Archives for May 2018

Go Arsenal! (Emirates Stadium)

Figure 1: Me in front of Emirates Stadium

Structure Information

Emirates Stadium was completed in 2006 and is located in Ashburton Grove, London [1]. The stadium is used for the Arsenal Football team’s home games. The structural engineer for the project was Buro Happold [2]. Funding for the stadium came from loans from many banks given to Arsenal Holdings plc, Granada, Nike, and sales from the land that was not needed for the stadium. Additionally, Emirates Airline paid £100 million for a 15 year sponsorship of the stadium as well as an 8 year sponsorship of team uniforms [1].


Historical Significance

A newer technique for creating steel parts was used by the steel contractor to insure the accuracy of the parts. The method included creating three-dimensional models of sections from individual X-Steel models to be used in manufacturing of the steel. The three-dimensional models could be rotated and moved in order to create the most accurate version of the parts for the stadium.  [2]

Other than this, the stadium was built as a typical football stadium, with the roof allowing sunlight to hit the field while also keep the sun or rain off of the spectators. Since the roof is not connected to the seating, there is also airflow to keep the stadium cooler without the need for air condition. What sets Emirates Stadium apart is that the stadium is an ellipse shape, rather than a rectangle, which is more common for football stadiums. [1]


Figure 2: Development at Past Stadium for Arsenal [2]

Cultural Significance

The stadium is situated inside of a 7.8 acre park, which is open to the public. Additionally, Arsenal built houses and other buildings around the stadium for the surround communities. The location of the stadium allows for access from the London Underground and helped push for improvements at the Holloway Road station and promotes politicians to obtain funding for improvements at two other stations. Arsenal also sponsored the conversion of their past stadium into apartments, student housing, a garden, and health centers. [1]

 

 


Structural Art

When looking at the roof of Emirates Stadium from inside, outside, and especially from Google Earth, the stadium, this structure displays structural art very well. The arched trusses that hold up the roof and the connection points of the roof to the elements holding the roof up are all visible and easy to find. The load paths are visible, and the structure looks light. Additionally, efficiency and economy were highly considered in the structure. Steel tubes were specifically chosen for the cost and efficiency, as well as the constructability.


Structural Analysis

The roof of Emirates Stadium is made up of polycarbonate and steel tubes [1]. Steel tubes were chosen for cost and weight purposes, as well as constructability since less surface area means less detail in the steel manufacturing process. The girders were built off-site in pieces and assembled on-site. Temporary structures were used until all of the trusses were put into place with cranes so that there was no deflection from the self-weight of the trusses. [2]

The roof consists of the polycarbonate covering and many trusses, varying in size. There is a circular truss around the perimeter, truss beams, and truss girders. Additionally, there are 8 tripod columns to stabilize and take loads. All of these parts work together to create a stadium roof that does not touch the seating area and draws the viewer’s eye to the pitch, rather than the roof [1].

The load path goes from the roof up to the smaller, triangular truss beams, up to the larger truss girders. The two secondary girders transfer the load to the two primary girders. The primary girders then transfer the load to tripod columns. A circular truss around the perimeter of the roof is attached to the roof and provides support for the beams. It also transfers load to the tripod columns, seen in Figure 3. There are also 64 props around the stadium to help transfer the load down [3]. All of the beams and girders can be seen in Figure 4, a bird’s eye view of the stadium. From the inside of the stadium, the load paths from the secondary and primary girders, as well as the columns can be seen (Figure 5). From the outside, the tripod columns can be seen connecting to the roof (Figure 6).

Figure 3: Load Path from Top View [6]

Figure 4: Tripod Column from Inside Stadium

 

 

 

 

 

 

 

 

 

 

Figure 5: Load Path from Inside Stadium

Figure 6: Load Path from Outside of Stadium

The primary girders span 204 m and the secondary girders span 100 m, with the 32 beams varying in size. The girders cross section is 15 m deep and 10 m wide. [2] The polycarbonate roof covers 27,200 m2 [4]. All of the steel on the roof weighs 3,000 tons [1]. The total weight of the roof is about 41,510,000 N [5]. This means that the average area load of the roof is 1,526 N/m2.

To idealize the roof, we can say that each beam takes the same amount of load. Figure shows the idealization schematic. The force from the roof that each beam takes is calculated by multiplying the area load by the area divided by 32. The load for each beam is:

The loads of 6 of the beams go to each secondary girder, meaning each secondary beam has 6 point loads and reactions the ends from the primary load. Due to symmetry, the reactions are equal and there are no forces in the x-dimension. Figure shows the free body diagram. The reactions are:

The loads from two reactions of the secondary girders and the loads from 10 beams are on the primary girders, seen in Figure . As with the secondary girders, there are no forces in the x-dimension and the reactions are equal. The reactions on the primary girder are:

The maximum moment in the primary girder is in the center, while the maximum shear force is right next to the reaction. Assuming the distance between the beams are all equal to 16 feet and the distance between the secondary girder and perimeter is 30 feet, the maximum moment is:

This very large maximum moment is one of the many reasons why a triangular truss in the shape of a moment diagram was chosen for the primary girders.

The design of the stadium included a huge development of the area around the stadium in addition to the stadium. Because of this, the elliptical shape was chosen since it meant that the closest residential building was over 100 meters from the stadium. Models of all of the initial designs were presented to stakeholders, and once a shape was chosen, a full model including the neighborhood was presented. [3]


Personal Response

I really enjoyed visiting Emirates Stadium. Researching it more and going into the structure was very interesting. The stadium is so massive! I didn’t even really realize at first that the roof wasn’t resting on the seating area, but when I did, I was so amazed at the structural engineering.


References

1 https://www.designbuild-network.com/projects/ashburton/

2 https://www.steelconstruction.org/design-awards/2006/commendation/the-emirates-stadium-arsenal-football-club/

3 https://issuu.com/jmurphy93/docs/dissertation_final-_emiratesstadium

4 https://www.independent.co.uk/student/magazines/emirates-stadium-new-goal-for-the-gunners-5331573.html

5 http://www-civ.eng.cam.ac.uk/cjb/schools/stadium/silcock_files/S2%20Emirates%20structural%20analysis%20Teachers%20Notes.doc

6 Google Earth

The London Bridge (the real one)

I think I can speak for everyone when I say that the current London Bridge is a big disappointment to whoever sees it. It does not appear to be special and looks awfully plain. No one would imagine that this is the bridge whose name conjures images of beauty and wonder and who, for most of my childhood, embodied the idea of London. I was disappointed, I will not lie, but through this blog, I will try to capture the magic surrounding this structure and show that this unassuming piece of concrete may deserve its fame.

 

1.  Structure Information

The London Bridge is very different from the Tower Bridge contrary to what Google seems to think. I have provided a picture of London Bridge in Figure 2 so that we may all be on the same page. I promise you, figure 2 really is the London Bridge.

Image result for london bridge

Figure 1: Tower Bridge, NOT LONDON BRIDGE

 

 

 

 

 

 

Related image

Figure 2: London Bridge (yeah I know :/)

 

 

 

 

 

 

The current London Bridge is actually the 3rd bridge officially of that name. It is referred to as the Modern London Bridge (1). It is located over the Thames River, between the city of London and Southwark and located between 2 other bridges that cross the Thames River: Cannon Street Railway Bridge and the famous Tower Bridge (see figure 1).

Construction for the bridge began in 1968 and ended in 1972 (1). The Modern London Bridge was opened in 1973. It was inaugurated by Queen Elizabeth II on March 17th of the same year (5).

The purpose of the Modern London Bridge was to replace the New London Bridge which had begun to sag. The bridge was sinking at a rate of an inch every eight years starting in 1896. By 1962, the problem was so prominent that the bridge had to be replaced (6); it was struggling to adapt to the higher traffic volumes of the 20th and upcoming 21st century.

The Modern London Bridge was designed by architect Lord Holdford, the engineers were Mott, Hay, and Anderson. The contractor was John Mowlem and Co (7). It cost £4 million at the time which equals to about £51.9million today (There was crazy inflation!). The costs were covered by the Bridge House Estate Charity.

Figure 3: London Bridge

 

2. Historical Significance

By the time the Modern London Bridge was constructed and opened to the public in 1973, many innovations had already been made in bridge design, especially in prestressed concrete. This bridge sadly did not contribute to any and this bridge did not serve as a model for any other bridges. The innovative part of this bridge is found during its construction. The bride was constructed using the cantilever method (1). They completed the span of the bridge by placing a concrete beam between the two cantilevered parts of the bridge. It represented a major innovation in bridge engineering post World War II. Yet this was not the first time someone had used this method. David P Billington himself said that the bridge itself is not of great historical significance(1). It mainly used existing innovative construction methods. It also used the hollow box girder previously developed by Maillard. The best existing example for that would be the Salginatoble bridge of 1929 and prestressing concrete, an innovation inspired by Freyssinet’s work.

 

3. Cultural Significance

The London Bridge has a long history. In fact, London Bridge is the name of any bridge that was constructed in the area. The first bridge had been built by the Romans around 55 AD. The majority of the first London bridges were made of wood. It was not until 1176 that the first stone London’s construction started thanks to the work of a priest of St Mary’s of Colechurch (1). This bridge, referred to as the Old London Bridge opened in 1209 and was the site of calamities.

It became an important commercial site and over time it also became a business and residential area (It still amazes me how they were able to fit houses on this bridge). Anyway, there were shops, houses on the shops (138 premises were recorded in 1358), walkways and rooms extending about everywhere. It got so bad that the bridge started to resemble a tunnel. At some point, watermills were added to the mix (in the 1580s) (1). The roadway was narrowed down to 12ft – this was used by carriages, travelers, merchants, and commuters. Somehow this chaos survived one fire in 1212 that killed 3000people (1), the collapse of 5 of its arches in 1282 and it wasn’t until 1762 that plans were made to remodel this bridge. This is the bridge that inspired the nursery rhyme ” London Bridge”.

Old London Bridge, lithograph after a manuscript illumination of c. 1500 in the British Library (Royal M.S.S.16.F.ii.XV.) .

Figure 4: Old London Bridge

By 1722, all the houses were removed to and the city decided to try and improve the bridge. This proved to be too much of a burden and they commisioned a renowned engineer, John Rennie to construct a new structure a few feet upstream (1).  The old one was demolished in 1831 after 622 years of use (Holy Moly!). It had seen most of London’s historic events and occupied an important place in the city of London. The new design would be known as the New London Bridge. The new London Bridge only lasted 140 years. The most interesting fact about this bridge is that is was dismantled and shipped to the United States Lake Havasu City in Arizona for a tourist attraction. It was sold to the millionnaire Robert McCulloch for 2.460 million dollars. He spent an additional seven million to build it (10). The Modern London Bridge was the site of a terrorist attack that injured 48 people and killing three on June 3rd, 2017. Three terrorists used a rented van to run over pedestrians on the bridge.

