The Structural Genome of Sphere

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Las Vegas’s Sphere, the next-generation entertainment venue located just east of the Strip, officially opened at the end of September 2023. A 516-foot-diameter semi-spherical building rising 366 feet above ground, Sphere encloses a bowl-shaped theater for approximately 18,000 guests, seated beneath a domed roof and suspended media plane. It is currently the largest spherical structure in the world (Fig. 1).

The overall structure of the venue has five distinct parts:

Although labeled as distinct systems, these structural systems act together to form a cohesive, balanced, elegant, and efficient superstructure, which significantly benefits the overall design and performance of the venue.

Sphere’s foundation is comprised of 24-inch diameter auger cast-in-place (ACIP) piles supporting cast-in-place concrete pile caps and tie beams. These piles extend up to 100 feet down into the bearing stratum (generally comprised of dense sand) to provide the necessary support for the massive structure, ensuring stability and load distribution throughout with minimal potential for differential settlement. The piles and foundation elements are arranged in two closely spaced rings at the perimeter; the outer ring supports both the outer venue columns and the Geosphere base, while the inner ring supports the inner column of the venue’s ring of paired columns. An array of individual pile caps supports the seating bowl and concourses. Pile supported concrete mats support the shear wall cores, providing additional stability and resistance for overturning moments and shears induced by lateral loads; the mats are generally 4-feet deep (Fig. 2).

Sphere’s interior is designed to offer an immersive theater experience for up to approximately 18,000 guests. The venue features a horseshoe-shaped seating bowl beneath the dome roof and suspended media plane. From the ground to the fifth level, the building is framed with concrete slabs, beams, and columns, providing a robust and durable base. Above the fifth level, structural steel is used to frame the building, allowing for greater construction speed and flexibility. The seating is supported by raker beams carrying precast concrete stadia, ensuring that the audience has a stable and secure viewing experience. Two 18-foot-deep composite concrete and steel transfer girders, similar to “Speed Core” (shear wall system comprised of concrete-filled composite steel plates) but horizontal, span the proscenium over the stage to create a column-free opening for versatility, while also minimizing differential settlement for the six-dome roof columns which transfer at this elevation.

Four concrete shear wall cores are coupled by diaphragm rings at each level to provide uniform lateral support for the entire venue (Fig. 3). The concourses, which encircle the seating to provide access, collect lateral loads and deliver them to the diaphragm rings which then deliver all the loading into the cores and stage walls. This integrated approach to structural design ensures that the venue can handle the stresses associated with large crowds and dynamic performances.

Sphere’s dome roof is a 440-ft. diameter steel-framed structure designed for efficiency and function (Fig. 4). It provides excellent load-carrying capacity and adequate stiffness, enabling the precise placement of the media plane's LED tiles (for discussion, see further on in article). The dome roof's design optimizes its depth and the number of circumferential rings, ensuring that it can support the significant weight of the roof and media plane.

Pairs of adjacent half-arches, intermediate framing, and temporary tie rods were prefabricated into units and lifted into place between the perimeter columns and a temporary center shoring tower (Fig. 5). This modular approach allowed for efficient construction and ensured that each component was accurately positioned, using only one shoring tower. A 10-inch-thick concrete slab on metal deck, placed by shotcreting where steeply sloped, offers permanent stability and acoustic damping. The flat roof at the base of the dome roof acts as a tension ring to resist the dome’s thrust; only vertical forces are delivered to the supporting columns under gravity load. The connections to the columns allow the dome roof to move radially without restraint, while circumferential restraint is locked in order to deliver lateral loads, mainly seismic loads, to the venue diaphragm ring and eventually into the concrete cores and walls.

All field connections of the dome were bolted —not field welded. Fabrication and erection tolerances were expected to be on the order of only three inches over the 400-foot long span of the dome roof (1/800); however, the steel contractor was able to deliver the dome to within about one inch of ideal geometry. Nonetheless, the 160,000 square-foot media plane—whose high-resolution LED display is key to the immersive experience—required even smaller tolerances. By layering in a hanging grillage structure, and several media plane structural layers, the tolerance of the media plane LED tiles (fractions of an inch) was able to be achieved.

