Evolutionary Optimization of Parametric Structures by aitoralsan

EVOLUTIONARY OPTIMIZATION O F PA R A M E T R I C STRUCTURES UND E RS TA N D I NG ST RUCT URE A ND A RCHI T ECT UR E AS A WHOL E FROM EA RLY D ESI GN STAGE S

Aitor Almaraz 39464195J ESTR-50 Degree in Architecture Thesis Supervised by Prof. PhD José Antonio Vázquez Rodríguez Academic Year 2015/2016 Delivery date 2/10/2015 Construction Technologies Deparment ETSAC · University of A Coruña

Authorâ&#x20AC;&#x2122;s Declaration

I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as approved by my supervisor. I understand that my thesis may be electronically available to the public.

ABSTRACT Despite the fact that parametric tools have an undeniable potential, nowadays there are very few references where they are used not only as a mean of structural optimization but also as a link between structures and the architectural space. This thesis aims to explore the possibilities of the implementation of parametric design as a linking tool for architectural spatial decisions, structure and costs -in economic and energetic terms- to analyze and determine their performance when implemented from early stages of the architectural design. Furthermore, through several case studies this thesis analyzes if the given solutions are feasible by comparing results with those achieved by widely studied professional tools.

RESUMO Aínda que resulte innegable o potencial das ferramentas de deseño paramétrico, actualmente existen moi pocas referencias nas que estas sexan empregadas non só cun obxectivo de optimización senón ademáis para potenciar a vinculación entre as estruturas e o espazo arquietctónico. Este trabajo trata de explorar as posibilidades de implementación do deseño paramétrico como ferramenta que vincule decisiones proxectuales espaciales, estruturais e de custo -en termos económicos e enerxéticos- para analizar e determinar a súa viabilidade e rendemento ao ser incorporados nas primeiras etapas do proxecto. Ademáis, a través de varios estudos de caso, este traballo analiza a validez dos resultados comparándoos con aqueles obtidos mediante ferramentas amplamente estudadas e avaladas empregadas no cálculo estrutural profesional.

RESUMEN Aunque resulte innegable el potencial de la herramientas de diseño paramétrico, actualmente existen muy pocas referencias en las que estas se empleen no sólo con objetivo de optimización sinó además para potenciar la vinculación entre las estructuras y el espacio arquitectónico. Este trabajo trata de explorar las posibilidades de implementación del diseño paramétrico como herramienta que vincule decisiones proyectuales espaciales, estructurales y de costes -en términos económicos y energéticos- para analizar y determinar su viabilidad y rendimiento al ser incorporados en las primeras etapas del proyecto. Además a través de varios estudios de caso, este trabajo analiza la validez de los resultados comparándolos con aquellos obtenidos mediante herramientas ampliamente estudiadas y avaladas empleadas en el cálculo estructural profesional.

keywords Architecture-Structure relationship; Evolutionary Solver; Karamba; Parametric Architecture; Structural Optimization

Acknowledgements

I would like to express my most sincere gratitude to everyone who has been by my side throughout my professional development as an architect. I am Especially thankful to my family and friends for their support, understanding and constant presence in my life. Thanks to Spotify and the BBC Proms for helping this work to be carried with pleasure by providing endless hours of enjoyment. I am indebted to those on my advisory panel including my supervisor José A. Vázquez and Félix Suárez for their time, effort, support, and for teaching me that structures are also architecture. My thanks also go out to Sonia Vázquez, not only for sharing her knowledge and passion for architecture with me but also for encouraging me to go further. Special thanks to Marta Piñeiro for her company during unending busy work days, immeasurable friendship and outstanding coffee-making skills. Besides this, I couldn’t end this work without thanking to my external reader and mate Kirill Karadzhov, for taking his time out of his schedule to lend me his critical view on the work I am doing. Ultimately, thanks to everyone who intentionally or unintentionally is missing in these acknowledgements, but who influenced my professional growth during my career in university. Aitor Almaraz, September 2015.

CONTENTS

foreword

part 1: theory

1. introduction

Architectural Project Process

Structure is also Architecture

2. PARAMETRIC TOOLS

3. aim of the study

4. methodology

Tools: Rhino and Grasshopper

Structural Analysis: Karamba

Evolutionary Solver: Galapagos

Construction of the models

5. case study analysis

Boundary Conditions

State-of-the-art examples of built optimized structures

part 2: praxis. authorâ&#x20AC;&#x2122;s developed case studies

CASE STUDY 0

CASE STUDY 1

CASE STUDY 2

CASE STUDY 3

conclusions

discussion 42 conclusions 43 further work

appendix: BENCHMARK ANALYSIS & references

case study 1 benchmark

case study 2 benchmark

references 52 list of figures

list of cS

foreword

This work should be read as an introduction or an early research about what may come afterwards as a PhD study. During the last five unbelievable years in the architecture school I have acquired an unconceivable knowledge I would have never expected to gain when studying in high school. Anyhow, it was the fourth year what left an imprint, a non-return checkpoint in my student life. The Norwegian University of Science and Technology besides serving me to forge essential relationships, taught me -among many other things- about the potential of architecture research. Our visit to Herzog & DeMeuron Office on the field trip to New York City spotlighted Grassopper to me. I would have never said that a Skyscraper could be designed by a bunch of different parameters. By enhacing mind connections, and simplifying the solutions of the geometrical problems with an unprecedent ease, this script-based user-friendly software instantly caught my attention. Although several former works helped me understanding and implementing parametric tools into my architectural thought, this work comes as an opportunity to master the way to heuristically understand spaces and structure in depth througout structural optimization. I hope this will be very useful at a later stage, especially when working on my Diploma Project. I chose this topic for the Degree Thesis not only because of my fascination on why things do not fall apart and why we like some spaces, but also because Parametric design, 3D Printing and Digital Fabrication have landed at a gallop in our lives; and I think a little reflection is needed to do not choke with them. Because although all this new ÂŤtechie thingsÂť are recently born, I think we are facing deep changes in our way of designing, understanding and living architecture.

part 1 theory «The architect must show an interest on research to develop the formal potential of structures, be ready to accept that it acquires a relevance and prominence in the architectural design (...) the architect also has to understand that designing implies to know how to build. In words of Arup: “design, cost and organization of the building site are not three separate operations, but need to be considered as one”» Bernabeu, 2007 (translated to English by the Author)

1. introduction Architectural Project Process Creative design is an unarguably process of exploration. Architectural design does not consist on a list of requirements that should be fulfilled. Architecture works are formal solutions, conceived in a balanced process among reason and sensibility, cognitive and affective aspects (Suárez, F. 2015) It is well known among architects and designers that design is not just a linear, straightforward process, where designer finds solutions to a given task. It is also about redefining and reframing the design problems that have been provided (YU, R. et al. 2014). In other words: once we have settled a room arrangement it may be subject of thousands of modifications as we add components to our design: plumbing, HVAC, structure, etc. (Figure 1). It does not consist on a simple goal checklist. Otherwise, when trying to achieve one goal at a time there is a risk of achieving none (Munari, B. 1995). Bernabeu Larena, A. & Azagra, D. (2012) pointed that architectural design consist on achieving compromised solutions: correct and adequate. It needs a declaration, an adoption of a firm position and taking one path among other possibilities.

Fig. 1 – (Left) Architectural design is not a linear process of goals achieved in a checklist. Fig. 2 – Levels of design. Project as a multi-level approach. Hand skecth of Nyhavna HRB Proposal.

It is an intrinsic characteristic of any design process to have levels of detail. This is that, the more evolved the design is, the more detailed it needs to be described. This is traditionally represented by a higher scale in drawings (1/100, 1/50 , 1/20...) entailing more decisions to be taken (Figure 2). Therefore, design problems are

approached from a very broad perspective in the beginning, during the so called «early design phase» (Méndez, T. 2013). This is when the fundamental decisions on the building shape and many of its defining components, such as structure and distribution, are taken. Thus, multi-disciplinary information is crucial to successfully address the project as a whole. Besides this, in the last decades we have experienced a change in the architectural design tools and methods. However, despite the facts that computers have become essential in the design process, it is still very common to use them only as a digitalization of the drawing table. Far from this, with inventions such as Buiding Information Models (BIM) and parametric design, computers have opened new possibilities in the design methods that have not been explored yet by architects. Allowing users being not restricted by the tools, such as drawing limitations, they offer the possibility to incorporate elements rapidly into the design at the early stages (for example, building structure) and therefore to have an inmediate feedback in this come-and-go design process. These are not only time-saving solutions, that may increase the overall productivity, but also as opportunities to have more time to think. Thus, create more heuristically coherent designs.

