PARAMETRICS : MATERIALS AND INTERVENTIONS

A DI SSERTATI ON ON

PARAMETRI CS MATERI ALSAND I NTERVENTI ONS

BY

RAHULAERON

BACHELOR’ SOFARCHI TECTURE

ACKNOWLEDGEMENT

I would like to thank my supervisors for their insight and guidance; for supporting me and giving the cofidence in needed during the undertaking of this dissertation.

Their knowledge and patience added to my experience and end result.

I would like to thank my family for their love and care throughout the entire process of the dissertation and beyond. And my peers ANUSHREE CHOUDHARY, MOHIT JAIN & UTKARSH GUPTA for showing confidence in me and helping me out through the hurdles encountered.

Lastly, I would like to thank the creator, for giving me the strength throughout the process of creating this dissertation.

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ABSTRACT

Parametric Design is a process based on algorithmic thinking that enables the expressionn of parameters and the rules that together define, encode and clarify the relatonship between the design intent and response.

It is basically the fluidity that appears to be flowing in a particular function to develop a form.

Installation is the art of architecture and when it is made with help of phenomenon of parametrics it generates an organic shape which blends with nature and gives a very smoothing shape and form. The level of detail of form generation is reduced so that it can be created in real world with proper tensile strength gained from material. Its just organic intervention which sometimes includes tesellation.

The purpose of choosing this topic is to throw light on the advancement in parametric installation and the phenomenon of "Function Creates Form". And thework done by different architects and artists on this phenomenon and also the different type of material used to generate the organic forms and shapes.

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INDEX ACKNOWLEDGEMENT ABSTRACT CHAPTER 1 :

INTRODUCTION

1.1.

AIM

1.2.

OBJECTIVES

1.3.

METHODOLOGY

CHAPTER 2 :

UNDERSTANDING THE FORM

2.1.

PARAMETERS

2.2.

PAST, PRESENT AND FUTURE

CHAPTER 3 :

LEARNING PARAMETERS

3.1.

EQUATION PHENOMENON

3.2.

CHANGE OF VARIABLE WITH EQUATIONS

3.3.

DESIGNING OF PARAMETERS

3.4.

MERGING OF PARAMETERS

CHAPTER 4 :

PARAMETRIC DESIGNING

4.1.

THE DESIGN PROCESS

4.2.

CONSTRUCTIVE SOLID GEOMETRY (CSG)

4.3.

BOUNDARY REPRESENTATION (BR)

4.4.

ADVANTAGES

4.5.

PARAMETRIC MODELLING TOOLS

4.6.

PARAMETRIC DESIGN SOLUTIONS

4.7.

SOFTWARE USED

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CHAPTER 5 :

FORM AND ITS UNDERSTANDING

5.1.

WHAT IS FORM????????

5.2.

LINE

5.3.

CIRCLE

5.4.

HELIX

5.5.

ELLIPSE

5.6.

ELLIPSOID

5.7.

FORM GENERATION

5.8.

THE MAOHAUS

CHAPTER 6 :

MATERIALS

6.1.

REINFORCED CONCRETE (RC)

6.2.

GLASS FIBER REINFORCED CONCRETE

6.3.

SOIL CEMENT

6.4.

PERFORATED METAL

CHAPTER 7 :

CASE STUDIES

7.1.

Case Study #01 Installation at SCI-Art Gallery

7.2.

Case Study #02 ULTRA THIN CONCRETE ROOF

7.3.

Case Study #03 DRONEPORT SHELL

7.4.

SPECIAL CASE STUDY Sub divided columns

CHAPTER 8 :

BIBLIOGRAPHY

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CHAPTER 1 INTRODUCTION

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1.1. AIM Parametrics is the upcoming and developing concept with a bright future. The organic forms with tensile strength and the different types of material used to form all the shapes and forms which can exist in real world.

The main aim is to do a complete study on the concept of "Function Develop Form" and in order to create all the forms the material used and techniques behind the development.

1.2. OBJECTIVES This study is a start point for the future research and possible applications by providing outstanding data that will be valuable. It will also contribute to the poor architectural literature on this topic. This dissertation aims to point out the design considerations of parametric structures depending on not merely engineering but also the architectural aspects.

One of the main objectives of this study is defining architectural design parameters according to the conditions and limitations of the surrounding in order to set the fundamentals for architectural approaches to parametric forms and shapes.

1.3. METHODOLOGY The basic methodology behind starts from the introduction about parameters and parametric equations with the history behind it and the development of techniques of forms it in ideal world which includes different types of platforms for developing concepts and it will go the development of the concepts in real world.

It also includes the different types of techniques and the methods of development of the forms and shapes with reference to the different case studies done on various architects and artists which excels in this field.

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CHAPTER 2 UNDERSTANDING THE FORM

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2.1. PARAMETERS It is a characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when identifying the system, or when evaluating its performance, status, condition, etc.

Parameter has more specific meanings within various disciplines, including mathematics, computing and computer, engineering, statistics, logic and linguistics. Within and across these fields, careful distinction must be maintained of the different usages of the term parameter and of other terms often associated with it, such as argument, property, axiom, variable, function, attribute, etc.

