Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium 2013 „BEYOND THE LIMITS OF MAN” 23-27 September, Wroclaw University of Technology, Poland J.B. Obr ębski and R. Tarczewski (eds.)

Norfolk Scope Arena: A US Dome with a Unique Configuration of Interior Ribs and Buttresses

Edward M. Segal 1, Sigrid Adriaenssens 2

1Ph.D. Candidate, Department of Civil and Environmental Engineering, Princeton University, Princeton, NJ, USA, [email protected] 2Assistant Professor, Department of Civil and Environmental Engineering, Princeton University, Princeton, NJ, USA, [email protected]

Summary: This paper compares Pier Luigi Nervi’s Norfolk Scope Arena (Norfolk, US, 1970) to his earlier domes and to other long span concrete domes built in the United States of America (US) in the 1960s and 1970s. The first objective is to show the progression in Nervi’s dome designs. This paper identifies chronologically when interior ribs and buttresses (inclined columns), prominent elements at Scope Arena, initially appear in Nervi’s domes. The second objective is to demonstrate the various ways Nervi details these elements in his domes. After showing this diversity broadly across eight of his works, the paper describes specifically how the interior ribs and buttresses are configured at Scope Arena and then compares this arrangement to those of the visually different Little and Large Sports Palaces (Rome, Italy 1957 and 1960, respectively). The third objective is to show that Scope Arena’s ribs and buttresses give the shell a unique form among other US domes from the same era. Comparisons in this paper seek to place Scope Arena in the context of its contemporaries so that its contributions to the field of thin concrete shell roofs can be better understood.

Keywords: Pier Luigi Nervi, reinforced concrete dome, thin concrete shell, precast, buttress, rib, tension ring

1. INTRODUCTION prominent elements at Scope Arena, initially appear in Nervi’s domes. The second objective is to demonstrate the various ways Nervi details Today, despite the international decline in the construction of thin these elements in his domes. After showing this diversity broadly concrete shell roofs that began in the 1960s [1], the dome is one across eight of his works, the paper describes specifically how the reinforced concrete shell type that is still being constructed in great interior ribs and buttresses are configured at Scope Arena and then numbers in the United States of America (US). Engineers have compares this arrangement to those of the visually different Little and continued to build domes because air-supported formwork makes Large Sports Palaces. The third objective is to show that Scope Arena’s construction of this shell type economical [2]. While dimensions vary, ribs and buttresses give the shell a unique form among other US domes there is little play in these forms; domes have smooth interiors and from the same era: the University of Illinois, Assembly Hall exteriors and the thrust forces at their bases are resisted by below- (Champaign, US, 1963), the University of Virginia, University Hall ground or elevated ring beams. These shells are economical, but are not (Charlottesville, US, 1965), and the Kingdome (Seattle, US, 1976 and as visually interesting as some of the domes that preceded them. The demolished in 2000). Comparisons in this paper seek to place Scope Norfolk Scope Arena (Fig. 1) is an example of a US dome whose form Arena in the context of its contemporaries so that its contributions to contrasts sharply with the domes built using air-supported formwork. the field of thin concrete shell roofs can be better understood. Studio Nervi consulted on the project and the structure features Pier Luigi Nervi’s characteristic interior ribs and buttresses (inclined 2. PROGRESSION IN NERVI’S DOMES columns). The structure’s design was completed collaboratively with Williams and Tazewell & Associates (architects) and Fraioli-Blum- Nervi designed a number of domes prior to Scope Arena. Table 1 Yesseleman (structural consultants). This paper does not attempt to summarizes key dimensions and design details for seven of these clarify the role that Studio Nervi and Pier Luigi Nervi specifically earlier domes and Scope Arena (terms in the table are defined in the played in the design and construction of Scope Arena. Whatever section as specific elements are discussed). Two of these designs, Nervi’s involvement, it is clear that the form of Scope Arena is competition entries for a Sports Palace in Vienna (Vienna, Austria, reminiscent of his earlier domes such as the Little and Large Sports 1953) and a Sports Palace and Exhibition Hall for the Genoa Fair Palaces. (Genoa, Italy, 1961), were never built. Once Nervi introduced elements such as interior ribs and buttresses they became part of his vocabulary and appeared in many, if not all of his later domes.