Structure is also Architecture In words of Engel (1968) structures both in nature and in technology, maintain object’s shape; the conservation of shape is essential so they can achieve the purpose they have been conceived to. Besides this, the technical-social function of buildings relies on the existence of a confined space. Space is confined by its boundaries. And structure is responsible of defining the boundaries. As we know, without structure there is no building, and therefore, there is a deep relation between the spaces and the structure.

Fig. 3 – (Left) Crematorium, Baumschulenweg, Berlin, Germany. Axel Schultes Architects, 1999. Condolence hall columns. Fig. 4 – (Center) Stuttgart Airport Terminal, Germany. Von Gerkan+Marg+Partner, 1991. Structural ‘trees’ Fig. 5 – (Right) Museum of Roman Art, Merida, Spain. Rafael Moneo, 1985. View along the nave.

The origin and the development of new structural and architectonic forms in the XIX and XX centuries has been deeply related to the development of new materials and structural systems (Bernabeu, 2007). Thanks to the technical advances, such as the enhacement of material’s properties and calculation tools architecture is nowadays in a position where it is possible to securely build structures with a high degree of complexity, not solvable until very recently (Charleson, 2005). The consequences of this are that nowadays almost every formal approach can be solved and built (Bernabeu, 2007) In words of Manterola: «Del reino de la necesidad se ha pasado al de la decisión proyectual» (From the kingdom of necessity, we have entered the kingdom of the architectural design decisions), meaning that due to this technical advances, it is possible to

get around structures; at least, during the first stages of architectural design. Therefore, at present, the relevance of the structure does not have to be explicit. Structural elements do not only guarantee the building’s stability; they can also contribute to the development and definition of spaces. For example, every structure has a rythm that is more or less apparent in the project (Bernabeu, 2007). As stated by Charleson in 2005, «Where structure is given a voice, it contributes architectural meaning and richness we can design structure so that its viewers not only see and experience it, but due to its architectural qualities, are enticed into ‘reading’ it. Structure is not a neutral architectural element. It influences the space around it, and its very presence invites architectural analysis or readings. This perception of structure creates opportunities rather than constraints». In short, structure is far from being only a design requirement, but rather a tool able to contribute actively to the design. In words of Suárez (2015), «unfortunately, we forget the etymological origin of the word (structūrae) that it only defines "disposition and order of the different elements considered in the whole" (...) this is considering the relations among the different elements so they work adequately and so the final result is unique. Efficient cause and formal cause. One form, one structūrae» (Figures 3 to 5).

Once stated, it should call attention the fact that there is no a unique solution for a structural problem. For any architectural design, designers face a considerable freedom of choices of possible structural solutions. Therefore, they can find solutions that foster and actively reinforce the design concept, in better, worse ways or just be indiferent to them. Architects then should choose the most convenient solution for each particular case and base their decisions not only on economical, technical and constructive reasons, but also on formal and conceptual criteria and their architectural implications. In words of Charleson (2005) «The impacts of structure upon those who experience it are also diverse. One structure, exuding a sense of tranquility, soothes emotions. Another sets nerves on edge. A raw and inhospitable structure contrasts with one that welcomes and expresses a sense of protection» (Figure 6). It is also important to highlight a remarkable fact: as we can learn from history, current and future technological advances in structural materials, analysis and design techniques will lead to a significant increase in the diversity of structural options. And besides this, in their possible architectural implications (Charleson, 2005).

Fig. 6 – Alterations in a uniform mesh of columns. Structure makes spaces to have different perceptual connotations. Kunsthal, Rotterdam 1988.(Bernabeu, A. 2007 from Balmond, C. 2002)

2. PARAMETRIC TOOLS But what about the tools architects and designers work with, when dealing with structures? At first, typologies’ based design process made drawing not only a communication medium but a system that enabled designers to explore and refine variations (Tedeschi, A. 2014). Later, the form-finding approach emerged in architecture in late 19th century, aiming to research optimized structures through complex and associative relations between materials, shape and structures. Pioneers like Gaudi, Otto and Musmeci (Tedeschi, A. 2014) are a clear example of this method (Figure 7). Early structural design and analysis based on descriptive geometry and drawing were developed in the second half of the 19th century by Karl Culmann, who considered drawing to be the true “language of the engineer”, opposed to analytical methods using purely numerical calculus (Lachauer, L. et al. 2011). The advantage of these techniques is the quick visualization of structural relations using diagrams of forces allowing for an intuitive understanding of complex technical dependencies. Furthermore, the manual process of drawing leads not only to visualization, but to an better understanding of structural problems by the designer. (Lachauer, L. et al. 2011) Fig. 7 – (Left) Gaudi catenary-based models for form-finding Fig. 8 – (Right) Example of parametric generated box

In 1939, the Italian architect Luigi Moretti created the definition for "Parametric Architecture". His research on “the relations between the dimensions dependent upon various parameters” (Tedeschi, A. 2014) show

designs that were linked to viewing angles and eceonomic reasons (Moretti et al. 2002) The term "parameters" is used to describe factors that determine a series of variations leading to a potentially infinite range of possibilities being generated (Kolarevic, 2003). (YU, R. et al. 2014.) Computer was introduced as a virtual drafting board, making it easier to edit, copy and increase the precision of drawings. This mode of working has been called as "computerisation" (Peters, B. & De Kestelier, X. 2013) being just another tool used by the architect. In words of Yu et al. (2014) «The technology is only as good as the people and ideas driving it» At the present time, what we understand as parametric tools is the application of Moretti theory to computer environment. Computer software allows designers to define parameters or factors that when correlated, combined and diferentiated can save designers from manually modelling thousands of components. Instead of describing -drawing- the final result as a model, the process of modelling itself is described by a sequence of instructions -an algorithm-.By varying the input values, different output can be generated (Scheurer, F. & Stehling, H. 2011), and being possible to immediately visualize the results. This makes the process incredibly visually understandable, and more important, flexible and quickly modifiable (Figure 8).

The parametric design environment (PDE), has become increasingly present in architectural design process over recent years. According to Kolarevic (2003), the change in design procedures associated with parametric tools is characterized by a rejection of the static solutions provided by conventional design systems. This is claimed to have stablished design processes both more flexible and more productive. Various studies support this view, arguing that parametric tools can advance design processes in a variety of ways (YU, R. et al. 2014), as it is easy to «test&drive». It is possible to create relationships between architectural elements, so as for evaluate and link spaces, efficiency in terms of cost -economic, ecologic, energy- and also take structures into account from the beggining of the design. As a direct consequence, a new figure called «Computational Designer» has appeared in big architecture firms. Existing in practices such as Foster + Partners, Herzog & de Meuron,Grimshaw, UNStudio or Skidmore, Owings & Merrill (SOM) among others, their work is to coordinate and involve parametrical tools from early stages of architectural design (Peters, B. & De Kestelier, X. 2013).

Parametric Tools and the Architecture-Structure relation As previously said, parameters defined can thus be easily modifiable, conducting results according to architectural interests or to archieve a desired expressivity. It comes then to consider the role that structure may take: are the structural requirements a parameter to consider in the equation? and, can this structural parameters actively take part in the architectural design? This questions sometimes drive projects to have an important dissociation among architectural form and structural approach (Bernabeu, 2007). Sometimes structure can be included from early stages of design, offering answers and participating through the entire design process, being a more or less optimal structural shape. This is that, the geometric criteria of structural efficiency participate on the definition of the architectural form. The relevance of the structure depends on the importance and expressiveness given in relation with the rest of parameters or constrains of the design process. Some other times, architecture decissions bend towards more sculptural forms, where the structure has no relevance, speaking in terms of design. It appears in late stages to solve the architecture, but without participating on its definition. This is the possibility of finding a structural response to any given form, and consequently not considering the structural logic nor the need of a previous conceptual shape. It is important to hightlight that any of those design approaches can be, a priori, perfectly valid (Bernabeu, 2007).

