The Nature of Gridshell Form Finding

Grids, shells, and how they, in conjunction with the study of the natural world, can help us develop increasingly complex structural geometry.

Foreword

This post is the third installment of sort of trilogy, after Shapes, Fractals, Time & the Dimensions they Belong to, and Developing Space-Filling Fractals. While it’s not important to have read either of those posts to follow this one, I do think it adds a certain level of depth and continuity.

Regarding my previous entries, it can be difficult to see how any of this has to do with architecture. In fact I know a few people who think studying fractals is pointless.

Admittedly I often struggle to explain to people what fractals are, let alone how they can influence the way buildings look. However, I believe that this post really sheds light on how these kinds of studies may directly influence and enhance our understanding (and perhaps even the future) of our built environment.

On a separate note, I heard that a member of the architectural academia said “forget biomimicry, it doesn’t work.”

Firstly, I’m pretty sure Frei Otto would be rolling over in his grave.

Secondly, if someone thinks that biomimicry is useless, it’s because they don’t really understand what biomimicry is. And I think the same can be said regarding the study of fractals. They are closely related fields of study, and I wholeheartedly believe they are fertile grounds for architectural marvels to come.

7.0 Introduction to Shells

As far as classification goes, shells generally fall under the category of two-dimensional shapes. They are defined by a curved surface, where the material is thin in the direction perpendicular to the surface. However, assigning a dimension to certain shells can be tricky, since it kinda depends on how zoomed in you are.

A strainer is a good example of this – a two-dimensional gridshell. But if you zoom in, it is comprised of a series of woven, one-dimensional wires. And if you zoom in even further, you see that each wire is of course comprised of a certain volume of metal.

This is a property shared with many fractals, where their dimension can appear different depending on the level of magnification. And while there’s an infinite variety of possible shells, they are (for the most part) categorizable.

7.1 – Single Curved Surfaces

Analytic geometry is created in relation to Cartesian planes, using mathematical equations and a coordinate systems. Synthetic geometry is essentially free-form geometry (that isn’t defined by coordinates or equations), with the use of a variety of curves called splines. The following shapes were created via Synthetic geometry, where we’re calling our splines ‘u’ and ‘v.’

A-Barrel-Vault
Uniclastic: Barrel Vault (Cylindrical paraboloid)

These curves highlight each dimension of the two-dimensional surface. In this case only one of the two ‘curves’ is actually curved, making this shape developable. This means that if, for example, it was made of paper, you could flatten it completely.

B-Conoid

Uniclastic: Conoid (Conical paraboloid)

In this case, one of them grows in length, but the other still remains straight. Since one of the dimensions remains straight, it’s still a single curved surface – capable of being flattened without changing the area. Singly curved surfaced may also be referred to as uniclastic or monoclastic.

7.2 – Double Curved Surfaces

These can be classified as synclastic or anticlastic, and are non-developable surfaces. If made of paper, you could not flatten them without tearing, folding or crumpling them.

C-Dome.gif
Synclastic: Dome (Elliptic paraboloid)

In this case, both curves happen to be identical, but what’s important is that both dimensions are curving in the same direction. In this orientation, the dome is also under compression everywhere.

The surface of the earth is double curved, synclastic – non-developable. “The surface of a sphere cannot be represented on a plane without distortion,” a topic explored by Michael Stevens: https://www.youtube.com/watch?v=2lR7s1Y6Zig

D-Saddle.gif
Anticlastic: Saddle (Hyperbolic paraboloid)
This one was formed by non-uniformly sweeping a convex parabola along a concave parabola. It’s internal structure will behave differently, depending on the curvature of the shell relative to the shape. Roof shells have compressive stresses along the convex curvature, and tensile stress along the concave curvature.
Pringle
Kellogg’s potato and wheat-based stackable snack
Here is an example of a beautiful marriage of tensile and compressive potato and wheat-based anticlastic forces. Although I hear that Pringle cans are diabolically heinous to recycle, so they are the enemy.
11 Tensile and Compressive behaviour of shells.jpg
Structural Behaviour of Basic Shells [Source: IL 10 – Institute for Lightweight Structures and Conceptual Design]

7.3 – Translation vs Revolution

In terms of synthetic geometry, there’s more than one approach to generating anticlastic curvature:
E-Hyperbolic-Paraboloid-Saddle.gif
Hyperbolic Paraboloid: Straight line sweep variation

This shape was achieved by sweeping a straight line over a straight path at one end, and another straight path at the other. This will work as long as both rails are not parallel. Although I find this shape perplexing; it’s double curvature that you can create with straight lines, yet non-developable, and I can’t explain it..

