The Baya Nest pavilion project: braided pattern optimization for hanging shell structures by dynamic relaxation

Abstract

Through the study of the Baya's weaverbird nest, we carried out our research on the braided hanging shells. It is a new experimental structure that is effective in terms of low use of materials. We developed a parametrical dynamic relaxion solution to calculate principal fields of stress on every type of the hanging shell project. Thanks to experimental measurements and another dynamic relaxation algorithm that takes into account bending forces due to the braiding process, we developed a law which define a relation between density and orientation of the stems and the fields of principal stresses on an idealized continuous surface: "each field of stress is related to an optimal braiding". The apparent complexity of this method makes it restricted to researchers and engineers, thus also making it inaccessible to architects. Therefore, we sought to adapt our algorithm, making it accessible and easy to use for architects and practitioners. The goal of this project is to make those concepts understandable for a group of architecture students and to build from scratch the set of necessary tools for the calculation, braiding optimization, designing, and fabrication of a human-scale braided hanging pavilion; allowing us to connect theoretical and practical fields. In order to popularize those notions, we engaged in three different activities:
• The development of a complete, generic, open-source and ergonomic algorithm, usable by all, for optimization of braided hanging shell using dynamic relaxation.
• The publication in La Villette editions of a collective book that compiles our study and the historical, scientific and conceptual knowledge over this subject in a pedagogic way, co-written with the master cycle students.
• The practical application of our study with the construction of a full-scale public pavilion hanging from trees in partnership with the municipality of Paris on the belvedere of the Butte du Chapeau Rouge park (Paris XIX).

Full text

Proceedings of the IASS Annual Symposium 2020/21 and
the 7th International Conference on Spatial Structures
Inspiring the Next Generation
23 – 27 August 2021, Guilford, UK
S.A. Behnejad, G.A.R. Parke and O.A. Samavati (eds.)
Copyright © 2021 by the author(s) as listed above. Published in the Proceedings of the IASS Annual Symposium
2020/21 and the 7th International Conference on Spatial Structures, with permission.
The Baya Nest pavilion project: braided pattern optimization for
hanging shell structures by dynamic relaxation
Marc LEYRAL*, Quentin CHEFa, Sylvain EBODEb, Pierre GUEROLDc
* Engineer Architect, Lecturer at ENSA Paris-La Villette, Teams and Projects Director at EVP engineering
144 Avenue de Flandre, 75019 Paris
marc.leyral@paris-lavillette.archi.fr
a Engineer Architect at EVP engineering, Supervisor at Ecole Centrale-Supélec and at ENSA Paris-La-Villette
b Engineer Architect, Lecturer at ENSA de Paris-La Villette, associate at Uruk V
c Engineer at RFR, Supervisor at Ecole Nationale Supérieure d’Architecture de Paris-La Villette
Studies conducted with the participation of ENSA-Paris-la-Villette students: Wided Zina CHERIF, Mélanie BENTO, Victor
BARDY, Marius BAUDURET, Albin BREUGNOT, Hanane GUIDOU, Marie MERLE, Morgan DANNENMÜLLER, Lu
GAO, Agathe MOMBAZET, Robin PELOUR, Mathilde ARMENGAUD, Sara BOUKILI, Denisa MIHAES, Martin
PROCUREUR, Léo PAUVAREL, Nathanaël THOMAS, Benoit ROYANNAIS, Annabelle CAMAIL, José Pablo SALINAS,
Caroline LEGER, Maxence FRISSON, Sarah KLEIN, Francisco GARCIA CRUZ, Zahra ASADOLLAHI, Victoria
GARCIA FLORES, Aurélia ANASTASI, Marius BAGREAUX, Louise BOUCHAUDON, Ronan LACROIX, Razan
DAHAM, Anne-Louise DE MASSARY, Luis Gerardo LIZARRAGA ROMERO et Ana MIRANDA, and of Centrale-
Supélec : Élodie ROBLIN, Jeanne BUGNET, Cornelia HULLER, Alice VILLATTE DE PEUFEILHOUX.
Abstract
Through the study of the Baya’s weaverbird nest, we carried out our research on the braided hanging
shells. It is a new experimental structure that is effective in terms of low use of materials. We
developed a parametrical dynamic relaxion solution to calculate principal fields of stress on every type
of the hanging shell project. Thanks to experimental measurements and another dynamic relaxation
algorithm that takes into account bending forces due to the braiding process, we developed a law
which define a relation between density and orientation of the stems and the fields of principal stresses
on an idealized continuous surface: “each field of stress is related to an optimal braiding”.
The apparent complexity of this method makes it restricted to researchers and engineers, thus also
making it inaccessible to architects. Therefore, we sought to adapt our algorithm, making it accessible
and easy to use for architects and practitioners.
The goal of this project is to make those concepts understandable for a group of architecture students
and to build from scratch the set of necessary tools for the calculation, braiding optimization, designing,
and fabrication of a human-scale braided hanging pavilion; allowing us to connect theoretical and
practical fields. In order to popularize those notions, we engaged in three different activities:
• The development of a complete, generic, open-source and ergonomic algorithm, usable by all,
for optimization of braided hanging shell using dynamic relaxation.
• The publication in La Villette editions of a collective book that compiles our study and the
historical, scientific and conceptual knowledge over this subject in a pedagogic way, co-written
with the master cycle students.
• The practical application of our study with the construction of a full-scale public pavilion
hanging from trees in partnership with the municipality of Paris on the belvedere of the Butte du
Chapeau Rouge park (Paris XIX).
Keywords: Hanging, shell, braiding, weaving, dynamic relaxation, grasshopper, optimization, teaching,
pedagogy.

