Structural+Analysis+of+Ponte+Sant'Angelo

1379466959 = History = toc

Introduction
The Roman civilization was founded on the east bank of Tiber River in the 8th century A.D. Tiber River has had both commercial uses—since it was used in early times to ship grain from Val Teverina and later to ship stone and other construction materials—and political, since it was the boundary between the two warring cultures of Etruria and Latium(Dr. Taylor). These influences shaped the development of the Roman community as well as provided water resources and fish. Although being a riverside community brought a lot of benefits to the Romans, they had to over come the challenge of transporting materials across the river.



Early Bridges
In order to cross the Tiber River, the Romans built several bridges, however the construction and architecture of the bridge determined its use and strength. Built nearly 1,900 years ago, Ponte Sant’Angelo, or the Bridge of St. Angelo, is one of two ancient Roman Tiber River bridges that still stands to this day due to it’s superior construction and structure(Dr. Taylor, 2002).

According to [|Dr. Rabun Taylor], associate professor in Roman Archaeology at University of Texas, the first means of transferring across the Tiber River was by ferry. The best place to launch being at the least pacing current right down stream from the Tiber island. According to Dr. Taylor, Pons Sublicius is said to be the first bridge over the Tiber. It was build in approximately 642 B.C. and is currently destroyed. Dr. Taylor mentions that as indicated by its name, //sublicius// refers to wooden piles. Pons Sublicius was a timber structure and no metal was used in its construction. This usage of material could be because Romans needed a bridge that could be destroyed easily in the event of war. The first stone bridge was built in 179 B.C. and the stone arches to this bridge were added to it in 142 B.C. (Dr. Taylor, 2002)

Types of Bridges
According to Dr. Taylor, there are four types of bridges over the Tiber River based on their usages. A few bridges were built for private usage only, some were built to support the extra urban traffic passing through the city, some were spans to serve aqueducts and some of the bridges, like Ponte Sant’Angelo, were public and served civic purposes (Dr. Taylor, 2002).



= History of the Ponte Sant'Angelo =

According to few Italian tourist guidance websites, Ponte Sant’Angelo, originally called Pons Aelius, was built by emperor [|Aelius Hadrian] in 134 A.D. This bridge was built to connect [|Campus Martius] to Hadrian’s Mausoleum, which is now known as Castle Sant’Angelo. Figure below shows a picture of the castle and the bridge of St. Angelo which connects the two sides of the river.



From the same websites it was found that the original name of the bridge comes from the family name of the Roman emperor who built the bridge. However, according to several sources legend has it that in the 6th century A.D when Rome was suffering from plague, Archangel Michael appeared on top of the Hadrian Mausoleum, with his sword in his hands. [|Pope Gregory I] announced this as a sign to end of plague in Rome. After this event the Hadrian Mausoleum was named Castle Sant’Angelo, and Ponte Aelius became Ponte Sant’Angelo. A statue of Michael was later installed on the roof of this castle.

According to different historical websites online, Ponte San’Angelo was built as a footbridge for the pilgrims to Hadrian Mausoleum. Later on when the Ponte Neronianus was not useable, this bridge became the means of transportation for pilgrims trying to get to Vatican valley. From 1488 to 1534 this bridge was used to expose the corpses of executed people, who were killed at the square in front of this bridge, to the public. Today, bridge of Sant'Angelo is the most convenient way to get to St. Peter’s Basilica. Tourists and locals use this bridge every day to get across the Tiber River.

The Bridge of St. Angelo and Pons Fabricius are the only known bridges of ancient times to stay more or less intact. However, according to ArtViva website the Bridge of St. Angelo has undergone several changes throughout its history. The original bridge used to be accessed by ramps from the edge of the river and later on it was extended to cross the river from bank to bank. Before 1400s there used to be houses and a Roman arch at one end of the bridge, However, after the Jubilee of 1450, when the handrails of the bridge yielded and about 200 people were trampled or drowned into Tiber River, these structures were pulled down to make more room for pedestrians.