3. aim of the study In words of Charleson, «Architects need to take an active role in all stages of structural design» (2005). This confronts with the worldwide tendence were architects specialize only on spaces-design while engineers and consultants are in charge of the technical tasks. This situation leads to cases where sometimes space and structure have very little in common; or even harming the functionality of buildings. For example this can be observed when analyzing some Chinese commercial center where the columns were placed standing in the way of the doors. This happened due to miscommunication between the architectural design and the structural design teams.

This work aims to research the inclusion of parametric tools to the structural design from the early stages of the project for achieving optimized structures and as an opportunity to foster the relationship between architecture and structure. It shall also be a work that encourages architects to incorporate these tools to their design strategies, demonstrating through a series of case studies that they are not only for specialized figures big firms have. Subsequently, this work aims to highlight the architects the need to be aware of structures and to encourage them to avoid calculate atrocities (Figure 9).

4. methodology Shape optimization is the process of calculating a geometry that minimizes the assigned fitness function within the boundary conditions. The optimization terms are Deflection and Weight. Deflection optimization will lead to a better use of material, meaning less redundant material, that implies lighter shipments, cheaper costs of production and transport. Therefore, the goal is to anticipate fabrication so that the design is not only buildable, but the process’ economic and energetic costs are reasonable.

A designer must seek to achieve the optimal solution to obtain the greatest benefit from the minimum use of resources; the result will be an efficient combination of elegance and economy (Bernabeu, 2007). This search for the efficiency may lead to the adoption of very complex systems This optimization will be achieved (structural and constructive). Efficiency by the number of parameters which and simplicity are two opposite terms; SOFTWARE E the structure can be determined and WAR SOFT the more efficient is the material the definition of the objectives. In usage, the more complex the structural other words: stablishing blockers. system and therefore, the bigger the Blockers shall be so there are limits on cost of construction and manteinance the carried optimization. For example: (Bernabeu, 2007). As said by Lachauer SOFTWARE

Fig. 9 – Visualizing static solutions when using structural analysis tools generate a risk of not-knowing if the solution provided is an atrocity.

Fortunately, in Spain architects are not detached from the structural design, considering architecture as a whole, and being qualified enough to not solely rely on engineers calculations. It is clear that for architects with a big experience, the heuristical design of spaces straightforwardly linked with stucture is a relatively simple process. Even though, some works need the collaboration with engineers, and process can sometimes be tedious when waiting for slow feedback from engineer consultants (Peters, B. 2013). Parametric tools have recently opened a new potential that is not perceived by the architecture and construction industry today. They let architects to integrate structural elements from the early stages of their design easily.

et al. (2011), «the aim of these computational tools is to bridge the gap between the "structural sketch" and sophisticated analysis software (...) Visualization and interactive feedback in real time will lead to an intuitive understanding of structural correlations and thereby advance creativity in the design process». The main impediment for scaling up the optimization was the time spent on computational calculation of static models, which may take up to days in some instances.

calculate the system using only two sets of beams, or optimize the system so the distance between supports is as big as possible. Blockers also can be used to avoid errors on building site. Nowadays, digital fabrication technologies opened a larger number of possibilities, like customized joints or building with a complete set of unique differentiated elements. There is also the possibility that results have an infinite number of solutions, leading to a high degree of irregularity (Bernabeu et al. 2012). Here, architecture blockers can take a fundamental role to achieve the desired result. For example: supports must have a separation of an even number of meters to allocate two-meter wide windows inbetween. The set of tools used to achieve the goals is described in the following:

Tools: Rhino and Grasshopper

Fig. 10 – (Left) Quick visualization of mistakes in the idealization of the structural model. It is also possible to evaluate its deflections. Fig. 11 – (Right) Galapagos linked to parameters to modify and goal to optimize

As previously mentioned, the answers for the questions raised previously are to be solved with Grasshopper parametric plug-in for Robert McNeel & Associates’ Rhinoceros®. This program is a interface-friendly scripting tool that permits to create connections between a generated geometry and certain user-established parameters in a graphical interface. This relations (also known as algorithms) are based on geometric and mathematical concepts, so in order to generate any model it is necessary to perform an abstraction: simplify the reality so the computer can understand and work with it (Almaraz, A. 2014).

Structural Analysis: Karamba Among the considerable number of Grasshopper plug-ins, we may find several structural analysis tools that can be implemented at early project stages. Kangaroo and Karamba shall be especifically highlighted because of their high-performance when calculating and showing results graphically, so designer can instantly see the results and evaluate its reliability; conceptual mistakes can be found out very easily (Figure 10). Karamba is a very powerful finite element (FE) Grasshopper plug-in for predicting the behavior of structures under external loads developed from a research project carried out at the University of Applied Arts Vienna in collaboration with Bollinger + Grohmann Engineers (Preisinger, C. 2013). It creates a fast tool that facilitates a seamless flow of data between structural and geometric models. It generates a model that reacts immediately to any change of input parameters, helping to understand structural mechanisms in the design process. Implementing Karamba implies a dynamic response of the designer. The consequences of the structural design are shown instantantly, not having to determine if the input information was outrageous once computation is over. The program engine allows to perform calculations using beams and shells, applying any load condition, and determining, among others, materials and cross sections. It also includes several calculation algorithms such as 1st order and 2nd order analysis or

Beam Evolutive Structural Optimizers algorithm (BESO) (Preisinger, C. 2013)

achieve? This will allow as to simplify our design to a workable level.

Evolutionary Solver: Galapagos

Once this question is being answered, it comes to work with the Algorithm. Contrary to a design problem, an algorithm has to be well defined: contrary to humans, computers cannot guess based on experience and intuition. Therefore, every step has to be completely and unambiguously determined by the previous steps. (Scheurer, F. & Stehling, H. 2011) Luckily, there are always almost infinite ways of how the mathematical and geometrical algorithms can describe a model.

Galapagos is a heuristic evolutionary solver (ES) that will find a solution to a problem expressed in a mathematical way: the problem has to be described by an objective function that we want to minimize or maximize, or by a set of variables defined by a range (Tedeschi, A. 2014). After defining a «fitness function», several parameters will be given to the the evolutionary solver. Galapagos will then find a solution that makes the previous statement true by adjusting the parameters (Figure 11). In words of Rutten, «it first it tries to find promising high ground, then it will fine tune its position in order to find the highest peak associated with this high ground. Evolutionary algorithms apply the biological principles of mutation, selection and inheritance. They will populate the landscape with virtual individuals and then proceed to breed the highest ones in the hope that their offspring will be closer to a summit».

We shall to forget that as designers -architects- we would like to perform modifications with the parameters to essay our design, and what on Schumacher words: «parametric design is a design method, not a style or an -ism» (2011).

It is necessary to note that in the work with solvers, the experience demonstrates that when dealing with complex problems, often the solution provided by the solver is not exact, but close to it. (Rutten, D. 2013) (Tedeschi, A. 2014)

Construction of the models Karamba will work with a model algorithmically described in Grasshopper. Model parameters will then be linked to Galapagos -the ES- to optimize the system. In words of Scheurer & Stehling (2011) a model, by definition, is always an abstraction of reality. Building a model means reducing the complexity of the real world to a level where it can be described with manageable effort. It must contain as little information as necessary to describe the properties of an object unambiguously. This abstraction work must be done by the designer prior to start working with Grasshopper: What do I want to

5. case study analysis

Fig. 12 – Proposals to demonstrate the power of parametrical tools. Their architectural raison d’être can be both functional and cost-effect a priori questioned

Boundary Conditions

A set of case studies has been researched, designed and developed in order to test the suitability and feasibility of implementing parametric tools in early stages of architectural design with its consequences. Besides this and in parallel with the previously mentioned research, four case studies have been developed for this work. These examples are intended to be easily understandable, rather than developing fancier examples that although seeking to prove the endless oportunities the program gives, they may be complex, being harder to test the feasibility and that may biase the reader through their powerful freeform images. With an a priori confusing architectural raison d’être (Figure 12). In words of Tedeschi (2014), «The particular aesthetic of parametric structures». Those studies can be found on the Second Part of this work.

Author’s developed Case Studies will only take a small glimpse on the possibilities of the software. Cases will have different approaches depending on analyzed aspects and progressing towards more complex systems, and hence requiring different boundaries, previously called «blockers». Anyhow, the are all oriented to the application of Evolutionary Solvers and have common general boundary conditions set in order to offer coherent examples.