Proceedings of the IASS Annual Symposium 2020/21 and the 7th International Conference on Spatial Structures
Inspiring the Next Generation
2
1. Introduction
The art of basketry goes back to the Neolithic period and is still used today. Wicker baskets, rattan
furniture, lampshades made of woven blades, peach pots, grape harvest hoods, etc. Examples of
everyday objects come to mind by the hundreds, but what about architecture?
The world of construction has remained quite insensitive to basketry and when it is used, it is mostly for
filling purposes. Examples of structural wickerwork architecture are extremely rare. Yet habitats with
braided structures exist by the thousands... in the animal world! This is the case of the nest of the Baya
weaver, among others.
The objective of this study is to design a methodology for the construction of load-bearing braided shells
and to apply it to the realization of human-scale pavilions suspended from the branches of trees in the
park of the Butte du Chapeau Rouge in the 19th district of Paris. Its scientific contribution is to provide
an answer to a question that has been imposed on us (and about which we have not found any studies in
the literature): knowing the field of the main constraints of a loaded shell, is there an ideal way to braid
it and, if so, what is it?
2. Nests: from reciprocal frame to braiding
2.1. Reciprocal frame structures
When we think about how a bird's nest works, reciprocal frame is
the first idea that comes to mind. This structural typology forms a
surface composed of inclined beams supporting each other.
It is regularly used in Japan for roof structures that do not require central pillars. The term nexorade is
sometimes used to define reciprocal frames in which each element, occasionally called nexor (from the
Latin node or link), is considered infinitely rigid (structure’s equilibrium by reciprocity of shear forces
and not by taking into account the flexural flexibility of the elements, unlike a braid for example).
Figure 2: Examples of reciprocal frames: model by Charlotte Gambotti, Leonardo da Vinci's military bridge,
Qingming rainbow bridge, Stonemason Museum (Yasufumi Kijima arch., Yoishi Kan ing.) [credits: Kelkaku-
Inc.], Exhibition Hall of the Bunraku Puppet Theater in Seiwa (Kazuhiro Ishii arch.) [credits: Kazuhiro Ishii].
The end of each beam rests on the next beam that supports it, forming a circularly
closed assembly since the last beam is finally placed on the first one. The failure
of a single beam leads to the failure of the whole structure.
However, it can be objected that if a strand is removed from
a bird's nest, it does not collapse, nothing very significant
would happen. In addition, some birds, such as the Baya
weaver, bend their blades so that each one flexes many other
blades over its entire length. This method of construction is
still analogous to a reciprocal structure: each blade, by its
bending, presses on the blades that it interlaces with,
generating a frictional force on them, and vice versa. The introduction of bending
into the reciprocal structure, each element mobilizing the many other elements that
intersect it, however, leads us to a new structural typology as part of this larger
group of reciprocal structures: woven objects on which is based the art of basketry.
Figure 1: Bird's nest and the project
Uchronia by Arne Quinze.
Figure 3:
Anthropomorphic
example of reciprocal
frame by Olivier
Prévost [7].
Figure 4: Baya
weaver weaving his
nest [DURAIRAJ].

