Dôme des Invalides

Figure 1: Les Invalides aerial view

Structure Information

Les Invalides, is the complex that houses the Dôme des Invalides. It was proposed by King Louis XIV on November 24th, 1670 as a home and hospital for elderly and sick war veterans. Before the King’s preposition, an establishment that served to accommodate elderly and disabled solders did not exist. The French Parliament funded this project under the King’s command and handed it over to War Minister Louvois, who appointed Libéral Bruant as the architecture of the project. During the completion of Les Invalides in 1676, the complex had fifteen courtyards and was largest court of honor for military parades.

A couple years later construction began on a chapel where the King and the solders could hear the mass in communal.  Due to protocol and decorum issues, the chapel was never completed as planned. As a result, the Minister of War appointed Jules Hardouin-Mansart to take over the architecture of the project. He decided to divide the church into two sections, one section purely solders and the other the royal church. The section of royal church incorporated a marvelous dome, the Dôme des Invalides, which is now the one of the major features of the complex. Jules Hardouin-Mansart completed the chapel in 1679 with the assistance of the notable Libéral Bruant in his last years. The gold-plated dome, which rises above the entire complex was completed in 1706.

By the end of the 17thcentury more than 4000 residents lived in the Les Invalides ruled in the same way as monasteries and barracks, with the solders being divided into companies where they were given tasks. The severely injured and disabled were taken care of in the hospital which was located in the South East section of Les Invalides. This hospital is actually still active today acting as hospital and retirement home for war veterans. This is amazing because the building still serves its original purpose.

Historical Significance

This building was built during the late 1600’s before the construction of Christopher Wren’s noteworthy St. Paul’s Cathedral. Domes during this time faced issues with load transfer from the dome to the walls of the structure supporting the dome. The walls could not support the tremendous load applied by the dome, resulting in the deformation of the entire structure. As a result, Jules Hardouin-Mansart with the assistance of Libéral Bruant incorporated double column buttresses in their design to resolve this issue. This idea was used in the structural design of many future domed structures after Dôme des Invalides. The idea of a three-part dome, as a solution to the tremendous load applied by the dome onto the walls of the structure was not until Christopher Wren’s St. Paul’s Cathedral in the early 1700’s.

The building that Dôme des Invalides rests on is elegant and symmetrical. The curve of the dome is offset by a straight angle of the building its supported by. As a result, the dome appears sits on the building like a crown. Besides the lantern on top the dome, the façade of Dôme des Invalides appears to be entirely symmetrical, evenly distributing the load path of the dome onto the buttresses.

Cultural Significance

Because Les Invalides was largest court of honor for military parades during its time, it was also a target during the French Revolution. On July 14th, 1789 Les Invalides was invaded by Parisian rioters who seized cannons and muskets stored in its cellars. The same cannons and muskets were used against the Bastille, which was a fortress in Paris known for its important role in internal affairs and a state prison, later the same day.

The First Consul of Paris ordered the installation Turenne’s tomb, under the Dôme in 1800 and dedicated a funeral monument to Vauban in 1808 opposite from Turenne’s tomb. Henri de La Tour d’Auvergne Viscount of Turenne better known as Turenne was a French Marshal General and one of the greatest generals in history. Sébastien Le Prestre de Vauban was French military engineer who served the King and was commissioned as a Marshal of France. During his time, he was a leading engineer because of his skills and innovation.

In 1846, the crypt of Les Invalides, which is located directly under the Dômewas prepared to receive Napoleon I’s tomb. On May 5th, 1821 Napoleon I died on the island of St. Helena, where he was exiled since 1815. He was buried near a spring on the island until 1840, when King Louis-Philippe decided to transfer his body. Napoleon was entombed with an honorable ceremony during his transfer. Napoleon Bonaparte was a French statesman and military leader who become notably prominent during the French Revolution. He dominated European and global affairs while leading France against a series of confederacies in the Napoleonic War.

The vault of the church is decorated with flags and trophies that were taken from French enemies. These flags and trophies were originally hung from the vault at the Norte Dame Cathedral until the French revolution. After the French revolution, the items that survived were transferred to Les Invalides in 1793. Today showcasing of these flags and trophies are positioned on the cornice of the church, showing the military history of France from 1805 up until the 20thcentury.

