Update : July 12, 2016

Jun Sato

Associate Professor, University of Tokyo

Jun Sato Structural Engineers Co., Ltd.


Transparent structures as Environmental Filters

Guidelines for Composing Morphogenetic Operations in Structural Design



Dynamics Operations

Approach using transparent glass, resin structure

Approach using Manual Form Optimization Algorithm based on safety ratio due to allowable stress, safety ratio due to buckling phenomenon, energy absorption

Approach using steel mesh forms based on welding technique and manipulation of buckling phenomenon


Geometry Operations

Approach using wooden mesh forms developed with traditional connection system Kigumi

Development of 2D projection method for 3D complicated geometry

Approach using accumulative form

Fuzzy Node Algorithm

1D Spectrum Analysis : 1/f fluctuation

2D Spectrum Analysis : Naturalness, Comfortableness, Preference


Workshop Scale Experiments

Composition of Morphogenetic Process

Lightweight and Ductile Structures : preventing death in the event of collapse


Energy consumption experiments

Manipulation of Buckling Phenomenon

Reciprocal System


Structural Tips


Little by little, learning Great Nature

Soul of Engineering


October 27, 2015, Lecture for Rhode Island School of Design RISD

October 26, 2015, Lecture for Harvard GSD

April 30, 2015, Archi-Neering Design AND in Nanjing

October 27, 2014, Lecture for University of Oregon

September 19, 2014, Keynote Speech for Smart Geometry in Hong Kong




Geometry of transparent / translucent structures have advanced into the phase where structural elements also serve as environmental filters.

We should compose a morphogenetic operation method for those complicated targets through these practices :

Dynamics Operations

Geometry Operations

Workshop Scale Experiments

Using these operations / manipulations we would be able to develop more morphogenetic forms based on geometry, materials, dynamics, craftsmanship, site matters and the spirit of engineering. These operations are also helpful for us to collaborate with architects.










Dynamics Operations


● Approach using transparent glass, resin structure



Extreme Nature, Venezia Biennale 2008

Architect : Junya Ishigami

Structure : Jun Sato

Slight, rahmen (rigid jointed frame) structure using ultra high strength steel with glass walls serve as tension bracing.




Left : Greenhouse of 2 m height

Right : First model


fix-fix         fix-hinge     hinge-hinge   fix-fix+sway   fix-hinge+sway

α=0.5         α=0.708       α=1.0         α=1.0         α=2.0


Buckling strength  :  Pcr =


E  :  Young’s modulus [tf/cm2]

I  :  Moment inertia of section [cm4]

Lk  :  Buckling length Lk =αL [cm]


While developing ideas with Junya Ishigami, we try brainstorming again and again for hours on each meeting day.

Through those detailed thinking of each phenomenon, sometimes a new idea can be generated.




Deflection, Bending stress diagram of rahmen structure due to gravity


Heat cambering of the steel is an important process in the fabrication of the structure as it reduces deflections as well as bending stresses.



Process to reduce deflections and bending stresses


Heating process by gas burner


Development of Manual Form Optimization Software is contributing for optimised location of columns.




Screenshot of form optimization software


Finally they are composed with columns 16x16mm, 32x32mm, glass wall t = 8mm.

こうして柱は 16x16mm32x32mm、ガラス壁は 8mm と絞られた。



Left : Greenhouse of 2 m height with 16x16mm columns

Right : Greenhouse of 6 m height with 32x32mm columns


Park Groot Vijversburg, Netherlands, 2015

Architect : Junya Ishigami, Marieke Kums / studio MAKS

Structural advisor : Jun Sato

Engineering : ABT

Curved glass wall structure generated by manipulating buckling phenomenon and load distribution.




The load distribution is manipulated by arrangement of beams.



Left : Latest shot of the construction site (Photo : Marieke Kums)

Center : Screenshot of form optimization software to manipulate load distribution

Right : Buckling analysis on curved thin wall


Buckling strength is manipulated by curvature.


Left & Right : Glass walls curved by cold bending (Photo : Marieke Kums)


Iz House

Architect : Sou Fujimoto

Structure : Jun Sato

Stacked structure of glass walls and acrylic resin walls.

A simple structural analysis model was developed for seismic response analysis.



Exterior and interior under construction, Structural Test


Structural Analysis Model


Section Drawing





Load displacement curve, Seismic response analysis


Stained Glass Structure

Design & Research : Jun Sato Laboratory, University of Tokyo

The stained glass panels are made by fixing glass in a slight metal frame, which represents the diverse forms in the manner mentioned below.

Structure in Architecture is appearing diverse forms composed of diverse materials, constructed by diverse methods, and exposed to diverse impacts. As we can see this stained glass structure is sufficiently complex composite to develop a dynamics operations, when completed, it can be adopted for many of other structures.




Left, Middle : Stained Glass Structure test specimen

Right : Pop-up Structure using brass frames, Workshop 2012, Jun Sato Lab


As the cushioning materials inserted between the glass and metal frame are required to be resistant to UV damage, we are using tin plates which we found to be effective.



Joint Detail


The development of the algorithm mentioned above is now under investigation using the condensation of the eigenvalue equation of buckling.