 

4. Structural Art

In order to determine if this is structural art, I will be looking at the three E’s economy, efficiency, and elegance and applying them to the structure.

This structure is elegant enough in its shape.  It is aesthetically pleasing and easily integrates itself with the surrounding environment. The concrete works well with the Thames River and it easily merges with the other buildings. Looking at it, it is hard to distinguish where exactly it begins and where it ends. The design is light and fluid, the deck is very thin and the arches are very wide. The abutments too are very narrow and integrate themselves well in the design  Nothing looks excessively bulky or out of place in this bridge; it is rather plain for my taste but I must admit that the elements work well together. The main issue with this bridge is that it is not exciting and does not inspire awe because of how plain it is, however, this bridge does have elegance.

The bridge cost £4 million at the time which equals to about £51.9million today with inflation. Comparing it with the Waterloo bridge that has a somewhat similar style, that cost around 1.3million in 1877 which equals to about 145 million today(8), we can conclude that the bridge’s price was reasonable. It was built using methods to reduce the price: hollow box girder, prestressed concrete, and thin overall bridge to reduce material.

The Modern London Bridge is a very efficient bridge. It was built with efficiency in mind to some extent. It does not have any superfluous unnecessary elements such as excessive decorations or facades and was built to be as slender and simple as possible. The main criterion for this bridge was for it to be simple and functional. They were looking for something to replace the old bridge and did not care much for anything else besides functionality. The bridge is very thin, due to its wide span arches as well as the use of a hollow box girder. The abutments are very thin and long, allowing for less use of material than if the arches were to continue all the way down. The bridge is made out of concrete which is a relatively cheap material, and it is prestressed allowing for the use of even less material.

I will qualify this bridge as structural art. It is very efficient, it possesses some elegance and was constructed at a reasonable price.  The three E’s are met.

 

5. Structural Analysis

The London Bridge is made of three prestressed-concrete box girders. It is 882.5ft long and 105ft wide. It has a minimum vertical clearance of 26.9ft. The bridge was constructed using the cantilever method. Construction started on both sides. Starting from the piers, segments were built and connect to the previous using high strength steel tendons. The two halves of the bridge were connected by a beam of concrete. The bridge had a very interesting construction process. The old bridge was used partly throughout the construction of the new one. They built the new bridge next to the old one and demolished the old one as they were constructing the new one. Construction began with workers excavating giant shafts under the existing bridge. At that point, the balustrades of the old bridge were taken down and a truss structure was built no the side of the bridge.  On this structure were assembled twin celled precast concrete box units (11). This was repeated on the other side of the bridge. The system is illustrated in Figure 5.  The old bridge was then demolished with spandrel and infills removed first. The gantry truss was used for the final two girder boxes on the new design.

 

Figure 5: Construction of twin-celled precast concrete box units over the river

 

The weight of the bridge, as well as the live loads acting on the bridge, are supported by the arches. The load travels down the arches and into the abutments then the foundation and then into the ground as can be seen in figure 4. It is important to note that arches generate thrust forces due to the tendency of arches to want to spread. This design has three repeating arches which cancel the thrust forces with the bridge. the remaining thrust forces are carried horizontally into the ground at the point where the bridge deck connects with the ground.

 

Figure 4: Load Paths

In order to analyze this bridge, we will be only using the dead weight of the bridge and we will be assuming an area load of 480lb/ft^2 (11). We will base our calculations on the central arch which has the largest span.  We will also be using the density of concrete: 150lb/ft^3. The span of the central arch is 109 ft and vertical clearance is 29.6ft (ref fig.5) and a width of 105ft. We will calculate the maximum force on the abutment at A.

Figure 6: Simplified load distribution

 

I was not able to find the thickness of the hollow box girder so I will be assuming a thickness of 1 foot.

w = (150lb/ft3 * 1ft+480lb/ft2) *105ft =66,150lb/ft

Sum of the forces in Y direction = 0

RAy = RBy = w*109/2 = 7,210.4k/2=3,605.2k

Sum of the forces in the y-direction

Make a cut at the center where h is max

Figure 7: Cut at the middle where h is max

 

Resultant = d*w= w*109/2 = 7,210.4k/2=3,605.2k

Sum of the moments about O = 0

0= RAy (109/2) – RAx(26.9) – Res (109/4)

0= 3605.2k(54.5) – RAx(26.9) – 3605.2k(27.25)

RAx = 3,652.1k = RBx

Force A = (3652.1^2 + 3605.2^2)^1/2 = 5,131.8k

By finding the maximum force on A we now know the maximum load that the abutments can take and help prevent the collapse of the arch. It is important to determine the maximum force as it will also allow to determine the maximum weight of trucks crossing the bridge.

 

The design of the bridge was chosen by a competition. The judges were mainly looking for a simple, functional bridge that was easy to maintain and that did not cost too much. The designers communicated their design to the judges by sending the schematics and plans. Upon examining these schematics, here is what some of the judges said: “The designers selected concrete for its low- maintenance characteristics and visual sympathy to its surroundings” (7) and “the bridge is a testament to both careful design and construction”(7). They appreciated the simplicity of the design.

Figure 5: Schematic of London Bridge Design [8]

6. Personal Response

Looking at the London Bridge for the first time can be a bit ( a lot) of a disappointment. It is beyond simple with its monochromatic facade, its lack of decoration and plain arches. It is all GREY. I believe that says it all. We have been blessed by so many marvelous pieces of structural art, that we sometimes fail to appreciate the simplicity of certain designs. The London Bridge may not be the prettiest (by far) or the most intricate design for a bridge but it carries its beauty in its history. With such an amazing background. it does not need much pump or circumstances to be important. Its importance goes much deeper then its aesthetics and if people took the time to learn more about it, I think they would be impressed. When you see a billionaire walking across the street, you will not see him in colorful, boisterous clothing with shiny and obviously expensive watches. He or she will easily blend in the crowd, he or she might even seem underdressed because they have reached a point where they have nothing more to prove. They are rich beyond comprehension and do not approval from anyone to know that they have achieved something wonderful in life.  I believe the London Bridge is making the same statement. Seeing it was very anticlimactic, but the more I researched it the more I realized that it did not need much to be fantastic.

 

References

[1] https://www.britannica.com/topic/Old-London-Bridge

[2] https://www.londonpass.com/attractions-london-bridge.html

[3] http://www.geograph.org.uk/photo/2630157

[4] http://projectbritain.com/london/bridges.ht

[5] https://uk.news.yahoo.com/on-this-day-queen-elizabeth-ii-opens-london-bridge-1973-121915868.html?guccounter=1

[6] https://www.citylab.com/design/2013/10/how-original-london-bridge-ended-arizona/7200/

[7] https://web.archive.org/web/20120420230132/http://www.buildingtalk.com/news/cyl/cyl123.html

[8] http://happypontist.blogspot.co.uk/2013/09/

[9] https://www.officialdata.org/1877-GBP-in-2018?amount=1300000

[10] https://www.citylab.com/design/2013/10/how-original-london-bridge-ended-arizona/7200/

[11] https://www.inti.gob.ar/cirsoc/pdf/puentes_hormigon/25-Lecture06-Design%20loads.pdf

The Mobile Walkway of Geneva

Last week I had the opportunity to travel to Switzerland. My days were filled with beautiful scenery, decadent chocolate, and too much cheese for my own good. While walking around the city of Geneva, a bridge caught my eye. Located right in the city center, this pedestrian bridge connected the esplanade to the main area, directly in front of the Jet d’Eau. When I got home that night, I knew I had to look it up and see what this bridge was all about.

Structure Information

Figure 1. Mobile Walkway located in Geneva in its upright position for boats to pass through [1]

The pedestrian bridge at the esplanade is located south of the Pier Eaux-Vives and officially called The Mobile Walkway of Geneva. The project was completed on June 25th, 2016 and serves as a symbol of inclusiveness to the Swiss. The project cost 4.5 million francs ($4,536,225) and was funded by the State of Geneva, the GIS, and a private foundation that wishes to remain anonymous.  Previously, the pier could only be reached by walking up a set of narrow stairs, making it not accessible to everyone. Designed by the structural firm Ingeni, this new walkway is a flat path, making it accessible to wheelchairs and strollers. Also, the unique design folds up into a set of stairs when a boat needs to pass underneath. Barbara Tirone, the vice president of the associated Handicap Architecture Urbanism (HAU) stated “It is symbolically very strong to allow everyone to finally reach this emblematic site of Geneva” [2].

Historical Significance

This new pedestrian bridge is the definition of innovative.

Figure 2. Jet d’Eau in Geneva [3]

The engineers, Etienne Bouleau and Gabriele Guscetti at Ingeni, even patented their invention of a mobile walkway. This pathway is typically a flat pathway allowing access to all pedestrians, but when a boat needs to pass below, it compresses together to form an arch bridge and allows the boat to pass. This project proposed the “widening and extension of the existing pontoon by a generous wooden esplanade” [4]. The bridge uses a scissor mechanism in order to change from an arch bridge to a cantilever bridge.

From my research, this seems to be the first bridge of it’s kind, hence the engineer’s patent on their design. The only previous example I could find is a trial run for scissor-like bridge to be used during emergencies. But that model was for transportable bridge, not ones that are meant to be permanent [5]. Because of this innovative design, I am sure that we will be seeing this style of pedestrian bridge popping up around the world within the next 5-10 years. The concept of allowing boats underneath the bridge while allowing accessibility for everyone to cross is a tremendous deal.

Cultural Significance

Figure 3. The mobile walkway lays flat to provide accessibility to the jetty for everyone [1]

The area around the Jet d’Eau is known as the Mecca of Geneva. The Jet d’Eau was built in 1886 to “control and release the excess pressure of a hydraulic plant at La Coulouvrenière” [6]. Soon afterwards, the fountain became a symbol of the city, so the pressure was amplified, and it was relocated to the center of the lake. To the people of Switzerland, the fountain became “the symbol of strength, ambition, and vitality” [7].