The term parametric originates from mathematics (parametric equation) and refers to the use of certain parameters or variables that can be edited to manipulate or alter the end result of an equation or system. While today the term is used in reference to computational design systems, there are precedents for these modern systems in the works of architects such as Antoni GaudĂ­, who used analog models to explore design space.

A process based on algorithm thinking that enables the expression of parameters and rules that, together, define, encode and clarify the relationship between design intent and design response.

Parametric design is a paradigm in design where the relationship between elements is used to manipulate and inform the design of complex geometries and structures.

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2.2. PAST, PRESENT AND FUTURE

If the plane to be introduced were 4P2 the parametric ratio of which is 4:2:1, we should in the same manner mark off 4 parts of e, 2 of ē and 1 of ë.

Dana 1837, 42

In this quote Dana is describing the parametric relationship between three parameters of the plane (4:2:1) and the respective division of lines e, ē, and ë.

Dana’s crystal equations resemble those that would be used by architects 175 years later to develop parametric models of architecture. Dana uses parametric in its original mathematical sense, a word given no more emphasis than other technical terms like parallel, intersection, and plane.

Sir John Leslie (1821), in his book on geometric analysis, proving the selfsimilarity of catenary curves using “parametric circles” Samuel Earnshaw (1839), wrote about “hyperbolic parametric surfaces” deformed by lines of force in a paper that gave rise to Earnshaw’s theorem.

Architecture that has a “crystalline splendour” according to Moretti (1957).

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T

here are a set of independent parameters (string length, anchor point location, birdshot weight) and there are a set of outcomes (the various vertex locations of points on the strings) which derive from the

parameters using explicit functions (in this case Newton’s laws of motion). By modifying the independent parameters of this parametric model Gaudí could generate versions of the Colònia Güell Chapel and be assured the resulting structure would stand in pure compression.

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T

he original mathematical definition of parametric remains unmodified, these analogue parametric models all have a set of quantities expressed as an explicit function of a number of independent parameters, however this is complemented by a utilitarian emphasis on exploring the

possibilities offered by the model.

Sutherland (1963) wanted to create a system that enabled “a man and a computer to converse” The 1960s and 1970s were an optimistic period in computing and Sutherland’s vision of computers replicating drafting tables was almost pessimistic compared to his contemporaries’ bullish calls for: automated architects (Whitehead and Elders 1964; Cross 1977), designed aided by evolution (Frazer 1995 [with projects from 1966]), self-replicating geometry and cellular automata (Neumann 1951), computer-aided design (Coons 1963 [Sutherland’s supervisor]; Mitchell 1977), shape grammars (Stiny and Gips, 1972) and Bézier curves (independently developed by Casteljau in 1959 and by Bézier in 1962 [Böhm, Farin, and Kahmann 1984]).

Twenty years later, in August 1982, a time when computers were becoming affordable enough for some people to own a personal computer, AutoCAD was released and quickly rose to dominate the fledgling computer-aided design industry (Weisberg 2008). Gone were the curves, the artificial intelligence, and the self-replicating geometries. Replaced in AutoCAD with commands enabling the designer to explicitly draft two-dimensional lines on screen using a keyboard rather than a pen.

At the time Gehry Partners was employing Rick Smith, a CATIA expert originally from the aerospace industry, to help realise geometrically challenging architecture projects like the Barcelona Fish (1991) and the Guggenheim Museum in Bilbao (1993-97). This work forms the basis of Gehry Partners’ sister company, Gehry Technology (incorporated in 2001), which went on to release the parametric modelling software Digital Project in 2004.

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Revit Technology Corporation was founded by former Parametric Technology Corporation developers who aspired to create the “first parametric building modeller for architects and building design professionals�.

Only in the last decade has parametric modelling gone from being a mathematical trick employed by Gaudi, Otto, Sutherland, and some engineers now to being a regular part of architectural practice. While in mathematics parametric signifies a set of quantities expressed as an explicit function of a number of independent parameters, in architecture this is complemented by a utilitarian dogma for exploring the possibilities offered by the model. This exploration is facilitated both through the modification of model parameters and through the modification of model relationships.

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CHAPTER 3 LEARNING PARAMETERS

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3.1. EQUATION PHENOMENON A set of equations that express a set of quantities as explicit functions of a number of independent variables, known as ‘parameters’ (Weisstein 2003, 2150).

This definition sets forth two critical criteria: 1. A parametric equation expresses “a set of quantities” with a number of parameters.

2. The outcomes (the set of quantities) are related to the parameters through “explicit functions”. This is an important point of contention in later definitions since some contemporary architects suggest that correlations constitute parametric relationships.

An example of a parametric equation is the formulae that define a catenary curve:

x(a,t) = t y(a,t) = a cos h(t/a) These two formulae meet the criterion of a parametric equation. Firstly, they express a set of quantities (in this case an x quantity and a y quantity) in terms of a number of parameters (a, which controls the shape of the curve; and t, which controls where along the curve the point occurs). Secondly, the outcomes (x & y) are related to the parameters (a & t) through explicit functions (there is no ambiguity in the relationships between these variables). This is the origin of the term parametric: a set of quantities expressed as an explicit function of a number of parameters.

