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Structural Imperative and the Origin of New Form ROBERT MARK AND DAVID P. BILLINGTON

Contemporary writing on architecture, following art history, tends to focus on formal analysis where visual ideas dominate the discussion of the origin and meaning of style. Technology is rarely touched upon; and structure, although generally understood as necessary, is hardly seen as a legitimate giver of form, even for large-scale building.'

This modern point of view must be understood, at least partly, as a reaction to the ideas of Eugene Viollet-le-Duc (1814-79), self-trained architect, restorer, archaeologist, and theorist. Mainly on the basis of his extensive practical experience with the restoration of medieval monuments, Viollet-le-Duc compiled a ten-volume encyclopedia, Dic- tionnaire raisonne de l'architecture franfaise du XIe au XVIe siecle (1854- 68), that remains even today probably the single most important published work on medieval building technology (fig. 1). He also inferred from this experience that many of the principal stylistic elements of the Gothic were originally derived from the demands of the construction process or the laws governing structural forces. Furthermore, he argued, since these laws apply to all building at all times, innovation in visual form springs from appropriate response to structural demands in terms of the materials of construction.2 In this light, he then

MR. MARK is professor in the School of Architecture and the Department of Civil Engineering, and MR. BILLINGTON is professor in the Department of Civil Engineering, at Princeton University. The authors gratefully acknowledge the support for these studies provided by grants from the National Endowment for the Humanities, the Andrew W. Mellon Foundation, and the Alfred P. Sloan, Jr., Foundation.

IThe need for structure, however, would not seem to be universally accepted. In the award-winning text by Alberto Perez-G6mez, Architecture and the Crisis of Modern Science (Cambridge, Mass., 1983), the late-18th-century architects Etienne-Louis Boullee and Claude-Nicolas Ledoux are especially lauded just because their unbuildable "architectural intentions .. . did not fit into the new, essentially prosaic world of industrial society" (p. 161). For writers like Perez-G6mez, the process of creative design is only hindered by considering technology.

2Viollet-le-Duc's polemical Entretiens sur l'architecture, originally published in Paris in 1863 (vol. 1) and 1872 (vol. 2), was translated into English by Henry Van Brunt as

? 1989 by the Society for the History of Technology. All rights reserved. 0040-165X/89/3002-001 $0 1.00

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FIG. 1.-High Gothic construction as illustrated in Viollet-le-Duc's Dictionnaire by his drawing of a portion of the nave of Amiens Cathedral.

302 Robert Mark and David P. Billington

attempted to demonstrate through new designs how the recently in- troduced metals of his own age might be used to develop a modern style of building. And although Viollet-le-Duc's designs may not have been persuasive in themselves, his writings on structural rationalism, which led Sir John Summerson to characterize him as "the last great theorist in the world of architecture," affected a whole generation of architects.3 He has been credited even with seeding the idea of the metal-framed American skyscraper.4

Rather than searching for elegant structure, many 20th-century designers found a more appealing basis for visual form in merely taking up the notion of a "machine aesthetic," often unrelated to machines but used, for example, to justify adopting Cubist forms in architecture-as when photographs of cylindrical reinforced-concrete grain elevators served as models for new styles of urban dwelling. Indeed, the onset of this new formalism can be marked, in 1923, with the publication of Vers une Architecture by the influential Swiss architect Le Corbusier. According to Le Corbusier, the engineer alone could never create beauty; it is only the architect "who by his arrangement of forms realizes an order which is pure creation of the spirit."5 And, as Summerson makes clear in his eccentric yet clever set of essays designed primarily to dispose once and for all of Viollet-le-Duc's theories, "[While Viollet-le-Duc's] disciplined, daring, economical, ingen- ious designs [lack] style, . . Le Corbusier's architecture was seen to be in the nature of an extension of the abstract painter's vision .... For [Le Corbusier] the obvious solution of a problem, however charm- ing, cannot possibly be the right solution.. . . Herein is Le Corbusier's poetry-or his wit. He sees the reverse logic of every situation. He

Discourses on Architecture (Boston: J. R. Osgood, 1875). The general argument of this work might best be summed up in a brief excerpt from the second volume: "A locomotive ... has its peculiar physiognomy, not the result of caprice, but of necessity. It expresses controlled power; its movements are gentle or terrible, it advances with awful impetuosity or, when at rest, seems to tremble with impatience ... its exterior form is but the expression of its power. A locomotive, then, has style. ... A thing has style when it has the expression appropriate to its use. ... We, who, in the fabrication of our machinery, give to every part the strength and the form which it requires, with nothing superfluous, nothing which does not have a necessary function, in our architecture foolishly accumulate forms and features taken from all sides, the results of contradictory principles, and call this art" (pp. 182, 186).

3John Summerson, Heavenly Mansions (New York, 1963), p. 135. See also Robert Mark, "Robert Willis, Viollet-le-Duc, and the Structural Approach to Gothic Architec- ture," Architectura 7 (1977): 52-64.

4Sigfried Giedion, Space, Time and Architecture (Cambridge, Mass., 1967), p. 206. 5Le Corbusier, Towards a New Architecture, trans. F Etchells (New York, 1960), p. 7.

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Structural Imperative and the Origin of New Form

sees that what appears absurd is perhaps more profoundly true than what appears to make sense."6

This negation of technology, we believe, is founded on a false interpretation of past monuments as well as a deep misunderstanding of the practice of structural design. In short, the form taken by the buildings that constitute the major architectural monuments of West- ern culture cannot be fully understood without detailed technical study and without recognition that the origin of much new form came directly out of structural rather than formal ideas. Le Corbusier was mistaken in assuming that the singular contribution of engineering to design is the solution of equations (or, more likely today, producing output from a computer) to derive the most efficient "scientific" form.7 Not only is the perception that engineers merely solve equations wrong; it is equally incorrect to argue that elegant form comes solely from architects. The best engineers imagine new forms that are scientific in the sense of being disciplined by the laws of nature, but these forms also reflect their designers' own aesthetic vision. And central to that vision is the engineer's observation of previously built structures that provided a basis for developments in structural form well before the availability of any scientific structural theory. Even today, with so- phisticated computer-analysis methods, such observations are still vital for design.

