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CABLE-NET WALLS; WHERE DO I EVEN START?

Aaron Mazeika PE, Associate Skidmore, Owings & Merrill LLP San Francisco, California [email protected] For the last seven years Aaron Mazeika has practiced in the San Francisco office of Skidmore, Owings & Merrill LLP, where he has led the structural engineering design team on a number of large scale projects. Recent projects include: Beijing Finance Street, 700,000m of mixed-use development including two cable-net faades and three cable-truss supported glass roofs; and The New Beijing Poly Plaza, a 100,000m mixed-use tower (office/museum) including a 21 story tall atrium space enclosed by two cable-net faades, one at 90m tall by 60m wide is the largest such faade in the world.

Kieran Kelly-Sneed PE ASI Advanced Structures Inc., Los Angeles, California [email protected] Kieran Kelly-Sneed has several years of experience in modeling and analysis of cable structures, beginning during his education at Cal Poly, San Luis Obispo. At ASI, he has been involved in the design of several cable supported glass structures and of many other custom faade projects. His role extends to the job site where he has provided extensive support during installation of these and other complex structures. Recently Kieran spent 8 weeks on site at the San Jose Civic Center to coordinate tensioning of the Rotunda's cable trusses, a complicated operation due to the flexible steel ribs that anchor them.

Abstract While cable-net supported glass walls remain unusual, even exotic design solutions for exterior wall enclosures, their highly transparent nature makes them an attractive option, particularly for building atria. The behavior of cable-net walls under lateral loading is conceptually easy to understand, but the large displacements likely under design wind events bring new challenges to Architects and Engineers not familiar with the design of large displacement structures. The design of cable-net wall systems involves a great deal of coordination between the designers of the cable-net wall and the designers of the base building structure (who are often different entities), due to the large loads transferred across the boundaries of the cable-net, and the large displacements which need be accounted for in the detailing of the interface zones. As complex as the design of cable-net walls can be, this complexity is repeated in the process of installing the wall. Specialist design-build contractors are typically engaged to ensure that the installation process is successfully completed. This paper provides background information on the development of cable-net wall systems and technologies, and descriptive summaries of the process of designing and constructing cable-net wall systems. Different examples of team make-up, and the roles and responsibilities of the members of the team are described. The fundamental theory behind the behavior of planar cable-net wall systems is presented and verified through the application of parametric analysis studies. By way of a project example, a detailed description is given of the design of The New Beijing Poly Plaza, the worlds largest cable-net wall recently completed in Beijing.

STRIVING FOR TRANSPARENCY

Architectural Ambitions Since the dawn of the modernist movement, architects have challenged engineers with an ambition for increased transparency in building faade systems. As engineering technology has evolved, increasingly lightweight structural support systems have been developed allowing a range of options for the construction of transparent wall and roof systems. Developments in structural glass technology have allowed the construction of all-glass solutions for short-span conditions, but for longer spans a steel backup system is typically required. The conventional solution consists of glazing elements spanning between a series of parallel lightweight steel trusses. Evolutions in the design of trusses have allowed the use of cable-trusses where the chords of the truss are replaced by cables, as can be seen in the exterior wall bracing at the Tokyo International Forum (Rafael Violy Architects P.C., New York & Structural Design Group, Co. Ltd., Tokyo, 1996). Tension is maintained in each chord for all loading conditions by pre-tensioning the chords against fixed support points or a single internal compression element. This solution can be considered as an optimization of the underlying beam and slab concept. However a paradigm shift was achieved with the conception and development of the structural solution for the exterior wall of the Kempinski Hotel at Munich Airport, (Murphy/Jahn, Chicago & Schlaich, Bergermann und Partner, Stuttgart, 1993). This planar steel net structure resists lateral loads through catenary action in the cables, completely eliminating the need for any flexural beam elements behind the glass faade.

Figure 1. Tokyo International Forum, Tokyo, Japan

Figure 2. Hotel Kempinski, Munich, Germany

Cable-Net Precedents While conceptually simple, due to their minimal structure and large in-service deflections cable-net curtain wall systems may still be considered an exotic solution for the support of glass walls. The completion of several major walls around the world, however, has established a proven track record of an achievable scale and level of transparency. Planar two-way cable systems support and stabilize glass facades through the resistance to deformation of the two-way pre-tensioned net. Gravitational loads from the glass elements are carried through the attachment nodes to the vertical cables, and up to a transfer structure in the base building above. Lateral deformations due to wind and seismic loadings are resisted by the tendency of each of the horizontal and vertical cables to return to its straight line configuration between supports, while being subject to a perpendicular force. The flexible nature of a planar cable-net under lateral loading means that the critical design goal is limiting deflection through adjusting axial stiffness of the cables, and the cable pre-tension. In-service deflection limits under a 50-year return wind loading condition are typically set in the range of L/40 to L/50 (with L corresponding to the shortest span passing through the considered point) to protect the integrity of the glass and sealants and to minimize a perception of movement by the buildings occupants. Oftentimes the controlling design criterion is the later issue concerning occupant perception. If well designed and detailed, a cable-net wall system may be to sustain the design level wind condition and beyond without structural or sealant failure. However, if the occupants of the building feel a sense of unease in the vicinity of the cable-net wall, then the project cannot be deemed a complete success.

Since the construction of the cable-net wall at the Kempinski Hotel in 1993, several significant cable-net wall systems have been installed around the world. As additional projects have been realized, larger and more complex walls have been designed and constructed, representing an evolution of the original design concept. Significant milestones in the development of the cable-net supported wall system include: The Kempinski Hotel in Munich, Germany, the first application of the planar cable-net concept, is 40m wide by 25m tall and was designed with the principal cable pre-tension installed in the longer-span horizontal direction. The 22mm diameter cables are spaced at 1500mm on center, and are pre-tensioned to limit deflections to 900mm. The AOL Time Warner building on Columbus Circle in New York, USA (Skidmore, Owings & Merrill LLP, James Carpenter Design Associates & Schlaich, Bergermann und Partner, 2003). This cable-net wall is 46m tall by 25m wide and both horizontal and vertical cables are 28mm in diameter. The Beijing New Poly Plaza in Beijing, China (Skidmore, Owings & Merrill LLP, 2006). The cable-net wall is 90m tall by 60m wide and consists of 34mm diameter horizontal cables at 1333mm on center, and 28mm vertical cables at 1500mm on center. The very large spans of this cable-net wall were achieved by faceting the net by folding it across large diameter cables (235-275mm). This solution will be described in more detail later in this paper.

