Forward Analysis for a Cable Stayed Bridge

In this case, the structural systems between backward analysis and forward analysis are different and therefore, key segment closure is different between the two analyses. This leads to the fact that the final member forces at the final stage from the forward analysis are different from the member forces from the initial equilibrium state analysis (at the final system (completed system)). In the initial equilibrium state analysis for the final system (completed system), after the self-weight of the structure, cable forces and superimposed dead loads are applied to the key segment, the member forces at the key segment are calculated. However, in the forward analysis, the girder is deflected by its self-weight and cable pretension at the stage immediately before the key segment closure. When the key segment is closed, it is not affected by the self-weight of other structural elements except for the key segment itself and cable pretension. These differences from different structural systems lead to the differences in analysis results. This problem is caused by not understanding the cable theory or by no existence of software taking care of this problem except for the software dealing with large displacement. But the above mentioned is unreasonable according to the following reasons:

Within elastic range, forward analysis result is the same as the backward analysis result. (e.g., not considering time-dependent effects).

If the key segment closure force is calculated, both forward and backward analyses will have the same result as that from initial equilibrium state analysis.

According to the cable theory, unstressed length of cable is calculated by the initial equilibrium state analysis, and in backward analysis the cable length changes as the structural system changes and accordingly cable force changes with cable length. Therefore, if the planned construction stages are applicable to the design, it is also possible to achieve the aforementioned with forward analysis. First, unstressed cable length is calculated based on the cable force from the final system (completed system) and cable forces for each stage can calculated by considering the cable length changes with construction stages. However, until now this theory has been feasible only with large displacement analysis. It is because when the cable is installed by the cantilever method the cable length should be a real displacement. In a large displacement analysis, a newly created member can be installed tangentially to the existing member. Tangent displacement is referred to as a virtual displacement. But in a small displacement analysis, it is difficult to calculate the cable force considering the virtual displacement. However, in midas Civil software, even in a small displacement analysis, a virtual displacement can be considered. Therefore, if the unstressed length is computed and thereafter the forward analysis is carried out, it is possible to perform construction stage analysis with forward analysis alone. 'Lack-of-Fit Force' function converts the relationship between the unstressed length and the cable length into pretension loads so as to calculate the cable forces for each construction stage. As long as 'Lack-of-Fit Force' function is used, it is possible to analyze staged construction with forward analysis alone without backward analysis. 'Lack-of-Fit Force'(LFF) signifies 'Additional Pretension', which is introduced during the cable installation where the change of structural behavior and structural system are considered, or 'Pre-applied Force', which is pre-applied to the key segment so that the key segment can be located at the same position as the completed system when the key segment is to be closed. During the forward analysis, if the program calculates the 'Lack-of-Fit Forces' for the cable and key segment elements and these 'Lack-of-Fit Forces' are reflected in the installation of cable and key segment, the final stage result from the forward analysis will coincide with the result from the initial equilibrium state analysis.

http://www.nbmcw.com/computer-software/500-forward-analysis-for-a-cable-stayed-bridge.html