computer optimization of innovative steel arena structure

Computer optimization of innovative steel arena structure illuminated with natural light

W. place1, 0. ~errn', T. ~ o w a r d ~ & M. williard2 l School ofArchitecture, NC State University, Raleigh, USA 2 Mark Williard Associates, Raleigh, USA 3 Synergetics, Inc., Raleigh, USA

Abstract

A three-dimensional computerized structural analysis tool was used to visualize and optimize the design of a 12,000-square-meter Wellness Center for Shaw University in North Carolina, USA. The Wellness Center contains all of the sports medicine, sports administration, gym classes, and intercollegiate sports activities for the University. At the heart of the center is a basketball and multipurpose arena covered by a roof spanning 70 meters. The roof is a steel network structure of an innovative geometry designed to admit highly controlled natural light for illuminating activities at the heart of the arena interior. The computer was used to generate, visualize, and perform preliminary structural evaluation of a variety of alternative geometries for the structure and then was used to do a detailed, multistage, structural optimization of the final network geometry. During the design development process, emphasis was placed on achieving an inspiring interior space and innovative structural shape, while also allowing for ease and economy of fabrication and construction. This paper will discuss the way in which the computer was used throughout the design process.

Introduction

The focus of this paper will not be on optimization in the pure algorithmic sense. Rather. it will be "optimization" in the context of architectural design, accounting for the multiplicity of issues that cannot be reduced to algorithmic form. It will deal with the highly iterative process in which quantitative explorations are periodically weighed against qualitative concerns having to do with how people are expected to use or perceive the building.

Transactions on the Built Environment vol 52, © 2001 WIT Press, www.witpress.com, ISSN 1743-3509

The design team consisted o f Mark Williard, principal architect for the project; his partner Ola Ferme; T.C. Howard, engineer of record; and Wayne Place, consultant for 3-dimensional, computerized structural analysis. For this design team, physical models had long been a major tool of design development. However, it became apparent early in the project that many iterations were going to be necessary in this design process and physical models of the precision required to accurately assess aesthetics and spatial issues were going to be much too time consuming to work within a realistic schedule. One detailed physical model was prepared near the end of design development, to qualitatively corroborate the behavior predicted by the computer simulations and for presentation purposes. Otherwise, the reliance on physical models was minimal.

The primary design software programs were A ~ C ~ ~ C A D ' , for space planning and 3-dimensional rendering, and ~ u l t i f r a m e ~ , for the 3-dimensional structural analysis. ArchiCAD is a quick and effective tool for generating 3-dimensional design information on conventional architectural designs, such as buildings with simple shear walls with punched openings and with simple roof forms such as gabled or hip roofs. Normally, ArchiCAD would be the major tool for development of building form. However, for a structure of this complexity, ArchiCAD loses its edge as a form-generating tool.

In contrast, the interface of Multiframe lends itself well to quickly and accurately mocking up structures of this complexity. Multiframe can also be used to perform preliminary evaluations of structural performance, which is a crucial issue for a structure of this span. In a kind of Darwinian process, Multiframe percolated to the top as the tool of choice in generating 3-dimensional form. ArchiCAD continued to be used in generating and refining floor plans and for presentations to the client, for whom Multiframe renderings would not be sufficiently expressive or informative. For the client, the Multiframe structural frame would be ported over to ArchiCAD, where it would be integrated with other architectural elements generated in ArchiCAD.

In the early stages of design, the Wellness Center was envisioned as a complex of several buildings. However, after much deliberation, it was decided that the urban context of Shaw University made efficient use of the land a major priority. In the light of that fact, the design was condensed to two buildings: a natatorium and the arena structure, which contains all the functions other than swimming.

' ArchiCAD, by Graphisoft Corporation. Graphisoft R&D Rt., Graphisoft Park 1, H-103 1 Budapest, Hungary, Phone (361) 437-3000, Fax Phone (361) 437-3099. [email protected]

Multiframe 4D, by Formation Design Systems Pty. Lmt.. Headquarters, P. 0. Box 1293, Fremantle, WA 6959. Australia, Phone: +61-8-9335 1522. Fax Phone: +61-8-9335 1526. [email protected].


This latter structure will be the focus of this paper, since that is where the major structural and architectural challenge resided.

The bottom floor of the arena structure was for exercise rooms, locker rooms, sports medicine facilities, coach's offices, etc. The second (main) floor supported the basketball court, the first tier of stands, concessions, bathrooms, and perimeter circulation. At the top of the first tier of stands would be a mezzanine supporting stands that could be retracted to open up the mezzanine for a running track and space for other sports activities.

The structural design problem can be broken down fairly cleanly into two parts: 1. The floors and stands, which can be analyzed using a variety of fairly

conventional methods, and 2. The long-span roof and associated perimeter supports and lateral

bracing, which require a 3-D, computer-based, structural analysis tool to be reliably and expeditiously evaluated.