The goals to be determined in these case studies are first of all, to demonstrate the feasibility of the introduction of parametric tools for structural development in early architectural design stages. Secondly, to evaluate the accuracy of results obtained thus evaluate the reliability. This will be done through a compared analysis with a similar structural calculation software (Matricial, FEM...) Thirdly, to discuss the affectation of the project through structural optimization conditions. Therefore, some restrictions must be provided from the architectural design process.

Secondly, the material used in the examples will be steel S235. This condition has been set not only because it is one of the most common material in buildings’ structure nowadays, but also due to its controllable isotropic properties, allowing to carry out accurate meaningful analysis.

First of all, the examples will be based on Active Vector Structural Systems. As classified by Engel, H. (1968) these are systems where the external loads are distributed among two or more pieces, being the system balanced by appropriate counterforces. These systems are very efficient in relation with the variable load condition, being very suitable for vertical constructions.

Thirdly, net weight and maximum deflection are the evidence of the effective estimation of the structural behavior of the structure. Therefore optimizations will be done so while the deflection may not exceed a certain limit, the net weight should be reduced as far as possible (Fahlbusch, M. et al. 2012).

State-of-the-art examples of built optimized structures: Some existing state-of-the-art examples have been researched prior carrying out the case studies development. It is important to remark the fact that most of nowadays proposals that can be found on literature have not been built yet, or are more oriented towards civil engineering, not fostering yet the active role in architectural concepts. It is interesting though, to show the potential of these tools applied with research and experimental purposes.

SKYLINK (Frankfurt) The Skylink is a bridge for Frankfurt’s Airport developed by the office Lengfeld & Wilisch with Bollinger + Grohmann Engineers. It is a trussed bridge whose diagonal elements have been placed by the Karamba design tool through a criteria based on the maximum displacement and mass of steel (Preisinger, C. 2013). Among this optimization, it was implemented a restriction of the number of possible configurations to facilitate the manufacture and assembly of the parts (Fahlbusch, M. et al. 2012) (Figure 13).

Fig. 13 – Image of the Skylink in Frankfurt airport. Diagonals are apparently placed randomly

Fig. 14 – Sketch of diagonals. They may overlap in different planes to facilitate construction operations

Boundary conditions were set up so the continuous truss structure consists of four straps and has a total cross-section of 5 m × 5 m. Standard cross-sections for the diagonal bracing have 120 mm and 140 mm wide, with wall thicknesses of 10 mm. Besides this, and to facilitate the previously mentioned ease of assembly, diagonals are always arranged so every set of beams lies in one plane, and therefore diagonals do not collide with each other. The bridge was prefabricated in parts with max. 13.50m to avoid abnormal shipments. The entire structure was supplied with a total of 80 shipments In words of Fahlbusch (2012), «The result has a high degree of irregularity; the supporting effect is complex and therefore no longer readily explainable» (Figure 14).

Tremenningen (Trondheim)

Fig. 15 – Tremenningen pier over Nidelva River in Trondheim (Norway)

Fig. 16 – (Left) Loads supported by the diagonals have been carved in the wood with CNC Milling machines Fig. 17 – (Right) Connections such as bolts have also been calculated and dimensioned with parametric tools

This construction began in late 2014 as a proposal from the Municipality of Trondheim, challenging architecture students at NTNU (Norway University of Science and Technology) to solve a urban problem in Kjøpmannsgata. Two students, Gunleiksrud, A. and Mork, J. H. designed and built a cantilevered timber pier from the edge of a public square into Nidelva river (Figure 15). In this pier, all beams and nodes have been designed, optimized and fabricated using parametric tools. To show the possibilities to the most sceptical, the stresses supported have been milled with a CNC Machine on each beam (Figures 16 and 17).

CCTV (北京 - Beijing)

Fig. 18 – CCTV designed by OMA in Beijing (China)

Fig. 19 – Detail on the skin. More diagonals appear were the higher stresses

Although not easily, it is possible to find some architectural examples where structure being rationalized and optimized takes an active role in the architectural design, as it is the envelope of the CCTV by OMA in Beijing (Figures 18 and 19). Knowing that the highest efficiency of load transmition is the one were loads are carried through tensions -with minimum bending- the evolutive solver may be led to optimize a system seeking the minimum deflection state (Bernabeu et al. 2012). This has an aparently random configuration, that has in fact been optimized with iterative and evolutionary solutions. The result proposes a way of driving the loads very innovatively, that definitely breaks with the structural conventions commonly accepted (Bernabeu et al. 2012).

The last selected projects have been selected for being inspiring examples to the purpose of this work. This is where architecture and structure are a whole.

Baloise Park Basel Fig. 20 – Elevation of the Baloise Park. Columns have different width at an apparently random configuration.

Fig. 21 – Render submited to the project competition.

Another example where structure takes an active role on architectural idea definition is this 2014 proposal for Baloise headquarters in Switzerland by Valerio Olgiati. It has not been possible to gather enough information to determine the exact procedure of façade design; but according to the architect’s description, columns become a symbolic element in the main façade due to its random arrangement (Figure 20). Anyhow it has been selected for this state-of-the-art because of it inspiring image to raise a question: What if pillars configuration was not random but based on structural reasons instead, acting as an image of the load driving system?

Tama Art University Library This project consists in a library for an art university located in the suburbs of Tokyo. Designed by Toyo Ito & Associates, in this example architecture and structure are a whole. The holistic approach allows the arches arrangement not only to stabilize the construction to be earthquake proof but also to create different spaces.

Fig. 22 – Axonometry of the arches’ generation curves, with an apparent random configuration

Fig. 23 – Picture of the building. Arches’ intersections define the library spaces

The arches are different in span and height, and are made out of steel plates covered with concrete. In plan these arches are arranged along curved lines which cross at several points. Those intersections permit to keep the arches extremely slender and still support the heavy live loads of the floor above. The spans of the arches vary from 1.8 to 16 metres, but the width is kept uniformly at 200mm (Figures 22 and 23). The design procedure also remains unknown. What if, from the early design stages they had been parametrically optimized so architectural spaces generated could also be evaluated?

part 2: PRAxis author’s developed case studies Principally following what an architect would want in terms of.... you know, there’s a shape, where do we put the columns? That’s the first question any engineer always gets. Where do you put the columns? And you think “I’m very clever doing this and I put the columns where it’s architecturally convenient”. (…) And you can’t recognize what is structure, what are the finishes ...it’s the whole thing. (…) With what architects never see, and no one ever sees. But only I had the extra eyes to see into the concrete, and to understand that I placed the steel in the way to do what I wanted to do, so it would not work any other way. (…) So that you can see, for me it’s first the Composition field. It’s nothing about anything or any structure, nothing, just the Composition Field. It could be anything. Alejandro Bernabeu: Interview to Cécile Balmond

CASE STUDY 0 KARAMBA AS STRUCTURAL ANALYSIS TOOL DESCRIPTION

METHODOLOGY

The purpose of this Case Study is to develop a basic script that will be valid to run further simulations with few changes. Its purpose is to illustrate the basic work of Karamba, its constituent parts and their relationship.

The first step in all case studies will be the determination of Boundary Conditions. This is done in order to perform analysis with the Evolutionary Solver.

A standard, not parametrical frame serves as test (Figure 26). Several script engines have been created to correctly stablish geometrical discriminations of the constituent parts. Comments to the most important ones have been done in the following developable page.

STUDY PARAMETERS BOUNDARY CONDITIONS Basic Dimensions Loads

Support conditions

Lenght: 6 meters Height: 4 meters linear load: 2kN/m point load: 1kN/m Restricted Movement in X, Y and Z Restricted Rotations in X, Y and Z.

Material

Steel S235

Analysis

Th 1ST Order Calculations

Use of profiles from the Other restrictions IPE Serie Max deflection l/300

GEOMETRY PARAMETERS

MODEL’S ELEMENTS

1 2

ANALYSIS AND OPTIMIZATION 5 6

Fig. 24 – General overview of the Karamba basic script

VISUALIZATION OF RESULTS

The first part of every script will be the definition of the geometry. It can be parametriced or it can be directly selected from an existing Rhino model. Following to it, we may find the authorâ&#x20AC;&#x2122;s developed script that allows to automatically discriminate supports from a set of nodes as well as separate beams in horizontal and vertical elements. This is done so work of identification of elements and supports set up can be done much quicklier. Other scripts have been developed to separate points by height in a very similar way, organizing them in trees.