Today Les Invalides is a historic museum that exhibits the tombs of the many important people to France. It also serves as a hospital for injured and disabled war veterans. This is remarking because it still serves its original purpose from so many year ago. In 1989 the dome went under construction. Major renovations were done with the efforts of embellishment. These renovations ended up using 12kg of gold and restoring paint on the underside of the dome. Although the costs of these renovations seemed a lot, the people of France did not mind. They adore this building for its rich history, and culture, along with the beauty and elegance its brings the to the skyline of Paris.

Figure 2: Napoleon I’s tomb

Structural Art

The evaluation of structural art depends on the equal use of the three E’s according to Billington: efficiency, economy, and elegance. The goal of efficiency and economy is to design a structure that uses the least amount of material, and money. The efficiency of the structure has to carry on even after the construction of structure is completed. This means that any repairs the structure may need as a result of initial design goes against efficiency in the terms how long the structure successfully performed its function without the adding of new material. It would also go against economy in terms of the money spent in structural repairs. As for elegance, the structure must be aesthetically pleasing, while defining its engineered structures and creativity.

The Dôme des Invalides seems to be efficient in the aspect of longevity. It has not needed a lot of repairs other than for embellishment. The materials used to create the structure were efficient for its time period. Although now structures made from masonry, where reinforced concrete can be used are not considered to be efficient. Likewise, the Dôme des Invalides seems to be economic because money did not have to be put into construction of structural repairs, and overall the building is socially accepted, attracting many Paris tourists. The Dôme des Invalides is extravagantly beautiful and aesthetically pleasing. The Dôme is wrapped in gold leaf and towers over much of Paris’s skyline. It also showcases its engineering creativity with its symmetry. Therefore, according to Billington the Dôme des Invalides exemplifies structural art.

Figure 3: Exterior view of Les Invalides


Structural Analysis

Basic design principles and assumptions of arch analysis were applicable to the analysis of masonry domes during this time period. Different methods, like equilibrium and elastic methods, were developed to analysis masonry domes. Equilibrium methods rely on the domes geometry and self-weight to determine its stability, while elastic methods use material strength to determine force. Both methods determine the primary internal forces of the dome, meridional force and hoop force. The Dôme des Invalides is made of brick, and the exterior is wrapped in gold leaf. Domes during this time faced issues with the transfer of the tremendous weight from the dome onto the walls of the structure. As a result, such as double-columned buttress was employed in order to be able to support the entire load of the dome. The golden dome itself is topped with a lantern that measures 107 meters in height making it one of the tallest structures in Paris.

Load Path

The lantern of the structure transfers its self-weight down to the gallery which then transfers its load to the hemisphere of the dome. The dome distributes this load into the walls of the structure which are supported by buttresses. These double-columned buttress take the entire load of the dome and transfer is down into the ground of the structure.


Diameter of dome: 114 ft (assumption) => Radius of dome: 57 ft (assumption)

Density of Brick: 115 lb/ft3(researched)

Thickness of dome: 18 inches or 1.5ft (researched)

Surface area of the dome: 20414.07 ft2

I assumed the measurement of the diameter of the dome based on the ratio of the entire height of the building, which was given from my research, to the measured length of the diameter on google maps. I used to google maps to establish this ratio by measuring the height and comparing it to the diameter forming a ratio. I assumed the dome to be a perfect hemisphere. I based this assumption on my research which stated the to be dome be symmetrical. Also just by looking at it, it looked symmetrical. As a result the radius of the dome is half the diameter throughout the dome, making the height of the dome equal to the radius.

Both the Meridional Forces and the Hoop force are in compression because meridional forces are like arches and are always in compression and we can assume the angle for the hoop force is less than 51.8 degrees, so it is also in compression.

As far presentation to stakeholders for the construction of this structure, there were none. The construction of this structure was a command from the King. As far the design, it did not have to be negotiated either because the architect was appointed so whatever he design was relatively what was going to be built. The only thing that may be changed was the appointment for a new architect, during the construction of the church which supports the Dome. This was a result of the original architects old age.

