Passerelle Leopold Sedar Senghor

Structure Information

The Passerelle Leopold Sedar Senghor, a pedestrian bridge, is located on the Seine River in Paris, France. It sits between the Tuileries Gardens and the Musée d’Orsay. You can see where it is located relative to the city in Figure 1.

Figure 1. Map highlighting the location of the bridge.

It was constructed between 1997 and 1999. This bridge was built during important years. I was born in 1997, and my sister was born in 1999. The bridge standing today was built to improve the area and create a better space for tourists. The bridge was constructed as a part of the Grand Louvre project. Marc Mimram, an architect and engineer, designed the bridge. He won a competition to replace the bridge that was demolished in 1992. It was funded by the French state as a part of the project. [3] Spanning the Seine, it includes two paths that connect at mid-span, which can be seen in Figure 2.

Figure 2. The bridge spanning the Seine on a beautiful day.

 

Historical Significance

This wasn’t the first time a steel arch bridge was built, but Mimram did put a new twist on the bridge. Two paths exist on the bridge. You can climb the stairs from ground level to the top of the arch, or you can walk across the deck. This innovative design of the two walkways merging at mid-span was very important for this area in Paris to bring together the two sides of the Seine. No new construction techniques were used. Before this bridge, Mimram had only helped design a few structures. Following this bridge, he came to fame and designed many other pedestrian bridges and structures for France and many other countries. The Leopold Sedar Senghor has a striking resemblance to one of Mimram’s later bridges, over the River “La Vilaine.” In Figure 3, you can see how there are two paths on the bridge. One is on the arch and the other is on the deck, which resembles his bridge from 1999.

Figure 3. La Vilaine Bridge which resembles his earlier bridge. [1]

Cultural Significance

The first bridge built here was the Passerelle Solferino, which was inaugurated by Napoleon III in 1861. This bridge got its name from the Battle of Solferino in 1959 in which Napoleon III defeated the Austrians. [4] It was demolished because of extensive damage, and a new pedestrian footbridge was put in its place. This second temporary bridge was also demolished in 1992. The bridge standing today was renamed the Passerelle Leopold Sedar Senghor in October of 2006 to recognize Senghor, a major African intellectual during the 1900s. He was the first Senegalese president for 20 years and was a member of the Academie Francaise, so they named the bridge after him. [3] Many adored this bridge for its elegance and light design. Mimram received the Equerre d/Argent (Silver T-square), a French architecture award, for this bridge. [6] Only one of these awards is given annually, so France admired this piece of work. When the bridge was opened, ministers of culture and equipment were there, which was huge for a Parisian structure. However, two issues arose when this bridge was opened. The wood surface of the deck was slippery, and the bridge swayed, sort of like the Millennium Bridge. To fix these problems, Mimram added anti-slip strips and dampers as shock-absorbers. [5] Controversy also arose from this bridge. One piece of controversy was that the minister of culture sent the Parisian Mayor’s invitation for the opening of the bridge a little late which caused the Mayor not to come. The bridge was closed for a short time because the city did not want to accept the bridge since the Mayor didn’t show to its opening. Also, many engineers who disliked architects from the Ponts et Chaussees school, where Mimram studied, attacked his project since he worked as both an engineer and architect. A third group brought controversy over the bridge. Environmentalists said that the wood Mimram used for the bridge was endangered, but he had gone to Brazil and studied forest conservation. [6] After a few months of the bridge’s opening, all the controversy went away because many appreciated its symbolism for Paris and its lightness across the Seine. The human cost involved with this bridge only occurred during construction and fixing the deck issues. Mimram and many other builders spent a lot of their time to make sure the bridge was almost perfect for the people. Now, the bridge serves as a pedestrian footbridge across the Seine.

