Elegant Structures: Diagrids take to the Sky

Terri Meyer Boake Professor of Architecture University of Waterloo Cambridge, ON, Canada tboake@uwaterloo.ca www.tboake.com

Terri Meyer Boake teaches and researches in the area of construction, environment and steel design. She has published three important books with Birkhäuser on architectural steel design, diagrids and AESS. She works with the Canadian Institute of Steel Construction to develop learning modules. She is an active board member of the Council on Tall Buildings and Urban Habitat.

Summary The word “diagrid” is a blending of the words “diagonal” and “grid” and refers to a structural system that is single thickness in nature and gains its structural integrity through triangulation. Diagrid structural systems have enabled significant transformation in the design of tall buildings. Diagrids are unique in their ability to assume all of the lateral and gravity loading of towers up to at least 50 storeys in height, eliminating the need for traditional columns and cores. Even in Supertall towers it is possible to reduce or eliminate dependence on the core in the top 15% to 30%, allowing for unique spatial opportunities.

Diagrids have created a particular elegance and lightness through efficiency, geometry and form. Where other contemporary structural systems such as megaframes and outriggers are typically repressed in the detailing of the façade and dependent building elements, diagrids are chosen to form the basis of the architectural expression of the building.

The author presents a methodology for the design of diagrid structures based upon the systematic analysis of major buildings constructed from 2004 to the present as documented in her recent book “Diagrid Structures: Systems, Connections, Details” published by Birkhäuser in 2014.[1] The design of diagrid towers will be demonstrated as based upon primary choices in module size, member type, node design, function of the core and the desired expression in the façade system. These translate into additional concerns of constructability and customized fabrication. Fire control systems will impact the ability to architecturally expose or conceal the steel, leading to detailing decisions.

Keywords: diagrid; steel; skyscraper; high-rise buildings.

1. Introduction Since the invention of the skyscraper in the late 1800s, the tendency has been towards the visual repression of its structural system, either by virtue of the particular sensibilities of the architectural style of the period or due to requirements to conceal the structure for reasons of fire protection. It is only in the last 10 to 12 years that a truly unique type of structural system has emerged that has drastically changed the role of the structural system of tall buildings to one that can become the focus of architectural expression. This is as a direct result of the elegance of this new system, the diagrid.

Although the invention of the system is credited to Vladimir Shukhov (1853-1939) and was used extensively as the support system for hundreds of water towers towards the end of the 1800s, it was really not until the offices of Foster + Partners with Arup re-interpreted the Shukhov system to create the structural system that was suited to a building. This was done for the Swiss Re Tower in London, UK in 2004 where the diagrid system emerged as a contemporary structural methodology. Major structural changes were required to transform the open lattice system that Shukhov had used for his water towers into one capable of supporting floors and cladding systems.

The developments by Foster of Swiss Re, and shortly thereafter the Hearst Magazine Tower in New

York City (2006), also acknowledge the influence of the aesthetic expression of the diagonal bracing systems in the façades of the John Hancock Tower in Chicago, IL, USA by SOM in 1969 and in the Bank of China Tower by I.M. Pei in Hong Kong in 1989. The important difference here is that the use of diagonal bracing in Hancock and the Bank of China was as a supplementary lateral system that was used in addition to vertical gravity columns and a core designed to resist lateral loading, and in a pure diagrid system the perimeter diagrid system carries all of the lateral and gravity loads and no vertical columns are required at the perimeter of the structure. As in the case of Swiss Re, this allows for an all steel structure and the use of columns at the service core/elevator/washroom area that are used to support the floor beams.

In respect of the theme of the conference, “Elegance in Structures”, diagrids have succeeded in creating a particular elegance and lightness through efficiency, geometry and form that had not before been a part of the language of structure for tall buildings. Where other contemporary structural systems such as megaframes and outriggers are typically repressed in the detailing of the façade and dependent building elements, diagrids are chosen to form the basis of the architectural expression of the building.