Our technical studies, of both historic and contemporary structure, have provided many insights into how new styles of building were informed by the behavior of previously constructed works. In this article, we shall discuss the effect of prior experience on designs before the Industrial Revolution by relating the Hagia Sophia to earlier large- scale Roman domed buildings, by describing the transition around the year 1200 from six- to four-part vaulting in the high vaults of Gothic churches, and by explaining the design rationale of Wren's dome for St. Paul's Cathedral. Post-Industrial Revolution examples include John Roebling's introduction of diagonal stays in long-span bridges, Robert Maillart's experience with the Aarburg bridge in 1912 that led to his development of a new bridge form, and the seminal ideas of Fazlur Khan on tall-building design.

Pantheon and Hagia Sophia Construction of large-scale domed and vaulted monumental build-

ings was facilitated at the turn of the 1st century A.D. by the Roman

6Summerson (n. 3 above), pp. 154, 189-90. 7Le Corbusier (n. 5 above).

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304 Robert Mark and David P Billington

adoption of cast structural concrete, a construction technique that had been developed over previous centuries but only for utilitarian use or for substructures. The building most representative of this new architecture is the Pantheon, constructed ca. 118-28 with massive, brick-faced concrete walls and a great bronze-covered semicircular concrete dome of 43-meter span. The height of the cylindrical interior wall is equal to the radius of the dome so that a sphere incorporating the dome surface would just fit within the building interior, as illustrated in figure 2. And, as might be expected, this aspect of formal design met with high approval from Le Corbusier.8

To understand better the structure of the Pantheon, we used a numerical, computer technique known as finite-element modeling.9 A first series of tests that assumed the concrete to act as a monolith without cracking revealed extensive regions of tensile hoop stress in the walls and the dome; but the maximum levels of stress were quite low, only about 15 psi (1 kg/cm2). Surprisingly, the maximum hoop stresses decreased by about 20 percent when the stepped rings near the base of the dome (fig. 3) were removed. Evidently, these rings do not have a salutary, reinforcing effect as had been generally assumed.10

Roman concrete, similar to modern concrete, has good compressive strength and hydraulic properties. Nevertheless, it differs from modern concrete construction in two crucial ways. First, the mix consis- tency of modern concrete is fluid and homogeneous, allowing it to be poured into forms. In Roman practice it was thick and layered by hand around large chunks of aggregate. Second, integral reinforcing

8According to Le Corbusier: "Architecture is the masterly, correct and magnificent play of masses brought together in light. . .. Cubes, cones, spheres, cylinders or pyramids are the great primary forms which light reveals to advantage. ... It is for that reason that these are beautiful forms, the most beautiful forms. ... Egyptian, Greek or Roman architecture is an architecture of prisms, cubes and cylinders, pyramids or spheres.... [On the other hand] Gothic architecture is not, fundamentally, based on spheres, cones and cylinders.... It is for that reason that a cathedral is not very beautiful and we search in it for compensations of a subjective kind outside plastic art. .. . The cathedral is not a plastic work: it is a drama; a fight against the force of gravity, which is a sensation of a sentimental nature. The Pyramids, the Towers of Babylon, The Gates of Samarkand, the Parthenon, the Colosseum, the Pantheon ... all these belong to Ar- chitecture" (Towards a New Architecture [n. 5 above], pp. 31-33).

9The model assumed a "typical meridional section." Because of extensive openings such as statue bays and passageways that take up a full quarter of the total volume of the cylindrical walls, no typical section actually exists. But since our interest was focused on the dome and the conceptual design of the basic structural configuration, we spec- ified an equivalent solid wall for the model. Further details of the analysis are found in Robert Mark and Paul Hutchinson, "On the Structure of the Roman Pantheon," Art Bulletin 68 (March 1986): 24-34.

'0See, e.g., Mario Salvadori, Why Buildings Stand Up (New York, 1980), pp. 230-33.


o 25m FIG. 2.-The Roman Pantheon (ca. 118-28); schematic section showing interior

geometry. (After Ward-Perkins.)

steel gives modern concrete structures great tensile strength. As Ro- man construction used no reinforcement, a second series of model tests was then based on an assumption consistent with modern engineering theory: that the unreinforced ancient concrete could with- stand no tensile stress. As would be expected, the model of the dome and supporting wall now indicated extensive meridional cracking, the crown of the dome acting as a compression shell above the cracking, and a circular array of wedge-shaped arches below; thus the lower, arched region can be freely cut into radial slices. In this case the extra loading of the stepped rings helps to maintain the arch segments in compression-not unlike the effect of the cut-stone surcharges placed over the haunches of Roman arch bridges. Moreover, the calculated extent of the cracking, predicted as 54 degrees above the horizontal plane of the dome base, agrees almost exactly with measurements made early in this century of cracks in the actual dome."

1 Albert Terenzio, "La Restauration du Pantheon du Roma," La Conservation des monuments d'art et d'histoire (Paris: Office International des Mus6es, 1934), pp. 280-85.

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FIG. 3.-Sketch showing stepped rings of the Pantheon dome. (Y. S. Huang.)

The coincidence of predicted behavior from the second test series with that of the actual structure indicates that, for practical purposes, Roman pozzolana could not be counted on to exhibit any tensile strength. As such, Roman concrete did not offer any significant structural advantage over conventional masonry construction of brick or stone. The decision to employ concrete in large-scale Roman architecture, therefore, seems to have been made on constructional rather than structural considerations. The placement of concrete by un- skilled slave labor was simpler than construction in brick or cut stone, which requires greater precision.