=Angels of Ponte Sant'Angelo=

In the 16th century, Pope Clement VII put a toll on the bridge and used the money to construct statues of St. Peter and St. Paul. Images of these two statues are provided below the image on the right is the statue of St. Paul and the figure on the left shows the statue of St. Peter.



In 1688, the bridge was decorated with ten sculptures of angles, five on each side of the bridge, all designed by Lorenzo Bernini. Each angle holds a symbol of Jesus’s suffering and death. The names of these angels along with a picture of each and their religious significance, according to the [|Bliefnet] website, is given below:

-“Angel with the Column with the inscription ‘ // tronus meus in columna // ’ meaning ‘my throne is upon a column’ (Sirach 24:4). The significance is that Roman prisoners were whipped while bound to a low pillar or column according to a tradition. A picture of this angle is shown below;



-Angel with the Scourge with the inscription ‘//In flagella paratus sum//’ meaning ‘I am ready for the scourge’ (Psalm 37:18). According to Mark 15:15, Pontius Pilate had Jesus scourged before having him crucified.

-Angel with the crown of Thorns with the inscription ‘ // In aerumma mea dum configitur spina // ’ meaning ‘the thorn is fastened upon me’ (Psalm 31:4). Based on Mark 15:17, Roman soldiers crowned Jesus with thorns before they crucified him.



-Angel with Veronica’s Veil with the inscription ‘ // Respice faciem Christi tu’ // meaning ‘look upon the face of your Christ’ (Psalm 84:9). According to Roman Catholic tradition, a woman named Veronica wiped Jesus’ face with a cloth while he was carrying the cross and the Jesus’ image was remained on the cloth. Below a picture of this statue is shown. However, the inscription was not available on the statue.



- Angel with the Garment and Dice with the inscription ‘//Super Vestimentum meum miserunt sortem’// meaning ‘for my clothing they cast lots’ (Psalm 22:18). According to Mark 15:24, Roman soldiers took Jesus’ well-made garments and played dice for them.



- Angel with the Cross with the inscription ‘ // Cuius principatus super humerum eius // ’ meaning ‘Dominion rests on his shoulders’ (Isaiah 9:6). This links the ‘wonder-counselor, God-Hero’ of Isaiah’s prophecies to Jesus. In the same Isaiah passage, the prophet announces that ‘a child is born to us, a son is given us.’ The cross on Jesus’ shoulders is symbolically linked to his dominion.



-Angels with the Nails with inscription ‘ // Aspicient ad me quem confixerunt’ // meaning ‘they will look upon me whom they have pierced’ (Zechariah 12:10). According to John 20:25, Jesus was nailed to the cross.



-Angel with Superscription with inscription ‘//Regnavit a lingo deus//’ meaning ‘God has reigned from the tree.’ The inscription INRI is an abbreviation of the Latin phrase “Jesus Nazarene, King of the Jews” According to the gospels, the INRI sign was affixed to Jesus’ cross.



-Angel with the Sponge with inscription ‘//Potaverunt me aceto’// meaning ‘they gave me vinegar to drink’ (Psalm 69:21) The gospels of Matthew and Mark report that just before Jesus died, one of the soldiers who crucified him placed a sponge dipped in "sour wine" on a stick and held the stick to Jesus' lips.



-Angel with Spear with inscription ‘//Vulnerasti cor meum//’ meaning ‘You have ravished my heart’ (Song of Solomon 4:9). According to John's gospel, after Jesus died, one of the soldiers pierced his side with a spear to confirm that he was dead.  According to the Bliefnet website, Ponte Sant’Angelo with all the angels that decorate it can reflect the shift from secular to sacred since it is used to cross the river to get from busy Rome to sacred churches of Vatican.

Ponte Sant’Angelo was constructed when Pons Neronianus was still in use for major pedestrian transportation across the river, therefore as Dr. Taylor mentions in his paper ,“Tiber River Bridgesand the Developmentof the City of Rome,” it seems like this bridge did not respond to any civic needs when it was constructed.The fact that Pons Neronianus was the more direct way to get to Vatican valley was another reason for the pedestrian to rather using this bridge over Ponte Sant'Angelo. However, as it will be further explained, this situation was changed after Pons Neronianus was ruined. = Structural Characteristics =

Material
The primary material of this bridge, like most of the other bridges built in ancient times, is stone. Just like most of the structures that were built around the same era, Ponte San’Angelo is built with a mixture of tufa, on the inside, and travertine, on the outside.

