Table of Contents
Table of Contents
– bhess19 Sep 16, 2013
Background
Saint Peter’s Basilica in the Vatican City is the largest church in the world, as it can hold up to 60,000 people and it is 22,000 square meters. Saint Peter is considered to be the first pope, and after he died as a martyr in 64 AD, it was believed that he was buried where Saint Peter’s Basilica stands today (E. Howard and M. Howard). The location (shown in Figure 1) of St. Peter’s Basilica is therefore highly symbolic.
Figure 1. Location of St. Peter’s Basilica.
Before the current Saint Peter’s Basilica was built, there was another Basilica that stood in its place for hundreds of years. This first Basilica is often referred to as old Saint Peter’s Basilica. Emperor Constantine, the first Christian Emperor in Rome, built the old Basilica over the small shrine believed to mark the burial place of Saint Peter. The construction of the first Basilica began between 319 and 322 AD and ended in 349 AD (E. Howard and M. Howard). This first basilica began to fall into ruin around the middle of the fifteenth century. The walls were leaning, and collapse was inevitable (Hauser 65). Additionally, it was becoming too small as it was filling up with monuments. Due to these issues, discussion of repairing, and possibly replacing the old Basilica began to take place. Pope Nicolas V began developing plans to replace the areas of the Basilica that were in the worst condition. Eventually, plans were made by Pope Julius and architect Donato Bramante to completely rebuild the Basilica (Bosman 60).
Over a century after the construction of the new Basilica began in 1506, the Basilica was finally completed and reconsecrated in 1626 by Pope Urban VIII (“A View on Cities”). Throughout the time period during which the Basilica was built, there were phases of efficient construction and phases of construction that were very slow and unproductive. This was a result of a lack in the necessary funding, poor leadership, or a combination of the two. From 1556 until 1561, construction stopped all together due to a lack of funds (Scotti 200). Also, the decisions made by each pope and head architect about the design of the Basilica and how to carry on with construction had a large impact on the level of efficiency at which the Basilica was being built. Although designing and building the basilica was a long process that took many years and presented many challenges, the resulting Basilica was magnificent in size and beauty. It has a 211.5 meter long nave and it has one of the world’s largest domes (E. Howard and M. Howard). The use of materials and engineering techniques resulted in a Basilica that still stands today (as shown in Figure 2).
Figure 2. Saint Peter’s Basilica today.The church has many
visitors that come to marvel at the enormous structure.
Design
Overview
Throughout time, the design of the new Basilica changed as new Popes and architects took control over the construction of the Basilica. While the new Basilica was constructed, only the parts of the old Basilica that interfered with the construction of the new Basilica were torn down (Bosman 66). This was due to the fact that it was undecided which parts of the old basilica were to be demolished and which were to be incorporated into the design of the new structure. When head architect Donato Bramante first began construction in 1506, he used the unusual strategy of building from the inside out. This allowed him to experiment with the shape of the surrounding Basilica. The design of the dome changed multiple times, along with the floor layout, which changed back and forth from a Greek cross layout to a Latin cross layout (Scotti 79). The Architect who is responsible for finishing the Basilica, Carl Maderno, made the final decision to change the design of the church from a Greek cross to a Latin cross. A Latin cross has one arm that is longer than the other three, rather than a Greek cross that has four arms of equal length. As a result, this elongated the nave and brought forward the façade. This created more space, but resulted in only the dome of the church to be visible above the roof from the square (Hauser 65). Figure 3 below shows a map of the floor plan of Saint Peter’s Basilica as it is today.
Figure 3. Floor plan of Saint Peter’s Basilica (“Al Pellegrino Cattolico”)
Most 16th century builders marked out a working plan on-site and then explained it in detail to his masons and stonecutters. There was often a scale model in wood or clay for them to follow, as well. For moldings, capitals, and other intricate work, full-size patterns were drawn to guide the artisans. This is how Bramante communicated his plans for the Basilica design to other workers. However, when
Raffaello Sanzio da Urbino, more commonly known as Raphael, was appointed head architect in 1514 to succeed Bramante, he added another dimension. He drew renderings that gave 3 views-ground plan, elevation, and section (rather than the typical linear perspective). This provided closer directions and freed the architect from being on site all the time (Scotti 135).