 

Structural Art

Following Billington’s criteria, I will first look at the efficiency of this bridge. Mimram tried to use the minimum amount of material for his bridge. It was so light that it even swayed in the wind. Therefore, Mimram attempted at using the least amount of material for his bridge, so the efficiency aspect of the bridge contributes to it being structural art. Next, I will look at the economy of the bridge. The bridge was funded by Paris, and Mimram won the project through a competition, so Paris thought that the Mimram’s design was best for the city. The bridge cost 9.8 million euro, which is a bit on the high end for pedestrian bridges, but considering this bridge has two pathways, sits in a busy area, and was built in two years, it fulfills most of the economy aspect of structural art. The last component of structural art is elegance. Just by looking at the bridge you can tell it is very elegant. The load path is clear, the bridge is very open, and the bridge is very light. Mimram wanted to make the bridge feel light and infinite. The Brazilian wood on the deck and the openness of the arch make it light and having the two paths makes the bridge feel infinite. I believe Mimram fulfilled this last aspect the most. He designed the bridge to fulfill the city’s needs, and followed the 3 E’s, so I believe this bridge is structural art.

 

Structural Analysis

Mimram became the designer for this bridge through a competition. Paris picked his design so that people would come visit this area and enjoy crossing the Seine. The arch is made of steel from the Eiffel company, which I think is really cool. [3] The abutments are made of concrete, and the deck is made of a Brazilian wood, Ipe. The foundations were built first, and they used a watertight enclosure so that they could work. The skeleton was built with supports, one of which was a pier from the older Passerelle Solferino. Builders divided the arch into 6 sections which were put together with the struts at the site of the bridge. Cranes put the large pieces together. Finally, the deck was placed on top of the arch and struts. The structural system includes two abutments (one on each side) and a steel arch with V-shaped struts that connect the deck to the arch. [7] The arch has two layers that are connected by a Vierendeel truss which doesn’t have any diagonal elements. The bridge consists of two pathways. One is at the bottom of the bridge and one is at the deck’s elevation. These two paths connect at mid-span. The live loads from pedestrians and the dead loads from the bridge’s weight are carried onto the deck and down through the V-shaped struts. The loads are then transferred as point loads onto the arch. The loads are transferred to the ground vertically and abutments horizontally, which can be seen in Figure 4.

Figure 4. Load path of the bridge.

To find the reaction forces of the bridge, I had to make some assumptions. I assumed the loads were transferred through the entire arch, not just where the V-shaped struts were. I assumed a live load for pedestrians of 90 psf. [2] I assumed an Ipe wood density of 69 lb/ft^3 and steel density of 7.85 g/cm^3. I then found the line loads associated with a bridge width of 15 m. I organized all the loads which you can see in Figure 5.

Figure 5. Load calculations.

I then found the vertical reaction forces through sum of y-components. Then, I cut the bridge in half and solved for the horizontal reaction force using the sum of the moments about the center. Since the bridge is symmetric, the horizontal forces are the same and the vertical reaction forces are the same. I then found the maximum force at the bottom of the arch. All of these calculations can be found in Figure 6.

Figure 6. Reaction forces calculations.

For this bridge, it was very important that Mimram communicate with the stakeholders about the bridge. He showed his design during the competition to communicate what the bridge would look like. He used drawings to highlight how light the bridge would be. He used the drawings to communicate with workers on the bridge as well. When the bridge swayed a little bit, he had to go back to his drawings and calculations with his workers and with authorities and show them how he fixed the resonance with dampers.

 

Personal Response

When I was in France, I passed this bridge a few times when we went to Musée d’Orsay. I initially saw someone running up the arch, and I had never seen that before. I never realized how awesome pedestrian bridges could be. The combination of the two pathways connects different groups of people like how the Seine connects two different parts of Paris. Being there made me realize that a bridge doesn’t have to be enormous to get people to fall in love with it; it needs to have a useful function and be a symbol for people who use it.

 

References

[1] http://www.mimram.com/en/?project=bridge-over-the-river-la-vilaine

[2] http://www.wsdot.wa.gov/eesc/bridge/designmemos/11-2009.pdf

[3] http://www.eutouring.com/passerelle_leopold_sedar_senghor.html

[4] https://translate.google.com/translate?hl=en&sl=auto&tl=en&u=http%3A%2F%2Fparis1900.lartnouveau.com%2Fponts%2Fpasserelle_leopold_sedar_senghor.htm

[5] https://translate.google.com/translate?hl=en&sl=auto&tl=en&u=http%3A%2F%2Fwww.planete-tp.com%2Fpasserelle-leopold-sedar-senghor-a96.html

[6] https://www.nytimes.com/2000/07/29/style/pont-solferinowater-under-a-troubled-bridge.html

[7] http://www.bath.ac.uk/ace/uploads/StudentProjects/Bridgeconference2011/papers/Vernet.pdf

Queen Elizabeth II Bridge

Structure Information

The Queen Elizabeth II Bridge spans the River Thames and joins Dartford and Thurrock. It is a part of the M25 London Orbital Motorway. In Figure 1, you can see where the bridge is in relation to the city of London.