Buckling analysis for 3D grid frame


This structure is representing a design that can take on diverse forms and are subject to the diverse phenomena :


Composed of multiple materials.

Composed of bar and plate elements.

The optimized framework pattern existent to make it stronger using curved line elements.

Elastic behaviour of the tin plate while in a plastic state.

Algorithm to describe plastic hinges, which also describes buckling behavior.

Mutual buckling resistance between the glass plates and the steel frames.









Apartment House in Wasedatsurumaki, 2015, Architect : Yoshio Sakurai



● Approach using the Manual Form Optimization Algorithm



Community Centre, Kawatana Onsen

Architect : Kengo Kuma

Structure : Jun Sato

Polyhedral form generated by adjusted position of nodes.


建築家:隈 研吾







Development of algorithm for form finding under several load combinations such as gravity, seismic load, wind and snow. The parameter to be focused will be safety ratio due to allowable stress, safety ratio due to buckling phenomenon, energy absorption. This software has been developed also for plug-in.






Polyhedral form for “ Community Centre, Kawatana Onsen”, architect : Kengo Kuma

Safety ratio color chart is displayed while transforming by mouse


This form finding software is applicable to various shapes such as Freeform, Stacked Clusters, Branched Tree, Randomly Located Columns.




Polyhedral mesh for “ Naoshima Pavilion ”, Kagawa, architect Sou Fujimoto



Free form for “ House of Pease HOPE ”, Copenhagen, architect Junya Ishigami



Twisted free form for “ Cloud Arch ”, Sydney, architect Junya Ishigami


Form Optimization Software Component : Hogan + Rhinoceros + Grasshopper



Stacking free curved wall, architect Sou Fujimoto : Genus of topology is rearranged in this case.



Free level floors for “ House NA ”, architect Sou Fujimoto



Branched tree, architect Sou Fujimoto

Randomly located columns for “ Extreme Nature in Venezia Biannnale 2008 ”, architect Junya Ishigami


Algorithm of operations :


Topological Operation  : Manipulate stiffness and stress by morphing the shape. Genus, which will be related to environment matters or space continuity, should be also manipulated.

Density Operation     : Manipulate stress by density / porosity of arrangement of elements.

Stress Based Operation : Arrange strong components onto stressful area.


Global / Macro Optimization : Optimization of global shape.

Local / Micro Optimization  : Optimization of local shape such as drapes, wrinkles, dimples.


Energy absorption diagram for “ New Hakushima Station ”, 2015, Architect : Kazuhiro Kojima / CAt


● Approach using steel mesh forms based on welding technique and manipulation of buckling phenomenon



Research Building, Hakodate Future University, 2005

Architect : Riken Yamamoto

Structure : Jun Sato

Steel mesh structure composed of vertical and diagonal elements.

Mesh tectonics shows the craftsmanship is necessary to generate these structural, environmental elements.


建築家:山本 理顕






Welding tecnique and reforming tecnique is necessary to fabricate these mesh.







Tsuda Veterinary Clinic, 2003

Architect : Kazuhiro Kojima / CAt

Structure : Jun Sato

Shelf shaped sturcture with 6mm steel plates, without backboard by controlling 3 dimensional buckling.


建築家:小嶋 一浩/CAt






When flat bar columns are located in radial arrangement, buckling strength can be found 4 times bigger than parallel arrangement.



Buckling control of flat bar columns : Radial, Polygonal, Parallel



Elevation of each grid structure based on buckling phenomena


In some case, forms generated by the optimization of buckling appears not visualizing the stress flow.








その場での簡素な計算 MOOM


Geometry Operations


● Approach using wooden mesh forms



Prostho Museum Research Center, 2010

Architect : Kengo Kuma

Structure : Jun Sato

1st examination of Kigumi with Kengo Kuma

Timber 3D grid structure without metal fixings at joint.




Starbucks Coffee in Dazaifu, 2011

2nd examination of Kigumi with Kengo Kuma

3D diagonal grid acting as a hunched portal frame.




Sunny Hills in Aoyama Tokyo, 2013

Architect : Kengo Kuma

Structure : Jun Sato

3rd examination of Kigumi – timber joints without metal plate fixings with Kengo Kuma




A mesh structure can serve as a filter of light, sight, air, heat, sound, water and ecosystem.

Inner space will be filled up with Komorebi – sunlight through leaves.


Discussion with Kengo Kuma is always just a brief moment. It is necessary to develop some imaginations from his few words such as “ scattering a lot of particles ”.




Joint zoom up, Processed timbers


Compared to Prostho, it has evolved into a very complicated geometry. It is difficult to tell how the elements are overlapping and how they should be carved just by looking at 3D images on a display.

Thinking about these operations of complicated geometry, we should develop a suitable way of projecting onto a 2D display.



Structural analysis model, 2D projection of overlapping timbers


Considering the geometry operation, this system can be composed as follows :



Local State (shape of components and connection type)

Component shape : with complicated but singular shape, with no parameters.

Connection type : singular with no parameters.


Component         Growth Process

Growth process is similar to stacking boxels.



As the growth process is easy, random operation can be composed as follows :

Growth process can generate many random global shapes, and each shape is evaluated individually. Finally a single shape is then decided upon.

