Software Used to Study Stability of Scandinavian Bridge

Bridges Article December 28, 2000
Printer-friendly version

The year 2000 will see the first cars and trains
cross the Fixed Link across Oresund, a body of water between
Zealand in Denmark and Scania in Sweden. Providing a historic
link between the cities of Copenhagen and Malmo, the new traffic
facility and its 204-m-high bridge pylons will be clearly
visible from the Swedish and Danish coastlines.

When, in
1990, the governments of Denmark and Sweden decided to build the
Fixed Link across Oresund, they also resolved that it would run
between Copenhagen and Malmo thereby serving two purposes: first
to link the rail and motorway networks in the Nordic area with
Central Europe via Denmark and, secondly, to connect Denmark's
capital, Copenhagen, with Sweden's third largest city, Malmš.
When completed the bridge will provide an economic boon to the
economies of both countries.

The Fixed Link's major
components from Denmark to Sweden are:

-- An artificial
peninsula extending 430 m from the Danish coast.

-- A 3,510
m immersed tunnel from the artificial peninsula to the
artificial island off Saltholm Island in the middle of Oresund.
The tunnel section will be constructed from prefabricated
concrete.

-- A 4,055-m-long artificial island.

-- A
7,845-m, two-level bridge across the Flinte Channel.

-- A
toll station and control center at Lernacken on the Swedish
coast.

Oresundskonsortiet is responsible for project design
and construction of the Fixed Link. The company exclusively
holds the concession to operate the link and to collect toll
fees from the users. The two countries are individually
responsible for project design and construction of the works up
to their respective coastline.

The bridge

Engineers are
taking every precaution to make the bridge safe. Because there
will be heavy traffic on both the bridge and in the waters below
they are even testing it to see what would happen if a large
ship crashed into it at the same time a high-speed train was
crossing it. To make sure that the 60-ton perimeter-weight
bridge will not crumble or the train not jump the tracks, the
engineers used finite element analysis (FEA) software from
Pittsburgh-based Algor Inc. (Write in 904).

"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 ¯resund," said Jakob Laigaard Jensen, an
engineer with ES-Consult, a Danish firm acting as a consultant
on the bridge project. "Analyzing the effects of a ship crashing
into the bridge was critical," Laigaard Jensen explained. The
strait of Oresund has heavy commercial traffic, including
barges, car and train ferries, super tankers and cargo ships.

"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. 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.

-- Trains traveling on a lower level and road traffic on an
upper deck. This design was narrower than the first, but taller.

"Our analysis 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 m and a
clearance of 55 m between the bridge deck and the surface of the
water, and two approach bridges, linking the main bridge to the
shore on each side of the strait.

Analyzing the bridge

The engineers chose to design and analyze the main bridge and
each of the approach bridges separately. Because each separate
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 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 because 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.

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.
They 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 bridge, designed
by Danish architect Georg Rotne, features a harp-shaped
cable-stayed construction with cable anchored to the
superstructure's girders at 20-m intervals. It will be supported
by two pairs of pylon legs consisting of two concrete towers,
cast in situ, rising 204 m above sea level. The total length of
the cable-stayed bridge will be 1,092 m. The length of the
entire bridge will be 7,845 m with two levels motor vehicles on
top and a high speed train on the bottom.

Construction work
on the coastal sections began in August 1995. The perimeters of
the peninsula and the island have been completed and backfilling
with materials dredged from Oresund is progressing rapidly. A
casting yard for the elements for the almost 4-km-long tunnel,
has been built at Copenhagen's north harbor, where casting of
the tunnel elements began in November 1996. The bridge elements
are constructed at a new plant at Malmo's north harbor. Casting
of the caissons for the two large bridge towers began in June
1996.

About the author: 
Banasiak is a Roads & Bridges editorial staff member.
Overlay Init