In the element component it is possible define the name of the elements (Element ID) for further easier operations. It is also important to clarify whether information shall enter as a tree or flatened in a list.

Loads can be configured as point loads, line loads, gravity, prestress and temperature increment. For these studies only three of them will be used.

The Material Selector and Cross Section Selector permit to run the optimization tasks. A selector will pick up the desired element from a table that includes by default all types of comercial steel and the most common structural profiles. Nevertheless, custom materials and cross sections can be created and then included in the simulation.

In the case of line loads it is important to highlight the fact that they will be applied to all elements in the model if not stated otherwise. Thus, it is important to have a clear identification of the beams.

The assembly model component gathers all the diferent elements and parameters we have previously created. It is fundamental to determine if information shall enter as a tree or flatened in a list. To perform the cross section optimization it will be necessary to provide the list of cross sections and the maximum tolerable deflection for the elements. As an output we find mass of the system, that will be the optimization goal to minimize in Galapagos.

In order to perform the cross section optimization, a deformation constrain will be determined. It depends on the relation among the lenght of the element and a coeficient.

The model viewer component allows to set the visualization in Rhino interface. Among its multiple options it is important to highlight the possibility to export the original and the deformed model to Rhino in 3D, even with its cross sections. If properly linked to another Grasshopper plug-in it can also export the geometry to BIM based software.

For the following studies n=300.

CASE STUDY 1 POSSIBILITIES OF EVOLUTIONARY SOLVER: SIMPLE BEAM DISCUSSION AND CONCLUSIONS

METHODOLOGY

DESCRIPTION

This case study has been the latest to be developed. It is a basic script that is the sum up of all the basic aspects learned from the following case studies. This script sets the basis for Karamba work, and it that will be repeated on the following studies with minimal variations (Figure 25). This is why it has been explained in an independent case study.

The purpose of this study is to explore and subject the ES Galapagos to achieve predictive and optimized solutions for a simple structural system. The goals set will be: optimize cross section, optimize the position of supports and evaluate the feasibility of the results comparing them with an analysis performed by another Structural Analysis Software. It is important to highlight the possibility of implementing an infinite number of parameters and restrictions that may be set up by the designer.

Given a standard beam where the main parameter is lenght -geometrically defined by the separation between two points- set in 5 meters for the study, the boundary conditions are set as follows:

STUDY PARAMETERS BOUNDARY CONDITIONS Basic Dimensions Lenght: 5 meters Loads

In a first optimization, the mass of material will be the factor to be optimized in relation to a maximal deflection, having to choose the most suitable steel profile among a number of options (built-in european profiles table). This will be done throughout the Optimization Karamba built in component.

linear load: 5kN/m 1. Restricted Movement in X, Y and Z 2. Restricted Movement in X and Y

Support conditions

Rotations are permitted.

As a second study intended to optimize even more the structure, Galapagos will be given a choice of 3 positions to place one of the supports (Restricted movement in X and y) aiming to optimice material (minimize mass of material) (Figure 27).

Material

Steel S235

Analysis

Th 1ST Order Calculations

Use of profiles from the Other restrictions IPE Serie Max deflection l/300

Fig. 25 – Karamba engine flowchart

Fig. 27 – Goals of the study

4 1

Fig. 28 – General overview of the Karamba basic script Fig. 26 – Simulation Output

The lenght of the beam is a preset number, a boundary condition. Distance to support is the parametriced element Karamba will optimize. For this purpose, three options are given as a list: distance from the origin 3, 4 or 5 meters. When changing this number, the position of the support changes. Please note that, the possible position of the supports is not a domain (3 to 5) but an integer value (3, 4 or 5). This is been done not only to make easier the optimization, but also because in an architectural design there is not a total degree of freedom: this tries to approach to architectural constrains.

A special script has been developed to convert line loads to point loads. Karambaâ&#x20AC;&#x2122;s inear load command only works when applied to a defined beam. Therefore, to run this analysis where the beams are an unknown factor, locally applied linear loads have to be manually decomposed into point loads.

Double clicking in Galapagos component it is possible to set up the optimization goals (minimize, maximize or achieve a preset value), as well as run the simulation. It may take a while until the solution converges. It is important to remark the fact that Galapagos can only optimize functions look for numeric values. If another parameter rather than mass wants to be optimized, it needs to be converted to a number through mathematical operators.

Special attention has to be paid to the Karamba Analysis imputs. If data is entered as a tree, Karamba will run one analysis for each branch of the tree. Therefore, if two loads are entered, the analysis will run twice, showing a result for each of them. If a combination of these loads needs to be done, data must be entered flattened.

The resultant forces component has been added at the end of the script to check the feasibility of the results comparing them with analysis run on another structural analysis software. Besides this, a number of panels have been linked to the most determinant components in the script to quickly control the simulation parameters, such as model general data, material, cross sections, max. displacement, and resultant forces.

CASE STUDY 2 ARCHITECTURAL & STRUCTURAL RELATIONSHIPS: MULTIPLE BEAM DISCUSSION AND CONCLUSIONS

DESCRIPTION

Karamba is a very successful environment to test the direct implications of an structure. Thus, it is possible to immediately evaluate the consequences of an error in the supports, the dimension of the elements or the affectations of structure to spatial decissions

Fig. 32 – Simulation Output. Support position x=5

An architectural design problem is set out with a very clear structural relationship. For solving this problem, a solution were structure is deeply linked with architecture must be provided. The study consist on the design of an entrance for an institutional building, where the façade has a remarkable interest. The position and dimension of beams and columns must be determined to create an optimized system whose rythm acts as a compositive element. The position of the door has to be considered within the boundary conditions (Figure 30).

Results have proven the feasibility of Karamba. Dimensioning results are very similar: IPE140 for Karamba and IPE 120 for CYPE. Differences may be due to boundary conditions in dimensioning algorithm. Anyhow, the results are good enough for its implementation as a tool for early design work, highlightin that differences in Karamba are on the side of security.

METHODOLOGY In a first optimization, no columns will be taken into account, being considered only as supports. As a second study, columns will also be dimensioned and considered in the optimization. For this study, the boundary conditions are set as follows: STUDY PARAMETERS BOUNDARY CONDITIONS Basic Dimensions

Lenght: 15 meters Height: 5 meters linear load: 3kN/m among x=1 and x=14

In the second study, the solution given has again proven not to be only what CYPE confirms as the more efficient solution, but also what intuition tells us is the best choice (Figure 31).

Even though loads have been chosen with essay purposes, they are meant to be potential real cases set by design reasons.

Accordingly, Case Study 2 can be carried out to evaluate systems with a higher degree of complexity. Please refer to the benchmark spreadsheet in the appendix of this work for more information about all the analysis and the performance of the simulations carried out.

Loads

linear load: 5kN/m among x=11 and x=13 point load: 4kN in x=5

Support conditions

Support conditions: Restricted Movement in X, Y and Z. Restricted Rotations in X, Y and Z.

Fig. 31 – Simulation Output. Support position x=4. Cantilevered beam counteracts the biggest bending moment resulting in the best choice.

Material

Steel S235

Analysis

Th 1ST Order Calculations

Other restrictions

Door among x=4 and x=7. No columns can be placed. Use of profiles from the IPE Serie Max deflection l/300

Fig. 30 – Goals of the study and Boundary Conditions 1

Fig. 33 – General overview of the Karamba basic script

Fig. 29 – Simulation Output. Support position x=3

Restrictions are very clear in this simulation: supports can be everywhere but in the domain 4 to 7. To achieve this, the Gene Pool Component has been added. It allows us to create a number of sliders, or possible parameters that Galapagos will play with. There are considered 5 parameters, thus, a maximum number of 5 columns can be generated. The door restriction is entered as a domain in which columns can not exist. Therefore, the Gene Pool will randomly generate 5 numbers that, once sorted, are culled if contained in the door’s domain through Cull Pattern component. This «restriction engine» is a modification of the «supports engine» explained in the Case Study 0.

In this case columns are generated moving the nodes generated with the Gene Pool in the Z axis. Sorting the nodes is very important to create straight lines. Lines created are then taken to a Line to Beam Karamba Component. This is done to do not interfere with the lenght of the beams that will be evalated to obtain the maximum displacement and perform the Cross Section Optimization.