Of course, these two parts were not purely separable, even structurally, since the floors and stands also rely on the perimeter structure for support and lateral bracing. Also, from an overall architectural design point of view, all of these things are spatially interrelated. However, to first order, the analysis of the structure can be largely broken down in this manner. For example, the roof and associated support system are stable by themselves under both gravity and lateral wind and inertial forces, deriving only some stiffening from the floor diaphragms. It will serve the purposes of this paper to make this separation and focus on the roof and its perimeter support system.

Thought processes involved in the development of form

The initial guiding principles were the following: 1. The main arena space should be well illuminated with natural light

for basketball and other activities occurring in the space. This means that the light should focus on the activities occurring and should not cause glare for participants or observers, regardless of whether the arena was configured as a single court for an intercollegiate game, as two courts for basketball practices. or for some other sports activity, such as gymnastics.

2 . The natural lighting system should be thermally efficient, avoiding beam sunlight during the cooling season and admitting beam sunlight during the heating season.

3. The structure should be innovative and aesthetic in form. 4. The structure should be economical, using structural logic to limit

the required amount of material and using standard fabrication and construction techniques in an efficient and practical manner.

One of the ramifications of the first two criteria was that the apertures admitting the natural light would be vertical, facing either north or south, with overhangs on the south-facing apertures. Criteria 3. was crucial to all the participants in the


design process, since all four participants are formally educated in architecture and all appreciated that an efficient and logical structure devoid of soul would be unworthy of the client or the effort. One might suspect that having so many architects on a project could become a case of "too many cooks spoiling the broth." However, the team dynamic was very good, partly because of the way that principal architect operated, allowing wide-ranging, free-wheeling discussion in which everyone's ideas were heard, but reigning things in when decisions had to be made.

The circular footprint emerged early in the design process, since, in conjunction with the rectangular court, it generates spaces for the stands along the long sides of the rectangular court. The circle was also deemed a pleasing form. One of the early schemes for the structure is shown in the next figure:

The boundary is stabilized by a horizontal, semicircular truss. Two undulating, tubular trusses support the center part of the structure. These tubular trusses run parallel to the main basketball court and would be fitted with glass on the vertical faces, to admit light for illuminating the court. Silvered mylar film stretched on frames would be used to reflect the light down onto the court. This combination of vertical glass facing north and south, with optical elements to direct light downward would be a feature on all subsequent designs. The roof areas over the stands would be supported by cables draped between the boundary trusses and the tubular trusses. These suspension cables would be stabilized against wind uplift by counter-tensioning cables pulled over them (not shown in the diagram).

Initial structural analyses indicated that the boundary truss would deform substantially unless it was quite deep, causing some problems with the extreme


cantilevering of that portion of the roof. Also, torsional deformation in the tubular trusses was substantial. (In the version of this structure that was analyzed, the tubular trusses were h l ly triangulated on all four faces, but some of that triangulation has been omitted in the diagram above, to make it simpler to read.) Based on the torsional deformation indicated by the analysis, it was decided that it would make more sense to run tension members straight through the center space to link tension members on the two sides of the structure. These tension elements, along with the truss members in the tubular trusses began to clutter the interior volume, interfering with both the movement of the light and the deployment of the reflective elements.

To address some of these concerns, the scheme above was modified by replacing the cables with inverted bow trusses, the top chord of which would counteract the tension in the draped elements. This allowed the replacement of the tubular truss with planar trusses, as shown in the next diagram:

This scheme seemed promising. However, it still has a complex surface for attaching a skin. In the search for simplification of the envelope materials, several other schemes were explored, including the one depicted in the next diagram. In this structure, the only complex and unusual parts are the two undulating trusses supporting the center of the structure. Even those trusses are only unusual on the top chord. The bottom chord consists of fairly long straight runs. All the other spanning elements are simple bow trusses and the roof surfaces are flat, simple cones, or portions of cylinders. The rectangular shape of the side volumes also logically accommodates the retractable stands. In the end, this scheme was rejected as not fluid enough.


Several more of these forms were generated before arriving at the final scheme, which is shown in the next diagram.

The columns are 324 mm O.D. steel pipe spaced approximately 3.7 meters apart. There are three levels of cross trusses that connect the columns into a rigid-frame system for resisting lateral forces. The lowest cross-truss is just below the main floor (where the basketball court occurs), the middle cross-truss is just below the mezzanine floor, and the top cross-truss is just below the top of the upper stands. The columns are located under critical intersections in the network roof structure. The exterior envelope wall (not shown) follows a generally circular


C'otiplter. .Aided Optinmm Desigu o f Str.uctwes I'll 133

plan, with minor variations, such as indents at egress points. The location of the envelope wall does not correspond to the locations of the columns shown in the diagram. However, the arrangement of spaces and utilities within the building has been resolved in a manner that reconciles to two distinctly different geometries represented by the envelope walls and the array of support columns.

