The engineering legacy of the FIFA World Cup Qatar 2022: Lusail Stadium – the games’ centrepiece

This paper provides details on the challenges and innovative solutions adopted in the design and construction of Lusail Stadium, drawing insights from a number of scholarly works in the field of stadium engineering and architecture, including Zhang and Li (2018) on the overarching engineering challenges in stadium construction, Ali and Taha (2021), who provide case studies and lessons learned from innovative structural systems in large stadiums and Chen and Zhao (2020), who discuss advanced construction techniques for complex stadium structures. In addition, Gupta and Sharma (2019) delved into the delicate balance between tradition and modernity in stadium architecture, while Khan and Park (2018) shed light on specific challenges and solutions pertaining to the design and construction of large stadium roofs. Furthermore, Li and Chen (2017) offer insights into innovative facade systems and Patel and Gupta (2016) contribute valuable perspectives on construction management techniques, particularly relevant for fast-track stadium projects. The aim of this paper is to provide a comprehensive understanding of the considerations involved in the design and construction of Lusail Stadium as a good example of modern stadium engineering and architectural innovation.

The design of the 80 000-seat Lusail Stadium (Figure 1), the venue where the final game of the FIFA World Cup Qatar 2022 was played, is inspired by the interplay of light and shadow that characterises the ‘fanar’ – an Arabic word meaning a lantern. The shape of the stadium and the facade echo the intricate decorative motifs on bowls, vessels and other art pieces found across the Arab and Islamic world. The natural environment of Qatar has shaped its culture and architecture; the need for shelter and shade in the hottest months of the year has led local architecture to create strong enclosures with protected internal spaces. As such, many large structures have very simple and small openings that are heavily veiled from the sun and wind. These then open up to protected courtyard spaces of varying scales that become the focal points for life within the structures. This was taken into account in the design of Lusail Stadium.

Designing a building’s facade to keep out heat but let in light can be an enriching opportunity to sculpt light and shadow. The deep contrast within a building as patterns of light fall on floors and walls can significantly enrich the interior. The exterior cladding of Lusail Stadium (Figure 2) forms the main architectural design feature seen by spectators: the ‘masharabia’, a delicate skin of repetitive and creative geometric form, controls light and lets its changing path decorate its interior through the day. At night, it creates a sparkle of light to define the building and cause it to stand out against clear skies as spectators come into the stadium. The double-curved surface of the facade vessel sets the geometric definition and panelisation of the facade. The facade is composed of flat panels that are supported by three-dimensional (3D) adjustable brackets off the steel structure. The panels are triangular along the diagonal grids to follow the warp of the surface. The name of the city where the stadium is located, Lusail, refers to a rare Arabian flower that grows amid the desert, taking from its roots the shiny golden colour. The triangular-shaped structure of the vessel and roof’s cladding was inspired by the growing process of the Lusail plant.

The structure forms the skeleton of the stadium, supporting the bowl, roof and facade. A rigid concrete seating bowl is held by concrete cores and columns, housing all of the terracing and accommodation areas of the stadium. The roof is supported by tubular steel columns, each oriented to meet at the apex and base, forming circumferentially stiff V shapes. The concept of the outer steel vessel system is to create the impression of a ‘floating’ stadium, separated from the ground, with discreet concrete plinths supporting the structure above.

The structural system consists of

• reinforced concrete (RC) for the bowl structure, core walls and shear walls, columns, beams and slabs

• a steel-framed flooring system with a composite concrete deck slab for the rear cantilever portion of the bowl structure at level 5 and above

• precast concrete elements for the tiers, rakers and bleachers, which will mostly be removed in the legacy phase

• A structural steel system for the compression ring, V frames and vessel facade support structure

• A cable net structure with tension and compression rings as the roof structure, supported by the perimeter V frames and the vessel frame structure.