Proceedings of the IASS Annual Symposium 2020/21 and the 7th International Conference on Spatial Structures
Inspiring the Next Generation
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2.2. Braiding: the art of basketry
Basketry is both an art and a craft whose product is the making of braided
objects with plant blades. The terms weaving and braiding are often used,
incorrectly, as synonyms. Weaving is the art of regularly interlacing textile
threads in an orderly and often orthogonal pattern to create a fabric. The term
braiding comes from the braid, the rope, which was made by assembling at least
three fibers by repeating a pattern of crossings. In basketry the material evolves
between the moment when it is braided (still green and flexible) and the period
when the produced object is used (the blades will then be dry and rigid).
Finally, it should be noted that the result of braiding is more likely to be a rigid surface than that of
weaving, which is instead a very flexible surface. It therefore seems more accurate to describe as
weaving a surface that can only resist traction (no rigidity) and as braiding a surface whose rigidity
allows it to resist both traction and compression. For these reasons, and although the name of the Baya
weaver obviously comes from the art of weaving, we will henceforth use the verb braid in our study.
Origins: Basketry appeared even before pottery and wood and metal working. It
was used to create natural barriers to protect against animals (hedgelaying). The
first traces discovered date back to the Neolithic period (negatives of braided
molds on coil pottery) and the oldest-found basketry work have been exhumed
in Fayum (Upper Egypt) and have been dated to more than 10,000 years ago.
Material’s choice: With the help of Roger Hérisset [4], we have chosen the materials of our study after
a multi-criteria analysis, each criterion having a weighted importance (between 1 and 5).
1. Execution’s easiness M1: from a practical point of view, braiding being a skill that requires
years of specific learning process. Ours being basic, this criterion has a weight of 4.
2. Availability and provenance M2: Some basketry materials are difficult to find in quantity and
at a reasonable cost for a project of this size. Following the traditions of French basket makers
also allows to integrate the local origin of the material or not. M2 has a weight of 3.
3. The cost M3 = fyt / Cl : as we demonstrate below, the dimensioning criterion for our suspended
shell project is the tensile strength, the quantity of material to be used being inversely
proportional to the tensile yield strength fyt (MPa). Thus, maximizing the strength/cost ratio
means minimizing the overall cost of the structure. This criterion has a weight of 5.
4. The durability M4 = E / (1 + kdef). We are looking for a stiff material (high Young's modulus E)
to limit the initial deformation, with a creep coefficient kdef as low as possible to limit the
deformation under long-term loading. It is a question, therefore, of maximizing the M4 criterion.
However, the Baya project is temporary: we chose for this criterion a coefficient of 2.
This analysis, conducted on white wicker, Buff wicker, split wicker, rattan, chestnut splinters, Provence
cane, bamboo blades, mulberry, hazelnut blades, rye straw and palm leaf, resulted in the selection of
three materials for the project: Buff wicker, split wicker, and rattan blades.
Wicker is obtained from willow stems, which can reach up to 3 m. According to Mellgren [6], they are
harvested in winter from willow stumps. There are four types of wicker. The newly harvested green
wicker is not used for basketry. Wicker is raw dry when it is dried naturally by keeping the bundles
upright. After drying, the bark can be removed from the stems. Either by immersing their feet in water
and placing them in a high temperature room, allowing the sap to “circulate again” and the bark to detach
(white wicker). Or by bathing the wicker in boiling water for three to five hours (Buff wicker). The
wicker is then dried again. It will be left in water for 8 to 15 days before weaving in order to soften it.
It is also possible to split larger wicker stems into splints. The end of the strand is notched in three or
four parts with a sickle, it is split along its entire length with a small wooden splitter. The ribs are finally
obtained after passing through a marking gauge or an éclisseusse.
Figure 5: Basket
maker's tools: pruning
shears, punches, pliers.
Figure 6: hedgelaying
[photo: Vincent Jones].

Proceedings of the IASS Annual Symposium 2020/21 and the 7th International Conference on Spatial Structures
Inspiring the Next Generation
4
Figure 7: Dry raw, white, and Buff wicker. Wicker splitting and an éclisseusse [Wicker Paradise / Ji-Elle].
Rattan is also very commonly used in basketry, especially for furniture making. Its production comes
from the climbing, sometimes thorny, palms; it is generally native to tropical regions. Rattan stems are
between 3 and 10 mm in diameter. The palms are cut at the base, then the trunks are cut into sticks.
These are removed from the leaves and thorns and dried in the sun. Using a splitter, two types of material
are woven from them: the strips, or ribs, of the outer region, and the round marrow of the inside, which
is used for fine basketry. For sizing, the ribs pass through a levelling machine and the pith through a die.
Figure 8: From left to right: climbing palm [Dinesh Valke], braided rattan blades, braided rattan pith, and splitter
for splitting the rattan into blade and pith.
There are many different braiding techniques, the ones we have used are crocane and layered.
Figure 9: From left to right: crocane, layered, loop, torch, knotted and spiral wickerwork.
Figure 10: Other examples of weaving in nature: social republicans [Diego Delso, delso.photo, License CC-BY-
SA], weaver ants [Frawsy Eklablog & Bernard Dupont] and caciques [Tanguy Deville].
Basketry applications can be found in primitive or vernacular habitat. In Ethiopia, in the Guge
mountains, members of the Dorze tribe weave ogive-shaped huts with false banana palms on frames
made of bamboo and stems of local timber. The structure is lightweight and can be lifted by three or
four people to be moved. They are initially built very high, about 10 to 12 meters because of the presence
of termites that destroy, by devouring them, the bases of the huts whose height then gradually decreases
in time! This habitat has an average lifespan of 60 years and can last up to 80 years.
The Molo tribe from Lake Turkana in Kenya, use acacia wood, grass or dried wood fibers to build their
spherical-shaped huts. The hut is composed of a structure made of acacia branches on which is braided
a cover of palm leaves and dried wood fibers. Some of the huts are raised by pilings to prevent pests.
Sickle and
splitter
Step 2: Split the wicker along its
entire length using the splitter.
Step 1: Notch the
wicker stem at its end