If the structure of the Pantheon was not revolutionary in the same sense as was the introduction of modern reinforced concrete in the late 19th century, it was nevertheless, because of its giant scale, a most daring experiment in construction. Observations of its behavior, or the behavior of other large domes of similar form that followed the Pantheon, led in turn to the development of new structural forms such as the dramatic array of windows around the base of the dome of the 6th-century Hagia Sophia in Constantinople.

The architectural treatment of this great church constructed by the emperor Justinian, long praised for its effect with diffuse light, cre-

Structural Imperative and the Origin of New Form 307

ating an image of the huge (33-meter diameter) dome "floating" above the interior space (fig. 4), was thought to have originated solely for visual effect.'2 This seemed a reasonable inference before the model study of the Pantheon was undertaken, except that the windows at the base of the Hagia Sophia dome are in a region where tensile hoop stresses would have been expected to be most critical. After the Pan- theon study, it became apparent that, if the base of the dome had remained solid, it would have been subject to meridional cracking similar to that experienced by the Pantheon; and, as with the Pan- theon, the lower portion could be freely cut by the window openings.

Anthemius and Isidorus, the principal "designers" of the Hagia Sophia and known respectively also as geometer and natural scientist, are often credited with having wrought new structural form from mathematical theory.'3 Yet there is no evidence that contemporary

FIG. 4.-Hagia Sophia (ca. 532-37); interior of the great dome. (Photo by R. Mark.)

12Procopius, OnJustinian's Buildings, sec. 7; trans. H. B. Dewing, in Buildings (London, 1940), pp. 20-21.

'3See, e.g., Richard Krautheimer, Early Christian and Byzantine Architecture, 3d ed. (New York, 1979), p. 215: "[Anthemius and Isidorus] were ... grounded in the theory of statistics and kinetics and well versed in mathematics . . . that could be applied to the practice of either engineering or building, be it a steam engine ... or the complex vaulting system of H. Sophia."


Byzantine mechanics was advanced enough to enable even the most elementary structural analysis. And our observation of great similarity between the profile of the original Hagia Sophia dome and that of the Pantheon further strengthens the conclusion that the later form came from an earlier one rather than from some new understanding of structure. The original dome was some 6 meters flatter than the present dome, erected after the collapse of the original following an earthquake in 558. Together with its pendentives, it formed a hemi- spherical surface whose major diameter was 46 meters, only 7 percent more than the interior diameter of the Pantheon.'4

This near-coincidence of dimensions belies a commonly held view that the scale of the Pantheon dome was matched only much later on, first by Brunelleschi's dome at Florence, completed in 1436, and then by St. Peter's in Rome, as discussed below. Moreover, the massive buttressing behind the Hagia Sophia pendentives provides support in much the same way as that provided to the lower portion of the Pantheon dome by its step rings and 6-meter-thick walls that rise well above the dome springing. Our conclusion, then, is that the designers of the Hagia Sophia also used previous experience to guide them. Although geometry did play a role in the conceptual design of this great building, it alone could never have insured stability, as is likewise illustrated by a similar development that took place seven centuries afterward in the vaults of High Gothic cathedrals.

The Transition in Gothic Vaulting With few exceptions, prior to the year 1200 square-planned, six-

part (sexpartite) vaults were used in the high bays of all the larger Gothic churches. After 1200, only rectangular-planned, four-part (quadripartite) vaults covered the soaring interior spaces (figs. 5-6). Not surprisingly, stylistic explanations for the sudden shift in vaulting predominate in the art-historical literature, which implies that the use of sexpartite vaults arose from the common practice of alternating the size and shape of the supporting piers. Since the number of vault ribs that spring from the piers with sexpartite vaulting is alternately one and three, this system is claimed to be a more logical visual com- plement to alternating piers. By the same reasoning, the stylistic theories attribute the adoption of quadripartite vaulting to the introduction of uniform, nonalternating piers.15

'4For a reconstruction of the original Hagia Sophia dome, see K. J. Conant, "The First Dome of the Hagia Sophia and Its Rebuilding," American Journal of Archeology 43 (1939): 589-91.

'5Whitney S. Stoddard, Art and Architecture in Medieval France (Middletown, Conn., 1966), pp. 130, 140, 181.

FIGS. 5, 6.-Top, clerestory and sexpartite vaulting of Bourges Cathedral (choir: ca. 1195-1214); bottom, clerestory and quadripartite vaulting of Chartres Cathedral (ca. 1194-1221). (Photos by R. Mark.)

310 Robert Mark and David P Billington Our model studies of medieval rib vaulting were originally under-

taken to determine the structural role of the vault rib.16 In the course of these studies, we found that the weight of a sexpartite vault was significantly less than the weight of quadripartite vaults covering the same area. Indeed, it became evident that the lighter weight of the sexpartite configuration derives mainly from its carrying fewer ribs than its quadripartite equivalent. The finding that the 13th-century builders, who generally favored light construction, would choose to construct heavier vaults over increasingly slender piers and walls in the tallest churches did nothing to clarify the enigma surrounding the abrupt change in vaulting form.

What provided the basis for an explanation of the change was a constructional constraint that arose during a previously unconsidered phase of vault erection.17 Consider first the salient structural feature of Gothic vaulting: the "focusing" of the distributed forces within the vaults at the points of vault support along the clerestory wall. There are three components of this focused force resultant at the springing: (1) a downward, vertical component equal to the weight of the ribbed vaulting supported by the clerestory wall, which is in turn carried by the piers of the main arcade; (2) a lateral outward, horizontal component tending to overturn the clerestory wall but resisted in the mature Gothic church by flying buttresses; and (3) a longitudinal, horizontal component against the adjacent bay along the axis of the church. This last force is ordinarily stabilized by the adjacent bay of vaulting whose longitudinal component acts in the opposite direction to that of its neighbor and eventually by the rounded apse with radial flying buttresses at one end of the vessel and by the pair of massive towers at the other end. In effect, the completed bays of vaulting all "lean" against one another.