Figure 1. Location of Queen Elizabeth II Bridge relative to the city of London.

Construction began in 1988, and the bridge was completed in 1991. This bridge was designed to allow for more roadway traffic using the M25, which circles London, to cross the River Thames. It consists of four southbound lanes, and this was important to match the needs of those using the M25. Instead of using the two  preexisting tunnels, southbound traffic moved to the bridge. You can see the four lanes in Figure 2.

Figure 2. Looking at Queen Elizabeth II Bridge from above. [2]

The bridge was designed by Dr. Hellmut Homberg, a German engineer, and other companies like Kvaerner Technology Limited helped in the design process. [2] In order to pay for the bridge, a Private Finance Initiative was created through the Dartford-Thurrock Crossing Act of 1988. This allowed for the toll revenue to pay off the debt from building the bridge. The Department for Transport manages the tolls. [1]

 

Historical Significance

When built, this bridge was the largest cable-supported bridge in Europe. Since the Pool of London is very important for large ships to access, this area was new territory for the bridge. Even though a cable-supported bridge did not use any new techniques, the design had to account for a height of 65 meters to allow ships to pass underneath, which is high. It is the only bridge east of the Tower Bridge on the Thames, so it was the first time a bridge was built high enough in this area to allow for large ships to pass through as well as support four lanes of traffic. [2] The cables are made of steel and the bottom piers are made of concrete and the pylons are made of steel, so no new materials were used. This bridge is relatively new, so it hasn’t been a model for future bridges yet, but since most of the other paths around this bridge that cross the Thames are tunnels, more people may start thinking of building more bridges or expanding this one. With the population of the London area growing, there will be more traffic, and the Department of Transport will have to determine how to increase traffic flow. What was cool about constructing the concrete pylons was that they were slip formed. Concrete was continuously powered for 24 hours a day for 10 days for each column. Also, no scaffold was used, so abseilers on ropes patched up holes as necessary. [4]

 

Cultural Significance

In an article I read, Dennis McNally, supervising the construction of the four piers, talked about how the area has become so industrialized since the construction of the bridge. In 1991, he could just see fields all around, but now it has changed significantly. McNally also expressed that there was controversy about what to name the bridge. On the Essex side, people wanted to name the bridge the Tilbury Bridge, not the Dartford Bridge. Its name is the Queen Elizabeth II Bridge because she opened the bridge in 1991, but many still refer to it as the Dartford Bridge. [4] One interesting thing that occurred earlier this year in February was the closure of the bridge for a brief time when a WW II bomb was found nearby. Luckily, it contained no explosives. [3] The present human cost of the bridge is a toll, which is used to help pay for the construction of the bridge and upkeep of the bridge. Today, the bridge is used for four lanes of traffic southbound for the M25.

 

Structural Art

Using Billington’s 3 E’s method to determine if the bridge is structural art, I will first determine if the bridge fulfills the efficiency component, or minimum materials. This type of cable-stayed bridge requires less material than a cantilever bridge and needs less cable than a suspension bridge. I believe that this bridge fulfills the efficiency component of structural art because it uses minimum materials with this design of the bridge considering the central span is 450 meters. Looking at the economy aspect of structural art, the bridge was estimated to be 120 million British pounds (about $160 million). The average cost of a cable stayed bridge is between $4500 to $5000 per square meter. [5] If I assume a width of 14.6 meters (4 lanes) and complete length of 2872 meters, the estimated cost would be about $187 million. The actual cost was less than that and compared to the cost of a suspension bridge ($8000-$9000 per square meter), is considerably less. [6] Therefore, I believe that this bridge fulfills the second requirement, which is economy or minimum cost. The third aspect I will address is elegance. This bridge is stunning and you can see the load path, but there is a disconnect between the piers and the steel pylons and cables. The color is different and the different material for the pylons creates a disjoint. The concrete piers also look bulky compares to the steel pylons and the thin cables. In Figure 3 you can see how it doesn’t look elegant. It’s not continuous. If the structure had been more cohesive, I would have given this bridge a point for elegance. Since this bridge satisfies two out of the three components for structural art, Billington would say it isn’t structural art because you need all three.