Karamba will convert Lines to Beams, so first the generation lines must be created in Grasshopper. It is very important to highlight the need of sorting the points by their position; this means that x=1 can only connect to x=2. If not sorted, we may find that beams have been created linking x=1 and x=4, leading to errors in the model. Sorting the elements can be done in many ways. One of them may be with the «supports and elements engine» explained in the Case Study 0, organizing nodes by coordenates in a data tree.

CASE STUDY 3 ARCHITECTURAL & STRUCTURAL RELATIONSHIPS: HOUSE IN TOKIO - FELIX CLAUS DISCUSSION AND CONCLUSIONS

DESCRIPTION

After carrying out the first optimization solution for the system appears to be a position of 2.0, 3.4, 7.4 and 11.8 meters far from the origin (Figure 34). Please note that posible positions’ precission has been set to 10-1 meters in order to simplify the iterations.

This project has been carefuly chosen for testing the suitability of implementing parametric tools in early stages of architectural design to show how architecture could have been influenced by them. Firstly, its small size allowed a relatively quick complete definition with geometrical parameters. Secondly, the building has completely been erected with steel elements and due to its restrictive urban constrains that give powerful boundary conditions to perform the study. Besides this, a quite complete description was found on the issue 116-117 of «Tribuna de la Construcción», with very descriptive axonometries that linked structure and spaces.

In the second optimization, taking vertical elements into account, supports’ optimal possition appear to be 3.5, 4.2 and 9.4 meters far from the origin (Figure 36).

Fig. 34 – Result of first optimization

To check the implications of this solution, it has been compared with a «standard» solution with equidistant supports (Figure 35). Given a set case of 5 supports (maximum number of options given to Galapagos) and the same boundary restrictions given to the second model, this is a span of 3.75 meters. As a direct consequence, without further considerations in joints or other accessory elements, its construction implies 660.58 kg of steel versus 539.81 kg of steel in the optimized solution.

According to the description given in the above mentioned magazine, although most of the surrounding buildings had already been substituted, plotting is still small and organic (Figure 37). Plot dimensions are 4.5x9 meters, the footprint allowed is 60%, the maximal floor ratio area is 60% and the maximal building height is 10 meters. No building is allowed on the first 2 meters of the plot. (Figure 39). Furthermore, an angle of 60% has to be mantained for lighting conditions. Construction of steel rests over a base of concrete pillars with 1 meter thickness and the steel structure was erected in one day.

This means a reduction of an 18% over the total mass.

Fig. 35 – Test frame with standard equidistantly distributed supports used as control element

With this feedback should the architect evaluate wether other project reasons make more suitable the adoption of the first or the second alternative.

Fig. 37 – (Upper) Site Plan Fig. 38 – ( Center) General view of the house Fig. 39 – (Lower) View of the house from the plot’s door

Fig. 36 – Result of second optimization, including columns

Fig. 40 – West Elevation

Fig. 41 – North Elevation

Fig. 42 – East Elevation

Fig. 43 – South elevation

METHODOLOGY As previosly said, this Case Study aims for linking structural optimization and its architectural implications. The urban parameters set the maximum volume that define the diffferent levels of the house. Therefore the dimensions of each storey are perfectly stablished. In this very case, structure is a hidden perimetral element that mantains the building. The fact of being a perimetral structure makes it to be embeded in the envelope not taking an active role in the façade definition. Floor slabs apparently transmit the loads to the outer frame directly.

Apparently being a very regular and simmetrical structure, it has some special alterations to open holes in the outer skin -windows and doors- (Figure 41). This elements will be considered the restrictions of the following structural optimization. Structure modulation takes an active role in spacial configuration. So as an example, columns modulate the space and create a subtle visual differenciation between living room and kitchen. It has been observed that the architect used tubular profiles in the vertical elements. As it is well known that this kind of profiles have a better behaviour to flexion in different planes, they will be incorporated to the script as another restriction.

Fig. 45 – Goals of the study and boundary conditions

Fig. 44 – House Plans

In a first study, the north frame of the structure is parametriced and optimized in Cross Section, taking into account architectural design restrictions for the façade holes.

A next goal of the optimization will consist on add the position of the vertical elements as a parameter to be defined by the ES Galapagos, thus reduce the amount of steel. In a third phase, optimization is would be carried to a next level: Why do have columns to be vertical? Can loads be driven more efficiently to foundation in another way and reducing even more the amount of material? Can this be used as a design strategy? Several test have been developed, parametricising the columns and making their direction based on a vector (with X, Y and Z components). After running several test, it has been determined that the amount of parameters set a huge degree of freedom, and therefore, Galapagos might be running the iteration for too much time. Instead, the approach of the study has been changed to test the «Force-flow finder» Karamba algorithm. Further work should be done to carry this analysis in three dimensions and study its architectural contributions to the design.

Fig. 46 – Axonometry of buildin’s structure

Fig. 47 – Pictures of the house’s spaces.

Fig. 48 – Longitudinal section

For the first analysis run, elements were not completely parametricised. Instead, a given Rhino geometrical model was given, being Karamba able to detect any modification to it and react automatically. It could be observed that, Karamba assumes all nodes to be rigid by default (this is that they transmit bending moments). In this case study it was discovered the possibility to select over 5000 thousand different profiles on the Karamba in-built profile component. After this, the model was parametrized, using the Gene Pool to generate the posible positions of the supports (displacing nodes in the X direction). Inmediately after this, a question was raised: Why do supports have to be straight? Then it was created a script were columns were based on direction vectors. Boundary conditions and restrictions were the same in both models. The parametric algorith, is explained in the dropdown page. Simulation was run in both algorithms, taking up to ten minutes to run each optimization. Results were not as expected in neither of the cases. After evaluating the deflection and bending moments graphs, it has been observed that beams’ joints should not transfer moments as the necessary stiffness causes Karamba to overdimension the cross sections.This problem was fisrtly addressed including the Joint Agent component, that adds joint conditions to the desired element. But when introducing the nodes where moment should not be transferred (Figure 41) some other problem was brought to light. This Case Study was designed so columns could be at any position but in the

restrictions; being then a choice among 2 and 5 columns and therefore a variable number of nodes. The joint agent component needs the name of the node to be able to run, and here is where the problem starts. Galapagos runs an evolutionary iteration, thus, varying the number of nodes and consequently its numbering. Nodes should be named in relation to the beam number so the component runs adequately, and this has not been achieved in any case. This problem was partially solved making all beams to do not transfer moment but having a diagonal element to stabilize the system (Figure 54). Even though the solution could be structurally optimized, its architectural implications could not be accepted, thus rejecting the solution. As a third solution, the model is evaluated with the flow-finder component (based on ESO algorythms). It does not work with the position of the elements. Instead, it begins with a mesh or grid of elements that will be analyzed and elements with a low utilization will be sequentially removed (Figure 55). This optimization will run until achieving a desired mass ratio (percentage over the initial mass). The flow-finder component has not shown easy understandable results, and as it is not the main subject of this work, further work should be done to implement with feasibility. These problems have spotlighted several questions that should be taken into account in the following and that are analyzed in the discussion and conclusions.

3 2

Fig. 49 – Axonometry of building’s structure Fig. 50 – General overview of the Karamba basic script

Firstly, the story height is done with the Gene Pool, organizing the data in a tree with as many branches as storeys.

Secondly, the parametrization of the columns is done with the Gene Pool, within the boundaries provided by design conditions. In addition, the upper and lower values are manually given, so storeys have the desired dimensions. After this, nodes are organized in a tree by the floor they belong to. Nodes are also duplicated in the next level, as columns need a begining and an end. The Joint agent component allows to define that beams do not transfer moments at the desired nodes. The problem comes when running the simulation, changing the naming of the desired nodes.

As a final test, the flow-finder component is connected to the model, beggining with a surface defined by the geometry outer points. This surface is divided in a mesh with a variable number of elements to perform the optimization. The algorithm has been created taking the Karambaâ&#x20AC;&#x2122;s website BESO for Beams example. The graph in the right shows if the simulation converges to a point or if more iterations are needed.

As a second solution, all the beams are set to do not transfer bending moments. Therefore, diagonals are created to stabilize the model with the â&#x20AC;&#x153;Near pointâ&#x20AC;? Karamba component.