Estimation values :

Structural dynamics values such as safety ratio, strain energy / Environmental factors / Space volume etc.


Random operation


In this system, constant porosity is guaranteed, which is making the problem simple when thinking about environmental matters.


In this case also a feedback operation is easy.

It indicates when we have a target global shape, we already have a way to compose the local state.

This process can also be understood as the topological optimization.


                    Target Global Shape

フィードバックも容易で、Topological Optimization を適用しやすい


¿ - cube, 2013

Design & Construction : Ken Yokogawa Laboratory, Nihon University

Structural Adviser : Jun Sato

An accumulated form like particles gathering into a protein molecule, 60 mm cubes made of hemlock spruce are connected by “ ¿ - inverted question” mark shaped eye bolts.

The structure gradually changes from a hard structure at the base to a soft membrane-like structure on the roof.

The distance between nodes should be the dimension of the cube with factors of x 1, x , x .






1, ,  の長さのみで形成されるとも理解できる。






In this case, the growth process and the feedback process are complicated.


Local State :

Particle shape : simple and singular with no parameters.

Connection type : simple but the angle coordination of the particle can be the parameter.


Growth Process

Adding a single particle : difficult but appears hard and strong

Adding multiple particles : easy but appears soft and weak



When we want to add a cube, the distance between the nodes might become a limiting dimensions.

As the compromised operation, we can add multiple cubes to span that distance but it appears to be soft and weak.



Fuzzy Node Algorithm

It seems we don’t have so many choice to compose the global / whole shape with only the 3 distances, but we could feel at the construction site, it is not so hard to add a cube.

It has been found because of the flexibility of the connection which can be called “ Fuzzy Node ”.

接合部にわずかなアソビを許すと格段に組みやすくなることが体感できる。このぼんやりとした節点は Fuzzy Node と呼べる。


Fuzzy Node


Growth Process with Fuzzy Node

ぼんやりとした節点 Fuzzy node


An algorithm to describe this fuzzy node is necessary to develop these operations.

形状制御において、ぼんやりとした節点 fuzzy node をアルゴリズム化することがひとつの手段。

Soft Computing の分野に通ずる。


Ashikita Community Hall - Communication Center of Local-Resource-Utilization, 2010

Architect : Akiko Takahashi, Hiroshi Takahashi / Workstation

Structure : Jun Sato

Woven-like interlocked thin laminated timber structure inspired by bamboo baskets.

The timber bands can be woven in various directions and the members follow a geodesic line of surface.




● Approach using accumulative form


Different Brick, Exhibition Real Size Competition 2013

Design & Construction : Yusuke Obuchi Lab, University of Tokyo

Structural Adviser : Jun Sato Lab

Masonry structure composed of ellipse shaped bricks.

The bricks are cast using cone shaped moulds. The moulds were soft enough to be deformed, so different ellipses could be generated from the same mould.

Ellipse packing is a very complicated geometric problem which is solved by finding the solution of simultaneous quartic equations. These are developed using the conditions that the length of circumference must be identical and every adjacent 2 ellipses should have single intersection. Here we proposed an approximate solution.









Not every global shape can be composed. This limitation should be considered as a characteristic of this system.

Another estimation other than those mentioned above will be the compression state, which necessitates that the final shape should be developed with no tension arising.

In this case a feedback operation is complicated to compose, but as we could develop an approximate algorithm of the relationship between the local state and the target curvature of the global shape, we could develop the growth , feedback and iteration processes.


● 1D Spectrum Analysis : 1/f fluctuation



Cafeteria in Chiba University of Commerce, 2015

Architect : Kazumi Kudo + Hiroshi Horiba / Coelacanth K&H

Structure : Jun Sato

Geometry Advisor : Takashi Chiba

Arranging thin LVL beams in a 1/f fluctuation pattern of spacings.

The 1/f fluctuation makes musics or visual patterns to be comfortable and natural.





薄っぺらいLVL梁を斜め格子状に並べ、そのピッチに1/f ゆらぎ」のリズムを持たせることが千葉氏より提案された。






Roof pattern 屋根伏図


Section 長手の軸組図


LVL屋根を支持する柱は φ141.3x30 で柱頭ピン接合。

鉄骨ラーメン構造部分の柱は H-125x125x6.5x9 柱頭剛接合。



Safety ratio diagram 安全率の色表示図


The location of columns was optimized due to the pattern of beams.

ルーバー状のLVL梁のピッチを並べた数列を波形と見なして 1/f ゆらぎの模様を描く。



Progression of spacings


Assume the number of data = N.

波のデータが N 個あるとする。(N は偶数とするのがよい)

am = a0, a1, a2,… aN-1 (m = 0N-1)

Assume the interval of data = Δt, total period Td results in as follows.

データ取得の間隔を Δt とすると、継続時間 Td は、

Td = N Δt

Assume Ck (k = 0N-1) as the factors of Complex Fourier Transform, Ck and the amplitudes Xk are expressed as follows.

複素フーリエ係数を Ck (k = 0N-1)とすると、フーリエ変換の式は、






Power Spectrum by Fourier Transform, logarithm scale

Horizontal axis : f = frequensy of wave

“ power ” can be understood as similar as “ amplitude “.