2.1. Interior Ribs in Nervi’s Domes The 40 m half-dome at the Exhibition Hall, Salone Principale (Turin, Italy, 1949) is Nervi’s first dome at a significant scale that featured interior ribs (Fig. 2). To construct the half-dome (Fig. 3), Nervi combined precast and cast-in-place elements in a way that he had only previously attempted on “. . . works of minor importance” [3, p. 69]. For the Salone Principale Nervi used precast diamond-shaped panels as forms (supported on scaffolding) for the cast-in-place concrete that once cured acted compositely with the panels to form a shell with interior ribs. Nervi’s decision to use precast ribs followed from his earlier difficulties with a cast-in-place monolithic dome for the church of San Marcellino in Genoa [4] and the shortage of timber in Italy that necessitated minimizing formwork [5]. At that time, Nervi had experience with combining precast and cast-in-place elements for his barrel vaults (e.g. airplane hangars for the Italian Air Force, Orbetello, Fig. 1. Scope Arena’s exterior showing Nervi’s characteristic buttresses Orvieto, and Torre del Lago, Italy, 1939-1941 [6], [7]) and he realized [Photo: Yoshito Isono/www.aloss.jp] that combining these elements (albeit in a different way) for a dome would offer construction benefits. He developed this specific The first objective is to show the progression in Nervi’s dome designs. construction procedure while his office was closed in 1944 during This paper identifies chronologically when interior ribs and buttresses, World War II [4].

1 Table 1: Dimensions and design details for Nervi’s domes

Precast elements Rib-to-buttress Dome Year i Buttresses Approximate shape in plan forming ribs member(s) 1. Salone Principale 1949 40 m diameter semicircle Diamond-shaped None -- 2. Salone C 1950 31.1 m by 45.8 m rectangle Diamond-shaped Inclined arches (one tier) Edge beams 3. Festival Hall 1952 25.9 m by 32 m ellipse Diamond-shaped None -- ii 4. Sports Palace, Vienna 1953 > 84 m diameter circle Corrugated Simple cross-sections Edge ring (multiple tiers) beam 5. Little Sports Palace 1957 59 m diameter circle Diamond-shaped Y-shaped in plan with simple Transitional cross-sections (one tier) elements 6. Large Sports Palace 1960 100 m diameter circle Corrugated Complex cross-sections Transitional iii (multiple tiers) elements ii 7. Sports and Exhibition Hall 1961 100 m diameter circle Corrugated Simple cross-sections Edge ring (multiple tiers) beam 8. Scope Arena 1970 99.5 m diameter circle Triangular-shaped Complex cross-sections (one Edge ring tier) beam i The authors used the clear span between supporting members at the dome’s base when listing plan dimensions. ii These domes were never built. iii The most visually prominent tier, the middle tier, has complex cross-sections.

interior ribs formed from these diamond panels, similar triangular panels, or precast corrugated elements with transverse stiffeners (Fig. 4). To build a corrugated dome, the precast elements were arranged on scaffolding, concrete was cast in the valleys of the corrugations, precast slabs closed the elements at their tops, and concrete was cast along joints between adjacent elements to create continuity [4]. The timeline in Fig. 5 shows by minimum span the type of precast elements used in the domes listed in Table 1. Note that the minimum span for Salone Principale is taken as half the diameter, 20 m. Aside from Scope Arena which has triangular panels, the corrugated elements were used or (planned to be used) for spans greater than 60 m while diamond panels were used for spans less than 60 m.

Fig. 2. Salone Principale is Nervi’s first dome with interior ribs [Photo: Nervi, P. L., The Works of Pier Luigi Nervi , p. 69]

Fig. 4. Precast corrugated element for the Large Sports Palace [Drawing: Nervi, P. L., Aesthetics and Technology in Building , p. 168]

2.2. Buttresses in Nervi’s Domes Fig. 3. Salone Principale under construction showing the precast elements in Unlike interior ribs, buttresses do not appear in all of Nervi’s major place [Photo: Nervi, P. L., Aesthetics and Technology in Building , p. 125] domes; they are not present in two early works, the Salone Principale When reflecting on Salone Principale Nervi stated : “The process proved and Festival Hall (Chianciano Terme, Italy, 1952). Nervi’s original to be very effective from a technical and economic point of view and sketches for Salone Principale indicate that he was considering using a resulted in great plastic richness” [4, p. 103]. This half-dome showed the combination of buttresses and vertical columns to support the dome potential of the construction method and the resulting elegance at a (Fig. 6). By then Nervi had experience using buttresses to support many large-scale. Nervi’s major long span domes that follow all feature of his barrel vaults including the one over the main area of the Salone