The bowl has six to eight levels, depending on the zone, and supports seating tiers, utilities and mechanical, electrical and plumbing (MEP) plants. The steel framing perimeter of the bowl on the rear side is supported by 24 RC plinths. A truss support system is used to transfer the loads of the extended floor area at level 5 and above. A composite slab system is used exclusively at the rear side of level 5 and the floors above that.

The global stability system of the bowl consists of core walls and shear walls, which reach up to the top, and floor slabs acting as diaphragms transferring the horizontal loads (wind, seismic and crowd dynamic actions) to the lateral stability system.

Based on available geotechnical investigations, isolated pad footings were selected for the columns and a raft foundation was chosen for the core walls and the perimeter cantilever concrete plinths. The 24 concrete plinths support both the bowl steel framing above level 5 and the roof structure on corbels through spherical bearings. They carry very heavy vertical and horizontal loads.

In order to allow the concrete to expand/contract due to temperature variations, expansion joints or movement joints were introduced at eight strategically selected locations without compromising the architectural design intent and at the same time meeting the structural requirements, especially due to strains induced in the slabs due to the presence of the rigid core walls and the curved shape of the slabs in plan. The expansion joints and zones are shown in Figure 3 and include the stadium bowl plus the perimeter at the level 1 podium independent structure.

Two sets of analytical 3D finite-element models were created for each zone (one for the tournament mode and one for the legacy mode). The RC beams, columns and core walls were designed using Etabs software.

Three Slab Analysis using Finite Elements models were developed for the RC suspended slabs for the design of the slabs – serviceability, strength and thermal models. The maximum requirement out of these three models was adopted in the reinforcement design. The thermal model was used to account for the long-term shrinkage and temperature variations and to evaluate long-term deflections and crack widths, present due to the restraints from the rigid core walls and the curved slab shape in plan view. Cracks on each slab face were plotted and, in all areas where the crack width exceeded 0.3 mm, additional reinforcement was added. Careful consideration was given to the application of loadings to cover the worst-case scenario between tournament and legacy modes.

The architectural configuration of the bowl structure from level 5 and above introduced an outward projection of the upper floor slabs relative to the floors below. The projected floors are supported by a truss system which spans between plinths (24 in total) spaced equally on circumferential grids around the bowl structure (Figure 4). These plinths also support the steel vessel structure and the stadium roof. In order to reduce the structural loads of the rear-projected areas that need to be transferred to the plinths, structural steel framing and composite deck slab were used at level 5 and above. Figure 5 shows a schematic diagram of the projected floors and the separation between steel and concrete construction.

The major elements of the transfer system are as follows.

• Cantilevers. The exterior columns around the perimeter of the floors project out approximately 9.0 m from the line of the support (the plinths). Cantilevers were required to support the projected slab of level 5 and the exterior columns above, as shown in Figure 6. The spacing of the cantilevers follows the spacing of the exterior columns, 7.6 m (grid spacing).

• Trusses. The cantilevers are supported by transfer trusses spanning 34 m between the plinths. The trusses are 4.5 m deep (centre to centre); the top chord is located underneath level 5 framing and the bottom chord is slightly below level 4 (Figure 7). The trusses are continuously connected within each zone (three trusses for each zone) and they are separated at the expansion joints between zones.

• Kickers. In order to reduce the deflection of the cantilevers and keep the steel section to a manageable size, kickers are provided, as shown in the snapshot in Figure 8. The lower ends of the kickers are connected to the vertical members of the transfer truss. Due to high compression forces in the kickers, horizontal struts are used to transfer the horizontal component of the kicker force to the level 4 diaphragm slab. The vertical component of forces in the kicker is resisted by the transfer truss.