F-Hyperbolic-Paraboloid-Tower.gif
Ruled Surface & Surface of Revolution (Circular Hyperboloid)
The ruled surface was created by sliding a plane curve (a straight line) along another plane curve (a circle), while keeping the angle between them constant. The surfaces of revolution was simply made by revolving a plane curve around an axis. (Surface of translation also exist, and are similar to ruled surfaces, only the orientation of the curves is kept constant instead of the angle.)
 
Cylinder_-_hyperboloid_-_cone.gif
Hyperboloid Generation [Source:Wikipedia]

The hyperboloid has been a popular design choice for (especially nuclear cooling) towers. It has excellent tensile and compressive properties, and can be built with straight members. This makes it relatively cheap and easy to fabricate relative to it’s size and performance.

These towers are pretty cool acoustically as well: https://youtu.be/GXpItQpOISU?t=40s

 

8.0 Geodesic Curves

These are singly curved curves, although that does sound confusing. A simple way to understand what geodesic curves are, is to give them a width. As previously explored, we know that curves can inhabit, and fill, two-dimensional space. However, you can’t really observe the twists and turns of a shape that has no thickness.

Geodesic Curves - Ribon.jpg
Conic Plank Lines (Source: The Geometry of Bending)

A ribbon is essentially a straight line with thickness, and when used to follow the curvature of a surface (as seen above), the result is a plank line. The term ‘plank line’ can be defined as a line with an given width (like a plank of wood) that passes over a surface and does not curve in the tangential plane, and whose width is always tangential to the surface.

Since one-dimensional curves do have an orientation in digital modeling, geodesic curves can be described as the one-dimensional counterpart to plank lines, and can benefit from the same definition.

The University of Southern California published a paper exploring the topic further: http://papers.cumincad.org/data/works/att/f197.content.pdf

8.1 – Basic Grid Setup

For simplicity, here’s a basic grid set up on a flat plane:

G-Geocurves.gif
Basic geodesic curves on a plane

We start by defining two points anywhere along the edge of the surface. Then we find the geodesic curve that joins the pair. Of course it’s trivial in this case, since we’re dealing with a flat surface, but bear with me.

H-Geocurves.gif
Initial set of curves

We can keep adding pairs of points along the edge. In this case they’re kept evenly spaced and uncrossing for the sake of a cleaner grid.

I-Geocurves.gif
Addition of secondary set of curves

After that, it’s simply a matter of playing with density, as well as adding an additional set of antagonistic curves. For practicality, each set share the same set of base points.

J-Geocurves.gif
Grid with independent sets

He’s an example of a grid where each set has their own set of anchors. While this does show the flexibility of a grid, I think it’s far more advantageous for them to share the same base points.

8.2 – Basic Gridshells

The same principle is then applied to a series of surfaces with varied types of curvature.

K-Barrel
Uniclastic: Barrel Vault Geodesic Gridshell

First comes the shell (a barrel vault in this case), then comes the grid. The symmetrical nature of this surface translates to a pretty regular (and also symmetrical) gridshell. The use of geodesic curves means that these gridshells can be fabricated using completely straight material, that only necessitate single curvature.

L-Conoid
Uniclastic: Conoid Geodesic Gridshell

The same grid used on a conical surface starts to reveal gradual shifts in the geometry’s spacing. The curves always search for the path of least resistance in terms of bending.

M-Dome
Synclastic: Dome Geodesic Gridshell

This case illustrates the nature of geodesic curves quite well. The dome was free-formed with a relatively high degree of curvature. A small change in the location of each anchor point translates to a large change in curvature between them. Each curve looks for the shortest path between each pair (without leaving the surface), but only has access to single curvature.

N-Saddle
Anticlastic: Saddle Geodesic Gridshell

Structurally speaking, things get much more interesting with anticlastic curvature. As previously stated, each member will behave differently based on their relative curvature and orientation in relation to the surface. Depending on their location on a gridshell, plank lines can act partly in compression and partly in tension.