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3.2. CHANGE OF VARIABLE WITH EQUATIONS X = cos(at) – cos(bt)j Y = sin(ct) – sin(dt)k

SEVERAL GRAPHS BY VARIATIONS OF k

j=3 k=3

j=3 k=3

j=3 k=4

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X = i cos(at) – cos(bt)sin(ct) Y = j sin(dt) – sin(et)

i=1 j=2

X = cos t Y = sin t

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X = [R + r cos (t)] cos[u] Y = [R + r cos(t)] sin[u] Z = r sin[t] where the two parameters t and u both vary between 0 and 2π.

R=2, r=1/2 As u varies from 0 to 2π the point on the surface moves about a short circle passing through the hole in the torus. As t varies from 0 to 2π the point on the surface moves about a long circle around the hole in the torus.

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Display parameters Note: in the default position, X is width, Y is depth and Z is height. If you don't like it, deal with it.

Surfaces You can edit this section to plot your own parametric surfaces.

Hint: Make z a binary function of x and y, set the functions so x=t and y=u.

Fx(t,u) = (R + r cos t ) cos (u) {â&#x2C6;&#x2019;đ??&#x2026; < đ?&#x2019;&#x2013; â&#x2030;¤ đ??&#x2026;} Fy(t,u) = (R + r cos t ) sin (u) {â&#x2C6;&#x2019;đ??&#x2026; < đ?&#x2019;&#x2022; â&#x2030;¤ đ??&#x2026;} Fz(t,u) = r (sin t)

The value of a, b, c and m defines the as follows a â&#x20AC;&#x201C; rotation around green axis b â&#x20AC;&#x201C; Rotation around orange axis c â&#x20AC;&#x201C; Rotation around blue axis m â&#x20AC;&#x201C; Defines the intersection of all the axes

-62.8 < a < 62.8 -62.8 < b < 62.8 -62.8 < c < 62.8

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Basic concept and the steps behind the construction of the following surface.

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xx = cos(c) cos(a) - sin(c) sin(a) sin(b) xy = cos(c) sin(a) sin(b) + sin(c) cos(a) yx= - cos(c) sin(a) - sin(c) cos(a) sin(b) yy = cos(c) cos(a) sin(b) - sin(c) sin(a) zx= - sin(c) cos(b) zy= cos(c) cos(b) 2 < n < 40 -10 < s < 10

3.3. DESIGNING OF PARAMETERS The programmeâ&#x20AC;&#x2122;s third component, concentrated on design creation, reflection, and the communication of architectural design proposals. Using the data of the first component and the skills of the second, the Architects and Designers then started to establish and visualise their designs in 3-D forms that created spatial expressions of their findings and explorations.

Due to the emphasis onto parameters, the studio was in particular interested in describing a building form by creating dependencies of parameters that defined the relationship of data to architectural expressions.

With the use of a parametric modeller, it was easy to create geometric entities, relate these soli ds and voids. This method made it obvious to learn about the design and explore alternatives by manipulating the parameters, variables and rules.

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3.4. MERGING OF PARAMETERS The programme concluded component brought together the various aspects and results of the modules. The Architects and Designers merge the individual designs into larger cluster files. This synthesis creates compound with descriptions and dependencies that were highly complex and interrelated, yet both the content as well as the tool allows seamless communication to a larger public by describing the rules and parameters. This phase created a design with shared authorship of all.

Main concern people study and understand the complexity and the interrelationships of architectural designing that normally would have been unable to perceive immediately. The change of a single variable modified the whole design. This helps in understanding the complex dependencies that one variable has in a large building and the impact in can have on the design.

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CHAPTER 4 PARAMETRIC DESIGNING

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PARAMETRIC DESIGNING uses the computer to design objects or systems that model component attributes with real world behaviour. Parametric models use feature-based, solid and surface modelling design tools to manipulate the system attributes. One of the most important features of parametric modelling is that attributes that are interlinked automatically change their features. In other words, parametric modelling allows the designer to define entire classes of shapes, not just specific instances. Before the advent of parametric, editing the shape was not an easy task for designers. For example, to modify a 3D solid, the designer had to change the length, the breadth and the height. However, with parametric modelling, the designer need only alter one parameter; the other two parameters get adjusted automatically. So, parametric models focus on the steps in creating a shape and parameterize them. This benefits product design engineering services providers a lot.

4.1. THE DESIGN PROCESS Models are built from a set of mathematical equations. For parametric models to have any legitimacy, they must be based on real project information. It is the modernity of the information examination techniques and the breadth of the hidden undertaking information which decides the viability of a modelling solution.

There are two popular parametric representation models:

4.2. CONSTRUCTIVE SOLID GEOMETRY (CSG) CSG defines a model in terms of combining basic (primitive) and generated (using extrusion and sweeping operation) solid shapes. It uses Boolean operations to construct a model. CSG is a combination of 3D solid primitives (for example a cylinder, cone, prism, rectangle or sphere) that are then manipulated using simple Boolean operations.