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Principale, so it is not surprising that he considered using them to The timeline in Fig. 10 shows which Nervi domes have buttresses (see support his domes. However, in the final structure the buttresses were Figs. 8 and 9 for load paths for domes with and without buttresses). For omitted. At the dome’s base the thrust forces are carried into a slab and those domes with buttresses the timeline makes three additional then into what Nervi refers to as “. . . special reinforced concrete distinctions: i) one tier vs. multiple tiers, ii) simple vs. complex cross- structures which remained hidden in the wall which divides the main sections, and iii) edge beams vs. transitional elements. One tier vs. hall from the semicircular area” [4, p.102]. While Nervi developed a multiple tiers indicates whether there are one or more buttress levels in feasible solution to accommodate the shell’s asymmetry, he elevation. Simple vs. complex cross-section refers to how much bi- uncharacteristically concealed the structural system. The buttresses directional cross-section variation the buttresses have along their would have clearly indicated how the thrust forces are carried to the lengths. Simple means little variation while complex means significant ground and additionally would have provided visual continuity at the variation. Edge beams vs. transitional elements differentiates between transition between the dome and adjacent barrel [7]. Nervi’s next dome, the types of members at the interface between ribs and buttresses. Edge Salone C (Turin, Italy, 1950), was his first to use buttresses, a set of beams are continuous members that act like transfer girders at the inclined arches (Fig. 7). dome’s base whereas transitional elements are discrete components that channel loads from multiple ribs to a single buttress.

Fig. 8. Section of a dome with buttresses showing the load path with black arrows and reactions with red arrows. The buttress carries the Fig. 5. Timeline showing by minimum dome span the type of precast loads directly to a below-ground tension ring. elements used in Nervi’s domes. Dome names are abbreviated. See Table 1 for full names.

Fig. 6. Original sketch for Salone Principale showing buttresses [Drawing: Nervi, P. L., The Works of Pier Luigi Nervi, p. 68]

Fig. 9. Section of a dome without buttresses showing the load path with black arrows and reactions with red arrows. A frame transfers the loads from the dome to the footings. An alternative to the frame could be a wall that supports vertical and horizontal loads. The timeline in Fig. 10 demonstrates that Nervi not only consistently included buttresses in his work beginning in 1953, but also varied the configurations of these elements.

3. SCOPE ARENA’S FORM Scope Arena is a multi-purpose stadium that is circular in plan. Covering the stadium is a dome with a clear span of 99.5 m. The base and crown of the dome are 12.6 m and 29.7 m above the ground, respectively. Fig. 7. Salone C is Nervi’s first dome with buttresses, a set of inclined Loads from the dome are carried compositely by the shell (14.3 cm arches [Photo: Nervi, P. L., Aesthetics and Technology in thick, minimum) and stiffening ribs (variable depth and width) to a cast- Building, p. 126] in-place edge ring beam (approximately 4.5 m deep by variable width)

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Fig. 10. Timeline showing which Nervi domes have buttresses and design details for those domes. Dome names are abbreviated. See Table 1 for full names. Schematics include examples of simple and complex cross-sections as well as domes with edge beams (shaded) and transitional elements (shaded) that is supported by a set of cast-in-place buttresses. An edge beam is 3.1. Scope Arena’s Interior Ribs required because the dome’s buttresses do not align with the ribs. The Early design drawings show the dome constructed with precast buttresses then transfer the loads to a below-ground cast-in-place post- diamond-shaped elements [9]. However, in the final shell precast tensioned ring (0.91 m deep by 6.43 m wide). Table 2 summarizes the triangular-shaped elements were used (Figure 11). In plan the precast dimensions for the dome, interior ribs, edge ring beam, buttresses, and elements create a set of hoop ribs and a set of ribs that radiate from the post-tensioned ring [8]. center of the dome (Figure 12). The direction of the dome’s hoop and meridian stresses align with the hoop ribs and the angle bisector of the Table 2: Dimensions for Scope Arena radiating ribs, respectively. The ribs vary in depth from 36.4 cm to 55.8 cm and in width from 11.4 cm to 33.8 cm [8]. Description Dimension(s)

