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Sunken Plaza & Atrium
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Złote Tarasy, Warsaw, Poland

Złote Tarasy (Golden Terraces) takes its name from Złota (Golden) Street, one of the "metal streets" established in the 18th and 19th centuries in central Warsaw. Jerde Partnership of Los Angeles was appointed concept architect, whilst Arup were brought in for the concept engineering design of the whole development.

Project overview

The design, inspired by the historic parks of Warsaw that were saved from wartime destruction, had as its main focus four retail levels grouped around a central atrium, with an undulating glass roof reminiscent of tree canopies. Canyons carve through the atrium area, allowing light to penetrate to the lowest levels, while on the south side the retail and dining areas step back in a series of curved terraces. Above these, the roof flows down to a sunken plaza, with pedestrian links to the station on two levels.

These terraced retail and entertainment levels are surrounded by two curved 11-storey office buildings ("Lumen"), a 22-storey office tower ("Skylight"), and a multiscreen cinema. Below ground are four basement levels, with 1,600 parking spaces. The scale of the project speaks for itself. A total area of 200,000m² includes 54,000m² of retail, restaurants and department stores, 24,000m² of offices, an eight-screen cinema including a premier auditorium of 780 seats, 14,000m² of public areas and malls, 40,000m² of underground car parking, a 6,000m² truck service yard, and 6,000m² of terraces and gardens.

The engineering challenges were immense. The basement car park occupies the site's full extent, requiring deep retaining walls next to live carriageways, and a raft foundation below the water table. The concrete frame had to be designed to counteract the overturning of the outwardly leaning Lumen blocks, and to support long cantilever walkways around the curved atrium perimeter. In addition, the atrium roof was of such convoluted geometry that it required some of the most complex analysis ever undertaken by Arup.

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Basement Excavation & Raft Construction

Raft foundation

To minimize the costs of retaining walls, Arup kept the deepest excavation to the site centre. Slabs were kept at a higher level on the critical north and south ends plus along the western perimeter. This resulted in several folds in the lowest slab, further complicated by the need for lift pits and lowered plant areas.

The Arup engineers decided that a continuous raft, free of movement joints, was the ideal way to control the risk of differential settlements and future cracking of finishes. As the loading intensity varied significantly, they used Oasys GSA Raft to predict the piled raft settlements, which were significantly higher under the Skylight tower. Using iterative analysis, GSA optimized the design, equalizing predicted settlements under the critical sections with the settlements of the surrounding areas. The raft is typically 1.6m thick, varying between 2.65m under the tower to 1.0m under the lightly loaded northern end.

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Basement Car Park

Basement structure

Due to architectural and functional constraints, the Skylight tower's structural core is limited in the basement levels to only 40% of its area on the upper floors. The loads are transferred to a set of push-pull columns by very large shear walls, which are 3.7m deep and 1.6m thick. The complex geometry of this transfer structure required a special finite element analysis using GSA to understand its behaviour and design the reinforcement accordingly. Apart from this unique structure, there are many transfer structures in the basement and discontinuities of some columns from the upper levels resulted in some complex beam arrangements. Arup's design, however, ensured that there was no comprise to the car park's functionality.

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Atrium Roof

The atrium roof

The spectacular glazed atrium was conceived as the project's heart. As well as enclosing the central malls, terraces and food court, the designers intended it to be an instantly recognizable architectural icon.

The over-riding architectural ambition was for the whole roof to appear as a uniform mesh, with constant-sized members. This proved extraordinarily difficult, though Arup achieved this through fine-tuning the GSA mesh design and its supports. The result is a continuous triangulated grid of steel rectangular hollow sections (RHS) of constant size, 200mm deep by 100mm wide, with wall thicknesses varying from 5mm-17.5mm depending on the forces in each member. In the end, each of the 2,300 nodes, 7,123 RHS members, and 4,780 glass panels has a unique geometry.

Structural modelling

The Arup engineers modelled the roof using GSA, with the support conditions imported from another analysis model of the reinforced concrete superstructure to ensure compatibility. They imported Jerde's basic roof mesh geometry from AutoCAD and manipulated it using additional software to orientate every RHS member perpendicular to the bisector of the angle of the two glass panels it supports. Some Visual Basic routines were also developed to map the wind loads from the wind tunnel test directly from each pressure tap location onto every structural member.

As the design developed and the wind tunnel, snow modelling, and thermal modelling results became available, the number of load cases and load combinations grew to include 14 wind load cases, 12 snow load cases, five thermal load cases, and 98 differential settlement load cases, including individual load cases with each support settling more or less than the adjacent ones. Altogether, there were 1,700 different load combinations for the ultimate limit state. The numbers of members and of load cases made this one of Arup's largest GSA model analyses, stretching computing power to the limit.

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The natural inspiration for the roof support trees

Second-order and buckling effects

In addition to the static analysis, second order buckling effects were also investigated. Simple linear static analysis is based on the assumption that straight members are perfectly straight, but in practice, any member may have fabrication imperfections. When compressive forces are applied, these imperfections cause additional bending moments, known as P-Delta effects, to arise. Bending moments are also magnified because of buckling. These additional stresses in members are collectively known as "second-order effects".

The design rules in structural codes ensure that standard components like columns and the compression flanges of beams have sufficient stiffness to prevent buckling, and are strong enough to resist not only the applied forces but also any secondary forces that arise because of their flexibility. However, these rules do not cover structures as complex as the atrium roof, which have to be designed from first principles in a similar way to the development of the code methods. Fundamental to any procedure is determination of the buckling mode shapes, buckling loads, and their associated deformations. Simple estimates of these properties are very difficult and any approximation is necessarily very conservative, leading to a much heavier roof design.

Arup developed the procedure to check the second order and buckling effects of the atrium roof several years ago, but its use was complicated by the necessary size of the GSA model. Buckling and second order analyses are more complex and take much longer than standard linear static analyses. In this particular case, the buckling analysis took over 12 hours of computer time.

The buckling analyses for the atrium roof produced a series of buckling mode shapes, with a critical load factor for each mode. Because most of the roof is highly curved in two directions, no overall buckling modes affected all of it. The significant buckling modes only affected local areas of it - generally an out-of-plane "dimple" comprising an area that is relatively flat, or of long span, or highly loaded. From the analysis results and subsequent calculations, the additional bending moments due to the second order effects were estimated for each "dimple" with a critical load factor less than 10. For most areas of the roof, these were less than 5% but in the worst cases, the moments were increased by 25%.

Another form of instability called snap-through buckling - such as when an umbrella blows inside out - was also investigated by comparing the small changes in curvature of the roof from the P-Delta analyses with the initial curvature. It was found that snap-through buckling could not occur under normal loads, because the roof is sufficiently curved to prevent it.

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Atrium Roof GSA Model

Model stats

Conclusion

The Złote Tarasy project involved one of the most complex structural analyses ever undertaken by Arup. The spectacular results were achieved through the power and flexibility of GSA.

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