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39638_3vol_1_89_110_ochsendorf.pdf Engineering Analysis for Construction History: Opportunities and Perils

John Ochsendorf

INTRODUCTION

Engineering education, unlike law, philosophy, art, or any field in the humanities, does not require

students to learn anything of the history of the profession. Engineering could be compared to medicine, which is a practical field with rapidly developing knowledge and with clear problems to solve. Similar to engineering education, medical students are not required to know the general

history of medicine, or even the specific history of a particular disease. Presumably the history of

the profession is irrelevant for the practitioners of the future. Fortunately, many engineers over the last century have researched the history of ancient and modern engineering and have made fundamental contributions to the field of construction history. This paper will not attempt to review the accomplishments of engineers in construction history, though the works of Jacques Heyman, Rowland Mainstone, and David Billington can be mentioned as examples of ground-breaking research. In fact, many of the problems facing the historian of construction can be considered to lie within the field of engineering today. The questions faced by

historical builders are the problems that today's engineers attempt to solve. Some of these questions

are: How to build it? How much does it cost? How much material is required? Is it a safe design? What is the maximum possible span? What caused the failure of a large structure? All are questions that have been foremost in the minds of builders throughout history. Yet these questions are often neglected by historians of architecture, leaving room for engineers to analyse such historical problems in construction. Though these questions are primarily associated with

structural engineering, there are other aspects of engineering which can help to illuminate history,

such as material science, construction engineering, manufacturing, etc. This paper explores the role of engineering analysis in construction history and proposes opportunities and pitfalls for the future. In particular, the aim is to demonstrate how structural 89
engineering analysis may provide a new understanding of construction history. Three ongoing

research projects will be used as examples to demonstrate the possibilities and to identify potential

perils for engineers working on historical topics. Each project is from a different time period and a

different region of the world, so they represent a variety of problems in construction history. The three topics are:

1. Early flying buttresses (11

th -12 th C France)

2. Inca suspension bridges (14

th -16 th C Peru)

3. Guastavino tile vaulting (19

th -20 th C United States) These projects are selected because of the author's experience using engineering analysis to better understand the history of each of these constructions. In each case, the paper will present opportunities and perils for the future.

EARLY FLYING BUTTRESSES (11

TH -12 TH C FRANCE) Working together with Andrew Tallon of Columbia University and Maria-Katerina Nikolinakou of MIT, the author has performed structural studies on early French flying buttresses. The goal was to develop a new understanding of the structure and form of some of the earliest French flying buttresses. As demonstrated by Heyman (1966), such structures can be analysed as an assembly of rigid blocks using limit analysis, in which the minimum and maximum thrust states can be determined from static equilibrium. (fig.1) New research at MIT has created interactive limit analysis tools which can be used to quickly investigate the forces in masonry structures (Block

2005). In particular, the minimum thrust values of flying buttresses are now straightforward to

determine.

Minimum thrust

Maximum thrust

Figure 1. Generic flying buttress with minimum and maximum thrust states (after Heyman 1995) Initially, twenty flying buttresses were studied in detail. (fig.2) Andrew Tallon surveyed the buttresses in France to provide the geometry for the structural studies. All buttresses were then 90
analysed to determine the minimum horizontal thrust values and the full results have been published in a French engineering journal (Nikolinakou et al 2005). Despite a wide range in spans and forms of the flying buttresses, most provided a minimum horizontal thrust value between 20% and 40% of the flyer weight.

Figure 2. Minimum thrust states of early flying buttresses in France, drawn at the same scale, with the darker

line showing the state of minimum thrust (after Nikolinakou et al. 2005) 91
The most significant discovery was that many flyers are in danger of sliding at a state of minimum

thrust, as illustrated by the sliding failure limit for a friction coefficient of 0.75. (fig.3) In fact, the

surviving flying buttresses appear to cluster on the safe side of the sliding limit. This suggests that

trial and error demonstrated this boundary of safe design. As Heyman (1995) has pointed out, measures were sometimes taken to prevent sliding at the head of the flyer, such as the addition of

columns under the head of the flyer. For example, the flying buttress at Saint-Julien in Royaucourt,

France, has experienced some sliding at the head of the flyer despite the use of a supporting column

affixed to the wall. (fig.4) Such movements may have occurred during the initial construction when the flying buttress acted at a state of minimum thrust.

