3 unit aggregation
Low water and flooding configurations. In low water, floors rest on pilings. In a flooding situation, monocoques lift off from pilings and float, sliding up and down along mooring posts which direct plumbing and electrical wiring into the ground.
15 unit aggregation
Zcorp print, structural frame with rectangular and round members
Shown here are several experiments conducted with a structural optimization software program (topological optimization based on finite element analysis). In each test case, the locaton of restraints, the magnitude, location and direction of loads, and material properties are specified. A an optimized structure (of minimum volume) is computed, given maximum von Mises stress. I was interested in creating a gradient environment and then observing how optimal structure evolves along this gradient as a critique of operations of morphing or blending, which I would argue offer an impoverished understanding of transitional mechanisms within complex systems. Above is an environmental gradient from a paradigmatic cantilever condition to catenary condition: from exposure to entirely lateral loads to vertical loads. Note that the optimized structure which develops as one moves between these two paradigmatic conditions is not a simple morphing of extreme shapes, but that there are unexpected jumps or shifts in morphology as one moves across this gradient.
Above (top row): a gradient between an ideal case of exposure to tensile force and to twisting. Bottom row: from lateral force to twisting.
A larger plot of a gradient from vertical to lateral force exposure.
Exposure of a surface to pure tensile force, plot of von Mises stress (far left), optimized structure (second from left), exposure to pure transverse force, von Mises stress plot (second from right) and optimized structure (far right).
Above, bottom row: The exposure of a surface to a gradient field, from tensile to transverse force. Plot of von Mises stress. Top row: At each extreme, optimized structure under exposure to transverse force (left) and tensile force (right), and the transitional pattern that develops between which is not a simple blend or morph between these extremes.
A surface exposed to a gradient voiding pattern which shifts from orthagonal to hexagonal in organization and loaded in tension. Left: von Mises stress plot. Right: optimized structure. Note transitional pattern.
Variation of optimized structure of a dome with a distributed vertical load as aperature size varies.
A 3-dimensional elaboration of the first experiment: exposing a structure to a gradient environment from cantilever to catenary condition. A structure supported by piles which wrap around its length,such that it cantilevers at one end and is vertically supported at the other. The structure is optimized to minimize volume based on maximum allowable stress. Blue piles may be removed from the optimized structure. The result is not a gradient pattern of pilings from the cantilevering to the vertically supported end. Gradient environmental conditions thus do not result in gradient (ie smoothly morphing) structures.
Figure 118: Flooding at + 8 cm above sea level (light blue) and at + 10 cm (dark blue.)
Venice is a city of dramatic variability of environmental conditions, both tidal and topographical. The architecture of Venice has developed in response to these environmental contingencies. Piles allow construction on earth with low bearing capacity, as do lighter Venetian bricks, 2 inches thinner than Roman brick, and special Venetian techniques of light roof construction. The traditional Venetian house is composed of two or three bays, the narrow width of these bays limited to a few standard dimensions by the low carrying capacity of the sandy or silty soil beneath. Light brick walls were protected from moisture erosion with a facing of marble reaching just above the highest expected tide level at time of construction.
Figures 108-110: Typical wall sections of canal and residence. In blue, the highest expected water level at time of construction as evidenced by the height of the marble facing.
Figure 105: 18th century design proposal for Venetian abbatoir, note highly specific program and soil contingent arrangement of foundation piles.
Figures 111-114: Ca’ d’Oro: a typical 2 bay residence. Facade; plan of ground floor and levels 1 and 2.
Figure 107: Ca’ d’Oro: section showing thin, closely spaced floor beams typical of traditional Venetian residential construction.
Figure 106, 107: Typical Venetian residential roof construction, note thin purlins and plaster cieling to reduce weight of structure.
Figure 103: Map of Venice, 1346. Settlement of Venice began on areas of soil of high bearing capacity. Architecture built at this time utilized conventional foundations. By the end of the 14th century, settlement advanced over soils with poor bearing capacity, and from this time on, pile or raft foundations were utilized.
Figure 104: Soil types, Venice lagoon
The existing architecture of Venice has reached a limit condition wherein strategies utilized to manage environmental variability can no longer effectively accomodate the increasing rate of change brought on by global warming. Lagoon water now routinely rises above the marble facing protecting building and canal walls, causing bricks to erode. Piazza San Marco has been repaved, stacking layer upon layer, as sea levels rise, but now paving has been installed at a level where it has begun to interfere with the thresholds of Saint Mark's. The paving cannot be raised again, yet the piazza is flooded an ever increasing number of days each year.
Figure 120: Erosion and sedimentation patterns in Venice lagoon. Erosion is occuring at an ever increasing rate each year.
