Archives for June 2018

Deptford Creek Pedestrian Bridge

I saw this bridge from pretty far away during our boat tour but it immediately caught my interest as it was a perfect little example of a cable stayed, fan-style bridge (stays originate from one point). The Deptford Creek Pedestrian Bridge is even cooler to me after I did some research and realized that it rotates 110 degrees on its main column to open up for boat traffic [1]. I’m interested in analyzing this bridge because it provides an opportunity to thoroughly investigate a cable stayed bridge without making many simplifications.

Figure 1: Deptford Creek Pedestrian Bridge from Bank

Structure Information

The Deptford Creek Pedestrian Bridge was contracted by Raymond Brown Construction Ltd, designed by Flint & Neill, and the engineering firm hired was Eadon Consulting. It was built for a total cost of £5 million and completed in Fall of 2014 with funding provided by a mixture of public and private entities [1]. The surrounding area has been experiencing rapid gentrification and increasing population density over the past few decades as it transitions from wharves and industry to apartments and shops [2]. A walking/biking path called the Thames Path has been added along the Thames on both sides, and before the Deptoford Creek Pedestrian Bridge, walkers had to take a long detour through a non-sightseeing friendly area and cross a road bridge with heavy traffic [1]. In order to solve this problem the area council gave permission for a pedestrian bridge to be built with the goals of: beautifying the area, increasing walk/bike conveniences, and increasing foot traffic to the surrounding shops [1].


Historical Significance

This bridge is very new (four years old), and thus has little history, and no historical significance to speak of. It is cable stayed, cantilevered and a swing bridge, but does nothing to innovate on any of these models. Deptford Creek is fairly thin (the bridge only spans 165 ft total) and the only major difficulty was the large change in tides that the Thames and its immediate tributaries experience, but this is easily avoided by timing construction periods and even assisted by making concrete foundations easier to pour during low tide. This is an excellent example of a pedestrian cable stayed bridge, but due to its lack of innovation it will most likely not serve as a model for future buildings.


Cultural Significance

While the bridge has little significance besides assisting in gentrification, the surrounding area and Deptford Creek itself have a long history. Deptford Creek is the tidal portion of Ravensbourne River, and the Deptford Dockyard (a Royal Dockyard) employed  many shipbuilders from the 16th to 19th centuries, who made up a large portion of those living in the surrounding area. Sir Francis Drake docked the Golden Hind in Deptford Creek after his circumnavigation of the globe and was knighted onboard in 1580 by Queen Elizabeth I [2]. The Golden Hind was moored in the creek for decades and became a tourist attraction/cultural symbol until it fell apart [2]. In the 19th and 20th centuries there was a large power station and many other industrial buildings along the creek, but in recent years the area has become much more residential with new highrise apartment buildings being built rapidly [2].

When it was proposed and being built, many local citizens were complaining about funding and approvals for apartment buildings that were linked with the proposal. After construction however there have been very few complaints, and generally positive feedback, although some vocal dissidents still argue that the benefits of the bridge were not worth £5 million [1]. The Deptford Creek Pedestrian Bridge is still used today (four years later, not much has changed) as it was initially intended – a pedestrian bridge –  that beautifies and shortens the walk along the Thames [1].

Structural Art

The “Three E’s of Structural Art” are: Efficiency, Economy, and Elegance. When it comes to efficiency, this small span bridge needed to somehow create space for river transit, and swinging was chosen. This reduces the materials needed by a lifting bridge, and the four cable sets use a low amount of materials in the superstructure, which together meant he structure is efficient. The Deptford Creek Pedestrian Bridge is also fairly economic in construction as it cost only £5 million, which although high for a normal pedestrian crossing, is low when also considering the swinging nature of the bridge. The bridge is also quite elegant, with a very simple cable structure, gently tapered deck, and lack of extraneous decoration. The only argument against this bridge being structural art is its small size, but I believe that it fills out the E’s so well that despite this limitation, the Deptford Creek Pedestrian Bridge is structural art.

Figure 2: Looking Up at the Mast from atop the Counterbalance



Structural Analysis

The Deptford Creek Pedestrian Bridge is a cable stayed bridge in the fan style that swings back and forth to open the creek to water traffic. The pivot of the bridge is far to one side which means that the cantilevered deck is much longer and thinner over the river and counterbalanced by a short, thick span on the bank. The deck, mast, and cables are all steel, but the huge column that serves as support and pivot for the swing bridge is mainly concrete (there are mechanical components inside). The structural system is a cable stay bridge and load from the deck is transferred to the cables in tension which compress the deck towards the mast. The cables transfer the vertical portion of their load to the mast which is compressed downwards into the support pivot and foundations. A foundation for the pivot was dug and then concrete was poured in a mini caisson, and the pivot was then cast up around the central motor for swinging the bridge. The deck was prefabricated as one large span and the massive counterweight (120 tonnes) was attached on site when they attached the cables and lowered the bridge by crane. It was not built in sections due to the asymmetry of the cables and the short total span of the bridge.

When analyzing this bridge I was able to find the height of the bridge (50 ft) and the weight of the counterbalance (120 tonnes), but I paced out the bridge length (165 ft), distance between paired main span cables (40 ft), and distance to the four counterbalance cables (15 ft). I used the weight of the counterbalance (264,555.7 lb) along with the height of the mast and the distance to the counterbalance cables to find the total tension in the cables and the lateral compressive forces. First I idealized them to a single cable and then found the angle from horizontal using: tan^-1(50/15) = theta. This gives an angle of 73.3 degrees. Next using the downwards force I found the total tension with the equation: T = 264,554.7/sin(73.3) which gives a total tension of 276,204.3 lb. Then multiplying by cos(73.3) I found the lateral compression of this shorter but thicker section towards the mast to be 79,370.2 lb. For the bridge to be in equilibrium this lateral force would need to be equaled out by the lateral force from the three paired-cable tributary areas on the longer span according to the equation: T1*cos(theta1) + T2*cos(theta2) + T3*cos(theta3) = 79,370.2. The farthest cable from the mast is cable 1, closest is 3.

Figure 3: Initial Diagram with Angle and Tension Calculations

First I needed to find all of the angles using inverse tan and the distances from the 50 ft tall mast, which were 40 ft, 80 ft, and 120 ft. This gives angles (from theta1 to theta3) of 22.6 degrees, 32.0 degrees, and 51.3 degrees. Now I needed two more equations in order to get all my tensions (idealizing each paired cable to a single cable) so I looked at the tributary areas of the cables by dividing the span halfway (20 ft) between each cable. This gave (again L1 is farthest from the mast) lengths of: L1 = 45 ft, L2 = 40ft, and L3 = 60 ft. With a constant bridge width and the simplifying assumption of constant deck depth I can assume that this creates proportional masses for each section no matter the density of the steel trusses. Using this proportional relationship to assume downward force in each section, I arrived at the equations of: T3*sin(theta3) = (1.5)*T2*sin(theta2) and T3*sin(theta3) = (1.25)*T1*sin(theta1). When I plugged this into my first equation I got a complex equation that you can check out in my work below because I don’t want to type it out… Ultimately this gives me: T3 = 25,496.7 lb, which I can plug back into my second and third equations I get: T2 = 25,033.3 lb and T1 = 41,423.2 lb. Now that I have all the tensions I wanted to find out just how thick the stays needed to be.