Proceedings of the IASS Annual Symposium 2020/21 and the 7th International Conference on Spatial Structures
Inspiring the Next Generation
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Figure 11: Dorze huts, Chencha village, under construction [Kevin Smith], and Molo huts, Turkana Lake [Eric
Lafforgue, Bjorn Svensson / Alamy Banque D'Images / Richardandmarthashaw.blogspot.com].
Some examples are also to be mentioned in modern architecture. However, all of them, with few
exceptions, have in common that braiding is only used as a filling element, it is not structural.
Figure 12: Ephemeral Beaubourg project built by Nikolay Polissky in the Nikola-Levinet park (Kaluga region)
and bamboo tunnel by Wang Wen Chih [Cave Urban]. Weaver's Nest project by Porky Hefer of Animal Farm
(South African materials and manufacturing techniques on steel frames) and another project from the same
design office [Deezen & Animal Farm].
3. Design of the “BAYA” algorithm
Our goal is to transpose the basket maker's skill to an architectural work. Our project, Baya, is a
suspended pavilion, but our thinking is broader: it must be applicable to any loaded surface, such as
shells, as well as simpler elements like beams.
These elements constitute the entire structure of the work. The loads
circulate through the entire thickness of the structural surface of the shell
and subject it to tensile and compressive stress. Our problem is to study these
constraints fields and to question the existence of an optimal braiding of the
shell in relation with them. This study consists in observing the behavior of
the stems, on a 30*30 cm specimen, and understanding the relations
between the geometrical characteristics of the braid and its mechanical
behavior when it is subjected to a given loads field in order to feed an
algorithm, called BAYA, capable of giving the optimal braiding of any shell
under various loading cases. Ergonomic and open-source, it will be available
on the site www.construire-l-architecture.com.
3.1. The laws of optimal braiding
Methodology: our numerical simulation is conducted by dynamic relaxation, a method that allows us to
solve static equilibrium problems by a fictitious dynamic calculation. Bouhaya [1] explains that the
objective is to find the equilibrium position of a structure subjected to a set of loads by a pseudo-dynamic
calculation : “it is an iterative method that describes the movement of the structure from the moment of
loading to its equilibrium (…)” and, “according to [Barnes], “the basis of the method is to trace step-
by-step for small time increments, Δt, the motion of each node of a structure (from an initial disturbed
instant) until, due to artificial damping, the structure comes to rest in static equilibrium.” A more
complete pedagogical presentation of dynamic relaxation applied to elastic gridshells (ELASTICA
algorithm) is given by Leyral et al. [5] in another paper of IASS 2021.
In a braid constrained in the plane, we observe three types of forces: the forces due to the bending of the
strands that one must bend to pass above and then below the strands of the other layer, the restoring
Figure 13: Diagram of a
braided specimen subjected
to a given stress field.
Compression force
Traction force
Specimen

Proceedings of the IASS Annual Symposium 2020/21 and the 7th International Conference on Spatial Structures
Inspiring the Next Generation
6
forces related to the axial deformation of the strands (Hooke's law) and the friction forces at the knots.
Knowing that we can simulate the latter by looking at the normal stress (by Hooke's law) in fictitious
bars connecting the two directions at each node, only Hooke’s law and the bending force are thus
necessary to simulate the behavior of a braid. These are therefore the same forces that are found in the
dynamic relaxation of elastic gridshells (whose own weight would be neglected).
From this observation, the choice was made to take over the core of the ELASTICA algorithm, by
modifying it so as to be able to study the reaction of a braided specimen subjected to a field of principal
stresses in compression and tension. The objective is to understand the influence of the different braiding
parameters listed below.
The material (fixed setting): the experiment is conducted on two of the materials used in the Baya
project: round wicker stems and thin rectangular rotten stems. They are modeled by their geometrical
and mechanical characteristics: the dimensions of the cross-section of the strands, the modulus of
elasticity E= 3000 MPa and the elastic limit stresses in tension and compression fyt = fyc = 25 MPa.
Input parameters: specimen geometry and external loading. The braid is a set of strands, braided in two
different directions. In each direction, the strands are parallel to each other, and pass alternately above
and below the strands of the other direction.
The specimen is subjected to forces that simulate the principal stress field in the shell
(it represents two directions of orthogonal stresses at the level of the considered finite
element, which has been oriented to only have normal stress components).
The simulation of the different principal stress fields therefore depends only on the
two following parameters:
• Traction / Compression.
• The value Fσ1 and Fσ2 of the efforts (N/ml) respectively in direction 1 and
direction 2 (| Fσ1 | ≤ | Fσ2 |).
Once the material is fixed, the geometry is defined by four parameters:
• The braiding densities n1 and n2 of each layer (in number of strands per ml)
• The orientation α of the braiding with respect to the principal stress field
(angle of the layer 1 with the orthogonal forces applied on the specimen).
• The angle θ of braiding: angle between the two layers of braiding.
Parameters
Example
n1
n2
α
θ
Figure 15: Input parameters on the geometry of a braided specimen.
Table 1: Input parameters and test steps.
Input parameters
Symbol
Unit
Range of variation
Step
Value of force 1