The load path of the upper levels load is shown in Figure 9. The exterior columns supporting the upper levels impose loads on the tip of the cantilever on level 5 at point 1. The cantilever is supported by a kicker, a transfer truss spanning between plinths and by the connection to the interior concrete diaphragm. The offset between the external columns at point 1 and the truss at point 2 creates an overturning moment equal to vertical column loads multiplied by the distance between point 1 and point 2. The overturning moment is resisted by pull and push forces at level 5 and level 4. respectively. The horizontal pull–push forces will be resisted by the level 5 and level 4 diaphragms respectively, which transfer the lateral pull–push forces to the concrete core walls of the bowl. The cantilever loads are transferred to the truss through the kickers and direct bearing on the top chord of the truss. Finally, the truss transfers the vertical loads onto the plinths. The design forces were large, for example, the maximum tension force on the cantilever beam was 12 500 kN, the maximum compression at the bottom of level 4 was 10 000 kN and the maximum diagonal force was 8800 kN.

The roof and steel structural system of Lusail Stadium consist of a roof cladding system, a roof cable net structure, a compression ring structure, a curved V frame system and the vessel structure; all the structural components are illustrated in Figure 10. The roof span to the inner bottom chord of the compression ring is 278 m while the tension ring diameter is 122 m. The steel tonnage of the bowl structure is 10 500 t while the total steel tonnage is about 23 000 t.

For a cable net roof structure, the geometrical non-linearity is usually not neglectable. Therefore, during the design phases, an integrated structural model (Figure 11) was developed to assess the design forces and movements of the whole structure.

The primary function of the steel vessel structure of Lusail Stadium is to support the roof structure and to form the main skeleton structure on the vertical elevation that supports the facade panel. The steel vessel structure sits at the rear of the bowl on 24 circumferential cantilever concrete plinths (through corbels); the plinths (shown in Figure 4) also support the cantilever part of the composite steel bowl above level 4. The steel vessel structure is supported by bearings that sit on top of the corbels and, as such, the roof and vessel structure are structurally independent of the concrete/steel bowl structure.

From an aesthetic point of view, the key design intention of the steel structure was to form a series of triangular shape lattices on the stadium elevation while at the same time ensuring adequate stiffness and strength to provide an overall covering ‘tegmen’ of the stadium. The steel structure consists of three main parts – the compression ring, the curved V frame and the vessel structure. The principal geometries of these were governed by the following.

• Compression ring. The geometry was governed by the roof shape and the setting out of the cable net grid on the facade. Figure 12 indicates the main principle and controlling geometry features for the compression ring.

• Curved V frame. The geometry was governed by the roof shape, the setting out of the cable net grid, the perimeter location of the concrete structure slab edge, the location of the concrete plinth and the facade geometry. Figure 13 shows the four primary steps to generate the curved V frame structure.

• Vessel structure. The geometry was governed by the roof shape and facade lattice geometry shown in Figure 14.

Four primary ring chords lie on the four vertices of the box-type truss, with vertical and plan bracing arranged between them, forming the main shape of the compression ring (Figures 15 and 16). Two additional rings in the centreline of the upper layer and bottom layer were introduced into the system to provide a more efficient structural element layout. The middle ring in the upper layer was shifted down by a certain distance to provide space for the roof perimeter gutter. All the lateral loads transferred from the cable net are collected by the compression ring and converted to compression forces in the four primary rings.

The main function of the curved V frame structure (Figure 17) is to take all the loads from the compression ring and the vessel structure to the supporting concrete plinth. To prevent clashes with the floor slabs, the originally straight V columns were eventually designed to curve outwards; a minimum of 400 mm clear space was maintained from the utmost inner surface of the steel frame section and the closest floor slab edge. However, the resulting curved column would sustain considerable additional bending moment due to the eccentricity of the loading, which would result in a significant steel tonnage increase. Therefore, to ensure structural efficiency, web bracings connecting this curved V column and the vessel diagrid structure were introduced. This generated a ‘semi-crescent’ shape curved V frame system (Figure 18). The curved V frame structure also provided higher stiffness in both lateral (radial) and vertical directions.

The vessel structure is made up of a double-skin diagrid structure (spanning between the curved V frames), which supports the external cladding system. Horizontal trusses acting as wind trusses, normal to the facade surface, resist lateral loads on the facade. The diagrid trusses take all the vertical loads from the facade panel to the outer chord of the curved V frames (Figures 19 and 20).