Figure 4: Three Angle Calculations and Three Equations for Solving Tensions

To check this I looked at the largest tension per cable, which ends up (logically) being in the four cables on the counterbalance side. I divided the simplified total tension by 4 to get the tension in each cable of 69,051.1 lb, and I had measured the diameter of each cable in my real life visit to be 2in, so that gives a cross sectional area (pi*r^2) of 3.14 in^2. Then I calculated the stress in each cable (stress = F/A) to be 21,979.6 psi, and I checked the tensile yield stress of steel on the internet and got around 50,000, which gives the cables under the strongest load a factor of safety of 2.31.

Figure 5: Large Tension 3 equation and Tension Calculations


Next I wanted to check how large the mast would need to be under all the compressive forces (in real life the mast is not a solid structure). To do this I added together all of the tensions multiplied by the sine of their angle. This gave a total downward force of 313,637.5 lb, and I used a compressive yield stress of 250 MPa (36,259.4 psi). Then (with the equation A = F/stress) I found the total solid cross section needed to carry this stress to be 8.65 in^2.

Figure 6: Stress Calculations for both Cables and Mast

Design drawings were published in local newspapers when the bridge was proposed in order to show the community what was being planned, and an animation was shown to the community council making the decision.


Personal Response

I’m personally a big fan (haha get it because it’s a fan style bridge…) of this bridge, I don’t think I’ve walked over a pedestrian swing bridge before, and I really like it’s bare simplicity. You can clearly see the cables taking the weight and that the shorter side is much heavier to balance the span. From far away on the boat I hadn’t been totally sure how the bridge rotated, but after going in person it was clear to see that the end of the main span only just barely rested on the approach and that it could easily spin on it’s massive pivot. I also hadn’t realized that there were four cables on the short approach span, but upon closer inspection they were clearly for dividing up the massive tensile forces needed.



Twickenham Bridge

Structure Information

Figure 1. Twickenham Bridge

The Twickenham Bridge was designed by Alfred Dryland, head engineer, and Maxwell Ayrton, architect, in 1931. Aubrey Watson Ltd built the bridge for £217,300 to connect the Old Deer Park in Richmond with the district of St. Margaret’s on the north bank. A crossing at the Thames River at this location was brought to discussion as early as 1909 (22 years earlier) but the bridge was known locally as ‘The Bridge that Nobody Wants’ [1]. With a title like that, I would also wait 22 years before acting… There were disagreements about the exact route and the financing of the bridge, but finally in 1926, the Ministry of Transport agreed to go ahead and finance the bridge. The Twickenham Bridge was part of a three-bridge road scheme, known as the Great Chertsey arterial road scheme, in order to relieve Hammersmith Bridge and alleviate congestion in Richmond [2].

Alfred Dryland was considered “the greatest expert in Britain of his day” and “a pioneer in the planning and construction of motorways.” The architectural ornamentation of the bridge was done by Maxwell Aryton. He apparently was a very famous architect and was an advocate for concrete stating concrete is “a material worthy of architectural recognition” [1]. Basically, the Twickenham Bridge had some successful people working on it.

Historical Significance

Twickenham Bridge was an innovative structural engineering design because it was the first large-hinged concrete arch bridge to be built in the UK. It is hinged at the crown and at the springing points of the arch, thus the arches overcame many of the defects are inherent in fixed arch bridges, particularly the difficulty in calculating abutment reactions. This is just good news for me because it makes my analysis easier.  Although the three-hinged arch was developed by many engineers in the mid-19th century for arched metal roofs and bridges, the concept was only applied to reinforced concrete structures in the early 20th century [1].

Cultural Significance

As I was researching the history of this bridge, I came across a ‘Transport for London’ journal that was written in 2008 and stated “Twickenham Bridge remains as important today, as it was seventy-five years ago.” The article was celebrating the bridges 75th anniversary and described how it greatly improved London’s traffic flow [2]. I can’t think of too many things that remain good with age (other than wine and cheese) so the fact that the bridge that was designed for traffic in the early 1900s is still relevant now is impressive.

Once the bridge design was finalized, there were mixed reactions towards the bridge. About 200 men were hired to construct the bridge which was a big deal because it was during a time of high unemployment. However, in order to construct the new traffic route, over 300 families had to relocate as houses and shops that were in the way were demolished. Also, the initial designed featured four 70-foot towers at the river banks and retaining walls that were 20 feet above the road level. The Daily Telegraph organized a local petition against the design claiming this was “inappropriate to the setting in Richmond.” Luckily, the engineers and architects were very responsive and changed the design. About 56,000 vehicles cross the bridge every day, which is significant. While the bridge was originally built to relieve traffic, it remains just as important today [2]. Fun fact: the bridge was declared a Grade II listed structure in 2008, providing protection to preserve its special character from unsympathetic development [3].

The Twickenham Bridge is supposed to represent a unity between architecture and structural engineering, but honestly after taking Historical Structures, I don’t know if I can look at an architect the same way ever again. The Art Deco theme is continued in the use of ornamental tiles that are embedded in horizontal seams and in the bronze cover plates over the expansion joints at the abutments [1].

Structural Art

Figure 2. Stairs leading up to the deck.

Scientifically, the arch does show the loads. All the loads are brought from the top deck to through the arch to the columns and to the footings. Socially, for the towns of Richmond and St. Margaret’s and the surrounding areas, this bridge was a big deal. It allowed for the towns to easily be connected and helped relieve the traffic congestion around the surrounding areas. Symbolically, this bridge is the first three hinged arch concrete large bridge in the UK. The architect wanted to make sure it was known to be a big technical feat and portrayed that through the design. From these statements alone, it would seem as though the bridge qualifies as structural art. However, this structure is heavily ornamented by an architect. Even though the architect’s main purpose was to accentuate the structure and loads, I think the ornamentation goes against what Billington defines as structural art; the structure should speak for itself without the need for additional design. Because of this, I would say this bridge is not structural art.

Structural Analysis

The Twickenham Bridge is a 145.5m long and 21.3m wide bridge that has 5 arches. The central span is 31.4m while the two arches next to that are 29.9m. The two arches on land each measure 17.1m. The bridge is made of reinforced concrete arches on top of very narrow piers. When looking closely at the bridge, you will notice some striations. This is purely architectural and textured by a bush hammer. One of the most distinctive features of this bridge are the decorative bronze cover plates. These are an Art Deco style (just like the Bank of America Plaza, my first blog post!) and help accentuate the three structural hinges at the crowns and springings of each arch. The architect, Maxwell Aryton, wanted to make sure the hinges stood out and “gave prominence to the bridge’s technical virtuosity” because it was the first large three-hinged concrete arch bridge to be built in the United Kingdom [1].

As mentioned in the cultural significance section, the construction of this bridge was a big deal. Many people who were unskilled were hired so the construction had to be simple. Although the form was a newer one for the UK, constructing bridges had been done before and this one was no different. Many parts were assembled at factories and then taken to the construction site. The footings were sunk into the water and the construction proceeded from there. Because the bridge was over water, many of the parts were floated to the site by boat.

The loads on the bridge travel from the deck to the arches and down to each of the springings/ footings. The arches are all in compression due to the reactions from the footings acting upwards.

In order to calculate all the reactions in the bridge, I idealized the bridge as a typical three-hinge arch bridge and only focused on the central span. I chose a live load of 952.4 kg/m as that is the average live load for a vehicular arch bridge of this size.

Consider the equilibrium of the entire structure:

∑Fy = 0

(952.4 kg/m)(31.4m) + RAV + RBV = 0

From symmetry: RAV = RBV

RAV = RBV = 14952.68 kg

Break into parts and only consider left side:

P1 = ()(952.4kg/m)= 14952.68 kg

∑MC= 0

(RAV) () – (P1)() – RAH (HMAX) = 0

(14952.68 kg) () – (14952.68 kg)() – RAH (6.1m) = 0

RAH = 19242.38 kg

∑FX = 0

RAH = RBH  = 19242.38 kg

Explaining this design to the stakeholders was important as it took about 17 years for the bridge to actually start construction from which the idea was brought up for the bridge. What finally persuaded the stakeholders to commit to the design was the *surprise surprise* finances and path of the new roadway. The design drawings were most likely used to explain how efficient the three-hinge arch design is and how an efficient design can save money because of less material and less need for restoration.