N
150 - 10000 N
1000 N
Value of force 2

N
100 - Min(Fσ1 ; 4000N)
500 N
Braiding density in direction 1

u/ml
10
n/a
Braiding density in direction 2

u/ml
10
n/a
Braiding angle

Degrees (°)
0 - 45°
5°
Orientation of the braid in the specimen

Degrees (°)
0 - 45°
5°
After each simulation, several outputs are collected and combined for failure criteria comparison.
Specimen
α
Sense 1
Sense 2
θ
Figure 14:
Fictitious vertical
bar simulating
friction forces at a
knot.

Proceedings of the IASS Annual Symposium 2020/21 and the 7th International Conference on Spatial Structures
Inspiring the Next Generation
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Table 2: Outputs and criteria controls.
Output
Symbol
Unit
Controls
Criteria
Max tensile stength in strands

N
V1 – Yield strength
    
Max compressive strength in strands

N
V2 – Buckling
   


Maximum axial force differential
between who consecutive strands

N
V3 – Knots no-
translation
  
with  the friction coefficient
Maximum strength in fictitious bars

N
V4 – Knots no-rotation
.sin(

)/  with

= angle between 2
strands; R = radius of the contact surface
Maximum displacement

mm
V5 – Global buckling
Kinetic energy has converged + specimen is still planar
The study of the specimen teaches us the following principles:
• As expected, the yield ratio Tmax / fyt is a linear function of the tensile strength Fσ1
• Local buckling (Cmax compared to Euler’s force) is not an issue with regular n1 and n2 densities
• Global buckling (non-planar specimen) depends mainly on compressive strength Fσ2
• Friction forces raise with Fσ1 and fall with Fσ2 ; which explains why instability failure appears
with lower compression values when tension is not high enough (cf. second chart)
• High values of Fσ2 lead to knots translation or rotation, even negative friction (decompression)
• Positive friction force possesses a physical limit (depends on the diameter of strands)
• Changing the braiding angle θ has little effect if input forces are almost parallel to the strands
(α close to zero); which validates the idea of braiding along the principal stresses.
3.2. BAYA algorithm for optimal braiding of architectural shells
The BAYA algorithm determines the principal stresses for any shell under a
given load. Thanks to the above optimal braiding laws, it is able to give the ideal
braiding for the shell. Algorithm can be applied to any loaded surface, including
basketry items such as baskets, we have chosen to illustrate its presentation on
an isostatic beam on two supports loaded by a uniformly distributed force.
1. Geometry of the studied shell: The shell surface, the position of the
support points and the loads are the input data of the BAYA algorithm.
2. Finite element mesh of the shell: The surface is discretized into small
rectangular isosceles triangles, each representing a finite element of it.
3. Obtaining efforts: in the finite element edges by dynamic relaxation.
4. Obtaining the principal stresses: deduced from the forces by rotation of
stresses’ coordinate system on the largest support reaction of the right-
angled isosceles triangle.
5. Braiding of the shell: by using the laws defined above.
Figure 16 – Test’s results and criteria charts examples: V1, V2, V3, V4 as Fσ1 functions; each
line corresponding to a different Fσ2 value).
Figure 17: Diagram of
the beam to be braided.
Figure 18: Principal
stresses on a finite
element.
σv
σ2
σ2
σ1
σ1
σv
σhσh
σh