Bearings (Figure 21) were used at the interface between the concrete corbels on the plinths and the steel V frame structure. These bearings have spherical slip surfaces to allow rotation and displacement: any arising eccentricity affects only the structure above the bearing, not the support column below. The bearings are arranged in an inverted style, as typically done for bridge structures where bearings sit at the top of a structural pier/column. The bearings were designed to always be in compression under code-based load combinations. However, an approximate 10% of the compression load allowance for the uplift resistance of the bearings was allowed to ensure the bearings have the ability to withstand any unpredictable actions.

The roof structure consists of a radial cable net that derives its load-carrying capacity and stiffness from a set of internal prestressing forces that are in equilibrium with the roof geometry and gravity loading. The structural system consists of tensioned radial cables spanning between the perimeter compression truss and interior tension rings (upper and lower tension rings) that form the central oculus of the roof. The upper and lower cable layers are pushed apart by spacer strut elements, which create the internal geometry of the roof (Figure 22). Additional plan bracing cables are also used to provide additional stiffness and deal with local variations in loading. The overall form of the roof structure is hyperbolic paraboloid and the geometry is derived mathematically to create a geometrically ‘pure’ form that will lead to an efficient cable structure.

Loads are collected by the membrane surfaces that span between the membrane-shaping arches and plan bracing cables. The fundamental vertical load-carrying principle is that vertical loads cause the prestressed radial cables to deflect through an angle and generate an equal and opposite reaction force. In this way, the roof responds dynamically to the applied loading for the applied load, cable geometry and internal prestress forces to reach an equilibrium condition.

Downward loading is collected from the nodes on the membrane surface by the internal strut element and transferred down into the lower cable net, which hangs as a catenary between the perimeter compression ring, with the internal tension ring compensating for the cables not being continuous from one side to the other, as shown in Figure 23(a).

The lower cable exhibits a downward drape in all directions and is therefore able to resist downward loads in pure tension, which is transferred into the perimeter compression ring. The compression ring takes the form of a box truss element that provides two types of support conditions to the radial cables. Every second cable is directly supported by the curved V frame inner chord under the lower chord of the box truss with the intermediate cables relying on the ability of the compression ring truss to transfer the resultant vertical and lateral forces over a span of approximately 36.5 m between the adjacent curved V frame apexes. The box truss arrangement of the compression ring provides excellent stiffness for the boundary condition of the cable net and two layers of utilities levels required for MEP. Uplift loading is carried out in a similar way by the upper layer cable (Figure 23(b)).

The spoke wheel type cable net roof system, consisting of two inner tension rings and one outer compression ring truss connected by radial spokes, is the most lightweight and thus structurally efficient and economical system for large-span roofs. A complete form-finding analysis and optimisation were conducted for the stadium roof structure. The cable net roof system of Lusail Stadium consists of a range of primary element types, shown in Figure 24 and briefly described in the following sections. Typical cable profiles of primary cable net structure and design parameters are presented in Table 1.

The structural performance of the 48 radial cables is governed entirely by the interaction between the applied loading and the curvature of the cables. Therefore, the three variables – the applied loading, the curvature of the cable and the prestress forces applied to the cable net – have to be ultimately balanced to achieve the architectural impression and the structural economy for the roof structure.

The cable net, consisting of upper and lower radial cables, crosses at the first division from the compression ring, creating a fishtail form that increases structural efficiency and stiffness. Radial cables are single lengths between the compression ring and the cross-over node and between the cross-over node and the tension ring. The upper and lower surface radial cables are held apart by vertical spacer strut elements. This arrangement maximises the performance of the lower cable net while maintaining the oculus level at an optimal position for cooling and daylighting of the stadium.

The radial cables are connected to an internal tension ring with both upper and lower cable nets around the oculus. The vertical spacing of the upper and lower tension ring cables is approximately 16 m. The upper and lower tension rings are spaced apart by vertical struts and vertical cross-bracing in between.