Personal Response

I spotted this structure from the second level of the Eiffel Tower during the Tour. It was so beautiful amongst the skyline of Paris. I asked around to see if anyone know what the structure was, but nobody seemed to know. Not too long after the tour guide started talking about the structure. I immediately listened in to find out it was the Dôme des Invalides. I was astonished with its history and the fact that it still fulfills its original purpose. Honestly if I had just read about this structure, I probably wouldn’t have been as interested. The gold glistening in the skyline is what really caught my attention.






Waterloo Bridge

Structural Information

Figure 1: Location of the Waterloo Bridge [4]

The first Waterloo Bridge also known as Strand Bridge was a masonry bridge in 1809. The Strand Company came up with the idea of building a toll bridge across the River Thames, hence the nickname Strand Bridge. When Parliament learned about this idea they funded The Strand Company with 500,00 pounds for the creation of a bridge that would connect north bank with SouthBank, Lambeth. The Strand Company appointed John Rennie with the honor of the chief engineer of this project. Rennie’s designed a nine-span masonry classical styled bridge. The structure measured 2890.4 feet in length with 27 feet of headroom above high tide. In the late 1800s Rennie’s bridge faced serious issues with its piers as a result of increase water flow in the River Thames and by the mid 1900s pier five failed and the entire bridge was closed for repairs. Just a little over ten years later, in June of 1934, the London County Council had enough and demolished Rennie’s bridge, but that was not the end of the Waterloo Bridge.

The second bridge was engineered by Ernest Buckton and John Cuerel of Rendel Palmer & Tritton and designed by Sir Giles Gilbert Scott, with an approximate cost of 1.3 million pounds. Parliament did not fund this project until the approval of the London County Council Money Bill in 1936. The actual construction of the bridge was put on hold because of World War II and was partially completed a little less than ten years from its proposal. On August 11th, 1942 the bridge opened two lanes of road traffic, following with the opening of foot-paths in same year on December 21st. Two years later all six lanes of traffic were in full use. The official opening of the bridge wasn’t until December 10th, 1945, by the leader of the council Herbert Stanley Morrison.

Historical Significance

Until the beginning of the 19th century there was only one bridge, Blackfriars, that connected the north bank to the south bank of the River Thames. The construction of the Westminster Bridge soon followed, resulting in rapid development in Lambeth. This development stimulated the idea for a toll bridge that would connect Westminster to Lambeth. This bridge was the most expensive bridge built in Britain at the time. Therefore, Parliament believed that the toll from the bridge would pay itself back. This idea was a complete fail because the people of London just detoured the bridge to avoid paying the toll. As a result the toll was abolished in 1877.

Rennie’s design of the first Waterloo bridge was said to be a remarkable design, because if its eye-catching beauty and elegance. His bridge lasted longer than most bridges that crossed the River Thames at the time, but when the river began to rise the timber foundation platforms were exposed. During the late 1800’s efforts to save the bridge began, and more than 60,000 pounds were spent laying concrete slabs around the platforms to protect against erosion. After much blood, sweat, and tears were put into saving Old Waterloo the council finally deem these measures unsuccessful and closed the bridge to traffic in May of 1924.

Figure 2: First Waterloo Bridge [3]

Figure 3: Second Waterloo Bridge [4]

A temporary bridge was constructed and discussion over the fate of Old Waterloo was held for the next ten year. During these years, three alternatives were discussed. Alternative one, Rennie’s structure should be strengthened and repaired, alternative two, Rennie’s bridge should be rebuilt based on the old design, but lanes should be added to accommodate a greater volume of traffic, or alternative three, a new build should be built in place of Rennie’s bridge. After years of discussion, the London County Council finally made a decision and the demolition of the first Waterloo Bridge took place in 1934, along with a proposition of a new bridge with less span arches.

The second and current Waterloo Bridge is a five span bridge and was the first bridge made of reinforced concrete to cross the River Thames in London. The new bridge is almost twice the area of the old bridge but weighs about a third less than Old Waterloo, and crosses the River Thames with four piers instead of eight. Rennie’s original foundation forms a part of the embarkment wall on the north side of the new bridge as well as a memorial to Rennie composed of two columns and railing from Old Waterloo at the southern part of the new bridge. The elliptical arch faced with marvelous stone spanning Belvedere Road still remains, forming a part of the southern approach of the new bridge. I guess this was London’s way of thanking Rennie and showing they will never forget Old Waterloo.