Proceedings of the IASS Annual Symposium 2020/21 and the 7th International Conference on Spatial Structures
Inspiring the Next Generation
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Figure 19a: Meshing, strains and principal stresses, and optimal braiding by the BAYA algorithm.
The predominant mode of failure of a suspended nest is due to the breaking of the strands. We lead the
verifications in the elastic domain with a safety factor on the results of the calculations taking into
account various parameters: variations in modulus of elasticity E (between the different blades, due to
moisture and due to creep), accuracy of shape of shell, variations in loading, accuracy of computer
model and assumptions, nature and significance of collapse and consequences of failure. Our global
safety factor is 6.30 (4.50 x 1.40 security coefficient on ULS combination).
4. Experimental verifications
4.1. Comparing BAYA to Pratt
In the making, the braiding algorithm was tested on a 2D
rectangular surface since the principal stresses of a uniformly
loaded isostatic beam are familiar (see Figure 19a).
Further to this test, we decide to braid the result, in order to
compare our “Baya beam” to a Pratt truss made out of stacked
and connected stems. For identical sizes, loads and safety
factors, Baya needs half the quantity of Pratt.
This will soon be verified by loading the two specimens up to
failure.
4.2. Laws of optimal braiding by studying physical specimens
The numerical model idealizes reality, and several simplifying
assumptions were made for the verifications. As the results could not be
compared with the bibliography, since we did not find any equivalent
studies, it was necessary to verify them by a similar experimental study.
The preliminary results of this physical experiment, which is still in
progress, tend to confirm, with a satisfactory margin of accuracy, those of
the numerical model.
Figure 20: Experimental
device.
Figure19b: Braided beam according to Baya
laws (in progress)

Proceedings of the IASS Annual Symposium 2020/21 and the 7th International Conference on Spatial Structures
Inspiring the Next Generation
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4.3. Principal stresses
4.3.1. Photoelasticimetry
Light is an electromagnetic wave whose electrical component
propagates orthogonally to its magnetic component. This
polarization can be modified by a polarizer placed downstream
of the light source, which transforms the light wave into a
linearly polarized wave. If we place a second polarizer, called
an analyzer, after the first one, all the light coming out of it
will be transmitted if their axes are parallel, and no light will
come out of it if they are perpendicular.
Some materials are birefringent when subjected to stress: they
are capable of polarizing light along the axes of the principal
stresses within them. This is the principle of
photoelasticimetry.
Plane Polariscope: a birefringent material is placed between
a polarizer and an analyzer, we obtain an experimental device
called a plane polariscope. It can be shown that the light
intensity at the output of the experimental device is equal to
   
 (1)
α is the angle between the principal stresses and the angle of the polarizer. When sin²(2α) = 0, the light
intensity is equal to zero and a black band is observed: these are the isoclines. Along these isoclines, the
stresses are parallel to the angle of the polarizer. To obtain the lines of the principal stresses, called
isostatics, we thus draw the isoclines for different angles of the polarizer, place the directions of the
principal stresses σ1 and σ2 on them and then connect them.
Figure 23: Isochrones for one specific load (A), isoclines drawn for various polarizer angles (B),
merged drawings (C), isostatics (D), comparison with the principal stresses from the algorithm (E).
4.3.2. By photogrammetry on a physical
shell
A suspended balloon is filled with water
(pretension gives the shell compression
capacity) and loaded with a mass. A
picture analysis algorithm recognizes
marker points; then Hooke’s law converts
the grid deformation into strengths.
Figure 21: Polarizer principle
E= wavelength
Figure 22: Plane polariscope principle.
[https://cours.polymtl.ca/]
Figure 24: Photogrammetry compared to algorithm results.