This paper will examine a number of recently constructed diagrid towers to identify a methodology that can be used to approach the detailed design of this new building type. The aesthetic expression of the structure in the architecture, its form and façade requires a better appreciation of the impact of decisions made when conceiving of the building. This includes setting out the overall module, deciding on the precise type of structural elements, designing the nodes and understanding the implications on the façade and fire protection strategies.

The methodology is intended to be applied during the design phase of the project, to be followed by detailed calculations to substantiate decisions in the sizing and particular nature of the members, nodes and floor systems.

2. What is a Diagrid?

2.1 Definition

The word “diagrid” is a blending of the words “diagonal” and “grid” and refers to a structural system that is single thickness in nature and gains its structural integrity through triangulation. Diagrid structural systems have enabled significant transformation in the design of tall buildings. Diagrids are unique in their ability to assume all of the lateral and gravity loading of towers up to at least 50 storeys in height, eliminating the need for traditional columns and cores. Even in Supertall towers it is possible to reduce or eliminate dependence on the reinforced concrete core in the top 15% to 30%, allowing for unique spatial opportunities.

2.2 The Diagrid System

The work of Shukhov was important as it presented a new approach to creating a structural system that was devoid of more normal vertical elements to carry the gravity loads, substituting instead a parabolic system of overlapping diagonals that were restrained by a series of “hoops” at intervals going up the tower. The nature of the diagonal members used by Shukhov – predominantly angle sections – was very light. Their parabolic curvature was possible not through intentional pre bending of the elements, but through the erection process, gravity and the sheer scale of the buildings. A modularity was established based on the hoop intervals. The connections between members was quite informal, using lapped joints and unlike trusses, forces were not required to meet at a predetermined panel point. The alignment of the hoop was slightly above or below the crossing points of the diagonal members. This is important to note as a major variation from

Fig. 1: The Bank of China, Hong Kong, I.M. Pei Architect

contemporary diagrid structures where the converging members meet at a very precisely designed nodal point.

The contemporary diagrid system that is used to structure tower type buildings is comprised of a system of linear elements that are connected at nodes that are spaced on a predetermined module. Although this references the work of Shukhov, the invention of the node is a critical improvement and defining characteristic of the system.

Another important difference between contemporary diagrid structurs and Shukhov’s towers is in the requirement to create an environmentally closed system. The open latticework of the Shukhov towers provided much less resistance to the wind than do tall towers. Diagrid based façades have been shown to assist in improving issues of vortex shedding on tall towers directly as a result of the natural faceting that ensues as a function of the scale of the module that is applied.

This same system and nomenclature can be applied to contemporary lattice systems, such as those that have been used by Foster + Partners at the British Museum Courtyard and Massimo Fuksas at the Milan Convention Center. Significant differences in scale and loading requirements between these glazed steel lattice systems and structural diagrids require that their discussion be separated from the topic of this paper.

2.3 Materiality

The materiality of diagrids makes predominant use of steel. In some instances the members make simple use of standard steel sections such as wide flange (Universal) or hollow structural tubes (HSS). Some high profile projects with architecturally exposed

systems have also used completely custom fabricated members. There is a growing tendency in parts of China and the Middle East to employ concrete filled steel tubes. The material choice is feeding directly into the requirements of the base elements of the system, in particular the function of the node and the connections to the node. Reinforced concrete or other site cast systems are unsuitable.

2.4 Scale

The issue of scale is the first aspect of the design to be considered. This will feed directly into the selection of the sizes of members and the modularity of the design. Taller or larger buildings will allow a wider range of choices in the expression of the diagrid as the variation in the size of the module will be greater. Larger or taller buildings will also have signficant load issues to contend with and this will necessarily increase the sizes of the individual diagrid members as well as the nodes. This will in turn impact decisions made in façade design.

2.5 Fire Protection and Exposed Systems

Issues of protection for reasons of fire control must be ascertained at the outset of the project as this will either allow or disallow the actual exposure of the members. This varies greatly by jurisdiction so cannot be taken for granted. Significant advances in the degree of protection by intumescent coating systems as well as the benefits of concrete filled steel tubes have allowed a number of diagrid buildings to expose their steel systems.