4.3. BOUNDARY REPRESENTATION (BR) In BR, a solid model is formed by defining the surfaces that form its spatial boundaries (points, edges, etc.) The object is then made by joining these spatial points. Many Finite Element Method (FEM) programs use this method, as it allows the interior meshing of the volume to be more easily controlled.

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4.4. ADVANTAGES These are the benefits offered by 3D parametric modelling over traditional 2D drawings: 

Capability to produce flexible designs



3D solid models offer a vast range of ways to view the model



Better product visualization, as you can begin with simple objects with minimal details



Better integration with downstream applications and reduced engineering cycle time



Existing design data can be reused to create new designs



Quick design turnaround, increasing efficiency

4.5. PARAMETRIC MODELLING TOOLS There are many software choices available in the market today for parametric modelling. On a broad level, this software can be categorized as: 

Small scale use



Large scale use



Industry specific modelling

4.6. PARAMETRIC DESIGN SOLUTIONS The architects employ the tool as an amplifier to generate their design.

Subsequently, they were not limited by their knowledge or level of skills in order to be able to create their designs. They produced a variety of individual design proposals as well as one large design-cluster. They created rules and parameters that allowed complex and interrelating designs to emerge. These representations, however, could not be communicated using traditional architectural design methods or tools.

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For example, one proposal related street lighting, neon-signs and displaywindows with human activity around the building site. These parameters provided the engaging surface for the building mass.

Subsequently they controlled the use, orientation and appearance of the building.

The author took references to Japanese inner cities, where innovative ways of spaces are created by the means of lights, advertising and projections. Void, volume and density is controlled and created by the rhythm and intensity of lights.

The student transferred this concept into parameters, which redefined the spatial understanding of the site and used these variables to create an architectural proposal.

Another solution explored biological growth models based on Lindenmayer system fields. It explores the possibilities that a topological approach to designing with a parametric tool will yield an emergent architecture that is governed by a bottom-up hierarchy.

Topological forms created a variety of physical and programmatic instantiations.

The author had however, difficulties to translate the theoretical aspects of his parametric design studies into a buildable and inhabitable form. He acknowledged that he would require more time to become fluent with this novel approach to design. Therefore, he presented his work in two stages, the

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theoretical and the practical. The process of analysis and theory on the left side and the translation into a workable build form on the right.

Other results used parameters that related to the relationships between people and attraction to spaces with responsive structures. Students created selfopening canopies that reacted to people activities, ferry schedules, weather conditions and the possibilities to collect rainwater to provide a comfortable environment in all conditions.

They demonstrated a high level of thinking processes resulting in the generation of compound rules and dependencies that finally create the architectural design schemes. They gained a high level of expertise with digital parametric tools as part of their development at the studio, and used this knowledge to design parametrically. The outcome clearly showed that thinking, learning and creating within parametric designing requires a novel and deeper understanding of the overall design goal and its anticipated outcome. This differs from design that deals with one problem at a time, regardless of its dependencies.

4.7. SOFTWARE USED for modelling 

SolidWorks



CATIA



Siemens NX



SketchUp



Rhino with Grasshopper



AutoCAD



VectorWorks



Fusion 360



3DS Max



Inventor

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CHAPTER 5 FORM AND ITS UNDERSTANDING

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5.1. WHAT IS FORM????????

Curves and surfaces described by parameters Understand how we can represent a curve in a plane or space with a parameter that "runs along" the curve.

In many situations like curve adjustment, surface adjustment and animations it is smart to describe curves parametric. It makes it easier to reason and calculate and it makes it easier to program.

5.2. LINE Let us study a straight line in a plane as a simple first example.

The triangles P1, A, P and P1, B, P2 are similar and we can set up the following:

and find for example y expressed by coordinates for the two known points and x.

As an alternative we could set up a parametric equation for the line. Parametric means that the expression contains a parameter, t that changes when we run along the line. For a line in the plane we get two parametric expressions, one for x and one for y. Since we have a line, both are linear.

P=P1+t·(P2-P1) x(t)=x1+(x2-x1)·t y(t)=y1+(y2-y1)·t

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We see that x(0)=x1 and y(0)=y1, and x(1)=x2 and y(1)=y2. Since the expressions are linear we know that when t runs from 0 to 1, x and y runs from P1 to P2.

A parametric form gives control over the length of the line, not only the line direction.

Even this simple example can be useful in some situations. If we are going to carry out an animation that moves in a straight line, we can control the animation with small t-steps. We control speed by varying the t-steps. More compound movements can be controlled by a sequence of linear movements, if we don't come up with something cleverer.

An extension to include lines in space is simple. If we know the end points: P1(x1, y1, z1) and P2(x2, y2, z2), we get:

P=P1+t·(P2-P1) x(t)=x1+(x2-x1)·t y(t)=y1+(y2-y1)·t z(t)=z1+(z2-z1)·t

5.3. CIRCLE The most common way to write a circle is: x2 +y2 =r2.

Parametrically, this can be written as: y(t)=r·sin(2·pi·t) x(t)=r·cos(2·pi·t)

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or if we state the angle in degrees: y(t)=r·sin(360·t) x(t)=r·cos(360·t)

When t runs from 0 to 1, the angle argument runs a full circle, and the point ( x(t) , y(t) ) describes a circle.