Piers
A pier is a solid support that sustains vertical pressure. The piers of the new Basilica were going to be so large that the foundation trench for each pier had to be 25 feet in depth. In order to dig out these trenches, workers had to lower baskets into the pit by a series of pulleys, fill them with dirt, raise them up to empty them, and then repeat the process (Scotti 7). The height of each of these large piers is 45 meters (Howard and Howard). The construction of the Basilica started off very fast paced, with 2,500 men at work in 1507. The intense surge in construction continued through 1510, and during these first four years of construction, Bramante raised the 90 foot piers and joined the piers with coffered barrel vaults that soar 150 feet (Scotti 78). Figures 4 and 5 show the piers that support the dome.
Figure 4. One of the piers inside of the Basilica.
Visible in the upper left hand and right
hand sides of the picture are the coffered
barrel vaults that join the piers.
Figure 5. Another picture shows two of the piers thatsupport the dome.
Each of the four piers were crowned with Corinthian capitals that were six feet in height. All the double pilasters and columns throughout St. Peter’s repeat the same colossal Corinthian order. By the time Bramante died, the four great concrete piers were complete up to the cornice, including the arched connecting structure, covered with appropriate masonry (Steiger, “St. Peter’s Cathedral” 62).
Space was an active element in Bramante’s architecture, and because of this he wanted to keep the central circle beneath the dome (the core) open. This would allow for the arms of the Basilica to extend from it like roads from a hub. The four discrete piers would have to absorb the full weight of the enormous dome. After Bramante died, there was great concern that the piers he had designed wouldn’t be strong enough to support the dome. Bramante’s concept was untried. No one in history had ever vaulted such a broad expanse at such a large height and balanced it on such dubious supports (Scotti 124).
Before Bramante died, Michelangelo di Lodovico Buonarroti Simoni observed one day that the workmen were not properly mixing the material for the piers. Typically, one portion of cement is mixed with three or four portions of sand; however, the workers were mixing ten or twelve portions of sand for each one portion of cement. Along with this, only the walls were being built with cement, while the inside was being filled with rubble from the old Basilica and other debri (Steiger, “St. Peter’s Basilica” 62). When Michelangelo reported his observations to Bramante, Bramante refused to listen. Not long after Bramante died, cracks began to appear in the piers. Antonio da Sangallo, the new head architect, altered and reinforced the piers many times in order to be able to support the enormous load of the dome (Sperandio, Zander, and Zappa 32). The cracks were once again reinforced later by Michelangelo, who also redesigned the outer design of the piers (Steiger, “St. Peter’s Cathedral” 63). To strengthen the piers, Michelangelo sank well-holes under their foundations, which he filled with concrete. He thickened both the piers and the exterior walls, shortening the distance between them. This reduced the breadth of the crossing from 69 to about 58.5 feet. Michelangelo also checked the strength of the Basilica foundations and devised a series of ramps so that mules could haul loads of material up to the various stages of scaffolding. Although subsequently altered and strengthened, Bramante’s piers have remained as the governing supports for the great dome (Steiger, “St. Peter’s Basilica” 3). Figure 6 demonstrates the importance of having stable piers in order to support the other parts of the dome.
Figure 6. Parts of the dome (Scotti 52).
Basilica Floor
Antonio da Sangallo was head architect between 1540 and 1546. He spent 162,000 ducats per year building the Basilica and a large portion of this money was spent on raising the floor of the Basilica by 12.5 feet. This enormous structural change altered the interior perspective that Bramante had designed. Da Sangallo’s reasoning behind raising the floor of the Basilica is unknown, but it may have been in response to Bramante’s crumbling foundations. The ground beneath the Basilica was marshy, and with the Basilica being so enormous in size, there was a danger of the Basilica sinking. In order to support the raised floor that he had designed, da Sangallo built a series of parallel walls that were almost three feet thick and some seventeen feet apart, connected by barrel vaults. Due to the raised floor, the niches that Bramante had cut into the piers appeared too close to the floor. As a result, Antonio filled them in a strengthened the piers, squaring them off and chamfering, or fluting, the side under the dome (Scotti 188).
