Emergent Technologies & Design Biomimetics, 12 January 2015
ADDITIVE SYSTEMS IN BRANCHING
GROUP 8 Alican Sungur__Felix Tseng__Kuber Patel__Thaisorn De Vapalin
[ABSTRACT] A definition which mostly valid for woody plants is probably “Form with body of logics” which also illustrate its behaviours of growth regarding competition and efficient production. Trees forms their self fluid distribution system. This “equal distribution system” or “vascular system” also includes equal mass distribution which makes these systems efficient in terms of load capacity/ self weight and also proportion. Our purpose is to analyze its geometrical advantage in other words its mass distribution quality and applying this logic as an “Additive temporary structural system” proposal. As a starting point we analyzed different tree species, their growth, geometries and reasons of their differences by means of previous research done. At the same time we made experiments on local and material level to identify how to construct and develop this additive system with industrial manufacturing processes as regional and global scale respectively. In larger scale,we investigated this system developed by both digital explorations and physical experiments comparing to primitive systems. Ultimately, we observed that due to its logic , There is a high potential that this system could provide a better efficient and sufficient temporary structure for certain structure.
Group 8 Alican Sungur__Felix Tseng__Kuber Patel__Thaisorn De Vapalin
[CONTENTS] 1 TREE SPECIFICATION MORPHOLOGY 6 EXCURRENT TYPOLOGY 8 DECURRENT TYPOLOGY 10 2 RESEARCH OVERVIEW 12
3 BRANCHING SYSTEMS
L-SYSTEMS 14 H-MODEL 15
4 DIGITAL EXPERIMENTATIONS
STRUCTURAL ANALYSIS OF VARIATIONS 16 CONCLUSION 24
5 MATERIAL LEVEL RESEARCH
JOINT SYSTEM 26 BALL JOINT 28 FORK JOINT 29
6 ARCHITECTURAL APPLICATION
INTRODUCTION 30 PERFORMANCE 32 VARIATIONS 34 7 CONCLUSION 35 8 BIBLIOGRAPHY 36
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Tree specification_ Morphology
TREE PHOTO
Quercus robur
Tree morphology consist of three zone, gathering, distribution and production zones. Moreover, for the inspected area as branched structure where distribution function fulfills is mostly phloem and xylem cells. From different parts of the world each species has different adaptations from their environment,these adaptations are also valid for branching patterns even different species that using branches for different purposes are share common behavior. Basically,branched structures can be classify in two main categories; Excurrent and Decurrent.
Group 8 Alican Sungur__Felix Tseng__Kuber Patel__Thaisorn De Vapalin
leaves
twig crown branch
trunk
roots
Other variables of tree branch patterns are environmental features and trees response to these variables. Especially for the particularly growing at undulating environmental conditions, due to perpetual feedback process form that tree emerges through is significantly complex and rather different than ground zero condition of the pattern defined by its genotype. Trees achieve these forms with perpetual data gathering and simple responses. In our research we focused on different branching sequences and their effects on structural performance under additional statical loads and self-weight only on branched structure.
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Tree specification_ Excurrent
Pinus, Pinaceae family
Excurrent branch system
In Excurrent type,basically there is a single trunk at the centre that controls the growth process. Expansion succeeding by subdivisions of this leader trunk. Consequently, cone-shaped crown is observable for the species.(Harris, 1980) Pinaceae family Pinus is a good example for the excurrent trees.
1
Steeply cone-shaped with short and often downward-sloping branches
2
Movement of needle leaves (for species in dry environments)
3
Angle of branches differs from bottom to top
Group 8 Alican Sungur__Felix Tseng__Kuber Patel__Thaisorn De Vapalin
shedding snow
1
1 day light-low angle
3
2 leave movement
1
Shedding snow load; system distributes snow load through all branches Increase the area of surface to gather sunshine (Northern hemisphere conditions)
2
Prevent water loss by different light conditions
3
Tall shape maximize capability of light gathering with lower sun-light angles
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Tree specification_ Decurrent
Quercus, Fagaceae family
Decurrent branch system
For Decurrent type, there is no leading mother branch, only within first year of growth young tree is dominated by main trunk. Botanists keeps growth of decurrent types under control by often pruning. Unless crown of these types tend to grow equally at height and spread. (Brown, C.W, 1967) Decurrent types mainly tends to overgrow both width and heigth to get maximum efficiency from sunlight. Oak trees are good examples of decurrent trees in terms of efficiency with its form.
