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Cable Bridge Created Edited

Suspension Bridge Form-Finding


  • The suspension bridge model created from Suspension Bridge Wizard is modified to suit the user's intention and analyzed once again to determine an accurate initial configuration. Suspension Bridge Wizard performs an initial configuration analysis only considering the cable system. To perform an initial configuration analysis considering the global system of a bridge, re-analysis using this function is needed.
  • This process is required for a self-anchored suspension bridge, as the coordinates of the entire cable system are changed by the axial displacement occurring in the girder.



From the main menu, select  [Structure] tab > [Cable Bridge] group > [Cable Bridge] > [Suspension Bridge Form-Finding]




         (Initial Force) dialog box                          (Optimal Approach) dialog box

Fig. Suspension Bridge Form Finding


Control Parameters

Number of Iterations: Enter the number of iterations for nonlinear analysis.

Convergence Tolerance: Enter the convergence tolerance, which will be used for acceptance of errors.


Analysis Method

Initial Force: Determine the initial configuration of a suspension bridge model by updating initial forces.

Optimization Approach: Determine an initial configuration of a suspension bridge model by updating design parameters satisfying the specified constraint condition.


When the Initial Force is Selected

Node Group to be Updated

Select the node group whose coordinates will be updated. The nodes for the cable elements of a suspension bridge are continuously updated in the process of optimizing the equilibrium state. Accordingly, it is recommended to group all the cable nodes.

NOTE.png Nodes at each end of a cable, which are affixed to supports, are excluded. However, the node at the sag point is included in the group although it is not updated.


Sag Point Group

Since the sag value of the main cables at the center of the center span is defined by the user, these nodes must be excluded from being updated. Therefore, one Sag Point node (2 nodes for a 3-D bridge) must be assigned to a group.


Constant Horizontal Force of Cable

Using an initial configuration analysis, determine the equilibrium state that exhibits the horizontal cable forces inputted by the user.

Main Cable Group: Select the Element Group to which the main cables of a suspension bridge are assigned.

Horizontal Force: Enter the horizontal cable force.


Define Girder Z-Displacement Condition

When the rigorous method is used in the initial configuration analysis for the global system of a suspension bridge, bending moment forces may occur in the girder.
By defining a Hanger Cable Group using this option, you can control the vertical displacement at nodes where the girder and hanger cross, and accordingly, you can minimize the moment resisted by the girder.


Hanger Group: Select the Hanger Group created in the Structure Group. When the Hanger Group is selected, the bottom point of the hanger is recognized, and it allows for the displacement and movement of the rigid body.


Define Girder Z-Displacement Condition

Fig. Define Girder Z-Displacement Condition 


Girder Group: Select the Girder Group created in the Structure Group.

Target Disp.

Zero Disp. : Controls the displacement of the reinforced shape to be zero.

User-Defined Disp. : Controls the displacement of the reinforced shape with user-defined values. This method is applied when the camber of the reinforced shape is known as a base value.


When the Optimization Approach is Selected

Cable Group to be Updated: Select the cable element group whose design parameters will be updated by the optimal approach.


Sag Point Group: Since the sag value of the main cables at the center of the center span is defined by the user, these nodes must be excluded from being updated. Therefore, one Sag Point node (2 nodes for a 3-D bridge) must be assigned to a group.


Define Constraints: Define the constraint condition for Truss Force, Displacement, and Beam Force. To obtain the desired initial configuration from the optimal approach, we can control the girder moments by defining the constraint condition of beam forces. By clicking the [Table] button, we can use the Copy & Paste command from MS Excel.


truss force.png    displacement.png    beam force.png

           Truss Force dialog box                  Displacement dialog box                  Beam Force dialog box

Fig. Define Constraint


NOTE.png When setting multiple constraints, it is important to consider their impact on convergence. The designer should judiciously choose appropriate constraints.


Load Cases to be Considered

Load Case: Select the load conditions that determine the cable tension and equilibrium. Typically, this includes the permanent loads (self-weight, fixed loads, etc.) acting on the structure.


> To enter a new or additional load case
Enter the Load Case and Scale Factor and click Add.


> To modify the scale factor for a previously entered load case
After selecting the relevant load case, modify the scale factor, and click Modify.


> To delete a previously entered load case
Select the relevant load case, and click Delete.


NOTE.png After completing the data input and clicking the OK button, performing the analysis will update the coordinates and tensions of the main cable through rigorous analysis. It will also calculate the equilibrium forces generated in the structure due to the self-weight of the reinforcement and cable tension. These equilibrium forces can be viewed in tabular form in the menu Load > Initial Forces > Equilibrium Element Nodal & Member Forces. After executing the rigorous analysis, clicking the performing analysis button again will perform the rigorous analysis again, taking the previously updated coordinates and cable tensions as the initial values. This rigorous analysis involves iterative analysis to find the optimal equilibrium configuration of the structure, continuously updating the internal forces of the members. During this process, Spring Supports cannot be used. If Spring Supports need to be applied, Elastic Link elements must be used. To consider the self-weight of the cable element, it is essential to include a load condition with the self-weight defined among the selected load cases.


To perform another analysis or to delete the entire inputted data, click on Remove Suspension Bridge Analysis Data.

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