

Three-tower suspension bridges with unequal-length main spans more easily adapt to different terrain features and therefore, have broader application prospects. However, due to the unique central tower effect of the three-tower suspension bridge, it is required that the lateral stiffness of the central tower in the longitudinal direction of the bridge girder should be neither too large nor too small. To calculate the reasonable range for the central tower stiffness in the three-tower suspension bridge with unequal-length main spans, this study proposes an analytical algorithm based on the segmental catenary theory. Firstly, hanger tensile forces under the joint action of dead and live loads are calculated. Next, the governing equations for the main cable shape of each span are constructed for the following conditions: closure of elevation difference, closure of span length, moment balance of splay saddle, and conservation of unstrained length of the main cable. The solutions of the derived set of simultaneous equations are obtained for (i) deflection-to-span ratio limit of the stiffening girder and (ii) anti-slip control between the main cable and saddle conditions, which yield the lower and upper limits of reasonable stiffness of the central tower, respectively. This study discusses a three-tower suspension bridge spanned as 248 m + 1060 m + 1360 m + 380 m. The calculation is performed for the two cases of the live load application: (i) to the longer main span and (ii) to the shorter main span. The results obtained proved the feasibility and effectiveness of the proposed algorithm. The following findings are reported: The upper and lower limits of reasonable central tower stiffness are derived from the above two cases, respectively. Therefore, it is not sufficient to consider only the former case when calculating the central tower stiffness of the three-tower suspension bridge with equal-length main spans. The dead-to-live load ratio and friction coefficient between the main cable and saddle also strongly influence the central tower stiffness: their increase can expand the reasonable range of the latter but if they are too small, no such optimization can be provided.