The architectural design of Jinji Lake Mall in Suzhou, China, has foreseen a continuous, 35,000 m² free-form glass roof to partially cover and conceptually rein in the four individual buildings of the mall ensemble, as well as a central atrium space. The light-weight grid-shell design envisaged was to rest directly on the seven-storey buildings and cover various out- and indoor spaces, ranging from food courts over roof gardens to plant rooms. The client envisaged its appearance to apprehend the wings of a phoenix.
schlaich bergermann und partner were appointed to devise a structural system to turn the conceptual ideas into a feasible design. The system had to cope with the different support and boundary conditions while staying truthful to the original design intent. The surface geometry was to be rationalised within limits and a panel layout proposed which was at once aesthetic and easy to manufacture. A holistic approach to design was therefore adopted. Structural considerations paralleled architectural ambition as basis of important design decisions.
The development of the form, structural analysis and their mathematical optimisation all resided within a unified, digital work-flow. Multi-resolution mesh modelling stood at the core of this work-flow which optimised for geometric and structural criteria in a combined pipeline. The parametric dependencies from subdivision modelling were employed to find optimal forms on a fully detailed finite element model of the structure. Unlike other form-finding techniques, this method assured that the nodes of the final mesh would at any point lie on a curvature continuous surface.
Given the location inside a high-grade earthquake zone, resting on four independently supported buildings incurred special requirements to the structural design of the roof. Client and architect demanded the roof be joint-free along the entire length not to impede on the unified appearance – of course, under no circumstance could the phoenix’ wings be severed! The resulting joint free length of over 600 m necessitated accounting for large thermal deformations and relative movement of seismically excited buildings below.
It was decided that the best way to cope with these challenges was to suggest a structural system with twofold flexibility. First, it needed to be insensitive to distortion. Second, it needed to perform differently in different parts of the roof.
A flexible quadrangular panel layout was chosen as it permitted deflections by changes to the inscribed angles of panels. To reduce bending moments and cross-section dimensions, a tensile hanging net of approx. 60 m span was introduced over the atrium. For the vertically supported roof parts, slender branching columns were introduced spaced at 15–25 m. These branches divided the free spans into segments shorter than 9 m, drastically lowering associated bending moments. Branches were further aligned to meet the roof at specific lateral axes. With box-sections of 350 × 120 mm assigned to beams in these axes, the remaining majority of the grid could then be as slender as 250 × 120 mm. The more vertical parts of the façade were suspended from the top part of the roof. Wind loads were transferred to the floor slab via horizontal pendulum columns, permitting unrestrained thermal elongations.
The versatility of the problems and their variation over building parts was to be captured and addressed in a combined work-flow. To establish a method which combined both structural and geometric optimisation, specially developed software was used. Using tools developed by schlaich bergermann und partner’s geometry and optimisation group sbpGo, an automated feedback loop was established between parametric models developed in Grasshopper, a parametric design plug-in to Rhinoceros 3d, and Sofistik, a finite element package. This loop was extended to be controlled by a mathematical optimiser, returning optimal parameter configurations in Grasshopper based on results evaluated in Sofistik.
The structural considerations established the requirement for a quaddominant mesh be generated over the surface. Alongside the structural benefit discussed above, quadrilateral mesh layouts in architecture have numerous geometric advantages such as higher transparency, lower beam and panel count and simplified nodes. They do, however, introduce constraints on the mesh layout or surface geometry. The mesh needed to fulfil stringent criteria with regards to regularity of beam lengths, warp of facets and uniformity of their inscribed angles.
Methods trialled to generate a suitable quad mesh included periodic global parameterisation, tracing tensor field lines and generating a mesh from a base complex using subdivision surfaces. Subdivision surfaces provided the most fruitful base framework. A bespoke implementation of the Catmull-Clark method accessed from Grasshopper was augmented to address project specifics, such as dealing with boundary conditions or simply to permit triangles at the mesh perimeter.
Changes to a base mesh were carried forward to down-the-line meshes, and the results could instantly be evaluated quantitatively for their suitability for further optimisation. This way, appropriate meshes could be created quickly and presented to the architect for discussion. The design eventually chosen had no extraordinary vertices other than at the perimeter. Lateral seams were aligned with the principal grid layout of the building using dynamic relaxation.
The second essential component to the combined work-flow was the generation of a parametric finite element model. A bi-directional Grasshopper-Sofistik interface, implemented inhouse, permitted the assignment of most standard Sofistik element attributes such as material, cross-section type, couplings or support conditions directly inside Grasshopper. The topological information already present in the geometric model was exploited to assign finite element data to individual elements quickly and intuitively, with instant graphical feedback. Moreover, variable data such as the local coordinate axes of beams would respond parametrically to changes to the geometry. The element-wise definition in Grasshopper permitted by-passing any time-consuming meshing of elements upon exporting to Sofistik. On-the-fly updates of the structural model were crucial to permit its automated optimisation to follow.
Earthquakes constituted the governing load scenarios. Relative deflections of the comparatively flexible buildings below required their being part of a global structural model. According to Chinese building regulations, structural verifications had to be carried out for frequent, moderate and rare earthquakes, allowing for different performance criteria (e.g. no yielding in principal elements). Besides the standard response spectrum analysis a time history analysis was necessary to cross-check the results.
Given these regulatory boundaries, an iterative optimization process on the 20,000 roof beams and 11,000 nodes was carried out using an algorithm developed in-house. Complementing the geometric optimisation described in section 3, the distributed steel weight could be reduced to 60 kg/m2.
By their nature, free-form façades exhibit little repetition of elements. A reduced unique panel count can carry economic benefits such as simplified manufacturing and construction site logistics. Geometrically similar facets were therefore grouped and assigned a single panel. This template panel was then mapped onto each facet of the respective group, obviously producing varying joint widths between neighbouring panels.
The minimum and maximum permissible width of these joints imposed constraints on the suitability for clustering. Yet again, these were determined on the basis of structural considerations. Interior angles of quad elements would change when deformed under load. Consequently, joints needed to allow for this deformation and contact between adjacent panels needed to be ruled out. The required tolerances were evaluated for all SLS load combinations, including seismic. Only for rare earthquakes with a return period of 2000 years inplane damage to the glass was permitted, assuring nonetheless they would rest in place.
Using these tolerances to guide joint width, the number of unique panels could be significantly reduced. For instance, unique panel count for the central hanging net was cut to about one tenth of the total facet count, with some panels repeated up to 60 times.
The Jinji Lake Mall project is an excellent example of engineering rationale driving crucial decisions to turn an ambitious concept into an inspiring proposal.
The liberating work-flow fused architectural intuition and engineering motivation. Interactive and indepth, it prompted exploratory potential greater than the simple sum of individual expertises. The playful yet highly optimised design reflects the fruitful ambition of, and collaboration between, client, architect and engineer. We look forward to the phoenix rising.
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