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

 

The Granada Bridge

Structure Information

The Rockefeller Memorial Bridge, known by locals as The Granada Bridge, spans the Halifax River or Intracoastal Waterway. The bridge links the peninsula and mainland parts of Ormond Beach, Florida, USA. The current standing bridge was built in 1983, however, the current bridge is the fourth bridge to exist in this approximate location since 1887. The Granada Bridge is shown in Figure 1 below.

Figure 1: The Granada Bridge [1]

The purpose of the bridge is to carry highway, pedestrian, and cycling traffic over the Intercoastal Waterway. The bridge was funded and is currently maintained by the Florida Department of Transportation. The designer of the bridge is unknown due to the lack historical construction plans and records accessible to the public through the Florida Department of Transportation.

Historical Significance

The structural engineering design of the Granada Bridge is not an innovative design in a historical context. The Granada Bridge is a stringer or multi-beam bridge [2]. The beams making up each span are supported at each end by a box girder which sits atop the vertically supportive piers. There are large abutments at each end of the bridge. The structural principle of this bridge design has been used for millennia, and the most common type of highway bridges  in Florida have this same structural design. Additionally, the bridge was built using foundation and general construction technology that had been used before. The foundations for the piers were built using cofferdams installed where the piers exist in the river. The foundations, columns, and girders are cast-in-place concrete, the beams are pre-stressed concrete and the deck is cast-place concrete. The best existing example of this type of structural design is the Lake Pontchartrain Causeway over Lake Pontchartrain in Southern Louisiana, USA. The Lake Pontchartrain Causeway spans a total of 23.83 miles. It consists of four traffic lanes and has the same structural design principles as the Granada Bridge, but is 65 times longer. Figure 2 below shows an abbreviated view of the causeway.

Figure 2: Lake Pontchartrain Causeway [3]

Since the Granada Bridge is such a standard highway bridge, the actual structural design should not be considered a model for any future bridges. However, its function as a connection between the peninsula and mainland parts of Ormond Beach since 1887 has inspired the construction of multiple bridges in the greater Daytona and Ormond Beach area.

Cultural Significance

The history surrounding the Granada Bridge is fascinating. The progress and construction of the series of bridges leading to the existing bridge is reflective of the progress of industrialization and influx of population to the area. The first bridge built in the location where the existing bridge stands was the result of a competition between builders in Daytona Beach and Ormond Beach to see who could cross the Halifax River the fastest. It was a wooden bridge with a drawbridge device finished in 1887. In 1890, Henry Flagler, owner of Florida East Coast Railway bought out all shares of the Ormond Hotel, and in 1905 built a second bridge near the first that could support rail and carry passengers directly to the hotel. Figure 3 below shows the Hotel with the wooden bridge in the bottom right hand corner. Flagler later redesigned the bridge for automobiles to be able to drive to the hotel, and the first wooden bridge was demolished shortly after [4].

Figure 3: Vintage Ormond Hotel postcard with bridge in lower right-hand corner [5].

Henry Flagler was not the only notable man to leave his mark on Ormond Beach. The man known as the richest in modern history, John D. Rockefeller made his summer and retirement home at the southeast corner of the bridge. After Flagler’s redesigned railroad bridge became too old to be maintained, a new two-lane wooden bascule bridge was built in its place and named the John D. Rockefeller Memorial Bridge opening in 1952 [4]. Eventually the bridge had to be rebuilt to accommodate the widening of the connecting roads. This new bridge was constructed in 1983 and stands as the Granada Bridge today.

The first bridge built made it possible for the world’s first automobile race to take place on Ormond Beach in 1903. People loved the bridge because it allowed them to indulge in the luxury of the Ormond Hotel and the excitment of industrialization and the recreation that it made possible. Since then, the bridge has remained a north star for residents and tourists in Ormond Beach. Although there are only minor historical events surrounding the Granada Bridge, it means a lot to the residents of Ormond Beach, myself included. I was born and raised in Ormond Beach, and I know that I am home every time I reach the apex of the bridge looking towards the Atlantic Ocean. The combination of the Intracoastal Waterway and the succeeding vast ocean in front of it reminds me of watching fireworks sitting on the sloped bridge abutments on the 4th of July, or running up the steepest side during high school cross country practice.