0.200.300.400.500.600.700.80

0 102030405060

Flying buttress angle

6 4 3

Length

Thickness

Variable:Example of shapes:

8

LengthAngle

Flyer geometry

Sliding failure

Friction coefficient: 0.75

0 1020304050600.200.300.400.500.600.700.80

Flying buttress angle

Nv BaBCx Cd Lc LmNc Pc MSe Sg Ss Ve EPn Sl VoR

Figure 3. a) Minimum horizontal thrust values for flying buttresses with varying length-over-thickness ratios

and different inclinations; b) Corresponding thrust values for case study early Gothic flyers

There is tremendous potential for such studies to shed new light on the structure and construction of

historic masonry monuments. By developing new interactive limit analysis tools, researchers from a

wide variety of disciplines will be able to find new answers to old questions. The opportunities for a

new understanding of design and construction of masonry architecture can go together with new educational tools for students and professionals. By emphasising static equilibrium as the most important principle, a new level of understanding can emerge among historians of construction. Ongoing work at MIT aims to make such analysis methods more accessible for non-engineers (Block et al. 2006). Simple analysis tools are available for free over the internet for other researchers to use at http://web.mit.edu/masonry.

This type of study suggests a number of perils for historians of construction as well. In some cases,

engineers are applying modern analysis tools that are not appropriate for historic structures. First

92
and foremost is the use of elastic analysis for masonry structures. As an example, consider the two

semicircular arches of Figure 5, one with a thickness/radius ratio of 8% (fig.5a) and the other with a

ratio of 16% (fig.5b). A typical finite element analysis is shown on the left, in which the resulting elastic stress patterns in the masonry are indistinguishable between the two arches (Block et al

2006). Yet, a simple thrust line analysis at right immediately shows the difference between the two

structures. The 8% arch will not stand unless the material can withstand considerable tension, which

is not the case for historic masonry construction. In short, elastic analysis says nothing about the

collapse state of masonry and cannot be used to describe the actual state of a historic masonry structure. Unfortunately, many e ngineers are applying elastic analysis to unreinforced masonry,

which generally does not offer useful information for the historian. Elastic finite element analysis,

which purports to find the "one true state of a structure", is seeking exactness in vain (Ochsendorf

2005).

Figure 4. Sliding near the support of a flying buttress at Saint-Julien in Royaucourt,

France (Photo: Andrew Tallon)

This study of flying buttresses suggests another peril facing engineers. Without proper historical training, an engineer may tend to adopt an evolutionary view of history, in which some designs are "better" or more "efficient." To apply such an idea to the early French flying buttresses would be

fruitless, because without additional archaeological or historical knowledge, it would be difficult to

draw strong conclusions on the evolution of flying buttress designs. The desire to look for evolution

based on engineering analysis is tempting, but should only be undertaken with the appropriate 93
historical and archaeological research in support of the engineering analysis. In modern

engineering, there is a prevalent notion that each generation of engineers will surpass the previous

generation in a constant march of progress. With new technology (such as faster computers) engineering will always move forward to a more enlightened state of knowledge. Such notions are dangerous for modern engineering, and can be even more dangerous when applied to history.

Figure 5. Two semicircular stone arches of varying thickness a) 8% and b) 16% are analysed by finite elements

(at left) and by thrust lines using limit analysis (at right). (Block et al. 2006)

The example of flying buttresses has illustrated how the use of simple equilibrium analysis can shed

new light on the performance and construction of historic masonry structures. While this example has illustrated how engineering analysis can offer greater understanding of a specific element of a masonry building, the next example suggests that engineers can uncover wider societal questions that have been neglected by historians.