Figure 3. AOL Time Warner, New York, USA

Figure 4. The New Beijing Poly Plaza, Beijing, China

Service deflections of a cable-net wall can be significantly reduced by curving the wall in an anticlastic fashion: cables running in the two principal are curved in opposing directions, creating a stiff grid of intersecting nodes. In this arrangement lateral deformations due to wind and seismic loadings are resisted with less deflection than for a comparable flat net because the wall has been built with a partially deflected form. This pre-curved configuration of cables avoids the softest portion of the non-linear lateral response of a planar cable-net (the undeformed, initial condition). When the anticlastic cable-net is subjected to lateral loads, only half of the cables resist the loads applied in each direction. The cable-net behaves essentially as two separate one-way cable-nets, rotated 90 degrees from each other, and each optimized to resist lateral loads in a given direction. Because of this configuration the support points on each side of the cable-net must be able to resist half the total

applied wind loads on the gross area of the wall, necessitating strong boundary conditions on all four sides. Despite only half portion of the cables being loaded for a given direction of wind loading, the cables which are mobilized offer such an increase in stiffness over planar cable-nets, that curved cable-nets can efficiently be designed to deflection limits as high as L/120. They may also be designed in the range of L/40-L/50 using less pre-tension than a comparable planar cable-net. As with planar cable-nets occupant comfort and perception are often the determining factors in establishing the deflection limit. Double Curved cable-net projects include: The Station Place/Securities & Exchange Commission Headquarters building in Washington, USA (Kevin Roche John Dinkeloo and Associates LLC & ASI Advanced Structures Inc., 2005). This anticlastic cable-net consists of a wall 27.5m tall by 19m wide and a roof portion 19m wide by 16m deep with a curved delta truss to transfer loads at the corner where the two nets meet. All cables are 28mm in diameter and deflections are limited to 250mm. The Seattle-Tacoma International Airport Central Terminal Expansion in Seattle, USA (Fentress Bradburn Architects Ltd. & ASI Advanced Structures Inc., 2005). This wall runs 108m in length and spans 16m in height. Both horizontal and vertical cables are 20mm diameter.

Figure 5. Station Place / SEC HQ, Washington, USA

Figure 6. Seattle-Tacoma Intl. Airport, Seattle, USA

CABLE-NET TECHNOLOGIES

Cables and Cable Fittings The cable-net is made up of cables held together at their intersections by cable clamps, which also serve as the point of attachment for the glazing, typically supported only at its corners. Plain, threaded, turnbuckle, or eye hook terminations are swaged or speltered onto the ends of cables and anchor them to the base building structure. Swaging is a process in which a fitting is mechanically pressed onto the cable end. The less commonly used spelter socket connection consists of a cone shaped termination into which the splayed wires of a cable are inserted and bound by a poured zinc or resin wedge. Each cable is composed of individual cold-drawn wires twisted together in a variety of arrangements, the most basic of which is called wire strand. Strand consists of individual wires twisted about a central core wire. Wire rope is made by twisting strand cables about a central core strand. Cables are named for the number of strands and wires they contain: 1x37 describes wire strand composed of thirty-seven individual wires. 6x19 describes wire rope consisting of 6 strands of 19 wires each. In addition to the standard strand and rope constructions, individual manufacturers also offer a variety of special locked windings designed to increase the constructions stiffness and improve its resistance to corrosion by making the surface less permeable. Cables are either galvanized steel or stainless steel. Untreated cable is not generally used in cable-net applications. In most designs, the cables are on the interior of the building and corrosion is only an issue during construction. Cables are specified and ordered pre-stretched with end fittings to meet or exceed 110% of the cables minimum breaking load (MBL). Pre-stretching removes tightens the helical construction of the cable and significantly reduces creep (relaxation) after installation. The designer determines a cables allowable working load based on the MBL, and must apply additional strength reduction factors based on the end fitting type and angle of deviation at saddle supports. These factors are based both on code requirements and on manufacturers recommendations. Other sources of capacity reduction may include effects of fatigue or of fire. Fatigue can be pronounced in places where cables are subjected to changes in their curvature, especially if a sharp edge is present. Such an edge will have a tendency to bite into the outermost wires of the cable. For this reason, design codes give recommendations about the maximum allowable angle of deviation of a cable across a support, and the German DIN code specifies edge radii for cable clamps to eliminate sharp edges. The heat of a fire can reduce a cables strength both by softening it and by annealing the cable from its cold-drawn state, thus permanently reducing its strength. In this manner cables which have survived a fire may be over-stressed after the event due to a reduction in their capacity.

Figure 7. 1x19 wire strand

Figure 8. 6x19 wire rope

Figure 9. Swaged cable fittings

Glass Attachments Drilled glass bolt fittings or patch plates are typically used to fasten the glass to the cable nodes. These attachments must be designed to accommodate the environmental loads, in addition to the resulting deflections. For this reason rotational glass bolts are a common solution, allowing upwards of ten degrees of rotation between the glass and its support point. Patch plates are a more economical solution because a single plate can take the place of four bolts, and the glass does not need to be drilled. The plate penetrates the glass joint to clamp multiple pieces of glass to a common node. Deflections and rotations are accommodated by a neoprene bearing pad between the glass and patch plate and by localized deformation of the glass.

Figure 12. Rotational glass bolt

Figure 13. Glass patch plate

Glass Technologies Glass can be annealed, heat-strengthened, or fully tempered. Heat strengthening and tempering are treatments in which annealed glass is heated then rapidly cooled, placing its surface in compression and center in tension. This increases the strength of the glass as higher applied loads can be resisted before the outer surface fractures. Issues of concern when heat treating glass include nickel-sulfide inclusion, roller wave, and bow or edge warping. Of these, nickel-sulfide inclusion is the only problem with structural implications; it can cause spontaneous breakage in fully-tempered glass. Heat-soaking after tempering will usually cause glass with inclusions to break, so the process is often specified in contract documents to reduce the likelihood of breakage after installation. Most cable-nets employ laminated glass as a safety measure against breakout. Broken panels remain in place, held by the polyvinyl butyral (PVB) interlayer. Heat-strengthened and fully tempered glass sheets have different breakage patterns giving added strength after glass breakage to a laminated panel containing both.

Figure 10. Heat treated glass

Figure 11. Laminated glass breakage

CABLE-NET DESIGN TEAMS

Roles and Responsibilities The design team for a cable-net structure tends to consist of a variety of entities who are involved in the design of the cable-net wall system, the base building structure or both. For each portion an entity may be involved as the Architect or Engineer for the design phases of the work and/or as the Architect of Record (AOR) or Engineer of Record (EOR) for the construction documentation phase of work. The principle roles in the design team are as follows: Design Architect: Lead architectural designer of the building in the Schematic and Design Development phases. Architect of Record: Architect responsible for preparation of the construction documents for the building structure, often the

Design Architect. Design Engineer: Lead engineering designer of the building in the Schematic and Design Development phases. Engineer of Record: Engineer responsible for preparation of the construction documents for the building structure, (Base Building) often the Design Engineer. Cable-Net Designer: Lead Designer of the cable-net wall system. This could be the Design Architect, the Design Engineer

an associated designer, or a design-build contractor. Engineer of Record: Engineer responsible for preparation of the construction documents for the cable-net structure. (Cable-Net) This could be the Engineer of Record for the Base Building, but more commonly is the cable-net

design-build contractor. As can be seen from the above, there are many possible arrangements of different entities that can make up a team for the design of a cable-net wall system. Several arrangements that have been employed in the past are highlighted in a following section. Contractor Engineered Systems In any large building project there will likely be several elements and components of the structure which are defined as Contractor Engineered Systems. The items could be a single component, such as a cable with end fittings that is specified to be provided engineered by the contractor to resist the load demands shown on the structural engineering drawings, from pin-to-pin. At the opposite end of the spectrum an entire system can be thus specified, such as the entire exterior wall of a building. The reasons for specifying Contractor Engineered Systems are as varied as the elements and systems thus specified, and include: Design Efficiency: Any structural engineer can design an open web steel roof truss. But it is not an efficient use of

resources when the truss manufacturer can do the detailed design in a fraction of the time, allowing the structural engineer to select from a catalogue of pre-designed components.