The building of a bridge that has done so much for Ormond Beach did not come without hardships. During the construction of the existing bridge in the 1980’s, three workers fell from a scaffolded platform on to a barge below. One of the workers lost his life [6]. In addition, there have been multiple fatalities associated with normal traffic usage of the bridge. Traffic accidents are common in highly trafficked areas, and with an ever-increasing daily vehicle count using the bridge to cross the Halifax River, this is unfortunately expected. In addition to vehicular traffic, the bridge has pedestrian pathways on each side of the deck which connect four different recreational parks on each corner of the bridge.

Structural Art

By David Billington’s definition, The Granada Bridge does demonstrate some degree of structural art. The load path from the deck to the foundations is discernable. This is representative of some degree of efficiency. In addition, the bridge is owned and maintained by the Florida Department of Transportation, which indicates that the structural design was performed under certain economic constraints. Designing for a publicly funded piece of infrastructure means that the design that is sufficient at the lowest cost will be built. According to Billington, structural art only flourishes under the constraint of economy. This pillar of structural art is present in this bridge. I may be biased because the bridge is so central to my adolescence, but I think that the Granada Bridge is an elegant one. I think its elegance comes from the transition you experience when you cross it. The columns and deck are thin and intentional when compared to the vast, chaotic ocean that comes in to view as you cross over the high point of the bridge. Although you cannot do the actual experience justice, Figure 4 below shows the view of the ocean as you descend the bridge.

Figure 4: View of the Atlantic Ocean descending the Granada Bridge [6]

Even though the bridge does demonstrate some degree of structural art, I think that it generally cannot be considered structural art by the criteria provided by David Billington. I think this is mainly because of the nature of materials used and the form of the bridge deck. I think that structures made from prestressed concrete are inherently not structural art. Because the concrete is in compression before it is under service load, the true load path in final form is never actually realized. In addition, the curvature of the deck is asymmetrical relative to each land mass, meaning the apex of the bridge is closer to one end. If the bridge was symmetrical I think it would be more elegant, thus, closer to the ideal for structural art. Figure 5 below shows the asymmetry in form of the granada bridge.

Figure 5: Asymmetry of apex of Granada Bridge [6]

Structural Analysis

The Granada Bridge is a stringer/multi-beam or girder bridge. The superstructure consists of 19 spans of average length of 101 ft [2]. Each span consists of thirteen prestressed concrete I-beams. Atop of these I-beams is a cast-in-place concrete deck reinforced by steel. The ends of each beam sits atop a bearing pad which are flush with the corrugated top of a modified cast-in-place reinforced concrete box girder. The girder is the start of the substructure. The girders are supported by two cast-in-place reinforced concrete columns which are round in cross-section. The columns located closer to the center of the bridge are taller than those at the bridge ends, so they are laterally braced together at their midspan to prevent buckling. The columns are supported by cast-in-place reinforced concrete foundations located in the water only. The foundations are rectangular in cross-section. At each end of the bridge there are massive abutments. The abutments are covered in grass, but it is assumed that they are constructed using mass concrete or reinforced concrete. The construction method used to build this bridge is typical of girder bridges. The foundation for one bridge bent is built using a cofferdam. Cofferdams are watertight structures constructed using metal sheet piling or similar material which are pumped dry to permit construction below the waterline [2]. The reinforcing cage for each column is then set on the foundation and concrete is poured. The reinforcing cage for the modified box girder is then set on top of the two columns and concrete is poured. This process is a completed bent. A bearing pad is set on the girder at the location of each beam. The beams are prestressed and constructed off-site then transported to the site. The beams are set and tied to each other and to each bent that they are set on. One span consists of thirteen beams connected at each end by a bent. The bridge was built one span at a time. It is assumed that the first span would start at one end abutment and connect to the first bent. A reinforced concrete deck is then poured in sections, usually a span at a time.