On another note:

While geodesic curves make it far more practical to fabricate shells, they are not a strict requirement. Using non-geodesic curves just means more time, money, and effort must go into the fabrication of each component. Furthermore, there’s no reason why you can’t use alternate grid patterns. In fact, you could use any pattern under the sun – any motif your heart desires (even tessellated puppies.)

6 - Alternate Grid
Alternate Gridshell Patterns [Source: IL 10 – Institute for Lightweight Structures and Conceptual Design]

Here are just a few of the endless possible pattern. They all have their advantages and disadvantages in terms of fabrication, as well as structural potential.

Biosphere Environment Museum - Canada
Biosphere Environment Museum – Canada

Gridshells with large amounts of triangulation, such as Buckminster Fuller’s geodesic spheres, typically perform incredibly well structurally. These structure are also highly efficient to manufacture, as their geometry is extremely repetitive.  

Centre Pompidou-Metz - France
Centre Pompidou-Metz – France

Gridshells with highly irregular geometry are far more challenging to fabricate. In this case, each and every piece had to be custom made to shape; I imagine it must have costed a lot of money, and been a logistical nightmare. Although it is an exceptionally stunning piece of architecture (and a magnificent feat of engineering.)

8.3 – Gridshell Construction

In our case, building these shells is simply a matter of converting the geodesic curves into planks lines.

O - Saddle 2
Hyperbolic Paraboloid: Straight Line Sweep Variation With Rotating Plank Line Grid

The whole point of using them in the first place is so that we can make them out of straight material that don’t necessitate double curvature. This example is rotating so the shape is easier to understand. It’s grid is also rotating to demonstrate the ease at which you can play with the geometry.

Hyperbolic-Paraboloid-Plank-Lines
Hyperbolic Paraboloid: Flattened Plank Lines With Junctions

This is what you get by taking those plank lines and laying them flat. In this case both sets are the same because the shell happens to the identicall when flipped. Being able to use straight material means far less labour and waste, which translates to faster, and or cheaper, fabrication.

An especially crucial aspect of gridshells is the bracing. Without support in the form of tension ties, cable ties, ring beams, anchors etc., many of these shells can lay flat. This in and of itself is pretty interesting and does lends itself to unique construction challenges and opportunities. This isn’t always the case though, since sometimes it’s the geometry of the joints holding the shape together (like the geodesic spheres.) Sometimes the member are pre-bent (like Pompidou-Metz.) Although pre-bending the timber kinda strikes me as cheating thought.. As if it’s not a genuine, bona fide gridshell.

Toledo-gridshell-20-Construction-process
Toledo Gridshell 2.0. Construction Process [source: Timber gridshells – Numerical simulation, design and construction of a full scale structure]

This is one of the original build method, where the gridshell is assembled flat, lifted into shape, then locked into place.

9.0 Form Finding

Having studied the basics makes exploring increasingly elaborate geometry more intuitive. In principal, most of the shells we’ve looked are known to perform well structurally, but there are strategies we can use to focus specifically on performance optimization.

9.0 – Minimal Surfaces

These are surfaces that are locally area-minimizing – surfaces that have the smallest possible area for a defined boundary. They necessarily have zero mean curvature, i.e. the sum of the principal curvatures at each point is zero. Soap bubbles are a great example of this phenomenon.

hyperbolic paraboloid soap bubble
Hyperbolic Paraboloid Soap Bubble [Source: Serfio Musmeci’s “Froms With No Name” and “Anti-Polyhedrons”]
Soap film inherently forms shapes with the least amount of area needed to occupy space – that minimize the amount of material needed to create an enclosure. Surface tension has physical properties that naturally relax the surface’s curvature.

00---Minimal-Surface-Model
Kangaroo2 Physics: Surface Tension Simulation

We can simulate surface tension by using a network of curves derived from a given shape. Applying varies material properties to the mesh results in a shape that can behaves like stretchy fabric or soap. Reducing the rest length of each of these curves (while keeping the edges anchored) makes them pull on all of their neighbours, resulting in a locally minimal surface.

