Le Pont des Arts

Structure Information

The Pont des Arts is an iconic bridge spanning across the Seine River in Paris, France. Construction of the current bridge began in 1981 and finished in 1984. Figure 1 below is a photo of the bridge today.

Figure 1: Le Pont des Arts, Paris, France

In english, “Le Pont des Arts” translates to “The Bridge of the Arts.” The name of this bridge is very fitting for its function because it serves as a pedestrian bridge that links the Institut de France and the central square of the Palais du Louvre. The Institut de France is a French learned society that houses French Academies such as the Academies of Music, Humanities, and Sciences. The Palais du Louvre is a former royal palace which is now the largest art museum in the world. Figure 2 below shows the bridge name carved in to the abutment closest to the Institut de France.

Figure 2: Bridge name carved in to the stone of one abutment

The Pont des Arts was designed by Architect Louis Arretche, and the structural engineering was done by Enterprise Morillon Corvol Courbot (EMCC) [1]. The bridge was built as a replacement for the former bridge built under Napolean Bonaparte. This bridge is a structure paid for by French Public Works.

Historical Significance

As previously stated, the Pont des Arts was built as a replacement for a bridge that was built in the same place across the Seine in 1804. The current bridge is almost identical in design to the original bridge, so by modern standards, the current bridge cannot be considered an innovative structural engineering design. However, the original bridge, completed in 1804 was the first metal bridge to be constructed in Paris, 19 years after the building of Iron Bridge in England. Napolean Bonaparte asked engineers to design a bridge that resembled a garden that was suspended over the Seine [2]. The original bridge was elegant, lightweight and constructed from cast iron, placing it on the cutting edge of engineering in its day. The piers of the original bridge were constructed in masonry as were all the piers of bridges along the Seine, but the use of cast iron was a very new construction technique. The construction of the present bridge did not involve any new construction techniques.

The current Pont des Arts is a steel arch bridge. Its historical connection and consequently almost identical design to the original bridge in the same location makes it unimpressive structurally by modern standards. The best existing example of a steel arch bridge is the Syndey Harbour Bridge in Sydney, Australia. It is the largest steel arch bridge in the world. Figure 3 below shows an image of the Sydney Harbour Bridge.

Figure 3: Sydney Harbour Bridge

Cultural Significance

The current Pont des Arts bridge is internationally known and is one of the most famous bridges in Paris. It is first iconic because of its location–the link between two of Paris’ most iconic buildings. The Palais du Louvre on the bridges right end has housed French kings since its construction in the 1200’s, and is now the largest and arguably most famous art museum in the world. On the left end of the bridge, the Institut de France houses the agency that manages over 1000 foundations, museums and chateaux that are open to the public, making it a major cultural landmark.

In addition to its locale, the Pont des Arts is a cultural landmark because of its connection to history. The bridge that was originally in its place was ordered to be built at the beginning of the rule of Napolean Bonaparte. Napolean’s empire dominated the French Revolutionary wars and facilitated the development of Paris with structures such as the Arc de Triomphe and the Pont des Arts.

The original concept for a metal bridge in Paris in the beginning of the 19th century was largely rejected by famous Parisian architects of the day. These experts thought that it would lack monument because of its lightness and metal form. The aesthetic of metal was vastly different from the monumental stone bridges between which the Pont des Arts was to be built. However, when construction was completed, the Parisians “took the bridge to heart” [3]. As with most bridges of the time, the Pont des Arts was a toll bridge which cost one cent to cross. On the day the bridge was opened, 65,000 Parisians paid their penny to cross the new bridge [3]. The permanence of the original design that continues in the Pont des Arts today describes the iconic and loved nature of this bridge.

There is no record of injured workers in the construction of the original Pont des Arts built in 1804 or the new Pont des Arts built in 1984. However, the original Pont des Arts was demolished in 1980 because of structural weakening and damage from barges. There were barge collisions throughout the life of the original bridge, considered to be the human cost of the bridge.