When the logarithm scale graph with the horizontal axis “ f ” shows a distribution of -1 gradient, it indicates 1/f distribution.



Spectrum analysis is expected to be useful for manipulating environmental factors. There might be some other formulae or parameters existent which are related to environment elements.

1/f ゆらぎ」は他にも多様な形態に適用できそうです。

建築家が「ランダム」と言うのは「心地よいランダム」であり、それは「1/f ゆらぎ」のことかもしれません。



● 2D Spectrum Analysis : Naturalness, Comfortableness, Preference



Spectrum analysis is applicable to 2D phenomena.

Using 2D Fourier Transform for 2D image resuts in a spectrum diagram as follows.

Values of R/G/B of the pixels are interpreted as 2D wave.



Original image / Power spectrum image drawn in 2D gray scale

White = high power, Dark gray = low power, Navy = 0.0


Power spectrum drawn in 1D graph

The gradient of the distribution is around -1 to -2 ( = 1/f to 1/f2 ).


There are some options for this method :

Use color / monochrome image

Use full / fluctuation wave

Filter by some functions before Fourier Transform


Finally we can notice some categories of spectra, for example,

Natural / Artificial / Comfortable / Color oriented preference



Original image / Monochrome / 2D power spectrum / 1D power spectrum


Komorebi (sunlight through leaves), Full wave



Komorebi (sunlight through leaves), Fluctuation wave




Pampas grass, Fluctuation wave



Kigumi in Sunny Hills, Fluctuation wave

Sunny Hills,「平均値」からの「ゆらぎ」のパワースペクトル


Uncomfortable ground, Fluctuation wave






Komorebi (Sunlight through leaves)

Japanese Pampas Grass

Kigumi structure of Sunny Hills Japan

Uncomfortable Ground


The spectrum image of this Kigumi structure looks in between Komorebi scene and Japanese Pampas Grass scene. It is indicating the type of naturalness.

Uncomfortable Ground is showing similaritywith White Noise.





Foliage : Gray and RGB respectively

Color preference will be analyzed by spectra of such as RGB, CYM, HSV.





Mesh Structure in Stanford University 2016


From these spectra, we can see some contrast of density will be interpreted into naturalness.


Workshop Scale Experiments


● Composition of Morphogenetic Process 形態生成アルゴリズムの構築


Through performing design-build process in workshops or ephemeral installations, we can compose the process as a morphogenetic operation.

In this process we use these operations in parallel.

Learn material properties / Form study / Structural Experiments / Structural Calculations / Construction





Creative Structures : art4d workshop in Bangkok, 2012

Using local materials, 4 teams constructed pavilions of 4 to 8 m spans, in only 2 days.










Experiments on Geometries and Dynamics : workshop at Stanford University, 2014


Beverly Choe, Architect, BACH architects / Stanford University

Jun Sato, Structural Engineer, Jun Sato Structural Engineers / University of Tokyo

Students studied 2 categories and materials of my proposal for 2 days in February and constructed it in 2 days in May.




Category 1, Tensegrity Volume : Tensegrity to have 3 dimensional volume.



Left : “3D” Tensegrity Volume composed of 18 galvanized bars and lengths of stainless cables (photo by Nick Xu)

Right : Tensegrity model, Pop-up Tectonics model



Dimensionality of Tensegrity

It is hard for a basic tensegrity to find a stable shape as a “3 dimensional” volume with not a modular system.





Category 2, Pop-up Tectonics : Foldable structure like a pop-up book, composed of 22 panels made of washi, traditional Japanese paper, and timber frames.

Washi paper provided by Takeo Co., Ltd.

Echizen Washi production : Shimizu Washi Co., Ltd.




Raising process of Pop Up Tectonics,

(Top right, bottom left : photo by Nick Xu)

(Top left, bottom right : photo by Jun Sato)


It is hard to find an exactly foldable shape when using thick plates.

Extensions of sides should cross at the same focus point.

Panels belonging to the same layer should not be overlapped when they are folded down and the total angle of the sets of panels, which coupled, should be same.




Geometrical conditions can be recognized by studying the model.

For example : from the top view, a ridge line or thalweg line should be seen to lie on a straight line.

When the loop is connected, panels have twisted shape like a Mobius loop and it is hard to find the focus point.




Community Week 2014

Dhillon Marty Foundation international workshop in Punjab, India

Schools       : The University of Tokyo, Stanford University, The University of Oregon, Rhode Island School of Design, Guru Nanak Dev University

Students from : Japan, U.S.A., India, China, Greece, Columbia, Indonesia


Public Toilet Design Competition in 3 days

5 clusters of students proposed the public toilet design.

Public toilet represents the social problems in India as follows,

Sanitation on water, foods, streets

Gender problem such as safety against crimes for ladies

Gap between rich and poor




Design Build Workshop in 2.5 days

Design build team was composed with 2 or 3 spies from each 5 clusters of students.

A kind of private space, also imagining the public toilet, was designed with some elements extracted from those design proposal of 5 clusters. The spies had to bring those informations from each clusters.