Here are a few more examples of minimal surfaces you can generate using different frames (although I’d like stress that the possibilities are extremely infinite.) The first and last iterations may or may not count, depending on which of the many definitions of minimal surfaces you use, since they deal with pressure. You can read about it in much greater detail here: https://tinyurl.com/ya4jfqb2

Eden_Project_geodesic_domes_panorama.jpg
The Eden Project – United Kingdom

Here we have one of the most popular examples of minimal surface geometry in architecture. The shapes of these domes were derived from a series of studies using clustered soap bubbles. The result is a series of enormous shells built with an impressively small amount of material.

Triply periodic minimal surfaces are also a pretty cool thing (surfaces that have a crystalline structure – that tessellate in three dimensions):

Another powerful method of form finding has been to let gravity dictate the shapes of structures. In physics and geometry, catenary (derived from the Latin word for chain) curves are found by letting a chain, rope or cable, that has been anchored at both end, hang under its own weight. They look similar to parabolic curves, but perform differently.

00---Haning-Model
Kangaroo2 Physics: Catenary Model Simulation

A net shown here in magenta has been anchored by the corners, then draped under simulated gravity. This creates a network of hanging curves that, when converted into a surface, and mirrored, ultimately forms a catenary shell. This geometry can be used to generate a gridshell that performs exceptionally well under compression, as long as the edges are reinforced and the corners are braced.

While I would be remiss to not mention Antoni Gaudí on the subject of catenary structure, his work doesn’t particularly fall under the category of gridshells. Instead I will proceed to gawk over some of the stunning work by Frei Otto.

Of course his work explored a great deal more than just catenary structures, but he is revered for his beautiful work on gridshells. He, along with the Institute for Lightweight Structures, have truly been pioneers on the front of theoretical structural engineering.

9.3 – Biomimicry in Architecture

There are a few different terms that refer to this practice, including biomimetics, bionomics or bionics. In principle they are all more or less the same thing; the practical application of discoveries derived from the study of the natural world (i.e. anything that was not caused or made my humans.) In a way, this is the fundamental essence of the scientific method: to learn by observation.
Biomimicry-Bird-Plane
Example of Biomimicry

Frei Otto is a fine example of ecological literacy at its finest. A profound curiosity of the natural world greatly informed his understanding of structural technology. This was all nourished by countless inquisitive and playful investigations into the realm of physics and biology. He even wrote a series of books on the way that the morphology of bird skulls and spiderwebs could be applied to architecture called Biology and Building. His ‘IL‘ series also highlights a deep admiration of the natural world.

Of course he’s the not the only architect renown their fascination of the universe and its secrets; Buckminster Fuller and Antoni Gaudí were also strong proponents of biomimicry, although they probably didn’t use the term (nor is the term important.)

Gaudí’s studies of nature translated into his use of ruled geometrical forms such as hyperbolic paraboloids, hyperboloids, helicoids etc. He suggested that there is no better structure than the trunk of a tree, or a human skeleton. Forms in biology tend to be both exceedingly practical and exceptionally beautiful, and Gaudí spent much of his life discovering how to adapt the language of nature to the structural forms of architecture.

Fractals were also an undisputed recurring theme in his work. This is especially apparent in his most renown piece of work, the Sagrada Familia. The varying complexity of geometry, as well as the particular richness of detail, at different scales is a property uniquely shared with fractal nature.

Antoni Gaudí and his legacy are unquestionably one of a kind, but I don’t think this is a coincidence. I believe the reality is that it is exceptionally difficult to peruse biomimicry, and especially fractal geometry, in a meaningful way in relation to architecture. For this reason there is an abundance of superficial appropriation of organic, and mathematical, structures without a fundamental understanding of their function. At its very worst, an architect’s approach comes down to: ‘I’ll say I got the structure from an animal. Everyone will buy one because of the romance of it.”

That being said, modern day engineers and architects continue to push this envelope, granted with varying levels of success. Although I believe that there is a certain level of inevitability when it comes to how architecture is influenced by natural forms. It has been said that, the more efficient structures and systems become, the more they resemble ones found in nature.

Euclid, the father of geometry, believed that nature itself was the physical manifestation of mathematical law. While this may seems like quite a striking statement, what is significant about it is the relationship between mathematics and the natural world. I like to think that this statement speaks less about the nature of the world and more about the nature of mathematics – that math is our way of expressing how the universe operates, or at least our attempt to do so. After all, Carl Sagan famously suggested that, in the event of extra terrestrial contact, we might use various universal principles and facts of mathematics and science to communicate.