From this brief description of the vault-supporting mechanism, it is evident that the skeletal form of the developed Gothic church could handily support either sexpartite or quadripartite vaulting. A different condition was present, however, during the vault construction, which we may assume was carried out, one bay at a time, on movable centering. Since the erection of the vaulting was necessarily preceded by the erection of the piers, walls, and flying buttresses, the vertical

16Robert Mark, John F Abel, and Kevin O'Neill, "Photoelastic and Finite-Element Analysis of a Quadripartite Vault," Experimental Mechanics 13 (1973): 322-29; and Kirk D. Alexander, Robert Mark, and John F Abel, "The Structural Behavior of Medieval Ribbed Vaulting," Journal of the Society of Architectural Historians 36 (1977): 241-51.

17William Taylor and Robert Mark, "The Technology of Transition: Sexpartite to Quadripartite Vaulting in High Gothic Architecture," Art Bulletin 64 (1982): 579-87.


weight and the outward, horizontal vault force components after the vault centering is removed are resisted by the same structural elements as in the finished church. The longitudinal component, by contrast, must at this stage have been supported mainly by the clerestory wall since there was not yet in place an adjacent vaulting bay to stabilize it. And as the springing of the vaults was raised further upward from the base of the clerestory in the later buildings (see figs. 5 and 6), resisting this thrust became a crucial problem during construction.

The modeling of Bourges sexpartite vaulting indicated a longitudinal force component of 19,000 kg, whereas, for the even slightly larger bays of Cologne Cathedral's quadripartite vaulting, the longitudinal thrust was found to be only 9,000 kg, more than a 50 percent force reduction for the quadripartite compared with the equivalent, but lighter, sexpartite vaulting. The constructional problems pre- sented by the intensity of these forces do not appear to have been acute in the early Gothic churches, where the vault springing was anchored in the typically massive wall below the clerestory. Countering this force became a major problem only with the demand for larger windows and the accompanying greater clerestory height. Hence, the later Gothic builders needed a vaulting system that generated consid- erably less longitudinal force; that is, quadripartite vaulting.

This conclusion is borne out by observing the manner in which sexpartite vaults were deployed. In every major Gothic church pos- sessing square-planned, sexpartite vaulting, the vaults spring from a massive section of wall below the clerestory. The fact that quadripartite vaulting exhibits less than half the longitudinal thrust of sexpartite vaulting must have been generally understood by the unknown master who first raised the vaults at Chartres. Its rectangular quadripartite vaults springing from a point well above the base of the clerestory allowed the potential for more light to illuminate the interior of the cathedral. The entire clerestory at Chartres is over 14 meters high, or about the same height as the nave arcade (see fig. 6). The vaults spring from a point nearly 4 meters above the base of the clerestory, a remarkable departure from earlier designs.

Quadripartite vaulting, then, helped to satisfy the Gothic urge for greater height and light. Its adoption, which allowed the structure of the mature churches to become more truly skeletal, provides addi- tional evidence of the Gothic designer's understanding of the dis- position of structural forces during the construction of the giant buildings-knowledge that could have been perceived only from observing earlier performance. It also illustrates how a primary stylistic change did not spring from formal visual analysis but, rather, from structural ideas.

312 Robert Mark and David P Billington The Domes of St. Peter's and St. Paul's

Christopher Wren (1632-1723), the architect of St. Paul's Cathe- dral, London, is often portrayed as a prototypical "scientist-architect." This reputation seems to follow from his career as professor of as- tronomy at London and Oxford, a founder and president of the Royal Society, and his appointment as Surveyor General (Royal Architect) of England as well. Yet, for historians who have searched through the documents of the era, one of the most perplexing aspects of Wren's career is the elusiveness of demonstrable connections between his scientific inquiries and his architecture. Even Wren's greatest technological and visual triumph, the design for the central dome of St. Paul's Cathedral, came not from scientific inquiry but rather from the experience of earlier construction. To understand this best, once again we return to 2d-century Rome.

The "rediscovery" of the Pantheon by the Renaissance inspired a number of major building projects. The most important of these, particularly as it relates to St. Paul's, was the rebuilding of St. Peter's Basilica in Rome, begun in 1506. Under the direction of the first principal architect, Bramante (1444-1514), construction started on the four massive piers that would support the central dome. Although Bramante apparently made no detailed design for the dome itself, these piers set the clear diameter at only a meter less than that of the Pantheon. It was left for Michelangelo (1475-1564) to plan and begin the construction of the dome, which was finally completed in 1593.

The dome of St. Peter's was plagued with structural problems from the outset. The major cause of these becomes evident when one com- pares the section of St. Peter's with that of the Pantheon (fig. 7). In the ancient building, the dome outer profile is relatively flat, and buttressing against the outward thrusts of the dome is well provided for by the massive cylindrical concrete wall. At St. Peter's, the dome exerts even greater outward thrusts, but there is only the vertical portion or the relatively thin cylindrical drum below the dome to provide resistance, and this proved to be inadequate. Thus, the dome began to crack along meridians as it spread outward. Over the years, a total of seven iron chains have been placed around the dome to prevent this spreading, but the problem is aggravated by the great weight of the masonry dome itself, which generates extremely large forces.

Although the diameter of Wren's dome was to be but three-quarters that of St. Peter's, he seems to have been alarmed by reports of problems with the Roman basilica. His close friend and fellow charter


FIG. 7.-Comparative section through the domes of the Pantheon and St. Peter's, Rome (1506-93). (After Dorn and Mark.)

member of the Royal Society, John Evelyn, had examined St. Peter's, and it was he who probably provided Wren with a firsthand account of its structural problems. Wren worried over this problem for years. He hesitated in making the final design almost until construction of the dome was begun in 1705, by which time he was already in his mid-seventies. As late as the period between 1689 and 1694, there are several references in his notes to experimental dome models, and some dome sketches made under his direction and dated 1703 are not yet the final version.

