BLOG BRIDGE INSIGHT

Finalizing the Forces in the Cables for a Cable-Stayed Bridge

1. Introduction

A cable-stayed bridge is the most popular long-span bridge in which cables support the bridge deck and transfer the load to one or more towers(or pylons). Mostly the cables form a fan-like pattern or series of parallel lines. The main span of cable-stayed bridges, which consists of two towers, ranges from 100m to 1100m. Analysis of cable-stayed bridge involves two main stages:

1.1 Final Stage Analysis

Starting Point of a cable-stayed bridge is an idealized stressed state at a given time for permanent loads, and this is called the final stage. Initial cable forces are determined for this final stage. Further static and dynamic analyses are undertaken using the final stage.

1.2 Construction Stage Analysis

Construction stage analysis of a cable-stayed bridge can be in backward sequence or forward sequence. As the determination of the initial cable forces of the final structure does not consider the actual construction process, a detailed construction stage analysis is needed to determine the forces in the cables at each construction stage. Further, we check stresses in the girder, pylon, and cables at each construction stage such that cable forces of each stage are finalized.

2. Unknown Load Factor Method to Optimize Cable Pretensions

In the design of cable-stayed bridges, we often face a problem where we would seek a solution to cable forces necessary to satisfy a given design requirement. Midas Civil can solve this type of problem using an optimization technique by calculating the optimum variables for given constraints and object functions. For constraint conditions, equality and inequality conditions are permitted.

By using the optimization technique, a solution satisfying the equality/inequality conditions is obtained. Numerous solutions to the unknown loads exist depending on the constraints imposed on the Equality/Inequality conditions. Midas Civil finds a solution to Equality/inequality conditions, which uses variables that minimize the given object functions. Midas Civil allows us to select the sum of the absolute values, the sum of the squares, and the maximum absolute values of variables for the object functions. Weight factors can be assigned to specific variables to control their relative importance, and the effective ranges of the variables can be specified.

A comprehensive understanding of a cable structure is required to use the above optimization technique for finding necessary design variables. Since Equality or Inequality conditions may not have a solution depending on the constraints, selecting appropriate design conditions and object functions is very important.

Unknown Load Factor Method can be used for:

The procedure of calculating the initial prestress for the cable-stayed bridge by the unknown factor method is outlined in Figure 1.

Figure 1. Flowchart for initial cable pretension calculation

4. Main Factors to be Considered for Cable Optimization

3.1 Creep and Shrinkage Properties

Creep and shrinkage effects will be significant in long-span bridges like cable-stayed bridges. Optimized pretension without considering the erection sequence can be obtained using an unknown load factor method and further these pretensions shall be used for creep and shrinkage.

3.2 Multiple Tensioning of Cables

As Unknown Load Factor does not support multiple tensioning in finding the cable forces, we have to assign the first tensioning as “Unknown” and then optimize the cable forces.

3.3 Large Displacement Effect

Large displacement effects can be significant, and there can be convergence issues if the large displacement effect and creep&shrinkage effects are considered simultaneously in the first run of the unknown load factor method. Hence it is recommended to optimize the cable pretension first by considering creep and shrinkage only. Then in the next step, a large displacement effect (Non-linear construction stage analysis) can be considered with these pretensions.