Dome span 99.5 m

Height of dome crown above 29.7 m ground

Height of dome base above 12.6 m ground

Shell thickness Varies: 14.3 cm to 19.1 cm

Precast 5.1 cm

Cast-in-place Varies: 9.2 cm to 14 cm

Rib depth (precast only) Varies: 36.4 cm to 55.8 cm Fig. 11. Scope Arena under construction showing the precast elements being placed [Photo: Rome, MAXXI, Archivio Pier Luigi Nervi] Rib width Varies: 11.4 cm to 33.8 cm 3.2. Scope Arena’s Buttresses Edge ring beam 4.5 m by varying from 0.67 m There are forty-eight buttresses with complex cross-sections arranged to 1.18 m in pairs to form twenty-four V-shaped elements. The bottom of each V frames into a base element that transfers the loads from the buttresses Buttresses Complex cross-sections to a below-ground post-tensioned ring. These base elements increase in dimension at the ground to almost the full width of the tension ring Post-tensioned ring 0.91 m by 6.43 m (Fig. 13).

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Fig. 13. Scope Arena section showing edge ring beam at base of dome, buttress, buttress base element, and below-ground post-tensioned ring. Annotations added by the authors. [Drawing: Courtesy of the City of Norfolk, Virginia, excerpted from Drawing A-119]

Fig. 12. Scope Arena quarter plan showing ribs, edge ring beam at base of dome, and buttresses. Annotations added by the authors. [Drawing: Courtesy of the City of Norfolk, Virginia, excerpted from Drawing S-159]

4. A COMPARATIVE ANALYSIS OF SCOPE ARENA AND THE LITTLE AND LARGE SPORTS PALACES Among Nervi’s domes, Scope Arena is most similar to the Little and Large Sports Palaces; however, all three feature different configurations of interior ribs and buttresses. Table 3 expands on Table 1 and Fig. 10 to provide additional information on these elements in the three domes.

4.1. Interior Rib Comparisons – Nervi’s Domes Scope Arena’s span, 99.5 m, is approximately the same as the Large Sports Palace’s span, 100 m. However, Nervi opted to use precast triangular-shaped panels closer in form to the diamond-shaped panels at the Little Sports Palace (Fig. 14), than to the corrugated elements at the Large Sports Palace (Fig. 15). The triangles produce hoop ribs that interrupt the continuity of the ribs radiating from the center. This rib Fig. 14. The Little Sports Palace’s interior showing ribs formed from network is visually dense; more of the shell body would have been precast diamond-shaped panels [Photo: David P. Billington] visible if triangular elements were combined into diamonds as shown in early design drawings. Table 3: Dimensions and design details for the Little Sports Palace, the Large Sports Palace, and Scope Arena

Little Sports Palace Large Sports Palace Scope Arena Year 1957 1960 1970 Diameter in plan 59 m 100 m 99.5 m Precast elements forming ribs Diamond-shaped Corrugated Triangular-shaped Buttresses Number in one tier 36 48 48 (24 pairs) Number of tiers 1 3 (one tier consists of the 1 transitional elements) Form Y-shaped in plan with Linear in plan with complex cross- Each pair is V-shaped in plan with simple cross-sections sections (middle tier) complex cross-sections Rib-to-buttress member(s) Transitional elements Transitional elements Edge ring beam

5 The Large Sports Palace’s transitional elements are similar to those used in the Little Sports Palace except there are no openings between elements in the latter (Fig. 18). Transitional elements clearly articulate the load path and provide visual continuity between interior ribs and buttresses that do not align. Scope Arena lacks these transitional elements and instead features an inexpressive ring edge beam that is made worse by a precast gutter on the exterior. While at the Little Sports Palace the true thickness of the shell is visible from the exterior, at Scope Arena the edge elements obscure the shell’s lightness and disrupt the visual tie between the dome’s interior and exterior.

Fig. 15. The Large Sports Palace’s interior showing ribs formed from precast corrugated elements [Photo: David P. Billington]