DISCUSSION AND CONCLUSIONS Even though results were not as expected when this Case Study was designed, the problems brought to light have an incredible interest. Several conclussions can be extracted from them. Firstly, it is very important to highlight the need of clearly determine which ones are the parameters that are to be optimized and the degrees of freedom. A large number of parameters or wide systems not only slows down the computer, it also may lead to weird solutions. Besides this, the more complex a model is, the more complicated it will be to keep track of the data. Secondly, the importance of reviewing the script and reflecting on the obtained results; flow finder optimization algorithms and evolutionary solvers can converge to solutions that may not be easily understood.

Fig. 52 – During the first optimization of the model, stiffness problems lead to an overdimension of the elements that needed to be corrected

Thirdly, that structure can surprisingly influence design conditions; structure can be optimized in many ways, not only in terms of cross section, but also in terms of position, direction and relations between elements. In previous cases it has been possible to achieve more optimized solutions that could have given a clearer voice to the structure if explored in early stage design phases . Thus, it is possible to obtain unexpected results that may lead the structure to be linked more deeply with spaces and with the final architecture. Ultimately, in a 3D analysis and optimization it would have been interesting to evaluate the consecuences of introducing horizontal loads such as wind and sysmic actions (very important in Japan) evaluating how structure could be optimized with this elements contributing to the architectural design. It would have also been interesting to develop several load cases that Karamba would evaluate and use to optimize the system; for example, permantent loads, wind loads, earthquake conditions, etc.

Fig. 51 – Bending moments diagram. An indicator of a stiffness problem on the over diomension of the cross seciotns.

Fig. 53 – (Left) First simulation of a more complex frame in Kaaramba. On the right, the solution to the first optimization, whose results are out of bounds.

Fig. 54 – Galapagos’ output result of the third optimization, including diagonal elements. The result is quite far from the desired, and therefore is not considered as a valid solution.

Fig. 55 – Flow-finder component with a set of test loads. Beams are sequantially removed to diminish material wastage. Further research should be done to accomplish its implementation.

conclusions

discussion This work focuses on potential aplications of Parametric tools to structural optimization and its relation with architecture through structural analysis. Then it should not be forgotten that these tools do not substitute architectural thought in the slightest; quite the opposite, they encourage and facilitate a deeper analysis on the ongoing designs to also consider psychologycal, spatial and other qualities. The purpose of the work has been to go one step further and not only optimize structures in terms of cross section but also about the position of the elements and its architectural consequences. This means to reflect in depth about what it is been designed, to discover and explore alternative solutions that may make us radically change our architectural design (Figure 56). The work has focused on a narrow part of the Karamba software, not including shell elements in the analysis nor deepen in algorithms and utilities for a more advanced optimization and form-finding. Some complex script examples can be found in the engineer’s website; besides it, Karamba’s manual shows how some features of the plugin work. But unfortunately, not how to develop use nor how to apply them to architectural purposes.

Fig. 56 – Parametric tools and ES optimization as a form-finding and architectural design research process

The Case Studies have been developed to research the potential of these tools in combination with the ES Galapagos, producing encouraging results. All in all, it must not be forgotten that this optimizations have been carried out with the purpose of spotlighting new ways of understanding structure and architecture as a whole from early design stages. We must not forget though, that construction and economic factors have to be taken very seriously even during early desing stages. Therefore all the results shown throughout the case studies should be afterwards reviewed in terms of building ease, joints, transportation, etc.

conclusions Parametric design tools have brought an undeniably powerful possibility of exploring new ways structures can foster and actively reinforce the design concept. In other words, they let you create your own tools and set your own limits. This newly opened world of possibilities has started to deliver fresh free-form proposals, now become trendy and fashion in architecture repositories. Unfortunately their powerful forms very often have no further meaning nor architectural implications. Throughout several case studies it has been tested the implementation of structural analysis in early design stages as a means of giving a voice to the structure in the project through its optimization. Karamba has been chosen as a structural analysis tool because of its feasibility when used in professional environments. Special attention has been taken when creating the architectural model and setting the boundary conditions to achieve optimization goals. The quickly responsive analysis undeniable lead the tools to be considered as time saving, with more than satisfying results for its implementation in early design stages. They can also help to take a huge leap in digital fabrication. Prefabrication of building elements results in the diminish of building costs, increase of precission and thus meaning fewer mistakes. To sum up, the main outcome of this work is to highlight the importance of encouraging architects and architecture students to cultivate their interest on using and put these tools into their practice, seeking a better understanding of the structures and the architectural space.

further work Although parametric tools are very powerful, as previously stated, there are very few theorical references that deepen on structural rationalization and their implication with the design concepts in nowadays architectural proposals. And this seems very necessary observing the great amount of freeform proposals that lack of a structural logic. As a research, it may be interesting a conducted study with two branches. On the one hand, benefits of structural optimization have already been highlighted in this work as well as some procedures of beam-structures analysis. It is necessary then, to introduce what might be the next step for structural optimization, working with the concept «Biomimicry»: Innovation Inspired by Nature (Benyus, 1997).

Fig. 57 – (Left) Human Femur. Plate 455. NETTER, F. H. 2010. Atlas of Human Anatomy, Elsevier Health Sciences. Fig. 58 – (Center) Natural Structure of a Giant Waterlily (Victoria Amazonica) Picture by the Author. Royal Botanic Gardens, Kew (United Kingdom) Fig. 59 – (Right) Cholla Cactus (Cylindropuntia)Bone. An example of «building with holes»

Biomimicry research uses an ecological standard to judge the suitability of the designs and innovations. After 3.8 billion years of evolution, nature has determined what works, what is appropriate. What lasts. In the natural world the cost is energy, where competition for available resources favors the organism that can grow, survive and reproduce with the least amount of required materials and energy expenditure (Panchuk, N. 2006). For example, the shape of a human femur is as it is the most efficient way of transmiting the loads to the feet with the minimum amount of material (Figure 57)

In a very similar way, a designer -architect- must seek the balance of design variables to equate functionality and cost -economic, ecologic, etc- as the design that offers the best product for the least amount of investment will often be the one produced. Analyzing many structurally efficient non-orthogonal forms which create structures , nature was studied by the often touted as “the first biomathematician” D’Arcy Thompson, who suggested that the influences of physics and mechanics on the development of form and structure in organisms were underemphasized (Panchuk, N. 2006) (Figure 58). On the other hand, Илья Р. Пригожин (Ilya R. Prigogine), mathematician who also studied nature patterns, suggested the idea of «building with holes», bringing up the idea that afterwards brought out the research on Topology Optimization (Figure 59). This field brings mathematicians, engineers and architects to investigate how to use material more efficiently. The first functioning algorithm was presented in 1992 by Xie and Steven under the name of Evolutionary Structural Optimization (ESO) (Tedeschi, A. 2014), where through a series of FE analysis, it is possible to discard inefficient material using rejection criteria defined by Von Mises stresses and he Rejection Ratio. In short, structures that adapt their shape depending on their resistance behaviour (Figures 60, 61 and 62).

This work has focused on the potential of parametric tools, grasping on procedures for aplying it to beam-based architectures. Further work should be carried out to understand the above mentioned concepts, that will lead to unprecedent architectures when developed aside new fabrication techniques. In words of Knippers (2013) «the introduction of automated fabrication technologies requires a new interpretation of the entire design process (…) However, the potential of these technologies is not perceived by the architecture and construction industry today».

Two examples have been chosen to illustrate this: firstly, the achievement of ARUP Engineers to 3D print with steel at a good resolution. This feature combined with ESO opens a huge field of technical development, resulting in cheaper, customized and optimized building elements (Figures 63 and 64). Secondly, a technology developed by MX3D, a Netherlands based company that research 3D Printing self-sustained structures. Its bridge in Amsterdam is based on a ESO optimization afterwards brought to reality thanks to their «iron axis printing technology» (Figures 65 and 66). All in all, we have just begun to experience a huge development on digital tools and techniques that will help architects take their designs to levels without precedent, providing ashtonishing results. If digested adequately.

Fig. 60 – (Left)Beam optimization . tedeschi pg. 416 Fig. 61 – (Center) Extended evolutive structural optimization (XESO) flowchart tedeschi pg. 417 Fig. 62 – (Right) NU:S parametric shoes (2012) designed by M. Degni, A. Spinelli and A. Tedeschi (Sinterized Nylon Powder). Picture by G. Catani and L. Sorrentino.