The structural systems employed in this structure begin at the bridge deck. The reinforced concrete deck is statically loaded by primarily vehicular traffic. Additional load comes from the self weight of the deck. The deck transmits a compressive uniform line load on to each beam based on the tributary area of each beam. Each beam is modeled as a simply supported beam because there is no moment transmitted at supports. The beam transfers the load from the deck as well as its own self weight as point loads to each bearing pad that it sits atop of, and the bearing pad transmits that point load to the girder. The girder transmits that load  as well the load of its own self weight as two point loads, one going to each supporting column. The columns then transfers that load and the load of its own self weight to the foundations which distribute the total load to the ground. It should be noted that the abutments carry the axial force transmitted by the beams at each end of the bridge. The structural system of one bent is shown in Figure 6 below.

Figure 6: Load path on structural system

The structural system can be broken down in to structural elements with load path applied to analyze the structure. The Granada Bridge is 1923 feet in length with 19 main spans, indicating an average span length of 101 ft. The edge-to-out width is 94.5 ft. Therefore the tributary area with beams shown can be modeled as shown in Figure 7 below.

Figure 7: Model of tributary area for one span

The tributary area for Beam 1 and Beam 13 is the same are found using the calculations below

The tributary area from the remainder of the beams is the same and can be found using the calculations below.

The design load used for this bridge was AASHTO Specification HS 20 [2] which assumes an axle load of 32,000 lbs and a tire load of 16,000 lbs with a tire contact area of 200 square inches. Combined with the load of the self weight of the concrete having density assumed to be 150 pcf, the total surface load transmitted by the deck to the beams is as shown below.

Traffic Load: (32,000+16,000) lb/(200 in^2/144 in^2) = 34560 lb/ft^2

Assuming deck thickness of 1 ft,

Self-weight load: (150 pcf)*(1 ft) = 150 lb/ft^2

Total Area Load = (34560+150) lb/ft^2 = 34710 lb/ft^2

To find distributed load on Beams 1 and 13,

w=(34710 lb/ft^2)*(1/2)*(93.4 ft/13) = 124689 lb/ft

To find distributed load on remainder of Beams (2-12),

w=(34710 lb/ft^2)*(93.4 ft/13)=249378 lb/ft

Using the distributed load on Beams 1 and 13, the beam can be modeled as being simply supported as shown in Figure 9 below.

Figure 9: Beams 1 and 13 modeled as a simply supported beam

Using structural analysis and symmetry, the reactions, Ra = Rb = 629694.5 lb

Using the distributed load on Beams 2-12, the beam can be modeled as being simply supported as shown in Figure 10 below.

Figure 10: Beams 1-12 modeled as simply supported beam

Using structural analysis and symmetry, the reactions, Rc = Rd = 12593589 lb

These reastions exist as point loads on the girder as shown in Figure 11 below.

Figure 11: Girder modeled as beam

The self weight of the girder can be modeled as density of concrete time area of cross section assuming a width of 2 ft,

Self Weight = 150 pcf*(93.5 ft * 2 ft)=28050 lb/ft

Using Mastan, the reactions are found to be, C1 = 1.046E8 lb, C2 = -3.026E7 lb, and C3 = 1.046E8 lb. Assuming that the columns are not fixed to the girder, the reaction at C2 can be considered negligible, and the load will not be used in further analysis.

Using the reactions, the axial load in the columns are equal to C1, and C3. Assuming column diameter as 5 ft, the stress in the columns can therefore be defined as

stress1, stress 3 = F/A = 1.046E8 lb/2827.4 in^2=36994.7 psi

To find the load on the foundation and therefore the load transmitted to the ground, the self weight of the column can be calculated assuming an average column height of 65 ft (clearance requirement)

Self-weight = 150 pcf (pi/4)*(5 ft)^2*(65 ft) = 191440.8 lb

Therefore total load on outer foundations = (1.046E8+191440.8) lb = 1.048E8 lb.

