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Ponts des Arts Bridge

Ponts des Arts Bridge

The Ponts des Arts Bridge is known by most people, especially tourists, as the bridge of Loveeee. Ever since the bridge was built, couples in love would write their names on a lock and lock it to the bridge gates, declaring their love to the world and making it everlasting in history. Sorry, I’m trying not to gag at the cheesiness. Talk about PDA. Anyway, the locks were removed in 2014, but the bridge still stands as the bridge of love to those who visited it. What most people don’t realize is that this bridge carries far more cultural significance than the locks. Technically this bridge is the second Ponts des Arts bridge, but since it is meant to replicate the original as closely as possible, the importance still stands. The original bridge was a symbol of France’s competition with Britain, and Napoleon ordered the original bridges creating personally. So, can we please move away from the love and focus on the interesting stuff? Because the both the past and present Ponts des Arts bridges are nothing if not interesting.

Figure 1: Ponts des Arts Bridge [1]

Structure Information

Okay, now we can get down to the basics, so stick with me.

Location: River Seine, Paris, France

Purpose: Connects the Louvre to the Insitut de France

Type: Deck arch pedestrian bridge

Main Material: Steel

Abutment and Piers Materials: Reinforced Concrete dressed in stone

Deck Material: Timber

Elements:

  • 7 arches
  • 6 piers
  • 2 abutments
  • Deck
  • Deck gates

Total Length: 509’

Arch Span Length: 72’

Width: 36’

Figure 2: Ponts des Arts Close Up

 

As I mentioned in my introduction, this is the second Ponts des Arts bridge. The first bridge in some ways is more historically and structurally significant because it was the first iron bridge in France, and Napoleon wanted it to compete with the Iron Bridge, the first bridge made of iron in the world. However, the bridge that currently stands is modeled to resemble the original, but has two main differences that must not be confused:

  1. The CURRENT bridge is made of STEEL. The original bridge was famous for being made of cast iron in the early 19th century, but since steel is much more efficient and widely used now and when the current bridge was built in the 1980s, it is made of steel, NOT IRON.
  2. There are SEVEN arches on the CURRENT bridge. The original bridge had nine arches, but when remaking it, they decided that it would fit in more with its neighboring bridges over the River Seine if it only had 7 arches.

Historical Significance

To properly explain the significance in terms of technology, I have to address both the original bridge and the current one. The original bridge was much more innovative for its time being the first even iron bridge in France and one of the first few in the world. It was far more lightweight and elegant when compared to the Iron Bridge

or other stone arches at the time.

Figure 3: Original Ponts des Arts Bridge circa 1804 [2]

Figure 4: Iron Bridge [3]

Every member of the Ponts des Arts held a purpose and it efficiently used material, whereas the Iron Bridge was designed to show off its designer’s iron working skills, not its efficiency as a structure. So, the original Ponts des Arts Bridge is extremely historically significant and could be considered structural art in its own right.

Now moving on to the current bridge and the subject of this blog, this bridge is not as historically significant in terms of technology. However, since it does make adjustments like using steel instead of iron and forming fewer arches, it can still be seen as historically significant in regards to a better version of the original. It is not however the first of its time to use steel or anything like that.

 

Cultural Significance

The Ponts des Arts bridge is massively culturally significant for three reasons. The first being that it is a replica of the original bridge which was a statement of French power and engineering competition. So, while the first bridge was destroyed, its symbolism is renewed and everlasting in the current bridge. So Yay.

Secondly, this bridge is hugely popularized as the bridge of love, and is known worldwide through movies, popular culture, writers’ and painters’ depictions, and celebrity social media to people. So, not surprisingly, the decision to remove all of the locks and place glass in their place so that no additional locks could be added was extremely controversial. Being the dork that I am, I think the glass better highlights the structural prowess (and yes, I just used the word prowess) of the bridge which was obscured and came in second to the wall of locks that stood before. But I by no means represent to universal person; I don’t even really represent the normal person considering I like to look at and analyze structures for fun, so I can see why this is a big deal to people. But, as a structural engineer, any additional and unnecessary weight (especially one that equals 50 tons) should be added if it takes away the structure’s ability to fulfill its primary function: to resist natural forces. If part of the bridge collapses, because of the locks, the locks have got to go. But like I said, many don’t agree with me, so this has been somewhat of a hot topic since the bridge gate collapsed in 2014. In fact, when you search the bridge on Google, headlines after headlines come up that look like the one below.

Figure 5: Lock Gate Collapse Headline in Independent Co [4]

Despite all of this, the bridge still is popularized by tourists, locals, and artists alike because it stands at the core of Paris’ draw and art center. And to mitigate the anger, Paris auctioned off the love locks and donated all of the proceeds to a charity for migrant workers and refugees, which I have to say is pretty fricken awesome! So don’t feel bad if your lock was removed, because it was for a good cause and we can now happily move on.

So, lastly, this bridge is popular simply because of what it connects: the Louvre and the Insitut de France. Tourists and students can be seen not only walking on it (which, duh because it’s a pedestrian bridge), but Ponts des Arts is also a common picnicking location, the site of different art exhibitions, and a hub for local artists to make money off of tourists (which can be quite annoying having just been harassed by street vendors in Paris). Nonetheless, the bridge is still widely loved both around the world and locally.

 

Structural Art

Now, let’s take a look at Billington’s Three Es (probably dreaded by those of you who have read of these over and over again, so sorry): efficiency, economy, and elegance.

Efficiency

This bridge is extremely efficient. It uses very little material, reduced the number of arches to seven instead of the original nine, and is very transparent.