Fig. 2: Diagrid Tower by Vladimir Shukhov. Image courtesy Sergei Arssenev, Shukhov Foundation. [2]

As will later be discussed in façade treatment, the exposure or covering of the steel diagrid members will impact the design of the façade and the nature of the expression or translation of the placement of the diagrid through to the exterior of the building.

The decision to architecturally expose the diagrid will radically alter the decision making matrix for the project. An architecturally exposed diagrid is more likely to require fully welded connections – both within the node and for the connections between the nodes and the diagonals. This puts added pressure on the fabrication tolerances in order to ensure that the butt welds are closely aligned to ensure a seamless transition. Site welding may also require pre-heating of the material, so scaffolding and weather protection might also be required.

3. Modules and Modularity

3.1 Optimization of the Module

A diagrid tower is modeled as a vertical cantilever. The size of the diagonal grid is determined by dividing the height of the tower into a series of modules. Numerous studies have been conducted towards the optimization of the module size as a function of the building height and angles of the inclined members.[3] Normally the height of the base module of the diamond grid will extend over several stories. In this way the beams that define the edge of the floors can frame into the diagonal members providing both connection to the core, support for the floor edge beams, and stiffness to

the unsupported length of the diagonal member. As a significant portion of the expense of the structure lies in the fabrication of the nodes versus the steel that comprises the diagonal element, efforts are towards minimizing their frequency and simplifying the connection between the node and the diagonal to speed up erection.

Much engineering research is underway to establish the optimal module size, which directly impacts the “shape” of the diagrid, window size and placement as well as the amount of resources used in the project. The impact of “shape” is viewed differently by Architects and Engineers – structural concerns also being impacted by wind and vortex shedding issues.

The work of Moon established for a 60 storey tall building, based on a 1:6 ratio, measuring 36m x 36m with an 18m x 18m gravity core at the center with floor to floor heights of 3.9m that 69o is the most effective angle for a uniform diagrid.[5] This value changes as a function of the building height as well as its width to height ratio.

As a tall building functions as a vertical cantilever, the taller and more slender the building, the greater will be the differentiation between the function of the diagrid elements at the base to those towards the top. This has suggested that a variation in the inclination angle of the diagonals can be used to reduce the amount of steel and provide needed resistance in the structure. The members and connections at the base of the building must be designed to resist moment while those at the top to resist shear.

Research into module optimization by SOM in the design of the (unbuilt) Lotte Super Tower in Seoul, Korea extended the earlier research by Moon and suggested a differentiation in the height and width of the module along the height of the tower. This means that the diagonal members towards the base of the tower will be steeper as their function requires an increase of gravity load resistance as well as moment, given the action of a tower as a vertical cantilever. The diagonal members towards the top of the tower should be more inclined and the module smaller as these members have less gravity loading associated with their function and must resist more wind loading. The decrease in the size of the module towards the top of the tower has the added benefit of creating more finely faceted surface and corner conditions, which is helpful in vortex shedding. In some

Fig. 3: Current exploration into the best geometry for diagrids is based on this Figure as established by Kyoung Sun Moon in his research. [4]

cases the diagrid structure will be expressed and exposed at the top of the tower to assist even more with wind issues. This has the added benefit of creating a more interesting completion to the architectural top of the tower.

The research by SOM into the impact of module design on Supertall towers is significant if diagrids are ever to be used on towers of this height. The tallest diagrid tower constructed to date is the Guangzhou IFC by Wilkinson Eyre Architects in Guangzhou, China. It is 439m tall. The proposal

for the Lotte Super Tower was to 555m.

The current tendency, which is valid for towers that are well below 400m in height, is to keep a consistent module dimension over the height of the building. This results in the greatest economy in the prefabrication of the nodes and members as it keeps consistent geometry and relationships to the façade. Regularity in the façade is of great economic benefit in the design of the façade systems as the glazing unit sizes can be kept more uniform.