The introduction of bracing cables within the cable net aims to provide stability and stiffness to the primary cable net structure and membrane cladding structure, respectively. The bracing cables consist of

• plan bracing cables, cross-over in plan view between the adjacent upper radial cables to weave all the primary radial cables into a stable giant net and form a supporting point for the membrane-shaping arches (Figure 25(a))

• vertical bracings, which cross-over in the vertical plane between adjacent upper and lower radial cables and support intermediate strut posts connected to the membrane secondary shaping arches (Figure 25(b)).

The diamond shape of the roof membrane creates the impressive and unique architectural appearance of the stadium. However, to achieve this diamond shape membrane using lightweight cables and arches also created a significant challenge to the structural engineers. The special shape of the diamond required the arch to be laid along the radial direction; however, half of the arches would have nothing to sit on, except the cross-over point of the plan bracing cables. This was structurally very unfavourable as the vertical loads from the arches had to be supported by the almost horizontal cables and, once the vertical loads from the arches increased, the cables then had to deflect a lot to create adequate curvature to achieve equilibrium. In order to achieve the architectural appearance, vertical bracing cables with additional strut posts were introduced to provide extra support for both uplift loads and downward loads at the midpoint of the secondary arches and, at the same time, maintain minimum prestress for better constructability. Figure 26 demonstrates the arrangement of the two layers of plan bracings, arches and cladding membrane system. The bracing system described above ultimately simplified the roof structure to achieve the aesthetic requirement while maintaining structural stiffness and integrity.

Vertical strut posts are located at each cable intersection along the radial cables. These posts are tubular steel elements that push the upper and lower layer cable net apart and prop between the two cable nets to transfer loads between the two surfaces.

As the roof is a tension structure, it relies fundamentally on the geometry of the cable elements within it to generate load-carrying capacity and stiffness. Compared with a traditional rigid structural system, the roof cable net structure will sustain relatively larger deflections and high non-linear structural performance. This requires the connections to both connect the cables and to be able to generate local deflection of the cables to counteract angle changes. Figures 27–30 demonstrate the designs of several connections in detail.

• Radial cable to compression ring connection (Figure 27).

• Radial cable to lower tension ring connection (Figure 28).

• Radial cable to upper tension ring connection (Figure 29).

• Radial cable cross-over node connection (Figure 30).

A PTFE membrane cladding system was adopted for the roof, which covered all the seats to provide shading for spectators. This membrane cladding system was supported and formed by the roof's secondary arches and the plan bracing cables, which act as the skeleton of the membrane and generate the final diamond-type pattern to the membrane surface (Figure 31).

Adopting a spoke-like cable net system, the roof was a complex structure that exhibited strong non-linearity and required a well-developed comprehensive process to fulfil both the architectural aesthetics and structural efficiency. This process involved modelling, form-finding, non-linear analysis and, eventually, detailed design of the roof structure, as illustrated in Figure 32. The following sections provide more detail.

The generation of the structural roof geometry was the foundation of the entire design process. A parametric modelling program was developed using mathematical formulae, by which the coordinates of the master nodes and the topology could be generated directly. The structural geometry data could be exported automatically for the subsequent form-finding analysis. In the design process, the roof geometry needed to be regenerated over and over again due to architectural considerations; the regeneration was performed quickly by the parametric modelling program, allowing time during each iteration for interrogation of the analytical results to draw conclusions about the performance of the roof and guide decisions on how to increase efficiency.

The guiding geometry of the roof was that of a hyperbolic paraboloid. This form of geometry utilises a circular perimeter to create an internal saddle-shaped surface. The surface defines the upper boundary of the cable net structure as the nodes must not protrude from the surface in order to offer support for the roof cladding from below.

The fundamental process of roof geometry generation comprised the following steps (Figure 33).

• Separate paraboloid edge curves were generated for the roof’s external perimeter and tension ring. Each of these curves was divided into 48 segments to create the master nodes on the external perimeter and tension ring upon which the rest of the roof was built.