Wren's final solution is based on a majestic, lightweight outer dome profile of lead-sheathed timber supported by a thin, unseen, chain- girdled brick cone that also supports a stone lantern of some 850 tons, and a separate brick dome that is seen only from the interior (fig. 8). The conical brick cone of St. Paul's, formed from straight-line gen- erators, is compressed by the heavy lantern. Hence the cone, which provides almost all of the support for the outer dome, experiences

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FIG. 8.-St. Paul's Cathedral, London (1675-1710); section showing Wren's structural solution for the dome. (J. Gwin, ca. 1800.)

compression throughout rather than the pernicious tension charac- teristic of heavy spherical domes.18

In further contrast to St. Peter's, Wren's single iron chain proved sufficient to maintain the integrity of the relatively light structure against outward thrusts. Numerical model studies of the dome structure indicated that stresses within the supporting masonry are gen-

18It has been suggested that Wren's structural cone might have been inspired by the experiments with catenaries of his architectural collaborator and fellow member of the Royal Society, Robert Hooke, but evidence is inconclusive. See Harold Dorn and Robert Mark, "The Architecture of Christopher Wren," Scientific American 245 (July 1981): 160-75.


erally low under both gravity and wind forces and that the single chain is well'placed to fulfill its role. Had Wren arrived at this final design for the dome at an earlier stage of the project, before beginning construction of the central supporting piers, he might have perceived that the piers could have been lightened and some of the distress resulting from their settlement might have been avoided. In fact, Wren's structural scheme became the standard for all the large dome projects that followed St. Paul's well into the 19th century, including that of the dome over the U.S. Capitol. Once again, a successful form arose from careful reflection on structural difficulties observed in earlier buildings.

The origin of major new forms to allow a new scale of building in masonry derived from a structural imperative. We now see these new forms as elegant examples of the building styles of their eras. But some early architectural writers saw them as ugly (the original con- notation of "Gothic" was "barbarian"), and others explained away their origins by imagining formal connections unrelated to structure.19 The same misconceptions continue into this century, both with respect to the ancient forms and especially with the new forms that came from the introduction of new industrial building materials: metals and reinforced concrete. On more careful historical and structural study, however, we find the same structural imperatives shaping the best new forms of the modern era. Three examples will illustrate how close attention to structural performance has stimulated new form in the recent past, just as it has in the more distant eras of our culture.

From the Niagara Bridge to the Tacoma Narrows Collapse As a first example, we take the experience of John A. Roebling

(1806-69), the leading 19th-century designer of suspension bridges. Roebling is now best known for his Brooklyn Bridge, which represents the last century in the same way as a Gothic cathedral represents the 13th century. He developed his ideas for suspension bridge forms by close observation of bridge performance in the field, not by abstract reasoning. Before designing his three great bridges-at Niagara, completed in 1855; Cincinnati, completed in 1866 (fig. 9); and Brooklyn, completed after his death by his son, Washington, in 1883-Roebling carefully observed the action of numerous completed suspension bridges, including many of his own smaller ones. In 1846 he wrote: "High winds have, in several instances proved destructive to suspension bridges [designed by others] ... the injury was caused by the

19Giorgio Vasari, The Lives of the Painters, Sculptors, and Architects [1550], ed. W. Grant (New York, 1963), 1:12-13, 274-75.

315


FIG. 9.-Ohio River Bridge, Cincinnati, 1866, by John A. Roebling. (Courtesy the National Museum of American History, Smithsonian Institution.)

undulations of a very flexible floor, the rise and fall of which produced a succession of shocks. ... In [an earlier] part of this report I have explained the necessity of a stiff floor, which of itself will prevent short undulations."20 These observations led Roebling to introduce diagonal stays radiating down from the tower tops to the deck below.

Following the 1854 collapse of Charles Ellet's Wheeling Bridge of 1848, Roebling criticized Ellet's belief that the great weight of the bridge would prevent failure: "Weight is a most essential condition where stiffness is a great object, provided it is properly used in con- nection with other means. If relied upon alone, as was the case in the plan of the Wheeling Bridge ... it may become the very means of its destruction. That bridge was destroyed by the momentum acquired by its own dead weight when swayed up and down by the force of the wind." He then goes on to describe how a deck of great weight will not be much affected by moving traffic loads, but, if it has no other form of stiffness, it will be in danger of oscillation from the wind, thus: "... although the weight of a floor is a very essential element of resistance to high winds it should not be left to itself to

20J. A. Roebling, "Report and Plan for a Wire Suspension Bridge," Order of Preference of the Supreme Court of the United States (Saratoga Springs, N.Y, 1851), p. 257.


work its own destruction. Weight should be, simply, an attending element to a still more important condition, viz: stiffness."21 For Roeb- ling, that stiffness was given by a combination of diagonal stays, floor trusses, and great weight. Similar insights can be found in his abun- dant writings about his own completed works. Roebling also wrote about the aesthetics of his designs; his observation of full-scale structures was a matter of both aesthetics and safety.22

Roebling's perception of actual behavior has been obscured in the 20th century by a belief that new mathematical theories rendered past experience of little value for designers. Quite unlike Le Corbusier's idea or Summerson's belief, it never was mathematical theories that dictated handsome engineering forms. Rather, it was the experience with earlier works and the engineer's own aesthetic preferences that together permitted the new arrangements of forms-to realize a new set of orders representing pure creations of the modern era. Roebling, like such engineers as Gustave Eiffel and Thomas Telford, found the possibility for making new forms by personal aesthetic choices-choices, however, that never departed from the strict disciplines of efficient performance and economical construction. And these disciplines came directly from observations of earlier works.

With the planning of the George Washington Bridge (fig. 10) in the late 1920s, engineers did begin to rely on formulas that led to designs in violation of Roebling's mid-19th-century observations. Based on these formulas, designers once again argued that weight alone would keep the bridge stable in wind, and the result was a series of suspension bridges that had too little overall stiffness. A number had to be stiffened afterward and some are still too flexible under wind loads even today.23 One, the Tacoma Narrows Bridge, collapsed in full view of motion-picture cameras in 1940. On the basis of his experience, Othman Ammann, designer of the 1931 George Washington Bridge, recognized the basic problem and corrected his ideas, thus

21j. A. Roebling, "Memoir of the Niagara Falls Suspension and Niagara Falls Inter- national Bridge," Papers and Practical Illustrations of Public Works (London, 1856), pp. 4, 5.