Today the Pont des Arts is an internationally known landmark. The bridge is a favorite for artists, musicians and people in love. In 2008, a tradition began which gave the Pont des Arts the unofficial name of the “Love Lock Bridge.” Couples would write their initials on a lock, attach it to the side rails of the bridge and throw the key in to the Seine River as a symbol of eternal love. The tradition became so popular that there was an additional 45 tons of weight added to the bridge from the locks [4]. This loading caused structural weakening and eventual collapse of one railing section. In 2014 the railing sections were removed and replaced with plexiglass sheets. Figure 4 below shows a railing section with the love locks in tact.

Figure 4: Pont des Arts railing with love locks attached [4]

The Pont des Arts is still used as a pedestrian bridge and remains an iconic part of Paris.

Structural Art

The design of the current Pont des Arts was dictated by the original iron design in 1804. The structure has been described as “light” since its original construction, which has been considered a good and a bad thing depending on the critic. I think that the original design boldly rejected the heavy monument of stone that was the norm for Parisian bridges at the time. The structure was able to be made light because of the new material of iron. In this sense, form was dictated by function. I think this is a major requirment of structural art, and the Pont des Arts embodies this requirement. David Billington states that aesthetics should be the final judgement when deciding if something is structural art. I was immediately drawn to this bridge. It stood out to me while strolling along the Seine because of its elegance and lightness when compared to the countless bridges of heavy stone that span the Seine. I think that the only thing that subtracts from the status of the Pont des Arts as structural art is the fact that the modern bridge was designed by an architect and not an engineer. Similar to this, the piers of the modern bridge are made of reinforced concrete, but faced in stone to pay tribute to the design of the original bridge. Hiding the true material that takes load is a way that the structure does not demonstrate structural art.

Structural Analysis

The modern Pont des Arts is designed to replicate the original bridge that was built in 1804 and demolished in 1980. The original bridge was a cast iron arch bridge with nine iron arches spanning a total of 509 feet. The form of the bridge was modeled after the British metal arch bridges that preceded it. The supporting bridge piers were constructed of stone masonry using cofferdam systems to block the water around the pier and pump it dry with buckets. The deck was contructed using wooden planks.

The design of the modern Pont des Arts bridge is almost identical to that of the original bridge. The differences lie mostly in construction materials used. The current Pont des Arts superstructure is constructed in steel. Steel is lighter, stronger and more ductile than iron, making it the clear modern choice after the failure of the original iron bridge. The piers are constructed in reinforced concrete but faced with masonry to pay tribute to the original bridge. The deck is constructed in timber, another tribute to the original bridge design. Another departure of the modern bridge from the original bridge design is the number of arches. The current bridge has seven arches instead of nine, a design choice that was made to be consistent with the number of arches of the adjacent Pont du Neuf, and made possible because of the ability to make longer arch spans with modern construction materials and technology.

The structural system employed in this bridge is repeating three-hinged arches. There are seven arches from bank to bank and there are five repeating arch systems that span from edge of deck to edge of deck as shown in Figure 5 below.

Figure 5: Five arches which span from edge of deck to edge of deck meeting at one pier

Figure 6 below shows an elevation view of contiguous repeated arches meeting at one pier.

Figure 6: Arches meeting at one pier

The repeated arches are supported by reinforced concrete piers and abutments on either end of the bridge.

Load from pedestrian traffic and the timber deck is transmitted from the deck to the spandrels connecting the arches to the deck. The load moves through the spandrels to the arches. The arches are in compression. Since the structural system consists of repeated arches, the horizontal thrust generated by each arch at the arch connection to the pier is cancelled out by the horizontal thrust generated in the opposite direction from the contiguous arch. The vertical load at eah arch end is transmitted through the bridge pier to the ground. The only horizontal thrust that is realized is at each end of the bridge and is taken by the abutments. The load path is shown in Figure 7 below.

Figure 7: Load path of one repeated arch

Using this load path and assumptions about the dimensions of the bridge, one of the total 35 arches can be analyzed. The dead load of this bridge is calculated using the density of the timber decking which is assumed to be 41.8 pcf [6]. Assuming the deck is 1 ft thick, the area dead load is equal to 41.8 lb/ft^2.