Proprietary Items: The tension capacity of a swaged steel cable connection is greatly influenced by the exact production

process specific to each manufacturer. As the structural engineer cannot determine this, the cable assembly is usually provided engineered pin-to-pin as described above.

Design Expertise: Certain elements or systems may require very specific knowledge to be safely designed, and may

therefore be beyond the experience of the typical structural engineer. In this case the structural engineer would wisely defer the design of these elements or systems to a specialist. Note that when the complicating factor is difficulty of design, the chosen course of action may be to place the design responsibility on a specialist design-build contractor, or to employ the services of a specialist engineering sub-consultant to assist the structural engineer in the design.

Contractor Expertise: Certain elements or systems may not be difficult to design, but may require specialized knowledge and

skills to safely construct. In such situations the success of the project hangs directly on the ability of the Contractor to perform the work correctly. In such situations designating this particular portion of the work as a Contractor Engineered System is a useful tool to ensure that only suitably skilled entities are contracted to perform the work.

Due to a combination of the reasons listed above, cable-net wall systems are typically designated as Contractor Engineered Systems in the building design documents, making the design-build contractor the EOR for the cable-net wall system. However the extent of early involvement in the design by the design-build contractor, and therefore the extent of development of the initial design by the Design Architect and Design Engineer, vary greatly depending on the team setup employed. Design Team Setup A traditional design-build approach recognizes the value of the expertise provided by a specialty design-build contractor. Potentially also in part due to a lack of familiarity of the systems involved, many architectural and engineering design practices will follow this approach and involve a the design-build contractor as early as possible in the conceptual design of a cable-net wall project. The design of the cable-net can be separated from the design of the rest of the building almost as soon as the decision has been made to include one in the overall design of the project. Typically the cable-net design-build contractor will wish to be involved early as their experience can be beneficial in guiding the design in the critical initial phases when decisions are made that will set constraints on the design of the net. The design of the cable-net, the glass and the glass attachments will then be undertaken by the design build contractor who will act as the Cable-Net Designer as well as the Cable-Net EOR, working in parallel with the AOR of the base building, to ensure that the net is designed in accordance with their original conceptual design intent. The design-build contractor will also work closely with the EOR of the base building to ensure that all load and displacement interactions that occur at the interface between the cable-net structure and the base building structure are duly considered. An alternate design approach that can be employed has the Design Architect and Design Engineer of the base building structure performing the role of the Cable-Net Designer. This approach may be employed for a number of different reasons including an evaluation that the design of the cable-net is so inextricably linked to the architectural and engineering design of the base building, thus making it impractical to separate this portion of the work; a desire on the part of the Design Architect and Design Engineer to maintain direct creative control on the cable-net design; or in the case of a Design Architect and Design Engineer with experience in the field of design of cable structures, a situation where this type of work falls within the range of work undertaken by these entities. However for the reasons of difficulty of construction listed in the previous section it is still typical to designate the cable-net wall as a Contractor Engineered System, making the design-build contractor the EOR of the cable-net wall. However as the design of the cable-net has been completed, the role of the design-build contractor is typically limited to one of engineering verification prior to the construction phase. An example of a project designed under this engineering verification approach is the New Beijing Poly Plaza project, which is described in more detail as a cable-net project example later in this paper. While the traditional design-build approach and the engineering verification approach represent perhaps the two clearest conditions in terms of separation of responsibilities, they do represent two ends of a spectrum and each project may lie somewhere between these two ends. The majority of cable-net projects are completed closer to the traditional design-build end of the spectrum. Construction Team Setup Early in the buildings design phase the cable-net designer and EOR should work with the design architect and engineer to establish the wall geometry, deflection limits, and perimeter reactions. A flat wall typically requires more pre-tension than a curved one; a one-way cable wall will load the building in fewer locations but with greater force, and will allow more deflection unless its pre-tension is increased. Depending on the wall geometry and deflection limit, cable reaction loads can easily range from 10 to 100 kips on intervals of five to ten feet. Thus it is critical that the team establish the design parameters and ballpark reaction values early in the design process.

Building movement, stiffness, and expansion joints must also be coordinated. Preliminary deflection and stiffness information must be provided to the cable-net designer for use in their modeling, as support displacement can affect the walls stiffness. Because the cable-net needs a rigid boundary designers try to avoid placing expansion joints across the wall opening. However, differential building movement can be accommodated through use of springs or hinged elements. Such issues must also be discussed at the beginning of design. As the design of the building and the cable-net proceed the cable-net designer coordinates the location of each cable anchor and associated reaction forces with the design engineer, who in turn supplies support displacement information based on the cable loads. Design of the attachment detail is usually coordinated between the two engineers, though the engineering responsibility typically rests with just one. The cable-net EOR always bears responsibility for the cable and swage, beyond which point responsibility is split on a case by case basis. Embeds in concrete are most often designed by the building EOR. Depending on the amount of anticipated support deflection, the cable-net designer may coordinate with the base building EOR just before beginning cable fabrication. Large building deflections may necessitate ordering cables slightly short to ensure that architectural tolerances or cable thread travel are not exceeded.

CABLE-NET PROJECT DESIGN Applicable Codes, and Design and Performance Criteria As with any development in engineering technology, there is a period of time where the system may still be considered to be an unconventional system. As such, typical building codes, which evolve over time to address the building systems in conventional use, often do not provide requirements or guidance for cable-net systems. Therefore cable-net designers must look to the intent of the typical building codes and look to a wider range of codes which provide guidance in the design of components of the system. Knowing that cable-net walls systems are flexible and deform out-of-plane when subject to lateral loads, the primary design criteria to establish at the start of the project is the span to deflection ratio that will be acceptable under the design lateral loading condition. The 1997 edition of the Uniform Building Code (UBC97), provides minimal guidance for deflection control: Table 16-D restricts the live load deflection of floors and roofs supporting plaster to L/360. The 2006 edition of the International Building Code (IBC2006) provides more detailed information concerning deflection criteria: Table 1604.3 lists deflection criteria for gravity and lateral loads, including wind loads on exterior walls. Again the focus on the deflection limits is the protection of finishes from damage due to deformations of the supporting structure, but the recommended limit of L/120 for exterior walls with flexible finishes could arguably be considered applicable for the design of cable-net walls. However for cable-net wall systems, damage to finishes (excluding the glass panes themselves) is generally not a consideration. The cable-net wall system, including all of its components, is specifically designed for the anticipated deflections, and the system is typically detailed to avoid any conflicts with unrelated parts of the building structure. The most important practical consideration for establishing deflection criteria for a cable-net are related to ensuring that the wall will remain air and water-tight as it deforms, ensuring that the deformations are not large enough to result in the flexural failure of any of the panes of glass, and more general considerations of human perception and comfort. Typically, before systems are too flexible to allow the first two technical issues to be solved, the more subjective considerations of human comfort limit the design. No building owner wishes to construct a glass wall which feels unsafe to the building occupants. For design of footbridges and floor systems human discomfort can arise due to the accelerations felt by the person traversing the span. In the case of cable-net wall systems, human discomfort is most often associated with the visual observation of large deflections in the glass wall. Although the appropriate limitation is very difficult to quantify, established practice has shown that a deflection range of L/40-L/50 is generally acceptable. There are some notable exceptions to this rule-of-thumb, most importantly that of proximity. A typical floor-to-floor exterior wall system will have its maximum deflection occurring close to occupant eye level in a location where the occupant can usually stand immediately adjacent to the glass. In such cases the L/120 limit for exterior walls per IBC2006 may be appropriate. However the typical cable-net wall is an atrium wall spanning several floors. In this case the building occupants can only be adjacent to the cable-net at the base of the wall where deflections are small. Care should be taken when designing long-span cable-net walls when building occupants may approach the net in an area where deflections are large (such as an atrium footbridge at mid height of the wall).