4.2. Buttress Comparisons – Nervi’s Domes The overall buttress arrangement at Scope Arena, a single tier of twenty-four pairs of V-shaped (in plan) buttresses is similar to the Little Sports Palace’s arrangement of thirty-six Y-shaped (in plan) Fig. 18. Transitional elements at the base of the Little Sports Palace’s ribs buttresses. In contrast, the Large Sports Palace has three tiers of [Photo: Edward M. Segal] buttresses to transfer the reactions from the dome to the ground (Fig. 16). The upper tier is essentially a set of transitional elements that The detailing of Scope Arena’s buttresses is closest to the detailing of direct the loads from the dome’s ribs to the linear (in plan) middle tier the Large Sports Palace’s middle tier of buttresses. These elements buttresses (Fig. 17). have complex cross-sections that vary in two dimensions. At Scope Arena this shaping is extended to the buttress bases. Visually, these bases are more prominent than those at the Roman domes and also express the tension ring required to resist the dome’s thrust forces. In contrast, where the Little Sports Palace’s buttresses meet the ground, the base is only slightly larger than the buttress. The tension ring is not directly below the ground and the buttress continues into the ground and then flares out into a larger base where it meets the tension ring (Fig. 19) [10]. There is no expression of the size of the tension ring above ground. The Large Sports Palace falls between Scope Arena and the Little Sports Palace in terms of expression at its buttresses’ bases. For the Large Sports Palace’s upper buttress tier, the bases are visible, but do not have to be significant in size because the loads are being transferred to the middle tier of buttresses. For the middle tier the bases again do not have to be that large. The change in cross-section occurs below the slab, at the top of the lower tier buttresses; there is no visual expression of the cross-section increase above the slab. Finally, the lower tier buttresses have significant bases, but they occur below ground (Fig. 16) [4]. Fig. 16. Large Sports Palace section showing three buttress tiers. Annotations added by the authors. [Drawing: Nervi, P. L., Aesthetics and Technology in Building , p. 157]

Fig. 19. Little Sports Palace section showing the buttress where it meets the ground and the below-ground tension ring. Annotations added by Fig. 17. Transitional elements at the base of the Large Sports Palace’s ribs the authors. [Drawing: Parme, CSAC, Archivio Pier Luigi Nervi, [Photo: Edward M. Segal] excerpted from drawing 128e]

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5. A COMPARATIVE ANALYSIS OF SCOPE AREAN AND OTHER US DOMES Scope Arena’s form shares some features with other long span, circular in plan US domes, but these similarities are not as evident as those between Nervi’s domes. Table 4 summarizes key dimensions and design details for these domes.

5.1. Rib Comparisons – US Domes All four US domes have stiffening ribs, but their configurations vary and produce different visual results. Assembly Hall (Fig. 20) is constructed from cast-in-place folded-plates with ribs stiffening the valleys and peaks [11]. The corrugations and ribs are visible from both the interior and the exterior with a visual effect that is closer to that of the Large Sports Palace than that of Scope Arena. Both the Kingdome (Fig. 21) and University Hall (Fig. 22) have radial arch ribs. At the former the ribs are on the exterior, while at the latter the ribs are on the interior and supplemented with transverse stiffening ribs. As a result of the ribs’ location and the dome’s scalloped geometry, the Kingdome’s exterior resembles University Hall’s interior. While University Hall’s two-way series of interior ribs are the closest visually to those at Scope Arena, they also articulate a different load path. At University Hall the Fig. 21. The Kingdome’s exterior showing the radial arch ribs and tension dome is a set of curved shell panels supported on a system of arches ring at the dome’s base [Photo: Jack V. Christiansen] and stiffened by transverse ribs. The arches transfer the dome’s loads to its base [12]. In contrast, at Scope Arena the ribs and shell work compositely to support the dome’s loads.

Fig. 20. Assembly Hall’s exterior showing its folded plates and Fig. 22. University Hall’s interior showing its two-way series of ribs buttresses [Photo: Yoshito Isono/www.en.structurae.de] [Photo: Greenstrat at Wikimedia Commons, in the public domain]

Table 4: Dimensions and design details for US domes

Assembly Hall University Hall Scope Arena Kingdome

Year 1963 1965 1970 1976, demolished in 2000

Structural Ammann & Whitney Severud Associates Studio Nervi and Fraioli-Blum- Skilling, Helle, Christiansen, designer Yesseleman Robertson

Diameter 121.9 m 85.9 m 99.5 m 201.6 m

Ribs Radial, interior and Radial and transverse, Radiating and hoop, interior Radial, exterior exterior interior

Buttresses One tier None One tier None

Tension ring Elevated, base of dome Elevated, base of dome Below-ground Elevated, base of dome location