Assuming a square cross-section of dimension 8 ft x 8 ft, the stress in the outer foundations is found using the following calculations,

stress = F/A = 1.048E8 lb/9216 in^2 = 11370.6 psi

Therefore, the strength of the soil has to be greater than or equal to 11370.6 psi.

Deformation in the columns can be found using the formula:

deflection = (PL)/(EA) = 5.7 in

5.7 inches is 0.73% of the total column height, making this deflection acceptable.

The tallest columns exist at the center of the bridge and maximum height is equal to 65 ft, therefore these columns are laterally braced for buckling. The critical buckling load can be found using the following equation,

Pcr = (pi^2*E*I)/L^2 = 7.54E9 psi

Therefore it seems that lateral bracing is not needed for stability in this analysis.

Since this bridge was constructed in the 1980’s, it is assumed that construction and design plans which follow the specifications of the Florida Department of Transportation were used to communicate the design principles used.

Personal Reaction

For years I have run, walked and driven over this bridge. To me it has always symbolized my homecoming. Looking at it from a structural engineering perspective gave me insights that I never would have gained about the history of the Granada bridge and its true significance to the growth and development of my hometown.

References

[1] https://rosebone.deviantart.com/art/Granada-Bridge-210251435

[2] http://www.city-data.com/bridges/bridges-Ormond-Beach-Florida.html#790132

[3] https://carynschulenberg.com/2015/08/lake-pontchartrain-causeway/

[4] https://ormondhistory.org/a-brief-history-of-ormond-beach-2/

[5] https://www.florida-backroads-travel.com/ormond-beach-florida.html

[6] https://www.redbubble.com/people/dbenoit/works/6631477-ormond-beach-bridge

 

Canopy Bridge at the Botanical Gardens

Canopy Bridge at the Botanical Gardens

The Canopy Bridge in the Atlanta Botanical Gardens is a structure that has always held a special place in my heart. I have been to the Botanical Gardens and walked across this bridge several times over my years at Tech, one of the most memorable times being when my girlfriend and I talked about our thoughts on the load paths of the bridge. And that conversation happened before this class started! So if you weren’t sure a nerdy Tech student was writing this blog you can now put any doubts you had to rest.

Structure Information

Canopy Bridge [1]

This bridge was constructed as part of an expansion of the Botanical Gardens that was completed in 2010 [2]. The purpose of this bridge is to provide guests with a way to see the gardens and flowers from a different perspective than they might get while on the ground. It also allows you to get from one part of the gardens to the other more quickly than walking on the ground. Jova/Daniels/Busby Architects of Atlanta were the architects that designed the bridge [2]. Halvorson and Partners (now a part of WSP) were the structural engineers that ran the analysis of the bridge design [3]. The design was inspired by the works of Spanish architect Santiago Calatrava. The bridge was part of a $55 million expansion project funded by a variety of private donors, the Kendeda fund, and the Botanical Garden itself [4].

Historical Significance

The design of the structure itself is not innovative, as the architects designing it were specifically modeling it after Santiago Calatrava’s works. Santiago’s bridge designs all featured cable stays. Instead of the bridge being supported from above by cables (such as the Golden Gate Bridge), the cables are anchored into the ground. In the figures below, you can see the comparison between the two styles.

Golden Gate Bridge, Suspension Bridge [5]

Canopy Bridge, Reverse Suspension Bridge [6]

The best existing example of Santiago’s work that influenced the design can be shown in the figure below. The style of using an anchored member with cables attached to it support the main structure is a signature style of Santiago Calatrava. That style can also be seen throughout the Canopy Bridge in the Botanical Gardens.

Reverse Suspension Structure at Quadracci Pavilion [7]

There was no special construction technique that was used for this bridge, but there was an incident regarding its construction that will be mentioned later.