Before this new foot bridge, the only way to get to the jetty was by crossing a narrow wooden bridge with steep steps. This made it nearly impossible for people with walking difficulties, or even strollers, to get to the other side. By constructing this new walkway, it enabled all people to cross over to the pier and see in Jet d’Eau in its full glory. The people of Geneva loved this new installation. They felt like their pride of the city was finally able to represent their feelings towards being welcoming to all. The bridge normally lays flat and raises into an arch when a boat needs to pass. Unfortunately, I found no details on the mechanism used to control the bridge’s movement; I assume it is a hydraulic system given its location.

Structural Art

Figure 4. Front view of the Geneva Walkway in arch form [1]

In my opinion, this structure is a great example of structural art. In regards to Billington’s first structural art criteria, the bridge checks the box for being scientific. This was the first of its kind in terms of engineering. The engineers worked hard to be able to please everyone, and certainly succeeded, justifying their decision to get a warrant for their design. Socially, this new bridge brought the people of Geneva together at their city center. It made everyone who visited the city feel welcome because they are now able to see such a big attraction. Symbolically, this bridge represents the kind and inclusive people of Geneva and how important the Jet d’Eau is to them. They spent 4.5 million Francs on this bridge in order to make it accessible to everyone. This certainly was not a requirement for the city,as you can see the Jet d’Eau from farther away (I saw it from the airplane when we were landing!), but the city decided to spend their money to truly showcase this symbol of the city.

Structural Analysis

The first thing you notice about the structure is the groundbreaking scissor mechanism that allows it to move up and down. The scissor mechanisms were cut using a water jet from a 20-60mm steel plate and are about 1.2 meters high and weigh 400kg. The pairs of the scissors are linked by a 12cm diameter metal aces that includes porous bronze rings in order to reduce friction and to be able to adjust the pairs of scissors easily. Duplex 1.4462 grade of steel was chosen because of it’s great resistance to wear, good corrosion resistance, and it has an elastic limit of about 500MPa [1].

Because of the design of the deck and how it extends, a standard bracing system couldn’t be used. Instead, horizontal stability is provided by the cross members in the load-bearing scissor mechanisms at both ends of the walkway [1].

I chose to analyze this structure when it is in it’s cantilever form because the entire time I was in the area, I only saw it lay flat.

Figure 5 illustrates the load path of the distributed load of pedestrians. I chose to use a distributive load because while the Jet d’Eau has light shows and during holidays, the entire lakeside it packed full of people. The load first goes to the deck where it then transfers to the pin supports. From the pin supports, the load travels to the trusses and works it way outwards to the column supports at the two ends.

 

Figure 5. The load path on the bridge due to pedestrians

Figure 6. Stress forces on the truss (plate) members

Figure 6 demonstrates where the stresses are the largest when the bridge is in cantilever form. Note, the stresses are almost the same throughout the whole bridge, except for the ends which have a slightly higher stress. This is due to the bridge being symmetrical and evenly distributing the weight of the live load.

I wanted to calculate the stress in the individual truss members. To do so, I first calculated the tributary area. Figure 7 shows how the forces are divided among the pins; there are 16 pins (represented by white circles) along each side. The red lines show how the tributary area is divided. I also added the green dashed line to show how the tributary area aligns with the elevation view. Figure 9 shows all the calculations.

Figure 7. Tributary area of the pin joints

Figure 8. Idealized truss system of the center 9 joints

I used a live load of 85 psf because that is an average pedestrian live load. I found the width of the bridge to be 12.5 ft. Figure 7 illustrates all the forces acting on it [8]. I calculated the dead load of the steel and assumed a width of .5 ft for the steel plates and found it to have a thickness of .2 ft. For the deck, I assumed it to be made of redwood because that is a popular wood for decks. I also assumed a thickness of .67 ft because that is the minimum standard according to codes for wood jetties. I started by calculating the tributary areas, then applying the area to the density of my materials to find all the loads on the connections. Next, I used method of joints to calculate the internal forces in the truss.

Tributary Area

Deck: (12.5 ft/2)(892 ft/ 16) = 348.44 ft2

Steel plates:

(sqrt(2.52+42))= 4.7 ft

(4.7 ft)(.5 ft)(.2 ft) = .47 ft3

Load on each pin

Live load: (85 lb/ft2 )( 348.44 ft2) = 29,617 lb

Dead load (steel): (490 lb/ft3)( .47 ft3) = 230.3 lb

Dead load (redwood deck): (32 lb/ ft3)( 348.44 ft2 )(.67 ft) = 7470.56 lb

Figure 9. Method of joints

Calculating internal forces

∑Fy = FAC(2/2.36) + FAB(2/2.36) – (29617+230.3+7470.56) = 0

∑Fx = FAC(1.25/2.36) – FAB(1.25/2.36) = 0

FAC  =  FAB

∑Fy = FAC(2/2.36) + FAC(2/2.36) – (29617+230.3+7470.56) = 0

FAC  =  FAB = 22,017.53 lbs or 22 K

Because the bridge is symmetrical, all the members of the truss have the same force of 22 K. Due to all the assumptions, my calculations were quite off from the stress values shown in Figure 6, however I verified the idea that the stress should be consistent throughout the structure.

Figure 10. Construction of the mobile walkway.

The construction of the walkway was unique because of the mechanisms. The entire walkway was pre-assembled in workshop shown in Figure 10. This way, the engineers were able to run a series of test on the structure before it was available to the public. The structure was mounted on a metallic frame that was used for constructing, transporting, and eventually hoisting the assembly.  Once on the wharf, a crane was used to place the walkway on the supports [1].

I think it was quite simple to show this design to the stakeholders considering it was built indoors first. Because it was the first design of it’s kind, many different tests were run on it and I am sure that the city of Geneva was involved throughout the process because they were funding it. The other known company that helped fund the project was GIS, who is actually a lifting solution company. I am sure that when a crane was needed GIS was the company that was selected. Sounds like a conflict of interest to me, but if it gets the job done I guess it’s alright?

Personal Response

From visiting this bridge, it was nice to see how many people were just sitting outside enjoying the view. From tourists to natives, there were many people outside just taking in the sunshine, laughing, and appreciating their time together. I understand how this place can be viewed as the “Mecca” because of the energy that is felt when you are there. I’m glad the city of Geneva wanted to make everyone feel welcome and made sure this bridge was a priority.

References

[1] https://ingeni.divisare.pro/projects/338960-the-new-mobile-walkway-of-geneva-s-jet-d-eau
[2] https://www.tdg.ch/geneve/actu-genevoise/jet-eau-presente-nouveaux-atours/story/22163401
[3] http://www.geneva.info/jet-d-eau-fountain/
[4] (http://www.ge.sia.ch/node/182
[5] http://www.engineersjournal.ie/2015/07/28/novel-scissor-like-bridge-structure-use-emergencies/
[6] (http://www.geneva.info/jet-d-eau-fountain/
[7] http://www.geneva.info/jet-d-eau-fountain/
[8] http://www.conteches.com/DesktopModules/Bring2mind/DMX/Download.aspx?Command=Core_Download&EntryId=9850&language=en-US&PortalId=0&TabId=144

Grosvenor Bridge

A favorite pastime of mine when visiting other countries is to just walk in a direction and get lost. Cities are composed of so many different communities, landmarks, and secrets that you never know what you’ll stumble across on an afternoon stroll. And that’s especially true for London, in part because of how diverse and bustling it is, but also because it’s so huge I get lost constantly. Grosvenor bridge was one such discovery I made after wandering across the Thames, where I found this bridge among a blooming new community.

Structure Information

Grosvenor Bridge is a multi-track railway bridge crossing the River Thames between Abbot’s Manor and Battersea Park, just adjacent to Chelsea Bridge. Initially known as the “Victoria Railway Bridge”, this bridge was designed by engineer John Fowler and opened for the London Brighton and South Coast Railway in 1860 [1]. At the time, the bridge’s scope was much smaller, with only two railways running across it, built at a cost of 84,000 pounds (funded entirely by the railway industry). Since that time, the bridge has undergone many expansions and redesigns – the current crossing is actually a series of ten parallel bridges carrying ten railways across the river. Grosvenor Bridge is the widest bridge on the Thames, and one of the busiest rail bridges in the city, connecting up Victoria Station with the rest of the nation [2].

Historical Significance

At a first glance, this bridge is easy to look past. It lacks fancy decoration and seems simple in form, which doesn’t betray its deep historical impact on the city of London. This bridge was the first rail bridge constructed over the River Thames in London, which was a huge milestone in improving the rail connectivity of the city. The bridge was initially constructed of wrought iron arches, and its designer John Fowler was bound by tight design constraints. The bridge had to have a clearance of 22 feet for shipping traffic by water below. It had to feature 4 spans, with mid-river piers lining up with Chelsea Bridge to the west [3]. By this time, construction with wrought iron was not a new practice – the bridge was built without issue over the course of a year. However, the designer, John Fowler, would go on to be one of the most influential rail engineers in London, growing the early London Metropolitan Railway, developing tunneling technology, and working with Benjamin Baker on the Firth of Forth Bridge in Scotland [4]. This bridge really was a starting point for his revolutionary career with trains!

Additionally, this bridge design was used as a template for further expansions of rail crossings at this spot on the Thames. As capacity increased, additional adjacent river bridges were constructed in similar design, and simply connected via deck to the original. It wasn’t until 1963 that the bridge underwent major renovations, mainly due to increased train loads and deterioration. The bridge continued on with its four-arch design for aesthetics and practicality [5], and kept consistent with history in that the bridge is really designed as 10 separate bridges able to carry 10 tracks. During reconstruction, it was necessary to keep 8 tracks open for use along this high-volume bridge – so each bridge and track was replaced one at a time and added to the expanding new Grosvenor Bridge, which is why the tracks and arches were kept relatively separate.

Cultural Significance

As previously mentioned, this bridge was one of John Fowler’s first landmark projects during his career in bridge design and railway work. As the first bridge in London to allow train passage across the Thames, it truly was a pioneering structure, if not in form than in purpose. By looking at a history of its widening, the history of railway expansion in general comes to light. As rail gained speed in London, so did this bridge gain width. Especially today, this bridge remains busy transporting people around the country – so busy that not even structurally integral construction to renovate the bridge in 1963 could halt its traffic.

Nowadays, the bridge serves a further social purpose to compound on its economic providence to the area. The southern end of the bridge meets with the Battersea Power Station. This region of London is an up-and-coming neighborhood situated around a large power station reaching up along the riverside. This structure was what allured me to the area to begin with – my curiosity of the construction zone led me to finding a hip residential area with plenty of new restaurants and hang-out spots. Grosvenor Bridge’s southern end meets the boundary of this place, and the community has begun to integrate this old bridge into new life. Below the bridge runs the Thames Path, a popular walking route connecting up neighborhoods and parks along the River. This tunnel running beneath has turned into quite the social scene: pop-up restaurants, ping-pong tables, and relaxing residents can all be found here. Grosvenor Bridge is becoming popular part of this new scene, adding to its importance here in London.