The design wind pressure that needs to be considered when calculating the deflections of the cable-net wall is also a subject of application of the intent of the code. The design wind event should be that prescribed by the governing code (0.02 probability of being exceeded in any given year per UBC97), and the appropriate wind pressures can be established based on the location and physical form of the building. Some engineers may determine that a code-based approach for establishing the design wind pressure is acceptable, however due to the unusually flexible behavior of the walls, wind engineering studies are often recommended. For very large walls aero-elastic wind tunnel studies that account for the flexibility of the cable-net system in the wind tunnel model are beneficial. Note that wind engineering study reports will generally present recommended cladding design wind pressures, and structural design wind pressures. In long-span cable-net structures it is general practice to design the glass and glass attachments for local effects due to the local application of cladding pressures on each pane, and to design the system as a whole for the global application of structural pressures (cable forces, and stresses in the glass due to global deformations). This approach is reinforced by IBC2006 table 1604.3 note f which allows the calculations of deflections of supporting members to be made on the basis of applied wind pressures of 0.7 times the component and cladding wind loads. This design philosophy is intended to ensure that each pane can withstand the application of localized peak gusts pressures, whereas the system as a whole need only be designed to withstand the maximum pressure likely to occur when averaged over the full area of the wall. For the design of the components of the system, specialist codes and guidelines must be used for each item. The design of steel cables is not well covered in the typical steel design codes used in the United States, but is well covered in ASCE-19 Structural Applications for Steel Cables in Buildings published by the American Society of Civil Engineers. The German standard DIN 18800-1 Structural Steelwork, Design and Construction, also provides design procedures for the design of steel cables. DIN 18800-1 is commonly the code used in the development of load tables included in the product catalogues produced by the European cable manufacturers. Analysis Methods For the simplest of cable-nets, one-way spanning planar systems, hand calculations can be performed to accurately calculate the behavior of the net under lateral loads (see section concerning cable-net fundamental theory later in this paper). However for more complicated conditions such as two-way nets, irregular geometries, curved nets, or nets with non-rigid boundary conditions, computer analysis modeling of the system is required. Due to the highly non-linear response of cable-net systems under out-of-plane loading, an analysis program with full geometric non-linearity capabilities is essential. Additionally an analysis program that has been specifically developed to include a cable element as an inbuilt standard element type is usually a significant advantage. This allows cables to be modeled as single line elements in the analysis model from pin-to-pin. Some analysis models require that cables be modeled as a series of individual elements connected together in series, significantly complicating the analysis model. Programs which have been successfully used by SOM & ASI in the analysis of cable-net walls include S-Frame written by Softek Services Ltd, and Space Gass written by Integrated Technical Software Pty Ltd. Other programs include RS-Tab by Ing.-Software Dlubal GmbH and Strand7 by Strand7 Pty Ltd. It should be noted that due to the non-linear response of cable-net systems, linear combinations of analysis load cases are not applicable and all individual load cases and load combinations must be analyzed in turn. Therefore analysis of complicated systems subject to many load cases can result in very long analysis run times. This is especially true when the analysis of the cable system also includes an element of form-finding. The goal of the analysis model is to represent the cable-net structure at the end of the completion of construction and then investigate the effect of additional loads that may be applied to the cable-net during its service life. Generally the initial shape of the cable-net is a known architectural form, and the Cable-Net Designer establishes the initial pre-tension levels that are required to give the cable-net sufficient stiffness to meet the deflection criteria when subject to the design lateral load. This is a relatively simple process when the initial geometry of cable arrangements and the initial state of stress of the cables are independent variables. This is best visualized by considering a planar rectilinear two-way cable-net (such as the Kempinski Hotel cable-net described earlier in this paper), after installation of the cables but prior to installation of the clamps at cable intersections. At this point in time the geometry of the nodes is fixed (including end points and crossing points of all cables), but as each cable connects directly between support points at opposite sides of the cable-net without being physically connected to any of the other structural elements, the level of pre-tension in any cable can be varied without affecting any of the other structural elements. The process of establishing the initial state of the cable-net is more complicated if the initial geometry and initial stress state are not independent. A simple example of this would be a anticlastic cable-net. In this case each vertical cable forms a parabolic shape curve in one direction, and each horizontal cable

forms a parabolic shape curved in the opposite direction. The initial tension in the vertical cable and horizontal cables react against each other at each of the cable crossing points. In this example any change of initial tension in any one cable will result in force redistribution to possibly all of the other cables, and importantly a change in the initial geometry of the system. Therefore establishing the initial geometry and initial stress state is a complicated, often time consuming iterative process of establishing a balanced configuration of initial pre-tension values in the cables, maintaining the desired initial geometry, while achieving the stiffness required to resist lateral loads. As complicated as this form-finding process is in the analysis model, the process is repeated at full scale in the construction of the wall. A planar wall allows each cable to be stressed to its initial pre-tension more or less independently, whereas the complex curved wall will require a complex installation sequence taking into consideration the effect of stressing one cable on all the other cables. Interactions with Base Building Structure A significant portion of the design of a cable-net wall is related to the design of the areas around the perimeter of the cable-net wall. Due to the parabolic displaced shapes typical of cable-net walls under lateral loads, the relative rotations between adjacent glass panes are small, but the rotations between the perimeter panes and support conditions are large. Therefore the majority of architectural detailing considerations relate to maintaining suitable movement capacity at the perimeter to avoid glass damage as the cable-net displaces. The structural design of both the cable-net and the base building structure is significantly affected by the loads which are transferred across and the displacements that occur at the perimeter of the cable-net wall. Cable-net gain their out-of-plane stiffness due to the high levels of pre-tension that is installed in the cables during installation of the wall. These forces must be transferred to the base building structure around the perimeter of the wall. For larger cable-net walls these force levels can be a significant contribution to the overall design demand on the main lateral force resisting elements. The EOR needs to take into consideration the forces applied to the structure in the permanent condition (cable pre-tension) and the maximum cable force levels that occur during the design wind event. The design of the cable-net itself is also greatly affected by the structural solution that is employed at the perimeter of the cable-net. There are two principal base-building characteristics that influence the design of the cable-net. The first relates to the stiffness of the perimeter boundary condition elements. The cable-net is a flexible structure, therefore the rigidity of the cable termination points is critical in its efficient design. The second important point is the careful consideration of the deformations of the support points of the cables due to base building movement. This is particularly important for tall cable-net walls and cable-net walls spanning between separate structures. Racking of the cable-net wall due to drift of the base building, and changes in cable tension due to supporting structures at either side of the wall moving towards or apart from each other must be carefully considered in the design. Interactions with Building Officials Because the cable-net is rarely integral to the stability of the building and its design may lag that of the base structure, it is commonly treated as a deferred submittal, approved in principle on the strength of the base building AOR and EORs drawings and calculations at the time of permitting for the building structure. When its design is complete, drawings and calculations describing the cable-net are submitted. Aspects of the net which have bearing on the AOR and EORs scope should be addressed in their submittals at the time of permitting. For instance, glass adjacent to a walking surface is required to be safety glazing, and overhead glass must be laminated. These aspects of the wall are depicted in the architectural plans submitted for review. Structural plans and calculations should demonstrate that support requirements of the cable-net wall have been met. Many buildings with cable-nets are permitted on the basis of these documents alone, however the cable-net designer retains liability for his design. In cases where the wall and buildings performance are linked by interaction effects or the building department has concerns about the design of such an unusual feature, code officials often take stronger interest in the design of the cable-net system. Its designer may have to meet with them to explain the technology and analysis methods, review case histories of similar projects, and discuss the approval process and required submittals. Especially on large projects, owners faade consultants may play a supervisory role to supplement the checks of the building department. They work to ensure that the design meets code, project specification, and architectural requirements. Because they specialize in faades, consultants often have a better understanding of the design requirements and constraints of cable-net walls and can play a constructive role in bringing the project to successful completion. Large projects also often include wind tunnel testing and faade mock-ups, both of which can be used to help substantiate the cable-net wall design.