Remember: that the trigonometric functions in C, C++ and Java expects radians as parameters, while the rotation function in OpenGL expects degrees.

5.4. HELIX A part of a helix in space, around the z-axis, can be describes as: y(t)=r·sin(2·pi·t) x(t)=r·cos(2·pi·t) z(t)= k·t

Where k state the distance between two rings in the spiral. If we let t run over a larger interval, for example 0..5 we will get 5 rotations on the spiral. We also see that we have a handy mechanism to calculate circles and circle segments.

Sphere

We normally describe a sphere like this, with radius r:

Parametrically we can describe the coordinates for a point on the spheres surface like this: PARAMETRICS : MATERIALS AND INTERVENTIONS

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5.5. ELLIPSE

Normally we describe an ellipse like this:

Piet Hein, the Danish mathematician, poet an artist, introduced his super ellipse according to the following formula:

When the exponential increases, the form of the ellipse changes towards a rectangle. Piet Hein suggested that 2.5 gives us the best esthetical result. He designed Sergels torg in Stockholm as a super ellipse with the relation between the two radii 5:6.

Parametrically we describe an ellipse like this:

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We get a super ellipse in parametric if we use an exponent n on sine and cosine.

Note that the ellipse will grow towards a rectangle when n decreases. If rx = ry we end up with a circle, when n=1.

5.6. ELLIPSOID

In three dimensions we describe an elliptical form like this:

Parametrical form:

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Again we get a super ellipsoid by introducing an exponent on sinus and cosinus:

The normal in a point on the surface can be described by:

These formulas are sufficient to calculate, and thus render, a super ellipsoid. We let the two angle parameters run in a double loop and calculate neighbouring points and use these to render surface fragments.

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5.7. FORM GENERATION Forms can also be generated from data. This can provide a better or different way of visualizing and apprehending three-dimensional information. It can also make data something tactile. The key aspect of generativity here is that the generated forms are the result of an algorithm metabolizing some specific data.

Changing the data produces (or would have produced) different forms.

The form results from the data, instead of a random process (i.e. hit a button, get a new variation) or an interactive one (i.e. a user adjusts some sliders or performs some action which governs the outcome to their tastes).

Nowadays we use computers and digital fabrication machines. Maps are another easy-to-understand form generated from data.

Some designers have used algorithmic techniques to generate 3D forms from graphs, such as from the locations in which a person has travelled.

Some computationally-generated physical visualizations are not necessarily novel in their form, but allow new audiences to appreciate graphical representations of data.

Generative art and design are large fields with many different approaches, and many tools that support different objectives and workflows. Widely-used algorithmic modelling environments include Processing, PLaSM, Rhino+Python, and Grasshopper. In this section, we consider how people are using OpenSCAD, a C-style geometry scripting language and CSG compiler, to create parameterized everyday objects. OpenSCAD is free software and available for GNU/Linux, MS Windows and Mac OSX. It provides two main modelling techniques: First, constructive solid geometry (CSG) and second, extrusion of 2D outlines.

OpenSCAD is well-suited for creating parametric objects, such as a chain that can have any number of links, or a snowflake ornament with a changeable pattern

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5.8. THE MAOHAUS



Architects: AntiStatic Architecture



Location: Banqiao South Alley, Beijing, China



Principal Architects: Martin Miller, Mo Zheng



Fabrication and Installation: eGrow



Area: 2000.0m2



Project Year: 2017



Photographs: Xia Zhi

The structure of the façade leverages the material properties of ULTRA-HIGH PERFORMANCE CONCRETE to create novel architectural form. Ranging from 4 to 7 metres in height, 2 metres wide and a mere 7 centimetres thick, the 6 individual panels span the façade without the need for any substructure or support. Each panel is cast as a single unit from large CNC milled molds. Computationally generated through fluid-dynamics algorithms, the curvature of the thin porous surface serves to more efficiently carry the loads of the structure to the foundation.

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CHAPTER 6 MATERIALS

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6.1. REINFORCED CONCRETE (RC) (AKA reinforced cement concrete or RCC) is a composite material in which concrete's relatively low tensile strength and ductility are counteracted by the inclusion of reinforcement having higher tensile strength or ductility. The reinforcement is usually, though not necessarily, steel reinforced bars (rebar) and is usually embedded passively in the concrete before the concrete sets.

Reinforcing schemes are generally designed to resist tensile stresses in particular regions of the concrete that might cause unacceptable cracking and/or structural failure. Modern reinforced concrete can contain varied reinforcing materials made of steel, polymers or alternate composite material in conjunction with rebar or not. Reinforced concrete may also be permanently stressed (in tension), so as to improve the behaviour of the final structure under working loads. The most common methods of doing this are known as pretensioning and post-tensioning.

For a strong, ductile and durable construction the reinforcement needs to have the following properties at least: 

High relative strength

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High toleration of tensile strain

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Good bond to the concrete, irrespective of pH, moisture, and similar factors

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Thermal compatibility, not causing unacceptable stresses in response to changing temperatures.