The media plane is a key feature of Sphere, consisting of a high-resolution LED display that creates an immersive visual experience. The grillage system, hanging solely from the dome, supports rigging and catwalks and provides a transition from the dome roof to the media plane configuration (Fig. 6). Hydraulic jacks (approximately 330 total) were used during erection to adjust elevations of each hanger and reduce as-built out-of-plane-tolerances; the hangers connected to these jacks supports the primary structural frame of the media plane. Although locked off, the jacks were permanently left in place to make future adjustments, if necessary. Secondary framing with attachment clips allowed for precise positioning of the LED tiles, achieving a spherical surface within an eighth inch of theoretical. This meticulous approach to construction ensured that the media plane's high-resolution display would be perfectly aligned, providing an unparalleled visual experience for guests. The combination of precise shape and 16K resolution results in visual presentations that cannot be discerned from reality, immersing visitors in a truly unique and captivating environment.

The Geosphere is the venue's outer latticed grid shell composed of steel pipe sections and cast steel connecting nodes. It is covered with 580,000 sq. ft. of programmable LED lighting, presenting stunning visual displays. The Geosphere features a hybrid solution of 14 horizontal continuous ring members and 32 pairs of crisscrossing diagonal geodesic elements, continuous between the base and a ring near the crown (Fig. 7). The oculus (or apex ring), framed radially at the topmost part, adds to the structural stability and visual lightness of the design.

Starting from a traditional geodesic arrangement (icosahedron based spherical model), structural engineers employed parametric design and optimization to determine the lightest tessellation possible with pieces that could be easily shipped and erected. The design team, working in collaboration with the steel contractor, studied several alternate configurations that would facilitate fabrication and erection and finally arrived at the hybrid solution that was eventually built (Fig. 8). Extensive analyses revealed that fabricated nodes presented daunting constructability issues, mainly due to large, multi-pass welds and the potential for heat distortion.

Cast steel nodes, on the other hand, offered significant advantages starting with material optimization (Fig. 9). Without the need for stiffener plates and other appurtenances, the cast nodes resulted in a 40 percent reduction in weight compared to built-up nodes. Furthermore, the cast nodes have only a quarter of the surface area, which afforded significant savings in the Geosphere’s three-part, high-performance weatherproof coating. All the castings are essentially identical, eliminating concerns about fabrication tolerances. Grid shell structures are sensitive to angular variations at the nodes and length variations of the members. The geometry of the cast nodes, with computer numerical control (CNC) machining of the flanges, was very precise—with an order of magnitude smaller than for fabricated nodes.

Bolted end-plate connections allowed the use of shims to accommodate variations in the length of the members, which were fabricated slightly short by design. The system provided greater control of the overall geometry during erection, which reduced construction risk by simplifying erection and minimizing the potential for out-of-tolerance errors, resulting in further cost and schedule savings.

Parametric analysis played a crucial role in the structural design and engineering of Sphere. It helped address complex geometric challenges, ensuring structural integrity, optimizing aesthetics, and improving efficiency.

Parametric analysis involves running simulations using structural and architectural design parameters and systematically changing these parameters to evaluate their impact on the structure. This approach empowers structural engineers to tackle uncertainties and challenges involved in engineering complex designs.

Using computational algorithms, engineers optimized various sphere sizes concerning tessellations of the icosahedron. Conversations regarding fabrication and erection led to a more constructable spherical geometry, the Geosphere, which balanced costs, economies of scale, constructability, and tolerances.

The process involved several steps:

The engineering and selection of structural steel castings for Sphere were driven by the need to address complex geometry, tight tolerances, and load demands. The design process began with parametric modeling followed by more advanced 3D finite element analyses (FEA) of the superstructure but was intertwined with hand sketching to determine optimal shapes for the nodes. Early collaboration between design and fabrication teams ensured the feasibility of castings versus fabricated nodes.

Key challenges for fabrication and erection of the nodes included:

The team chose high-performance steel alloys capable of meeting strength and durability criteria while allowing for precision casting. This kept the structural weight of the casting to a minimum and matched the main member thickness.

Before full-scale production, prototypes were created and subjected to rigorous testing, including stress analysis and fatigue tests. This iterative process ensured the castings met design specifications, structural requirements, safety standards, and strict tolerances. Testing included simulating the environmental conditions and operational loads to ensure the castings' durability and performance.