INCA SUSPENSION BRIDGES (14

TH -16 TH C PERU)

The history of ancient suspension bridges is a fascinating topic which has scarcely been explored. In

ancient China, iron chain suspension bridges spanned long distances more than 1,000 years before

the iron bridge at Coalbrookdale in 1779, which is often hailed as the first metal structure. Joseph

Needham, the historian of Chinese technology, has provided a starting point for the study of ancient

94
Chinese bridges though much remains to be done. In his landmark study, Needham suggests that the ancient Chinese must have transferred their invention to South America, where ancient hanging bridges can be found throughout the Andes Mountains (Needham 1971). This type of technology transfer in construction is highly unlikely. It seems clear that mountainous regions of the world faced a similar problem in spanning deep gorges with minimal material, and builders arrived at the same solution: the suspended bridge, where the cables serve as the roadway. Figure 6. Inca bridge over the Apurimac River in Peru sketched in the 19 th century by Squier (1877) In 1532, when the first Spanish conquistadors arrived in the mountains of South America, they were astonished to find suspension bridges longer than any single known span in 16 th C Spain. (fig.6) Furthermore, the Spanish came from a tradition of compression, which emerged from the strong influence of Roman arch construction in the Iber ian Peninsula. Long span bridges in pure tension were unknown to them (Ochsendorf 2004). 95
The suspension bridges played a strategic role in the creation and control of the Inca Empire from the 13 th to the 16 th centuries. At its height, the Inca controlled nearly 15,000 miles of roads connected by hundreds of bridges (Hyslop 1984). These works of infrastructure were essential for

the organization of the Inca state as well as the initial conquering of foreign lands. Garcilaso de la

Vega (1609) wrote a chapter titled "Many tribes are reduced voluntarily to submission by the fame of the bridge," saying: [The bridge] alone sufficed to cause many provinces of the region to submit to the Inca without any reservations, one being the part called Chumpivillca in the district of Cuntisuyu, which is twenty leagues long and more than ten broad. He was welcomed as their lord with a good will because of his face as a child of the Sun and because of the marvelous new work that seemed only possible for men come down from heaven.

This chronicle, combined with ot

her historical evidence, suggests that the bridges played a crucial role in the expansion and development of the Inca Empire. Yet, historians of the Andes Mountains have not considered the bridges to be worthy of study and most books on the Inca Empire provide no details of Inca bridge construction. Upon encountering long span suspension bridges for the first time, the Spanish conquistadors reacted with a mixture of admiration and fear. Cieza de Leon (1553) gives an account of the Spanish forces crossing over a great suspension bridge "so strong that horses can gallop over it as

though they were crossing the bridge of Alcántara, or of Cordoba." But the Spanish reacted mostly

with fear. Pedro Sancho (1543) recalled how his first crossing terrified him: ...to someone unaccustomed to it, the crossing appears dangerous because the bridge sags with its long span... ...so that one is con tinually going down until the middle is reached and from there one climbs until the far bank; and when the bridge is being crossed it trembles very much; all of which goes to the head of someone unaccustomed to it. The sketch published by Squier (1877) gives a sense of the experience of crossing an Inca hanging bridge. (fig.7) The Inca suspension bridges successfully supported the loads of large armies in addition to the weight of horses and cannons, so it is apparent that these structures had significant load capacity (Ochsendorf 1996). As the Spanish became accustomed to the suspension bridges, they grew bolder, though they marvelled at the technology: I have seen many Spaniards cross without dismounting, and some on horseback at a gallop to show how little they were afraid: the feat is rather a rash one. The fabric is 96
begun with only three osiers, but the result is the bold and impressive work that I have described, however imperfectly. It is certainly a marvelous piece of work, and would be incredible if one could not still see it, for its very necessity has preserved it from destruction, or time might have destroyed it like many others which the Spaniards found on the same highways, some as big or even bigger. (Garcilaso 1609) Figure 7. Inca bridge over the Rio Pampas in Peru sketched in the 19 th century by Squier (1877) It is no wonder that the Spanish were impressed by the Inca bridges. In fact, 16 th century Spanish technology was incapable of spanning the long distances of the Inca suspension bridges over the raging waters of the Andean rivers. The Inca bridges achieved clear spans of at least 50 metres and some spans were certainly greater. This span was greater than any span in masonry achieved by that point in history. The longest Roman bridge in Spain had a maximum span of only 29 metres and did not have to be built over a deep gorge (O'Connor 1993). Masonry arch construction requires extensive centring to be built during the construction process for the arch, and such centring was

beyond the technical capacity of the Spanish at the time. Efforts to build a masonry arch bridge over