Triply periodic minimal surfaces _topology

start

Frequently occuring in nature, minimal surfaces are defined as surfaces with zero mean curvature.  These surfaces originally arose as surfaces that minimized total surface area subject to some constraint. Physical models of area-minimizing minimal surfaces can be made by dipping a wire frame into a soap solution, forming a soap film, which is a minimal surface whose boundary is the wire frame.

The thin membrane that spans the wire boundary is a minimal surface of all possible surfaces that span the boundary, it is the one with minimal energy. One way to think of this “minimal energy” is that to imagine the surface as an elastic rubber membrane: the minimal shape is the one that in which the rubber membrane is the most relaxed.

 

A minimal surface parametrized as x=(u,v,h(u,v)) therefore satisfies Lagrange`s equation

(1+h(v)^2)*h(uu)-2*h(u)*h(v)*h(uv)+(1+h(u)^2)*h(vv)=0

(Gray 1997, p.399)

This year`s research focuses on triply periodic minimal surfaces (TPMS). A TPMS is a type of minimal surface which is invariant under a rank-3 lattice of translations. In other words, a TPMS is a surfaces which, through mirroring and rotating in 3D space, can form an infinite labyrinth. TPMS are of particular relevance in natural sciences, having been observed in observed as biological membranes, as block copolymers, equipotential surfaces in crystals, etc.

From a mathematical standpoint, a TPMS is the most interesting type of surface, as all connected RPMS have genus >=3, and in every lattice there exist orientable embedded TPMS of every genus >=3. Embedded TPMS are orientable and divide space into disjoint sub-volumes. If they are congruent the surface is said to be a balance surface.

The first examples of TPMS were the surfaces described by Schwarz in 1865, followed by a surface described by his student Neovius in 1883. In 1970 Alan Schoen, a then NASA scientist, described 12 more TPMS, and in 1989 H. Karcher proved their existence.

The first part of my research focuses on understanding TPMS geometry using a generation method that uses a marching cubes algorithm to find the results of the implicit equtions describing each particular type of TMPS. The resulting points form a mesh that describes the geometry.

Schwartz_P surface

schwartz_p_formation   Schwartz_p

Neovius surface

Neovius_formation neovius

Gyroid surface

gyroid_formation gyroid

Generated from mathematical equations, these diagrams show the plotting of functions with different domains. Above, the diagrams on the left illustrate the process of forming a closed TMPS, starting from a domain of 0.5, which generates an elementary cell, which is mirrored and rotate 7 times to form a closed TPMS. A closed TMPS can also be approximated by changing the domain of the function to 1.

The diagrams below show some examples generating a TMPS from a function with a domain of 2. The views are front, top and axonometric.

FRD surface

dd = 8 * Math.Cos(px) * Math.Cos(py) * Math.Cos(pz) + Math.Cos(2 * px) * Math.Cos(2 * py) * Math.Cos(2 * pz) – Math.Cos(2 * px) * Math.Cos(2 * py) – Math.Cos(2 * py) * Math.Cos(2 * pz) – Math.Cos(2 * pz) * Math.Cos(2 * px)

FRD

D Prime surface

dd = 0.5 * (Math.Sin(px) * Math.Sin(py) * Math.Sin(pz) + Math.Cos(px) * Math.Cos(py) * Math.Cos(pz)) – 0.5 * (Math.Cos(2 * px) * Math.Cos(2 * py) + Math.Cos(2 * py) * Math.Cos(2 * pz) + Math.Cos(2 * pz) * Math.Cos(2 * px)) – 0.2

D_prime

FRD Prime surface

dd = 4 * Math.Cos(px) * Math.Cos(py) * Math.Cos(pz) – Math.Cos(2 * px) * Math.Cos(2 * py) – Math.Cos(2 * pz) * Math.Cos(2 * py) – Math.Cos(2 * px) * Math.Cos(2 * pz)