Dome
Giacomo della Porta was named the head architect of St. Peters in 1574. While many designed and redesigned the slope, contour, rise, and angle of elevation of the dome over time, Giacomo della Porta was the architect who created the final design of the dome. Today, the dome stands 120 meters, as measured from the ground of the Basilica to the roof of the lantern, and the inner diameter of the dome is 42 meters. The dome only took 22 months to build and was completed in 1590 (Howard and Howard).
The dome was originally designed by Bramante to be a shallow hemisphere that was a horizontal, saucer-shaped dome with a single shell of cemented masonry. This design was modeled off of the Pantheon’s dome (shown in Figure 7). Originally, Bramante had planned to make the dome of the Basilica using concrete that the ancient Romans used to build the Pantheon. He was planning on trying to replicate their use of concrete made lighter by mixing pumice stone that comes from volcanoes (Scotti 53).
Years after Bramante’s death, Antonio da Sangallo took over the position as head architect in 1518 and redesigned the dome to have a structure that was similar to a tiered wedding cake. The design changed once again when in 1546, Michelangelo was appointed as the head architect and designed a rounded dome, which was based off of Filippo Brunelleschi’s Dome of the Florence Cathedral (shown in Figure 8). Brunelleschi’s Dome had taken 16 years to complete and it was the only dome that was comparable in size to the Saint Peter’s dome (Scotti 54). Michelangelo’s design consisted of two shells, a ribbed construction, and windows in the drum and cupola. The double shells allowed the dome to be more visible and offered protection against the weather. The final design for the dome made by della Porta was the same as Michelangelo’s design; however, the outer shell diverged radically, changing the shape of the shell from a sphere to an ellipse (shown in Figure 9). He believed that by designing the shell to be higher and more pointed, that he would disperse the weight and lessen the lateral thrust (Steiger 62). Michelangelo had intended for the pilasters of the drum and the ribs of the cupola to act as buttressing forces, but by increasing the angle of elevation so radically, della Porta reduced those elements to little more than ornamentation. His heightened cupola is an almost perfect catenary curve. All its parts should support one another by their own weight, allowing it to hang freely between its two points of support in perfect equilibrium (Scotti 55).
Figure 7. The shallow, saucer-shaped dome of thePantheon (“Famous Wonders”)
Figure 8. Burnelleschi’s rounded dome.
Figure 9. Saint Peter’s Basilica’s elliptical dome.
The shells of the dome were made almost entirely of heavy concrete masonry laid in a herringbone pattern, which was a common technique used by architects of ancient Rome. A herringbone pattern was formed by fitting the bricks together in an inverted V design. This applied pressure equally from both sides, preventing hoop tension. The two shells of the dome start as one and diverge after approximately 28 feet. Starting where the two shells diverge, 16 ribs divide the cupola into sections, creating a frame or skeleton. Additionally, three iron hoops were fitted on the dome to support the weight and further counteract the outward thrust. The cupola was faced with thin slabs of travertine that were coated with a protective lead covering. (Scotti 197).
During this period in time, architects and engineers had little understanding of physics principles required to create a stable structure. The science behind statics and equilibrium were not understood; however, architects did know that the thrust exerted by an arch had to be either balanced by another arch or absorbed. They used this knowledge building domes because a dome is essentially a series of arches. However, any calculations made were often faulty (Srubar III 12).
Barrel Vaults
Barrel vaults are tunnels essentially formed by a series of adjoining arches. Barrel vaults press so heavily against their walls and buttresses that those walls and buttresses had to be very heavy and thick to support them. Continuous abutment must be applied to absorb the thrust carried down along the haunches to the walls supporting it (“Parts of an Arch”). Due to the fact that rigid concrete vaults do not exert a lateral thrust, the Romans could span vast expanses of height and width (Srubar III 15). Figure 10 is a diagram of a simple barrel vault, and Figure 11 is the barrel vault inside of St. Peter’s Basilica that leads from the entrance of the Basilica to the dome.