Cultural Significance

This bridge was built as part of a large expansion of the Botanical Gardens in 2003 and finished in 2010 [2]. The expansion was able to take place because of a special and unique addition to the garden. In 2002, the Chihuly exhibit was presented for the first time in the gardens, and its impact was dramatic [8]. Numbers of attending people more than doubled from 200,000 to 425,000 [8]. Memberships to the garden increased from 12,000 to 19,000 [8]. Mary Pat Matheson, executive director for the gardens, said ‘The Chihuly exhibit was our coming out party. It was very deliberate. I knew what the impact would be: tremendous’ [8]. Matheson was purposely trying to make people want to visit the gardens, for more than economic reasons. She wanted people to see the garden as ‘more than just a pretty place. I want the people of Atlanta to see it as a cultural asset’ [8]. The spike in interest for the gardens made investments easier to come by when the expansion was announced in 2003.

Chihuly Exhibit [9]

Part of that expansion was making use of the previously undeveloped Storza woods, which included the Canopy Bridge. However, the building of the bridge did not come without cost. During construction of the bridge, a section collapsed killing one worker and injuring several others [3]. The metal frame of the bridge had been constructed with the shoring beneath the bridge, each column spaced out 30’ each [3]. When concrete was being poured into the top of the bridge for people to walk on, the bridge collapsed. The shoring contractor made several mistakes (or cut certain corners) which led to the collapse. The column was spaced at a distance greater than 30’ from another column, the steel beams in some towers were discovered to be W10x12 instead of W10x19, and the contractor failed to provide required lateral bracing between anchors, which were embedded at insufficient depths (anchor embedment distances on seven different towers ranged anywhere form 43” to 17”) [3]. This accident was a black mark on the expansion, but the overall public opinion of the opened section was overwhelmingly positive. Visiting numbers increased further and the gardens now featured a ‘Monet piece’ in the canopy bridge as Matheson describes it [8]. It is used today as it always has been as both a way to transport people across the gardens, or to be viewed and admired with everything else the gardens have to offer.

Structural Art

Structural art can be defined using three principles: efficiency, economy, and elegance. Efficiency describes a structure’s ability to carry the maximum amount of load with the smallest amount of material. Economy describes a structure’s cost versus utility. Ideally, a structure has minimal cost and maximum utility. Elegance is the aesthetic choices that a designer makes.

In terms of efficiency, this structure seemingly fits that role. The bridge is cantilevered at the ends and suspended by thin metal rods along the span. With its unique shape that curves around the Storza Woods, the design allows the bridge to withstand loads while keeping materials to a minimum. Solid rectangular supports could have been used as well, but it would have used much more material and not increased the capacity of the bridge. The horizontal profile of the bridge is also very small, so the bridge as a whole uses minimum materials considering its shape and carries the necessary capacities.

Speaking to its economy is a bit more difficult. The bridge costs were included in the total expansion which was $55 million [2]. The expansion was mostly privately funded by organizations and people that were interested in making the Botanical Gardens a more beautiful place. The money came in quickly so there was a high public interest in this project being undertaken [2]. The expansion brought in an increase in visitors and was beloved by all. Considering the quick funding that came in and was quickly repaid by the increase in visitors and acclaim of the gardens, I would say this structure fulfills the economy portion of structural art.

The elegance of this structure is undisputed. The bridge as a whole is very thin and and does not obstruct views in the garden, but rather becomes a part of it. The inspiration for the design came from Santiago Calatrava, but pop culture had an influence on the design as well. The bridge had a connection to the performers Fred Astaire and Ginger Rogers. The cable stay design looks like the two dancing. This attention to the appearance of the bridge checks the elegance box for me.

Figure 6, Canopy Walk Concept Art

Canopy Walk Concept Art [10]

Overall, I would definitely qualify this bridge as structural art. The design itself is not innovative but the way it is implemented shows off its beauty and strength.