Personal Response

To be honest, one of the reasons I chose to analyze this bridge because it was located far from our hostel, so I knew that no one else would choose it. But once I actually looked into the history of the bridge, I didn’t realize how important it was to the surrounding communities and the city of London. This bridge has been alleviating traffic for over 75 years and was the first large concrete three hinged bridge in the UK. That’s actually pretty impressive! I guess I chose well.



The BT Tower

Walking through Fitzrovia in London, it’s hard to miss this tower of steel, glass and radio disks jutting vertically into the sky. At first glance it appears to be a case of wild and modern architecture, but this structure is older than you think, and has a deep history in the city. Known previously as the General Post Office Tower and the Telecom Tower, it now goes by BT Tower, and remains one of London’s signature structures.
Related image

Fig. 1 The iconic BT Tower. [11]

Structure Information

The BT Tower was commissioned by the General Post Office in 1961 to support the growing use of microwave aerial transitions in London. The tower replaced an older, shorter steel truss tower that could no longer transmit and receive effectively in Fitzrovia London. With buildings rising up all around, it was about time for the tower to get a boost too, lest the airways would get blocked by progress. The solution was a 620-foot tall, 66-foot wide complex tower made of concrete clad in glass, 13000 tons worth of a building, costing £2.5 million to construct. The first 16 floors consist of utility platforms for communication; the next 35 meters open up to house 57 antennae and satellite dishes; 6 more floors are used for utility and functional space; the 34th floor is a revolving room for restaurant use; and finally a 40-foot weather radar caps the tower off. Construction took three years and the GPO Tower was opened for use in 1964. The building was designed by the Ministry of Public Building and Works, the chief architect being Eric Bedford, who was most famous for this tower.

Historical Significance

The design of this building was very tricky to get right, because in order for the communication satellites to function properly, the building could not sway more than 25 centimeters under wind loading. Wind force is very strong for a structure of this size and for the area it stands in. Designers took inspiration from circularly designed buildings that survived in Japan after nuclear bomb strikes in World War 2 to design a building that would resist high wind loads. The end result was a narrow cylindrical tower built around a tapered concrete core. The concrete core runs through the building and is anchored into the ground via a 6.7-meter deep concrete foundation, consisting of a 27.4 square meter prestressed concrete base and a concrete pyramid to support the core, which held the record for deepest foundation in London until 2004 [1]. It was also the tallest building in London until 1980. This structure is designed to bend only 10 inches at its top under wind speeds of 150 km/hr. If this seems like over-designing, that’s because it is – a sturdy structure is necessary due to the important need of accurate and steady microwave links. As such, it was a glowing example of structural stability through its core and its cylindrical design proved beneficial in reducing wind deformation. Its structure also makes the tower able to withstand nuclear blasts landing as close to a mile away, which during the cold war was an important consideration. To prove the initial structural analysis of this building, a model was tested using wind tunnels to confirm minimal swaying and stability.

Cultural Significance

Despite changing technologies and its growing age, the BT Tower remains one of London’s most important telecommunications tower, proving that old dogs can indeed learn new tricks. Originally used for microwave and broadband linkages, the tower has expanded its use in becoming a hub for fiber-optic cables, and currently about 95% of television content is channeled through the tower in its journey to people’s screens [2]. This became possible when Margaret Thatcher opened the tower to privatization in 1984 [4].

The tower has also acted as more than just a hub for UK communications – it has also been a tourist attraction. Upon its completion, the tower featured a revolving restaurant only 3.35 meters wide on the top floor. The tower and restaurant opening attracted huge celebrities, including the Prime Minister Harold Wilson, entrepreneur Sir Billy Butlin, and politician/write Tony Benn [3]. The tower proved to be hugely popular, attracting 1.5 million visitors during its first year alone! The tower was proving to be an enormous success both in utility and public popularity. Unfortunately, the restaurant did not have a peaceful history. During 1971 the restaurant was bombed, blowing the windowed walls straight out, injuring none but requiring 2 years of maintenance and tons of cause for alarm. Indeed, the restaurant was closed in 1980 for security reasons, and hasn’t been reopened since.

While I cannot find examples of persons dying at this site, it wouldn’t be inaccurate to state this tower as the location of many disappearances. This is because until 1993, this tower was considered a secret by the UK government. Yes, you read that right – a 620 foot tall tower in the middle of London was top secret, with its location missing from any city maps and its address in no books. This seems a bit odd considering how obvious a tower of that size is to spot, but the reasoning behind this is because of the military importance it held in transmitting signals. Its secret location was “revealed” in 1993 by Parliament when a member noted how dumb this was to keep under wraps. The tower has been seen elsewhere in a number works, including Harry Potter, The Fog, and V is for Vendetta (where the tower was blown up, so perhaps some fictional carnage has existed) [5].

Structural Art

Fig. 2 The BT Tower as it stands today.

This tower truly stands as a landmark in London, but the question of its place as structural art requires a closer look. Structural art must satisfy the three E’s – efficiency, economy, and elegance – and otherwise must be clear in the way it structurally works. I’m going to break down this structure based on the requirements.


Efficiency and economy are all about minimizing material and monetary use during construction and design. This tower tackled several huge problems for stable tall buildings in pretty effective ways. The slender form of the building and its cylindrical shape both contribute to the reduction of wind loading and the effects of dynamic loads without resorting to bulky framework. The substructure of the building was also efficient. The deepest suitable bedrock at this site was 174 feet below ground level, so a concrete large concrete base with a concrete pyramid supporting the concrete core shaft was constructed only 26 feet below the ground. This was a stable and economical solution. Additionally, the building cost only $2.5 million to construct. Elegance-wise, the tower is relatively simple and doesn’t feature unnecessary features. I even believe it to be pretty good looking, despite architects like Christopher Woodward calling it “poorly proportioned” [7], and it remains popular in opinion to the masses.

The one drawback of this tower is that its primary support, the concrete core and substructure, is completely obscured. However, I think the thin shape speaks for itself in protecting against exterior forces, and taking a look inside the building, the pyramid providing lateral support to the core is definitely visible in the bowels of the basement [6]. Based on the innovation in design and the satisfaction of the 3 E’s I conclude this building to be considered structural art, and an example for future buildings where stillness is key.

Structural Analysis

As stated several times previously, the tower’s circular cross section was chosen in the design because of its resistance to wind loads and other external forces. To explain why this is requires more knowledge on aerodynamics than I have ever been taught or ever wish to be taught. However, basic diagrams showing flow of air around a cylinder, such as the one below, do help in understanding the concept. When moving around a curved surface, air tends to bend around smoothly instead of impacting the surface dead-on. This would imply that cylindrical surfaces feel less wind load than those with rectangular surfaces. The building is built to withstand force of up to 150 kmph, and is able to do so with minimal deformation due to its cylindrical shape. During construction, a model 1:67 scale was tested in wind chambers at the National Physics Laboratory to prove this design could minimize deformation to the GPO and designers [1].