Figure 10. General form of barrel vault (“Heater09’s Blog”).
Figure 11. Coffered barrel vault in St. Peter’sBasilica. It soars 150 feet.
Materials
Travertine
A main material used in the construction of Saint Peter’s Basilica was travertine, a naturally occurring lime-based material. It is a sedimentary rock that is formed by the precipitation of carbonate materials from solution in ground and surface waters. Travertine is a very durable material, and high quality travertine possesses a great mechanical strength. It has the appearance of a fibrous or concretic material, and is tan, white, or cream-colored. It was the main material used in the facade of the new Basilica, as shown in the picture below. The Basilica was faced all around with polished travertine that came from quarries nearby Tivoli (Hauser 66). Figure 12 shows a portion of the facade, and it is visible that cream-tan colored travertine that was used.
Figure 12. Basilica Facade.
So much travertine was needed that mounds of it were carted from quarries nearby Tivoli. This distance from the building site to the quarries was as much as twenty miles, which required a complete transportation system to move the materials. The stone was first moved by barge from Tivoli down the Anio tributary that flows into the Tiber River. After traveling a distance by water, mule trains and oxcarts carried the stone the remainder of the distance to the building site (Hauser 66).
When Pope Julius II wanted to limit the spending on building the new Basilica in interest of economy, he ordered Bramante to minimize the use of costly material for construction. In particular, this meant travertine, which was costly to both quarry and transport. As a result, cheaper materials were used as much as possible to build the walls. These materials included bricks and breccia, a form of crushed tufa that was cheap and plentiful. On one of Bramante’s previous projects, he had used a fake travertine finish to convey the illusion of real travertine, and he planned to use this technique for the Basilica walls as well. He was casting the vaults and the shafts of the giant columns and using travertine for only the bases, capitals, and cornices (Scotti 83).
MarbleThe interior of the Basilica is decorated with many milk-white marble decorations and sculptures. One of the most famous marble sculptures within the Basilica is Michelangelo’s Pieta, a sculpture of the Virgin Mary holding Jesus after he was crucified, as shown in Figure 13.
Figure 13. Marble sculpture by Michelangelo that dates 1499.
On the inside of the Basilica there are many marble columns of varying types of marble. Twelve ionic marble columns in pairs, two of “pavonazzetto,” two of “africano,” and eight of “cipollino,” flank the three main entrances of the façade. They are each 12 meters high. The side isles of the Basilica are decorated with 44 of these marble columns (Sperandio, Zander, and Zappa 32).
SpoliaThe reuse and recycling of materials from other structures is an integral part of the construction of many structures in Rome. A prime example of this is when the colosseum became an informal quarry during the Middle Ages. For the construction of the St. Peter’s Basilica, ancient stones were pilfered from colosseum on pope’s orders (Scotti 8). In addition to this, broken arches and columns from the Palatine were recycled in the new church. Other secondhand materials that were used were marble columns pilfered from public buildings and temples of pagan Rome (Hauser 66).
Engineering Problems
Cracks in the Dome
By the 18th century, severe cracking appeared at the base of the Basilica dome despite the original tension hoops placed in the dome, and minimal cracking occurred in the upper shells where the lantern is laid down (Marconi 5). Originally, Della Porta added three iron hoops to the internal shell of the dome between 1589 and 1592. Two of these rings were placed in the solid mass of bricks where the curve begins, and the third was placed midway to the apex of the dome. The two larger hoops weigh more than 18,000 pounds, while the smaller ones weigh more than 16,500 pounds (Scotti 222). Historically, masonry domes are built in the form of hoops without centering and remain stable mainly due to compression in hoop and meridional directions. The lower portion of the dome, during and after construction, has the tendency to bulge out which imparts hoop tension. Masonry, when constructed in shell form, is a unique combination of durability and spanning capacity (Varma, Jangid, and Achwal 7). However, even with the three tension hoops in place, cracking still progressed, which is what led to the addition of five iron hoops in the 18th century.