Figure 3. Noncontinuous aspects of the bridge. [7]

Structural Analysis

The design process consisted of a highway scheme under the “Department of Transport’s design, finance, build, operate, and transfer (DFBOT) principle.” [8] Once designed, construction took place. The four main pylons are made of steel and rest on top of concrete piers. The deck is made of reinforced concrete over steel. 112 cables support the bridge. Viaduct sections connect both sides of the bridge to the roadway. Construction lasted for only about three years, but like I mentioned before, there were some cool construction techniques used for this bridge. The concrete pylons were slip formed in which concrete was continuously poured. Also, abseilers on ropes checked everything after construction was completed to make the finishing touches because no scaffolding was used. Reinforced concrete caissons were used to support the piers, and these were constructed in the Netherlands. [8] When building the deck, they built the deck away from the pylons, which acted as a cantilever. The cables were installed as the deck was built. The structural system is a cable stayed bridge in which cables are attached to pylons and these cables hold up the deck. The bridge supports its own self weight, a dead load, and a live load from cars moving across. All the cables are in tension and the pylons and piers are in compression. The deck is also in compression. The dead load from the weight of the bridge (I assumed a concrete bridge with a certain cross-section for the box) and the live load from cars and trucks driving across are transferred to the deck and then the piers. This can all be seen in Figure 4.

Figure 4. Depiction of the load path for the QEII Bridge. [11]

Assuming the deck is a hollow box, I made assumptions based on research about the size of the deck’s cross section considering it’s four lanes across. I found the total cross-sectional area of the deck and then divided it by two because each section of the bridge has two adjacent piers, so the load on one pier only covers half the cross-sectional area. Assuming the deck is concrete with a density of 145 lb/ft^3, I found the dead load to be 9177.31 lb/ft. I also used AASHTO’s specifications for H20-44 and HS20-44 trucks (640 lb/ft) to ensure that the maximum load was used for safety. [10] Since traffic is very congested on this bridge, I assumed that the load was applied over the entire bridge. As seen in Figure 5, I calculated the entire load for the bridge.

Figure 5. Calculations for the loads.

Once I found the load I assumed lengths in between each cable. Each pylon had 14 cables on each side. With my distances assumed based on the length of the main span, I calculated the angles of each of the 14 cables. I only needed to do calculations on one side because the cables are symmetrical to the other side of the mast. As seen in Figure 6, I calculated the angles. I labeled cable 1 as the inner cable and cable 14 as the outer cable.

Figure 6. Calculation of cable angles.

Considering that cable 1 includes the area between the pylon and the cable and the half the area in between cable 1 and 2, I found the weight force, tension force, and force in the deck. All of these calculations can be seen in Figure 7.

Figure 7. Calculations for the tension in cable 1 and bridge force.

I found the forces for the other 13 cables, which can be seen in Figure 8.

Figure 8. Calculations for all the cables.

Once I found this for all the cables, I found the force in the mast. Since there are identical cables on the other side of the mast, I multiplied all the weight forces by 2. This can be seen in Figure 9.

Figure 9. Calculation of the mast force.

By finding the tension forces and the force in the mast, designers can determine how large the cables need to be and how large the pylons need to be to support the bridge based on the materials used. To communicate the design to stakeholders, plans were printed so they could follow them. Many supervisors like McNally oversaw different aspects of construction of the bridge. Models weren’t used for this type of bridge, but since it was built close to the end of the twentieth century, plan sets and standards were used to guide builders. Since a Private Finance Initiative was used for this bridge, it was important that engineers were clear with the stakeholders about all aspects during construction of the bridge with plan sheets. Construction of this bridge was relatively quick.

