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This work was carried out in 2004 by researchers in the Innovative Structures Group and the Spatial Information Architecture Laboratory at RMIT University. The objective of the project was to explore opportunities for closer collaboration between architects and engineers. One

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(a) (b)

(c) (d)

(e) (f)

Figure 9.3 Photos of the office building after completion (Ohmori et al. 2005): (a) second floor inside view; (b) another inside view of second floor; (c) first floor inside view; (d) ground floor outside view; (e) west side view; (f) south-west view. Reproduced by permission of Information Processing Society of Japan.

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Figure 9.4 Perspective view of proposed Florence New Station (Cui et al. 2003; Architect: A. Isozaki). Reproduced by permission of International Association for Shell and Spatial Structures.

Figure 9.5 Evolution of Florence New Station structure (Cui et al. 2003). Reproduced by permission of International Association for Shell and Spatial Structures.

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of the case studies conducted by the team was on Antoni Gaud´ı’s Sagrada Familia church in Barcelona, Spain (Burry et al. 2005; Felicetti 2009). Gaud´ı’s reference to natural growth and morphogenesis and his use of analogue modelling techniques had much in common with the basic concepts of ESO/BESO. Gaud´ı famously used cords with sacks of pellets hanging from them to create funicular structural systems and inverted these models upside down to obtain compression-only designs suitable for masonry buildings.

In this study, the ESO method was used to untangle some of the mysteries of Gaud´ı’s design rationale. To find the optimal design for a masonry structure, an ESO algorithm based on the principal stresses was devised in which material with the highest level of tensile stress would be removed iteratively, resulting in a design that was predominantly in compression throughout the structure. Note that it is not always possible to obtain a design that is purely in compression.

The Passion Fac¸ade of the Sagrada Familia church was partially completed as shown in Figure 9.6. From a surviving photograph of Gaud´ı’s original drawing for the Passion Fac¸ade (Figure 9.7), a sketch shown Figure 9.8 was produced as the starting point for the structural optimization process. The corresponding finite element model of the initial design shown in Figure 9.9 was then generated. Gravity loading was applied to the finite element analysis.

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Figure 9.7 Part of surviving photograph of Gaud´ı’s original drawing for Passion Fac¸ade (Burry et al. 2005).

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Figure 9.9 Initial finite element model based on the sketch drawing above (Burry et al. 2005).

Figure 9.10 shows the evolution of the fac¸ade. The final result could be considered as a structure that would transfer the gravity loading mostly efficiently under the specified conditions for the boundary supports, the amount of material, and the type of material (in this case, masonry). It is noted that each of the lower columns supports a well defined group of branching upper columns, as in Gaud´ı’s original drawing. Interestingly, both the lower and upper columns exhibit bone-like characteristics. Perhaps Gaud´ı had an unusual insight into optimal structural forms, which is hardly surprising given that he created so many structures which later proved to be highly efficient. It is also possible that he simply drew inspiration from natural load-carrying structures such as bones and shells etc. Apart from structural considerations, the bone-like columns were suggestive of both the tomb and Christ’s physical suffering in the crucifixion scene depicted in the sculpture in the porch (see Figure 9.6).

Gaudi’s ingenious work on structural optimization was conducted through analogous funic- ular models under static gravity loading. The digital tools such as ESO/BESO make it much easier to explore a large number of design requirements and options for complex architectural form finding problems. For example, Burry et al. (2005) investigated the effect of earthquake loading on the columns for the Passion Fac¸ade.

Burry et al. (2005) also carried out a series of other studies which revealed remarkable similarities between Gaudi’s designs and ESO solutions. Figure 9.11 shows three prototype column models mounted on the upper level of the Passion Fac¸ade. These models had been developed from study of Gaudi’s original drawing and use of intersecting ruled surfaces by the consultant architect to the Sagrada Familia church, Professor Mark Burry, without any input or influence from the ESO researchers. After these prototype models were created, structural optimization of columns on a sloping surface was performed using a two-dimensional finite

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Figure 9.10 Evolution of Passion Fac¸ade of Sagrada Familia church (Burry et al. 2005).

element model shown in Figure 9.12. The resemblance between the ESO results and the actual columns to be built was amazing. Note that in this case a uniformly distributed vertical load was applied to the top surface, simulating the weight from the gable lintel over the upper level colonnade. Compared to the heavy weight of the large gable lintel, the gravity loading of the columns themselves was negligible. In order to preserve the loading and support conditions, a thin layer of nondesign domain was specified at the top surface and another at the bottom surface.

Burry et al. (2005) then applied the same ESO procedure to the three-dimensional model shown in Figure 9.13. Again, the objective was to find a structure that would be in compression. In this example, the top and bottom surfaces were both horizontal. While the bottom surface was fixed to the ground, the top surface was subjected to a uniformly distributed vertical load. In the initial design, there were two narrow necks connecting the top and bottom blocks. After a number of iterations the columns branched out at the top like trees, much akin to the schema of Gaud´ı’s design for the central nave columns shown in Figure 9.14.

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Figure 9.11 Three full size prototype column models positioned on Passion Fac¸ade (Burry et al. 2005).

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Figure 9.13 Evolution of columns on a horizontal surface (Burry et al. 2005).

Figure 9.14 Nave columns of Sagrada Familia church with branching elements at the top (Burry et al. 2005).

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5.7 M PIER CL _PIER 1.8 M MAX RISE FOR 72 M ARCH CLEARSPAN 65 M CLEARANCE UNDER FOR ROAD TRAFFIC WITH 5.7 M MINIMUM

MIDSPAN OF ARCH CL

Figure 9.15 Initial sketch from the architect indicating geometrical constraints of the footbridge. Reproduced by permission of BKK Architects.