Fig. 3 Streamlines around a cylinder. [6]

The building is composed of 13,000 tons of concrete, 790 tons of structural steel, and 50,000 square feet of glass glazing, specialized to reduce heat variations from the sun. Assuming architectural glass is .5″ thick, the total dead load of the building due to material is 14,119.2 kips, giving the vertical reaction of the building supports. The building is cantilevered into the ground, and 26 feet below the surface, a 3-foot thick, 88-square foot square base anchors the building, sometimes referred to as a “raft”. The foundations are sunk 173 feet down into London blue clay. This base is connected to a 23-foot tall concrete pyramid which provides support to a hollow concrete core. This core shaft is 34.4 feet in diameter and 2 feet thick, and reduces to 24 feet in diameter and 1 feet thick after the 205 foot elevation mark. Each floor is a cantilevered concrete disk radiating out from the core. At its widest (near the top) the tower is 64 feet in diameter, however the main width of the tower in its lower levels is 51.8 feet diameter. The contractor used for construction was Peter Lind and Co. The main tower was constructed using slip-forming techniques and cranes to reduce the use dangerous scaffolding for such a high elevations [1]. Additionally, the pyramid structure in the foundation allowed contractors to avoid digging all the way to bedrock to support the building. Below is a diagram of the tower’s vertical exterior plan.

Fig. 4 Tower vertical plan, showing the varying cylinder widths and the pyramid foundation. [8]

The tower acts as a vertical cantilever structure, and each floor acts as a rotated 3-D horizontal cantilever. Each cantilevered floor transfers the dead and live loads they carry to the central core. The self-weight of the structure is carried purely by the central concrete core and is transferred down into the ground. The structure’s stability relies in part on this core and in part on the concrete pyramid below ground, photographed below. The pyramid and plate base help distribute the load of the tower above and increase its surface area to the ground. A stable foundation was critical not only in supporting the load above, but also in reducing movement of the core.

Fig. 5 Pyramid substructure to the BT Tower [9]

Personal Response

This structure is an example of smart engineering decisions made to address problems greater than just keeping the tower standing. The BT Tower was built in order to reduce deformation to the greatest degree possible, due to its importance in telecommunications. I know unfortunately little about aerodynamics and wind loads on cylinder surfaces, however learning about this structure provides me a better understanding about how surface geometry is an important consideration in design. This building is a striking landmark in the city, deeply ingrained in the communications infrastructure of London. Learning about its history and design give me a greater appreciation for its form, and make me look critically at building design going forward.












Centre Pompidou

Structure Information

Figure 1 : Centre Pompidou

Centre Pompidou, also known as the Pompidou Centre, is a multipurpose building located in the 4th arrondissement of Paris. The project came in response to the desire of then-president Georges Pompidou to implant a unique multidisciplinary cultural center in the Beaubourg area. The final design had been selected among 680 others during an international contest that involved 49 different nationalities [1]. The building, considered as one of the most emblematic of the 20th century was designed by Renzo Piano, Gianfranco Franchini and Richard Rogers, all architects unknown of the Public at the time. The structural engineer in charge of the project was the renowned Ove Arup. Opened to public in January 1977 after 6 years of construction, the challenges of this building were to be able to cohabit different activities within the same complex while facilitating the relationship between them and, make possible the contact with the public through the art and cultural centers. Hence, Pompidou Centre serves as public library, national modern art museum, music creation center and contemporary arts exposition center. The project cost was 993 Million of French Franc in 1972 and since the President was himself the pioneer of the project, it received public funding and had been government-owned since.


Historical Significance

Figure 2: Elevation East (detail) [2]

The structural engineering design for this complex was unique and its originality reflects through the total clearance on each of the ten floors of 7500 m2. The area had to be free of any physically obstructing structure, hence involving long spans between the columns that were designed to be outside. As noticeable on the picture below, the architects also wanted any piping to be visible from the exterior; providing the sense of “clarity and transparence” to viewers. They’ve combined the need for space with the materialization of their vision: Nothing need to be hidden in a building, everything need to be revealed. This approach was for them a game and a taunt. The structural engineering design had to adjust to those need in sort to make it possible: this required 15,000 tons of steel and 11,000 m2 of glass; unusual practice for the construction world of the time. This innovative and revolutionary character of the building was the fuel that boosted the Pompidou Centre to its rank between the most popular of the twentieth century.




The design and impressive architecture of the Pompidou Centre had laid foundations for a totally new ideology in terms of design across the world. Not just for the Centre itself that expanded internationally -Europe, Asia, North & South America- but also for the following generations of designers.


Cultural Significance

The Building had seen eleven presidents since creation, all of them appointed by the Ministere de la Culture; equivalent of the U.S Department of Arts and Culture in France.

Figure 3: Inside of the center

In the 70s and 80s, the center offered to visitors, majors expositions that contributed to the art world during the twentieth century. Among others, multiple tv series such as “memoire du future”, “les immateriaux”. The center had been used for the casting of the movie Moonraker of James Bond. Expositions from artists of different background, renowned or beginners had been presented at the Pompidou Centre. Among others, we could cite Paul Davis, Henri Michaux, Bonnard, Etienne Martin, etc.


This building has been loved from day one and had become one of the most visited cultural center in the world and the most visited in France. The center had a daily average of 16,000 visitors in 2000. In general, the center is said to handle between 3.5 and 3.8 million of visitors on a yearly basis the past couple of years.

The center is used to promote modern and contemporary arts through multiples expositions. As said earlier, the structure serves today as public library, national modern art museum, music creation center and contemporary arts exposition center. Street performers are constantly performing on the outside of the building. I’ve personally witnessed this around little before midnight despite the fact that the center was closed couple of hours earlier! I was amazed by the dedication, or passion I should say.


Structural Art

With the main structural elements clearly exposed as shown in the pictures, it was clear and evident to identify the load path throughout the building. Initially, all of the functional structural elements of the building were color-coded: green pipes for plumbing, blue ducts  for climate control and electrical wires encased in yellow, and circulation elements and safety devices in red. Check the following picture for an illustration.

Figure 4 :Color coded piping visible from exterior [3]



I would also argue that Elegance was there. Certainly, it’s a relative appreciation but considering the purpose to which the building was dedicated and everything else about it; I believe majority of readers would agree that this marvel is just Elegant! Economic aspect? The expected functionality of the structure had impacted a specific design which could have been less costly without those constraints. However, with all the income generated by the center since its creation, I believe that the Building had paid for itself long ago!  That was actually one of the greatest investment the government had made so far, in my opinion!

So, Yes!  the structure demonstrates Structural art.


Structural Analysis

Figure 8: Structure of the building

Some massive earthworks of 300,000 m3 was needed on the site to reach the 60 feet deep. As reflected in the images, the building is a typical one with concrete slab over beams and column. Hence, we are in presence of a uniformly distributed load that carries over to the reactions (columns) through the beams. The structure is essentially metallic -columns, beams, connection elements- and with 50,000 m3 of concrete poured to make up the flooring. Of course, they were prefabricated off-site (Germany) and assembled on site. The assembly of the metallic structure began from the first floor and involved the creation of a fixed connection of the posts (columns) inside concrete. On the top of each of these erected posts, exist a pin connection which will be used to hold where needed, the beam that serves as support for the slab.

Figure 5: Typical device for connection column-beam [7]






Figure 6 : Earthworks



The metallic beams were 45 meters long and weighted 75 tons while the columns were of various height of 5, 21 and 23 meters with diameters as big as 3 feet. The escalators were strategically designed as a corridor in cantilever with the building as shown on the first picture. As most structures, the load path for the overall structure is from the top to the bottom. Each floor’s load is added to immediate one beneath it and so on until it reaches the foundations. A better description would be: the outmost slab -designed with the dead load and live load- would transmit its weight to the beams according to the tributary area rule. That tributary “weight” is then carried to the metallic columns which got bigger as we go down the stairs. The constraints of longer spans drag along the need of having column’s drop by location in order to contend the flexural and compressive moment due to the live loads essentially.