Personal Response

On the way to the Cliffs of Dover, this striking bridge caught my eye. In the main area of London, the height of many bridges is realistic. Sitting on the train, the bridge caught my attention almost immediately because of how tall and different is was. Being there, I never realized how different this bridge was than the other bridges along the Thames west of this bridge. The size and style of the bridge aren’t like any of the bridges down the river. Looking at this bridge shows how far we’ve come in the bridge design process since the other London bridges were built.

 

References

[1] https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_

data/file/604529/59263_Dartford_unnum_cov_and_text_A4_v2.pdf

[2] http://www.transporttrust.com/heritage-sites/heritage-detail/queen-elizabeth-ii-bridge-dartford

[3] http://www.echo-news.co.uk/news/15990727.Dartford_Crossing_bomb_contains_no_explosives/

[4] http://www.bbc.co.uk/news/uk-england-kent-15467112

[5] http://www.partnershipborderstudy.com/pdf/Cable%20Stay%20Bridge_2.pdf

[6] http://www.partnershipborderstudy.com/pdf/Suspension%20Bridge_2.pdf

[7] http://www.geograph.org.uk/photo/1515684

[8] http://www.engineering-timelines.com/scripts/engineeringItem.asp?id=105

[9] https://www.newscientist.com/article/mg13217924-900/

[10] http://www.ce.memphis.edu/3121/notes/notes_06c.pdf

[11] https://www.flickr.com/photos/dgeezer/13179342704

Connecting Railway, Schuylkill River Bridge

Structure Information

The Connecting Railway, Schuylkill River Bridge is in Philadelphia, PA, and it crosses the Schuylkill River. Construction began in 1866 and was completed in 1867. The bridge has seen modifications, which took place in 1873, 1897, and 1912-1915. The main purpose of the bridge was to help create a more direct route in the railroad system from Philadelphia to New York City. It was designed by the Chief Engineer of the project, John A. Wilson. The Pennsylvania Railroad (PRR) helped fund the Connecting Railway. The bridge in Figure 1 came from reconstruction in 1912, which was designed by Alexander C. Shand at the discretion of PRR. [3]

Figure 1. View of the bridge across the Schuylkill. [1]

Historical Significance

Initially, the bridge had a cast and wrought iron, double-intersection Whipple truss in the center of stone arches. When this type of truss couldn’t carry the increasing railway loads, the Whipple truss was replaced by a Pratt truss. They switched the trusses in under two and a half minutes, which paved the way for fast construction techniques. When traffic began to pick up in the twentieth century, the PRR wanted to widen the bridge. This new bridge did not use any innovative structural engineering designs because it was made of stone. Some marked how unusual it was because reinforced concrete was already available. During this time, city authorities like the Fairmount Park Commission most likely influenced the use of stone. It made the bridge quicker to construct and less expensive. Even though the construction techniques weren’t new, it was the first bridge to eliminate the detour between West Philadelphia and the waterfront across from New York City. [3]

 

Cultural Significance

What was interesting about the initial construction of the bridge was that Wilson wasn’t in charge during construction. He took a job with the Philadelphia & Reading Railroad, so George B. Roberts oversaw construction. In both major construction periods, the designer didn’t do much. Roberts oversaw construction in the first bridge and the builders made decisions about how to construct the 1912 bridge. Many appreciated this bridge when it was first built because it made the commute time by rail between Philadelphia and New York City less. This bridge was used as inspiration for many artists, including Thomas Eakins and Edmund Darch Lewis. This part of the Schuylkill River is also used by many rowing teams. I found the bridge when I was at the Dad Vail Regatta recently. Many people row under the arches of it and can see the design. In Figure 2, you can see a painting by Eakins that portrays a man in a single, rowing. Today, Amtrak and Pennsylvania Transportation Authority’s passenger trains use the bridge. [3] Even through all of the reconstruction phases, the bridge is still used for the reason it was created.

Figure 2. Max Schmitt in a single scull. [2]

Structural Art

By using the stone, the PRR was able to save money, which fulfills the economic portion of structural art. However, even though the old bridge had a truss, the new one has stone arches. The truss would have been lighter and more open, but you can’t see through the stone arch. This makes the bridge not aesthetically appealing. Also, the new bridge wasn’t trying to conserve material. They built it out of stone instead of concrete even though concrete or another material would have been stronger. Since large span stone bridges can’t support trains, multiple arch spans had to be used for this bridge. The builders for reconstruction were more focused on making the new bridge look like the old bridge instead of trying to create structural art.