CONSTRUCTION IMPLEMENTATION

Construction Means & Methods Engineering. Because cable-nets are relatively uncommon, few installers have experience erecting them. Indeed, this is one of the primary reasons that cable-nets are typically constructed on a design-build basis. The installation sequence and procedure are planned in tandem with the design of the wall. Clearances need to be allowed for the tensioning apparatus, and provisions made for tension adjustment during the buildings service life, should it be required. Planning also includes determining the exact cable length to order, usually specified as a length at a specific load. Pre-stretched cables are used to minimize creep over their installed lifetime, but their effective modulus of elasticity varies by cable construction and batch. Also crucial to ensuring their fit is the base building EORs estimate of deflection resulting from cable installation and the position tolerance of that supporting structure. If cables are ordered after the support structure has been installed and surveyed its tolerance need not be considered. Ordering cables at their service tension and having a reasonable estimate of the support deflection ensures they will fit properly. However, it is still important to know their approximate modulus of elasticity to ensure that tensioning is possible. A cable expected to stretch 50mm during installation needs to have at least 50mm of free thread to tension by. In practice it needs far more thread than that to accommodate erection tolerance, jacking apparatus and permanent connection hardware. Temperature loads are a further factor to consider in planning an installation. Indeed, they must be considered throughout the walls design. Typical operating temperature ranges for buildings are relatively well defined and controlled, but until construction is complete and the building is enclosed and occupied, the range can be quite large. This affects both the cable tension at time of installation as well as the installation sequence. If the site is very cold, the cables must be installed with a higher tension value than their service tension since they will relax once the building is enclosed and conditioned. This can affect the tensioning sequence if the required tension exceeds the allowable temporary or permanent load for the cables, depending on the installation duration. The tensioning sequence represents the final component of means and methods engineering, and can be used to solve issues related to temperature limitations. If need be, the cables might be tensioned to a percentage of their service tension, the building then enclosed and conditioned, and the cables finally brought to their full tension. In such a scenario the cable-net designer would need to verify the walls ability to perform at a reduced tension for a specified period of time. ASCE 37-02, Design Loads on Structures During Construction, gives guidance on load adjustments based on various durations. Installation Sequence and Tensioning Layout and survey of the cable anchor positions are the first and arguably most important steps in the installation of a cable-net. Small changes in length or geometry can dramatically affect the cable tension, ability to properly tension the net, or the fit up of the glass, so it is essential that the anchors are placed in the correct positions. By designing adjustable connection points and allowing an additional length of threaded cable end, the cable-net designer can ease this first step. Provided that the anchors have been properly located, the remainder of installation can be relatively simple. Cables are hung, tensioned, and clamped together. Selected nodes may then be surveyed and the glass installed and caulked. Though the process is simple, it is important that the cable-net installer work with the buildings general contractor (GC) to schedule and coordinate the installation. The base building EOR should be notified sufficiently in advance of the planned tensioning to be able to plan a structural observation visit to the job site. Though the visit may be informal, its focus should be to ensure that the perimeter structure supporting the wall has been properly installed, necessary welds completed, and concrete sufficiently placed and cured. Because ultimate responsibility for proper installation rests with the GC, it is important that the cable-net installer educates the GC about the installation procedure and coordinate its scheduling. Cable hanging and preparation for jacking may take just a few days or weeks depending on the size of the wall, but when ready the actual tensioning operation can take just a few hours. Hydraulic jacks are required to bring the cables to full tension for all but the smallest of walls. In a typical arrangement a hollow-core jack is mounted on a jacking chair that straddles the threaded cable end swage. On the swage are a permanent nut, the jack, and a temporary nut used during

tensioning. The jack is extended, engaging the temporary nut and tightening the cable. The permanent nut is run down snug against the cables ultimate bearing surface and pressure is released from the jack, allowing it to be disassembled. Commonly, jacks are installed on multiple cables and pulled simultaneously, linked to a common hydraulic reservoir. In this manner the actual tensioning can be completed with relative speed.

Figure 14. Cable jacking

Figure 15. Cable tension measurement

Installation is completed with affixing or tightening the cable clamps, which are often installed at the same time the cables are hung, and with placement of the glass. Provided that the cable anchors were properly located and installation correctly planned, the glass often installs very easily. Here, again, the cable-net designer can do much to ease installation by detailing adjustable connections between the nodes and the glazing. This serves as further evidence of the advantage of design-build contractors in completing a successful cable-net project.

Figure 16. Glass installation

Figure 17. Caulking of joints

Post Construction Performance. Once construction is complete and the building enclosed, the cable-net has relatively few requirements beyond occasional cleaning and tension monitoring. Cable tension is generally checked one hundred hours after initial tensioning, and record tensions are taken once glass has been installed. The record tensions should be noted on as-built drawings submitted at the completion of the job. Typically tension measurements are then performed after one year and every five years thereafter to ensure that the wall is working as it was designed and no significant creep or other factors have affected its capacity.

CABLE-NET FUNDAMENTAL THEORY

Planar cable-net walls derive their out-of-plane stiffness from the geometric non-linearity behavior of a flexible element spanning between pinned supports. The element has negligible bending stiffness, but its axial stiffness provides resistance to lateral deformation into an alternate configuration that will necessarily be of a longer length that the original straight line connection between two points. Therefore, the elastic potential energy stored in the extended elements in the deformed shape can be equated to the work performed by the applied load displacing from the original to the deformed shape. Although the cables can deform into any number of configurations due to uneven load conditions, the deformed shape of a single cable under a uniform distributed lateral load w, can be shown to be a parabola of the form of equation (1). This differs from the typical hanging chain catenary profile due the fact that the wind load can be assumed to be uniform along the length that is a horizontal projection of the deformed shape: 2xay = (1) The parabolic displaced shape under a constant projected horizontal load can be verified with the following proof:

Figure 18. Parabolic free body diagram

The horizontal component of force in the cable (TH) is constant. The vertical component of force in the cable (Tv) increases linearly with respect to x from zero at the center to wL/2 at the support: xwTV = (2) Taking moments around the origin for a free body extending from the origin to an arbitrary point on the curve (figure 14):

( )xxwTyxxw H =+

2

(3)

22

xTwy

H

= (4)

As the applied load and the horizontal cable tension is constant, the cable will deflect to a parabolic form, with the parameter:

HT

wa2

= (5)

If we consider the maximum allowed ratio of deflection under wind loading to span be a constant, R.