FRD_prime

Double Gyroid surface

dd = 2.75 * (Math.Sin(2 * px) * Math.Sin(pz) * Math.Cos(py) + Math.Sin(2 * py) * Math.Sin(px) * Math.Cos(pz) + Math.Sin(2 * pz) * Math.Sin(py) * Math.Cos(px)) – 1 * (Math.Cos(2 * px) * Math.Cos(2 * py) + Math.Cos(2 * py) * Math.Cos(2 * pz) + Math.Cos(2 * pz) * Math.Cos(2 * px))

gyroid_double

Gyroid surface

dd = Math.Cos(px) * Math.Sin(py) + Math.Cos(py) * Math.Sin(pz) + Math.Cos(pz) * Math.Sin(px)

gyroid

This method of approximating a TPMS is high versatile, useful in understanding the geometry, offsetting the surfaces and changing the bounding box of the lattice in which the surface is generated. In other words, trimming the surface and isolating parts of the surface. However, the resulting topology is unsuitable for fabrication purposes, as the generated mesh is unclean, being composed of irregular polygons consisting of triangulations, quads and hexagons.

The following diagrams show the mesh topology for a Gyroid surface, offset studies and trimming studies.

 

1

4  23

For fabrication purposes, my proposed method for computationally simulating a TPMS is derived from discrete differential geometry, relying on the use of Kangaroo Physics, a Grasshopper plugin for modeling tensile membranes. Bearing in mind that a TPMS has 6 edge conditions, a planar hexagonal mesh is placed within the space defined by a certain TPMS`s edge conditions. The edge conditions are interpreted as Nurbs curves. Constructed from 6 predefined faces, the initial planar hexagonal mesh, together with the curves defining the surface boundaries are split into the same number of subdivisions. The subdivision algorithm used on the mesh is WeaveBird`s triangular subdivision. The points resulted from the curve division are ordered so that they match the subdivided mesh`s edges, or its naked vertices. The naked vertices are then moved in the corresponding points on the curve, resulting in a new mesh describing a triply periodic surface, but not a minimal one. From this point, Kangaroo Physics is used to find the minimal surface for the given mesh parameters, resulting in a TPMS.

Sequential diagram showing the generation of a Schwartz_P surfaces using the above method.

Page29

A Gyroid surface approximated with the above method

gyroid_full  8

This approach towards approximating a TPMS leads to a study in the change of boundary conditions, gaining control over the geometry. The examples below present various gyroid distorsions generated by changing the boundary conditions.

6  7

5  4

Being able to control the boundary conditions defining a gyroid, or any TPMS, opens up to form optimization through genetic algorithms. Here, various curvatures for the edge conditions have been tested with regards to solar gain, using Galapagos for Grasshopper.

1_1                2_1

3_1                 4_1

The following examples show some patterns generated by different topologies of the starting mesh.

1_12

34

56

78

gif_1

2

 

 

 

 

 

 

 

 

 

 

 

 

 

Tensegrity

Tensegrity structure or also known as tensional integrity, a portmanteau term that was coined by Buckminster Fuller in the 1960s. It is a structural principle which is based on the use of detached components in compression inside a net of continuous tension.It is also known as “floating compression”, a term that was promoted by Kenneth Snelson. Each compressed members such as struts or bars do not touch among another and the prestressed tensioned members , tendons or cables for example, define the system spatially. Snelson defines tensegrity as a closed structural system composed of a set of three or more elongate compression struts within a network of tension tendons, the combined parts mutually supportive in such a way that the struts do not touch one another, but press outwardly against nodal points in the tension network to form a firm, triangulated, prestressed, tension and compression unit. Triangulated network are stronger and even more firm, if compared to non-triangulated network. 

Basic tensegrity structure made up a tower. Photo courtesy to LiftArchitects
Basic tensegrity structure made up a tower. Photo courtesy to LiftArchitects
Precedent project  by students of Ball State University
Precedent project by students of Ball State University

Biotensegrity

Biotensegrity, is a term coined by Dr. Stephen Levin, is the application of tensegrity principles to biologic structures.Harvard physicians and scientist Donald Ingber has developed a theory of tensegrity in molecular biology to explain cellular structure.The shape of cells are all can be mathematically modelled if a tensegrity model is used for cell’s cytoskeleton. Cytoskeleton is a network of fivers composed of proteins contained within a cell’s cytoplasm, which is dynamic structure, parts of which are constantly destroyed, renewed or newly constructed.