The roof geometry is based on portions of two sloped cylinders that intersect and pass through each other. The cylinder has the advantage that the roof panels are rectangular and identical in size. A circle was chosen for the exterior wall and the roof is truncated to a circular boundary in plan. This simple geometric construct leads to an undulating boundary edge that is visually more complicated and subtle than the underlying geometry would suggest.

Clearstory mullions are set to be perpendicular to the straight "rafter" elements in the portion of the cylinder below the clearstory. The outwardly sloping mullions provide an effective overhang to protect the glazing from excessive exposure to beam sunlight. The shape of the upper boundary edge (at the top of the clearstory) has no specific mathematical description, but rather was arrived at by digital tweaking, governed by the design team's collective sense of aesthetics. In establishing the shape of that boundary edge, an attempt was made to make as many as possible of the clearstory mullions, land along one of the circular arcs in the network below. This was deemed to be appropriate for both structural and fabrication reasons. The computer proves particularly useful in this design approach, since member lengths are automatically supplied, once the desired visual effect is achieved. Prior to the advent of the computer, having a precise mathematical expression for the shape of the boundary was crucial to being able to accurately determine member lengths for shop drawings. In a sense, the computer supports a more artistic and intuitive approach to establishing the building form.

While the underlying geometry of the structure is that of two cylinders that intersect and pass through each other, the structural action is quite different. The structural spanning action is provided by the portions of the cylinders below the line of intersection. The portions of the cylinders above the line of intersection contribute little to the overall spanning action and those portions of the cylinders have been sized and detailed without the diagonals and with much lighter members, reflecting the secondary role of that portion of the structure.

The collective action of the portions of the network below the line of intersection bears some resemblance to a dome, with the straight "rafter" elements and the "arches" working in compression and the boundary working in tension. However, in some regards, the shape of this structure is radically different from a dome, being triangular in shape when viewed from east or west and arched when viewed from north or south. This lack of symmetry in the network causes serious shearing action within the surface of the network. This shearing action is resisted by the "diagonal" elements in the network.


Using the computer for structural optimization

After arriving at the intersecting-cylinders concept for the overall geometry, over a hundred distinctly different computer simulations were performed, exploring such issues as:

- Varying the spacing of the elements; - Using different enclosure materials; - Using trusses running through the interior volume; - Using different materials for the structural elements (e.g., curved

glulam purlins were evaluated in conjunction with steel trusses running through the interior volume);

- Using open versus closed steel structural sections; - Using fully curved (rolled) arches versus segmented (bumped) arches; - Determining where elements could be removed to reduce complexity

and material expenditures (e.g., some of the straight "rafter" elements were not performing a significant structural function in resisting shear in the trussed network and those "rafter" elements have been reduced to a series of short segments, the sole function of which is to brace arch elements against buckling at mid-span);

- Determining where elements could be removed to enhance the passage of natural light through the structural network;

- Sizing of elements to resist bending and local buckling; - Deciding on a logical sequence of construction; - Calculating deformation to assess diaphragm stress on the decking and

decking connections; and - Calculating the stiffness of the network under asymmetric load for

purposes of assessing resistance to general buckling, which is a very difficult and extremely important aspect of the design of such a structure. (This particular structural form has never been addressed directly in the literature on general buckling. For example, the literature addresses domes'~233x425 and simple, un-braced arches, both of which bear some resemblance to the structure being developed. However, the situation in this structure is clearly not akin to an un- braced arch, since the web members in the network tie all of the arches back to the boundary, which represents a substantial stabilizing influence. Also, this structure is not closely akin to a dome, since it does not have double curvature in the conventional sense in which we use the term for domes. The literature also contains examples of parts of networks that are portions of cylinders with some sort of boundary constraint^^'.^. However, none of the boundary shapes or boundary loading conditions reported in the literature matches the boundary in this structure. In the light of the lack of precise analogs in the general buckling literature, the stiffness analyses performed on the computer were crucial to building confidence that the issue of general buckling of the network had been properly addressed.)


Prior to the advent of computers, a structure of this sort would probably not have been built, even if someone had imagined it, since performing even a single complete analysis by hand would have been prohibitively time-consuming and too subject to error. In the course of this design, literally hundreds of simulations were performed, no one of which could have been accomplished before the advent of the computer.