3.2 Regular Modules

Although the expression of the diagrid is translated most directly through the diagonal members, the horizontal elements are extremely important in maintaining the stability of the system. Ring beams that connect the nodes constrain the shape and act in a very similar manner to the hoops in the Shukhov towers. In smaller modules, those with heights tip to tip of the diamond in the range of 2 to 4 floors, the beams are designed in conjunction with the edges of the floors. For taller modules there may need to be some interaction between the floor edge beams and the long diagonals, in addition to the dedicated function of the horizontal members that frame directly into the node. The longer the diagonals the more likely they are to require additional lateral bracing if the desire is for slenderness. Alternately, if unbraced, the member size must be substantially increased to provide self-support. This is common if the diagrid is used in conjunction with a large atrium space where there are no floors to assist with this function. The interaction between the floor edge beams and the diagonals can be seen in the construction photo of the Citic HQ. The horizontal members at the nodal levels are more

Fig. 4: The design for the SOM version of the Lotte Super Tower examined the relationship between height and loading, coming to the conclusion that the modules should vary. [6]

Fig. 5: Citic Bank HQ by Foster + Partners works with varied modularity to create the extreme form of this diagrid building. Image courtesy Foster+Partners.

substantial than the floor edge beams.

The relationship between the overall height and number of floors of a tower is more critical in the case of a diagrid tower as the façade expression needs to terminate at a full module. Therefore the number of storeys will directly influence the decision on the primary module height. These can range from 2 floors ‘tip to tip’ on the lower end and up to 16 storeys ‘tip to tip’ on the higher end. As it is desired to avoid splicing diagonal members, leaving the issue of connection to occur only at the node, transportation and shipping issues will need to feed into this discussion. A 16 storey module will result in a long diagonal member of approximately 8 storeys in height. For this reason module choices seem to fall in the mid-range of around 8 to 10 storeys as these present less challenge in shipping and erection.

3.3 Irregular Modules and Non Optimal Angles

That the driver behind the choice of the diagrid as a structural system is architectural seems to be supported by some current designs that are choosing modules and angles that are against any of the established “rules of optimization”. Such would be the case for Citic Bank HQ by Foster + Partners in Hangzhou, China and the Poly Diamond Lantern by SOM in Beijing China. Both buildings use non optimal angles for the diagrid based on aesthetic choices in the expression of the structure as a key component of the architecture. The Citic Bank employs an extremely low slope to the diagrid members at the base of the tower, which results in an increase in the size of these supporting members that is clearly evidenced in the photo.

The faceted nature of the Poly Diamond Lantern, in the creation of a “lantern like” expression, also employs a slope to the diagonals that is well below the optimal 69o suggested in Moon’s research. This results in an increase in the size of the concrete filled steel tubes and the structure of the node.

The Poly Diamond Lantern has also modified the more standard diagrid structure as a result of the double façade envelope. This has resulted in the need to hang alternate floors to create the cavity behind the outer façade layer. This has also added significantly to the loading of the tubular system.

Where there is a desire for a variation in the floor to floor height of a building due to a change in the functional requirements of the use, this can be accommodated. In the case of the Guangzhou IFC the tower is used as a commercial office for the lower 2/3 of the tower and as a hotel for the upper 1/3. These necessarily have different floor to floor height requirements. The length of the primary diagonals was kept uniform for the height of the tower after having been carefully calculated to accommodate 12 floors of office and 16 floors of residential within the same overall dimension. Again modularity feeds strongly into the aesthetic decisions as this also had an impact on the subdivision of the glazing and curtain wall system for the façade.

4. Member Design

4.1 Member Type Selection

Understanding that the size of the module will feed directly into the structural requirements and sizing of the diagrid system, including members and nodes, there are additional factors that will also

Fig. 6: The Poly Diamond Lantern employs a shallow angle to the diagrid.

bear on this decision. The type of member chosen will depend on additional interdependent factors:

What is the fire protection required for the structure?

Is/can the structure to be architecturally exposed?

Will standard structural members suffice (wide flange or HSS most typically chosen)?