22j. A. Roebling, "Report of John A. Roebling, Civil Engineer, to the President and Board of Directors of the Covington and Cincinnati Bridge Company," Cincinnati, Ohio, April 1, 1867; and J. A. Roebling, "Report of John A. Roebling, Civil Engineer, to the President and Directors of the New York Bridge Company on the Proposed East River Bridge," Trenton, N.J., September 1, 1867, pp. 17-19 (published in Brooklyn, N.Y., 1870).

2SDavid P Billington, "History and Aesthetics in Suspension Bridges," Journal of the Structural Division (American Society of Civil Engineers) 103, no. 478 (August 1977): 671-87. None of these bridges from the 1930s seems in danger of collapse now, but some must be closed in very high winds, and all must be carefully maintained.


FIG. 10.-George Washington Bridge, New York, 1931, by Othmar Ammann. (Photo by J. W. Williams.)

leading to the great designs of his later years, culminating in his masterpiece, the Verrazano-Narrows Bridge of 1964.24

It was thus that the designs of our longest spanning structures evolved from the observations of previous works and careful attention to the structural performance. Indeed, Thomas Telford designed his 1826 Menai Straits Bridge, the first modern suspension bridge, having in mind the 1818 failure of an earlier bridge at Dryburgh. New ideas proposed on the basis of research using mathematical theories proved to be misleading when disconnected from the observed experience of earlier structures. This same stimulus, difficulties with earlier structures, led Robert Maillart (1872-1940) to develop radically new forms in concrete bridges during the early 20th century.

From Aarburg Cracks to the Schwandbach Curves Robert Maillart graduated in 1894 from the Technical Institute in

Zurich just as reinforced concrete entered the practice of structural engineering. By 1902, when he founded his own firm for design and construction, he already had considerable experience with the new material. In 1903, Maillart observed cracks in his first hollow-box

24George Schoepfer, "Performance the Ultimate Judge," Long Span Bridges: O. H. Ammann Centennial Conference (New York, 1980), pp. 157-60. The Verrazano-Narrows Bridge has proved to be a model of reliable design with a minimum of maintenance.


bridge (the first one ever built in concrete), the three-hinged arch at Zuoz. That observation stimulated him to see the possibility of a completely new form that he realized in 1905 with his lens-shaped Tav- anasa Bridge.25 The same type of experience occurred again a decade later.

In 1912 Maillart completed a 60-meter-span, fixed-arch bridge at Aarburg (near Bern) over the Aare River (fig. 11). The roadway rested on concrete beams running parallel to the traffic and supported on slender columns that carried their loads to the solid arch below. As was usual then, Maillart visualized the roadway loads as carried through the beams to the columns to the arch, each element acting separately.

Some time after completion, the roadway beams developed cracks in a wholly unanticipated location: at their lower edges near the column supports. According to accepted mathematical theory, such cracks could not exist. Following World War I, when Maillart returned to bridge design, he began to think about the Aarburg problem and realized that the accepted analysis was incorrect. The observed cracks provided the clue to how the bridge really performed. The arch,

FIG. 11.-Aare River Bridge, Aarburg, Switzerland, 1934, by Robert Maillart. (Cour- tesy of M.-C. Blumer-Maillart.)

25David P. Billington, Robert Maillart's Bridges: The Art of Engineering (Princeton, N.J., 1979), pp. 34-38.

319

320 Robert Mark and David P Billington assumed immovable in the accepted analysis, must of course deflect somewhat, and that deflection must pull down the beams where they are connected to the columns. Maillart realized that it was wrong to visualize the bridge as a collection of independent elements; it had to be seen as a whole in which all the parts acted together. Then it became clear that the columns could settle (as if they were founded on com- pressible soil) and cause the beams to crack as they had.

The Aarburg Bridge, itself the problem, also provided the solution. Rather than a railing, Maillart had designed at Aarburg solid, non- structural parapet walls above the bridge deck. These walls looked stiff, and Maillart realized that he could have designed them as structural members to prevent the beam from cracking.26

In 1922, Maillart designed a small bridge over the Flienglibach above Lake Zurich, where he first put that Aarburg experience into practice. He turned the solid parapet into a structural beam by reinforcing it properly, and he considered all of its parts-beam, column, and arch-to act together as a unit. In that way, without adding much to the parapet and columns, he was able to reduce the arch thickness drastically and arrive at a structure without unsightly cracks. Much more important to Maillart, however, was the aesthetic expression of arch thinness. He found, through the discipline of field experience, the means of expressing a new vision of structure through a solution that was not at all obvious. At the same time, he found, in the writings of his former teacher, Wilhelm Ritter (1847-1906), a simple mathematical theory (first published in 1883) that could account for the behavior of this new structural form.27 Following these ideas, he went on to design masterpieces at the Schwandbach in 1933 and over the Toss River in 1934 (fig. 12).

Maillart never applied the complex new mathematical theories so popular in the 1920s which, like the suspension bridge theories (discussed above), would have taken him away from those design ideas leading to new forms with improved performance. Moreover, Maillart's bridge forms stimulated him to see possibilities for new building design, the best known of which was the Chiasso shed of 1925. The frame of the Chiasso roof consists of a gabled upper chord stiffened by the concrete roof slab and a light lower chord in the form of an inverted arch.28 The combination of stiff and more flexible slender

26Ibid., pp. 70-73. 27Wilhelm Ritter, "Statische Berechnung der Versteifungsfachwerke der Hange-

briicken," Schweizerische Bauzeitung 1, nos. 1-6 (January 6, 13, 20, 27, February 3, 10, 1883): 6-7, 14, 19-21, 23-25, 31-33, 36-38.