Travertine, also called caltictic tufa or calc-tufa, is “a dense finely crystalline, massive or concretionary limestone, of white, tan or cream, often having a fibrous or concentric structure and splintery fracture formed by rapid chemical precipitation of calcium carbonate from solution in surface and groundwater” (Pentecost). According to Pentecost, Pedley argued that this type of stone is different from tufa in the sense that it is less spongy and more compact; additionally, it is well lithified. (Pedley, 1990) Unlike tufa, which is not very durable and generally needs to be covered with another type of material in order to be preserved, travertine is a durable limestone. The reason why tufa is durable is that this type of stone has very high water intake and direct exposure to rain and humidity can cause to decay rapidly (Jakson, Marra,Hay,Cawood,Winkler). As discussed by the same authors, even if a structure was made out of tufa, some critical areas such as keystone of the arch or capitals of the columns would’ve been out of travertine. Newly formed travertine has a porous surface that is the result of gases escaping as travertine is formed.

Different colors of travertine are mined and have different properties. Light travertine has a bulk density of 2,450 kg/m^3, compressive strength of 115 N/mm^2 and water absorption of 2%. Both red and gold travertine have larger bulk densities but their compressive strengths are only within 5-10 N/mm^2 larger. These compressive strengths are much bigger than the compressive strength of the concrete we use today. Just like any other stone, travertine is very weak in tensile strength. The tensile strength of travertine is almost 32 times smaller than the compressive strength of this stone (Pentecost).

In the case of Ponte Sant’Angelo, by looking at the bridge it could be said that the arch is entirely made of travertine. The primary reason for not using travertine entirely is the fact that travertine is more expensive and heavier than tufa. On the figure below the color difference between the two materials can show how the inside of the arch is made out of tufa, the grey blocks, and the outside is made out of travertine, the light cream color. Therefore, as Ponte San’Angelo is made out of travertine and tufa, that means it has very good capacity in compression but it is not very strong in tension. <range type="comment" id="452479388_8">This explains why the bridge openings had to be in the shape of arche</range id="452479388_8">s.

= Roman Arch Bridge Construction =

** Pre-Construction **
Before starting the construction of a structure the constructors had to consider some important factors. They needed to know the dimensions and geometry of each part and they needed to have some knowledge about how to cut stone accurately. Along with these physical considerations, they had to come up with methods of construction, plan the schedule and organize the labor (Janossy, 2011).

Purpose
In a structure with openings, the member on top of the opening is supported by two columns at its two ends. In a stone structure, the member on top of the opening is generally a heavy piece of stone. Due to gravity loads, the bottom face of the member will be in tension and—as mentioned in the material section travertine—is very weak in tension. Therefore the member would tend to break if the span of the opening is too big. Today, concrete, which is very much like stone, is reinforced with steel. Steel, unlike concrete, can take tension but buckles in compression. Therefore, by placing steel at the places where tension forces are expected, the concrete is prevented from being cracked. However, <range type="comment" id="452479388_9">Romans did not have the knowledge or the technology to achieve the type of steel used today; therefore they came up with arches as a way to have larger openings</range id="452479388_9">. Arch bridges are among the oldest forms of bridges.



** Construction of Foundation **
According to the Rochester Bridge Trust website for construction of each pier, Romans would make cofferdams to redirect the water from where the piers were about to be constructed. Two rings of piles with clay in between as means of making it watertight were driven into the riverbed and the water and silt in side ring would’ve been removed. Then they were able to excavate the ground and build the foundation. Romans normally would dig until they got to the bedrock and in cases where this was not possible they would drive piles of wood or rock deep into the riverbed. As noted in Mariamilani website, even if the wooden piles were used as foundation since there is no oxygen available and there is wet mud where the wood is driven to, the bacteria that would cause the wood to decay would not grow. Therefore it can be unexpectedly concluded that wooden piles could make durable foundations.