Structural Analysis

The Canopy Bridge has a fairly simplistic design to it despite looking complex. The main member that carries the deck is the HSS30″ diameter by .25″ thickness tube that is cantilevered into concrete abutments at each end [3]. In the middle of the bridge is a straight span that is 70′ long and 11′ wide that is supported by two sloping HSS 16″ diameter by .625″ tubes in a V-form [3]. There are four HSS 24″ diameter by .5″ thickness pipes that have cables attached to them that support the deck of the bridge in various locations along it [3]. The framing of the bridge mainly consisted of HSS 8″x8″ members that were welded slightly above the center of the main HSS pipe [3]. These pipes were spaced at a 10′ interval from each other [3]. These pipes were diagonally braced with 6″ diameter pipes [3].

The construction of this bridge started with the concrete abutments being poured and the main HSS tube being installed [3]. The rest of the framework was constructed after that. Shoring towers were constructed to support the bridge while the concrete was being poured. As mentioned prior, the shoring towers were not constructed properly and the bridge collapsed during the first attempted construction effort [3].

The type of structural system employed for this system was a cable stay bridge [8]. The dead load of the bridge is supported by the cantilevered ends and the four HSS members with cables attached to the deck. Each HSS member had three cables connected to the deck and two cables attached behind them as backstays [3]. The pipes beneath the deck take a linear dead load but their main purpose is to provide an area for the deck to sit on. The cables in the HSS members are what keeps the entire bridge suspended.

Canopy Bridge Components [11]

Cable Tension Load Paths [12]

An analysis can be done on the bridge itself to see how much capacity is needed in the cables to support the structure. We can simplify the bridge into a straight segment to analyze a part of it via methods we have learned in class. We can take an 80′ span of the bridge and one of the sets of the cable connections to determine the strength needed in the cables. I am assuming a density of 145lb/ft^3 for the concrete and ignoring all but the main HSS member that has a density of .284lb/in^3 for the self-weight of the bridge. The calculation and analysis of the bridge is as shown below.

Simplified problem set up

The cables are assumed to be at 45 degree angles from the deck. All other assumptions that were made in the problem are listed in the calculations.

Cable tension forces and deformation

The tension in the second cable resulted in an almost zero force because of its orientation in this simplified example. In reality, the curvature of the bridge would result in non-zero tensions in each cable.

The design drawings successfully communicated the idea of the beauty of the bridge to stakeholders as many people were very eager to invest in the building of this bridge and the gardens. The technical drawings were less successful in communicating ideas between different parts of the job. The shoring consultant left out details regarding the type of steel that should be used and the shoring contractor ignored parts of the instructions from the structural engineers. Communication breakdowns between the companies ultimately led to its collapse during construction.

Personal Response

I have always admired the Canopy Bridge from my visits to the Botanical Gardens in the past, but it has taken on a whole new meaning now that my civil engineering background keeps developing. The first time I noticed that change was that first conversation I had about its function as a structure.

Researching this project and seeing the passion behind the bridge’s design process and construction has made this an even more special part of the gardens to me. I am definitely going back to the gardens in the future and dragging along any friends that will listen to me talk about its bridge.

References

1. Shell, B. (2018). Atlanta Botanical Garden Canopy Walk Images. [email].

2. https://www.myajc.com/blog/arts-culture/atlanta-botanical-grows-support-for-nourish-and-flourish-enhancements/xknBqvbdeSFd1AvTSj8HoK/

3. https://www.osha.gov/doc/engineering/2008_12_19.html

4. https://kendedafund.org/grantee/inspiring-the-public-through-beauty/

5. https://wall.alphacoders.com/by_sub_category.php?id=160347&name=Golden+Gate+Wallpapers

6. Shell, B. (2018). Atlanta Botanical Garden Canopy Walk Images. [email].

7. https://www.bluffton.edu/homepages/facstaff/sullivanm/wisconsin/milwaukee/calatrava/calatrava.html

8. https://www.accessatlanta.com/entertainment/calendar/atlanta-botanical-garden-grows-phase-opens-saturday/HGedrkVTonq00qRMImLbIN/