28Robert Mark, James K. Chiu, and John E Abel, "Stress Analysis of Historic Struc- tures: Maillart's Warehouse at Chiasso," Technology and Culture 15 (January 1974): 49-63.


FIG. 12.-Toss River Bridge near Winterthur, Switzerland, 1934, by Robert Maillart. (Photo by D. P. Billington.)

members comes from his deck-stiffened arch bridges, of which the T6ss was Maillart's last example.

The potential for roof forms promised by this remarkable work has yet to be fulfilled, largely because architects, and engineers too, are caught in the trap of imagining that only architects can move us by their forms-because engineers merely carry out mathematically de- termined results. Yet the works of John Roebling and Robert Maillart show clearly that those engineers were guided as much by aesthetics as by mathematics. Within the discipline of performance and cost, they found the means to play with form in a personal and expressive way.

To see how this discipline and play lead to new forms when focused on the structural imperative, we turn in conclusion to the works of a later engineer, Fazlur Khan (1930-82), who, partly under the influ- ence of Maillart, showed how completely new forms can arise in large urban buildings when the designer takes to heart the supposedly outmoded ideas of Viollet-le-Duc.

High Buildings and New Orders Just as Viollet-le-Duc's rationalism influenced architects of the stat-

ure of William Jenney, Louis Sullivan, John Root, and Ludwig Mies

322 Robert Mark and David P. Billington van der Rohe, so have their works and ideas stimulated a new generation of designers, mainly in Chicago, to seek new forms out of new materials.29 By the 1960s, this search had begun to take seriously the efficiency of structure as well as the symbolic value that had been so important to the earlier architects. From this synthesis of the symbolic nature of structure with its purely load-bearing meaning came a series of urban buildings whose forms are original in the same sense as the Hagia Sophia dome and the Chartres vaulting. Indeed, the problems of structure that gave rise to those innovative ancient forms are the same ones that stimulated the new forms of the 1960s. The difference, of course, lies in the new materials: reinforced concrete and structural steel, whose properties differ radically from those of masonry.

A group of engineers and architects working in the Chicago office of Skidmore, Owings & Merrill (SOM) sought in the 1960s to understand these characteristics through a series of designs that stand today as exemplars of Viollet-le-Duc's ideas.30 We shall illustrate these studies by a set of buildings in reinforced concrete which are typical of the approach of Fazlur Khan, structural engineer-designer of these new forms. Khan worked closely with two architects, Myron Goldsmith and Bruce Graham, who both well understood how the specific visual forms discussed here could come essentially from structural engineering ideas.

In the Hagia Sophia, the elegant lightening of the support of the dome arose out of structural ideas first discerned in earlier domes such as the Pantheon. This same inseparable synthesis of structure and form accounts for the fully original transfer girders of the Walker Building at Two Shell Plaza in Houston, Texas (fig. 13), and the Marine Midland Bank Building in Rochester, New York (fig. 14).

The fundamental difference between reinforced concrete and masonry is the tension resistance of the former, which can therefore be formed in long straight elements (girders and columns). The ancient domes, vaults, and buttresses could not be formed with straight elements of any but very short spans (such as Greek lintels). Yet the straight elements of reinforced concrete lead easily to forms themselves copied from wooden or metal structures of the 19th century. The Chicago designers avoided both the temptation to conceal the transfer of forces and the tendency to express that transfer through forms derived from wood or metal structures-but they did not arrive at the new forms without earlier experience.

29Carl Condit, The Chicago School of Architecture: A History of Commercial and Public Buildings in the Chicago Area: 1875-1925 (Chicago, 1964).

30Myron Goldsmith, Buildings and Concepts, ed. Werner Blaser (New York, 1987).


FIG. 13.-Two Shell Plaza, Houston, 1968. Skidmore, Owings & Merrill: Bruce Gra- ham, architect; Fazlur Khan, engineer. (Photo by J. W. Williams.)

The horizontal girder was clearly isolated as a load-carrying element in the Dewitt-Chestnut apartment house of 1963 and then even more powerfully in the 1965 Brunswick Building; in both cases these transfer girders are visually distinct from the closely spaced grid above. This expression would be natural for prefabricated elements in wood or steel but not for cast-in-place concrete. Khan, reflecting on these earlier solutions, explored other load-transfer designs that would be more appropriate to reinforced concrete.


FIG. 14.-Marine Midland Bank Building, Rochester, New York, 1968. Skidmore, Owings & Merrill: Bruce Graham, architect; Fazlur Khan, engineer. (Photo by J. W. Williams.)

As with Maillart, Khan was strongly influenced by observing cracking in earlier concrete works. An engineering colleague, Mark Fintel, relates how Khan reacted when "I invited Khan to visit a newly completed 30-story apartment building in which every other column in the ground floor was eliminated without adding a transfer girder. The entire 30-story elevation of exposed columns was handled as a Vi- erendel [sic] truss (a truss without diagonals). We happened to visit


the building after a rain, and the shear cracks in the spandrel beams of the lower stories were visually amplified by the rain. This picture was not lost on Khan as shown in the two approaches he subsequently used in buildings he designed."31

In one of these, the 1968 Walker Building, Khan, working with Graham, abandoned the separate transfer girder with its very high shear forces and instead played with the columns and beams of the standard grid above. By forming haunched beams (vertically deeper near the columns) and by widening the columns, he created a structural means of transferring the forces within the grid without creating a separated horizontal girder. In the same year, again with Graham, he explored another solution, for the Marine Midland Bank, where he kept the beams straight but increased the columns near the base in both width and thickness. He emphasized the thickness increase by allowing the columns to protrude beyond the facade and thus gave the lower stories of the building an undulating wall.

