On the Job: FEA Plays Part in High-Profile Olympics Project14 Apr, 2005 By: Cadalyst Staff Cadalyst
Engineers use Strand7 to model and analyze a new roof structure for the centerpiece stadium of the 2004 Summer Games
A highlight of the 2004 Summer Olympic Games in Athens, Greece, was the Olympic Athletic Centre of Athens Stadium. This venue, called OAKA Stadium, was used for both the opening and closing ceremonies of the Games as well as for numerous high-profile athletic competitions and other events.
As part of the redevelopment of the Olympics site for the Games, a new roof structure was built over the main stadium. This new roof was designed by the renowned Spanish architect and engineer Santiago Calatrava. Sinclair Knight Merz was engineering consultant on the project. SKM's brief was to engineer the entire OAKA roof structure. Working from the firm's London office, a team of SKM engineers from the United Kingdom, Australia and New Zealand used Strand7 finite-element analysis software to undertake this project.
Details of the Roof Structure
The OAKA Stadium roof structure consists of two coverings, each spanning more than 300m in length and varying in width from 60m to 100m. Each covering is supported by a curved arch structure comprising an upper arch tube and a lower arch torsion tube (figure 1). The upper arch is constructed from a circular, hollow section 3m in diameter with a variable wall thickness of as much as 100mm. The lower arch is similar to the upper arch but is 3.6m in diameter.
Figure 1. In-progress construction of arches.
The two arches on each covering are connected by a row of steel cables arranged in a vertical plane. Steel diaphragm plates are installed at every cable connection point. The main roof rafters are built into the lower arch and cantilever on both sides of the arch. An additional row of cables connected to the top arch supports the external rafters along the perimeter of the stadium, while another row of cables supports the internal rafters at approximately midspan. Transparent cladding (polycarbonate roof tiles) are installed over the rows of purlins, perpendicular to the rafters.
Erecting the Roof
The entire roof structure is pin-supported at only four points. It was initially erected in two symmetrical halves at temporary locations at each side of the stadium (figure 2); this allowed construction on the roof to proceed without hindering work on the main stadium.
Figure 2. Aerial view shows the east side arch in position and the west side arch ready to be moved into position.
Each half was then moved into its final position by sliding it along temporary supports. Finally, the bases were fixed to permanent supports.
SKM used Strand7 finite-element analysis software extensively for modeling and analyzing the OAKA Stadium roof structure (figures 3, 4 and 5). The system was used not only for modeling the complex stadium roof structure but also for simulating the entire construction process.
Figure 3. A screen capture from Strand7 shows finite element analysis of the new OAKA Stadium rood structure.
Figure 4. Strand7 model shows connection of roof girders to lower torsion tube.
Figure 5. Strand7 model shows the arrangement of cables between the upper and lower arches.
For modeling the construction process, one of the most useful features of Strand7 was its ability to start a new analysis of the model using the results of a previous run as the initial conditions.
"Using this and other features of Strand7, we were able to simulate the stages of construction by applying new conditions and loads to a model that was already solved in a previous run," said Ljubisa Petrovic of SKM. Another use of this feature was to establish the pre-tensions in the cables required to achieve a desired final roof shape and final levels of tension in the cables. This procedure can be easily automated using the Strand7 API.
Another extremely useful feature for SKM was Strand7's ability to save the deflected geometry of the model and reuse it as a new and unloaded model for a subsequent run. This approach was used for calculating the preset roof geometry and to determine the initial shape that would produce the required final shape under the applied loading. As the two sections of the roof structure were to be assembled using a temporary support structure, these tools enabled SKM to establish the initial geometry such that when the complex construction procedure was complete, the entire roof deflected into the final shape as designed by the architect.