1
Flat-top shaded crown shape having dense foilage
2
Shallow growth with wide branching
3
Phyllotaxis happen upwards in along single axis with no leaves underneath
4
Angle of forking by the branches is limited to a certain range of acute angles
Group 8 Alican Sungur__Felix Tseng__Kuber Patel__Thaisorn De Vapalin
1
large surface area
2 density of branching
3
4
forking angle
1
Large surface exposed to the sun allows more photosynthesis
2
Help to keeps itself out of heavy winds.
3
Cloudy conditions forces the tree to make maximum use of sun in less time.
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Due to extreme weather changes sharp angle help transfer fluid faster in summers to avoid drying of leaves and get neccesarry minerals. Emergent Technologies & Design I Biomimetics Architectural Association10 I 11
Research overview
RESEARCH
Global Geometry
Local Level
Digital explorations_a Species / Pinus / Quercus
Joint system / Ball joint / Custom joint
Digital explorations_b Analysis of variations
F/8
PL A’ A
Architectural Proporsal
Group 8 Alican Sungur__Felix Tseng__Kuber Patel__Thaisorn De Vapalin
System expected to perform under statical loads.The local analyzation will compose the different beam sizes and materials. At the same time,branching patterns of different species generated and the digital replications can be explor furtherwhich according to previous research done (Honda and Lindenmayer). Since these systems are expected to work under self-weight and additional load, generated geometry will be firstly test without joints as solid beam systems. In such system, higher stresses which expected to occur on joints. As a consequence,different joint types has been introduced and analyze (1-2 iterations) in order to find the optimum solution in terms of stress distribution and fabrication techniques which will proposes in 1:1 scale. After these observations, it is possible to implement an architectural proposal further.
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Branching systems
sister branch( “, ! )
vertical angle( ^, &)
FFFA : definition of length A=!""[B]////B : tactical rotation of each iteration B=&FFFAJ : vertical rotation of each iteration
tactical angle: (/, \)
F: Move forward at distance “L” / and \: rotation counter clok-wise and clock-wise “: multiply current length (ratio of sister branch) [ and ]: start and finish branch A: rewrite the algorithm
^ : rotation at counter direction of gravity & : rotation at direction of gravity ! : multiply current thickness (sister branch thickness)
To make structural analysis in digital medium different species and organisations needs to formulated. Previous researches that have been done explains how to formulate generation processes and forms of different species, these research and geometrical formulation models applied to our tools. For decurrent typology or Quercus specifically we applied an L-system model due to its fractal based geometry. L-system from Aristid Lindenmayer is a way of reproducing body of rules. Rules that defined verbally represents different inputs such as angles, length ratios reproduced according to previous generation. Final geometry is achieved according to number of iterations that defined as an input.
Group 8 Alican Sungur__Felix Tseng__Kuber Patel__Thaisorn De Vapalin
Model representing the plane organisation of H-Model (Hotta et. all., 2004)
Another research done by Hisao Honda formulates tree geometry rather different. Similarly, sister branch relation defined at forking points. However, for each iteration different plane organisations applied according to previous branch. Honda used this system to explain gravotropism and phototropism in addition to growth patterns of different species. The system that explain phyllotaxis and gravitational forces named as H-Model (Honda,1982)
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Digital experimentation_ Analysis
Max. Displacement(cm)
10
9 8 7 6 5 4 3 2 1
self weight
50
100
200
400 Load (kN)(addition to selfweight)
VARIATION #1
A’
Graphic explains expansion of beams according to point loads applied. Aim is to understand optimum range of angles which can efficiently work under additional statical loads.