 

Structural Analysis

At first design, stone arches were placed on both sides of a cast and wrought iron, double-intersection Whipple truss. The arch spans were 60’ stone-faced brick, and they were separated by 7’ piers to support the arches. In the 1873 reconstruction, builders increased the thickness of the stone piers at both ends. Then, a Pratt truss replaced the Whipple truss in 1897 to support increased railway loads. When the Pennsylvania Railroad wanted to increase the number of tracks going across, Shand initially designed two 103’ spans and a pier in the middle of the river which would go underneath the existing truss. Eyre Shoemaker, Inc., the construction company, was not able to build on the old arches because they were damaged. Instead, Shoemaker tore down the arches and rebuilt it trying to resemble the preexisting bridge as much as possible. Today you can see what Shoemaker built. There is a 22’ pier in the center of the river that supports the two main arch spans of 103’. On the outside of these arches are two more piers that are slightly larger resembling the 1873 reconstruction. Next to these two piers lay more stone arches that have only a 60’ span. [3] The arches were slightly corbeled so that the bridge could take more load as well. The bridge involves a dead load from the stone, which can be very heavy, and a live load from the trains. As seen in Figure 4, the load is transferred down the arch and to the pier.

Figure 4. Load distribution of the arch.

Next, I analyzed the different parts of the arch. As seen in Figure 2, I assumed that the depth of the bridge was about 90 feet since there are five train tracks, that the height of the load was 10 feet, and the weight of sandstone is 150 lb/ft^3.

Figure 5. Calculation of weight of sandstone.

Once I got a number for the load distribution, I decided to calculate the live load at different parts of the main span since the train is a live load. I assumed the train load as a uniform load, and I also assumed the passenger train weighs 1.08 million pounds and with 6 cars and a locomotive, is around 600 feet in length. This came to a uniform load of about 1800 lb/ft existing on top of the dead load of the sandstone. Using this information, I was able to calculate the vertical reaction forces, as seen in Figure 6.

Figure 6. Finding vertical reaction forces.

Once I did this, I made a cut in the middle of the arch. I was then able to solve for the horizontal reaction force and the maximum force at point A, as seen in Figure 7.

Figure 7. Calculation of the maximum force.

Since the train is moving, I decided to treat the train as a uniform load only in the first quarter of the arch, which can be seen in Figure 8.

Figure 8. Live load on part of the arch.

Using the entire beam, I was able to calculate the reaction forces at A and then the maximum force at A. All the calculations can be found in Figure 9.

Figure 9. Calculations to find the reaction and maximum forces.

Since these calculations were for the main span, I also included one analysis of a bridge with the smaller, 60-foot span. Again, I made all of the assumptions I previously made for the 103-foot span arch. As shown in Figure 10, the span is 60 feet, but everything else is the same.

Figure 10. Loads on the 60′ span arch.

I was then able to calculate all of the forces, which can be seen in Figure 11.

Figure 11. Calculations for 60′ span arch.

Engineers like Shand and others would have made calculations like I did (and more complicated ones since I only know so much structural engineering) to figure out how much load a pier could take through combining the maximum loads of two arches. It was especially important for this bridge that the engineer make the piers large enough to support the weight of the stone and of the trains moving across. When Shand’s design didn’t work initially, Shoemaker took his own initiative to make sure that the bridge was stable and would hold the railway load.

 

Personal Response

You see old railway bridges in books and movies from the past, but you never realize how different a stone arch bridge across the Schuylkill is from the surrounding area. Philadelphia houses many types of bridges, and surrounding this bridge are many up-to-date bridges that make this bridge seem out of place. I really enjoy looking at historic structures, but it is a little odd to see this kind of bridge still used among all the newer bridges. I’m sure it sticks out like a sore thumb to many who see it visiting Philadelphia.

 

References

[1] https://en.wikipedia.org/wiki/Pennsylvania_Railroad,_Connecting_Railway_Bridge

[2] https://www.metmuseum.org/toah/works-of-art/34.92/

[3] http://cdn.loc.gov/master/pnp/habshaer/pa/pa1600/pa1646/data/pa1646data.pdf