**Construction of Pillars**
According to the Mariamilani website once the foundation was built, the bottom of the pillar was constructed within watertight barrels. In order to reduce the force of the river on the pillars, the pillars were made in lozenge shapes. This way the pointy front of the pillar would part water and prevent the foundation to be washed away by the water stream. As it is seen in Figure 27, bridge of St. Angelo has these pointy shapes at the bottom of its pillars.



** Construction of Stone Arch **
Arches are constructed of separate stones, all cut in trapezoid shapes. During the construction of an arch, there are pieces of timber, called falsework, that work as supports for the stones to be placed on them (Janossy). Figure 28 shows what the <range type="comment" id="452479388_10">falsework looked like and how it was used.</range id="452479388_10">



The arch then is erected on the skewback or abutment (Holmstorm). The stone at the very top of the arch is called the keystone and is the last stone that is inserted to the arch. Before the keystone is placed, the two sides of the arch are completely unstable, which is why arch construction is challenging. When the trapezoid-shaped keystone is put in place, it will try to slide down and this causes the sides of the keystone to push on the two sides of the arch and put them in compression (Janossy). The compressive force in each stone is transferred downward and outward until it is transferred to the foundation. It should be noted that this only works if the area on top of the sides of the arch are also filled with stones so the outward pressure is resisted. According to Heyman, the fill has to be done in symmetrical order so that the structure remains in equilibrium. As soon as the keystone is placed the falsework can be transferred to the next arch. In Figure 29, Keystone, the middle stone in grey, is shown as well as the two sides of the arch and the abutments on the bottom of the arch.



Bridge with Multiple Arches
With multiple arches, the outward forces of one arch will counter act the outward forces of the arch next to it therefore the structure stays stable.

It should be noted that in the event of multiple arches, there had to be two or three falseworks used at the time since the middle arches would have been unstable until the arches next to them were constructed and were able to counteract the outward forces (Janossy).

On the sides of an arch bridge where one side of the arch is meeting the bank of the river, the outward force needs to be transferred to a wall or big column. In case of Ponte San’Angelo there are two 12m walls that the bridge is attached to on each side so it could be assumed that the forces of the last arch are transferred to these walls.

Structural Integrity Factors in an Arch
Certain structural characteristics are required for the structural integrity of an arch: the length of the span needs to stay constant, elevation of the ends has to stay unchanged and the inclination of the skewback must be fixed (Beall). As consulting architect, Christine Beall discusses in the paper “Designing the Segmental Arch” a change in any of the above-mentioned requirements due to settlement, sliding or rotation of abutments can cause in failure of the bridge.

** Economical Aspects **
In terms of economical concerns there are many factors involved with the stone arch bridges that suggest that these arches would have been very expensive to construct. This type of bridge requires trained labor in different areas. For example, since there was no mortar used to put the stones together, all the stone had to be cut in order that they will fit into each other, like key and keyhole, to prevent them from moving. Also, cutting the stone for the arch part of the bridge, specially the keystone was very critical and the constructors had to make sure that the stones fit perfectly together. Constructing the falsework is very labor intensive. There needed to be trained labor to make sure that the two sides of the arch will actually meet at the same place.

Another potentially expensive factor could be material and transportation of them. As it will be discussed later in the structural analysis section, the capacity of the stone bridges are a lot higher than the live load that will ever been applied to it. Therefore, in the stone arch bridges a lot more material has been used only because the bridge had to support its own weight rather than supporting the traffic on top. However, with the technology that Romans had back in ancient times, this type of construction was the best they could do.

In terms of transportation of the material it was very important to use local material. Both tufa and travertine could be transported from mines inside Rome, or worst case from Tivoli close to Rome, therefore, the cost of transportation seems to be reasonable. However, it should be noted that since these stones were heavy and a great number of them are used in the construction of the Ponte San’Angelo, the transportation would still play a great role in the cost.

