Algor Software Helps Design Bridge To Minimize Risk Of Catastrophic Accidents

When the Øresund Link, connecting Denmark and Sweden over the strait of Øresund, opens in the year 2000 it will include the first bridge between the two countries. There will be heavy traffic on both the bridge and in the waters below. The charge to civil engineers working on the bridge was to design it to withstand a catastrophic accident. The engineers at ES-CONSULT, a Danish firm acting as one of many consultants on the bridge project, have used Algor software to take every precaution to make the bridge safe.

Using Algor finite element analysis software, engineers designing the Øresund Link Bridge were able to test variations of two different designs. They analyzed the main bridge and approach bridges separately because each model was less complicated than if all were analyzed together. The engineers reduced total computation time.

Øresund Link Includes Bridge and Tunnel

The Øresund link will connect Copenhagen, the capital of Denmark, with Malmø, a major Swedish commercial and industrial city. The link will consist of three parts.

1. A 3.7-kilometer sunken-tube tunnel, claimed to be the world's longest, will connect the Danish coast to a reclaimed island.
2. The 3.9-kilometer reclaimed island will support a viaduct which provides a transition between the tunnel and the bridge.
3. The 7.47-kilometer bridge connects the reclaimed island to Sweden.

The link, which will carry both train and vehicular traffic, will provide an economic boon to the economies of both countries since it will connect the regions to the European high speed railway network. ES-CONSULT was chosen from several organizations to consult on the bridge project.

Ensuring Safety

ES-CONSULT's goal was to propose a bridge design which was both safe and economical. They even tested for what would happen if a large ship crashed into it at the same time a high-speed train crossed its length of 7,470 meters. To make sure that the 60 tons per meter weight bridge would not crumble or the train not jump the tracks, the engineers conducted a number of finite element analyses on each of their designs.

"The simultaneous crash of a large ship while a train is using the bridge is not an unlikely occurrence given the traffic we expect over and under the Øresund," said Jakob Laigaard Jensen, an engineer with ES-CONSULT.

Analyzing the effects of a ship crashing into the bridge was critical, Laigaard Jensen explained. The strait of Øresund has heavy commercial traffic, including barges, car and train ferries, supertankers and cargo ships. The stakes are high. The high speed trains will carry hundreds of passengers. A train derailment could cause the loss of lives.

"We used Algor software to test variations of two different designs on the computer and weigh the pros and cons of each," said Laigaard Jensen.

"We chose Algor software for the analysis because it was cost efficient and user-friendly. We compared Algor's results with other FEA software, and found that Algor provided the high degree of accuracy we needed," Laigaard Jensen said.

Bridge Design

The engineers analyzed two basic design concepts:

• Trains and road traffic traveling on one level. With this design, the bridge had to have a wide bridge deck, the surface on which the traffic travels.
• Trains traveling on a lower level and road traffic on an upper deck. This design was narrower than the first, but taller.

"Our analysis with Algor software didn't reveal that either bridge configuration was superior. Rather, it showed that either design could work and provided us with critical information about both designs that we could compare against complicated cost-benefit criteria," Laigaard Jensen explained.

Each bridge design had three parts:

• A cable stay main bridge with a span of 490 meters and a clearance of 55 meters between the bridge deck and the surface of the water. A cable stay bridge can support a long bridge deck, which is what was required on this project. The bridge deck is supported by piers anchored in the bottom of the waterway and also by rows of cables which are fixed at the top of two pylons which rise vertically from the surface deck.
• Two approach bridges, linking the main bridge to the shore on each side of the strait, each 120 meters long with varying clearances between the bridge deck and the water.

The engineers designed the main bridge with 7,400 degrees of freedom and the approach bridges with 3,066 degrees of freedom. Degrees of freedom measure how much the model can move. The number of degrees of freedom controls the complexity of the model. The more degrees of freedom, the more equations and unknown variables have to be evaluated by the software, but also the more realistic the model will be.

How the Bridge Was Analyzed

The engineers chose to design and analyze the main bridge and each of the approach bridges separately. Because each model was less complicated than if all were analyzed together as one model, the engineers were able to reduce total computation time.

Laigaard Jensen, along with Eihf Svensson of ES-CONSULT, created a finite element model of the bridge using standard beam elements provided in the Algor software. They used sets of equivalent discrete linear spring models with the springs arranged vertically and horizontally to represent the foundation of the bridge.

The engineers performed dynamic analyses on the bridge to assess the impact on the bridge deck of a ship colliding with one of the support piers. The analyses were linear since deformations in the bridge materials would not be significant for the overall behavior of the bridge.

The engineers conducted six collision cases in detail for each of the two conceptual designs. The scenarios accounted for derailment by rolling off the track and rising off the track. For both rolling and rising, they considered a number of ship sizes and collision points.

"Algor software's fast numerical algorithms and high degree of accuracy enabled us to calculate our scenarios quickly," Laigaard Jensen added.

The engineers also used Algor's modal analysis, which tests where the natural frequencies will occur. They conducted a reference analysis based on direct time integration to corroborate that the modal analysis results were consistent with what more time-consuming direct time integration analysis computations would have revealed.

The engineers used a derailment formula that assumed a peak acceleration exceeding one meter per second squared would lead to derailment. The engineers were able to determine that a ship collision could potentially lead to derailment of a train on the bridge. The results were included in a risk analysis study which concluded that to reduce the risk of derailment it would be necessary to build islands in front of selected piers to provide a "buffer" between the bridge and water traffic.

The engineers analyzed the dynamic interaction between trains and the bridge using the Algor FEA models. "These same models will also be useful during the design and construction phase when answering technical queries about different accident scenarios," said Laigaard Jensen.

Construction Underway

Contractors for the bridge were selected in October 1995. Island reclamation, tunnel construction and bridge design detailing is already underway. Contractors have begun building a precast concrete facility near Malmø to support the bridge-building effort. Bridge pylon construction is slated to begin next April with steel erection beginning in September 1997. The Øresund link is expected to be completed in the year 2000.

ES-CONSULT will assist the builder and future owner of the bridge, The Øresundskonsortiet, to manage the design and construction process in collaboration with other consulting engineering companies and contractors.