Figure 7 : Inside the outside escalator [5]


As decrypted in figure 9, different layers of materials consist the slab.

Figure 9: Different layers of materials









A partial section throughout two floors reveals much details about the structure in Figure 10.

Figure 10: Partial section of slabs

Load path

As shown in the figure above, the load -in red- from the slab and the cantilever items -escalators mainly- goes through the columns which are in compression. The warren trusses under the slab provide extra support/ resistance against flexure. Maximum moment for the structures in cantilever are observed at the joint and maximum shear for the slab is expected to happen right at the connection slab-column while maximum bending should be expected at mid-span.

In the following, a lot of assumptions about the numbers will allow us to attempt the analysis. Assuming that beams are distant from each other for about 12 feet and that the span between the columns are 100 feet. This leave each beam (except the periphery ones) to have a tributary area 12’x100′. Thickness estimated to be 8 inches. During my searches, Ive came across the value of 5000 psi for concrete. Assuming that the thickness was taken into account, I’ve converted that value to a linear weight by multiplying it by the tributary width which is 10’x12”. The linear weight of 7200 k/ft. as then obtained. From here we could deduct the reaction by each of the column to be wl/2 which is equal to 3,600 K.

Assuming the same load considerations for the following floor, we’ll have this weight plus another 3,600K at that level and so on. The increasing weight as we go down the fl0or levels result in an increasing section of the columns as well.

Personal Response

The Pompidou Centre is a really impressive structure. The designers of this marvel have constructed something innovative from a very playful background. They  were able to draw attention and create uniqueness while having fun, which is very inspiring. We gotta do what we love and do it big to the point of inspiring generations to come.













Blackfriars Railway Bridge

Structure Information

The new Blackfriars Railway Bridge began development in 2008. The cost was estimated around 350 million pounds [2]. The bridge opened in February 2012 and began operation the following summer. The new bridge was a part of the Thames Link Project by Network Rail and First Capital Connect to decrease congestion and increase capacity of the passenger train routes in London [2]. Tony Gee and Partners of London designed the station-bridge and Jacobs designed the building [2]. The Department of Transport’s Safety and Environmental Fund funded the solar panels [2].

Figure 1: Blackfriars Rail Bridge

Historical Significance

The Blackfriars Rail Bridge has 4,400 photovoltaic panels that provide up to half of the energy for the London Blackfriars station located within [1]. The bridge is the world’s largest solar powered bridge and the largest solar array in London [1]. These panels required careful design and installation. They needed to be light so prevent exuberant additional load on the structure and crack resistant, for safety. The instillation also had to be paused for the London 2012 Olympic games.

Blackfriars Rail Bridge is also completely accessible to travellers with disabilities. Although this seems like the norm, it is quite uncommon in London [5]. On the tube it is particularly noticeable that only a few stations are handicap-accessible, this, however, could be due to the old age of the underground system in London. Even the accessible stations seem to be a challenge with ramped corridors and gaps getting into the trains. The new rail bridge station makes it easy for travellers with disabilities to make their way on the bridge and through the station.

The new Blackfriars Rail Station is the first in London to span the entire length of the Thames [2]. The deck station allows station access from both sides of the bridge and therefore both sides of the river [7].

The bridge also used innovative construction techniques to keep the lines functioning in the station and not impede traffic on the Thames. Most major new features (concrete pieces and steel arches) were prefabricated and brought in on barges and placed by cranes held by the old Blackfriars Road Bridge piers. The designers, Tony Gee & Partners, said that half of the work in the Blackfriars renovation and rebuild was construction engineering (figuring out how they would put their plan into action without much public disruption) [5]. See the rail bridge piers in Figure 2.

Figure 2: Blackfriars Road Bridge Piers

Blackfriars Rail Bridge exemplifies ideal features of modern bridges. The embodiment of Green structures and inclusion cover the main goals of society today. These two features alone make the bridge and station a perfect model for future buildings. The creative and efficient construction process also model futuristic construction, although each project differs in this regard.

Cultural Significance

The Blackfriars Rail Bridge is located above the remains of the original Victorian railway station [5]. This caused obstacles in the design process, yet it remains as a historic passageway, following the foundations of the existing bridge across the Thames.

The construction and rehab of the new and improved Blackfriars Rail Bridge was managed with both railways operational most of the time and without disturbing Thames traffic [5]. This connects to the true significance of the bridge, smooth passage in London. The station relieved previous congestion and has provided easy travel for all passengers, including those with disabilities. The train station located on the deck allows 12 car trains to function and permits over 24 trains per day to pass through [1].

Since the construction, the bridge has served as a reminder of London striving to become a sustainable city with its central location and functionality during the Olympics [1]. It is now considered an “Iconic Landmark” [6]. This rail station also, for the first time, connects London’s “cultural quarter”, the South Bank to a mass transit system [7]. This new location sparked conversation over renaming the bridges to “Blackfriars and Bankside” but, as we see today, this was never pursued [7].

Structural Art

The Blackfriars Railway Bridge is not a quintessential example of structural art. However, the Blackfriars Railway Bridge seems like a modern example of structural art. While it does have expensive features, each of these contributes to the efficiency of the bridge. The solar panels make an efficient green structure and the handicap features simply satisfy the necessities of today’s facilities. The extension of the deck allows for larger trains, which are occupied and will be heavily used as London’s population skyrockets. The foundations built off of existing structure and reinforced bracing, saving money and contributing to economy. The use of the existing road bridge piers and prefabrication also contributed to economy. The load path is clear and elegant, as the arches flow across the Thames. It seems clear that the Blackfriars Rail Bridge and Station are structural art.

Structural Analysis

Blackfriars Rail Bridge is a wrought iron girder bridge with five arches [4]. Much of the originally wrought iron deck has been replaced with mild steel and concrete [4]. The foundations are made of wrought iron plated caissons [4]. The piers are concrete and stone, converted with granite and sandstone [4]. The abutments are made of cross arches of brick. The bridge acts as five separate arches as arch girders on the piers and abutments, which take the deck and arch load [4]. This could partially due to the bridge being built over an existing railway, which, at its time, had no standardization. Each precast concrete structure had to be individually measured and made off site [5]. A quick-stiffening concrete was needed so the pieces could be handled soon after being cast. The steelwork was also pre-assembled and brought in by barge. The existing piers from the old Backfires Road Bridge were used as support for equipment in demolition and expansion of the existing rail bridge. The existing rail bridge was reinforced to allow for the addition of lanes for trains.

Load Path

The loads on the deck are assumed to evenly distribute onto the arch. From here the arches send the load to the piers or abutments on either side of them, which translate the load to the ground. The load path can be seen in Figure 3.

Figure 3: Load Path


Figure 4: Span Information [4]

Blackfriars Rail (m) 6.9 6.9 7.0 7.2


Passenger trains have a maximum live load of 1.71 tons per foot.

There are 15 steel arched members per arch.

Each arch weighs 45 tonnes [3].

Solar Panels each weigh 15kg  and there are 4400 of them [1].


Each arch varies in size, and therefore produces a different load. Since the bridge built from a pre-existing structure, the piers are large enough to handle some of the force from the arch. Because of this, I assume all differing horizontal forces cancel through the piers although they are not equal. The dead load embodies the load of the steel and concrete deck and steel arches and the live load includes the train and people load. With this information, the reaction forces of each arch were calculated. These calculations are in Figure 5.