Are custom fabricated sections desired for aesthetic reasons?

Is there a desire or requirement to cover the structure, noting this can be program directed as a function of interior décor and not fireproofing.

Are there preferences or differences in expertise based on the skills and practices in the region that will inform or limit the member selection? This feeds into abilities in welding or safety preferences for bolting.

The form of the building – round versus rectangular – will create nodal geometries that will be better served by circular versus rectangular members. This was the case in the design of Swiss Re that used round tubes to work with its cylindrical form.

Concealed systems have tended to make use of standard wide flange (Universal) sections as these are cost effective. Such systems have also made use of bolted connections as they are quicker to erect and feed into worker safety concerns. Concrete filled tubes have also been used in a concealed fashion in China where this composite structural system is a common choice for many tall buildings.

Architecturally exposed systems have tended to choose amongst hollow structural steel (HSS), concrete filled steel tubes and custom fabricated sections. HSS would sit at the lower end as for cost and custom sections at the high end. The concrete filled steel tubes used in Guangzhou IFC had an additional fire protective coating applied to permit their exposure.

4.2 Hoops

The member selection for the horizontal bracing rings or hoops is quite different from that of the diagonal members. Generally speaking these rings are acting

in tension in contrast to the diagonals which are normally acting in compression. These members can therefore be more slender and assume a different structural profile. There will be differing requirements for the beams that frame the edges of the floor system as a function of whether or not these will additionally be used to brace the diagonals.

5. Node Design

5.1 Function

The design of the node is of significant importance to the integrity and function of the diagrid system. The node will be required to provide the load path through the members, using geometries that are angular and therefore not within more normative structural steel design. In the most basic design the node will need to receive four incoming diagonal members as well as the hoop elements at each side – for a total of 6 connections. The nodes tend to assume a large X shape to create a

Fig. 7: Round tubes were used on Swiss Re to work with the gherkin shaped geometry of the tower. The shape allowed for a very tight fitting, diamond shaped column cover, keeping to a slim finished profile to the members. The ring/hoop elements are different as they are acting here purely in tension, where the diagrid members must resist compressive forces. Image courtesy Arup.

distance from the central point of the load transfer in order to facilitate easier site connections. The extensions of the node also thereby slightly diminish the length requirements of the diagonal members. This is useful in the design of very large modules in excess of 8 storeys.

The connections between the node and diagonal members will normally be designed to be quite tight in order ensure that cladding is trim looking or in the case of exposed connections, to work with the aesthetics of the exposure. Connections will vary from bolting to welding as a function of the incoming members. Concrete filled tubes require fully welded and sealed connections as a function of the structural type. Concealed systems using wide flange members will normally bolt and exposed systems will use a combination of bolting and welding as suits the design.

5.2 Constructability

As with any deviation from standard framing techniques, constructability is an important issue in diagrid structures. Both the engineering and fabrication of the joints are more complex than for an orthogonal structure, and this incurs additional costs. The precision of the geometry of the connection nodes is critical, so it is advantageous to maximize shop fabrication to reduce difficulties associated with erection and site work. Some nodes are many tonnes and it is desirable to be able to lift and turn the elements with a crane to provide access for fabrication, welding and finishing.

Although in theory a node performs a similar function to the panel point in a truss, transferring only horizontal and vertical shear forces and is not intended to be moment resisting, a certain level of rigidity is essential in the design of the node to assist in the construction of the building frame. Diagrid towers are erected without temporary shoring, and so the node is required to hold the diagonals stiff during the erection process. In the case of smaller modules, two diagonals will be attached to a node in the staging area and the assembly lifted as an inverted V. Very large systems will erect the diagonals and nodes separately, so the diagonals must be adequately held stiff by the nodes as they will extend in an angled cantilever awaiting the next node.

