Numerical analytic algorithm for form-finding of suspension bridge main cables considering frictional contact

ObjectiveSuspension bridges exhibit significant geometric nonlinear effects. During the iterative calculation for finding main cable form in completed bridge state, the issues (e.g., calculation divergence and low computational efficiency) exist due to the influence of initial calculation values and iteration increments. To investigate the influence of frictional contact between main cable and main cable saddle on the form-finding of suspension bridge main cables during construction, this paper conducts research on a numerical analytic algorithm for cable form-finding.MethodFirst, a recursive calculation formula for cable height was established based on the relation between the slope at cable end and the cable force slope. Second, the mechanical relational expressions for hanger points were established according to mechanical equilibrium conditions. Third, an analytical equation set for finding main cable form in the completed bridge state was formulated based on closure conditions for mid-span elevation and end-point elevation. Finally, the main cable form-finding for the completed bridge was achieved by solving the constructed nonlinear equation set. The analytical equations for main cable during construction were established based on the principle of unstressed length conservation, the frictional contact equations between main cable and saddle, and the compatibility conditions.ResultThe differences between cable alignment and unstressed length calculated with the proposed analytical algorithm for finding completed bridge main cable form and the finite element values are controlled within 3.0 mm. The analytical algorithm offers advantages, e.g., high computational efficiency and parametric modeling capability.ConclusionThe frictional contact effect between main cable and saddle has different influences on mid-span and side-span main cable. As the girder erection proceeds, the difference of these influences becomes nonlinear, and the nonlinear effect becomes increasingly significant. The fundamental reason for the influence of frictional contact on main cable alignment calculation result is revealed to be the change in the tangent point position of cable on the main saddle. Attention should be paid to the frictional contact between main cable and saddle during the construction of suspension bridges.