9. https://www.pinterest.com/pin/182958803590374050/

10. Shell, B. (2018). Atlanta Botanical Garden Canopy Walk Images. [email].

11. Shell, B. (2018). Atlanta Botanical Garden Canopy Walk Images. [email].

12. Shell, B. (2018). Atlanta Botanical Garden Canopy Walk Images. [email].

 

Spanish Arch in Galway

Structure Information

The Spanish Arch is in fact two arches in the Irish city of Galway, so the name can be a little misleading in my opinion. The Arch is on the left bank of the Corrid River, where the river meets Galway Bay. [1] It was constructed in 1594 by Wylliam Martin, who was the 34th mayor of Galway. The name of the arch was originally Ceann an Bhalla (“the head of the wall”) and it did not become known as the Spanish Arch until much later. It was called “The Head of the Wall” because it marked the start of the city walls, which were designed to protect docked ships from thefts. The city walls also included a bastion, which allowed the soldiers stationed on the walls to fire cannons from them. [4]

 

Figure 1: The Spanish Arch in Galway, Ireland [3]

Historical Significance

The Spanish Arch extends from the wall which was built in the 12th century during Norman times. Arches have been around since ancient times so the structure is not any innovative structural engineering design, nor was a new certain construction technique used. The wall itself does not have as much significance throughout history, but currently the area around Galway Bay is used for eating, drinking, and playing music. [3]

Cultural Significance

Soldiers lived in the town wall and manned cannons on the roof. [1]The fact that the structure is called the Spanish Arch in a small city on the Irish west coast showcases the historical links between Ireland and Spain. The reason for the name is believed to be due to the merchant trade of the region of Galway to Spain, and Spanish ships would often stop at the docks in Galway. In fact, Christopher Columbus is believed to have visited the city in 1477. There is a “Latin Quarter” of the city so the influence of Spanish culture is still apparent. However, there is not a proven link between the Spanish people in Galway and the building of the Arch. [4] Today the Spanish Arch is used as a part of the Galway City Museum, which is located next to the Arch.

Structural Art

I would not call this piece structural art according to David Billington’s requirements for structural art: efficiency, economy, and elegance. There is a well-known sculpture on the top of the Arch called Madonna of the Quays designed by the artist Claire Sheridan. [4] The area around the Arch is a part of the lively Latin Quarter of the city, so the symbolism behind the Arch reminds me of the public’s reaction to the Brooklyn Bridge, but on a much smaller scale.

Structural Analysis

The medieval city walls in Galway were constructed using stone since the stone arches were a method perfected throughout Roman times. The load on the arch would be a distributed load since the only applied load is the self-weight of the stone. If there is a person or a cannon on the city walls (as there was in medieval times), a point load would be applied to the free body diagram. However, for this case the only load is the self-weight.

Figure 2: Load Paths in Spanish Arch [5]

Figure 3: Free Body Diagram of loads on arch

 

Figure 4: Calculating max force in arch

In order to calculate the max forces in the arch, cut the arch at the point where it is the tallest (in the middle of the length in this case). Take the sum of the forces in the y- direction and the sum of the forces in the x-direction to obtain the max force at the pinned ends. The max force occurs at the ends of the arch.

Personal Response

I knew that the concepts behind arches have been understood for thousands of years, but it was actually pretty cool to be able to walk under an arch that has been standing around for close to 500 years. While the arch itself is not that impressive, knowing the load paths behind the arch is interesting and I think it’s fascinating that people were able to understand this in order to successfully build them. Also I was able to witness the area around the Bay being used as a social setting during a nice and sunny day in Galway.

References

  1. https://www.galwaytourism.ie/pThe-Spanish-Arch.html
  2. https://www.historyireland.com/volume-9/ireland-spain/
  3. http://snoozleshostelgalway.ie/spanish-archcladdagh/
  4. http://galwaycity.galway-ireland.ie/spanish-arch.htm
  5. https://pbs.twimg.com/profile_images/935815544053358592/zmC63ql-_400x400.jpg