Proceedings of the IASS Annual Symposium 2020/21 and the 7th International Conference on Spatial Structures
Inspiring the Next Generation
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5. Applications
5.1. Study of the of the Baya weaver’s nest
5.1.1. The Baya weaver
The Baya project, described below, is a colony of suspended pavilions whose skin, the very structure of
the object, is a braid of long and fine elements. It echoes many habitats of the animal world, in particular
bird nests. Among them it appeared to us that the one of the Baya weaver was an
object particularly close to our intention.
The Baya weaver (Ploceus
philippinus) is a small bird of the
Ploceidae family, which lives in
Southeast Asia and builds
suspended nests in the shape of
weighted down stockings (close
enough to a drop of water). The
etymology of its name comes from
the Sanskrit word vaya meaning
the one that weaves. Most of the colonies (50 to 100 nests in general) are in India,
on coconut trees in the northeast and thorny trees in the southwest.
The weaving of the suspended nest begins during its reproduction period, the
period of rains associated with the monsoon, caused by an unidirectional
exchange of warm air loaded with humidity moving from the ocean to the land.
The nest serves to protect the bird, its eggs and young from predators and the
climate. The location of the tree (overhanging the water to limit the entry of
rodents), its species (thorny trees are preferred), the position of the nest on it (on
the side protected from the wind), and its orientation are thus judiciously chosen.
The nest, composed of 1.000 to 1.500 long strands of 20 to 60 cm, is braided
during eighteen days for breeding purposes.
Table 3: Stages of nest construction according to Crook [2].
Stage
Wad stage (2 days)
Advanced wad stage
Ring stage (5 days)
Illustration
Knots used
Description
The bird ties the first either to a palm leaf making a hole in it or to a
hanging branch, forked or not. If the branch is forked (the most common
case), it weaves strands around each element formed by the Y. Thus, the
nest and the branch are completely interdependent and move together. If
the branch is straight, it must first make a small notch or use a defect in
the branch to hold the first strand. Baya's weaver then makes a bundle, a
ribbon in the shape of a circle that will serve as a perch to tie the other
strands without having to fly in static around his nest.
Continuous addition of strands extends the wad downwards while
increasing the thickness and length of the ribbon that serves as a
support. It then braids two horn-shaped protrusions on either side
and connects them at the ends, forming a ring around himself.
It braids around the ring to widen it and add an opening
downwards. The base of the nest is then made up of a first rather
thick ribbon forming a temporary scaffolding during the
construction. The base of the ring will then divide the chamber
into two equal halves.
Stage
Helmet stage (6 days)
Padded helmet stage
Completion (3 days)
Illustration
Figure 27: Davis'
hypothesis [3]
of its
orientation to the wind
with respect to the risk
of egg fall.
Figure 26: General architecture of a Baya
weaver's nest according to Quader [8] at the
helmet stadium and at the final stage.
Nest length
Brood chamber
Entry
Threshold
Entry
Brood chamber
Suspension
Suspension
10 cm
5 cm
Nest depth : 14 cm
4 cm
10 cm
20 cm
First strand in
palm, grass or
banana tree
End of the strand
pulled by the beak
Top of the right branch
Notch to
facilitate the
holding of the
strand to the
branch
First strand in palm,
grass or banana tree
First temporary
perch
End of the strand held
by the leg
Final nest form
Top of the forked branch
Figure 25: Studied
Baya weaver’s nest.

Proceedings of the IASS Annual Symposium 2020/21 and the 7th International Conference on Spatial Structures
Inspiring the Next Generation
11
Knots used
Description
The bird, perched in the initial ring, adds, strand by strand, material to the back edge of
the upper part of the ring to make a flange that will form the roof of the egg chamber. At
the same time, the front edge is also enlarged forming a porch-shaped roof that will later
become the roof of the antechamber. Two openings are made in the ring: one for the
entrance tunnel and the other to access the egg chamber. The shape of the nest then evokes
that of a helmet.
The male then calls, through whistles, the females which inspect all the nests by making
them pass strength tests, pushing on the walls with their beak and pulling on fibers to
check the quality of the work. The female then chooses the best nest, the builder of this
one becoming her companion. At this stage, the male has designed and structured the egg
chamber.
Waiting for a female, the bird pads the exterior and interior surfaces increasing the
thickness of the walls and strengthen the attachment point.
As soon as a female accepts a nest at the helmet
stage (whether padded or not), the male spreads
the wall of the egg chamber downwards and
then braids the bottom (one day's work). It still
pads the inside while the female brings a sparse
lining of fibers and a few feathers that make up
the floor of the egg chamber. The eggs can then
be laid. They add drops of mud, clay or cowpat
to the walls, perhaps in order to ballast the nest
against the wind. During this time, and for two
days, the male adds a long vertical tubular tunnel
that will protect the entrance from rodents.
5.1.2. Study of the nest and comparison with the BAYA algorithm’s results
The objective of this part of the study is to answer the following
question: does the Baya weaver follow, when it makes its nest,
the laws of optimal weaving that we have defined? To answer
this question, we have first carried out a survey by laser surface
scanner and by photogrammetry of the nest with the support of
Ph.D. Professor François Guéna, Scientific Director of the
MAP-MAACC laboratory and
François Goussard and Delphine Brant, researchers at the National
Museum of Natural History.
Thanks to the color saturation and the bump pattern obtained, we have
built an image recognition algorithm able to isolate on the nest surface
most of the strands and recognize their diameter. We deduced the main
directions and the density of the strands on each area of the nest. The
results seem to betray the ghost of the temporary scaffolding used by Baya
weaver to build its nest from the ring stage. To confirm this, we scanned
the nest with X-rays thanks to the help of Dr. J.-R. Blondeau, head of Pont-
l'Abbé hospital’s radiology dept., and accessed to the interior of the nest’s
walls.
Figure 30: Sections of the RX scanner, reconstructed 3D model compared with predictions of BAYA algorithm.
This study enlights the static scheme of the weaver's nest, which functions as a
"swing" with the two sides perpendicular to the entrance hole being much more
stressed. The braiding of the nest, which follows broadly that of its temporary perch,
is not only justified by the construction’s method: it is also the most efficient
structural scheme for the object. This is confirmed by the striking proximity between
the ideal nest braid provided by the BAYA algorithm and the one actually made by
the bird. This study proved of the relevance of the optimal braiding laws and of the
BAYA algorithm, and helped to determine the final static scheme of our project.
Figure 31: More
stressed zones of
the nest, as
predicted by the
BAYA algorithm.
Figure 29: Preferred
directions and density
of braiding on the
surface of the nest.
Figure 28: Nest modeling by laser
surface scanner and by photogrammetry.