12

11

The study of tensegrity structure started through geometric remodeling the tensegrity model using digital softwares, to understand the deployability of the system . The basic form of tensegrity is being explored through addition of struts in the cell modules . The basic cell module is then are combined according to geometry tessellation . They were applied on regular surface and also irregular surface ,  while maintaining the structural frequency and mesh tension .

1

TUTORIAL_05_05

By using basic cell module of 3 struts, the tensional components were explored both using cables and fabric . The fabric helps in creating enclosures and more aesthetically pleasing in installation. It is still in the beginning of the design by studying the behavior of the system, with the goal to expand the possibilities of design in the future , either for Burning Man or Buro Happold.

TUTORIAL_05_02

TUTORIAL_05_03

TUTORIAL_05_04

TUTORIAL_05_06

For the next project, the possibility of the tensegrity structures will be explored more and the design will be highlighted on the playful intervention of tensegrity structure and the advantages of this super lightweight system for both proposal for Burning Man and Buro Happold .

Lotus Hypars

Lotus Hypars – A study of hyperbolic bamboo structures

The Lotus Hypars symbolise the “Caravansary” trading centre. The structure is assembled as the centre for exchange after journeying across land and water to a resting point, Burning Man. Hammocks offer a space for the festivals unique style of trading to be discussed and carried out. The tangible nature of the Lotus also creates a playfulness in an otherwise formal system of resources exchange. The lightweight structure evolves from the horizontal lines of the desert and forms a hyperbolic shelter. The user can inhabit not only underneath the structure, but also the petal shaped hammocks. Here, individuals can exchange stories, supplies and treasures.

LH.1

In Buddhism, the Lotus flower is symbolic of fortune. It grows in muddy water, and it is this environment that gives forth the flower’s first and most literal meaning: rising and blooming above the murk to achieve enlightenment. The Lotus Hypar story has evolved from the same principles. In the harsh desert environment, man can create beauty. The folded geometries are playfully excited by human participation. A twist, a fold and a push.

LH.2

The structure is assembled using bamboo sticks that are arranged in a reciprocal formation. These canes are then bound using high strength elastic bands. This allows for the flat cells to twist and take on new shapes. The Lotus Hypar is formed by a repetitive series of folds and the result forms petals. These are symbolic of the Lotus flower. The cells are covered with a white semi-elastic membrane that adds to the strength of the structure and the petal geometries become more visible. These are also the hammocks that can be inhabited by the Burning Man users.

LH.3

In order to test the structural performance of the proposal, I constructed a series of 1:1 scale models. This was done using 6m and 3m bamboo canes (35mm diameter). By testing a small segment of the full proposal, it is easier to determine the success of the final proposal.

LH.4 LH.5

Black Light Tower by Luka Kreze

Midnight Butterfly Release

My design for this year’s Burning Man Festival is titled ‘Black Light Tower.

Black Light Tower is a membrane tensegrity structure which is constructed out of 38 metal rods and a transparent structural membrane. One of the most important characteristics of the Black Light Tower tower is also one of the most important principles of Burning Man Festival – Self Reliance. Just like people of Burning Man are encouraged to rely solely on themselves and their own resources this structure is fascinating mainly because it does not use any additional support such as columns or cables, but relies solely on its own structure. The membrane almost miraculously holds the structure up and in tension. To be more precise, instead of the structure holding up the cover, cover is holding up the structure.

Tensegrity structure of this kind seems to be a perfect allegory of the Burning Man principles and a symbol of self reliance.
Black Light Tower will provide a unique experience to its users.

Its interior space is essentially a ladder which leads towards the top of the structure. From the day one the space is filled with hundreds and hundreds of butterflies which cannot escape the tower.

Butterflies then fill the tower storey by storey as the days go by. Every day the net which separates one storey from the other gets removed and butterflies can fly higher into the structure. Visitors can climb only as high as the butterflies go.

On the final day magic happens as the butterflies are symbolically released in the air, at the same time as the Burning Man Figure is set on fire. Butterflies are lit with UV light which allows the visitors to see them in their true colours, in the same way as butterflies see each other, while creating a spectacular event for the viewers’ eyes.