• The upper radial curves of the crossing fishtail profile cables, defined by a set of arcs, were generated between the master nodes on the lower external perimeter and upper tension ring. The master nodes on these curves were created simultaneously based on mathematical principles. The locations of these master nodes would remain fixed during the form-finding analysis as they were directly relevant to the shape of the roof cladding.

• The lower radial curves of the crossing fishtail profile cables were generated between the master nodes on the upper external perimeter and lower tension ring with indicative curvature. The only constraint was that the curves should pass the cross-over nodes, which were among the master nodes on the upper radial curves. The master nodes on the lower radial curves could then be created as their horizontal coordinates were assigned to be the same as the corresponding master nodes on the upper radial curves. The form-finding analysis would modify the starting vertical coordinates of the master nodes on the lower radial curves and the lower tension ring, which did not affect the geometry of the roof cladding.

• The structural elements of the roof's primary structure, including tension rings, radial cables and strut posts, were then assembled according to the topology.

• The structural elements of the roof's secondary structure, including bracing cables, membrane-shaping arches, oculus canopy and so on were then assembled in defined patterns.

Once the starting geometry of the roof structure was established, the geometry database, including the coordinates of the master nodes and the topology, was then transferred to the next step of the process to allow the form-finding analysis to be carried out.

The goal of the form-finding analysis was to find an updated geometry relative to the roof structure starting geometry for subsequent non-linear analysis, which was in equilibrium with the self-weight of the roof. Only the vertical coordinates of the master nodes on lower radial cables and lower tension ring were modified during the form-finding analysis, leaving the rest of the geometry data unchanged to keep the strut posts vertical throughout the process and not produce any potential conflict between the cable net structure and the predetermined shape of the roof cladding.

The applied prestress forces in the cable structure were adjusted simultaneously such that only very slight deformation would occur under the self-weight of the roof; that is, the geometries of the zero state and the initial state of the cable net were almost identical, providing remarkable convenience for both the rest of the design process and the construction procedure.

The results of form-finding were particularly sensitive to the self-weight of the roof structure, so the form-finding process had to pass through several complete stages before the results were reliable. At the end of each stage, the geometry data were updated to the results of the previous stage and the whole cycle was then repeated until no significant changes were apparent between the stages.

Once the form-finding process was complete, the roof had a different shape compared with the starting position, with a specific set of internal prestress forces. This model now represented the at-rest equilibrium roof structure, which was in balance with its self-weight, and upon which the effect of any additional applied loading could be assessed.

Non-linear analysis was mandatory in the design of the cable net structure as the deflections were significant in carrying the applied loading, which also meant that the linear superposition of results from separate load cases was no longer valid and a full analysis run had to be carried out for each combination being considered.

Figure 34 shows a typical set of non-linear analysis results. The results of these non-linear analysis cases were then used as the basis for the design of the roof cable net structure.

As per the specification, some of the requirements regarding accuracy were

• permitted tolerance of ±20 mm on the centre of pinhole of the cable connecting node plate at the compression ring inner upper chord

• permitted tolerance of ±25 mm for any other node position of the steel structure

• ±50 mm in plan for each system point of the tension ring

• ±120 mm in height for each system point of the tension ring

• ±10% of the tension force in the radial cables which were directly connected to the compression ring during the construction stage

• ±0.6 kN/m of the 4 kN/m design prestress of the roof membrane.

For the scale of this project, it was very challenging to achieve those accuracy requirements, especially with a limited construction duration. There was no chance to fabricate the membrane and facade based on the as-built geometry to adapt the deviation. All the construction work needed to be carried out immediately once the work front was open. All the elements had to be fabricated following issued for construction (IFC) geometry, and then had to be assembled properly.

To achieve the required accuracy, the following steps were taken.

• A detailed and accurate software simulation and sensitivity analysis of the construction process was developed.

• The construction sequence was decided on the simulation and analyses results.

