After the initial planning, the next stage of erection design involves the step-by-step staging analysis for the incremental launching stages. At the planning stage, decisions related to the launch configuration such as number of girder line to be launched, length of launch bed, temporary works such as launch nose size, number of temporary supports have been made. This may have required some simplified line analysis whereby a single representative girder line is modeled using beam elements and typically the longest cantilever is assessed.
Incremental Launch Stages
For a detailed analysis, the first task is to define the launch stages. Sequencing the initial launch stages is crucial for every launch design to ensure stability until the first pier is reached and the continuous girder system, including the nose, spans at least two permanent supports. Before reaching the first pier, the erection engineer must verify that there is enough counterweight (from the weight of the connected segments or supplemented with external counterweight) on the launching pad side of the abutment to have a sufficient factor of safety against overturning. The figure below shows the initial launch stages requiring three temporary supports in the launch bed and two launch steps of 9m and 15m before touch down at Pier 1.
Analysis Model Creation
To perform the analysis, an FEM software with construction staging capabilities such as Sofistik, Midas Civil, CSI Bridge, or Larsa 4D can be used. The model of the launched structure will need to be created. For this, summarize geometric parameters such as span lengths, girder spacing, and cross-frame members. Specify the material properties for the steel girders and the launch nose. Identify the types and locations of temporary and permanent supports, including their relative elevations.
Create the finite element model by defining the bridge geometry. This involves creating nodes at critical points such as supports, intermediate points along the girders including locations where secondary cross members connect. Connect these nodes with appropriate elements representing components of the structural steel.
For the Sombrio Bridge, shell elements were used for the girder webs and beam elements for the flanges to capture torsional and warping effects accurately. Similarly, in the Gilbert River Bridge case, plate elements were used for the webs and beam elements for the flanges to capture the effects of horizontal wind loads and the local punching effect of the lateral guide on the bottom flange of the exterior girder. Include diaphragms or cross-frames if applicable. Input the material properties for the steel, such as the modulus of elasticity, Poisson's ratio, and yield strength. Define the cross-sectional properties of the girders, including the area, moment of inertia, and section modulus. Assign boundary conditions to represent the supports, whether they are pinned, or rollers, and include any temporary supports used during the launching process.
Analysis Process
The incremental launching process is divided into multiple stages, each representing a specific segment length that is added and launched. The model reflects the erected state of the girders for each stage, including active and inactive segments. Deactivation of segments is managed using the staged construction features in FEM software. Initially, only the segments that are part of the current stage are active, with new segments activated incrementally in subsequent stages. Boundary conditions are updated to reflect the new support conditions as the girder progresses across the supports.
For each stage, loads and boundary conditions are carefully applied. The self-weight of the active segments, launching forces, frictional forces at the rollers, and environmental loads such as wind are considered. Boundary conditions are adjusted to simulate the roller supports, with positions updated to reflect the new stage configuration and the relative motion between girders and supports during launching. Movable supports are modeled to account for changes in location and elevation, matching the cambered profile and slope.
In the Sombrio Bridge launch, fifteen critical stages of the launch were analyzed in one file. In the Gilbert River Bridge case, approx. thirty three stages of the launch were analyzed at every tenth of a span. The supports were activated at varying locations along the girders to simulate the launching process rather than moving the girders over the supports.
Treatment of Girder Camber
There are several approaches to capture the effect of girder camber on reaction distribution. If the software has the capability, the path coordinate system can be used to define the cambered shape of the girder segments, as done in the Sombrio Bridge launch analysis using Larsa 4D. If not, a workaround can be applied using a thermal load case to introduce camber into the girder segments, mimicking the actual camber effect and providing a realistic representation of the girder geometry during launching. This method involves a trial-and-error process where roller supports showing tension are deactivated, and the analysis is re-run until only compression supports are active. This approach was used in the Deh Cho Bridge launch analysis.
Another approach, used in the Gilbert River Bridge launch analysis, models the girders with uncambered geometry. Instead of using a thermal load case, the vertical positioning of supports is adjusted to account for camber and the launch slope. The cambered shape, launch slope, and launch nose slope are calculated in Excel. These calculations determine the necessary displacement of each support joint to engage properly in the FEM software. After running the analysis, deflections are checked to ensure the girder bottom flange elevation is above all supports. If any support needs to be engaged, indicating incorrect initial support conditions, adjustments are made and the analysis is re-run.
Results Interpretation
After conducting the analysis for each stage sequentially, ensure that the software accurately solves for deflections, internal forces, and stresses. Verify the results by checking deflections, stresses, and stability against allowable limits and criteria such as yield and buckling. If any stage produces results outside acceptable limits, iterate the staging process, adjust support conditions, or modify the model to achieve acceptable results. For the Gilbert River Bridge, dead loads and other relevant loads were applied in a non-linear static analysis, allowing the girder to lift off supports that would otherwise be in tension due to camber effects.
Erection Manual for Incremental Launching
Perform post-processing to generate detailed reports of the analysis results for each stage. Create plots for deflections, moments, shears, and stresses. Document the entire staging analysis process, including assumptions and results, ensuring compliance with the relevant project standards. Typically, the analysis results for each stage are documented in an Erection Manual for use by the launching crew on-site (see sample in the figure below). This manual includes relevant force and geometry control data, allowing the erector to foresee potential problems and implement mitigation measures in good time. Finally, have the model and results checked through a rigorous quality control process and reviewed by a qualified senior engineer to validate the analysis and ensure accuracy and reliability.
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