Cultural Significance

Figure 4: Duke of Wellington at the Battle of Waterloo [5]

Although most of the towns people knew this bridge as the Strand Bridge, an act of Parliament officially named it the Waterloo Bridge as “a lasting Record of the brilliant and decisive Victory achieved by His Majesty’s Forces in conjunction with those of His Allies, on the Eighteenth Day of June One thousand eight hundred and fifteen” (Craig). Old Waterloo was opened on June 18th, 1817 by Prince Regents and the Duke of Wellington, in honor of the second anniversary of the battel of Waterloo. The Battle of Waterloo was fought in 1815, in present-day Belgium where a French army commanded by Napoleon Bonaparte was defeated by a British army commanded by the Duke of Wellington, and a Prussian army commanded by the Prince of Wahlstatt. The defeat of the French marked the end of the Napoleonic Wars.

Rennie’s Waterloo Bridge was the only bridge to be damaged in World War II by the Germans and ironically in January of 2017, Waterloo was closed after an unexploded second world war bomb was found in the River Thames relatively close to the bridge. Luckily police force was able to remove the bomb and perform a safely controlled detonation.

The first bridge definitely resulted in a loss of money for Parliament, because the toll on the bridge was unsuccessful. Despite the loss of money, the bridge was delightful to look at and everyone seemed to love it. An Italian sculptor Canova said, “the noblest bridge in the world”…“it is worth going to England solely to see Rennie’s bridge” (Craig). Today the current Waterloo bridge still has a number of recycled features from Old Waterloo and is used as a road one of the busiest foot and traffic bridge crossing over River Thames.

Structural Art

I believe that the Waterloo Bridge demonstrates structural art and I think Billington would agree with this. The bridge seems to give equal weight to the three E’s of structural art: efficiency, economy, and elegance. The current bridge is composed of reinforced concrete, which was a new practice at the time. This method is economic in such a way that the current bridge is stronger, stiffer, and offers more stability, than Old Waterloo resulting in a longer lasting bridge. Likewise, the strength, stiffness, and stability of reinforced concrete allowed the engineers to use less material across a greater area resulting in a efficient design, because although the current bridge is around twice the size of Old Waterloo, less material was used and the weight of the bridge remains less than Old Waterloo.

As for elegance the bridge showcases this one hundred percent. The entire length of the five span bridge showcases a skeletal structure that is visible from below. The five shallow span skeleton structure allows the bridge to look light and airy, while being aesthetically pleasing. The skeletal structure also allow the engineering techniques of the bridge to be showcased.

Differently, the face of the bridge is cased in granite and Portland stone which cleans itself whenever it rains, and London is a rainy city, so you can image how clean the face of the bridge looks. The granite on the bridge is used from Old Waterloo, which I believe meets all the E’s of structural art. It’s economical and efficient because materials were recycled and elegant because remains of the noble Old Waterloo are still showcased on the current bridge.

Figure 5: Lightness of the current Waterloo Bridge

Structural Analysis

Figure 6: Underside skeletal structure view of bridge

The current Waterloo Bridge design was composed of a shallow five-span structure, made of reinforced concrete, Portland Stone, and granite. The use of reinforced concrete was pretty new at the time, and the bridge was designed by an architect with little engineering background. As a result, during its construction, advice was sought from reinforced concrete expert Oscar Faber. The current Waterloo Bridge design put the bridge at almost twice the area of the Old Waterloo and three times less the weight of Old Waterloo. It is designed to accommodate a total of six lanes of traffic, with a 58-foot multipurpose lane, and 11 feet, footpath on each side.

The bridge is comprised of twin multi-cell reinforced-concrete framework with connecting diagonal slabs, supported by a watertight, pressurized box. The five shallow spans are an average of about 250 feet each with a deck supported by two lines of arches.

The center suspended span is supported by hinge joints, comprised of pre-stressed concrete. A detail analysis to determine the ultimate stress of the bridge allowed a better understanding of bridge performance resulting in the future maintenance planning. Sir Giles Gilbert Scott employed the structural system of repeating arches throughout the Waterloo Bridge with buttresses at either ends of the bridge.