97
the Apurímac River from 1588-1595 as a replacement for the Inca suspension bridge were unsuccessful and the bridge construction was abandoned after great loss of life and money (Harth- Terre 1961). Bridge technology did not offer a better solution to crossing the deep gorges of the

Andean region until the 19

th century and the great advances of the Industrial Revolution. The origin of the modern suspension bridge owes nothing to the Inca achievements, which went unnoticed as a new technical concept in Europe at the time despite the detailed descriptions by the Spanish chroniclers. Long span suspension structures did not begin to be built in Europe until the late 18 th century, over 250 years after the Inca conquest (Peters 1987). For wheeled traffic, the development of the level roadway suspension bridge was an essential step and it would be several centuries before European engineers developed this idea. In the study of Inca suspension bridges and their impact on the history of the Andean region, engineering researchers have many new perspectives to offer. By answering questions about the

load capacity of the bridges, the abutment details, the maintenance plans, the construction materials,

and the timeline and geography of bridge construction, engineers can make fundamental new contributions to our understanding of the development and organization of the Inca Empire. Ten years of the author's research has revealed that the bridges played a more important role in Andean history than anyone may have imagined before. By working together with historians and archaeologists, engineers can bring new context and new questions to the study of human achievement in construction. However, the study of ancient suspension bridges suggests an additional peril for engineers in the field of construction history. There is a danger of imposing modern ideas on historical constructions. A lack of historical knowledge or collaboration with experts in the field can lead engineers to impose modern notions on a historical society. Such is the case for the ancient Mayan city of Yaxchilan, where an engineer has proposed an enormous suspension bridge as a gateway to the ancient city (O'Kon 1995). The invented bridge has a level roadway, tall towers, and large anchorage blocks, which are all characteristics of modern suspension bridges. (fig.8) There is no historical, archaeological, ethnographic, or written evidence that the Maya ever built suspension

bridges. It is highly unlikely that a suspension bridge existed on this site, and it certainly did not

have the many modern features that are postulated. For example, the Maya did not have wheeled vehicles, so there would have been no need for a level roadway. The lesson from this example is that engineers should be cautious of their own lack of historical training and should work together with experts to ensure that the engineering studies are supported by historical and archaeological evidence. The example of Inca suspension bridges illustrates how engineers can raise new questions and

illustrate new interpretations of the history of society. The final example suggests the potential for

engineers to contribute to the study of individuals in construction history. 98

Figure 8. Postulated susp

ension bridge at the 8 th C Mayan city of Yaxchilan (O'Kon 1995)

GUASTAVINO VAULTING (19

TH -20 TH C USA) From the 1880's through the 1950's, the R. Guastavino Company built thin tile vaulting in hundreds of buildings around the United States (Collins 1968). Such vaulting is known as timbrel vaulting, and is made with fast-setting mortar to minimize the required centring during construction. Through rigorous load testing and materials development, Rafael Guastavino (father and son) transformed the vaulting from a traditional Mediterranean construction method to an engineered floor system. Though the vaulting is a central feature of some of the most important American architecture from the early 20 th century, architectural historians have paid little attention to this constructive element. The primary reference on the subject was published in Spain as the catalogue for a major exhibition on the company's work (Huerta 2001). The company built hundreds of long span masonry vaults, whose designs are noteworthy for their constant innovations over a period of more than 50 years. (fig.9) Few scholars have differentiated between the technical contributions of the father Rafael Guastavino Moreno (1842-1908) and the son Rafael Guastavino Esposito (

1872-1950). To

understand the technical and historical contributions of the company, it is necessary to examine the

originality of the work by each individual. Ongoing studies on this subject have shown that the son was responsible for the vast majority of the vaulting built in the United States and that his contributions have been overshadowed by his father's reputation as the founder of the company. Following his studies at the Escuela de Maestros de Obras (School of Master Builders) from 1861 to 1865, Rafael Guastavino Moreno began a successful career as an architect and builder in 99
Barcelona. Tarragó (2002) has provided an overview of the works of Guastavino in Catalonia. Though he designed and built numerous projects, Guastavino is best known for two large works: the Batlló Factory of 1868 in Barcelona and the Teatro "La Massa" of 1881 in Vilassar de Dalt. These

projects established him as a leading architect and builder of the period. His work was visionary in

terms of construction and design, though additional research is needed on the originality of Guastavino's work in Barcelona of the 1860's and 1870's. Without question, the dome of La Massa, spanning 17 metres with a rise of 3 metres and a thickness less than 10 centimetres, shows the ability of a great designer and builder (Dilmé and Fabré 2002). (fig.10) Figure 9. Promotional poster of the Guastavino Company (Source: Avery Library, Columbia University)