Structural Art

Now comes the difficult task of assessing the Grosvenor Bridge and its place as structural art. Based on the current structure of the bridge, I have decided it to be a good example of structural art, especially when examining it as a renovation of previous form.

The 1963 reconstruction of the bridge constructed the arches as steel-box girders connected to an orthotropically stiffened steel deck through slender spandrels [6]. Orthotropic steel decks, a relatively new concept at the time, strengthen the deck against the vehicular loads above by resisting bending. This results in lighter forms allowed in supporting the bridge. Despite efficiency increases in the 100 years between construction and renovation, essentially the same bridge design was used. This could be seen in two lights – one that conserves cost by utilizing existing piers, or one that fails to innovate given an opportunity.

Economically, the bridge’s continual expansion over the years became very costly. The most recent renovation from 1963 to 1967 was long-winded and expensive due to the continued use of railway above. However, the new integration of stiffened steel decks and hollow steel box arch supports required relatively little material to be used. Additionally, the fact that this is 10 separate bridges in essence reduces the material needed to support each segment of the bridge.

Elegance is where the bridge seems to lack the most. The bridge doesn’t come across as a complete structure, and in reality, it isn’t – this is a crossing consisting of 10 bridges joined at the same piers. Additionally, despite being a fairly modern bridge, it doesn’t look it. The bridge relies on the same design as the original back in 1860, failing to show off too much new in the ways of bridge forms. However, the simplicity of design and openness of the structure really do shine.

Structural Analysis

This structure is interesting to analyze because the deck is disconnected in a way such that each individual track is supported by an individual bridge structure yet also connected by the same concrete piers. Each of the 10 possible tracks is kept separate, rather than acting as one individual structure. This really simplifies analysis on the bridge, since only one live load can exist on each structure at any time, and each structure is essentially a copy of the next. Also fortunate is that dimensions of the truss structure itself are known, and other loads such as that of the deck and trains can be reasonably assumed.

As stated before, the structure is composed of 4 arches spanning over the river, connected to concrete piers above. Each rail bridge is connected to two arch spans supporting it on the sides. These arches are hollow steel box girders measuring 1.13 (3.7 ft) meters tall by 0.61 (2 ft) meters wide, approximately 0.1 feet thick, pin connected to the concrete piers and supporting the orthotropically stiffened steel deck above via tubular steel spandrels (which appear to be approximately 0.5 ft in diameter). The arches each have the same clear span between piers of 50 (164 ft) meters. Each arch connects to the bridge deck with eight slender spandrel columns symmetrically spaced and at the apex of each arch. The rise of each arch is 5.4 (17.6 ft) meters. Each rail bridge deck segment is approximately 5.4 (17.7 ft) meters wide, and plan views show the deck thickness to be 5/8″ ft. These measures give a good idea as to the dimensions and can help determine forces felt in arch members under load.

This bridge acts essentially the same way any arch bridge would: the dead load of the bridge deck and live load from crossing trains is transferred downward via the steel spandrels and center connection to the arch tube. Each spandrel is designed to transfer load from its individual tributary area and does so through compression forces. These loads are transferred to the arch through compression forces, moving down to the ends of the arch and finally into the concrete piers supporting the bridges. There are two arches, so the overall load to be carried is split in half.

Idealizing the bridge as a distributed load including deck weight  and both arches acting as support, the bridge can be described as below:

Because of even areas, the load distributed to each arch is similar. For the center three concrete piers, the horizontal forces of the archways cancel out, resulting in only a vertical resultant force. The end piers do have to support horizontal loads produced by the arches. When a live load (train) is introduced on the deck, more horizontal loading occurs. I will be analyzing the reaction and member forces in one arch span. Construction documents specify the deck to be of mild steel, which has a density of 0.284 lb/cu. in, or 490.75 lb/cu. ft. Using a single span length this results in the deck weight being 890,343 lb. Assume a passenger train load weight of 200,000 lb, resulting in a total vertical load of 1,090,343 lb. Due to symmetry, the vertical reactions on each side of the arch are the same, so each end has a vertical reaction force of 545,172 lb. To find the horizontal reactions at each end, cut at the arch center and take the moment about the center of the arch. (Distributed load [-6648.43lb/ft]*82ft*41ft) + (Vertical reaction [545,172lb]*82ft) + (Horizontal reaction *17.6ft) = 0. This equation results in the horizontal force being 1,270,003 lb, acting inward towards the arch. This exists on both sides. The force in the steel box member then would be 1,382,071 lb, or since in the actual bridge there are two arches supporting each deck, a member force of 691,035 lb. Further, the member stress can be calculated by dividing this force by its area (found to be 0.56 square feet), which gives the result of 8,569 psi.

Personal Response

Along the River Thames, communities are growing, and Grosvenor Bridge has not been left out. Below the bridge, families take walks and friends play ping-pong. Above the bridge, trains cross the river carrying passengers away. This structure plays a large role integrating into the community today, and it holds great importance in the history of London as the city’s first rail bridge to cross the Thames. There is more to Grosvenor bridge than meets the eye as I discovered through my research. Even its simple form goes further than surface level, being truly one bridge composed of 10, increasing the efficiency of its design and paying homage to its long history of expansion and heavy use. When first approaching this bridge I did not expect it to be significant. It felt basic from a distance. Only when examining it closer did I come to appreciate this simple arch bridge more for what it was and is.

References

[1] http://thames.me.uk/s00160.htm

[2] https://londonist.com/london/transport/9-secrets-of-the-grosvenor-railway-bridge

[3] http://www.semgonline.com/structures/struct_34.html

[4] https://www.britannica.com/biography/Sir-John-Fowler-1st-Baronet

[5] http://www.engineering-timelines.com/scripts/engineeringItem.asp?id=697

[6] http://happypontist.blogspot.co.uk/2011/06/london-bridges-8-grosvenor-railway.html

Blackfriars Bridge

Structure Information

Figure1: Location of Blackfriars Bridge [1]

I’ve came across Blackfriars Bridge during my last bicycle ride around Jubilee Gardens. Blackfriars Bridge is an arch designed structure that crosses the River Thames about a mile away from the famous London Eye and located between Waterloo Bridge and the Millennium Bridge.

Opened  for public circulation in November 1869, the 5 spans bridge is 923 feet long and, was designed by the English Civil Engineer Joseph Cubitt. Due to an increasing traffic, the initial 70 feet wide structure had been widened to the actual 105 feet. Funding came from a charitable trust “Bridge House Estates” on behalf of the City of London

 

Figure 2: Blackfriars bridge in 2018

Historical Significance

The original Blackfriars Bridge was the third to be constructed in central London after London Bridge and Westminster Bridge. The present Blackfriars Bridge consists of five wrought iron arches and was built in replacement for the first crossing toll bridge “William Pitt Bridge” designed by Robert Mylne with nine semi-elliptical arches made out of Portland stone and was poorly executed. The use of wrought iron was unique at the time of the inauguration, however not the first time to be used. Joseph Cubitt was conjointly working on another similar project: the Blackfriars railway Bridge adjacent to this structure. Both structures look a lot alike with the use of the material iron which made construction much less time consuming (five years) versus the nine years of construction for the original stone designed by Mylne. The structure was inspired and also inspire tourists across the world. Here is an old image of the Original Blackfriars Bridge

Figure 3 : Original Blackfriars Bridge in 1775 [2]

Cultural Significance

Figure 4: Blackfriars at night

Blackfriars Bridge was inaugurated by Her Majesty the Queen Victoria herself on the 6 th November  1869. The international notoriety of the structure came into play thirteen years after the opening when a former chairman of a renowned Italian bank was found dead on one the arches. What seemed to be at first a suicide was later proven to be a murder by the Mafia to whom he was related and indebted. Sounds like a movie isn’t? Decorations on the structure are historically meaningful. It is said that this bridge marks the boundary between sea water and salt water in the Thames and the choice of bird subjects reflects this idea: sea birds on the downriver side, fresh water birds on the other. For instance, the pulpit-like shape at the ends of the bridge is purposely designed in reference to Black Friars while the stone carving on the piers of the bridge was in respect for the marine life and seabirds. The dedication of the bridge to Queen Victoria was represented by her statue which was by the way funded by a certain Alfred Seale Haslam. Used as road and pedestrian bridge, the Blackfriars’ structure boosted the pride of the Londonians, especially of the merchants crossing the bridge for their daily activities leading to donations from the wealthy ones for the funding of the House Estate Trust which is an organization in charge of four other Thames bridges. Guess who is the trustee? The City of London! Yes, the City relies on these funds to insure repairs and maintenance of the infrastructures within the limits of the city.

 

Structural Art

The Bridge has to qualify for the rule of the three E’s (Economic, Efficiency and Elegance) in order to be called a structural art. As shown in the following section, the load path for the structure is clearly represented despite the multiples decorative elements in place which consolidate the aesthetic-elegance aspect of the design. The load path could be seen from the deck trough the multiple trusses and transmitted to the piers. It has been relayed that the City of London had been clear during the design phase of their expectations of an ornamental structure which justify the decorative semi-circular columns on both side of the bridge. The bridge costed  £151,000 at the time; worth a roughly  amount of £17M in 2017 [3] , which make me consider the costs to be within the limits of reasonable during that period. Don’t get me wrong, I’m not saying that the same structure -if it had to be designed today- couldn’t be evaluated more cost-efficiently! Anyway, with the three E’s checked out, I could affirm that the Blackfriars Bridge is definitely a structural art.