Load Path

Figure 7: Overall load path of arches

Figure 8: Load path at the meeting point of arches

The dead and live loads from the bridge are transferred to its arches. The arches then take this load and transfer it to the abutments of the bridge. The abutments absorb the overall load of the bridge and transfer it into the ground.


Figure 9

Figure 10

Figure 11 shows how I calculated the analysis for the arches of my bridge. I used google maps the approximate the depth of the arch as seen in figure 9. I knew the measurement of the span from research, so I used the ratio between the span of the arch and depth of the arch to approximate both the height and thickness of the bridge. I used these calculations and the weight of reinforced concrete to calculate the dead load on the bridge seen in figure 10. Next I researched the average lane load on London Bridge’s and through my research I calculated the approximate live load on the bridge. I then incorporated the dead and live loads on the bridge into my calculations for the vertical, horizontal, and Fmax force on my bridge for the arches that have a span of 232.20 feet. There are two arches with this span on the ends of the bridge.

Figure 11: Calculations of forces on arch

Figure 12: Forces applies on arch


Figure 14: Calculations of forces on arch

Figure 15: Forces applies on arch

I repeated the process above for the arches that had a span of 252.63 feet seen in figure 12. There are three arches with this span. These arches are located in the middle of the bridge.

The stakeholders of the current Waterloo Bridge would be London’s Parliament. They had to see and agree on a design that would be efficient, economical, and elegant in the central city of London. The previous bridge had many short comings so when the current design was presented, I designers and engineers had to showcase the issues they had resolved from Old Waterloo. They did this by implimenting shallow arches that look light and airy and cost less money than Old Waterloo but would also be long lasting and efficient.

Personal Response

The Waterloo Bridge is nicknamed the Ladies’ Bridge so of course that caught my attention. It is said to be built by a largely female workforce during the World War II as a result of their husbands going to war. This was a myth for a long time because of course people could not believe women were accountable for such a marvelous bridge. Well guess what, in the words of Betty Hutton, “Anything you can do I can do better! Eventually the myth was turned into a fact when documentaries and interviews proved it to be true. I never realized how much history such a structure can have. I have heard of this bridge and actually got to see it from a unique point view at the top of the London Eye, but I can say I was never fully interested until I started to research the bridge. The Waterloo Bridge made me appreciate simple elegance and years of history. I realized that a structure does not have to look complicated to have extravagant beauty.

Figure 16: Dorothy, a female welder at Waterloo Bridge [1]


[1] Craig, Z. (2017) “13 Secrets of Waterloo Bridge”. <https://londonist.com/london/history/secrets-

of-waterloo-bridge> (May. 25, 2018).

[2] Roberts, H. Godfrey, W. (1951) “’Waterloo Road’, in Survey of London: Volume 23, Lambeth:

South Bank and Vauxhall”. <http://www.british-history.ac.uk/survey-london/vol23/pp25-31> (May. 25, 2018).

[3] “Waterloo Bridge (1945) <http://www.engineering-

timelines.com/scripts/engineeringItem.asp?id=1483> (May. 25, 2018).

[4] “Waterloo Bridge (1945) <http://www.engineering-

timelines.com/scripts/engineeringItem.asp?id=1484> (May. 25, 2018).

[5] https://www.ldrb.ca/pages/books/3612/robert-alexander-hillingford-subject-artist-field-marshal-arthur-wellesley-1st-duke-of/the-duke-of-wellington-at-waterloo-chromolitho-with-some-hand-colouring-print


Gardiner Building’s Chart House


Structure Information

[Figure 1: Gardiner Building’s Chart House]   

Chart House, once known as Gardiner Building, is located on Boston’s historic pier Long Wharf, at 60 Long Wharf, Boston, MA 02110, USA. Gardiner Building was built in 1763 after the 1710 to 1721 construction of Long Wharf.

The Gardiner Building was once used as office space and cargo storage. Captain Oliver Noyes constructed Long Wharf and the buildings that occupy it, including the Gardiner Building. The historic pier, Long Wharf, once served as the heart of Boston’s maritime trade and was leased to the government for customs work.