The father and son each made substantial contributions to the development of the traditional timbrel

vault as an engineered structural system, extending the system well beyond anything built in Spain

prior to 1900. As part of his efforts to create a modern constructive system, Guastavino Sr. carried

out controlled material testing at MIT in 1887. These results were used to develop design tables for

his arches, which Guastavino published in his first book (1892). As part of the construction process

for the Boston Public Library, Guastavino also carried out load testing of a timbrel vault in 1889, which he called "the first breaking load test ever made" (Mroszczyk 2004). Additional load tests

were used in the future to promote the technical rigor of the construction method as well as to instil

public confidence in Guastavino's unknown system. The load testing was carried out mostly by the father prior to his death in 1908. 100
Fig. 10. Teatro La Massa, Vilassar de Dalt, Spain, 1881 (after Dilmé and Fabré 2002) Figure 11. Patent for reinforced timbrel vault by Guastavino Jr., 1910 (U.S. Patent Office) 101

Rafael Guastavino Jr. did not have formal training in architecture or engineering. He arrived in the

United States at the age of nine, and he began working in his father's office when he was only 11.

His education came from years as an apprentice in the office, including training in graphic statics

from a senior engineer in the office. Remarkably, Guastavino Jr. received four U.S. patents in 1892 for innovations in tile vaulting when he was only 19 years old (Ochsendorf 2006). He also innovated by using metallic reinforcing as an integral part of the masonry construction system. In

1910, the son received a patent for reinforced masonry in which he illustrated the use of metallic

reinforcing between layers of brick for arches, walls, and vaults. (fig.11) The son used similar reinforcing in the dome of the Cathedral of St. John the Divine, which spans over 30 meters and is one of the largest masonry domes every built. The dome was built in a little more than three months, without any centring for support, and it was celebrated as a public marvel at the time. (fig.12) Though the dome was meant to be temporary, it still exists today. The reinforced timbrel

vault has the primary advantage that it can be built with no formwork, unlike the case of reinforced

concrete shells (Ochsendorf and Autuña 2003). Figure 12. Cathedral of St. John the Divine under construction, New York, 1909 (Avery Library, Columbia University) 102
Another important structural innovation by both Guastavino father and son was the use of new calculation methods. Though the father often spoke of timbrel vaulting as a "cohesive" system which had significant tensile strength, he generally assumed that the structures acted in compression. Huerta (2003) has provided an outstanding overview of the history of the structural theory of the timbrel vault and has exposed this "schizophrenia" which existed in Guastavino's mind. Despite his confusion about the exact structural behaviour of his system, Guastavino Sr. illustrated a sophisticated knowledge of possible thrust lines within his masonry vaults and he

designed primarily according to equilibrium. His description of the thrust lines due to live loading

on a vault is a clear example of the "safe theorem" of limit analysis (Heyman 1995). (fig.13) Similarly, Rafael Guastavino Jr. designed using equilibrium methods of analysis and his

contributions to the graphical analysis of domes are particularly interesting. The son was among the

first to adapt new innovations in the use of graphical methods for his design and construction projects. (fig.14) Such equilibrium methods of design for masonry are the correct approach, given the low values of stress in traditional masonry structures. Figure 13. Illustration of the live load carried on a tile vault with backfill (Guastavino 1892)