Structural Analysis

Figure 5: Load path on Blackfriars Bridge

The bridge is a 5 spans structure made of cast-iron arches assembled on site with the deck made of reinforced concrete built on site as well. As the Thames was well-known to be a fast flowing river causing damage from scouring, iron caissons were used to help deep into the clay riverbed. These caissons were half filled with concrete and surmounted by the granite-faced piers. Thorn and Co. the builder of the structure had to deal with the use of caisson for the first time on this project for the piers which was a challenge that was won. In terms of materials, wrought iron was used for the ornamental elements. Portland stone, well-known for its strength and polished red granite was used for the piers. The 5 spans structure bridge has been designed to cover 922 feet over the river and in between we have the 3.3m high columns, said to weigh over 30 tonnes each carrying loads from the 56.4 m central arch of the bridge followed by the next two 53.3m span. As expected for the load path, the use of repeated circular arches helps reduce the lateral loads at connections (columns/piers) with the exception of the exteriors ones which are contained by the abutments on both banks of Thames. The piers collect both the dead load and live load according to the respective tributary area. The deck, by the way provides a uniformly distributed load on the top the structure over the entire length. The reaction of the soil below the piers prevent the entire structure from failure. In order to design this structure, I’ll assume the extreme cases scenario in terms of live loads especially; meaning I’m considering the following at an instant t on the bridge: 10 trucks of 10,000 lbs each, 100 pedestrian of 120lbs each. These assumptions are computed in the following as:

Evaluating for example the lateral and horizontal forces for the central span requires the following:

ΣFx= 0 => Cx = Dx

ΣFy = 0 => Cy + Dy – W (185’) = 0 but since there’s symmetry between both reactions,

We have Cy = Dy = (WL/2) = 7,832/2 = 3,916 K

The lateral load equals to Cx = Dx = (wl2/8h) = 42,333*1852/ (8*10.8 ft.) = 16,769 K

Resultant Force to be cancelled by neighboring arch Rx = Sqrt. (Cx2 +Cy2) = 17,220 K.

From here, with the same increment method we could determine the force coming from the immediate left’s span until the left side abutment. Due to symmetry, the value on the left side is more likely to be the one on the right side as well.

Furthermore, Shear and Buckling could also be checked out to ensure the appropriate section for the piers in order to avoid failure.

Personal Response

Maintenance on this structure has been said to occur on a yearly basis. However, my impression is that the maintenance is exclusively focusing on the structural aspect of the Bridge. The sidings looked rusty and off paint which, not only affect the aesthetic but could be a trigger for much bigger structural issues in the future. There’s always this strong feeling being in physical contact with structures constructed centuries earlier. I’ve never realized the need for a more thorough maintenance schedule for public structures until my eyes captivated the rusty trusses on Blackfriars.

Figure 6: Structural concerns, Please HELP!

 

References

[1] https://www.google.com/maps/d/viewer?msa=0&mid=1Yv2q2kSjL-2fqJczikCqxQGiJy8&ll=51.51021609855225%2C-0.10235587337115248&z=16

[2] http://www.thehistoryoflondon.co.uk/the-original-blackfriars-bridge/

[3] https://www.bankofengland.co.uk/monetary-policy/inflation

http://www.engineering-timelines.com/scripts/engineeringItem.asp?id=693

The Jewel Tower

Structure Information

The Jewel Tower is located in Westminster, London, England. The building was originally constructed between 1365 and 1366, with later additions constructed in the 1600’s and again in the 1700’s to serve the buildings changing purpose. A photo of the building today is shown in Figure 1 below.

Figure 1: Front view of the Jewel Tower

The Jewel Tower was originally built to securely store royal treasure within the private palace of Edward III. Its use has changed since its original construction. The succession of monarchs dictated the use of the Jewel Tower until its transition to containing the records office of the the House of Lords sometime before 1600. In 1869, the tower underwent another transition from a parliamentary office to a testing facility for the Board of Trade Standards Department, better known as Weights and Measures. The Department vacated the building in 1938, and the building is currently a monument and facility to display historic artifacts [1].

The Jewel Tower was designed by Henry Yevele, the most succesful master mason and architect of his time. Henry Yevele was the principal royal-appointed architect during the reign of Edward III, and the Jewel Tower was one of his many royal works during this time [2]. This indicates that the building was paid for by the monarchy of England. Other notable surviving works by Yevele include the naves of Westminster Abbey and Canterbury Cathedral.

Historical Significance

The Jewel Tower is a three-story L-shaped structure with a turet structure on the backside of the building. Each floor is comprised of a large rectangular room and a smaller room in the turret tower. Each floor is distinguishable by its ceiling vaulting. The ground floor of the Jewel Tower is the only floor with the original medieval rib vaults in place [3]. Although the Jewel Tower may not have been the first building of its time to employ the technique of ribbed arches and resulting ribbed vaults, it was constructed around the time of the forefront of the use of ribbed vaults leading to what we now know as Gothic architecture.  This structural engineering technique for constructing more efficient buildings with higher ceilings was not new, although the Jewel Tower may have helped architect Henry Yevele in perfecting his techniques for this type of vault used in his works Westminster Abbey and Canterbury Cathedral built after the Jewel Tower. Ribbed vaults were continually used in succeeding Gothic Architecture. Figures 2 and 3 below show a ribbed vault in the ceiling of the ground floor of the Jewel Tower and the ribbed vaults in the nave of Canterbury Cathedral, respectively. As previously mentioned, both were works of Henry Yevele–The Jewel Tower preceded Canterbury Cathedral.

Figure 2: Ribbed vaults in ground floor of the Jewel Tower [2]

Figure 3: Vaulting at Canterbury Cathedral [2]

 

 

 

 

 

 

 

 

 

 

 

 

 

It should be noted from the Figure 2 that there are extra ribs in the vaults. This forms a small fan. The vaulting at Canterbury Cathedral is full fan vaulting. Fan vaults are the most recently developed and most complex form of vaulting. The development of such vaulting was said to begin in 1351, only about 10 years earlier than the construction of the Jewel Tower. The development of fan vaulting is also attributed solely to England [4]. It can be concluded that the works of Yevele, especially the Jewel Tower, were a contributing factor to further development of fan vaulting. The motivation for the development of fan vaulting is mostly aesthetic, but the additional ribs did not compromise the structural safety of high vaults, and ultimately required less formwork [4].

The best existing example of a building with fan vaulting is Bath Abbey, shown in Figure 4.

Figure 4: Fan vaulting in nave of Bath Abbey, England [5].

 Cultural Significance

The Jewel Tower is associated with three distinct, successive functions: the royal keeping of jewels, the storage of the records of the House of Lords, and the Weights and Measurements office.

The Jewel Tower is one of four surviving buildings that made up the medieval palace of Westminster, which was the central residence for the English monarchy for the majority of the middle ages. The tower served Edward III through Henry VIII as a place to store royal treasures and things of great value. Figure 6 below shows the Jewel Tower in its original location as a part of Westminster Palace.

Figure 6: Jewel Tower in position of original construction as a part of Westminster Palace [2].

In 1512, the use of Westminster as a main royal residence was ended due to the destruction much of the Privy Palace in a fire. The function of the Jewel Tower as building of Parliament is arguably more significant than its function as royal jewel storage. This building was the safeguard to many documents sacred to England’s history. Finally, the function of the Jewel Tower as a testing facility of the Weights and Measurements office was short-lived, but the results of the decisions made by this office dictated trade policy for the British Empire [6].

There were no marked major historical events centered on this building, but its persistence to remain standing throughout fires, demolition, and 650 years of history makes this building special. The Jewel Tower as a historical whole embodies the transition of the British state from a monarchy to a Parliamentary Democracy to a highly developed imperial power [3].

A funny little anecdote about the perception of the construction of the Jewel Tower has perpetuated throughout history. Edward III built the Jewel Tower and its moat (maximum medieval security) encroaching on the grounds of the Benedictine Abbey, to the great dismay of the monks who resided there. According to the record-keeping ‘Black Book’ of Westminster, the monks blamed the land grab on William Usshborne, keeper of the royal Privy Palace. Upon completed construction, Usshborne stocked the new moat with freshwater fish and is said to have died choking on a pike which was caught there. The monks saw this as a perfect example of divine retribution [2]. Although no workers were recorded to have died in the construction of this building or its history of use, the death of William Usshborne by moat fish could be considered the human cost of this building.

The Jewel Tower today functions as I believe it should–a testament to its history that is open to the public.

Structural Art

The Jewel Tower demonstrates some degree of structural art in a very discrete manor. The Jewel Tower is a blocky, rectangular structure. Its frame seems to be based on post-and-lintel construction, making it fairly easy to see how the load is transferred through the structure. Even though the facades are not open or light, the structure is somewhat transparent in its load-bearing manner. Another way that the Jewel Tower demonstrates structural art is there are no added elements of decoration. It is a plain building which has a form that communicates its function.

Even with the previous aspects considered, I would not consider the Jewel Tower an example of structural art. The stone masonry construction is far too heavy and imposing to fit in to David Billington’s efficiency criterion to describe structural art. With the developing trend of gothic architecture, this structure could have used much less material to go much further. In addition, the rectangular, blocky nature of the facade and plan of the Jewel Tower was far less technically advanced than structures that were being built during the same time period. This was likely a product of its function as a safe place for royal valuables.

Structural Analysis

The service function of the Jewel Tower dictated its design and final form. The tower was meant to be fortified in order to protect the royal treasury. Consequently, the Jewel Tower was made a three-story building, each level being more secure than the preceding level. The turet structure was built to house the spiral staircase and also in part for added security. The structure is L-shaped in plan and is an example of medieval masonry construction. The process of masonry construction involves building from the ground up. The Jewel Tower has a stone masonry foundation that is slightly larger in plan than the building itself. A portion of the foundation can be seen on the left side of Figure 7 due to the moat that surrounded the building when it was constructed.

Figure 7: Stone masonry foundation of the Jewel Tower

The stone foundation was supported by timber piles which are still on display in the Jewel Tower today, as shown in Figure 8.

Figure 8: Original timber foundations on display in the Jewel Tower

From the foundation, the Jewel Tower would have been built by laying each stone individually and securing the stones together with mortar. Timber formwork was used to keep the exterior of the structure stable until the mortar cured. The Jewel Tower is built using Kentish ragstone. The interior-facing walls of the L-shape of the building are built using roughly coursed rubble masonry whereas the remainder of the walls are rectangular-shaped ashlar masonry. All surviving windows and doors were 18th century additions to the Jewel Tower. The windows and doors are framed in three-hinged arches using Portland Limestone [3]. There is also a stone section at the crown of the building which   The moat as seen in Figure 7 is contained in two ashlar masonry walls. The interior of the building is a little more interesting than the exterior. The main rooms on each floor are approximately 25 x 13 ft and the turet rooms are 13 x 10 ft [3]. The rib vaulting used as the ceiling for the ground floor is the only ceiling that is original to the Jewel Tower. The vault incorporates tiercerons, which are intermediate ribs between the diagonal and transverse ribs, which forms a small fan. The plan view of the rib vaulting in the ground floor can be seen in Figure 9 below.

Figure 9: Plan of ground floor showing vault forms [7]

The view looking up at the vaulted ceiling is shown in Figure 10 below.