6. Core Design

6.1 The Role of the Core in a Diagrid

As was previously stated, a ‘true’ perimeter diagrid does not need a reinforced concrete core to assist in handling lateral loading. This is based on Shukhov'’ original designs that made exclusive use of the steel system to resist all gravity and lateral loads. The decision to create an all steel building, including the structuring of the central elevator/stair/washroom zone is quite significant these days as the majority of construction is proceeding as either composite or as traditional reinforced concrete throughout. For this reason the majority of diagrids that are employed in towers are used in buildings that have elected to use a traditional reinforced concrete core.

6.2 Steel Framed Cores

The Swiss Re Tower remains one of the purest applications of a true diagrid as its central zone was designed only with steel columns to assume gravity loads and break up the span of the floor beams.

Fig. 8: The nodes of The Leadenhall Building were created from custom plate and accommodated ‘active alignment’ during fabrication brought on by the asymmetrical loading of the tapered tower.

Even Foster’s Hearst Magazine Tower in New York City required additional steel bracing be added to the steel framed core as a result of the need to offset the core within the plan thereby creating more difficult conditions of asymmetrical loading. New York City has long been a stronghold of steel construction, but here too current towers are deferring to use reinforced concrete in their cores as a new safety precaution following the outcomes of the 9/11 World Trade Towers collapse.

Although The Leadenhall Building in London, England makes hybrid use of a diagrid frame for its front façade and a megaframe with vertical supports for its side and rear walls, it also avoids the use of a reinforced concrete core. Leadenhall is quite unusual in its placement of the core services outside of the main office floor plan, locating these at the back of the tower.

What has yet to be established is the maximum height or width to height ratio for a pure perimeter diagrid system. That is, at what height is assistance required to resist lateral loading that is best answered by a reinforced concrete core. The storey heights of Swiss Re (180m/40 floors), Hearst (182m/46 floors) and Leadenhall (224m/50 floors) provide us with tested built limits of this system.

6.3 Reinforced Concrete Cores

Diagrid towers of varying heights have made widespread use of reinforced concrete cores. In the cast of Supertall towers such as Guangzhou IFC or the Canton Tower in Guangzhou, China, this has been required to address additional lateral loading criteria resulting from wind and seismic issues.

What is of interest in the design of Guangzhou IFC is the ability to terminate the large central concrete core that services the office floors at the point of the change in floor to floor height that establishes the hotel use. Here, at the 72nd floor the core splits into three smaller cores which are located in the corners of the triangular plan and allows for the creation of a central atrium space. The diameter of the exterior concrete filled steel tubes has been substantially reduced by this point.

An additional interior diagrid tube is employed to complete the structuring of the floor beams, creating a donut like shape around the central atrium. This would not be readily possible using a more traditional high rise framing system. A similar arrangement was proposed for the upper floors of the SOM version of the Lotte Super Tower.

Capital Gate in Abu Dhabi, UAE designed by RMJM Architects has also used a reinforced concrete core, in this instance prestressed to counterbalance the 18o lean of the tower. Like Guangzhou IFC the lower portion of the tower is designated commercial office and the upper portion as hotel. Capital Gate also uses the strategy of an exterior perimeter diagrid in conjunction with an interior diagrid to allow for the creation of a multi-storey atrium for the upper half of the tower. Similar to Guangzhou IFC the member size for the

Fig. 9: The Leadenhall Building, shown under construction in 2013, has its yellow core located completely outside of the office floor. Additional inverted K braces provide more lateral support, establishing this as a hybrid application of a diagrid.

Fig. 10: The atrium at the upper hotel levels of Guangzhou IFC uses a smaller diagrid of concrete filled steel tubes to structure the 30 storey tall opening.

interior atrium diagrid is smaller as a result of lighter loading. The additional interior diagrid assists in resisting lateral loads.

7. Façade Design

7.1 Expressing the Diagrid in the Façade

Diagrid buildings tend to set themselves apart from the balance of tall or Supertall buildings by virtue of their unique appearance. The current tendency in design is to express the use of the diagrid on the building.