The Guastavinos made countless othe

r contributions to the development of new structural systems in brick, and these few examples offer only a brief overview. However, by the 1940's, Guastavino vaulting was rarely considered for thin shell domes and the company closed its doors in 1962. The

study of such structural systems could be seen as a false trail in history, since the true path would

lead to the systems of reinforced concrete and steel that are prevalent today (Heyman 2005). Yet, it

is essential for engineers to research subjects such as Guastavino vaulting. By placing the accomplishments of such builders in their historical context, engineers can gain a new understanding of the development of structural innovations. Furthermore, the profession could discover potential possibilities for new design in the future. And the study of history could be a valuable resource in the crisis of civil engineering today, as described by Werner Lorenz (2003). There is great potential for improved engineering education by studying master works of the past and by emphasizing equilibrium methods of design. Finally, a greater appreciation for technical aspects of construction history could help to identify and preserve important works of construction history. 103
Figure 14. Graphical calculations by Guastavino Jr. for a thin masonry dome (Avery Library, Columbia University) The study of Guastavino vaulting suggests additional perils for engineers. In the 20 th century, there were numerous cases where Guastavino vaulting was torn down and replaced with concrete slab construction, simply because the consulting engineers could not calculate the capacity of the thin masonry vaulting. Structural engineering education focuses on steel and concrete as the two primary structural materials, and engineers often do not know how to approach historical construction

systems. Thus, the peril for engineers is that historic buildings will be lost, perhaps causing the loss

of irreplaceable artefacts of engineering heritage. The loss of engineering history can be prevented

by engineers who take an active role in identifying and celebrating significant historical accomplishments.

CONCLUSION

In Cambridge in 1959, C.P. Snow delivered his famous Rede lecture that became the basis for his book "The Two Cultures" on the divide between the sciences and the humanities (Snow 1998). Today, much of the most exciting research in universities is multi-disciplinary, often working

across the "two cultures." Anthropologists work together with biologists to understand the historical

104
migrations of humans and other species around the planet. Art historians work together with physicists to understand the composition of paintings. Artists work together with computer scientists to create new works of electronic art. Similarly, engineers can work together with historians to bring new understanding to construction history. Engineers have made fundamental contributions to our knowledge of construction history and there is even greater opportunity for engineer s in the future. As illustrated by the three examples in this paper, such studies can provide new understanding in construction history as well as an increased awareness of engineering heritage. More broadly, such studies can serve as educational models for the role of construction in the history of human society. These studies have great value for both engineering and the humanities. The three examples presented in this paper give an overview of the problems that engineers can

contribute to, ranging from the level of a single structural element, to the development of an entire

geographical region, and to the works of individuals. Yet, these three studies also suggest perils for

the profession of engineering. To summarise, engineers should: work closely with historians and archaeologists, and avoid a tendency to look for progress in structural history based on engineering analysis alone be careful not to impose modern approaches without considering the appropriateness of the approach work to identify and understand engineering heritage before it is lost

There are unlimited possibilities for engineering to contribute to the study of history and there is

ample room for the growth of research programs and university courses which focus on historical studies in engineering.

ACKNOWLEDGEMENTS

I would like to thank Professor Mary Sansalone of Cornell University, who encouraged my studies of civil engineering combined with archaeology and who has continued to serve as an important mentor. Professors Jacques Heyman, David Billington, Santiago Huerta, and Stephen Murray have all been valuable advisors and colleagues. I would also like to thank the many students who I continue to learn from, in particular Andrew Tallon, Maria-Katerina Nikolinakou, and Philippe

Block who contributed to this work.

REFERENCES

Block, P, 2005. "Equilibrium systems: studies in masonry structure," Unpublished M.S. Thesis, Department of Architecture, Massachusetts Institute of Technology, Cambridge. 105
Block, P, Ciblac, T, and Ochsendorf, J, 2006. "Real-time limit analysis of vaulted masonry buildings," Computers and Structures, (under review). Cieza de Leon, P, 1553. The Discovery and Conquest of Peru. (Translated and published by Duke University Press, Ed. A.P. Cook and N.D. Cook, 1998). Collins, G, 1968. "The Transfer of Thin Masonry Vaulting from Spain to the United States," Journal of the Society of Architectural Historians, Vol. 27, No. 3, pp. 176-201. Dilmé, L and Fabré, X, 2002. Teatre 'La Massa' de Guastavino, Vilassar de Dalt 1881-2002,

Barcelona: Edicions UPC.