We can design structural elements which also work as environmental elements by designing filter for light, heat, air, water, sight, insects, person.

Keywords Delivered : water filtering

air ventilation

use waste for fertilizing

natural material

lift up the floor

These can be not yet actual solutions but indicating what we should think.


Shopping for materials and tools

Materials : local fabrics, bamboo, metal wire, strings, metal bars, plywoods, screws

Tools : saws, pliers, hand drills, hammers, needles, screwdrivers


Studies on bamboo frames

Brick and timber for lifted platform.


Instable frames stabilized by fabrics

Mesh structure with semi-transparent fabrics for filtering light and sight

Cellular spaces by branching membrane


Final shape with 15m length, indicating a gate, lifted private room covered with layered filters,

rest space, air ventilater.


Transparent Structures as Perceptual Filters

Stanford University seminar and workshop : Winter semester January ~ March, 2015

Tokyo session : June 13 ~ 14th, 2015


Beverly Choe, Architect, BACH architects / Stanford University

Jun Sato, Structural Engineer, Jun Sato Structural Engineers / University of Tokyo

Using 1.3 mm thick engineered, high strength glass panels, joined by an aluminum clamp system, the installation was formed into a triangulated matrix resembling a 3 dimensional truss, reciprocal compositions, or polyhedral shapes.

These forms are generated by controlling the buckling phenomenon through the geometrical configuration and optimization method.

Leoflex, Dragontrail を使用したガラス構造を構築するセミナー&ワークショップ。



Glass : “Leoflex” and “Dragontrail”, 1.3mm thick, with holes, with safety film,

size = 600x600mm, 600x440mm, 300x300mm

Connection : Aluminium straps, rubber washers, metal washers, glazing tape, bolts & nuts






Leoflex and Dragontrail are ultra high-strength and elastic/flexible glass products manufactured by Asahi Glass Company.

It is an alkali-aluminosilicate sheet glass, chemically strengthened and therefore much stronger (6 to 8 times the strength of normal glass), and thinner than conventional tempered glass.

As it is chemically strengthened, it can also be drilled or notched after the strengthening process.





1.3 mm thick glass panels with dimensions of 600x600mm, 600x440mm, 300x300mm were provided.

Structural analysis was resulted in the manipulation of buckling length to be less than 400mm.

These forms are generated by controlling the buckling phenomenon through the geometrical configuration and optimization method.







パネルは 600x600mm, 600x440mm, 300x300mm の3種類



Vault shape with buttress was developed in Stanford University.






Branching dome was developed in Tokyo.






Inthis case we might also apply the fuzzy node algorithm related to Soft Computing.


これも、ぼんやりとした節点 fuzzy node を持つ幾何学操作であり、前述と同様にアルゴリズムの構築を目指す。


Fuzzy Node のイメージ







DFL Pavilion 2013

Collaboration with Obuchi Lab, G30 Digital Fabrication Laboratory

Tensegrity structure composed of X shaped components work as compression element and cables work as tension element.

計画  :東京大学小渕祐介研究室 (G30 Program)







Geometric non-linear analysis is necessary for this structure because it stabilizes after large deformation such as 47 cm at its center.


極端に剛性の異なる部材が混在する場合の非線形解析は収束しにくい。この解析により、φ3mmの「ケーブル」がピンと張ると概ねφ6mmの「丸鋼」と同等の硬さの部材と解釈すれば計算が収束しやすく、収束回数が少なく済むことが分かった。コンポーネントに発生する圧縮は 0.4 tf 程度、ケーブルに発生する張力は 0.3 tf 程度。



Compression test for a X shaped component, Tensile test for a cable joint


The X shaped component consists of 3 stainless steel plate of 0.3 + 0.8 + 0.3mm thick.

Ultimate compression strength of this component has found 0.41 tf.

コンポーネントの圧縮試験は 200 tf 試験機を使用、ケーブルの引張試験はテコを応用してバネ秤で載荷した。

圧縮試験で得られた最大荷重は例えば 0.41 tf など。

これを再現できるよう解析モデルの設定を調整する。板厚は実際と同じ 0.3 + 0.8 + 0.3 mm とし、部材幅 40 mm と設定すれば座屈荷重が 0.29 tf となり、概ね再現しながら少し安全側の算定ができることが分かった。

Once it is found possible to use 40mm wide elements for these grid model, we can find the strength of other options only by the analysis without loading tests.

モデル化の方針が分かれば他の形状の強度や、強度不足のコンポーネントの対処法も解析のみで見つけることができる。板厚を 0.5 + 1.2 + 0.5 mm とすれば座屈荷重が 0.758 tf となり十分なことなどが分かる。












Poured Sticks Structure in DFL Pavilion 2014

Obuchi Lab, G30 Digital Fabrication Laboratory

Sticks are connected in simple way just touching. But they have the parameter of 3D angle and connection point, which makes the geometry complicated.

To make the problem simple, poured sticks are interpreted as the porous volume material.

計画  :東京大学小渕祐介研究室 (G30 Program)



Zoom out from detail




Finally the way of calculation was found different from Sunny Hills, structure of complicated Kigumi joint.