L
A(tactical angle): 15° A’(vertical angle): 90° L(sister branch): 1/1
A Group 8 Alican Sungur__Felix Tseng__Kuber Patel__Thaisorn De Vapalin
Max. Displacement(cm)
10
9 8 7 6 5 4 3 2 1
self weight
F/4
50
100
200
400 Load (kN)(addition to selfweight)
F/4
VARIATION #2 F/4
F/4
Forces revealed at the graphic divided into number of free-standing beams and applied from end points at the growth direction
A(tactical angle): 45° A’(vertical angle): 90° L(sister branch): 1/1
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Digital experimentation_ Analysis
Max. Displacement(cm)
10
9 8 7 6 5 4 3 2 1
50
self weight
100
200
VARIATION #3 A’ L A(tactical angle): 60° A’(vertical angle): 90° L(sister branch): 1/1
A Group 8 Alican Sungur__Felix Tseng__Kuber Patel__Thaisorn De Vapalin
400 Load (kN)(addition to selfweight)
Max. Displacement(cm)
10
9 8 7 6 5 4 3 2 1
self weight
F/4
50
100
200
400 Load (kN)(addition to selfweight)
F/4
VARIATION #4 F/4
F/4
A(tactical angle): 45° A’(vertical angle): 90° L(sister branch): 3/4
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Digital experimentation_ Analysis
Max. Displacement(cm)
10
9 8 7 6 5 4 3 2 1
self weight
50
100
200
VARIATION #5
A’
L A(tactical angle): 45° A’(vertical angle): 90° L(sister branch): 1/2
A Group 8 Alican Sungur__Felix Tseng__Kuber Patel__Thaisorn De Vapalin
400 Load (kN)(addition to selfweight)
Max. Displacement(cm)
10
9 8 7 6 5 4 3 2 1
self weight
F/4
50
100
200
400 Load (kN)(addition to selfweight)
F/4
VARIATION #6
F/4
F/4
A(tactical angle): 45° A’(vertical angle): 90° L(sister branch): 2/1
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Digital experimentation_ Analysis
Max. Displacement(cm)
10
9 8 7 6 5 4 3 2 1
self weight
50
100
200
400 Load (kN)(addition to selfweight)
VARIATION #7 For decurrent models different algorithms generated with H-model approach. Consequently, different parameters define the geometry.
PL A’
A(tactical angle): 45° A’(vertical angle): 15° PL(plane dimension ratio to trunk): 1/2
A
Group 8 Alican Sungur__Felix Tseng__Kuber Patel__Thaisorn De Vapalin
Max. Displacement(cm)
10
9 8 7 6 5 4 3 2 1
self weight
F/8
50
100
200
400 Load (kN)(addition to selfweight)
F/8
VARIATION #8 F/8
F/8 For decurrent types same amount of load applied to structure. However, load divided more.
F/8
F/8 A(tactical angle): 45° A’(vertical angle): 25° PL(plane dimension ratio to trunk): 3/4
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Digital experimentation_ Conclusion
Max. Displacement(cm)
10
9 8 7 6 5
var #5 var #2
4 3
var #7
2 1
self weight
50
100
200
400 Load (kN)(addition to selfweight)
Variation (no.)