The treatment of the expression of the diagrid frame varies between projects as a function of the desired aesthetic for expression of the frame (or not). The size of the diagrid is often expressed in the cladding of the building. The modularity of the curtain wall normally will scale down the dimensions of the diamonds or triangulated shapes to suit the height of the floors and requirements for both fixed and operable windows. The decision to use a triangulated versus rectilinear curtain wall system is not consistent and seems to be a function both of the overall size of the diagrid structure as well as the form of the building itself. Buildings with more curvilinear forms tend to use triangulated windows as these easily adapt to the form. Larger module diagrids are easier to “fit” on the façade and can more easily accommodate standard rectilinear based curtain wall systems as infill. The expression (or not) of the diagrid in the curtain wall also varies from project to project. Again this is a function of the desired architectural expression.

7.2 Triangular Patterns

Many diagrid buildings, in particular those with a curvilinear form, tend to subdivide the diagrid into triangulated glazing. The use of triangular geometry works like a “mesh” to allow for the approximation of the curved form through the use of non-curved elements. This is far more economical than using true curves, even if the glazing system itself is more expensive.

Aldar HQ in Abu Dhabi, although covering the steel diagrid on the interior of the building with gypsum board, chooses to express the location of the grids on the exterior façade. Physically this was not required as the envelope is outboard of the steel. It was an aesthetic choice. This creates a prominent diamond pattern on the façade that clearly presents the diagrid module as an element of design. Capital Gate in Abu Dhabi also uses triangulated glazing but makes a more unobtrusive gesture on the façade regarding the location of the diagrid situated behind the glass. The very small 2 storey module size for Capital Gate, to support the 18o lean, has resulted in one of the smallest modules to date. The member sizes are large and to translate this to the façade would have been quite overbearing. Instead a slight color change at the grid is used to acknowledge the pattern. These sorts of twisted forms tend to subdue the reading of the module through to the façade.[7]

Glazing choices will need to also consider the inclusion of operable windows as sustainability concerns increase. Operable windows have been incorporated into a number of the diagrid buildings using triangular windows. Awning types with the point down seem to be the choice.

Fig. 11: The large caps on the exterior of Aldar HQ indicate the position of the diagrid that sits behind the façade. The glazing units have been triangulated within this system.

7.3 Orthogonal Patterns

Rectilinear curtain wall is often chosen for projects whose forms are more planar. It is typically less expensive than the customized triangulated option. For commercial office functions these windows are a practical solution for the provision of blinds and shades and also partitions if subdivision of the interior needs to extend to the perimeter of the building. Many of the façade solutions for tall diagrid buildings will employ windows that are the same height as the floor to floor distance. Larger glazing units are more economical than systems comprised of smaller units. The designer can begin to play with the visual scale of the building in the choice of window proportion.

The frequency and nature of operable units is also important when selecting or designing the curtain wall system. Natural ventilation is seeing an increase, even in some high rise types. If operators are desired the size of the unit, nature of opening, and protection from fall hazard must be considered. Combined uses, such as office and hotel, might also infer differentiated glazing, both in terms of transparency as well as inclusion of operable windows.

The bottom line with respect to the selection and the design of the curtain wall is that it is greatly impacted by the dimensions of the base module for the diagrid. Larger modules allow more flexibility in the choice of curtain wall. Smaller modules are more restrictive and invariably lead to more complex glazing systems that tend to be triangulated. This impacts labor costs as these tend to be more time consuming to install and maintain as they cannot be fitted with standard window washing

equipment. In the case of Capital Gate, the interaction between the BIM modelling system for the diagrid structure and the façade design software was essential to addressing the design of a structure that boasts having no two of the 822 nodes or 8,250 members alike.

8. Exterior Diagrids Although the majority of diagrid tower types that have been constructed to date have placed the diagrid on the inside of the curtain wall to protect it from the environment, keeping the steel structure in a temperature controlled environment to minimize issues of thermal expansion, some diagrids have been completed that place the structure on the exterior. These are either located in more temperate environments where thermal expansion is less of an issue, or in situations, such as sightseeing towers, where the exposed structure is quite critical to the aesthetic expression of the building.