RLy =max when 2

Lx = (6)

Equating (1) & (6):

2

2

=

LaRL

(7)

LR

a 4= (8)

The angle of deviation the cable makes at the intersection with its support point is:

=

H

VMAX

TT1tan (9)

Equating (5) & (8)

8

LRwTH = (10)

2

wLTVMAX = (11)

Gives:

=

R4tan 1 (12)

For any given span to deflection ratio R, the shape of the deflected cable is similar: parabolic with a fixed angle of deviation at the supports that is independent of the span. For the condition R = 45, as used in the design of the New Beijing Poly Plaza project described in more detail later in this paper, the angle of deviation at the supports is approximately 5.1 degrees. As the deflected shape is similar for a given value of R, we know that the ratio of extended length to initial length is constant. The length of the parabolic shape can be established through the summation of a series of small sections of the parabola.

( ) dxdsS L= 2/02 (13) By Pythagoras rule: 222 dydxds += (14)

+= 2

2

1dxdy

dxds

(15)

dxxaSL += 2/0 22 )41(2 (16)

The integral is can be shown to equate to:

( )

++=

aaLLaLS

4sinh1

42

122 (17)

Substituting with equation (8) gives:

++=

16

4sinh116

412

1

2R

R

RLS

(18)

That average geometrical strain in the cable due to the deformation under lateral load is constant for a given value of R:

00132.01 == L

SAVG when 45=R (19)

The strain varies with the tension in the cable, from a minimum at mid-span, to a maximum at the supports:

( ) ( )

+

=2

2

2xw

awxT (20)

( ) ( )22412

xaa

wxT += (21)

The average tension in the cable will be:

dxxTL

TL

AV = 2/0 )(2 (22) By analogy to the integration of equation 16 is:

++

=

16

4sinh116

412

8

1

2R

R

RLRwTAV (23)

HAV TT 00132.1= when 45=R (24) The average tension in the cable and the average geometrical strain in the cable due to its deformation under lateral load are both independently fixed for a design solution that meets the design span to deflection ratio. This apparent incongruity is explained by the fact that although the average tension in the cable is fixed by the geometry and loading condition, this tension can be achieved by a combination of initial pre-tension in the cable and additional tension due to elastic strain: EATT AVGiAV += (25)

For a given geometry and loading condition, there are a series of compatible pairs of axial stiffnesses and pre-tensions which will exactly meet the deflection criteria. These range from the impractical: zero pre-tension and large axial stiffness, to the implausible: pre-tension equal to the average tension in the cable under lateral load and effectively zero axial stiffness. As the elastic modulus of a given material is fixed, reducing the stiffness requires reducing the cable area. As the maximum cable tension is defined by the loading condition and geometry, there becomes a point when the cable size is reduced to the point of not having adequate strength capacity to resist the design load conditions. Knowing the material characteristics of the proposed cable elements, we can establish the minimum cross-section that can resist the design tension. This will result in the compatible pair with the highest pre-tension, however there is generally no negative economic effect on the design of the adjacent supporting structure. Although the pre-tension is high, the design of the supporting structure is typically controlled by the maximum in service tension and not the pre-tension force. Special conditions such as flexible support conditions consisting of materials adversely affected by high permanent load conditions (concrete or timber) may warrant the selection of a compatible pair of higher axial stiffness and lower pre-tension. For R = 45: kNLwTH 625.5= (26)

kNLwTVMAX 5.0= (27)

kNLwTAV 632.5= (28)

kNLwTMAX 647.5= (29) If we use Pfeifer GmbH 1x61 and 1x91 stainless steel spiral strand cables in the diameter range of 20mm to 36mm (a range which includes the most common sizes in cable-net wall construction), we can then establish from the manufacturers published technical data the elastic modulus of the cables and an appropriate design stress limit in the cables. The design stress limit value does not vary significantly for the range of cable diameters considered:

2.130 = mmkNE (30)

2, .688.0 = mmkNA

Z dR (31)

For the above example the minimum cable area shall be:

22 208.8688.0

mmLwmmTA MAXMIN == (32)

And maximum compatible pre-tension value shall be: kNLwEATT MINAVAVMAXi 224.4== (33) The above results confirm that the minimum required cable area, the compatible pre-tension value, and the maximum cable tension under design loading conditions are all linearly proportional to both the length of span under consideration and the uniform lateral load. As an example, a one-way spanning cable-net consisting of 22mm diameter cables (A = 281mm2) could be designed to span 22.8m when subject to a uniform lateral load of 1.5kN.m-1 per cable. The pre-tension for this solution would be 145kN, and the maximum design tension in the cables would be 193kN.

PARAMETRIC ANALYSIS STUDIES

To verify the theoretical results of the previous section, a series of parametric studies on the required cable sizes and levels of pre-tension that would be required to install cable-net systems of varying sizes were performed. Analysis models were created to study both one-way and two-way spanning cable-net systems. To minimize the number of variables involved the following parameters were set for each of the models considered: y The design loading condition was set at 1kN.m-2. y The span to deflection ratio was set at 45 under the design loading condition. y The cables were limited to Pfeifer GmbH stainless steel spiral strand cables in the following configurations: 1x37 (6-

18mm), 1x61 (20-28mm) and 1x91 (30-36mm). y The cable-net spacing was set at 1.5m. y For two-way models the cable-net model was always square with equal cable sizes and pre-tensions in each

direction. The analysis models were built using S-Frame version 6.22 (written by Softek Services Ltd.), a three-dimensional analysis program capable of accurately modeling the geometric non-linearity of cable elements under lateral loads. All elements were modeled as S-Frame cable elements, each 1.5m long between nodes. Lateral loads were applied as node loads at 1.5m on center. This loading condition represents the load transfer to the cables through the glass support fittings.

Figure 19. Span vs. cable area (one-way)

Figure 20. Span vs. cable pre-tension (one-way)

The results of the one-way cable-net analysis models support the theoretical relationships established in the previous section. A clear linear relationship is observable in the data points resulting from the analysis models (figures 19 & 20). When plotted against the theoretical linear relationships established in the previous section, we see that the data points differ from the theoretical relationship by varying degrees. The reason for this variation is that the cable selection is limited to the 16 discrete cable sizes available in the diameter range from 6-36mm (note that the 75m span analysis model requires the use of a cable diameter larger that those available an estimated cross sectional area was used for a 40mm diameter in this case although limitations on the cable end fitting technology may preclude the use of such a cable). The cable-net models were built using cable lengths that were multiples of the typical glass size, and the cable size selected was the next larger size available than the minimum cable area theoretically required. Certain data points which are close to the theoretical relationship represent situations when the required area was just less than an available cable, for other data points the next largest cable size was significantly larger than the minimum required. All analysis model cable area data points are above the theoretical relationship. A similar situation can also be observed in the data points relating required pre-tension to span length. As the modeled cable sizes are all larger than the minimum required, the compatible pre-tension values are all lower than the theoretical maximum pre-tension values. Given these limitations the correlation between analysis model and theory is very strong.