Immediacy is probably one of the most important values of the Burning Man culture. As written in the ten principles immediate experience means to seek to overcome barriers that stand between us and a recognition of our inner selves, the reality that surrounds us and contact with a natural world exceeding human powers.
The experience of climbing the tower will definitely make the climbers fell more alive aware of their inner selves. The night view of the Black Light Tower should be spectacular as all of the rods will be equipped with UV light which will reveal not only the magic of the floating structure under the membrane but ever changing projection of butterflies in flight under the Black Light. One of the most thrilling experiences, however, will most probably be the sublime view of the Playa from the top of the tower on the last day of the festival, that seems like its going to collapse any minute.

Elevation View of the Black Light Tower

Precedent Study

Large Scale Test Model

Timeline Drawing of the Butterfly Release

Section Drawing

MOOM Tensegritic Membrane Structure (Noda) by Kazuhiro Kojima

Architectural students at the Tokyo University of Science developed an experimental, extremely lightweight, load-bearing structure for a temporary pavilion. The 26-metre-long, up to 7,5-metre-wide and 4,25-metre-high volume is self-supporting and comprises only two kinds of component: the metal bearing elements and a delicate space-enclosing skin consisting of an 0,7-mm membrane of elastic polyester fabric. The membrane is drawn over metal tubes that create a tensegrity system and forms the tension element. The 131 compression bars are 25-mm diameter aluminum tubes of various lengths and there is no contact between them; instead, they are connected to the skin by sliding the ends into sheaths sewn on. The membrane is anchored at the base like a conventional tent with pegs consisting of aluminum tubes with tips pressed together to form a point. The compression members are pushed into these pegs and fixed in position by means of steel pins. With a weight of only 600 kg, this airy structure covers a ground area of 146 square meters. The pavilion was erected by 70 students in a single day. Initially, they laid out the ready tailored skin, then slid the tubular members into the sheaths. The overall structure was tensioned on all sides, pushed upwards at the same time in the interior and finally fixed to the ground. The convex and concave forms resulting from this create an animated surface and a lively interplay of light and shade. Since the membrane screens off 80% of the UV radiation, but allows 50% of the daylight to pass through, the softly filtered light creates a fascinating spatial impression internally. When illuminated, the translucent pavilion has the appearance of a lighted sculpture.

Via Archetipo

WATER CATHEDRAL by GUN Architects

“The Water Cathedral is a large, horizontal urban nave for public use, discreetly exposed so that enigmatic and semi-dark atmospheres can be made out through its topographic lines of floor and ceiling. Both topographies are surface systems shaped by numerous slender, vertical components, which hang or rise like stalactites and stalagmites in a cave, varying their heights and concentrations. A physical organization with regimes of proliferation and differentiation; a series of columns, platforms, arches, curtains, domes and caverns emerge, qualifying the project spatially and atmospherically.Water embedding / Dripping, duration, delay by integrating water within its spatial and material logics, the project promotes a form of architecture that systematizes dripping pulses and speeds, consistently exacerbating the water drop as primal atmospheric matter.”

“This is accomplished through the hanging components of the roof topography, constituted geometrically and materially like textile prisms placed upside-down with a partial granular substratum filling. They are fed by a hydraulic network that continuously irrigates using measured doses. When filled with small amounts of water, these elements act as regulators or atmospheric interfaces, experiencing a phenomenon of absorption and release where, through capillarity, water drops gradually flow against gravity along the prism edges, slowing down the time of concentration and fall. This delay process that consequently produces multiple dripping rhythms over the ground topography, formally demonstrates management of duration. It materializes an architectural form in which water can be particularized in a system that has extensive effects over an area. The delay principle, established through mediation by the prisms, is translated into the possibility to define the layout and use the water as it drops.Form Principles as an abstraction and geometrical transposition of the stalactite, a three-dimensional spatial component, is developed. A three-phase prism with an equilateral base that varies in height and area. These elements proliferate in a grid system, forming curves of different lengths and intensities. This variation capacity component, allows to effectively producing diversity of spaces, textures, patterns and interactions with environmental dynamics based in a principle of material abundance.Geometrical studies from two dimensional curve variation and three dimensional arrangements constrained to equilateral modules. These forms of proliferation deliver rich arch formations, defining interiorities, structural points and modular connectivity.”

WATER CATHEDRAL | GUN Architects

WATER CATHEDRAL | GUN Architects

WATER CATHEDRAL | GUN Architects

via WATER CATHEDRAL | GUN Architects.