Figure 14. Vanvitelli’s Drawings of dome cracksand tension rings (Marconi 5).
Architect Luigi Vanvitelli‘s drawings from 1748 (shown in Figure 14 above) show where the cracks occurred in the dome and the position of the five new rings that were added by Giovanni Poleni. A sixth hoop was added in 1748 when Vanvitelli realized that one of the sixteenth-century hoops had broken up. The addition of these six hoops ensured the structural strength and rigidity of the dome. This helped prevent further cracking and deformations (Marconi 5).
Issues with Travertine
Travertine is known to be a very durable material, composed almost exclusively of precipitated calcium carbonate. Defective layers of the travertine, such as spongy material, trapped soil, and large holes, are frequently present in the sediment, but these are normally discarded in quality construction. High quality travertine possesses great mechanical strength and a remarkable resistance to environmental attack. As a result, one might conclude that the conservation of travertine should not pose great problems; however, travertine requires serious attention because a lot of iron was used in their construction (Torraca 82).
Iron that was used in the construction of the façade within the travertine stone presents many issues. In order to connect façade blocks together, cramp irons that were bonded by molten lead were used frequently. Additionally, in order to connect decorative elements to the front of the façade, Iron bars, rings, and other pieces of hardware were used. Metal elements are necessary in travertine construction because stones are unreliable when subject to tensile or flexural stresses. However, when this metal corrodes, not only does the metal weaken, but it also increases in volume. Due to the expansion of the metal inside of these blocks, a great amount of stress may result, causing massive blocks of stone to be shattered. To solve this issue, inspection and maintenance by sealing all ways of water penetration that could cause metal corrosion, filling cracks and other voids, and repairing old fillings with lime paste and crushed travertine is necessary (Torraca 83).
Additionally, Lime-based materials, such as travertine, are attacked by pollutants brought to the stone surface by air (in gaseous or aerosol form) or water (acidic rain). This results in corrosion of the stone. Plants and bushes also threaten the state of travertine. When seeds are blown into crevasses by the wind, these seeds grow into plants and bushes that create stress and cracks. Therefore, careful maintenance of the travertine is important (Torraca 83).
Poor Foundation
The new Basilica shifted somewhat to the West in comparison to the old Basilica. This meant that the new Basilica was positioned farther from the Tiber River in comparison to the old Basilica, and it was therefore built on slightly better soil (Macchi 309). The weak foundation of the old Basilica was a major issue that led to stability problems, and although the position of the new Basilica was slightly different, this Basilica would soon face problems as a result of a poor foundation as well.
The foundation of the new Basilica begins with the foundation of the old Basilica due to the fact that the Basilica was built at the same site. Constantine made the decision to erect the Basilica not only on top of an existing cemetery, but also on top of Vatican Hill, which has a steep slope (Hauser 66). He chose to do so because he believed the remains of Saint Peter to be buried there, and as a result he was wanted to build the basilica at that location no matter how difficult the task proved to be. In order to build the church on top of the cemetery, Constantine destroyed the cemetery, which was in active use. Constantine transferred approximately 1,500,000,000 cubic feet of hard blue clay from the upper part of hillside, to the lower part, in order to carve a level platform upon which the basilica could be built. The emperor’s engineers embedded the cemetery with clay and built the church on top (Hauser 66). The tombs that were left somewhat intact were the ones located under the western half of the old Basilica, where the hill slopes steeply to the South. Constantine left the roofs of these tombs intact, and just filled the interiors with rubble in order to make a firm foundation (E. Howard and M. Howard). Additionally, the area around the Vatican was pervaded by swamplands and the surrounding terrain was yielding and unstable (Torraca 32).
The location of the new Basilica ended up having large negative impacts on the façade of the Basilica. The good soil, or Vatican loam soil, underneath the façade occurred at different depths. On the Northern side of the façade, the good soil was 15 meters below the surface; however, on the southern side of the façade, the good soil was 25 meters below the surface (Macchi 309). Other challenges with the foundation of the Basilica that presented many issues for the façade include the presence of water springs, the presence of the remains of the Circus of Nero, and the enormous weight of the façade, which amounts to be 140,000 tons (Macchi 309).