Figure 5: Calculations

Drawings were used to communicate the design to the stakeholders in order to show that components of the existing bridge could be retrofitted for the new bridge. By expressing this, the designers showed their cost effective solution for the congestion at this central London location. The drawings also conveyed the importance of handicap accessibility and energy conservation and how they were employed to the new bridge and station.

Personal Response

            By visiting the bridge and walking through the station, I saw first hand the attention to detail put into the structure. The combination bridge and station, green initiative of London, and handicap inclusion are all striking from within and around the structure. I also saw the true extent of 4,400 photovoltaic panels crossing the entire Thames. The bridge panels even stuck out from the top of the London Eye, which is when the bridge first struck me.

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.










Villa Savoye ( Villa Sav-wa)

  1. Structure Information

Villa Savoye was a weekend home for the Savoye family during the 1930s. Mr. Savoye was a wealthy insurer who hired architect, Le Corbusier, to design their perfect weekend home in a Poissy France. The house can be seen below in figure 1.  This house was carefully designed as every single part of this house was built with a purpose and this is because Corbusier followed the idea that form follows function.

Figure 1: Villa Savoye

  1. Historical Significance

What makes this house such a great engineering design is its simplicity. The entire house is supported by reinforced concrete beams and columns, which means all the walls are non-load bearing. Reinforced concrete was still fairly new material at this time and was not used by most architects. Corbusier chose this material as it was the best for a framed system which was needed to create a thin and light appearance.  Since none of the walls were non load bearing Corbusier could use  large windows to allow natural light to flood the inside. Also, this design allowed a lot of flexibility for the floor plans. This house was so ahead of its time that it was the  start of a worldwide movement called Modernism.


  1. Cultural Significance

As stated earlier, this house was a weekend house for the Savoye family. It sat on large plot of land where the Savoye family had a huge garden filled with fruit trees and vegetable plants. Since the Savoye family was wealthy and had a large plot of land they had servants and a grounds keeper. The servants lived on the first floor, which was a new concept at this point in time as servants usually lived on the top floor/ attic while the home owners lives on the lower levels. The grounds Keeper had his own home which can be seen in figure 2 below. As you can see, this house is very similar to the villa.

Figure 2

Even though this home lead the way to modern architecture and has been highly praised by architects from around the world, the Savoyes absolutely hated it. Since the home had a many windows and natural light it was incredibly hard to control the extreme temperatures. IN the summer it would get unbearably hot and in the winter the house was so cold it was impossible to heat up. Also, the roof would always leak no matter how much it rained. Its funny, just like the blog post I did on the albert bridge the structures completely failed to serve it purpose but was loved by the general public.

  1. Structural Art

I am going to say that this is structural art. This house has a very simple design and has very clear load path from slabs to columns, that is it. None of the walls are load bearing. Also, it was extremely innovative and was and  is still an inspiration to architects all around the world. Another interesting aspect of this house and how it relates to structural art is that Corbusier designed following the principle “form follows function”. An example of this is the back of the house. The radius of the curtain wall was designed specifically for the turning radius of the home owners car. This was done to make parking into the garage effortless for the owners. There are many more examples of this but are not related to the structural engineering. So leave a comment and ask me about it (LOL). The one thing that would not count it as structural art is that Le Corbusier had almost unlimited amount of money to spend on this house. Although most of the money did go to aesthetics like furniture and appliances.

  1. Structural Analysis

This structure is a reinforced concrete frame that supports three slabs with columns and beams. None of the walls take loads, only the beams and columns. The weight of the walls are lines loads which are transferred into the slab and then into the nearest column. The load path can be seen in figure 3 below


For the calculation I wanted to checked the buckling capacity of the column. The column that I checked is circled in figure 4. For the slab that is resting on that column and beam I assumed a density of 150 lb/ft3 and I also assumed a dead load of 15 lb/ ft.  All the dead loads can be converted to an area load onto the slab and then a line load onto the beam. Then the reaction forces of the beam can be determined which will give the load applied to the column. Then I can calculate the critical buckling load and compare it to the load applied to the column. Calculations are shown below.

Figure 4



  1. Personal Response

By coincidence there a free tour started 30 minutes after I arrived at Villa Savoy. Those first 30 minutes I was walking in and around the house and observing the load path and what not but that tour totally changed how I viewed the house. The tour made me understand how passionate Corbusier was about this house and that he designed everything for a reason. I have a new perspective now on buildings and how/ why they were built. Below are more pictures of the house to give you an idea of what I saw on the tour.

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.



The Alexandre III Bridge

I was in Paris, France just this weekend only to see how much it resembled the city of London. Don’t see how? Let me explain. If you saw my last blogpost, you know that I did a bridge tour to see about 10 bridges in line that sit on the River Thames. Well, a similar thing happened. Except this was now a boat tour. And instead of 10 bridges, I’m pretty sure I saw double the amount of bridges. But there was this one bridge that stood out to me the most: The Alexandre III Bridge. It made me want to research about it due to how elaborate and extravagant it is and was designed to be. It actually represents how I see the history of Europe to be: old, exquisite and still standing.

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Figure 1: Pont Alexandre III (Alexandre III Bridge)

Structure Information

The Alexandra III Bridge, known as Pont Alexandre III in French, is a bridge that sits across the Seine River in Paris, France. Construction of it started on October 7th, 1896 and it was completed in 1900 [2]. It was constructed to fulfill two purposes: “to celebrate the achievements of the last century” and to allow pedestrians to cross the river. To elaborate on this first purpose, there was the 1900 World Exposition that was held to celebrate achievements in fields like architecture, engineering, science and technology. This bridge along with many other structures were built to be showcased and represent Paris during this exposition. Secondly, a bridge was needed to allow visitors to cross the River Seine from the one side consisting of the Champs-Elysees to the side of the Eiffel Tower. The bridge was designed by architects, Joseph Cassien-Bernard and Gaston Cousin and it was constructed by engineers, Jean Resal and Amedee d’Albly [1]. The bridge was funded by the French government and it was named after the Russian Tsar, Alexandre III in celebration of Russian and French diplomatic relations [3].

Historical Significance

Although the focus of the bridge is its architectural work, the structural forms of its time must be recognized too. The arch hangs low to make sure that it does not block the view of the Invalides and Champs-Elysees and this was rarely done before. The bridge was also made quite slender–“tape-like proportions and wide, flat profile”. These two factors raised doubts of if the bridge would still work or even stand. To emphasize once again, these two factors–a low-hanging arch and “the slender nature of the bridge”–were rarely used or even experimented with during this time [3]. Therefore, the bridge was able to use an innovative structural engineering design that made it a structural masterpiece while it was already an architectural masterpiece.

Up until the time of the construction of the bridge, steel was used and produced using a process called open-hearth. This process involved increased temperature usage for melting metals and using the heat released as waste [4]. Also, steel was used only in small quantities because it was expensive to produce at this time. For example, steel was used when supported by brickwork and even then, “intermittent columns” were used. Speaking in regards to the connections, only simple bolting was used to join different structural members. However, with the construction of the Alexandre III Bridge, new construction techniques were used to an extensive point. The connections that were used for this bridge included bolting or riveting to join members especially in steel framed structures. Pre-cast members were made off site, shipped to the site and then bolted together on-site [1].

