Design of Structures 11/20/2017. Autumn Studio. Structures. Toni Kotnik. Jørn Utzon: Sydney Opera House, (Eng.: Ove Arup)

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1 Design of Toni Kotnik Professor of Design of Aalto University Department of Architecture Department of Civil Engineering Jørn Utzon: Sydney Opera House, (Eng.: Ove Arup) 2 Toni Kotnik, Professor of Design of 1

2 Computation & Construction Sydney Opera under construction, 1966 (photo: Max Dupain) 3 Toni Kotnik, Professor of Design of Computation & Construction simulation material behaviour fabrication Sydney Opera, 1:60 perspex roof model testing of stress distribution in shell Southampton University, Toni Kotnik, Professor of Design of 2

3 Computation aim: analytic description mathematical models FEM optimization precision of description enables predictability material system economic use of means performance efficiency simulation mathematics science of pattern & order materialized form form DIGITAL matter formed material 5 Toni Kotnik, Professor of Design of Form-Finding Heinz Isler: experimental Antoni Gaudi: hanging model for Colònia Güell, Toni Kotnik, Professor of Design of 3

4 Form-Finding Frei Otto: hanging model of Munich Olympic Stadium roof, Toni Kotnik, Professor of Design of Formfinding funicular form finding with Rhinovault by Philippe Block 8 Toni Kotnik, Professor of Design of 4

5 Computation Computational thinking is influencing research in nearly all disciplines, both in the sciences and the humanities. [The Computer] is changing the way we think. If you want to understand the 21th century then you must first understand computation. Alan Bundy a new eco-system of consultancies that stabilizes the understanding of structural design in architecture! 9 Toni Kotnik, Professor of Design of Computation & Computational thinking is influencing research in nearly all disciplines, both in the sciences and the humanities. [The Computer] is changing the way we think. If you want to understand the 21th century then you must first understand computation. Alan Bundy beam vault column frame a new eco-system of consultancies that stabilizes the understanding of structural design in architecture! truss arches cables building elements domes typologies 10 Toni Kotnik, Professor of Design of 5

6 Dominance of Engineering Thinking Engineer: that means analysis and calculation; Constructor: that means synthesis and creative action. Le Corbusier aim: analytic description mathematical models FEM optimization precision of description enables predictability material system economic use of means performance efficiency simulation mathematics science of pattern & order materialized form form DIGITAL matter formed material 11 Toni Kotnik, Professor of Design of Structure /ˈstrʌktʃə/ noun a building or other object constructed from several parts the arrangement of and relations between the parts or elements verb construct or arrange according to a plan give a pattern or organization to physical conceptual level of abstraction 12 Toni Kotnik, Professor of Design of 6

7 Urban Life in the Iron Age Tel Kinrot / Tell el- Orēme Israel, Toni Kotnik, Professor of Design of Urban Life in the Iron Age Tel Kinrot / Tell el- Orēme Israel, Toni Kotnik, Professor of Design of 7

8 Urban Life in the Iron Age when is a stone a stone and when is a stone part of a wall? Tel Kinrot / Tell el- Orēme Israel, Toni Kotnik, Professor of Design of ta mathēmata Imagine the purely physical world. This would have to be a giant aggregate composed of all the physical stuff in the universe. There is nothing nonphysical in this, but most philosophers prefer a less amorphous characterization; they begin with all physical objects, or all particles, or all spacetime points.... To add even this small amount of structure - the differentiation of the amorphous mass into individuals of some kind - is already to broach the mathematical. Penelope Maddy, Realism in Mathematical, 1990 similarity proximity continuation closure symmetry periodicity 16 Toni Kotnik, Professor of Design of basic principles of Gestalt Theory 8