** <range type="comment" id="452479388_11">Construction of Ponte San’Angelo</range id="452479388_11"> **
Even though there are no documents available specifically about the construction of Ponte San’Angelo, we can assume it follows the general method of construction of stone arch bridge is as discussed in the previous sections. Because of the characteristics of stone and its great capacity for compression, this bridge is built so that extreme compression loads are applied to the block masonry units. Since Ponte San’Angelo was built in the 2nd century B.C. it is assumed that no mortar was used in its construction. With further site inspections no sings of using metals clips, like the ones used in Coliseum was found. However, since it has been standing up for such a long time it can be assumed that the stones were fixed into each other by having puzzle-like cuts.

** Construction of Arch Bridges Today **
Arch bridges today are generally constructed of concrete and reinforcing steel. Today most of these bridges are prestressed and <range type="comment" id="452479388_12">therefore are precast.</range id="452479388_12"> In this method, the reinforcing steel is tensioned first and then concrete is poured. Once concrete gains strength the steel tendons are released, causing the concrete to be in compression. Having concrete in compression is beneficial because when tensile force is applied to the prestressed member, the force would have to first counteract the compression that already exists in the concrete.

Having a precast member would reduce the time of construction on the actual river. Prestressed concrete members allow having shallower and lighter members with the required strength. This therefore, results in less material used and lower costs. Also, prestressed concrete elements allow having longer spans with no supports, along with allowing to have different shapes of members rather than being limited to arches.

=** Structural Analysis **=

** Structural Analysis Methods **
Methods of analysis of arches have changed over time. Unreinforced masonry arches have been very popular before the elasticity theory was developed(Frunzio, and Gesualdo). At the time that most of the ancient bridges, including bridge of St. Angelo, were built methods of analysis were mostly based on experience and rule of thumbs. Romans developed different height to length to width proportions for designing arch bridges.

In general, as Dr. Thomas Boothby mentions in his paper, “Analysis of masonry arches and vaults”, even though arches are one of the oldest structural elements, the analysis of them requires a high level of sophistication. However, rigid block theory can be used for understanding the behavior of stone arches (Boothby, 2001).Finding reliable methods of analyzing the arch bridges is important in the sense that it helps with maintaining them in good condition and estimating their safety factor when its needed. (Frunzio, and Gesualdo). Today, computer programs can do most of the hand-based analysis. Some of the methods that can be used to perform an analysis on stone arch bridges are limit analysis and F.E.M. Among the Limit analysis methods there are different methods such as Plastic limit analysis, thrust line analysis and discrete limit analysis. Here only the plastic limit analysis have been explained.

** Plastic Limit Analysis **
In a plastic limit analysis the ultimate loaded needed for failure of a member, by using enough hinges, is found. According to M. Gilbert, a professor at the Department of Civil Engineering at University of Sheffield, Heyman strongly believed that plastic analysis has to be used in analyzing the arch bridges. Heyman has argued that applying elastic methods to arch bridges is difficult since there is no calculable equilibrium state for masonry (Heyman 1998). Plastic limit analysis requires certain conditions to apply (Gilbert): I. Equilibrium condition: There must be equilibrium between internal and external forces. II. Mechanism condition: “Sufficient releases must be made to transform the structure into a mechanism.” III. Yield condition: “The stresses in the material must be everywhere less than or equal to the material strength.” In order to simplify the plastic analysis, Heyman made the following assumptions: I. Masonry in the arch has no tensile strength. II. Masonry in the arch is incompressible. III. Sliding between masonry units cannot occur.

** 3D F.E.M. Analysis **
Similar to plastic analysis, F.E.M. is a non-linear method of evaluating failure loads. In this method, the assumption is that the structure consists of finite elements and each element, or mesh, is analyzed separately. More meshes results in more accuracy and a better understanding of behavior of the structure. Because of the complexity of this method it is best to use computer programs to perform this type of calculation. As Frunzio and Monaco mention in their paper, “3D F.E.M Analysis of a Roman Arch Bridge,” the numerical analysis of this method can result in a 3D map of the stress and strain distribution.