Figure 119: Remaining stands of sea grass, Venice lagoon. Poisioning of sea grass by industrial pollutants has increased the rate of erosion.
Top left to bottom right: Flooding pattern at current sea level, at +1 M, +2 M, and +3M. Greater Venice is located on an enormous flood plane which could become entirely submerged if the polar icecaps continue to melt.
Figure 122: MOSES flood gate. The MOSES rests at the bottom of the ocean near the lagoon inlet and is raised pneumatically during high tides. It is estimated that within 25 years, it will be raised so many days per year that it will interfere with the natural tidal flushing of the lagoon, allowing a dangerous level of bacteria and pollutants to concentrate in the canals.
Figure 121: Current velocity at lagoon inlet. The reconfiguring of the inlets of the Venice lagoon have increased the current velocity, thus increasing rates of erosion.
Figures 115-117: Flooding in Venice
Principle lines of stress created by loading a vault with internal beams and columns
Figures 99-101. Theodor Teichen, Market Hall
Placement of reinforcing along lines of tensile stress. Plan, Detail section of reinforcing.
Research Proposal
This thesis is a reconsideration of concepts of openness, integration, and multiplicity within architecture. Recognizing that contemporary algorithmic and morphogenetic architectural projects which seek to critique modernist modularity fail to offer a compelling alternative vision of integration which does not rely on reduction and homogenization to foster coherence, this project seeks to integrate elements which fundamentally differ in kind, exploring such phenomena as the catastrophe and phase shift as mechanisms which bridge between singularities which produce fundamentally different qualities, behaviors, patterns and protocols. The project seeks an alternative both to building systems based on standardized building components and those based on a single building component which is varied to produce a rhetorical parametricism (unable to productively respond to multiple independent environmental variables, and thus ultimately nothing more than an aesthetic of self-similarity). The closed self-consistent organism based either on compulsive repetition of standardized modules, or on a formally driven production of self-similar components is to be countered through the insertion of foreign codes (patterns, logics, protocols which regulate parts-to-whole relations) into an architectural body, building new potentials, competencies, and affiliations with systems outside of its interior.
Flow of principle lines of stress on a surface around two holes, tensile loading.
Figure 59. KVA monocoque frame hybrid chassis
Figure 60. The Jaguar XK monocoque
Red: cast aluminum
Blue: extruded aluminum
White: stamped aluminum
Sections joined by welding and blind rivets
Figure 61-76, C. Mattheck.
Column 1 (left): Design space, loads and restraints.
Column 2 (middle): von Mises stress
Column 3 (right) Design proposal
Row 1 (top): Tensile loading
Row 2: Twisting
Row 3: Shear loading
Row 4: Transverse loading
Row 5: Transverse loading, moment connections
Topological optimization algorithms input various environmental contingencies (support/restraint conditions, forces, specific material properties, clearance zones within the design domain which must be free of material, maximum deflection and typically the maximum allowable mass of the part/body to be designed). Goals are typically to minimize stress, or maximize stiffness. These algorithms, therefore allow an interaction between external logics (nature of restraints, position and size of loads, etc) and internal logics (material behaviors due to elasticity, plasticity, isotropic or non-isotropic composition, etc.)
Figure 81,82. Arata Isozaki, Automobile Museum
Above: Increasingly refined iterations (stresses progressively decreased) created through a topological optimization algorithm.
Below: Sections, elevation
Arata Isozaki’s Automobile Museum is one of the few architectural projects which utilizes topology optimization. Its topologically optimized roof and supports are developed as a monolithic body subject to generalized forces. (See Mike Xie’s very similar bridge structures below, which utilize the same ESO algorithm and are based upon a simple design scenario: 4 supports and an equally distributed load.) A structure which is subject to varied local loading conditions, rather than a generic distributed load, would be more highly differentiated. In addition, a field of linked components, rather than a monolithic structure, would create a finer grain of resolution, more clearly registering the effects of local stress gradients. This thesis will explore the creation of pattern, which, like the above geometric tesselation, is a highly differentiated, yet continuous field of modules, and a fusion of different regimes with different rules and behaviors, but unlike the geometric pattern, informed by material and environmental conditions.
Figures 90-95, M.P. Bendsøe.
Objective: Find optimal arrangement of tiles to minimize the weight of the structure while retaining sufficient structural stiffness.
Given: Four tiles of varying material density.
Top left to bottom right:
1. Four tiles available to build structure
2. Design space, loads and restraints
3. Topology optimization result
4. Magnification of result
Multi-scale optimization
Bendsøe, Diaz, and Chellappa have worked on the problem of introducing multi-scale modularity into a topological optimization algorithm.(109) They introduce a finite number of modules which vary in density/mass into an optimization algorithm. Predetermining the arrangement of mass within the module and limiting the number of different variables creates a compromise between optimization and standardization. It creates a microscale weave which anticipates fabrication to a greater extent than monolithic optimization solutions, breaking it into assemblable components, but does not allow optimization to inform/deform this microstructure. This thesis will seek to design an architecture that achieves optimization at both the scale of the global and at the scale of the component/microweave.