Historical Significance

The entire pier was built from a 2,200-foot-long barricade composed of a wharf of stone and wood piles. Gardiner Building House was built with large cellars that would store cargo, then later sell the same cargo at its doors. There was nothing really structurally innovative or new about this building. It is a basic three-story brick and concrete, routinely shaped house.

Cultural Significance

Chart House is Long Wharf’s oldest surviving structure and was once home to the offices of John Hancock, also known as John Hancock’s Counting House. The historic restaurant attracts many different people from your fascinated Boston tourist, to your everyday Bostonian who just loves the food, and the experience of Gardiner Building’s Chart House. I do not know of any backlash or outright love for the construction of Gardiner Building, as well as the human cost in the building it, but I can imagine a relatively low human cost for this uncomplicated, three-story building. Today the structure serves as delicious, historic waterfront restaurant, and a great place for date with your significant other, or maybe even a lonely happy hour.

Structural Art

In my opinion the Gardiner Building does not demonstrate structural art. According to David P. Billington, structural art gives equal weight to the three E’s of a structure: efficiency, economy, and elegance. Although the structure may exhibit efficiency and economy, it does not showcase elegance, therefore it cannot be referred to as structural art. In regard to efficiency the structure was built on a historic pier with the use of old materials, while money and time seemed to be used successfully, and without waste. As for economy, the structure was used offices and storage space during Boston’s colonial era. Nevertheless, the structure is an uninteresting three-story house, therefore is does not present structural art.

Structural Analysis

The Gardiner building is the great grandfather of all buildings on Boston’s waterfront, so engineers had been watching it closely. In 2001 Gardiner started showing its age, and monitoring indicated that the structure was in danger of crumbling. As a result, PAF architects worked with a team of engineers and construction mangers to save little old Gardiner. They used low overhead drilling equipment when repairing the exterior walls, in an effort to protect the original structure. Reinforced concrete was used as rebar for new subgrade beams as the support for the exterior walls. During the repair, temporary corner bracing was also added in order to save the integrity of Mr. Gardiner. This work was completed on a fast track schedule and took only about six months to accomplish. I guess the people of Boston were eager to see Mr. Gardiner up a running again.


[Figure 2: Load path of the Gardiner Building]

Load Path Analysis

Red : Surface load

Green : Point load

Blue : Uniform load

The roof of the structure has a uniform surface load, from its own weight, and any wind, snow, or birds it may encounter. The chimney applies a point load on the section of the roof that supports it. The roof is then supported by beams that receive and uniform line load from the roof. The beams are then supported by trusses that receive point loads from the points of intersection. There are numerous arches throughout the building that all receive uniform loads from beams they support. The arches are also subject to point loads in the downwards direction from their columns. The concrete beams collect a uniform load from the beams they support and transfer the specific load back to the columns of the structure. Lastly, the columns of the structure transfer a point load to the concrete base that supports them.

[Figure 3 : 3D load path of the top portion of the structure]

[Figure 4: Structural analysis calculations]


Dead load for concrete: 145 lbs/ft^3

Approximated tributary area: 180 lbs/ft^2

Approximate base length of arch: 10 ft

Approximate height of arch: 6 ft

W = (Dead load)(Tributary Area)

Selected arch supports a uniform load

 Fmax is the maximum force applied to the arch as well as the maximum force the arch applies to the beam that supports it.


[Figure 5: Me wishing I could afford to eat at Chart House]




Personal Response

You all may be wondering why I would pick such a random structure, and I can honestly say I did not plan this. The cheapest way to London, resulted in a seven-hour layover in Boston. I am always one to make the best out of any situation, so I decided to explore the city. Initially I was just looking for a good, unique, cheap place to eat, but in my journey, I stumbled upon an exquisite, historic waterfront. I did not end up eating at Chart House because my funds are a bit rocking at the moment and it did not meet my criteria of a cheap place to eat, but I did get a great blog post idea from it. If I would have just seen this structure in a book or a video I would not have been able to appreciate the beauty of the location of the structure and its rich history. The entire waterfront has an inimitable exquisiteness that captures the historic aroma Boston.