8 7 6 5 4 3 2 1
1.6
Group 8 Alican Sungur__Felix Tseng__Kuber Patel__Thaisorn De Vapalin
1.8
2
2.2 Height (m)
F/4
F/4
A(tactical angle): 45° A’(vertical angle): 90°
F/4
L
A’
F/4
A
L(sister branch): 1/1
F(additional force): 50-400 kN
According to analysis of two typology and different variations, different types of structural responses observed. For decurrent type, although closer tactical angles to 45° and sister branch length 1/1 examples has higher deflections under selfweight, under perpendicular statical loads their deflection graphics are more stable. For excurrent typologies when compared to decurrent type, this type have less declection under selfweight and have better graphics of deflection under additional load. However, these typology have smaller expansion and height under the same volume with excurrent types. To conclude, decurrent typologies with variables similar to variation #2 have chosen for further structural development. Emergent Technologies & Design I Biomimetics Architectural Association24 I 25
Material Level Research_ joint design
forking connection and assembled model
During structural analysis one of the main points that underestimated is joint solution. At such systems higher stresses occur at connection elements. For structural development two types of solution predicted and analysed for initial organisation. First alternative is beam-like forking system work with waffle-connections(REVİSE!!!!) and multiplation of these forks required angles achieved. This system works with three forking parts and each one succeed one neccesarry anguler movement and these parts are relatively big compared to other solutions but shows characteristics of the system.
Group 8 Alican Sungur__Felix Tseng__Kuber Patel__Thaisorn De Vapalin
Ball joint and assembly directions
As second alternative a ball joint proposed. Such systems are popular for one to multiple forking structures. Our proposal consists of two parts. For one to four connection first part is only for primary beam when twice use of second part for secondary coloumns provide four connected beams. Main advantage of this system is that it solves the connection at single point and it is smaller than the other solution. However, for assembly and stability of the joint screwing between faces is compulsory.
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Material Level Research_joint analysis
high: moderate: minumum:
Ball joint and stress distribuion of assembled model
Branching condition: Tactical angle: 90° Vertical angle: 45° Sister branch ratio: 1/1 Custom beam size: 112x4x2 (cm)
Evaluation and comparison of data
Maximum Displacement :
Ball joint and 3 member-forking joint system have tested on same beam organisation and stress distribution observed. Main aim of the test is comparing these system according to deflection amoun, stress distribution and maksimum stress values. According to structural analysis we compared two system according to maximum deflection, maximum stress and stress distribution and following observations explored. Group 8 Alican Sungur__Felix Tseng__Kuber Patel__Thaisorn De Vapalin
Maximum Stress : Stress Distribution :
forking joint and stress distribuion of assembled model
Branching condition: Tactical angle: 90° Vertical angle: 45° Sister branch ratio: 1/1 Custom beam size: 112x4x2 (cm) Forking joint cause higher values of deflection at the system. Moreover, even generated maximum stress amounts are approximate with respect to stress distribution forking connection is more homogenious.
high: moderate: minumum:
Evaluation and comparison of data
Maximum Displacement : Maximum Stress : Stress Distribution :
Although both systems performs within the limits of previous analysis due to its stiffer behaviour ball joint have chosen for further development. Emergent Technologies & Design I Biomimetics Architectural Association28 I 29
Architectural Application
Temporary dome supports, renovation of Statehouse, Ohio US (Source: JE Dunn Construction. Image by Tim Carpenter)
Advantages of system such as fast assembly, compounding from single component and shape of its crown curvature it has potential to take place of temporary dome support systems and scaffoldings. Moreover, with modification of crown shape in digital model flat supports could also propose with the samel logic , when beam sizes and joint angles become custom system would lose the logic of repetition and practicality but it would still spend less material compared to similar support systems. (Statehouse dome construction)
Group 8 Alican Sungur__Felix Tseng__Kuber Patel__Thaisorn De Vapalin
Crown shape emerges from fractal system defines single curved dome-like surface. This border condition differs according to tactical angle and vertical angles values of branching system. Same dome condition applied to a traditional scaffold structure with same beam size and similar joint types and rectangular grid. Later on these two systems compared according to structural performance and material use. After compression towards dome, branching structure with deflects with lesser amount as expected from previous analyses due to additional weight comes from dome support.