Garcilaso de la Vega, I, 1609. Royal Commentaries of the Incas and General History of Peru, Trans. H.V. Livermore, University of Texas Press, 3 rd Ed. paperback, 1994, Book 3, Chapter VIII.

Guastavino, R, 1892.

An Essay on the History and Theory of Cohesive Construction, Applied Especially to the Timbrel Vault, Boston: Ticknor, 2 nd ed.

Harth-Terre, E, 1961. "El historico puente sobre el río Apurímac," Revista del Archivo Nacional del

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Heyman, J, 1966. "The stone skeleton," Intl. J. of Solids and Structures, Vol. 2, 1966. Heyman, J, 1995. The Stone Skeleton. Cambridge: Cambridge University Press. Heyman, J, 2005. "The history of the theory of structures," Essays in the History of the Theory of Structures, S. Huerta (Ed.), Madrid: Instituto Juan de Herrera. Huerta, S, 2001. Las bóvedas de Guastavino en América. Madrid: Instituto Juan de Herrera. Huerta, S, 2003. "Mechanics of Timbrel Vaults: A Historical Outline," Essays on the History of Mechanics, Ed. Becchi, Corradi, Foce, y Pedemonte, Basel: Birkhauser Verlag. Hyslop, J, 1984. The Inka Road System, New York: Academic Press. Lorenz, W, 2003. "History of construction: an estimable resource in the actual crisis of civil engineering?," Proceedings of the 1 st International Congress on Construction History, S. Huerta (Ed.), Madrid: Instituto Juan de Herrera. Mroszczyk, L, 2004. "Rafael Guastavino and the Boston Public Library," Unpublished BSAD thesis, MIT Department of Architecture, Cambridge, MA. Needham, J, 1971. Science and Civilization in China: Volume Four, Part III, Civil Engineering.

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Nikolinakou, M, Tallon, A, and Ochsendorf, J, 2005. "Structure and Form of Early Gothic Flying Buttresses," Revue Européenne de Génie Civil, Vol. 9, no 9-10, pp. 1191-1217. Ochsendorf, J, 1996. "An Engineering Study of the Last Inca Suspension Bridge," Proceedings of the 13 th Annual International Bridge Conference, Pittsburgh: Engineers Society of Western

Pennsylvania, pp. 398-404.

Ochsendorf, J and Autuña, J, 2003. "Eduardo Torroja and Cerámica Armada", Actas del Primer Congreso Internacional de Historia de la Construcción, Madrid: Instituto Juan de Herrera. Ochsendorf, J, 2004. "Expansion and Construction in the Andes Mountains: The Role of Inca Suspension Bridges," Unpublished paper, presented at the Meeting of the Society of Architectural

Historians, Providence, RI, April 17.

Ochsendorf, J, 2005. "Practice before theory: the use of the Lower Bound Theorem in structural design from 1850-1950," Essays in the History of the Theory of Structures, Ed. S. Huerta, Madrid:

Instituto Juan de Herrera, pp. 353-366.

Ochsendorf, J, 2006. "Los Guastavino y la bóveda tabicada en Norteamérica," Informes de la Construcción, Madrid: Instituto Eduardo Torrojo de la Construccion (in press). O'Connor, C, 1993. Roman Bridges, Cambridge: Cambridge University Press, p. 198. O'Kon, J, 1995. "Bridge to the Past," Civil Engineering Magazine, Vol. 65, no. 1, pp. 62-65. Peters, T, 1987. Transitions in Engineering: Guillaume-Henri Dufour and the Development of the Wire Cable Suspension Bridge in the Early Nineteenth Century. Basel: Birkhauser Verlag. Sancho, P, 1543. Relación para S.M. de lo sucedido en la conquista y pacificación de estas provincias de la Nueva Castilla y de la calidad de la tierra, Translation by P.A. Means, 1917, New

York: Cortes Society.

Snow, C, 1998. The Two Cultures, Cambridge: Cambridge University Press (originally published in

1959).

Squier, E, 1877. Peru: Incidents of Travel and Exploration in the Land of the Incas, New York:

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Tarragó, S, (Ed.) 2002. Guastavino Company (1885-1962), Catalogue of Works in Catalonia and America, Barcelona: Collegi d'Arquitectes de Catalunya. http://web.mit.edu/masonry 107

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