Figure 10: Interior view of rib vaulting [3]

The walls and floor of the second story were built before the vault in the ground floor. The self weight of the second story and above rests on the lateral stone walls. The construction of this vaulted ceiling required careful coordination between the mason and the carpenter. Timber formwork was used to to stabilize the stone as the ribs were constructed and the intermediate panel sections were installed.

The structural system employed for the structure as a whole is a simple gravity-load controlled system. The load on the building has only to do with the self-weight of the stone and potential static load of occupents or materials inside the building. The ceilings of the second and first floor have varying structural systems in place to support the weight of the slab above and load on the slab. The ceiling of the second floor has a timber truss structure that transmits the self-weight of the stone roof to the outer lateral walls. The first floor has a timber joist and girder system that transmits the self-weight of the slab above it to the outer lateral walls. The load-bearing system of the ground floor is the same as the system used in the first floor. The load on the wider plan stone foundation and original wooden piles is a function of the density of the stone and the height of the building. This would yield a differential area load on the foundation as shown below, assuming that the density of stone is 170 lb/ft^3 [8] and one storey is roughly 15 feet high. The self-weight of the roof and the floor slabs rest on the lateral stone walls. Figure 11 below shows the structural system of the overall structure.

Differential area load = (170 lb/ft^3)(15 ft)=2550 lb/ft^2

Figure 11: Load path of structure as a whole

The more interesting structural system is the interior rib vaulting in the ground floor ceiling. The ribbed vaults are composed of arch ribs and panels. From this point on, this analysis will consider one rib vault, which spans half of the square footage of the main large room on the ground floor plan shown in Figure 9 above. Crossed ribs arise from the four supports at each corner of the vault which act as engaged columns and intersect each other at the keystone. The vault only has to support its own self-weight.

The load path for the general structure begins with the self-weight of the stone roof. The weight transfers as a surface load to a line load on each of the inclined timber joists in the ceiling truss structure of the second floor. The line load is transferred as point loads on to the center girder and the lateral exterior wall. The point loads from each joist on the center girder are transferred as a point load on to the exterior wall at each end of the girder. The weight of the slab (floor) of the second floor is transferred as a surface load to each joist in the structure of the ceiling of the first floor. There is a line load on each joist which is transferred as point loads to the lateral exterior walls. The same system is in place between the first and ground floor. All loads in the lateral walls are transferred to the stone foundation which are then transferred to timber pile foundations to the soil. The load path of the overall structure is shown in Figure 12 below.

Figure 12: Load path of overall structure

The general load path of a ribbed vault is displayed using the model shown below in Figure 13.

Figure 13: Load path of a ribbed vault [9]

The load path starts at the key stone and transfers through the ribs to the supports. The horizontal thrust and vertical load are transferred to the lateral stone walls.

The ribbed vaults can be analyzed by finding the tributary area of each rib and calculating the self-weight of the vault. The self-weight can be calculated using the density of the stone and the thickness of the vault. Assuming a thickness of 0.5 ft, the self-weight is found using the following calculations.

Vault self-weight=(170 lb/ft^3)(0.5 ft)=85 lb/ft^2

Using the geometry of the plan view shown in Figure 14, the tributary area for each rib can be calculated.

Figure 14: Plan view of the rib vaulting

The rib vault covers half the square footage of the ground floor main room. The square footage of the bay of the vault is given by the following equation.

Bay square footage=(25 ft x 13 ft)/2=162.5 ft^2

The four column supports are located at the corners of the plan view. By geometric symmetry, each column takes the same amount of load. One quarter of the bay is shown with dimensions assigned in Figure 15.

Figure 15: Tributary area layout for one column support

Tributary Area for rib 1: At1=(0.5*6.25 ft*2.17 ft)+(1/3)((0.5*6.25 ft*6.5 ft)-(0.5*6.25 ft*2.17 ft))=11.29 ft^2

Tributary Area for rib 2: At2=(6.25 ft*6.5 ft)-(11.29 ft^2+11.28 ft^2)=18.10 ft^2

Tributary Area for rib 3: At3=(0.5*2.08 ft*6.5 ft)+(1/3)*((0.5*6.25 ft*6.5 ft)-(0.5*2.08 ft*6.5 ft))=11.28 ft^2

Multiply the tributary area of each rib by the self-weight of the vault to find load transmitted to column by each rib:

Rib 1: Load to column = (11.29 ft^2)*(85 lb/ft^2)=959.65 lb

Rib 2: Load to column = (18.10 ft^2)*(85 lb/ft^2)=1538.50 lb

Rib 3: Load to column = (11.28 ft^2)*(85 lb/ft^2)=958.80 lb

Total load to column = (959.65+1538.50+958.80) lb = 3456.95 lb = 3.46 kips

Note that rib vault is in total compression.

Therefore the horizontal thrust generated at the base of the column taken by the lateral wall is given by the equation below, assuming that the pointed arches that make up the rib vault direct the load more vertically and minimize horizontal thrust. Therefore the load travels to the lateral walls at an assumed angle of 70 degrees

Horizontal thrust=3.46 kips (cos(70))=1.18 kips

Vertical load is given by the following equation.

Vertical load = 3.46 kips (sin(70))=3.25 kips

The lateral stone wall must be strong enough to resist 1.18 kips horizontally, and an additional 3.25 kips is transferred to the foundation vertically at each of the eight columns.

Personal Response

I never really thought about how the principles of construction have remained relatively constant for over six centuries. Somehow aa building which was built in the 1300’s is still standing and still has some of its original features. Studying a building with this much history makes you think about how constant civil engineering has been and always will be as time moves forward.

References

[1] http://www.english-heritage.org.uk/visit/places/jewel-tower/history/

[2] http://www.countrylife.co.uk/out-and-about/theatre-film-music/great-british-architects-henry-yevele-died-1400-24443

[3] http://www.english-heritage.org.uk/visit/places/jewel-tower/history/description/

[4] https://www.britannica.com/technology/fan-vault

[5] https://visitbath.co.uk/listings/single/bath-abbey

[6] http://www.english-heritage.org.uk/visit/places/jewel-tower/history/significance/

[7] http://www.english-heritage.org.uk/content/visit/places-to-visit/history-research-plans/jewel-tower-phased-plan

[8] https://www.simetric.co.uk/si_materials.htm

[9] https://www.sciencedirect.com/science/article/pii/S0141029617301864

The Albert Bridge

Structure Information

The Albert Bridge is a road bridge over the River Thames, connecting the Chelsea part of Central London to the Battersea district. The Chelsea Bridge and the Battersea Bridge were opened previously, but the link between the two neighborhoods was not adequate for the growing area so the Albert Bridge was built. The neighborhood of Chelsea expanded in the 1800’s, and Prince Albert proposed the idea of a new and improved bridge to replace the existing ones. The Albert Bridge Company was established in 1863 to build a better bridge, and an 1864 Act of Parliament authorized the construction of the bridge. [1] They were tasked with the operation of the bridge, and toll booths were implemented to generate revenue and cover the cost. [4] The engineer for the Albert Bridge was Rowland Mason Ordish of Messrs Ordish and Le Feuvre, and the construction of the Albert Bridge began in 1871 after initial delays. Ordish was supervised on the project by engineer F.W. Bryant, and the iron and steel work for the project was provided by Britannia Ironworks of Derby. The Albert Bridge was opened to the public in 1873 and given the name in honor of Prince Albert, the husband of Queen Victoria. [1] It was later modified and strengthened by Sir Joseph Bazalgette between 1884—87. The Albert Bridge was once again restored between 1972-1973 and a central pier was added during this time. Last but not least, the Albert Bridge was refurbished in 2010-2011. [1] This is hopefully the last time it will need maintenance, but better safe than sorry!

Figure 1: http://janbutcher.co.uk/?attachment_id=1525

Historical Significance

The historical significance of the Albert Bridge is that it is one of the two central London road bridges to have never been replaced (the other being Tower Bridge). The original design was a suspension bridge but the addition of cable-stays make this a hybrid type of bridge. [1] The six year delay on the start of construction for the Albert Bridge allowed Ordish to design and build the Franz Joseph Bridge in Prague. He used the same principles on the Albert Bridge as the Prague Bridge so the design was not innovative on the Albert Bridge, but he was able to patent this new design after it was utilized on both bridges. [4] In 1857 Ordish patented his system to combat dynamic movements with the catenary cables and the stays each taking a proportion of the loads. [2] The Ordish-Lefeuvre principle, as it was known, was only utilized on those two bridges. When I saw the Albert Bridge, it reminded me of the Brooklyn Bridge with the combination of cable-stayed/suspension bridge design. However, I was not able to find a direct link between the principle patented by Ordish and the Brooklyn Bridge design, which came after. The addition of a central pier in 1973 to strengthen it led to the more traditional beam bridge which still stands today. [4] The weight limit of two tonnes is present, as well as a traffic island at the southern end of the bridge to decrease the size of the vehicles which cross it. [4]

Cultural Significance

The Albert Bridge is an important part of the Chelsea Embankment and the surrounding Battersea Park area around the Thames River. [1] The toll booths were in operation for six years before the structure was bought by the Metropolitan Board of Works, who then made it free to cross the bridge. [3] Proposals to demolish the bridge began in 1926. Both before and after World War II, the Albert Bridge faced the threat of demolition; a 1957 public campaign against demolition saved the bridge. The public campaign was headed by Sir John Betjeman, who described the Albert Bridge as “shining with electric lights, grey and airy against the London sky, it is one of the beauties of the London River.” [1] After the campaign, a weight limit of 2 tonnes was imposed on vehicular traffic on the bridge to combat the fear of bridge failure, and it was almost made an entirely pedestrian bridge. [3] The Albert Bridge was therefore nicknamed “The Trembling Lady” because there was concern that the vibrations from the Chelsea Barracks would cause damage to the bridge. Soldiers from the barracks were advised to break step when marching over the bridge, but those fears and cautions are not present today on the Albert Bridge. [3] When soldiers would march in step, it would cause vibrations of the bridge. This would also occur when large numbers of people cross the bridge simultaneously, with their steps accidentally synchronizing. It’s interesting that this phenomenon happened with the opening of the Millennium Bridge in 2000, with the same problems leading to the vibration and movement of the bridge. [4] I guess we didn’t learn from the mistakes of the past!