• The accuracy during construction was controlled in stages. Each stage had built-on mechanisms to adapt and consume any tolerance deviations from the previous stage.

• This was achieved by adding a series of adjustable connections that were designed to accommodate tolerance deviations and hence avoid their accumulation as the construction progressed.

A detailed construction simulation, using non-linear analysis, was conducted by specialist subcontractors. The forward iteration method and Midas Gen software were used to analyse the process of the steel structure installation. All the changes to structures (stiffness, mass, loading, boundary conditions etc.) were considered. In any particular analysis, for newly added structures, the stiffness and mass were added to the structure in an unstressed state. For removed structures, the stiffness and mass were removed from the structure immediately.

The backward iteration method and Ansys software were used to analyse the process of the roof structure, including the roof membrane, canopy, arches, secondary cable net, catwalk, primary cable net and other miscellaneous components hanging from the roof. Based on the simulation, the processes for the steel structure and the roof structure were divided into eight stages

• V frame installation

• compression ring installation

• vessel truss V segment installation

• temporary support tower de-propping

• vessel truss A segment installation

• primary cable system installation

• secondary cable system and arch installation

• roof membrane installation.

Seven points on the outer chord of the V frame and compression ring (see Figure 35) were selected to conduct the geometry sensitivity analysis. As an example, the movements of the east–west section are presented in Table 2, in which R = movement in the radial direction (positive direction towards the pitch), C = movement in the circumferential direction (positive direction is clockwise) and Z = movement in the vertical direction (positive direction is up).

The simulation data revealed the following.

• The V frame movement in stage 1 was significant due to self-weight and weak out-of-plane stiffness. This movement could be managed by pre-camber.

• Considering the movement of stage 1 could be eliminated by pre-camber, the accumulative movement from stages 2 to 8 could then be evaluated to decide the timing of the facade installation and to design the adjustability of the facade bracket.

• After installation of the compression ring was complete, the impact of the vessel truss was very minor. In contrast, the impact of the primary cable installation was very significant.

• After the primary cable was installed and pre-tensioned, the impact of the secondary roof structure and membrane was minor.

• Considering economic efficiency, the adjustability of the facade brackets could not be too large. As such, the facade below point ② in Figure 35 could be installed before stage 6. The facade above point ② could be installed after stage 6, which was the completion of primary cable tensioning.

The final target of accuracy control was to guarantee that the facade and roof membrane could be installed smoothly. To achieve that, the geometry of the steel structure, including the cable nodes and arches, needed to be within the tolerances specified. The cable forces were also critical because they related to the safety and stiffness of the roof structure.

In total, 48 pieces of V frame were installed on spherical bearings and supported by temporary towers (see Figure 36) sequentially. According to the simulation, the out-of-plane stiffness of the V frame was relatively small; in addition, when the deformation of the temporary tower was taken into account, the biggest deformation during the installation of a single V frame was calculated to be 74 mm, located at the middle of the V frame.

To consume this deformation, pre-camber was introduced during the V frame assembly. The value of the pre-camber was based on the deformation value during the simulation. Instead of the IFC coordinates, the simulated coordinates of installing each single V frame were used as the inspection target during construction.

The compression ring was divided into 24 segments (Figure 37). The perimeter of the compression ring was about 1 km and, as such, the temperature effect was significant. Based on the simulation analysis, four closure segments were designed in four corner zones. As in stage 1, the simulated coordinates of installing each segment of the compression ring were used as the target. The pinholes of the cable connection plate on the compression ring were used as geometry control points.

According to the simulation analysis, the circumferential stiffness of the V frame was relatively small. It could be enhanced by installing the vessel truss V segments, which was not impacted by the temporary support tower before de-propping. Structural safety could also be improved during the de-propping process. The sequence of vessel truss installation could be flexible since the deformation caused by the vessel truss was very minor.