A further investigation into the behavior of two-way cable-net configurations has also been performed to investigate the additional efficiency and span capability that can be achieved by running pre-tensioned cables in two-directions across a square wall, rather than in one direction alone. We observe from the analysis results that the relationship between span and required cable area as well as between span and required pre-tensioning, appear to maintain the linear relationships observed in the one-way theoretical and analytical studies (figures 21 & 22). The analysis results indicate that the two-way cable-net system is capable of achieving a certain span to the same deflection criteria and resisting the same lateral loading condition, employing the use of both smaller cables and lower pre-tension values. This does not however necessarily indicate that the two-way cable-net system is more efficient. As both analysis models considered a cable spacing of 1.5m, the two-way system uses twice as many cables to support a square cable-net wall as the one-way cable-net system of equivalent dimensions. To evaluate the relative efficiencies of the two different cable-net systems, a more telling comparison is between the two-way system and a one-way system with an equivalent density of cables per unit area of wall supported. Doubling the horizontal cable density in a one-way cable-net system is equivalent to reducing the applied lateral load per cable by one half. As shown in equations (32) & (33), the effect of this reduction in lateral load per cable is a 50% reduction in minimum area and maximum pre-tension required.

Figure 21. Span vs. cable area (two-way)

Figure 22. Span vs. cable pre-tension (two-way)

Plotting the theoretical relationships determined for the one-way cable-net system with a reduced cable spacing of 750mm we see that the two-way analysis model requires greater cable sizes and pre-tension loads that the one-way system. This suggests that the two-way system is less efficient than the one-way system of equivalent cable density. This is supported by an evaluation of the status of each of the cables in the two-way system under the lateral load condition. When the center cables in each span direction exactly meets the specified defection criteria, the other cables running parallel to these deflect to lesser degrees. If all the cables are designed to the same criteria, most of the cables are under utilized, reducing the efficiency of the system. All the cables in the one-way system can be simultaneously fully utilized. If we design each cable in a two-way system with a span to deflection ratio that is compatible with the deflection of the whole system, we can hypothesize that the efficiency of the one-way system can be equaled. This would require varying cable sizes and levels of pre-tension which would complicate the detailing and installation, potentially resulting in higher overall costs. While the efficiency of the one-way system is high, the detailing of the boundary conditions is complicated. Two sides of the cable-net deflect through the know angle of deviation of the parabolic displaced shape, however the other two sides must be detailed to accommodate a sliding condition caused by the maximum cable-net displacement also occurring close to two sides of the net. This difficult problem is avoided with a two-way system which has small deflections at all sides of the cable-net.

PROJECT EXAMPLE THE NEW BEIJING POLY PLAZA

Architectural Concept The clients goal is for a new headquarters building that represents the companys disparate subsidiaries as a unified whole. The program for the building contains a wide range of spaces including office, retail, restaurants and the Poly Museum. The museum, established by one of the companys subsidiaries, has the unique purpose of repatriating Chinas cultural antiquities through purchases at international auctions. The project is prominently located at a major intersection along Beijings second ring road, northeast of the Forbidden City. The sites primary orientation is northeast towards the intersection and beyond to the clients existing headquarters building. The triangular form minimizes the perimeter length exposed to the elements, while a series of interior atria provide additional interior surface area to give office areas maximum access to daylight. The result is a simple L shaped office plan that cradles a large atrium (figure 23).

Figure 23. Atrium concepts.

Figure 24. Museum lantern.

Figure 25. Northeast rendering

The Poly Museum is suspended within a lantern in the main atrium space (figure 24). Its crystalline surface of laminated patterned glass is pleated to increase its light reflecting/refracting qualities (figure 25). Inside the lantern, exhibit and lease spaces are enclosed by wood walls which control daylight while common circulation areas occupy the void between the solids and the glazed perimeter walls. Secondary sunset and all-day atria cut through the west (figure 26) and south (figure 27) legs of the L to act as daylight chambers for bringing direct sunlight into the main atrium. The exterior walls of these atria are comprised of minimal glass membranes, supported by two-way cable-nets in order to maximize visual and solar transparency. The main atriums cable-net is stiffened by two V-cables that are in turn counterweighted and kept in tension by the self-weight of the suspended museum lantern..

Base Building Structural System The base building is a composite concrete and steel structure, roughly triangular in shape, and 24 stories tall above grade. The lateral system is a dual system consisting of reinforced concrete shear wall cores at the three corners of the building, (figure 28), and steel moment resisting frames in the north-south and east-west wings. The floor framing system above grade consists of structural steel trusses acting compositely with metal deck slabs and lightweight concrete fill. The building also has a rectangular four-story basement, the lowest slab being located at approximately 20 meters below surrounding grade. Gravity framing in the basement consists of conventional concrete beam and slabs framing. The structure is underlain by a mat foundation anchored against hydrostatic uplift using tie-down anchors, where required. Two areas of the base building structure required special treatment. The first area was the entire south wing of the building. To open the atrium up to direct sunlight from the south, steel columns in the southern wing do not continue below the tenth floor creating a bridge between the cores and columns at the east and west ends. The bridge structure is supported by vierendeel trusses over its entire height from level 10 to level 24 (figure 26). The bridge structure is considered part of the lateral system, acting, along with the columns at each end as a mega frame. The bridge and floor slab diaphragms tie the three cores of the structure together to form a monolithic structure, modeled and analyzed as such (figure 28). Lightweight concrete fill was typically used on metal deck floor slabs, but critical connecting diaphragms at the bottom of the vierendeel structure and at the top of the tower, used a thickened normal weight slab with supplemental diaphragm shear reinforcement..

Figure 26. Typical high-rise plan

Figure 27. Typical low-rise plan

Figure 28. Reinforced concrete cores

Figure 29. Lanternstructural system

The second area requiring special engineering treatment was the museum occupancy termed the lantern, which protrudes from the southeast core towards the building atrium. The lantern consists of an eight-story tall (starting at level 2) cross-braced steel frame that cantilevers 24m from the building core. There are no column elements underneath the lantern. The tip of the cantilevered frame is effectively propped by its connection to the primary diagonal cables which simultaneously stiffen the cable-net wall (figure 29). The gravity load bearing elements of the lantern are the southeast building core, and the primary diagonal cables which transfer gravity loads back to the cores at the top of the building. To provide a redundant gravity load path, the braced frame of the lantern has been designed to achieve a life-safety performance level when cantilevered from the shear-wall core without the load supporting benefit of the primary diagonal cables. Lateral forces in the lantern are resisted by the shear wall core at the south-east side acting as a torsion box. The shear wall core is torsionally restrained by the ground floor slab at level 1 and by its connection to the main building through the level 12 and higher level diaphragms. The lantern floor diaphragms transfer the lateral force to the core on a level by level basis. The Cable-Net Wall The New Beijing Poly Plaza project includes a 90 meter-tall atrium enclosed by a cable-net glass wall, 90 meters high by 60 meters wide. The scale of this wall greatly exceeds that which has been built before, introducing specific challenges that are not critical in smaller walls. SOMs preliminary analysis showed that the cable-net spans were too large to be economically achieved using a simple two-way cable-net design. SOM determined however that the cable-net could be achieved by subdividing the large cable-net area into three smaller zones by folding the cable-net into a faceted surface, and introducing a relatively stiff element along the fold lines. The faceted cable-net solution allows the individual sections of the cable-net to span to a virtual boundary condition at the fold line, effectively shortening the spans. Rather than introduce a major beam or truss element to stiffen the fold line, a large diameter cable under significant pre-tension is used. The cable-net wall system was designed to meet a span to deflection ratio limit of 45, when subjected to the service level wind load condition (50-year wind event). The cables were designed to meet the requirements of ASCE 19-96: Structural Applications of Steel Cables for Buildings. The design strength load factors of ASCE 19-96 were increased from 2.0 and 2.2 (depending on load condition) to 2.5 to meet additional requirements set by the committee of Chinese Structural