Fig. 63 – (Left) Steel 3D Printing technologies developed by ARUP Fig. 64 – (Center and Right) Comparison between traditional structural steel node and an optimized solution

Fig. 65 – (Left) Self-printed bridge by MX3D in Amsterdam. Designed with parametric and ESO tools. Fig. 66 – (Right) elevation of the optimized bridge.

appendix: BENCHMARK ANALYSIS & references

case study 1

When optimizing cross sections results have been once again slightly different if selecting the option «quick dimensioning» in CYPE Metal 3D; resulting in an IPE 120 profile for CYPE and an IPE 140 for Karamba.

As previously referred, this spreadsheet gathers the data from all the simulations run on the first case study, to stablish the benchmark of feasibility.

Anyhow, for an «optimal dimensioning», CYPE offered the same result as Karamba.

Both CYPE and Karamba input models were entered with exactly the same geometries and boundary conditions. A significant difference has been found on the resultant forces. This could be beacuse of any mistake on the load case assumptions. In contrast, deformations where practically identical. Karamba output for deformation is in meters with a precission of 10-2, which may indicate that although results would be the same, Karamba rounds them off.

BENCHMARK PERFORMANCE ANALYSIS ID

NAME / DATE

LOAD CASE POINT L

LINE L

SUPPORT CONDITIONS

DEFLECTION TOLERANCE

SECTION IPE

RESULTS

MASS MAX N

KARAMBA (FEM) MAX V MAX M

MAX DISP

MAX N

CYPE (MATRIX) MAX V MAX M

MAX DISP

29,99

7,65

9,56

0,15

10,34

12,9

0,0148

100

40,43

7,7

9,63

0,07

10,34

12,9

0,0701

120

51,51

7,76

9,7

0,04

10,468

13,09

0,038

140

64,37

7,82

9,78

0,02

10,551

13,19

0,0226

160

78,89

7,89

9,87

0,01

10,647

13,31

0,0142

180

93,81

7,97

9,96

0,01

10,746

13,43

0,0095

200

111,86

8,06

10,07

0,01

10,866

13,58

0,0065

220

131,1

8,16

10,19

10,993

13,74

0,0046

240

153,47

8,27

10,33

11,14

13,93

0,0033

270

180,16

8,4

10,5

11,31

14,15

0,0023

300

211,17

8,56

10,69

11,52

14,4

0,0016

330

245,71

8,73

10,91

11,75

14,69

0,0012

360

285,35

8,93

11,16

12,01

15,02

0,0009

400

331,66

9,16

11,45

12,32

15,4

0,0006

450

387,79

9,44

11,8

12,69

15,87

0,0004

500

455,3

9,78

12,22

13,14

16,42

0,0003

550

525,95

10,13

12,66

13,6

17,01

0,0002

600

616,3

10,56

13,2

14,719

17,72

0,0002

9 10

CASE STUDY 1A 9/9/2015

N/A

3 kN/m

A: 111000 B: 111000

l/300

Table A – Benchmark spreadsheet with analysis results

case study 2 In order to check the feasibility of the results in this Case Study, models have been double checked in CYPE Metal 3D. Graphs were obtained in order to compare them with Karamba outputs. Even though, Bending moments and Shear forces did not have the same numeric value, the range was very similar. Displacements were very close and dimensioning resulted to be the same as for Karamba.

Fig. 67 – Bending Moments diagram. Output from CYPE calculation

Fig. 68 – Deformation diagram. Output from CYPE calculation

Fig. 69 – Bending Moments diagram. Output from CYPE calculation

Fig. 70 – Deformation diagram. Output from CYPE calculation

references ALMARAZ, A. 2014. Envelope In Zero Emission High Rise Buildings. Norges teknisk-naturvitenskapelige universitet, Article for MSc Course Use and Operation of Zero Emission Buildings BERNABEU LARENA, A. & AZAGRA, D. 2012. La estructura de las formas libres. Informes de la Construcción, 64, 133-142. BERNABEU LARENA, A. 2007. Estrategias de diseño estructural en la arquitectura contemporánea: El trabajo de Cecil Balmond. Tesis Doctoral. Departamento de Estructuras de Edificación Escuela Técnica Superior de Arquitectura Universidad Politécnica de Madrid. BLOCK, P., KNIPPERS, J., MITRA, N. J. & WANG, W. 2014. Advances in Architectural Geometry 2014, Springer International CHARLESON, A. 2005. Structure as Architecture: A Source Book for Architects and Structural Engineers, Elsevier/Architectural Press. CLAUS, F. 2014. Casa en Tokio. Japón. TC. Tribuna de la construcción, 116-117, 328-343. COOREY, B. P. & JUPP, J. R. 2014. Generative spatial performance design system. Artificial Intelligence for Engineering Design, Analysis and Manufacturing, 28, 277-283. DIPETTE, S., URAL, A. & SANTHANAM, S. 2015. Analysis of toughening mechanisms in the Strombus gigas shell. J Mech Behav Biomed Mater, 48, 200-9. ENGEL, H. 1968. Structure systems, Deutsche Verlags-Anstalt. FAHLBUSCH, M., HOFMANN A., HEISE A., BOLLINGER K., GROHMANN M., MAHLKNECHT J. 2012. Skylink am Flughafen Frankfurt. Stahlbau, 81, 638642. FRAZER, J. 1995. An Evolutionary Architecture, Architectural Association.

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list of figures Author’s Original Figures Figures 1, 2, 8, 9, 11, 15-19, 24-36, 45, 50-56, 58, 67-70 Table A as well as the totality of Grasshopper scripts, unless otherwise stated.

Other Sources Figures Figures 3, 4 and 5: CHARLESON, A. 2005. Structure as Architecture: A Source Book for Architects and Structural Engineers, Elsevier/Architectural Press, 17, 42 and 85. Figure 6: BERNABEU LARENA, A. & AZAGRA, D. 2012. La estructura de las formas libres. Informes de la Construcción, 64, 133-142. Figure 7: http://www.streets-ofbarcelona.com/wp/wp-content/ uploads/2012/02/Picture-1.jpg last access Sept. the 22th of 2015 Figure 10: http://www.karamba3d.com/ wp-content/uploads/2012/09/ PortalFrame.jpg last access Sept. the 15th of 2015 Figure 12: http://www.karamba3d.com/ digital-design-fabrication-2012/ http://www.karamba3d.com/ infobox-competition/ last access Sept. the 27h of 2015 Figures 13 and 14 : http://karamba3d.com/ wp-content/uploads/2012/04/ Skylink120201-4_BG_ES.jpg last access Sept. the 15th of 2015 Figures 20 and 22: a+t magazine, Workforce A Better Place To Work 2. 2014, 44. 6, 8.

Figure 21: https://www.baloise.com/en/ home/media/news/2014/winnersof-the-architecture-competition-forbaloise-park-have-been-decided.html

Figure 24: http://www.justinteriorideas.com/ wp-content/uploads/2014/06/58005__ arup-animation.gif last access Sept. the 6th of 2015

last access Sept. the 27h of 2015 Figure 23: h t t p : / / w w w. d e z e e n . com/2007/09/11/tama-art-universitylibrary-by-toyo-ito/

Figures 65 and 66: http://mx3d.com/projects/bridge/ last access Sept. the 15th of 2015

last access Sept. the 27h of 2015 Figures 37-44, 46-49: CLAUS, F. 2014. Casa en Tokio. Jap贸n. TC. Tribuna de la construcci贸n, 116-117, 328-343. Figure 57: NETTER, F. H. 2010. Atlas of Human Anatomy, Elsevier Health Sciences. Figure 59: https://s-media-cacheak0.pinimg.com/736x/86/ aa/96/86aa967b167d491dda2fb68ecc6f0b13.jpg last access Sept. the 15th of 2015 Figures 60, 61 and 62: TEDESCHI, A. 2014. AAD Algorithms-Aided Design. Parametric Strategies Using Grasshopper, Le Penseur. Figure 63: http://images.gizmag.com/hero/ arup-laser-sintering@2x.jpg last access Sept. the 6th of 2015

list of cS Attached to this work, they can be found the Grasshopper original scripts that have been necessary to develop the Case Studies for this thesis and learn to work with Karamba from scratch. Files can be accessed from the URL: https://drive.google.com/foldervie w?id=0B2wlmFUp0EAhc2hjS2VZb19q bXc&usp=sharing

Name: House Frame Not Param. From: 11/09/2015 To: 23/09/2015

CASE STUDY 3A III it has been described in this work Name: House Frame

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