Sunny Hills Japan, 2013, Architect : Kengo Kuma

Structural analysis model for Sunny Hills, composed with every timbers modeled into bar elements.


Compression Test

Left : Initial 3 specimens

Middle : Improved 2, provided 2 by Shimizu Co.


Specific Gravity ρ= 0.06 tf/m3

Young’s Modulus E = 1.0 kgf/cm2

Yield Stress σy = 0.108 kgf/cm2


Bending Test

Specific Gravity ρ= 0.04 tf/m3

Young’s Modulus E = 0.6 kgf/cm2

Yield Stress σy = 0.209 kgf/cm2


Representing values for structural analysis :



Specific Gravity

Young’s Modulus

Yield Stress





Urethane Sponge




Poured sticks




Styrene foam




Balsa wood




Cedar wood









Even the material was found soft and weak, still we can use it for structure with thick volume.



 Structural analysis for the mock up, gravity and wind speed 10 m/sec loaded.

Operated by Mika Araki, Jun Sato Lab



Structural analysis for the mock up, gravity and wind speed 20 m/sec loaded.

Red elements indicating the lack of strength.

Operated by Mika Araki, Jun Sato Lab



Structural analysis and Optimization progress for final shape.

Operated by Mika Araki


Interface for adjustment of Karamba+Grasshopper to Hogan

Developed by Masaaki Miki



Stainless cables inserted in the wall for extra safety.

They work as tension rings.


● Lightweight and ductile structures preventing death in the event of collapse


Nebuta Tectonic – preventing death in the event of collapse

Structural Design Studio, IEDP Integrated Environmental Design Program, University of Tokyo, 2014 & 2015

Operations will result in developing a lightweight and ductile structure which will prevent death in the event of collapse.

From this studio we proposed Nebuta Tectonics composed of steel wire frame covered with Washi paper.

“ねぶた構造”− 壊れても死なない構造

建築構造デザインスタジオ, 東京大学環境デザイン統合プログラム 2014 & 2015





Japanese traditional Washi papers are made from fibers of “ Kozo ” or “ Mitsumata ” plants. It is an organic material, made of only the fibers of plants, without chemical glue. It is strong as the fibers are longer than other papers.



Nebuta ねぶた




Nebuta floats in Nebuta Festival, Aomori, Japan are made of Washi paper, steel strings.




Japanese traditional umbrella Wagasa, representing a lightweight structure,

made of Washi paper coated with linseed oil or perilla oil for waterproof.

The frame is slight and woven with colorful string to prevent buckling.







To resist against the first blow in spring (February or March) called “ Haru Ichi-ban ”, imagining the wind speed 20 m/sec, we practiced a materially nonlinear analysis, concerning the Washi papers as tension elements and controlling the buckling phenomenon and the plastic state of 3 mm steel wires.

In this case the buckling length was found to be manipulated to less than 40cm.

The shape was decided through structural analyses, material strength tests, drag coefficient tests, anchor strength tests.

東京大学柏キャンパスは強い風が吹き抜けます。「春一番」を想定して、大きく変形しながらも風速 20 m/sec に耐える形態を目指しました。和紙を引張に効かせ、3 mm の針金の座屈と塑性化を制御し、材料非線形解析で推測しています。構造計算、材料試験、模型による抗力係数の計測、抗力係数の解析、アンカー用スクリューペグの引張試験を経て、空気抵抗の少ない形状を決定しました。


Captured model



Drag coefficient analysis, experimentation



Washi paper tensile test, Screw peg plucking test


Materially Nonlinear Analysis









Nebuta Tree House, 2015 (Photo by Ying Xu)


When the Washi papers are coated with oil, they turn into translucent material. They will work not only for bracing but also serve as Filter for environmental elements.




● Energy consumption experiments


Copper Shell, “Earth : Material for Design” by The National Museum of Emerging Science and Innovation, 2010

Design & Build : Jun Sato Laboratory, University of Tokyo

A copper shell structure with 8m long fabricated by only hammering from a flat plate, with 40 students.

Considering the total energy consumption for this structure to appear, we discovered the energy consumption in processing the copper shell by hammering was only 7 %, of the total energy, while 93 % for manufacturing copper plate.




● Manipulation of Buckling Phenomenon


NYH, 2006

Architect : Makoto Yokomizo

Cylindrical steel plate wall structure stacked up to 4 strories.

NYH : 2006年,建築家=ヨコミゾマコト


円形壁は、9mmの鉄板にリブ FB-16x38 @300mm をつけて作っている。

PICT3279 PICT3273 八木04-Pict2887

Steel plate 9mm thick with reinforcing flat bar 16x38@300mm



PICT2986 PICT3018 八木06-Pict3022


Buckling strength of thin plate comes bigger when the curvature got bigger.



Structural analysis model, Buckling strength - Curvature diagram



Water Pavilion, World Exhibition in Aichi 2005

Design & Build : Naomi Sakuragi + Postgraduates of the University of Tokyo

Booth composed of dimpled acrylic resin walls. Thin plate wall comes 4 to 6 times stronger when dimpled.