The Alexandre III Bridge can be characterized as a great example of work of its time for two reasons or elements: it’s structural arch that is “both simple and fluid” and its architectural decor [1]. As mentioned above, the low-lying and very fluid arch was unseen of its time, and a risky venture but it stands today as a structural masterpiece. It is also said to settle in quite well into its surroundings. Talking about the time the bridge was designed and built, it was when architecture flourished and this can be seen by the statues and facia pieces that were designed and put upon by French artists. Together with the combination of planned structural engineering and architectural work, the Bridge was a success of its time [1]. However, it does not stand as a model for future building as the heavy and elaborate decoration does not go well with the structural members that were intended to flow [1].Image result for old alexandre iii bridge

Figure 2: An old image of the Bridge

Cultural Significance

This bridge has been in use for about a century and it was built in the late 1800’s. Considering this fact and all the research I was able to do, I was not able to find the impact the bridge had on lives–both living and dead. As for those who lived at the site of the bridge, that is not applicable as the bridge was built on tourist/visiting areas to allow pedestrian traffic to flow across the bridge.

The bridge was constructed at a time that reflected the strength of France-Russian relations. This can be seen to have an impact on the bridge: “the first stone..[of the bridge]..was laid in 1896 by Tsar Nicolas II of Russia and the bridge was dedicated to his father Alexandre III” [1]. One of the decorative features of the bridge also reflects this alliance. The Nymph of the Seine and Neva rest on the keystone which represents the relationship between Paris and Russia. Built to be showcased at the World Exposition of 1900, the bridge served to represent Paris and its accomplishments in architecture which could be seen from the varying ornamental decor on the bridge [7].

The impact of the bridge is not limited to history; we can see it appear in pop culture–particularly films. The bridge has appeared in the last scene of the 2011 movie, Midnight in Paris [5]. It has made appearances in multiple other movies like Anastasia, Ronin, A Very Long Engagement, and A View to Kill. This reference is my favorite–the bridge has appeared in the background of Adele’s video of the song, “Someone Like You” which I have yet to notice [6]!

Although the behavior of the tourists and visitors of the bridge aren’t clear as to either being loving towards it or absolutely hating it, most people like or at least admire the bridge for its grandeur. Also considering that the bridge was designed to allow 50 million people to cross it, the bridge rose from a need or a purpose which would not allow hate to flourish [1].

This bridge is still used as a pedestrian walkway connecting opposite sides of the Seine River to each other. It allows tourists to visit both popular areas–the Champs-Elysees commercial area to Les Invalides–by just crossing the walkway. Till this day, the Alexandre III Bridge is known as “one of the most elegant and artistic bridges in the French capital” [3].

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Figure 3: Sketch of the Aleaxandre III Bridge

Structural Art

Although this bridge can be characterized by me as art, I would not consider this bridge as structural art. I have made this judgment based off of David Billington’s criterion of the 3 E’s.

Firstly, looking at the economy of this bridge, I was not able to find any values representing the cost of the construction. Nonetheless, an assumption can be made by looking at the grandeur of this bridge that it was quite expensive especially considering all the artwork that was put into place. Therefore, the bridge is not very economical.

Secondly, looking at the efficiency of the bridge, minimum amount of material was not used. Although the arch is smooth and low, it creates larger horizontal forces for which large abutments and foundations had to be put in place [1]. This takes away from the whole idea of structural art as one part of the bridge is smooth and minimal while the other part takes up the consequences (notably the abutments). Therefore, the bridge is not efficient.

Lastly, we talk about elegance which is more of an opinion. I do agree that the arch of the bridge is smooth and fluid, the load path can be easily seen and it has used methods that were not seen previously. However, as soon as my eyes move past the arch to the deck, I see these huge architectural pieces that I personally don’t think belong on a bridge. Instead of making it look grand and exquisite, it makes it look heavy and unnecessary. Therefore, this bridge is not elegant either!

In conclusion, the Alexandre III Bridge fails to pass the structural art test of the 3 E’s developed by Billington and used by me–so, it’s definitely not structural art!

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Figure 4: Alexandre III Bridge with Eiffel Tower in background

Structural Analysis

Although the bridge is analyzed from a structural engineering perspective, I still think it’s necessary to talk about the architectural pieces that sit on the bridge. There are two pillars on each side of the bank that stand at a height of 17 meters that act as counterweights for the arch. In front of each pillar, there is a female statue. On top of each pillar, there is a golden statue of Renommee, the Fame restraining Pegasus. There are also hammered copper sculptures at the keystones. Across the bridge, there are 32 candelabras, or lamp posts that light up the bridge [9].

Figure 5: The decorative pillar shown above and the candelabra shown beneath it.

The bridge is a three-hinged arch bridge with a total length of 16o meters. The main span that makes up the only and largest arch is 107.5 meters in length. The width of the deck is 40 meters [2]. The deck is so wide that it encompasses three traffic lanes of each direction, bike lanes, and sidewalks. The arch itself is composed of steel [3]. There are two masonry viaducts that sit at each bank on both sides. Since the arch hangs very low, it creates large forces that must be resisted by large abutment foundations [7]. Pneumatic caissons made of steel were put into place [1]. This is just an overall idea to build the picture of the bridge in your head–more details to come below!

At this time, mainly wrought or cast iron was used to construct large structures. However, this bridge was able to use mass quantities of steel due to the open-hearth process. The steel components were made in a French factory, Le Creusot. The caisson itself was made of steel  and its walls were composed of corrugated steel plates [1]. The girders are made of cast steel. Masonry was used for the side viaducts [7].

The bridge sees extensive use of wholly steel-framed structures that are made of bolted or riveted arrangement of members. Members were pre-cast off site and then brought on side to the River Seine to be bolted on parts of the bridges [1].

Now, we talk specifically about some of the structural systems put into place that allow the bridge to function as it does. Firstly, the arch stands at a height that is 1/17 to its length which is very low to the standards of that time. This steel arch is supported by bracing members. There are also 15 arch ribs that are arranged in a parallel manner in the front and back side of the bridge. Underneath the bridge, there is a complex array of braced-trussed structures as can be seen in the image below. As the arch is a 3 hinged arch, it must be recognized where each of the 3 hinges are: one at each abutment and the 3rd one at the apex, or the highest point of the bridge.Steel Structure

Figure 5: Steel bracing structure below the bridge



Figure 6: Parallel Ribs and Foundation at Right Edge of Span

Now, talking about the foundation, pneumatic caissons of heavy weight with open tops and bottoms were sunk and then used as abutment foundations of the bridge. Two masonry viaducts are put on each side of the arch at the banks that can be considered as part of the foundation to resist the thrust forces from the arch [1].

The load path of this bridge can be simplified to include the dead and live loads of the weight of the bridge, other structural and architectural members, occupancy and weather loads. This combined load is acting on the deck, downwards. From the deck, it gets transferred to the 15 parallel ribs that seem to hold up the deck in a stiff position. It is transferred in response to its tributary area from the deck. From there, the loads are transferred to the arch which is in compression. The loads that are being transferred from the deck have horizontal and vertical components. The vertical components are transferred from the arch to the foundation on either side of the arch then into the ground. The horizontal components from both the arch and each viaduct(because each viaduct is shaped like an arch which thicker ends but act as arches) are transferred to the abutments.

Figure 7: Load Path of Bridge

In the analysis of the central span, some assumptions and idealizations are made. Firstly, AASHTO Specifications were looked at to see the dead loads that could be applicable for this bridge. The dead load unit weight that is used for steel is 490 lb/ft^3 [8]. This measurement was multiplied by the width of the bridge, 131 feet, to get a load per linear feet. Although this load and the values seem quite high, it works out at the end because of the extensive architectural pieces resting on the bridge. In that case, the uniform load cannot be characterized as just dead loads.

Figure 8: Free Body Diagram of Middle Span with uniform load

Figure 9: Calculations to find Vertical Reactions

Figure 10: Cut made at middle hinge

Figure 11: Calculations for horizontal reactions or thrusts

The vertical calculations found in the image above are the loads that are transferred into the foundations at the ends of the span. The horizontal reactions are the thrusts that are developed from the compressing of the arch and they are transferred to the abutments.