The façade of the Basilica was built in three parts. First, the central part of the façade was built, followed by the two towers on either side. Due to the fact that the southern edge of the central portion of the façade wasn’t built on good soil, differential settlement, or the unequal settlement of a building’s piers, occurred. This was what first caused the façade to begin cracking (Macchi 310). Following this, when the construction of the southern tower began in 1618, a foundation by pits and piles was adopted. However, the size of the cracks only increased when Bernini attempted to superimpose the tower in 1638. As a result, the tower had to be torn down. There were four main vertical cracks that ran along the entire wall from the top of the façade wall to its foundations. At the widest point, the cracks were 22 cm wide (Macchi 311). Currently, the cracks are still present, and Figures 15 shows the location of these cracks. Additionally, the present differential settlement is 40 centimeters (Macchi 312).
Figure 15. “Cretti” (large cracks) shown on thephotogrammetric view (Macchi 312)
Figure 16. Vertical crack in the facade attic(Sperandio, Zander, and Zappa 94).
Figure 16 shows vertical cracks on the base of the attic of the East façade. These cracks were previously described by architects Domenico Costa and Giovanni Antinori in 1786. A “swallow tail” in Carrara marble was introduced (visible at the bottom left) in order to control movement after an earthquake that occurred in 1812 (Sperandio, Zander, and Zappa 94).
Façade Statues
13 statues decorate the façade of the new Basilica. Over several centuries, and especially in the first half of the 19th century, the façade statues went through many restoration programs in response to cracks that had formed and parts of the statues that had become unstable. To repair the statues, iron bands and special iron ties were used; however, now those iron parts show serious signs of deterioration. The iron has thinned as a result of deposits of rust, and they are no longer capable of providing support for the statues. Additionally, the ties are coming loose and the decorative elements of the statues are showing visible signs of decay (Sperandio, Zander, and Zappa 96). Figures 17 and 18 show the positions of the statues on the facade.
Figure 17. 13 Facade Statues (E. Howard and M. Howard).
Figure 18. The pictures above show the 13 statues that are lined across the top of the facade
Visiting Saint Peter’s Basilica
Prior to entering the Basilica, one must walk through St. Peter’s Square. The square is surrounded by colonnades and statues that lead up to the Basilica itself, whose facade is decorated with elaborate columns and statues. The front of the facade states “IN HONOREM PRINCIPIS APOST PAVLVS V BVRGHESIVS ROMANVS PONT MAX AN MDCXII PONT VII”, which when translated in english, means “In honor of the prince of Apostles; Paul V Borghese, Pope, in the year 1612 and the seventh year of his pontificate.” The fact that a church of such grand scale and detailed decorations was constructed without modern technology and tools demonstrates the great amount of ingenuity and engineering knowledge of the contributors to this project. As a result, I researched a few things that drew my attention during my visit. I was intrigued by the use of materials, the current restoration taking place, and the weight of the dome.
Materials
In the interior of the Basilica, there are several columns that were made of different types of marble. Pictured below in Figures 19-22 are the four distinct types of marble that I saw inside of the church. These mismatching marble columns could be a result of recycling materials from other monuments and structures. Oftentimes, pieces of older structures were reused in the construction of newer structures. After Christianity came to Rome, parts were often taken from older Pagan structures.
Figures 19-22 (from left to right). Marble columns inside St. Peter’s Basilica.
From a distance, marble and travertine can sometimes look similar. Analyzing the materials up close and in person, I realized that the main similar characteristic that marble and travertine can have in common is their color. Travertine is a very porous and rough material, whereas marble is much smoother and gives a much more clean cut appearance. Figure 23 shows a magnified view of the travertine used for the façade.
Figure 23. Up-close view of travertine.