Today, the lack of parks or open green spaces on the north side of the Thames River leads to a lot of people walking their dogs across the Albert Bridge to the Battersea Park on the others side. This would not appear to be a huge problem, except that the frequent dog urination on the timber deck causes the deck to rot. [3] However, when I walked across the bridge I did not see (or smell) that this was a problem! The bridge has been used in the background of several movies: Absolute Beginners, Maybe Baby, A Clockwork Orange, Sliding Doors, among others. [3]

Structural Art

Today the Albert Bridge is painted pink, blue and green, a color scheme that is supposed to last around 25 years. There have been numerous color schemes throughout the history of the bridge, but the reason for the most recent one is to increase visibility during fog and dim light. The bridge is supposed to be one of the prettiest bridges in London, so it has the elegance and maximum aesthetic expression part of structural art. However, the bridge started out as a cable stayed bridge but extra supports were necessary to carry the load and suspenders were added. This means the bridge did not use minimum materials so it does not satisfy the efficiency aspect of structural art. By David Billington’s definition of structural art, the Albert Bridge is not structural art.

Structural Analysis

The Albert Bridge was originally intended to be a cable stayed bridge which utilized the Ordish-Lefeuvre principle. The design for the original bridge was a suspension bridge with a “parabolic cable to help take the weight of the central span, aided by 32 inclined stays of wrought iron, inked to one of four octagonal cast iron towers.” [6] The suspension cables were made out of wire steel rope, and they took the weigh of the flat wrought-iron diagonal stays. The diagonal stays provided support for the deck of the bridge. The four towers are made out of cast-iron and stand on the four tapering piers, which are cast-iron cylinders filled with masonry and concrete. The cylindrical iron casting weight 10 tons and had to be transported down the Thames River from the Battersea foundry to the location of the Albert Bridge. The tower pairs on each side of the span are connected by a girder and arch. [6] Sir Joseph Bazalgette, the Chief Engineer of the Board of Works, made modifications on the bridge after seeing that corrosion of iron was already present in 1884. He replaces the steel cables with steel link chains and added a new timber deck. This gave the Albert Bridge more of the traditional suspension bridge appearance, and started the hybrid combination of bridge types. [1] The part which makes the Albert Bridge a suspension bridge is the “deck supported by vertical hangers suspended from catenary chains hung between pairs of towers.” The part which makes it cable-stayed is the “support of the deck from the inclined stays fanning out from the top of the tower, providing greater rigidity.” [1] Strengthening work during 1972-1973 include the addition of “two circular piers connected by a transverse steel beam beneath the middle of the bridge.” In the 2010-2011 modifications, the bridge was refurbished and repainted, and the decking was replaced once again.

Because the aspects of the bridge which make it more of a suspension bridge were added later 10 years after the original bridge opened, it can be assumed that the cable-stayed bridge was sufficient in carrying the load. For the purpose of this analysis, the Albert Bridge will be treated as a purely cable-stayed bridge because the Ordish-Lefeuvre principle is a patented early form of cable-bridge design in a modified form.

The Albert Bridge has a fan design since the cable stays fan out from one point on each of the towers. It a multiple span bridge: it originally had 3 spans before 1973, the addition of a pier in the middle of the main span made the bridge have 4 spans. The 3-span aspect of the bridge means the loads from the main spans are anchored towards the end of the abutments. In a cable-stayed bridge, the cables are in tension while the mast and deck are in compression.

The following are the current dimensions of the Albert Bridge: width of 12.5 meters, total length of 216.7 meters, main span length of 137.2 m, and a tower height of 21 m. To analyze this bridge, the first approximation is to ignore the stiffness of the deck and assume that the cable carries all the load. To simplify the analysis, assume that the cables on each side are lumped into a middle cable. The bridge has a weight limit of 2 tons, so it is assumed that the trucks which cross the bridge will have a max mass of 2 tons. The average length of a truck is 8 meters so approximately 27 trucks can simultaneously fit on one road lane on the bridge. If each truck is exactly 2 tons, then the max live load on the bridge would be 54 tons, or 17, 792 N. The live load along the whole length of the bridge is: (17,792 N)/(216.7 m)= 82.1 N/m. The tributary area for the truck will be half the width of the bridge. The live load on the bridge is calculated to be (82.1 N/m)*(6.25m)= 513.2 N

                                        Figure 2: Simplified live load on bridge

The timber deck is assumed to be English Elm, which has a density of 565 kg/m^3. To simplify the analysis, the deck will be (incorrectly) assumed to be a solid wood beam. With the assumption that the deck is solid wood which has a thickness of 0.5 meter, the dead load on the deck will be:

w = (565 kg/m^3)*(0.5 m) = 282. kg/m^2

The tributary area of the lumped cable is calculated to be:

Figure 3: Calculating tributary area of deck

The tributary area of the deck is calculated to be A=(68.6 m)*(12m)= 823. 2 m^2. Since the tributary area is 823.2 m^2, the load on the lumped cable is calculated:

W = w*A = (282.5 kg/m^2)(823.2 m^2) = (232 kg)

W= (232 kg)*(32.2 m/s^2)= 7470.4 N = 7.47 kN

The total load will then be the live load plus the dead load: 7470.4 N + 513.2 N= 7983.6 N. Since it is assumed that the lumped cable takes the weight of the deck and the live load, the following free-body diagram illustrates the forces acting on the cables:

                   Figure 4: Forces in cable

The angle in the figure above is calculated using the length of ¼ of the main span and the height of the tower. It is assumed that the height of the tower extends from the deck to the fan of the cable-stays.

Considering one cable in equilibrium the following forces are present:

The tension force in the cable is calculated to be 14, 167 N, and the compression force in the deck is calculated to be 11,704 N. A typical cable-stay diameter is 90 mm, so the area is 0.636 m^2. The stress on the cable-stay will be the force divided by the area, or 11,167 N/0.636 m^2= 17,553 Pa.

Personal Response

Going to see the Albert Bridge in person, I had high expectations due to the many praises it has received as the prettiest bridge in London. I thought it was a pretty bridge, but it did not seem like anything amazing. I think this is because the span and height of it seems small in comparison to some other bridges, where the sheer size of the bridge is what makes it so impressive. I think the colors are definitely a nice touch in comparison to other bridges, especially during the time of the day that I visited the bridge and snapped a picture in good light. I think seeing the bridge at night with the lights on would have made it seem even more appealing.

References

  1. https://historicengland.org.uk/listing/the-list/list-entry/1358138
  2. https://www.bristol.ac.uk/civilengineering/bridges/Pages/NotableBridges/Albert.html
  3. https://londonist.com/2016/10/secrets-of-albert-bridge
  4. https://alondoninheritance.com/tag/albert-bridge/
  5. http://www.interserve.com/latest-insight/2010/refurbishment-of-albert-bridge
  6. https://www.britainexpress.com/London/albert-bridge.htm

 

http://janbutcher.co.uk/?attachment_id=1525

 

Waterloo Bridge

Structural Information

Figure 1: Location of the Waterloo Bridge [4]

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

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

Historical Significance

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

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

Figure 2: First Waterloo Bridge [3]

Figure 3: Second Waterloo Bridge [4]

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

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

Cultural Significance

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

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

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

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

Structural Art

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

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

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

Figure 5: Lightness of the current Waterloo Bridge

Structural Analysis

Figure 6: Underside skeletal structure view of bridge

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

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

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

Load Path

Figure 7: Overall load path of arches

Figure 8: Load path at the meeting point of arches

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

Analysis

Figure 9

Figure 10

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

Figure 11: Calculations of forces on arch

Figure 12: Forces applies on arch

 

Figure 14: Calculations of forces on arch

Figure 15: Forces applies on arch

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

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

Personal Response

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

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

References

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

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

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

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

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

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

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

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

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

 

Westminster Bridge

Structure Information

The Westminster bridge is in central London. If that area is hard to visualize, it is the bridge that helps pedestrians get from the London Eye across the river to see Big Ben. When I rode the London Eye, his bridge caught my eye. The original Westminster bridge was designed by Charles Barry to connect the east of Westminster to the west next to the Houses of Parliament in 1750 [1]. There were only two bridges in London at the time, and the London bridge was closed. Over time the bridge was subsiding badly and expensive to maintain, so a new bridge was put into the works [1]. The new bridge, designed by Thomas Page and opened in 1862, consists of seven bold elliptical arches, with three flood arches on the Lambeth ride [2]. The bridge has two footways, two tramways at the sides, and two roadways for traffic. This bridge was funded by an Act from parliament. The Act appointed that £625,000 to be raised by a lottery by the sale of £5 tickets from which £100,000 was to be paid to the commissioners, another lottery that raised £197,500, and £380,500, was granted by Parliament [3]. The total cost of the bridge was £1,103,000.

Figure 1:Westminster Bridge from London Eye

Figure 2:Westminster Bridge

 

Historical Significance 

This bridge was the second bridge in London when it was originally built, so the designer of the present bridge Thomas Page modeled the old bridge which had 13 spans. The new bridge is simple in detail and has seven spans of which are all assumed to be symmetrical. It has a style of Gothic design, which matches with the Houses of Parliament [2]. The downstream parapet coincides on plan with the equivalent parapet of the old bridge, though with a 58 foot roadway and 13 foot footpaths at each side, the present bridge is of almost twice the width [2]. Another difference from the old bridge to the new was the materials that were used, which I will discuss in the structural analysis.

 

Cultural Significance 

Previously stated above, this bridge was built to connect the east of Westminster bridge to the west. There are a lot of tourists, such as myself who visit the London Eye and want to explore more. I used to bridge to get closer to the house of Parliament, where Big Ben is housed. Although, the House of Parliament was under construction, I could view the clock in front of Big Ben a little. From the London eye, this bridge made it easier to go visit may historical places in London with well-known landmarks around it. I thought it was funny how London scheduled the grand opening of the new bridge on Queen Victoria’s 43rd birthday, 24 May 1862 and she did not show [5]. I later learned that she was still grieving from the loss of Prince Albert, who died the previous December [5]. A huge event that happen was the terrorist attack on March 22, 2017. A man drove a grey Hyundai across the south side of Westminster Bridge and Bridge Street, injuring more than 50 people [4]. He then crashed the car into the perimeter fence of the Palace grounds and ran into New Palace Yard, where he fatally stabbed an unarmed police officer and was then shot by an armed police officer and died at the scene [4]. The UK thought the guy had ties with the Islamic military, but found no connections.

 

Structural Art

David Billington stated that structural art can be defined using three E’ principles: efficiency, economy, and elegance. The bridge is very efficient when it comes to holding its weight, and getting the traffic from the east to the west.  In comparison to the old bridge, the new bridge had less spans, which less materials were used. Using less materials would have lowered the bridge cost and made I more economical. The elegance of this structure is simple. The bridge is very thin and does not obstruct views in the river, but enhances it. The bridge reveals its most elegant secret when the sun shines at around 1pm on certain days. The beautiful trefoil cut-outs do a little reverse shadow play: the two lower ‘leaves’ keep their shape, while the top ones stretch out a little into one of the best (unintentional?) Architectural jokes the city has ever known [5]. I thought this was hilarious, because it is no way the designer knew this would happen and be made a joke of. Being able to view the load path and from the three E’s principals, I think this bridge is structural art.