Engineering Experts reviewing the design of the project. In addition to the application of increased load factors, the cable design forces were based on the internal forces resulting from a higher level wind condition (100-year wind event). The 50-year and 100-year wind loading conditions were determined through careful wind engineering studies performed by Beijing University. The wind studies included a traditional rigid model of the building massing placed within a proximity model, and an aero-elastic wind tunnel study. The aero-elastic study was performed on a flexible model of the northeast cable-net wall, constructed using wires and a flexible membrane and tuned to simulate the anticipated dynamic response of the cable-net system. This study allowed the effect of feedback between the dynamic behavior of the cable-net and the wind forcing function to be considered. This additional study was used to verify and modify where appropriate the results of the rigid model study. Analysis and testing shows that the New Beijing Poly cable-net wall behaves very much as conceived. The results from the static non-linear analysis (geometric non-linearity) clearly show that the strategy of subdividing the wall into facets with shorter individual spans was successful (figure 30). This strategy allows the overall displacements to meet the L/45 deflection limit between hard boundary conditions while maintaining the economic viability of the project.

Figure 30. Deflection under static wind load condition

Figure 31. Sub-division of cable-net wall

The final design solution was achieved with the largest of the four primary cables 275mm in diameter and consisting of a parallel strand bundle of 199 individual 15.2mm diameter 1x7 strands. The largest cable is pre-tensioned to 17,000kN, and experiences a maximum in service loading of 18,300kN during a 100 year wind event. Using the faceted design solution, the typical horizontal and vertical cables are limited in diameter to 34mm and 26mm, pre-tensioned to 210kN and 100kN respectively. Horizontal and vertical cables are spaced at 1333mm and 1375mm on center respectively (figure 31).

The Rocker Mechanism The four primary diagonal cables which support the self-weight of the lantern connect diagonally from the roof of the museum lantern at level 11, to the top of the atrium at level 23. As the base building structure will drift under anticipated seismic loads, the cables will act as braces and attempt to resist the base building drift unless the force levels in the cables are limited in some manner. Designing the primary diagonal cables to resist these brace forces while maintaining an appropriate factor of safety would have significantly increased the primary diagonal cable sizes that as employed in the final design solution. This would also have resulted in the initial level of pre-tension in the primary diagonal cables being a lower portion of the cable breaking strength, to accommodate the additional brace demands. Pre-tensioned cable systems typically rely on a high initial level of pre-tension to maintain the desired architectural form in the permanent load condition. When cable systems are installed with only a nominal level of initial pre-tension, the tendency of that system to exhibit significant deflections due to the self-weight of the cables is greatly increased. Therefore, it was determined that the design solution required that the primary diagonal cables (the only cables that may act as braces) be decoupled from the lateral system of the base building structure. The connection between the primary diagonal cables and the roof of the lantern is complicated by the need to decouple the primary cables from the lateral system of the base building structure, and to simultaneously provide a flexible wall system which allows the relative lateral movements between the roof of the lantern and the roof of the building to be incrementally accommodated over the height of the cable-net. Several connection concepts were evaluated before the final design solution was determined. One option connected the main cables to the lantern roof through a sliding connection (figure 32). This solution was difficult to achieve due to the resulting eccentric load path of the very large primary cable forces through the eccentric connection when the connection was displaced. It also resulted in the upper half of the cable-net moving with the roof of the building, and one course of glass at the roof of the lantern being required to accommodate the full drift between the roof of the building and the roof of the lantern. This resulted in this course of glass likely to fail given any significant lateral displacement of the building, causing a safety hazard in the atrium and street below. A second concept connected the bottom of the V cables to the top of the lantern through a 4m tall, pin-ended link element (figure 33). This solved the load eccentricity issue, but still resulted in the relative lateral drift of the upper half of the cable-net being concentrated in a small portion of the wall. This solution also induced tension in the main cables as the building drifts due to the downward movement of the lowest point of the cables caused by the rotation of the link around its base. The concentration of a significant portion of the lateral drift of the building in a 4m high zone still resulted in the high likelihood that glass panels would be lost during the design level lateral drift event, representing an unacceptable risk to the occupants of the building and adjacent outdoor spaces.

Figure 32. Slider connection concept Figure 33. Link connection concept The final solution is shown diagrammatically in figure 22. The decoupling mechanism consists of the equivalent of a pulley at the lower point of the V cables. As the overall building drifts, one half of the V tries to lengthen and the other half tries to shorten. By connecting them together using a pulley or equivalent mechanism, the strains are able to offset each other, without inducing additional load in the cables. A cast steel rocker mechanism was designed to perform the equivalent

function of the pulley. By crossing the cables and connecting to the rocker casting arms, the need to provide curved pulley surfaces and curved sections of the main cable were eliminated (figure 34). The rocker mechanism solution allows the load path at the connection to be concentric, and also allows the relative lateral drift of the upper half of the building to be distributed through the upper portion of the cable-net wall. Small relative movements between adjacent nodes on the main diagonal cables and the cable-net cables are accommodated using pin-ended tie-rod connections.

Figure 34. Pulley equivalent concept

Figure 35. Rocker clevis castings on site

Figure 36. The installed rocker mechanism

To evaluate the effectiveness of the design solution prior to completing in-depth analysis of the system, a physical model of the rocker mechanism was built along with a model of the link concept for reference comparison. The models were installed in a pin-connected frame, with soft springs installed in series with the diagonal cables. By racking the frame backwards and forwards, the relative effectiveness of the two concepts could be visually evaluated. The physical model test demonstrated significant extension in the springs using the link model and negligible extension in the springs using the rocker mechanism model, highlighting the ability of this connection to decouple the main cables from the base building lateral system. The final design of the rocker mechanism included five large castings per connection. The main cable clevis castings are approximately 4m in length. The clevis castings are designed to pass through each other to maintain concentric load paths through the connection (figures 35 & 36).

Summary At 90m tall by 60m wide, the New Beijing Poly Plaza represents a significant step in the design of cable-net wall systems. Completed in December 2006, the wall is believed to be four times larger than any cable-net wall system built to date. The engineering challenges of a cable-net wall of this scale required creative approaches to solving issues that have likely not been addressed on smaller projects. The design solution for the rocker mechanism is an example of an innovative design solution that employs conventional technologies to solve a truly unconventional problem. The architectural design team quickly embraced the rocker mechanisms as the central components of the machine that is the structural system of this atrium. As keystones through which the lantern and the cable-net support each other in a symbiotic relationship, the rocker mechanisms are celebrated accordingly. Prominently located in the center of the atrium picture window, they are approachable from the lantern rooftop caf and are expected to become a focal point in the experience of this building.

Figure 37. The New Beijing Poly Plaza

Diameter (mm) Spacing (mm)

Pre-tension (MN)

Main V cables 235-275 - 11.4-17.0

Horizontal 34 1,333 0.18-0.25

Vertical 26 1,375 0.08-0.10

Figure 38. Cable summary statistics

Acknowledgements Client: China Poly Group Design Architect: Skidmore, Owings & Merrill LLP Design Engineer: Skidmore, Owings & Merrill LLP AOR / EOR: Beijing Special Engineering (base building) & Design Institute Cable-Net Yuanda / Contractor: ASI Advanced Structures Inc.