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Durability in the concrete environment, irrespective of corrosion or sustained stress for example.

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6.2. GLASS FIBER REINFORCED CONCRETE GFRC is a type of fibre-reinforced concrete. The product is also known as glass fibre reinforced concrete or GRC in British English. Glass fibre concretes are mainly used in exterior building façade panels and as architectural precast concrete. Somewhat similar materials are fibre cement siding and cement boards. Glass fiber-reinforced concrete consists of high-strength, alkaliresistant glass fiber embedded in a concrete matrix. In this form, both fibers and matrix retain their physical and chemical identities, while offering a synergistic combination of properties that cannot be achieved with either of the components acting alone. In general, fibers are the principal load-carrying members, while the surrounding matrix keeps them in the desired locations and orientation, acting as a load transfer medium between the fibers and protecting them from environmental damage. The fibers provide reinforcement for the matrix and other useful functions in fiber-reinforced composite materials. Glass fibers can be incorporated into a matrix either in continuous or discontinuous (chopped) lengths. The design of glass-fiber-reinforced concrete panels uses a knowledge of its basic properties under 

Tensile

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Compressive

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Bending and shear forces

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Coupled with estimates of behaviour under secondary loading effects

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Thermal response and moisture movement.

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6.3. SOIL CEMENT Soil cement is a construction material, a mix of pulverized natural soil with small amount of Portland cement and water, usually processed in a tumble, compacted to high density. Hard, semi-rigid durable material is formed by hydration of the cement particles.

Soil cement is frequently used as a construction material for pipe bedding, slope protection, and road construction as a subbase layer reinforcing and protecting the subgrade. It has good compressive and shear strength, but is brittle and has low tensile strength, so it is prone to forming cracks.

Soil cement mixtures differs from Portland cement concrete in the amount of paste (cement-water mixture). While in Portland cement concretes the paste coats all aggregate particles and binds them together, in soil cements the amount of cement is lower and therefore there are voids left, and the result is a cement matrix with nodules of uncemented material.

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6.4. PERFORATED METAL Perforated metal, also known as perforated sheet, perforated plate, or perforated screen, is sheet metal that has been manually or mechanically stamped or punched to create a pattern of holes, slots, or decorative shapes. Materials used to manufacture perforated metal sheets include stainless steel, cold rolled steel, galvanized steel, brass, aluminium, tinplate, copper, Monel, Inconel, titanium, plastic, and more.

The process of perforating metal sheets has been practiced for over 150 years. In the late 19th century, metal screens were used as an efficient means of separating coal. Unfortunately, the first perforators were labourers who would manually punch individual holes into the metal sheet. This proved to be an inefficient and inconsistent method which led to the development of new techniques, such as perforating the metal with a series of needles arranged in a way that would create the desired hole pattern.

Modern day perforation methods involve the use of technology and machines.

Common equipment used for the perforation of metal include rotary pinned perforation rollers, die and punch presses, and laser perforations.

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CHAPTER 7 CASE STUDIES

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7.1. Case Study #01 Installation at SCI-Art Gallery

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MATERIAL: Fibre-C - SDA glass fibre-reinforced concrete

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LOCATION: Bedford Square, London, United Kingdom

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AUTHOR: Zaha Hadid Architects

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Parametric design and rapid construction thanks to use of this innovative material permitted creation of a prefabricated pavilion for assembly on-site, putting it together with neoprene joints and bolts. The project maintained a focus on design, with a high-impact look recalling the interior of a snail shell, and on minimalism, with simple lines created through elastic, simple, immediate design. The frame of the construction consists of a floor slab with little girders laid on the ground, the point of departure for curved weightbearing girders which are preformed and numbered for error-free assembly, normally joined in three or four segments and containing housings for secondary girders. Each slab of Fiber-C measures 13.4 millimetres thick and acts as both frame and roof, creating unusual 3D moirĂŠ effects of light and shadow. All the builder had to do was use a couple of ordinary tools to assemble and, if necessary, dismantle the pavilion, doing away with the need to create a big construction site for a small building, and the material used was light enough that a small crew could handle it without any logistical difficulties, so that in the end it took less time to construct the building than to design it. The final effect is a bold, iconic look, in some ways a little open-air manual of technology, not just a simple exercise in style.

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7.2. Case Study #02 ULTRA THIN CONCRETE ROOF 

FACADE MANUFACTURER: Jakob (cables); Bruno Lehmann (rods and cable-net components); Blumer Lehmann (timber); Dafotech (steel supports + plates); Bieri (fabric cutting + sewing)

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ARCHITECTS: Supermanoeuvre; Bollinger+Grohmann

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LOCATION: Zürich & Dübendorf, Switzerland

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DATE OF COMPLETION: 2017-18

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SYSTEM: Thin shell concrete with integrated systems

A full-scale prototype of the design was the culmination of a four-year research project by ETH Zürich, and now the thin-shell integrated system’s concrete roof is under construction. The razor-thin assembly, built over the course of six months, tapers to an impressive one-inch thickness at the perimeter, averaging two inches thick across its more than 1,700 square feet of surface area. The ongoing project, sponsored by ETH Zürich, NCCR Digital Fabrication, and

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Holcim Schweiz, will lead to the completion of a rooftop apartment unit called HiLo, which will offer live-work space for guest faculty of Empa, the Swiss Federal Laboratories for Materials Science and Technology.