Another analysis will be made about the stress experienced by the deck: this is applicable regardless if the load assumptions stated above are not true. The deck experiences heavy loading or forces and therefore will experience high amounts of stress. Therefore, from the stress equation (sigma/stress = force/area), it is reasonable to see what area of the deck is needed to maintain an allowable amount of stress under the force it experiences.

Since this bridge was built at an earlier time, the designers/architects and engineers were able to communicate the image they had in mind for this bridge through drawings. This allowed them to build the bridge in 2 years [7]. These drawings and drawn models were necessary to convince the French government that the bridge is in fact low enough to not obstruct Les Invalides as this was the main requirement by the government [3].

Personal Response

By actually traveling on the boat underneath this bridge, I realized how much more exquisite it is in person. No seriously, it seemed like I was in an outdoor museum! I also realized how heavy those architectural members must have been. But, it is this bridge that gives Paris its historical and expensive feel! It makes me realize that some structures aren’t built for engineering purposes but rather for the city’s name and honor as Pont Alexandre III has been built for Paris. Nonetheless, we reflect on these structures and take the best from them–such as the low-lying arch from this bridge!











Wellington Arch

Structure Information

The Wellington Arch is located at the corner of Hyde Park, but it was first located at Hyde Park Screen. Hyde Park Corner is thought of as the entrance to London. The arch was designed by Decimus Burton, an architect of the “eclectic style of the age,” and it commissioned by the Office of Woods and Forests. The Wellington Arch was built between 1825-1827, and it was constructed in honor of Arthur Wellesley, the 1st Duke of Wellington. A statue of the Duke was placed on top of the arch in 1846, and the quadriga (a chariot drawn by four horses) sculpture was erected in 1912. The Wellington Arch was built after the defeat of Napoleon at the Battle of Waterloo in 1815, and it is a distinct London monument. The Wellington Arch and the Marble Arch were both created during a period of “contemporary grand neoclassical building projects” The governing classes of Britain wanted London to reflect the country’s wealth and international status. [1]

Figure 1: Wellington Arch [1] 

Historical Significance

Decimus Burton was tasked with designing new railings and gateways for the royal parks in London, and his initial designs were fairly modest. Since Green Park was seen as the outer entrance to Buckingham Palace, Burton produced a more elaborate second design. Buckingham Palace was being remodeled by John Nash for King George IV, and the arch was designed in a more ornamental style to suit the monarchy. The estimate for the arch was approved in 1826, but the quadriga sculpture was not paid by the Treasury in part because the Buckingham Palace renovations were so expensive. The Wellington Arch was completed but left without the decorations from Burton’s second design. The Wellington Arch does not have any innovative structural engineering designs since arches have been around for thousands of years. It was built around the same time as the Marble Arch and the Euston Arch in the 1830’s. Great Britain was an emerging world power and the feeling of pride and confidence was reflected in the art and architecture. [1]

Cultural Significance

Committees were formed in the 1830’s to created national memorials to two heroes of the time: Lord Nelson and Duke Wellington. The Wellington Memorial Committee chose the equestrian statue of Wellington and approved Matthew Cotes Wyatt as the sculptor. This decision caused a lot of controversy at the time between the committee, the public, the press and Parliament. The equestrian state designed by Wyatt was called “both ugly and completely disproportionate to the arch.” There were demands to take down the statue, but Wellington strongly favored the statue and stated that he would resign from all public posts if the statue was taken down. Duke Wellington was the commander-in-chief at the time, so the Queen and government stopped their demands for the removal of the statue. The statue of Wellington and the controversy surrounding it has been called “the greatest sculptural fiasco of the 19th century.” It caused an artistic debate and is an example of the British attitude to public art. The Wellington statue was removed in 1883, and in 1912 the quadriga statue was placed on top of the arch. The quadriga state was designed by Adrian Jones and is “a masterpiece of British public sculpture from its Golden Age in the late 19th and early 20th centuries. Today, Wellington Arch is placed on an island in the middle of the Hyde Park Corner roundabout. It was rebuilt in the current location 1883-1885 reusing the original materials. The facing masonry is of Portland Stone, and beneath the facing masonry is London stock brick. The interior of the arch has five stories, with rooms and a flight of cantilevered stone stairs on both sides. Viewing columns on the columns on the east and west sides were created 1999-2000 by the English Heritage and refurbishment during 2011-12 created a temporary exhibition on the third floor. [1]

Structural Art

The Wellington Arch does satisfy the following requirements for structural art: scientific, social, and symbolic. The time period that the Wellington Arch emphasized the construction of elaborate triumphant arches, during a time when Great Britain emerging as a great world power. The symbolic natural of the arch is shown in the depiction of Duke Wellington, who was famous for defeating Napoleon at the Battle of Waterloo. The scientific aspect of structural art, however, is not satisfied since there is no new or innovative technique used for the construction. Since it does not satisfy all three aspects, it would be difficult to call the Wellington Arch a piece of structural art.

Structural Analysis

The construction materials used for the Wellington Arch was London stock brick, faced with Portland Stone. The beams are made from cast-iron for strengthening. It has Corinthian beams and pilasters. [2]

The structural system is an arch, and it carries loads through compression. The keystone is inserted into the center of the top of the arch and pushes the stones into compression. The load path of the arch is down and through the abutments.

Figure 2: Load Path of Wellington Arch [1]

The following are the material properties of Portland stone: compressive strength of 38-39.04 MPa, density of 2330 kg/m^3, and a flexural strength of 3.5-7.55 MPa. It is assumed that the width of the arch to be 6 meters, and the max height of the arch to be 18 meters. The diameters of the columns is assumed to be 0.8 meters. The modulus of elasticity of stone is assumed to be 50 GPa.

The thickness of the Portland stone above the arch is assumed to be 1.5 meters. To calculate the uniform load acting on the arch, the following formula is used:

The width of the Portland stone acting on the arch is assumed to be 3 meters. To calculate the uniform load acting on the arch, the following formula is used:

Figure 3: Reaction forces of arch [2]

To calculate the reactions at the supports, take the sum of the moments in the y-direction:

From the cables the following reaction force is calculated:

RAH = (w*L^2)/(8h)

=((102,858 N/m) *( 4m)^2) / (8*12 m)

RAH = 17,143 N

The max force in the cables is calculated as follows:

Fmax= ((RAH)^2+( RVH)^2))= (17,143)^2+(205,716)^2

Fmax= 206, 429 N

The max force at the abutments is equal to the force on the buttresses. The buttresses will need to be designed for overturning using the following analysis. The height of the buttress is assumed to be 2 meters.

The angle is determined as tan^-1(205, 716/17,143)= 85.2 degrees. The width of the buttress (d) is assumed to be 0.25 m. The length of the buttress into the page is assumed to be 3m, the same as the length of the thickness of the arch when calculating the uniform load from density. The flowing equation is used to the moment which would cause the buttress to overturn.

Figure 4: Force on buttresses

The moment that overturns the buttress is calculated to be 12,593.5 N*m.


Personal Response

I thought the Wellington Arch stood out on the roundabout so I could see why it was relocated to its present location of Hyde Park Corner. When I first went to Hyde Park, I thought a different arch was the Wellington Arch. I can definitely see that London has a lot of ceremonial arches, some fancier than others. The area around the Arch was very busy, but I unfortunately did not get to see the Life Guards pass through the arch to the Changing of the Guards at Buckingham Palace.

Figure 5: What I thought was the Wellington Arch (still a pretty cool arch)


Figure 6: The actual Wellington Arch (on a sunny day no less!)