Restoration of Statues
While visiting the Basilica, it appeared that several of the travertine statues that line Saint Peter’s Square were currently under restoration as shown in Figure 24. Scaffolding led up to multiple different statues. Bernini’s colonnade that surrounds Saint Peter’s Square is made up of 284 columns that are topped with 140 statues. There is an inner and outer row of columns, as pictured below. The sculptures are of saints that are both famous, and lesser known, and were sculpted between the 1660’s and early 1700’s. The statues were most likely deteriorating, possibly due to corroding iron of parts that connect the statues to the top of the colonnades. It is important that crumbling parts of the structure don’t fall off of statues and onto people standing below. Also, weather could have a negative impact on the statues, as they must face wind and rain. Additionally, wind could have transported seeds to the statues, and wedged themselves in cracks. Plants and moss could result from this, which would have to be cleaned off of the statue in order to prevent any further cracking or damage.
Figure 24. Bernini’s colonnades under restoration.
The project was started in 2009 and is expected to take a few more years to finish. Funding for the project first came from commercial sponsors, but now due to the poor state of the economy, there are less sponsors willing to fund the project. As a result, the Holy See issued a limited edition of papal stamps in order to raise three million euros to help fund the estimated 14 million euro project of restoring the colonnades. Below is a video that I took while in Saint Peter’s Square. In it, the current reconstruction taking place is visible (Squires).
Dome Weight Estimation
After visiting Saint Peter’s Basilica and seeing the massive dome in person, I decided to calculate the approximate weight of the dome. From the floor of the Basilica, it’s hard to comprehend just how big the dome must be close up. In order to better understand just how heavy the dome that was hovering above me was, I performed the following calculations.
Assumptions: Although there is a staircase leading to the top of the dome, I am assuming that the area between the inner and outer shell of the dome is solid in order to simplify calculations. I am also assuming that the inner shell is the shape of exactly half of a sphere, and the outer shell is the shape of exactly half of an ellipsoid.
Exterior height of dome: 65 meters (“St. Peter’s Basilica”)
The height of the dome from the ground of the basilica to the roof of the lantern is 120 meters, the height of the piers is 45 meters, and the height of the drum is 20 meters (“St. Peter’s Basilica”). Therefore, 120 meters – 45 meters – 20 meters = 65 meters.
Approximated interior height of dome: 21 meters
The inner shell of the dome is semi-circular; therefore, the inner height of the dome would be its radius.
Outer diameter of the dome: 59 meters (“St. Peter’s Basilica”)
Inner diameter of the dome: 42 meters
Estimated density of concrete masonry: 2000 kg/m^3
1. Calculating the volume of the dome.
To calculate the volume of the dome, I first found the volume enclosed by the inner surface of the dome, which is essentially half of a sphere. I then found the volume enclosed by the outer surface of the dome, which is half of an ellipsoid. To find the volume of the dome, I then subtracted the volume of the inner surface from the volume of the outer surface.
Volume enclosed by inner surface of dome:
The equation for the volume of half a sphere is V= (2/3)(pi)(radius^3). The inner diameter is 42 meters; therefore, the radius is 42 meters/2 = 21 meters. Therefore:
V=(2/3)(pi)(21^3)
V=1.94*10^4 m^3
Volume enclosed by outer surface of dome:
The equation for the volume of a half ellipsoid is V= (2/3)(pi)(radius^2)(height). The outer diameter is 59 meters; therefore, the radius is 59 meters/2 = 29.5 meters. The exterior height of the dome is 65 meters. Therefore:
V=(2/3)(pi)(29.5^2)(65)
V=1.18*10^5 m^3
Difference between outer shell volume and inner shell volume:
(1.18*10^5-1.94*10^4) = 98,600 m^3
2. Weight of the dome:
After finding the volume of the dome, I multiplied this value by the density of the heavy concrete masonry material used for the majority of the dome.
Weight= (98,600 m^3)*(2000 kg/m^3)
Weight= 1.97*10^8 kg
Conclusion
Although the Basilica took over a century to complete, the end result reflects the enormous amount of time, money, and resources that were put into building the structure. A strategic use of material, construction techniques, engineering principles, and restoration led to a Basilica that is still used and visited by many today. During my visit, I was able to witness the beauty that resulted from the intelligent engineering of the 16th century and analyze engineering related aspects of the basilica.
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