CONCEPT

CABLE NET

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NODE COMPONENTS

FABRIC

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WOODEN LOG EDGE BEAMS

CABLE NET FALSEWORK

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FABRIC SHUTTERING AND TENSILE REINFORCEMENT

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The rooftop structure rises about 24 feet high, encompassing 1,300 square feet.

Innovations in thin-shell building techniques were explored by the Block Research Group, led by Professor Block and senior researcher Dr. Tom Van Mele, together with the architecture office supermanoeuvre. The team purposefully avoided wasteful non-reusable formwork, opting instead to develop a net of steel cables stretched into a reusable scaffolding structure. The cable net supported a polymer textile that forms the shell surface. They were also able to provide a solution to efficiently realize completely new kinds of design.â&#x20AC;? The construction technique leaves the interior floor area below the roof relatively unobstructed, allowing interior construction work to proceed concurrently.

Altogether, this method is expected to condense construction to eight to ten weeks.

This level of optimization is perhaps most evident in the capacity of the reusable formwork system to hold around 25 times its own weight (20 tons of wet concrete will eventually load onto the formwork).

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CONCRETING

DECENTRING

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Experts from BĂźrgin Creations and Marti sprayed the concrete using a method developed specifically for this purpose, ensuring that the textile could withstand the pressure at all times. Together with Holcim Schweiz, the scientists determined the correct concrete mix, which had to be fluid enough to be sprayed and vibrated yet viscous enough to not flow off the fabric shuttering, even in the vertical spots. The innovative concrete structure offers more than a new method for constructing concrete shell structures: its aim is to be an intelligent, lightweight energy-producing system. This is achieved by careful assembly of multiple layers of building systems. Two layers of concrete sandwich together insulation, heating and cooling coils, while thin-film photovoltaic cells wrap the exterior surface. The residential unit, enclosed by this roof system, and an adaptive solar-shaded facade, is expected to generate more energy than it consumes.

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7.3. Case Study #03 DRONEPORT SHELL The Droneportâ&#x20AC;&#x2122;s location at the end of the Arsenale in Venice is symbolic as the gateway to a newly opened public park. The possibility of the structure remaining as a permanent legacy. A work by Architect Norman Foster

Stabilized earth bricks are a reliable, affordable and environmental-friendly building material. Compared to burnt clay bricks they do not require the intensive use of firewood or other fuel to achieve their performance. LafargeHolcim developed Durabric, a naturally cured building block made of compressed earth and cement, and launched it commercially in Cameroon, Indonesia, Malawi and Tanzania. As the technology is easily transferable, the LafargeHolcim Foundation for Sustainable Construction encouraged the use of Durabric to build the Droneport prototype at the Architecture Biennale in Venice as a symbol for future projects in Rwanda and other emerging countries.

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The Research Center of LafargeHolcim in Lyon developed customized bricks to meet the specific requirements of the Droneport vault. The challenge was to ensure a compressive strength of at least 10 MPa while minimizing the weight and size of each brick. The mix design was optimized in close cooperation with the Block Research Group at ETH Zurich and MecoConcept Toulouse. 18,000 Durabrics were made available for the Droneport construction in Venice. The heavy exposure to rain of the outer layer inspired LafargeHolcim to adapt the receipt of the waterproofing agent that is applied on the Droneport.

Dura Brick is customised by LAFARGEHOLCIM RESEARCH 

Low cost

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Earth based product

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Smaller than conventional bricks

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Delivers lateral strength req. in voltage structure

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Affordable

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Vocally produced

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Compressed almost like adobe brick, semi baked

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8% cement for durability and longitivity

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7.4. SPECIAL CASE STUDY MICHAEL HANSMEYER Sub divided columns

This project involves the conception and design of a new column order based on subdivision processes. It explores how subdivision can define and embellish this column order with an elaborate system of ornament.

An abstracted doric column is used as an input form to the subdivision processes.

Unlike the minimal input of the Platonic Solids project, the abstracted column conveys a significant topographical and topological information about the form to be generated. The input form contains data about the proportions of the column's shaft, capital, and supplemental base. It also contains information about its fluting and entasis.

The input form is tagged to allow the subdivision process to distinguish between individual components. This allows a heterogeneous application of the process, with distinct local parameters settings. In addition to distinguishing among tagged components, the process parameters can be set to vary according to the input form's topography as well as its topology.

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Effectively, the architect designs a process that produces a column, rather than designing a column directly. This process can be run again and again with different parameters to create endless permutations of columns. These permutations can be combined into new columns, and can form the point of departure for new generations of columns. The architect assumes the role of the orchestrator of these processes.

Unlike traditional design processes, the single subdivision process generates the form at all its scales: from the overall proportions and curvatures, to smaller local surface formations, down to the formation of a micro-structure. The process adds information at all scales, without resorting to any type of repetition. The result is a series of columns that exhibit both highly specific local conditions as well as an overall coherency and continuity. The ornament is in a continuous flow, yet it consists of very distinct local formations. The complexity of column contrasts with the simplicity of its generative process.