Figure 4:Westminster Bridge Trefoil Cut-outs

Figure 5:Westminster Bridge Trefoil Cut-outs at 1 p.m.

Structural Analysis

The cast iron spans are symmetrical in shape and spring from the piers which face the water.  The spans are 117’ in length and are separated by the 8’ pillars that are built in grey Cornish granite. The caisson method was used to get the base of the bridge.  This helped a portion of the bridge sink o its proper place to create the flat bottomed barged.A horse-powered pile driver and a sinking caisson was used to build the piers.

 

Since the spans are symmetrical, I analyzed one span and assumed that the depth of the bridge was about 71 feet based on the given lengths of the roadway and foot path.  I assumed the height of the load was 8 feet, and the weight of cast iron is 442 lbs/ ft^3.

 

Figure 6:Load path of span

Figure 7:Calculation of weight of cast iron & vertical reaction forces

When I got a number for the load distribution, I calculated the live load at different parts of the main span since the traffic is a live load. I assumed the traffic load as a uniform load. In London, the average weight of a woman is 150 lbs, man: 180 lbs, and child:70 lb. The average of those weights was 133 lbs, in which I assume 400 pedestrians could fit on the footpath giving me a weighted total of 53,200 lbs. The average weight of a passenger car in London is 4,000 lbs and 13 tons for a bus. I assumed 8 passenger cars and 2 busses could fit on the roadway. The total weight for 10 vehicles are 84,000 lbs. The uniform load is 137.200 kips existing on top of the dead load of the cast iron. Using this information, I calculated the vertical reaction forces.

Figure 8:Calculation for vertical reaction forces

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

 

Figure 9:Calculation of the maximum force

 

Personal Response

From research, I did not understand why the original bridge did not hold up and needed so much up keeping. By visiting the bridge, of course I realize that times had changed. Meaning, when the old bridge was built it was built to withhold houses and buggies, no cars, busses and people. Also, I felt a little uneasy being where the terrorist attack took place, because pedestrians on the footpath still are not protected. I think bollards should be put in place for the safety of the pedestrians.

Figure 10:Me on the Westminster Bridge

References

[1] http://www.victorianlondon.org/thames/westminsterbridge.htm

[2] http://www.british-history.ac.uk/survey-london/vol23/pp66-68

[3]https://www.bristol.ac.uk/civilengineering/bridges/Pages/NotableBridges/Westminster.html

[4] http://www.bbc.co.uk/news/uk-39365569

[5] https://londonist.com/2016/08/se

Mercedes-Benz Stadium

Here is someone else talking about the Mercedes-Benz Stadium, AGAIN! What can I do?! It is one of the newer and more iconic structures located in my home city of Atlanta and hence, I couldn’t stop myself from researching it. Although I have yet to visit the stadium for a game, I’m in constant awe of the structure for good reasons!

Structural Information

Figure 1: Mercedes-Benz Stadium exterior view

The Mercedes-Benz Stadium is located in the heart of downtown Atlanta, Georgia; it sits adjacent to what stood before, the Georgia Dome. Construction of the projected started in April 2014 and it finished in 2017. The first game was played in this stadium as early as September 2017. This stadium was built to replace the Georgia Dome and become the new home for the Atlanta Falcons National Football League team as well as for the new Atlanta United soccer team. Its purpose is not limited to just this; it will serve many other purposes for other teams and events.

The team responsible for this iconic design is BuroHappold Engineering and architect, HOK. The team at Birdair was chosen as the specialty contractor to construct the roof pillow system and the facade while a general contractor team consisting of differing firms worked on the stadium. The main member of the structure, the retractable roof, was designed by HOK and TVSDesign and put into place by Birdair. The funding to construct this project was a mixture of both public and private funds. The total cost to build it was about $1.5 billion and the Falcons partnered up with the Georgia World Congress Center Authority (GWCCA) to build it (GWCCA owns it while the Falcons operate it).

The stadium is set to be an optimal location for sporting events with big future plans for holding events like the Super Bowl and College Football Playoff Championship game.

Historical Significance

The stadium was designed to be as unique and iconic as efficient. Not seen in other stadium, the whole of the structure has something new and futuristic to offer. Starting at the top, the retractable roof acts like a camera lens and is made of three layered ETFE,ethylene tetrafluoroethylene, roof pillows resting on eight petals. This particular roofing material was chosen for 3 main reasons: aesthetics, performance and sustainability. It is inspired by the Roman Pantheon and when in action, behaves like a falcon’s wings. This facade can open within 10 minutes giving an outdoor feel to the indoors when pleasant weather allows.

A 360 degree Halo scoreboard lines the upper interior of the stadium to ensure that each spectator has the best experience possible.

Figure 2: Retractable roof and interior view of screens

The Mercedes-Benz Stadium has set the standard for stadiums across the U.S. It is the first LEED Platinum professional sports stadium achieving its goal of sustainability. Some of the features include reusing rainwater, use of solar panels, efficient lighting and encouragement of alternative transportation. It has achieved 88 LEED points–the most any sports venue has achieved in the world. The characteristics described above make the Mercedes-Benz stadium a model for future buildings particularly sports arenas as it shows that efficiency, sustainability and technology can all be achieved for a structure.

Cultural Significance

Although recently built with the newest technologies, there has been one injury reported in which a worker was injured while trying to move a metal tower. This individual is suing the general contractor and other companies for permanent and continuing injuries. Other than this particular case, no injuries or deaths have been reported during and post-construction of the stadium.

 

Figure 3: Construction of the stadium

One of the historical event concerns is the impact on poor neighborhoods near the stadium: English Avenue and Vine City. Arthur Blank has suggested that millions of dollars will go to improve these neighborhoods but it seems the opposite. The money in the form of either investments or revenues is not directed towards these neighborhoods at all. In fact, these areas are seen as blotted out neighborhoods and little to no money is spent on local businesses to generate their economy. Nonetheless, Blank is persistent on changing the quality of life of the people living in these areas through donations. As can be seen, the stadium is loved by the spectators of sports and disliked by residents of surrounding neighborhoods due to each of their interests either being upheld or tossed to the side.

As it is a recently-constructed system, the human cost in building it is seen to have low statistical values and it is still used today for the purpose it was built.

Structural Art

The structure, in my opinion, does not demonstrate structural art no matter how beautiful, pleasing and futuristic it looks to my eye. This can be explained through the 3 E’s: efficiency, economy and elegance. As previously described, the structure is efficient in its purpose as it is sustainable and environmentally friendly (LEEDs too!). In terms of economy however, the stadium is quite costly as it ended up costing $1.5 billion to build and twice the material was used for construction compared to the Georgia Dome. Elegance could be seen as either aesthetically pleasing and environmentally-friendly but all 3 of the E’s are not satisfied.

Figure 4: Mercedes-Benz Stadium

Structural Analysis

Starting with the iconic roof, it is designed to be retractable and its functions are explained above. Specifically, eight cantilevered petals move to create the effect of a camera. Resting on these petals are ETFE cushion that are light-weight and allow smooth movement through the use of a cable net system. The eastern side of the structure has an a facade made of lightweight steel to allow openness and views of the city to be seen. Deep foundations and shallow foundations were put into place for the precast inner bowl. There are also 19 mega columns that support the roof and 8 other columns that support the mega columns. The foundational structures were made of thick high-strength concrete and longitudinal and shear reinforcements were used. Then, the precast seats were made of columns, vomitory walls, raker beams, and seats and placed in the inner bowl. The concrete bowl consisting of different sections such as top of seating, upper mezz and etc. was placed. A total of 150,00 cubic yards of concrete and 27,000 tons of structural steel was used to construct the stadium.

Figure 5: Depiction of the Mega Columns in place
Figure 6: Depiction of Seating

 

A detailed analysis of each of the sections was done through graphics and software such as SAFE software and designing of individual components was possible due to software like Enercalc. The design drawings generated from these softwares made it possible to communicate to the entire team what would be built and how it would be built. Manipulations and changes could easily be made to these models to make the structure’s design as best as possible.

Figure 6: Stadium Breakdown

A even more detailed analysis can be presented upon the stadium for which a whole powerpoint would not be enough due to the extensive detailing and design.

The loads on this structure include the dead load (weight of the stadium which increases as you go down since the lower parts have to hold the weight of the higher portions). The live loads can be considered to be the moving population of the spectators. No usually large dynamic loads are present as it is a very still and static structure. The total of these loads moves from the top to the bottom as following: the weight of the roof structure and the components inside moves to the triangular facade then which the increase in weight due to the facade will then move to the columns put into place. The columns then take the load of the weight and the people and transfer it to the ground through the closest column from the bowl structure. Although the system seems complicated from the outside due to the interconnectedness of the facades, the loads simple move from the top to the bottom through the closest structural member. Although stadiums and buildings weren’t covered for load paths, the idea works the same way.

Figure 7: External View of Load Path in One portion of stadium

Let’s look at a specific example. From figure 6, the blue foundation can be seen to upheld by many different columns. The load on this foundational slab will flow through/into the columns geometrically if the columns are spaced equally apart or portions of this force will go to the closest foundation columns. Then, these columns will transmit the loads to the ground. Of course, it should be noted that the force or load is the greatest at the bottom for which the columns handle a large load and must made be designed to handle the appropriate load.

Figure 8: Internal View of Load Path from slab to column

Note: Many simplifications were made due to the complexity of the stadium.

Personal Response

Although I have yet to visit the inside of the stadium, standing outside made me realized the innovations in Atlanta that have allowed such a futuristic building to be built in a still developing city! It put me in awe because of its size and the capability of the retractable roof.

References:

[1] https://www.burohappold.com/projects/mercedes-benz-stadium/

[2] http://mercedesbenzstadium.com/stadium-fast-facts/

[3] http://www.birdair.com/projects/mercedes-benz-stadium

[4] https://www.stadiumsofprofootball.com/stadiums/mercedes-benz-stadium/

[5] https://www.constructiondive.com/news/injured-worker-sues-gc-on-14b-falcons-stadium/422265/

[6] https://www.nytimes.com/2017/01/12/sports/football/atlanta-falcons-stadium-arthur-blank-neighborhood.html

[7] http://www.seaog.org/Presentations/MBS/MBS%20Presentation_SEAOG.pdf