Proceedings of the IASS Annual Symposium 2020/21 and the 7th International Conference on Spatial Structures
Inspiring the Next Generation
12
5.2. Form finding: the drop of water and the weighted down stocking
Several authors compare Baya weaver’s nest to the shape of the drop of water at the
time of its detachment. Others, like Newton, prefer the comparison with a suspended
and weighted down stocking. These two forms have however their specificities, for
some similar to our object of study, for others departing from it. The suspended
stocking, like the nest and our architectural project, is punctually loaded by vertical
forces directed downwards. However, its surface is a weaving, i.e., unlike our braid,
it cannot bear any tensile stress, explaining why the free volume inside is greatly
reduced. The water drop has a synclastic and stretched surface, coming from a field
of pressure forces, that differs from that of the nest.
Thus, we carried out a comparative form finding study, looking for the shape minimizing the energy
involved on the two systems using the BAYA algorithm. A spherical shell held at its summit vertex,
modelized by mesh in taction only and without diagonals, submitted to a hydrostatic force field
converges to the shape of a water drop. The distance of this shape to the Baya weaver's nest is 91.54%.
But a very flexible spherical shell, without compression forces, forced to keep a constant volume at the
bottom, and subjected to a vertical force field, converges to the shape of a weighted stocking. The
proximity to the nest is 97.02%, which is therefore better, ruling in favor of Newton. It is only slightly
less good than the shape which best describes the nest, obtained by reactivating the shell’s possibility to
bear compressive forces (97.34%). This study helps us to decide on the ideal shape of our project.
Figure 33: Form finding studies on a model of water drop and on a model of weighted stocking, results are
compared with a 1:2 physical model.
5.3. Baya Project: application to a suspended pavilion at human scale
5.3.1. Context
The park of the Butte du Chapeau Rouge, developed from 1938 by Léon and Jean Azéma, is in the 19th
district of Paris. After various tests comparing numerical and model studies, we opted, following the
example of the colonies of nests of Baya weavers, for the realization of several pavilions implanted in
the chemin de ronde, a peripheral walk below the esplanade, lined with lime trees and plane trees.
Figure 34: BAYA algorithm results on the project, displacements are compared with a 1:2 scale model.

  


   

  


   
Figure 32: ideal
shape from a form
finding led on a
Baya weaver's nest.

Proceedings of the IASS Annual Symposium 2020/21 and the 7th International Conference on Spatial Structures
Inspiring the Next Generation
13
Figure 35: Sketches, photomontage, 3D and fabrication of the Baya project.
Before braiding the final pavilion, we decided to build a 1:2 prototype. The deformation of the prototype
was critical but fitted the algorithm prediction. The observation of the loaded surface guided us to
reinforce the density of the compressed area in order to avoid surface buckling.
6. Conclusions
The outcomes achieved so far are:
• Obtaining the optimal braiding laws
• Algorithm for braiding the shells
Outcomes expected during next steps:
• Construction of the project Baya.
• Going on experimental verifications.
Acknowledgements
The Paris City Hall and the 19th district City Hall, in particular Sophie Godard, Cécile Becker, Eric de
Grootte, Philippe Clayette and Sylvie Roudier, for their support, as well as the inhabitants of the
neighbourhood, Mr. Mayor François Dagnaud and Mrs. First Deputy Halima Jemni.
Valéry Schollaert, ornithologist, Roger Hérisset, basketry expert and doctor in ethnology at the UBO,
and Prof. Ph.D. François Guéna, Scientific Director of the MAP-MAACC laboratory (ENSAPLV).
Pierre Jehel and the Paris Centrale-Supélec school. Caroline Simmenauer for proofreading.
The National Museum of Natural History, in particular Delphine Brabant and Florent Goussard,
researchers in paleontology and comparative anatomy, and Dr. Jean-Robert Blondeau and the radiology
department of the Pont-l'Abbé hospital for their help in modeling the nest of the Baya weaver.
The ENSA of Paris-la-Villette, Caroline Lecourtois, director, Vincentella De Comarmond, deputy
director, Anne d'Orazio, President of the Board, Marc Fayolle De Mans, Jacques Bergna and Alain
Raynaud (model workshop), Philippe Agricole and Philippe Bourdier for logistics.

Proceedings of the IASS Annual Symposium 2020/21 and the 7th International Conference on Spatial Structures
Inspiring the Next Generation
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