The accuracy of vessel truss installation directly impacted the accuracy of the facade bracket installation, which in turn impacted the facade installation. To accommodate part of the tolerance deviation from stages 1 and 2, the coordinates of the ball connections (Figure 38) were controlled as per the simulated coordinates in stage 3. The angle of the truss elements was adjusted during ground assembly based on the simulated coordinates of the ball connections and the as-built coordinates of the connections to the compression ring and V frame (Figure 38).

The de-propping sequence was decided based on sensitivity analysis of the structure. The geometry changes were monitored throughout and no accuracy control was required.

The same principle of stage 3 was followed. After this stage, the steel structure installation was completed.

Before the primary cable tensioning, the as-built coordinates of the pinholes of the cable connection plates on the compression ring were surveyed and compared with the simulated coordinates at the end of stage 5 to understand the deviation of the pinhole in the previous five stages. The cable lengths of the outer segments of the upper and lower radial cable were adjusted to consume the deviations. All the deviations were kept in the part between the compression ring and the cross-over nodes. The theoretical locations of the cross-over nodes and all the elements between the cross-over nodes and tension rings would not be impacted by the as-built deviations. After the primary cable was tensioned, the cable forces of the outer segment of the upper and lower radial cable were checked and adjusted to meet the tolerance requirements.

Before starting stage 7, the as-built coordinates of the tension ring cable nodes and the secondary cable connection plate on the compression ring were surveyed and compared with the simulated coordinates to understand the deviations in the previous six stages. The secondary cable length of the innermost ring was adjusted based on the deviation of tension ring cable nodes, and the outermost ring was adjusted based on the deviation of the compression ring (see Figure 39) so the deviations were consumed by those two rings and the designed geometry of the parts in between could be maintained. The arches of the innermost ring and the outermost ring were fabricated according to the as-built geometry. The duration of secondary cable installation was used to fabricate the arches, without impacting the schedule.

Deviations were mainly in the inner ring and the outer ring. The membrane connections to the tension ring and compression ring were designed to have enough adjustability to adapt to those deviations. For other locations, the adjustability of the connections could be designed smaller in order to save cost but big enough to guarantee the membrane prestress could be achieved.

Figure 40 shows a comparison of the actual deformations achieved on-site during the de-propping stage (stage 4) and the simulated values. In the figure, the green values (on the outside of the ring) are the theoretical deflections and the red values (inside the ring) are the actual deformations. The actual values matched the simulated values very well, and the maximum difference was only 7 mm.

According to the as-built survey before stage 6, most of the cable connection plates on the compression ring were within the ±25 mm tolerance. The biggest deviation in the radial direction was 50 mm, which was within the 124 mm adjustability of cable length.

An as-built survey was done after the stage 6 (see Figure 41). The maximum horizontal deviation in the tension ring was 32 mm, which was within the 50 mm tolerance. The deviation of the cross-over nodes (in green) was controlled within 25 mm, which meant the cable length adjustment to consume the compression ring deviation (in light blue) was successful.

As a result of careful accuracy control during the seven stages, the accuracy of the membrane steel boundaries was also well controlled. The designed prestress of the membrane was successfully achieved. The adjustable membrane connections to the secondary cable also helped adapt the camber of the cable due to the tension of the membrane (see Figure 42). The straightness of the membrane valley line was maintained to guarantee smooth water drainage.

The design and construction of the magnificent Lusail Stadium, the centrepiece of the FIFA World Cup Qatar 2022 tournament, was a major engineering challenge. The complex geometry and nature of the roof, the curvilinear vessel structure coupled with the tight construction schedule and installation tolerances were some of the challenges that needed to be tackled. The design and construction teams employed cutting-edge technology along with the use of an observational approach to efficiently design and safely build the stadium.

The authors are very grateful for the cooperation and support received from Mr Deng Xuyang of the Beijing Institute of Architectural Design and The Supreme Committee for Legacy and Delivery throughout the process of writing this paper. The effort and support of engineers Hilal Al-Kuwari, Othman Zarzour and Tamim El-Abed is particularly acknowledged.