In order to complete the design of a cable-stayed bridge and to analyse the structure in full, a construction stage analysis must be included. The construction stages should be modelled to check the stability of each step separately. Depending on the erection method, the structural system can significantly change. Sometimes, a change of a system during the construction can result in a more critical condition for the structure compared to that of the final state. Therefore, an accurate construction stage analysis should be carried out to check and to review the stresses in the cables, the girder and the pylon. In no stage is a compression in the cables possible. This would be a theoretical case using truss elements for the cables in the analysis of the structure.
Furthermore, the geometric profile of the girder is also very important during the construction. To avoid serious problems, it must be ensured that both cantilever ends meet smoothly together in the final construction stages. It should be noted that the internal forces of the structure and the elevation of the girder vary in the construction process. This usually happens because of the bridge segments that are built by a few components, the heavy lifting operations during the erection in case of prefabricated segments and the erection equipment, which is often placed at different positions during the construction. Additionally, because errors such as the weight of the segment and tension forces in the cables, wrong values for material properties, etc. may occur, monitoring and adjustment during erection are absolutely needed.
The simulation of the construction process must be adjusted to the field measurements during the construction. In a later chapter, these procedures are illustrated in detail.
The general objectives of the simulation are:
• Determination of the required tension forces in the cable stays at each construction stage
• Specification of the fabrication girder geometry
• Setting the elevation of the girder segment
• Calculation of the structural deformation at each construction stage
• Controlling of the stresses in the girder and pylon sections
Construction state analyses for a cable-stayed bridge can be classified into the forward and the backward analysis. The forward analysis reflects the real construction sequence, whereas the backward analysis is performed by regarding the state of the final structure. The elements and loads are eliminated in the reverse sequence to the real construction sequence. It is assumed that all of the creep and shrinkage deformations of concrete are completed, i.e., a state 5 years or 1500 days after the completion of the bridge construction [5].The cable prestresses, which are induced during the construction, can be calculated by using the backward analysis. These results are the guidance for the forward erection and stressing. Using the forward analysis, time dependent effects can be considered and implied in the design.
To perform a construction stage analysis, construction stages must be defined. Main girders, cables, boundary conditions, loads, etc. are activated or deactivated to consider the effect and the change on the structure.
The changing of the structural system by modifying the boundary condition or removing certain elements might cause gaps between the forward and backward analysis. Activation errors can
Chapter 3: General description of a Construction Stage Analysis 36
occur and remain in the system or even increase as the construction stage analysis continues.
In the simple case of a steel structure, where no time-dependent effect must be considered, the last stage in the forward analysis should theoretically correspond to the first stage in the backward analysis. This will hardly be the case in an analysis considering time dependent effects, as the difference between the forward and backward analysis increases. However, these two methods may be alternatively applied until a convergence is reached within a tolerable range.
For the construction stage analysis, Bruer [17] proposes an extended method of the before explained Unit Load Method. The unit load cases are applied to the different structural systems, which exist at different construction stages, as illustrated in the figure below.
Figure 3-3: Unit Load Case Method for construction stage analysis [17]
The loading cases for each construction stage are combined to form the set of simultaneous equations, which are solved to find the required multiplication factors for the unit loading. In this procedure, the influence of the different stages is considered and by applying an iterative process, the calculation results in the defined ideal system in the final construction stage. In the analysis programme RM2000, time dependent effects, as well as non linearity can be included in this procedure using the AddCon function as it was briefly explained before. However, this programme has not been used in the construction stage analysis presented in this thesis and therefore it is difficult to comment this procedure or to judge about the reliability of this function.
The method of modelling a construction stage analysis by the computer programme MiDAS is explained in more detail in the following chapter. To give the reader an overview of the methods and the different phases of the calculation, a simple cable-stayed bridge is being analysed.