European building codes specify that the live loading associated with pedestrian footbridges is typically 5 kN/m^2 [5] which is equal to 104.4 lb/ft^2. The deck has 7 spans totaling 155 m or 508.5 ft and a deck width of 10 m or 32.8 ft. By the principle of superposition, to get total linear loading, the dead and live area loads are added and multiplied by deck width as shown below.

(41.8+104.4) lb/ft^2*(32.8 ft)= 4795.4 lb/ft

The length of one arch span can be found by dividing total span by number of arches as shown below.

(508.5 ft)/(7 arches) = 72.6 ft/arch

Height of arch is assumed to be 24.2 ft based on the visual proportion to arch length.

From these data and assumptions, and assuming the the load will be transferred completely to the arch by the spandrels, the following model shown in Figure 8 can be used to perform the analysis of one arch.

Figure 8: Simplified model of one arch

To analyze find the reaction forces the arch will be cut at the center hinge. A model of the left side of the cut is shown below in Figure 9.

Figure 9: Left side of arch cut at center hinge

By symmetry using the global structure, reaction force By is equal to zero. Ay can be found using sum of forces in the y-direction as shown below.

Ay – (4795.4 lb/ft)*(36.3 ft) = 0

Ay=174073.0 lb

Using the sum of moments about the top hinge, reaction force Ax can be found as shown below.

Ay(36.3 ft) – Ax(24.2 ft)-((4795.4 lb/ft)(36.3 ft)(1/2)(36.3 ft))=0

Ax = 130552.6 lb

From these equations we know that 174.1 kips of force is being transmitted vertically from one end of the arch to the pier and 130.6 kips of horizontal thrust is generated, which is counteracted by the contiguous arch. Since there are 5 pin connections at each pier with two arches connected at each pin, the total vertical force exerted on the pier can be calculated using the following equation.

(174073.0 lbs)*(5 pins)*(2 arches) = 1740730 lbs

We can use this force and assumptions about the geometry of the cross section of the piers to calculate compressive stress in each pier. It is assumed that the piers are rectangular in cross section, 32.8 ft in length, and 2 feet in width. The area of the pier can be calculated using the following equation.

Area = (32.8 ft)*(2 feet) = 65.6 ft^2

Assuming the cross-section is constant, the stress in the pier is found using the following equation.

Stress in pier = (1740730 lbs/ 65.6 ft^2)*(1 ft^2/144 in^2)= 184.3 psi

This value can be compared to typical strength of reinforced concrete, equal to 4000 psi.

4000 psi >> 184.3 psi

Based on these calculations, the piers are designed with a safety factor of 21. This is very high for a bridge, and should be considered higher than actual design because of assumptions made.

Sum of forces in the x-direction can be performed to find the horizontal reaction force Bx as shown below.

Ax – Bx = 0

Bx=130552.6 lbs (in the negative x-direction)

It is assumed that Bx represents the compressive force in the arch. We can use this force and assumptions about the geometry of the arch cross-section to find compressive stress in the arches. It is assumed that the cross-section of the steel arches are rectangular and the area of the cross-section is equal to 10 in^2.

Stress in arch = 130552.6 lb/10 in^2 = 13055.3 psi

Steel has a compressive strength of about 25000 psi. Comparing the design stress to material properties of steel,

25000 psi > 13055.3 psi

This indicates that the steel superstructure is designed with a safety factor of about 1.9. This value is close to what would be used in the design of a bridge.

It is assumed that since this bridge was built as a structure of French public works, drawings or plans were made to the specifications of French bridge building codes and communicated to the the owner (French government).

Personal Reaction

I saw this bridge while strolling along the Seine River from Notre Dame Cathedral to The Eiffel Tower. As I previously stated, I was immediately drawn to this bridge because of its lightness compared to the heavily ornamented stone bridges around it. Standing on the bridge with two huge French monuments on either side of me, it was amazing to me how much history and culture could be built in to a structure as simple as a foot bridge.

 

 

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

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

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

[4] https://www.citymetric.com/horizons/paris-has-replaced-padlocks-pont-des-arts-padlock-themed-graffiti-1113

[5] http://www.cbdg.org.uk/tech2.asp

[6] https://www.forza-doors.com/performance-guides/general-guidance/timber-density-chart.aspx

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 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