The central structural idea in both of these buildings is that each column, at any floor level, carries a portion of the total vertical floor load virtually equal to its contribution to the total stiffness at that level. Thus, if there are four columns, each of stiffness A (where A is the cross-sectional area of the column), and four other columns, each of stiffness 2A (giving a total floor stiffness of 12A), then one of the A-columns will carry one-twelfth of the total load and one of the 2A-columns will carry one-sixth of the total load. In that way Khan directed the path of the loads by the design of the columns, and he made sure that the stiffness differences were visually clear. We actually see the flow of forces in the facade. The function (load carrying) therefore follows form (the visual expression of relative stiffness).

The Marine Midland and Walker buildings achieve an arching effect with straight elements, yet those elements are freely shaped in ways quite inappropriate for wood or metal. In short, by abandoning forms of masonry arches or standardized steel shapes, Khan and Graham created transfer forms that are decisively new. The ideas grew out of earlier experience and from observations of cracks, but they also came from a motivation to play with concrete in a purely rational way. Khan's two quite different solutions show that rational design does not lead to a single optimal solution; rather, it opens up limitless new possibilities.

31Mark Fintel, "New Forms in Concrete," Technique and Aesthetics in the Design of Tall Buildings, Proceedings of the Fazlur R. Khan Session on Structural Expression in Build- ings, ed. David P. Billington and Myron Goldsmith (Bethlehem, Pa.: Institute for the Study of High-Rise Habitat, Lehigh University, 1986), p. 41.

325

326 Robert Mark and David P. Billington Just as the transfer girder provides a solution for vertical gravity

loads, high buildings also need a solution for horizontal wind (and earthquake) loadings. Under the supervision of Mies van der Rohe, Myron Goldsmith completed a Master's thesis at the Illinois Institute of Technology (IIT) in 1953; in it he proposed the design of tall buildings with exterior X-bracings fully exposed over each entire facade. In 1968, when Khan and Goldsmith were both teaching and practicing as partners at SOM, they developed as well a solution to create a rigid concrete tube in a student thesis project at IIT.32

It was not until the 1980s that Khan was able to design a major concrete building with that expression, and two were completed-but both after his death in 1982. He achieved the diagonal bracing merely by filling in windows and adding diagonal reinforcement. The rest of the wall members could be more lightly reinforced, and the resulting structure became stiff against wind loads as well as highly expressive. The first of these buildings, in 1985, was 780 Third Avenue in New York City, and the second, in 1986, was the Onterie Building in Chi- cago, designed with Graham.33 (See figs. 15 and 16.) In the latter, the concrete is exposed and the braced structure carries the visual design of the building fully to the exterior. The central structural idea in both of these buildings is that it is more efficient (i.e., requires less material) to carry wind loads by exterior walls than by an interior core, and that the designer can make those walls both light and stiff by forming the walls out of a few slender interconnected elements rather than from a solid mass. In principle, this lightness is similar to that achieved in the walls of Gothic cathedrals after the introduction of exterior flying buttresses.

Conclusion A major goal of our studies is to develop a critical approach to

contemporary, large-scale architecture from the perspective of engineering. This perspective, we feel, is best derived from detailed (and inseparable) archaeological and structural investigations both of past monumental buildings and of large-scale contemporary buildings as well as analyses of the working modes and backgrounds of their de-

32Myron Goldsmith, "Fazlur Khan's Contributions in Education," ibid., pp. 17-37. For Khan's work with Graham, see Bruce J. Graham, "Collaboration in Practice between Architect and Structural Engineer," ibid., pp. 1-15.

33J. S. Grossman, "780 Third Avenue-First High Rise Diagonally Braced Concrete Structure," Concrete International 7, no. 2 (February 1985): 53-56;J. S. Grossman, Mark Curvellier, and Bryan Stafford-Smith, "Braced-Tube Concrete Structure," Concrete In- ternational 8, no. 9 (September 1986): 32-42; and John J. Zils and Ray S. Clark, "The Concrete Diagonal," Civil Engineering, October 1986, pp. 48-50.

FIG. 15.-780 Third Avenue, New York City, 1985; structural form from Fazlur Khan. (Photo by J.W. Williams.)

FIG. 16.-The Onterie Building in Chicago, 1986. Skidmore, Owings & Merrill: Bruce Graham, architect; Fazlur Khan, engineer. (Courtesy of Skidmore, Owings & Merrill.)


signers. We seek to illuminate technological precedents that have important implications for contemporary design. For example, our past investigations, beginning with ancient Roman buildings, have indicated that builders have always taken a keen interest in minimizing costs of construction-which included the expense of obtaining and transporting materials as well as of shaping and erection. The early designers also appreciated the technical advantages of reducing structural weight that, in turn, diminishes internal forces in supporting members.

Carl Condit, the leading historian of American building, made similar observations about the "skeletal structure of modern skyscrapers, the most radical transformation of the structural art since the development of the Gothic." Condit recognized in both the ancient and modern an "indissoluble unity of structure and form."34 Indeed, this unity is the basis for a more complete understanding of all large-scale buildings. Yet all of these observations are strikingly at odds with much contemporary architectural theory in which the weight and cost of building play no role at all. By contrast, historical study shows the constraints of minimizing materials and costs to have been a spur to imaginative designs of great elegance.

The best engineer-designers did not devise building forms solely from applied science or out of any belief that efficiency and economy alone would lead to appropriate forms. Many other engineers, of course, hold such beliefs, but this is not the case with the best, with men such as Roebling, Maillart, Khan, and many others working today. These engineers design by combining passion with discipline and hold the aesthetic and the cultural meaning of their designs to be central. The major challenge is to convey to the nonspecialist the technical basis of structural form because there is so little writing by engineers aimed at interpreting their own designs. Without such interpretation, it is easy to think of engineering as merely an applied science and to conceive of the idea that only an architect can give modern structures aesthetic or cultural meaning. Our research and studies by many others show convincingly, we believe, that outstanding modern engineers have succeeded in expressing the highest aspirations of our society by designing buildings with that "indissoluble unity of structure and form" in the same general way as did the Gothic master builders.

34Condit (n. 29 above), pp. 79, 91.

structural imperative and the origin of new form - canvas

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