Installing castings required precise alignment and coordination between fabricators, contractors, and the design team. Digital modeling tools, such as Building Information Modeling (BIM) software like Revit and Tekla, played a vital role in streamlining this process. The integration of castings into the construction process ensured that the structural components aligned with both architectural and structural goals.

Erection planning and construction of the Sphere faced several challenges that were addressed through innovative design, early and thorough collaborations, and engineering solutions. The Geosphere's geometry included a full horizontal ring of steel at each latitude, providing temporary stability without the need for shoring and minimizing temporary support during construction (Fig. 10).

A staged construction analysis ensured minimal temporary shoring needed for geometry control. The Geosphere’s goal was to be within 2 inches of target geometry and out-of-tolerance between any two adjacent nodes to be less than 1/500. Only a handful of conditions exceeded these tolerances and were carefully reviewed for structural concerns. The staged construction analysis informed the erection sequence for the completely self-supporting Geosphere. The first ring cantilevered from the foundation, and once fully bolted, it and each succeeding ring was able to support the framing of the next, up to the oculus (apex), which was erected in a single unit (Fig. 11). With essentially no need for shoring, the overall cost was significantly reduced. The Geosphere is completely self-supporting and isolated from the rest of the building; it rests on its own ring of pile caps and grade beams. Diurnal temperature ranges are as high as 100 degrees in the summer and vary from one side of the structure to the other. Isolation allows the Geosphere to expand and contract—up to 2 inches in or out—without restraint from the venue within, which is insulated and less thermally variable.

The Geosphere base was anchored to the pile cap with anchor bolts and a shear key, supporting diagonal pipes for the subsequent latitudinal rings. The compression oculus was installed as one single piece, marking the topping-out milestone for the primary structure.
The final step was erecting the steel supporting the LED light bars, transforming the structure into a spherical screen. The trellis had a panelized design and was erected quickly to meet the schedule; this was accomplished by collecting up-to-the-minute survey data and using the data to pre-deform the panels prior to craning and setting (Fig. 12).

Early collaboration among stakeholders was instrumental in guaranteeing success. Integrating casting expertise into the design process from the start ensured that components aligned with architectural, structural, and construction goals. Collaboration among the design-construct team, Severud Associates, Populous (the Architect), W&W | AFCO Steel (steel fabricator and erector), CastConnex (casting designer and supplier), SDL (erection engineer), and MJ Dean (GC/CIP Concrete Contractor) allowed for precise integration of structural components and optimized the structural design.

Advanced modeling and analysis tools were essential for designing and testing castings, especially for complex geometries. Leveraging technology enabled precise integration of structural components and optimization of design and performance.

Balancing performance and cost were crucial in ensuring the project's success while meeting budget constraints. Sphere’s success underscores the growing role of castings in structural steel design, highlighting the importance of collaboration and innovation in achieving complex geometries with extremely tight tolerances.

During construction, Severud Associates had a full-time onsite presence to assist with immediate action to any construction issues as they arose. This involved working closely with various contractors to solve issues as quickly as possible, ensuring the project continued to move along smoothly. This hands-on approach allowed for rapid problem-solving and maintained the project's momentum, adhering to the planned schedule and quality standards.

The structural engineering of Sphere in Las Vegas demonstrates the power of computational design and parametric analysis in tackling complex designs. By leveraging software tools like Grasshopper and Dynamo, engineers were able to optimize design alternatives, enhance quality control processes and ensure accurate data management throughout the design and construction of the project. The lessons learned from Sphere’s structural design may inform future endeavors and drive innovation in structural engineering.

The use of structural steel castings addressed key challenges of complex geometry, tight tolerances, and load demands, ensuring durability and performance. Rigorous testing and precise alignment during installation ensured the castings met design specifications and structural requirements.

The successful collaboration between the design team, owner, and construction team highlights the importance of integrating everyone’s experience and expertise into the design process from the start. Leveraging advanced modeling and analysis tools enabled precise integration of structural components and optimized Sphere’s structural integrity. ■

About the Authors

Cawsie Jijina, PE is a principal at Severud Associates and served as the principal in charge of the structural design for Sphere.

Steve Reichwien, PE, SE is a principal at Severud Associates and served as the director of structural design for Sphere.

Sindi Krasta is an engineer at Severud Associates.