FABRICATION A full-scale, 2.7-meter high variant of the columns was fabricated as a layered model using 1mm sheet. Each sheet was individually cut using a laser cutter.

Sheets are stacked and held together by poles that run through a common core.

The calculation of the cutting path for each sheet takes place in several steps. First, the six million faces of the 3D model are intersected with a plane representing the sheet. This step generates individual line segments that are tested for selfintersection and subsequently combined to form polygons. Next, a polygon-inpolygon test deletes interior polygons. A series of filters then ensures that convex polygons with peninsulas maintain a minimum isthmus width. In a final step, an interior offset is calculated with the aim of hollowing out the slice to reduce weight.

While the mean diameter of the column is 50cm, the circumference as measured by the cutting path can reach up to 8 meters due to jaggedness and frequent reversals of curvature.

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X-RAY of a COLUMN SECTION

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SIXTH ORDER: GWANGJU DESIGN BIENNALE 2011 The Sixth Order installation at the Gwangju Design Biennale 2011 continues the development of a column order based on subdivision processes. It explores not the design of an object, but the design of a process to generate objects. This procedural approach inherently shifts the focus from a single object to a family of objects: endless permutations of a theme can be generated.

For the Gwangju Biennale, a single process was used to generate four individual columns. These four columns have not a single surface or motif in common, yet due to their shared constituent process, they clearly form a coherent group.

When entering the exhibition room, the viewer at first perceives sixteen columns.

This effect, created by the use of two floor-to-ceiling mirrors on adjoining walls, is intentionally accentuated by the columns' design. Thus, the columns are symmetrical along only a single axis, and they have different appearance when seen from the front or the back. In effect, two permutations are united in a single column - with eight virtual models for the four physical objects.

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LEARNING TO IMAGINE Effectively, the architect designs a process that produces a column, rather than designing a column directly. This process can be run again and again with different parameters to create endless permutations of columns. These permutations can be combined into new columns, and can form a point of departure for new generations of columns. The architect assumes the role of the orchestrator of these processes.

Unlike traditional design processes, the single subdivision process generates the form at all its scales: from the overall proportions and curvatures, to smaller local surface formations, down to the formation of a micro-structure. The process adds information at all scales, without resorting to any type of repetition. The result is a series of columns that exhibit both highly specific local conditions as well as an overall coherency and continuity. The ornament is in a continuous flow, yet it consists of very distinct local formations. The complexity of column contrasts with the simplicity of its generative process.

IMPORTANT Virtually 16 million facets Physically 2700 layers each of 1mm thick weighing 680 kilograms and 1620 m2 of sheets laser cut with a cutting path of 21.5 kilometers.

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CHAPTER 8 BIBLIOGRAPHY

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http://www.architectmagazine.com/design/culture/zaha-hadids-parametricinstallation-at-sci-arc_o https://en.wikipedia.org/wiki/Parametric_equation http://www.danieldavis.com/a-history-of-parametric/ http://www.michael-hansmeyer.com/subdivided-columns https://www.yatzer.com/Ornamented-Columns-by-Michael-Hansmeyer https://en.wikipedia.org/wiki/Soil_cement https://www.lafargeholcim-foundation.org/media/news/foundation/durabricthe-secret-behind-the-droneport-shell https://www.youtube.com/watch?v=u7mCk2_ERII&list=PLa2PbL9JBA94gLlPbNPgIaSSSHZ_3Fcy&index=11 https://en.wikipedia.org/wiki/Perforated_metal http://www.designtechsys.com/articles/parametric-modelling https://www.archdaily.com/886282/the-maohaus-antistatics-architecture https://www.sciencedirect.com/science/article/pii/S0898122115001716 http://blog.ramboll.com/rcd/articles/what-is-computational-design.html http://www.it.hiof.no/~borres/j3d/math/param/p-param.html http://golancourses.net/2015/lectures/parametric-3d-form/ http://www.floornature.com/ceramic-innovation/architecturalsolutions/pavilion-made-fibre-c-sda-concrete-reinforced-fibreglass-12789/ http://www.architectmagazine.com/design/parametric-design-whats-gottenlost-amid-the-algorithms_o https://www.desmos.com/calculator/vymzvpqp3k https://www.desmos.com/calculator/usy8hfrtbx

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https://en.wikipedia.org/wiki/Parametric_design https://www.youtube.com/watch?v=Ki1EcBCurqc https://www.youtube.com/watch?v=dsMCVMVTdn0 https://www.ethz.ch/en/news-and-events/eth-news/news/2017/10/innovativeconstruction.html https://archpaper.com/2018/03/ultra-thin-concrete-roof-cap-net-positiveenergy-rooftop-apartment/#gallery-0-slide-0 https://www.theb1m.com/video/fabricating-an-ultra-thin-concrete-roof https://materia.nl/article/ultra-thin-sinuous-concrete-roof/ https://www.arch2o.com/volu-dining-pavilion-zaha-hadid/

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