A serious issue when placing a diagrid, or any steel structure, outside in the elements is the use of a high quality coating system and a method of detailing that is durable and that will not collect

Fig. 12: Guangzhou IFC has placed the diagrid behind the curtain wall, using a rectilinear pattern that positions horizontal mullions at each floor level. Smaller units are required at the curved corners.

Fig. 13: The exterior diagrid of Shelley Street also employs a very shallow angle. Given the limited height of the project, this did not result in extreme issues with increased member size. The more flattened diamond worked well with the geometry of the building.

water or run-off. The Shelley Street building in Sydney, Australia, designed by Fitzpatrick and Partners with Arup, first galvanized the steel diagrid structure prior to installing a sealed metal covering system. As the climate of Sydney is coastal, corrosion is a serious issue – enough to warrant this double protection of the system.

The Canton Tower in Guangzhou, China and the Tokyo Skytree Tower in Tokyo, Japan are useful to compare as they would both appear to employ exterior diagrids comprised of concrete filled steel tube systems. The overlapping structure of the Canton Tower seems to more closely reflect the earlier work of Shukhov in the avoidance of the creation of nodes that complete the load transfer through a point and in one plane. The open nature of the Canton Tower structure has allowed for the overlap of the extremely large tubes, something that would not be possible within the constraints of a sealed envelope system.[8]

The Tokyo Skytree Tower uses a variation of a diagonal grid type system. As it also extensively uses vertical elements in the creation of the structure it cannot be classed as a typical diagrid. In great contrast to the design of Canton Tower, Tokyo Skytree relies on a dense network of tubular steel framing to complete the structural system – again deviating from the central idea that a diagrid for a tower is normally a perimeter system.

9. New Potential Going Forward At the time of the writing of this paper, contemporary diagrid towers have been in existence for little more than 10 years. As a structural system that can not only provide structure for tall towers, it is showing its capabilities at adapting to a wide range of building shapes and geometries, from curves to faceted crystalline shapes. The applications are indeed quite elegant and this can be quite directly attributed to the aesthetic potential of the diagrid in its form giving qualities that can also be translated through to the design of the façade.

Through the approach outlined in this paper, which is a summary of a much larger body of work presented in “Diagrid Structures: Systems, Connections, Details” it is relatively easy to approach the design of a diagrid building. The understanding of the relationships between the height/form of the building and module must first be understood prior to making the selection of the structural materials and their shapes. One of the major challenges for the design team will be in the design of the nodes, as these multi tonne elements must be designed with some efficiencies in order to facilitate quick and safe erection and work within the constraints of the design of the interior finishes, fire protection and façade.

Fig. 15: The design of the Tokyo Skytree employs some of the ideas of a diagrid structure, but relies heavily on vertical elements for its strength.

Fig. 14: The Canton Tower has a reinforced concrete core and several sections of enclosed space along the height of the predominantly open tower.

10. References

Unless otherwise noted, images taken by author. [1] BOAKE, T., Diagrid Structures: Systems, Connections, Details, Birkhäuser, 2012.

[2] Shukhov Tower Foundation. http://shukhov.org/

[3] MOON, K.S., “Optimal Grid Geometry of Diagrid Structures for Tall Buildings”, Architectural Science Review, 2008.

[4] MOON, K.S., “Optimal Grid Geometry of Diagrid Structures for Tall Buildings”, Architectural Science Review, 2008.

[5] MOON, K.S., Sustainable Selection of Structural Systems for Tall Buildings”, 5th Civil Engineering Conference in the Asian Region and Australasian Structural Engineering Conference, 2010.

[6] BAKER, W., BESJAK, C.M., MCELHATTEN, B.J., BISWAS, P., “555m Tall Lotte Super Tower, Seoul, South Korea.” Structures Congress, 2009.

[7] SCHOFIELD, J., “Capital Gate, Abu Dhabi.” CTBUH Journal, issue II, 2012.

[8] MAN, K., CHOI, T., LAM, V., YAU, J., WONG, W., LAM, K., “Engineering the World’s Tallest Freestanding Structure.” http://www.hkengineer.org.hk/program/home/article.php?aid=6418&volid=141