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Architectural Application_performance
+ 410 beams
370 beams
(150x15x3) cm
(r=20)cm
+ 230 beams (150x15x3) cm Group 8 Alican Sungur__Felix Tseng__Kuber Patel__Thaisorn De Vapalin
200 beams (r=20)cm
DEFLECTION 30 cm
0 cm
Gridal scaffold structure Self weight deflection: 5 cm Max. deflection: 10 cm (max load= x2 own mass)
Branched scaffold structure Self weight deflection: 25 cm Max. deflection: 30 cm (max load= x2 own mass)
Fractal system and crown geometry
Structural system spend approximately %50 less material than square gridal scaffold system with same beam size and similar joints. In addition to that structural performance slightly as accurate as square gridal system especially under additional forces from growth direction.
Same parameters adapted to flat surface as bedding to prevent excessive pressure
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Architectural Application_variations
Different curvatures from variations
To apply the system on surfaces with different curvatures different variations could be use to achieve different crown shapes. Also by equalizing the heights of the forking points after each iteration, flat system procured.
Equalizing generation points
Reverse used of variation for flat surfaces
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Conclusion
Analysis of digital models has proved to explaining that branching systems with particular values help trees to distribute their own mass and in order to transfer liquid and mineral efficiently.(Ball, 2009) This quality of branching leads us to research performance of these systems under selfweight and additional loads. For different species given (Quercus robur, Pinaceae family) as excurrent and decurrent types, digital test and optimum values finding has been used in a structural reflection in common use. Research done demonstrated mass and additional loads distribution of branched structures for different typologies and application of this potential as an alternative for an temporary architecture supported system.
Future investigations As an outcome , there are several topics that have potentials to investigate further from the reserch done. As our mainly focused experiment on dome-like structure.Our next step is to develop this particular system to support another shape of structure. For instance;flat surface in mostly building also more complex structure where this Temporary system could interpolate in. Patterns come from genotype of species significantly manipulating according to environmental data. Further research could explore how this data effects liquid distribution and naturally production speeed and structural performance of such systems. Emergent Technologies & Design I Biomimetics Architectural Association34 I 35
[REFERENCES] Ball, Philip, Nature’s Patterns: a tapestry in three parts – Branches, Oxford University Press, 2009 Fisher, J. and Honda, H., ‘Branch Geometry and Effective Leaf Area: A Study of Terminalia-Branching Pattern. 1. Theoretical Trees’ in American Journal of Botany, Vol. 66, No. 6 (Jul., 1979), pp. 633-644. Harris, R.W. , “Structural Development of Trees” in American Journal of Arboriculture, Vol.6, No.4, (April 1980), pp. 105-107 Harris, R, James, R. and Matheny, N, Arboriculture, Third & Fourth Edition, 2001 Fisher, J. and Honda, H.,”Ratio of tree branch lengths: The equitable distribution of leaf clusters on branches” in Proceedings of the National Academy of Sciences of the United States, Botany, Vol.76, No.8, pp.3875-3879, (August 1979) Honda, H., “Description of the form of trees by the parameters of the tree-like body:effects of the branching angle and the branch length on the shape of the tree-like body” in Journal of Theoretical Biology, Vol.31, (1971), pp. 331-338 Prusikiewicz, P. and Lindenmayer, A., Algorithmic Beauty of Plants, Springer Verlag, 2004 Gruber, P., Biomimetics In Architecture, Springer - Verlag, 2011 Statehouse dome construction, photograph, viewed 25 December 2014 <http://cjonline.com/news/2012-01-08/video-dome-restoration-moves-interior-cleaning >
Group 8 Alican Sungur__Felix Tseng__Kuber Patel__Thaisorn De Vapalin
EMERGENT TECHNOLOGIES & DESIGN 01/ 2014-15
ALICAN SUNGUR KUBER PATEL
FELIX TSENG THAISORN DE VAPALIN
ADDITIVE SYSTEMS IN BRANCHING
BIOMIMETICS GEORGE JERONIMIDIS
12/01/2015
12/01/2015
Emergent Technologies & Design I Biomimetics Architectural Association36 I 37
GROUP 8 Alican Sungur__Felix Tseng__Kuber Patel__Thaisorn De Vapalin
Emergent Technologies & Design Biomimetics, 12 January 2015