Figure 6: Structural Transparency

 

When passing under it, you can see all of its members, which are not that many, especially when compared to the other bridges around it made of stone. However, stone is used to hide the reinforced concrete on the abutments and piers, which is inefficient. Nevertheless, this bridge is efficient in its design and utilization of steel as a material in its own right. The form fits the material.

Economy

For some reason, the exact cost of construction of the Ponts des Arts is extremely difficult to find. But not to worry, we can use look at its use of material to gauge its economy. As stated above, the bridge uses very little steel in the superstructure, but uses extra material in the abutments and piers. Since stone is unnecessarily added to the reinforced concrete, that choice is not economical, but the superstructure is economical. So, I’d say that this bridge achieves half credit in the economy category.

Elegance

This bridge is extremely elegant. For one, it is just plain pleasant to look at. But in terms of Billington’s criteria, the load path is clear in how it travels from the deck to its foundations, it is transparent and uniform in its design throughout the bridge. The stone abutments are a bit bulky, but in my opinion do not take away from the overall aesthetic of the bridge. So, without a doubt, I would say this bridge is elegant.

When taking all of the aforementioned factors into consideration, I would say that this bridge is structural art, although not the best example of it due to the piers and abutments. While casing the reinforced concrete abutments in stone was purely architectural, the elegance seen in the actual superstructure of the bridge overpowers that and wins for structural art in the end.

 

Structural Analysis

As stated above, this bridge functions like a typical arch bridge, with redundant arches next to each other to help with horizontal thrust. The spandrels also form semi-arches with diagonal bracing to help stiffen the deck and distribute the load throughout the arches rather than all at one point. This prevents the arches from buckling, almost as a flying buttress would. The load path, as demonstrated in the diagram below, starts at the deck as a combined uniform live and dead load, moves down into the arches either at the top of the arch or first into the spandrels and then into the arches. The load then transfers to the piers, which send the load down below water level and into the river bed.

Figure 7: Load Path

 

As any other typical arch, all of these arches are in compression, that is an arch’s defining characteristic. The spandrels are in tension, connecting the deck to the arches, each side pulling on the spandrel. The piers are in compression because they act like columns, with the load from the bridge pushing down and the normal force from the river floor pushing back up against the pier.

Figure 8: Members in Tension and Compression

 

We can use the principles of equilibrium to determine the forces acting on each member. To simplify the model, the following assumptions are being made:

  • Assume Deck is one solid surface
  • Assume pedestrian live load = 85 psf
  • tdeck = 1” = .083’
  • ρdeck= 35 lb/ft^3
  • ρsteel=490 lb/ft^3
  • Assume piers are made only of reinforced concrete with no added stone dressing
  • ρconc=115 lb/ft^3
  • Width of pier = 2’
  • Depth of pier = 31’

There are 5 arches in each span and 7 spans in the length of the bridge. So, for each arch:

The arches are made of steel which also have a dead weight. The free body diagram for each arch is the same and can be seen below. Note that the horizontal force that counteracts the arch’s thrust is either the thrust from the juxtaposed arch or from the abutment. Either way, the value should stay the same in order to achieve equilibrium.

Figure 9: Arch Free Body Diagram

The horizontal reactions caused by the thrust of each arch cancel each other out, and therefore do not require any extra calculations.

Moving onto the piers, each of the 6 piers in the middle hold a reaction from the arches on either side of it, and extend the width of 5 arches. So, each pier must support 10 times the point load coming from the arches. The free body diagram for the pier is shown below.

Figure 10: Pier Free Boody Diagram

There are 6 piers, so the bed of River Seine is actually supporting 6 distinct surface loads all equaling 5,714.64 psf.

The reason the reaction at the ground has units of force per area is because it is a surface load acting over the bottom of the pier, which has a length of 36’ and a width of 2’.

 

Personal Response

Okay, so this is probably more of a side effect to the program and having the three E’s drilled into my head continuously, but I can honestly say that my reaction when taking the boat tour and passing under the Ponts des Arts Bridge was “damn, that’s a piece of structural art”. While I ended up doubting that more when I took the time to analyze it as I did above, I just really admired how I could see the load path so clearly and it was so transparent. I didn’t even realize it was the love lock bridge I had seen so many times in movies, but clearly taking away the locks brought out the real character of the bridge rather than distracting from it.

 

References

[1] https://structurae.net/structures/pont-des-arts-1984

[2] https://en.wikipedia.org/wiki/Pont_des_Arts#/media/File:Paris,_Pont_des_Arts_by_Neurdein,_c1885-90.jpg

[3] https://www.shropshirestar.com/entertainment/telford-entertainment/2018/04/16/let-there-be-light-restored-iron-bridge-to-open-with-permanent-illumination/

[4] https://www.independent.co.uk/news/world/europe/part-of-paris-bridge-collapses-under-weight-of-love-locks-left-by-tourists-9512594.html

[5] http://www.eutouring.com/pont_des_arts_history.html

[6] https://www.napoleon.org/en/magazine/places/pont-des-arts-bridge/

[7] https://www.cometoparis.com/paris-guide/paris-monuments/pont-des-arts-s959

Comments

  1. rlakhani7 says

    Firstly, it’s great to see how you included two images to portray the load paths. I am interested in the second one more because you show how the internal or hidden members allow the transfer of loads. It’s also great to see how you differentiate between members in tension versus compression. Question for you: I realize that you immediately characterized the bridge as being structural art but then returned to doubt yourself? Do you seen any other ideas or characteristics that should be discussed about structures when deciding if they are structural art or not?

    • nzukerman3 says

      I think that uniformity is not always the most elegant. I mean if you want to look at Billington’s description, he thinks it’s important, but if there is something that is inconsistent like the stone with the steel, I think that looks cool and has a purpose and I think it represents efficiency because he chose a different material for a reason.