Structural member selection and joint design

General buckling is a strong influence on the required depth of structural elements in the network. At first glance, steel W-sections have the geometry that is suited to achieving good shell thickness to resist general buckling. However, W-sections have some disadvantages in this application:

- W-sections of the depth required for resisting general buckling tend to be fairly heavy, since flange and web thickness required to avoid local buckling lead to members that are over-designed relative to stress.

- Aerial, field welding of joints is not feasible for achieving accuracy or reliability in a structure of this sort.

- Bolted connections for such a network would involve a huge number of bolts and would expend a lot of steel in the joining plates.

- Bolts and bolt plates at the joints create raised areas where the decking cannot seat itself properly.

To address the problems above, a structural network was devised with the arched elements consisting of top and bottom structural members knitted together with Verendeel framing elements. This achieved several effects:

- The arched members can be continuous through the joint, passing above and below the straight ''rafter" elements. thereby assuring the structural continuity of both the arched members and the straight rafters at all intersections without welding or bolting plates to carry the load from one section of the member to another section of the member.

- The tops of the arched members are smooth, without bolting plates and bolts, so that the decking seats effectively on the arched elements.

- Using the Verendeel system for the arched elements allows the use of light-weight members in a composite system that has substantial depth for resisting general buckling.

The diagram below shows how typical pre-fabricated sections of the roof would be lifted into place during construction. For stability in handling, at least two arches are always included in the prefabricated section of roof. The computer was used to "storyboard the entire construction sequence using a series of diagrams like the one shown below. This approach also allows each state of partial construction to be analyzed to avoid structural problems during construction. Forces from temporary bracing elements and cranes can also be accounted for in the analysis of the partially built structure.


The next diagram shows the axial forces under the full gravity load (structural frame, roof decking, and snowllive load on the roof). The arches and rafters are acting in compression and the web members are acting mainly in tension. The facia member is also working in tension.

The next diagram shows the member moments under the full gravity load (structural frame, roof decking, and snowllive load on the roof). Near the support boundary, the cantilevering effect of the overhang induces severe bending moments. The bending moment is greatest in the arched elements on the east and west sides and greatest in the straight "rafter" elements on the north and south sides. Special members are required where the moments are high. For example, near the ends of the arched elements, the top and bottom chords need to be connected with a continuous web, rather than spaced-out, Verendeel elements, in order to handle the shearing effects associated with the bending


action over the boundary supports. Near the boundary, the depth of the rafters is increased by creating a composite of the rafter plus members welded to and bottom to give the same overall depth as for the arches. Special attention needs to be given to achieving proper continuity of bending members at the boundary.

Conclusions

Using the computer facilitated an increased degree of creativity and efficiency at every stage of this design process. The tools are still somewhat cumbersome to use in some respects. For example, the methods for managing the angles at which member cross sections are set in Multiframe is still very cumbersome. This aspect of the project involved a substantial amount of external processing and extensive adjustment of angles in Multiframe. Upgrades to Multiframe that would have greatly facilitated this project would be:

- Allowing for the option that member cross sections would be appropriately rotated during rotational duplications of members.

- Allowing for the option that mirror duplications would not perform undesired "flips" in member cross section orientations.

- Providing a 3-point arc generator. Otherwise, Multiframe performed admirably. with a friendly, efficient, and utilitarian interface and a rock-stable, accurate, computational core.

References

[ l ] Crooker, J.O., & Buchert, K.P. Reticulated Space Structures. Journal of the Structural Division, Proc. of the American Sociefy of Civil Engineers, pp. 687-700, March 1970.

[2] Bushnell, D. Computerized buckling analysis of shells, Martinus Nijhoff Publishers, Dordrecht, Boston, and Lancaster, pp. 1 - 109, 1985.

[3] Blachut, J., Galletly, G.D., & Moffat, D.G. An expereimental and numerical study of into the collapse strength of steel domes. Proc. of the Int. Colloquiem on the Buckling of Shell Structures on Land, Sea, and in the Air,


Lyon, France, eds. J.F. Jullien, Elsevier Applied Science, London and New York, pp. 344-358, 1991.

[4] Katu, S., Mutoh, I., & Matsunaga, Y. Strength of reticulated shells designed by second-order elastic analysis. Proc. Of the 2nd Int. Conf: On Thin- Walled Structures, eds. N.E. Shanmugam, J.Y. Richard Liew, & V. Thevendran, Elsevier: Amsterdam, pp. 655-662, 1998.

[5] Farshad, M. Design and Analysis of Shell Structures, Kluwer Academic Publishers, Dordrecht, Boston, and London, pp. 343-41 1, 1992.

[6] Yamaki, N. Elastic stability of circular cylindrical shells, eds. E. Becker, B. Budiansky, H.A. Lauwerier, & W.T. Koiter, North-Holland, Amsterdam, New York, and Oxford, pp. 381-546, 1984.


computer optimization of innovative steel arena structure

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