Figures 86-89, M.P. Bendsøe.
Objective: To find optimal arrangement of perforated modules to minimize the weight of the structure while retaining sufficient structural stiffness.
Given: A finite collection of modules with varying perforation radii
Top light to bottom right:
1. Design space, loads and restraints
2. Conventional topology optimization result.
3, 4. Results using perforated modules, varying allowable radii range.
Seeding a field with multiple logics
This thesis will develop multiple unique localities which will together constitute an environment for the development of structure. These may include ground conditions allowing edge support and those requiring point supports, a locality required to channel water for drainage purposes, localities in which a structural interruption/discontinuity is required, a locality characterized by the necessity for cantilevering structure, a locality requiring minimal shell curvature, and thus evolving a structure which carries loads primarily in bending, a locality in which structure is required to bifurcate to partition space, a locality in which a space which is shaded, yet open to the air is desirable, necessitating the use of tension structures, localities subject to high levels of torque and areas subject to large shear stress. Unique components and connective protocols will be developed for each locality. Research will also be directed towards the margins between and overlap of localities and the special conditions created in these areas.
Figures 51-54, C. Mattheck.
Right to left: Growth a of tree around a railing
Finite element mesh, loads and restraints
Initial von Mises stress plot
Optimized design with stress plot
Figures 47-50, C. Mattheck.
Left to right: Growth a of tree constricted by a rope.
Initial von Mises stress plot
Optimized design with von Mises stress plot
Konrad Wachsmann, Aircraft hanger
Materiality
This thesis will develop several interdependent, behaviorally distinct material systems in order to create a structure which is highly responsive to local edge conditions, lines of stress, and local methods of load transmission (i.e. via membrane stresses). Material systems will at a minimum include a system of components developed to carry tensile forces (steel or fiber-based components), a system which carries compressive forces and glazing components.
Figure 102. BX-58 Grid, 3-way Tetrahedron
Integrated tensile and compressive systems
Reinforcement meshes are typically placed along principle lines of stress. A net system of tension components must be capable of local densification, shifts in weave direction, and local unstitching and reorientation to accommodate apertures. Principle lines of compression run at right angles to principle lines of tension. Weaving together tension and compression meshes requires a contingent connective system at right angle intersections.
Figure 97,98. George Wimberly, Howard Cook Windward City Shopping Center, Elevation, roof plan, reinforcing plan
Above: Tension and compression component couple, with principle directionality perpendicular to one another
Middle: Partial mesh oriented to principle lines of tensile stress (middle). Partial mesh oriented to principle lines of compressive stress (right).
Below: Principle lines of stress on a vault. Component based meshes following lines of principle tension (right) and compression (middle).
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108 see Architectural Design: Versioning, vol.72, n.5, (2002 ), particularly Ingeborg Rocker, Versioning: evolving architectures, dissolving identities - ‘nothing is as persistent as change’, p.[10]-17 for a discussion of versioning.
109 M.P. Bendsøe, Department of Mathematics, Technical University of Denmark and A. R. Diaz S. Chellappa, Department of Mechanical Engineering, Michigan State University, Design Optimization in a Multiscale Setting.
Figures 77-80. Top left to bottom right:
1, 2. E. Saarinnen, MIT Kresge auditorium
3. E. Lamm, structurally optimized shell
4. Deformation plotted against self-weight, original and optimized design
Saarinnen’s Kresge auditorium is a dome that is trimmed such that it rests on point supports rather than continuous edges. As Martin
Bechthold explains in Innovative surface structures: technologies and applications, this trimming created engineering difficulties that required undesirable design compromises. Removing segments of the dome created interruptions in the path of hoop forces, inducing bending moments that necessitated large edge beams. In plane shearing stresses developed at the junction between these edge beams and shell edges. These issues lead Saarinnen to add vertical supports in the glazed facades. E. Ramm later digitally modeled and analyzed the auditorium’s shell, optimizing its shape through FEA (finite element analysis) such that neither edge beams nor the added vertical support would be necessary. In this case, departing from primitive geometry by adding local curvature, it may be argued, rationalizes the structure.
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Bechthold, Martin. Innovative surface structures: technologies and applications. New York Taylor & Francis, 2008.
Figures 83-85, E. Ramm.
Figures 55-58, M. Xie.
Initial design domain with loads and restraints
Optimized structure
Revised design domain (gap inserted in domain)
Revised optimized structure