7 5.2. Buttress Comparisons – US Domes Yoshito Isono permitted us to use their photographs. David Fagan at the Department of Public Works in Norfolk, VA, provided us with copies of Unlike Scope Arena where its tension ring is below ground, the other the Norfolk Scope Arena drawings. three shells have their tension rings elevated above the ground at the dome bases (Fig. 23) [11], [12], [13]. With the thrust forces carried by 8. REFERENCES the elevated tension rings, only vertical forces are transferred to the ground. Vertical forces are carried by vertical columns at University [1] Billington D. P. and Segal E. M., The Decade 1960-1969: The Hall and the Kingdome and by buttresses at Assembly Hall. Assembly First Ten Years of the IASS , In: Mungan I. and Abel J. F. (eds) Hall’s buttresses lean away from the dome’s center in contrast to those Fifty Years of Progress for Shell and Spatial Structures; In at Scope Arena that follow the angle of the dome’s resulting forces. Celebration of the 50 th Anniversary Jubilee of the IASS (1959- Structurally, it is inefficient to transfer only vertical forces through 2009) , International Association for Shell and Spatial Structures inclined elements. Assembly Hall’s buttresses support loads from (2011). elements other than the dome that may justify their use instead of [2] South D. B., Economics and the Thin Shell Dome , Concrete vertical columns or perhaps the buttresses are provided for functional International, Vol. 12, No. 8 (1990) pp. 18-20. and/or aesthetic reasons. Visually these buttresses close off the base whereas at Scope Arena the base is open and looks lighter. [3] Nervi P. L., Structures , McGraw-Hill Book Company, Inc. (1956), Trans. Salvadori G. and Salvadori M. [4] Nervi P. L., Aesthetics and Technology in Building , Harvard University Press (1965), Trans. Einaudi R. [5] Nervi P. L., Concrete and Structural Form , The Structural Engineer, Vol. 36, No. 5 (1956) pp. 155-169. [6] Nervi P. L., Precast Concrete Offers New Possibilities for Design of Shell Structures , Journal of the American Concrete Institute, Vol. 24, No. 6 (1953) pp. 537-548. [7] Nervi P. L., The Works of Pier Luigi Nervi , Frederick A. Praeger, Inc., Publishers (1957), Trans. Priefert E., Figure captions, Joedicke J. [8] Final Norfolk Scope Arena design drawings, 1968, located in Norfolk, VA, Department of Public Works. [9] Early Norfolk Scope Arena design drawings, located in Rome, MAXXI, Archivio Pier Luigi Nervi. [10] The Little Sports Palace design drawings, 1956-1957, located in Parme, CSAC, Archivio Pier Luigi Nervi. Fig. 23. Section of a dome without buttresses showing the load path with [11] A New Machine Prestresses a Folded-Plate Concrete Dome , black arrows, the reactions with a red arrow, and the force in the tension Engineering News-Record, Vol. 168, No. 21 (1962) pp. 44-46. ring resisting the thrust force with a blue arrow [12] Berger H., Scalloped Prestressed Dome from Prestressed Elements , Journal of the American Concrete Institute, Vol. 63, No. 6. CONCLUSIONS 3 (1966) pp. 313-323. Scope Arena was constructed late in Nervi’s career and prominently [13] Christiansen J. V., The Kingdome , ASCE Fall Convention and features interior ribs and buttresses in a new configuration. By that time, Exhibit, San Francisco, Preprint 2946 (1977) pp. 1-26. these were Nervi’s characteristic elements; he had already combined them at previous domes in various ways. This paper began by identifying Salone Principale and Salone C as the first Nervi domes to feature interior ribs and buttresses, respectively. Next, this paper showed the variety in which Nervi configured these elements in his domes, first, broadly across eight of his works and then, specifically through comparisons between Scope Arena and the Little and Large Sports Palaces. The most distinctive features of Scope Arena are the buttresses and the buttress bases with their complex cross-sections. The buttress bases are especially significant because they express the below-ground tension ring required to resist the dome’s thrust forces. Finally, this paper compared Scope Arena to other US domes from the same era and showed that Nervi’s characteristic elements are not characteristic to other US domes. Scope Arena is a one-of-a-kind US dome that is a symbol of the time that it was built. Today, construction of domes in the US continues, but is commonly done with air-supported formwork. Domes built in this way have smooth interiors and exteriors that have little in common with Scope Arena. Due to the difficulty of constructing new concrete domes at the same scale and variation shown in this paper, it is important to preserve and maintain significant, existing shells, so that physical artifacts of this construction era remain. Scope Arena is a prime example.

7. ACKNOWLEDGEMENTS Funding for this work was provided by a Princeton University Sherrerd Fellowship awarded to the first author. Marco and Elisabetta Nervi from the Pier Luigi Nervi Project Association allowed us to publish the images of Nervi’s work. David P. Billington, Jack V. Christiansen, and

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