The semi-circular, unreinforced Roman arch Bridge of St. Angelo has a total length of 90 meters. This bridge consists of 5 arches with radii of 9 meters. The longest span of the bridge is 18 meters. The purpose of the St. Angelo Bridge has changed with the growth of population and tourists; a lot more people cross this bridge than it was originally designed for. However, since this bridge is a stone bridge, the dead loads are much bigger than any live load that will ever be applied to it. Therefore, it could be said that in practice the bridge would never fail under the live loads applied to it. As Monaco, Frunzio, and Gesualdo argue in their paper, loss of equilibrium is the major reason for failure of stone arch bridges and material failure is generally absent. In most of the case studies where the masonry structure has collapsed, the masonry blocks have been in perfect condition (Frunzio, Gesualdo, and Monaco). In general, in the case of stone arch bridges the material used to construct the bridge is so heavy that if the bridge is stable immediately following construction, it will stay stable under any applied live load. Therefore, it could be concluded that if this bridge ever wanted to collapse it has to be because of some massive external force such as a seismic event, settlement of the foundation, or hydraulic force such as a flood. Dr. Thomas Boothby mentions in his paper that Ng, Fairfield and Sibbald performed ultimate strength analyses on arch bridges. They varied some of the parameters such as compressive and tensile strength of the masonry, masonry modulus of elasticity and load dispersal angle through the fill. From the result of these experiments, they learned that the failure load is sensitive to compressive and tensile strength of the masonry and is not dependent on the elastic modulus of the block. (Dr. Boothby, 2001) According to Dr. Boothby, Loo and Yang also performed structural analyses on arch bridges. Based on their results, support movements could be quite critical in the failure of arch bridges. From this it could be concluded that the foundation and the type of soil on which the arch bridge is built are both very important factors in the design of a structurally sound stone arch bridge.

** Observations **
<range type="comment" id="452479388_14">As shown in the picture of the Bridge of St. Angelo below, the two sides which are not in the water are attached to long, sturdy walls. The length of the walls is approximately 12 meters. These walls could feasibly provide strong means of support for the thrust from the arches</range id="452479388_14">.



<range type="comment" id="452479388_15">After inspecting the arches from both sides and looking inside the arches, no cracks have been found, This could be a sign that even after multiple centuries, this bridge is still structurally sound. Furthermore, there are no signs of travertine being washed off.</range id="452479388_15"> Looking inside of the arches as shown in the figure 31 below, it demonstrates that the tufa blocks seem to be washed off even though they are not exposed to rain at all. This change in tufa could be as a result of humidity or it could have happened during the floods that have happened along the Tiber River. Despite this change in the tufa surface, the tufa blocks seem to be in a good condition. In addition to the Tufa inside the arch, the material that the piers are made out of seems to be tufa. As circled int the same figure, these blocks also seem to be washed off just a little.



=** Acknowledgement **=

Studying abroad in Rome has benefited me significantly in understanding the Italian culture and has added great value to my undergraduate experience. Also importantly, this experience allowed me to perform research on Ponte Sant’Angelo. Sant’Angelo bridge is an ancient bridge so information on this subject was not always readily available online, therefore seeing the bridge in person helped a lot with my research. My experience in Italy is one, which I will always look back at and I want to thank everyone who has helped make this happen. However I would like to express my special thanks to my instructor professor Muench as well as my T.A. Ashley Thompson for giving me the opportunity to work on the structural analysis of Ponte Sant’Angelo and guiding me through this project by giving me technical help as well as new ideas.

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Marra, F., M. D. Jackson, R. L. Hay, C. Cawood, and E. M. Winkler. //The Judicious Selection and Preservation of Tuff and Travertine Building Stone in Ancient Rome//. Tech. N.p., 2005. Web. 17 Sept. 2013. // Page 35 History of Visual Technology: Stone Construction and the Arch //. By Jim Janossy, Sr. Perf. Jim Janossy. //Youtube//. N.p., 2 Sept. 2011. Web. 17 Sept. 2013. <http://www.youtube.com/watch?v=CdNYTjXJPKE>. Pentecost, Allan. //Travertine//. 1. London: Springer, 2005. 386. eBook.

// Ponte Sant'Angelo/Architectural and Historical Heritage. // (2013): n. page. Web. <http://www.060608.it/en/cultura-e-svago/beni-culturali/beni-architettonici-e-storici/ponte-sant-angelo.html>.

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