愛知万博2005展示ブース : 2005年,建築家=櫻木直美+東京大学大学院生







03DSCN0039 04PICT2707 05PICT2712

Dimpled acrylic resin wall, Forming process using Chinese pan

Physical model made of aluminum, Buckling analysis



Moulded Pulp Installations : Seminar for master course of Tokyo University of Science

パルプモールド : 東京理科大学大学院講義, 2010




DVC00200 DVC00195

高さ1.8mの「シェルター」, 窓枠に取り付けられる「障子」


Rest house in Zoorasia

Architect : Riken Yamamoto

When flat bar columns are located in radial arrangement, buckling strength can be found 4 times bigger than parallel arrangement.


Buckling control of flat bar columns : Radial, Polygonal, Parallel



architecture as air, Venezia Biennale 2010

Architect : Junya Ishigami

Structure : Jun Sato

Rigid frame structure composed of 0.9 mm CFRP columns, 1.2 mm CFRP beams, and invisible braces made of 0.02mm polyalyrate fibers.


Left : http://contessanally.blogspot.jp/2010/08/venice-12th-biennale-of-architecture_26.html

Right : Screenshot of buckling analysis


Balloon, 2007

Architect : Junya Ishigami

Structure : Jun Sato

Aluminium “balloon” of 14m height, weighing roughly 1 tonne.

The balloon with aluminium lattice endoskeleton, filled with helium gas.



Aluminium lattice endoskeleton for “ Balloon ”, architect Junya Ishigami


● Reciprocal System


Rest house in the Forest, Seminar at Keio University, 2006

Free form shell structure composed of 19x140mm timbers. Each element is leaning on another element, mutally continuing. This system is called lamellendach or reciprocal system.

森の休憩所, 2006, 慶應義塾大学大学院生



細かな材が並んだ状態をラメラ(Lamella, Lamellen)と呼び、短い材がお互いに支えあうことで成立するという意図からも、これはラメラ架構の一種と言える。




● Tensegrity テンセグリティ




Kenneth SnelsonBuckminster Fuller により広められた。







3D Tensegrity Experiments on Geometries and Dynamics : workshop at Stanford University


Big Art, Exhibition Archi-neering

Tensegrity structure composed of a membrane supported by carbon (CFRP) pipes.

Designed and Constructed by 15 students

Structure : Jun Sato et al.

アーキニアリング展 “ Big Art ”, 2008






DVC00279 DVC00278 


MOOM (Membrane Oom)

Design & Construction : Kazuhiro Kojima Laboratory, Tokyo University of Science

Structure : Jun Sato

Membrane tensegrity structure composed of membrane and aluminum pipes.

Length 26 m, Span 8 m.

It was rebuilt 3 times for some events in Tohoku area, where the huge earthquake happened.



スパン 8m,全長 26m,総重量 600kgf で、40人程度で持ち上げることができる。




Structural calculations which I have provided were only these written on this paper at a meeting.

“ Omission ” is one of the tecniques of “ Engineering ”.

Not all the phenomena have been clarified, and as the “ project ” never have enough time and money we can not check all the matters which we want to check, but we engineers have the tecnique to imagine a simple model and find several critical matters to be checked, and finally we can find with just simple calculations if it can be built.








重さを w = 5 kgf/m2 とする。

スパン L = 8m、高さ H = 3m のアーチとする。

棒のピッチを 1m とする。

アーチを放物線で y = αx2 として y = 3 x = 8/2 = 4 を代入すると、

α= 0.1875

アーチの足元での傾きは y’= 2αx = 1.5 なので傾きは 1 : 1.5 だと分かる。


5 kgf/m2 × 1 m × 12 m ÷ 2 = 30 kgf


N =  × 30 kgf = 37 kgf



A = 4.91 cm2

生まれるデプスが 100mm とする。膜の断面積は不明だが、木材の棒と同じとしてみると、断面2次モーメントは、

I = 4.91 cm2 × 52 cm × 2 = 245 cm4

ヤング率は硬質樹脂程度で E = 20 tf/cm2 とする。

アーチの座屈長さ Lk = 0.4L0.5L 程度と知っておくとよい。Lk = 0.5L = 0.5 × 800cm = 400cm とする。座屈荷重は、

Pcr =  =  = 0.302 tf

これは N = 37 kgf に対して8倍の余裕があるので問題ないと分かる。




● Structural Tips


・材料特性 Material properties


比重 unit weight (ρ)

剛性 stiffness (K),ヤング係数(ヤング率,弾性率)young’s modulus (E)

ポアソン比 Poisson’s ratio (ν)

弾性 elastic,塑性 plastic,粘弾性 viscoelastic

降伏 yield

強度(引張,圧縮,曲げ,せん断)strength (tensile, compression, bending, shear)

終局強度 ultimate stress

線形 linear,非線形 nonlinear

伸び性能 ability of elongation,延性 ductility,靱性 toughness,脆性 brittleness

線膨張係数 linear expansion coefficient


・応力ひずみ関係 Stress - Strain Curve

鋼材 SS400 の引張試験

Tensile Test of Steel SS400


・荷重変形関係 Load - Displacement Curve


Typical Load-Displacement Curve       ガラス板(普通強度)の曲げ試験


Bending Test of Glass Plate

Glass has no ductility


・断面性能 Section Properties


断面積 Area                           A [cm2]

断面2次モーメント Moment Inertia     I [cm4]

ねじり定数 St. Venant’s Tortion Factor   J [cm4]

断面係数 Section Modulus              Z [cm3]


Example of rectangular section B x D

A = BD

I = BD3/12

Z = BD2/6



・構造計算 Structural Calculation





Basic formulae

These formulae will be also used for simplified calculations, understanding structural test, etc.


