Analytic Solution to Longitudinal Deformation of Suspension Bridges under Live Loads

Live load of moving vehicles has a very important effect on the fatigue life of suspension bridges, which causes not only vertical deformation but also longitudinal deformation. In this study, a general analytical formulation for analyzing the quasistatic longitudinal displacement of suspension bridges under vertical live loads is developed, and the underlying deformation mechanism is revealed. First, the analytical vertical and longitudinal deformation equations for the single main cable subjected to live loads are formulated considering the geometric nonlinearity. Then, the relation of longitudinal displacements between the stiffening girder and the main cable for a single-span suspension bridge is established through analyzing the geometric configuration of deformed deck-suspender segment and imposing the null longitudinal force condition. The relation is further modified to incorporate the effect of central buckles (CBs). Compared with the finite-element (FE) prediction, the proposed analytical solution is quite accurate for both concentrated and distributed loads. It is found that the coupling of vertical and longitudinal displacement of main cables and the longitudinal constraint between the cables and girder, are responsible for the longitudinal displacement of the girder. The effects of sag-to-span ratio, CB, and inclined suspenders are studied. The longitudinal displacement of the girder can be reduced by about 20% when the sag-to-span ratio is varied from 1/9 to 1/11, and the CB with proper stiffness is more effective in reducing the longitudinal displacements. The proposed formulation can be conveniently applied for parameter optimization in the preliminary design stage so as to avoid tedious repetitive FE analysis.