・バネの荷重と変形 Load – Displacement on spring

F = k x


F : 荷重 force (load)

k : バネ定数 factor (stiffness) of spring

x : 変位 displacement


・弾性曲げモーメント Bending moment in elastic level

M = σ Ze


M  : 曲げモーメント bending moment

σ : 縁部の応力度 stress on edge

Ze : 断面係数 elastic section modulus, for rectangle section Ze = BD2/6


・全塑性モーメント Bending moment in plastic hinge level (ultimate level)

Mp = σy Zp


Mp  : 全塑性モーメント plastic hinge bending moment

σy : 降伏応力度 yield stress

Zp  : 塑性断面係数 plastic section modulus, for rectangle section Zp = BD2/4


・集中荷重を受ける単純梁 Simple beam with concentrated load


bending moment   displacement


・等分布荷重を受ける単純梁 Simple beam with uniform distribution load


bending moment   displacement


・等分布荷重を受ける両端固定梁 Fixed beam with uniform distribution load


bending moment   displacement


・集中荷重を受ける片持梁 Cantilever beam with concentrated load


bending moment   displacement


・等分布荷重を受ける片持梁 Cantilever beam with uniform distribution load


bending moment   displacement


オイラー座屈荷重 Euler’s Buckling Load

fix-fix         fix-hinge     hinge-hinge   fix-fix+sway   fix-hinge+sway

α=0.5         α=0.708       α=1.0         α=1.0         α=2.0


Buckling strength  :  Pcr =


E  :  Young’s modulus [cm2]

I  :  Moment inertia of section [cm4]

Lk  :  Buckling length Lk =αL



アーチの形状 Arch Shape

等分布荷重に対しては放物線を描く Parabola for uniform distribution load

自重に対してはカテナリーを描く Catenary for self weight load


アーチの略算 approximate calculation

Approximate Buckling Length Lk = 0.4 0.5 L

放物線  で近似する。

αは、スパン L と高さ H により、 で求められる

傾きは微分して、 なので、端部での傾きは、1.0 :  = 1.0 :  となる。

鉛直荷重を w [単位 tf/m など] とすると、支点の鉛直反力

端部の軸力 N は、傾き方向なので、

これに対し、アーチの座屈荷重は、座屈長さを 0.4 L などとしてオイラー座屈の式に代入して求める。



Basic Process of Structural Analysis



(1) 材料と形状の想定 Assumption of Material Property, Shape of Members and Shape of Frame

(2) 荷重の想定 Decision of Loads as its Type and Level

Load Type : Gravity, Earthquake, Wind, Temperature

Load Level : Elastic / Ultimate


Diagram of diverse loads


荷重 Concerning Load

重力 Gravity          : 重力加速度 1G = 980 cm/sec2

静止している人 Stationary person = 80 kgf

階段を降りる人 Person descending stairs = 200 kgf

地震荷重 Seismic Load : 振動を静的荷重に換算する方法がある。数十年に1度の地震で重量の 0.2 倍など。

Seismic vibration load considering a couple of decades in Tokyo can be interpreted to 0.2 of factor of weight.

風荷重 Wind load      : 東京の建物では、数十年に1度の風速として 34 m/sec を想定し、概ね 100 kgf/m2 となる。


数ヶ月では 20 25 m/sec

数週間では 10 15 m/sec


Wind pressure considering a couple of decades in Tokyo can be estimated to be 100kgf/m2 due to the wind speed 34m/sec (10min. average speed).

Wind pressure is proportional to the square of wind speed.

20 25 m/sec for several months

10 15 m/sec for several weeks



 (3) モデル化 Modeling for Analysis

Finite Element Method (FEM)

Element Type : Bar element (Wireframe), Plate element, Solid element

Joint Type : Rigid, Hinge (Pin), Half rigid (Spring)

(4) 構造解析 Calculation

Results       : Deformation, Stress

Bending Stress Diagram, Deformation Diagram


(5) 強度のチェック(部材断面設計) Analysis of Stress


Basic Case

Safety Ratio = N/Na + M/Ma 1.0

N : axial force

M : bending moment

a : allowable


Structural analysis software HOGAN

Safety Ratio = M/Ma / (1.0 - N/Na) 1.0


● Little by little, learning Great Nature


We are learning little by little about Great Nature such as ground vibration, water flow, air flow, optical permeability of vegetation, porosity of insect bodies, buckling phenomena and the elastic / plastic state of material.

Even a little the more we learn, the more lives we can save.


Everytime a disaster happens, we engineers feel

it is impossible to know everything about great nature,

it is impossible to control great nature,

but if we could know a little bit more about the vibration of earthquake, a little bit more about the flow of water,

we could save a little bit more people.

Our mission and dream.