9 ta mathēmata this genuine learning is an extremely peculiar taking, a taking where one who takes only takes what one basically already Mathematics has. The is the mathemata, science of thepatterns mathematical, basedis onthat about bodily things or mental whichperception we alreadyofknow. the surrounding Therefore we world. do not firstmathematics get it out ofis things, a construct but, of in the a certain humanway, brain! we bring it with us. Martin Heidegger: Modern Sciences, Metaphysics, and Mathematics Kasimir Malevich Eight Red Rectangles, Toni Kotnik, Professor of Design of Structuralism design freedom perceive DIGITAL generate diagrammatic mathematics science of pattern & order materialized form descriptive form DIGITAL matter formed material physical necessity 18 Toni Kotnik, Professor of Design of 9

10 formal design in architecture Architects and engineers both claim to be designers, though how they define design and the approaches they use to realize it vary widely. Hanif Kara precision typology principle topology analytic mathematics science of pattern & order synthetic computability correct constructability right 19 Toni Kotnik, Professor of Design of Graphic Statics The most advanced chapters of theory of structures can only be used to check the stability of a structure. They can be used only to analyze numerically a structure already designed, not only in its general outline, but in all its dimensional relations. The formative stage of a design, during which its main characteristics are defined and its qualities and faults are determined once and for all (just as the characteristics of an organism are clearly defined in the embryo), cannot make use of structural theory and must resort to intuition and schematic simplifications Pier Luigi Nervi principle topology constructability right 20 Toni Kotnik, Professor of Design of 10

11 Graphic Statics equilibrium geometric description the forces add up to zero the line of action of the forces intersect in one point x = 0 = y M = 0 analytic description 21 Toni Kotnik, Professor of Design of Graphic Statics tension compression 22 Toni Kotnik, Professor of Design of 11

12 geometric logic of the flow of inner forces the forces add up to zero ( x = 0 = y ) the line of action of the forces intersect in one point ( M = 0 ) reciprocal relationship between form and force 23 Toni Kotnik, Professor of Design of geometric logic of the flow of inner forces topological understanding of relation between form and forces 24 Toni Kotnik, Professor of Design of 12

13 geometric logic of the flow of inner forces building elements of increasing complexity cable arch cable-arch truss slab frame cable net membrane dome shell dome shell space truss plate traditional approach to structural design: typological classification of structure systems 25 Toni Kotnik, Professor of Design of geometric logic of the flow of inner forces essence ETH Structural Design folddesk Zurich, Switzerland, Toni Kotnik, Professor of Design of 13

14 geometric logic of the flow of inner forces essence ETH Structural Design folddesk Zurich, Switzerland, Toni Kotnik, Professor of Design of geometric logic of the flow of inner forces essence ETH Structural Design folddesk Zurich, Switzerland, Toni Kotnik, Professor of Design of 14

15 geometric logic of the flow of inner forces essence ETH Structural Design folddesk Zurich, Switzerland, Toni Kotnik, Professor of Design of geometric logic of the flow of inner forces essence ETH Structural Design folddesk Zurich, Switzerland, Toni Kotnik, Professor of Design of 15

16 ETH Structural Design folddesk Zurich, Switzerland, Toni Kotnik, Professor of Design of Working with basic principles continuum of flow of forces through space 32 Toni Kotnik, Professor of Design of 16

17 Material Behavior Bending 33 Toni Kotnik, Professor of Design of Material Behavior Bending deformation as metabolic process 34 Toni Kotnik, Professor of Design of 17

18 Structural Form The resistant virtues of the structures that we make depend on their form. It is through their form that they are stable and not because of an awkward accumulation of materials. There is nothing more noble and elegant from an intellectual point of view than this, resistance through form. Eladio Dieste 35 Toni Kotnik, Professor of Design of Structural Transformation move mirror the force flow is a flexible pattern that can be adapted to design ideas Redirection 36 Toni Kotnik, Professor of Design of 18

19 Flow Transformation cantilevering canopy, SUTD East Coast Campus, Singapore Toni Kotnik, Professor of Design of basic principle Santiago Calatrava Stadelhofen Railway Station Zurich, Switzerland, Toni Kotnik, Professor of Design of 19

20 Flow Transformation Santiago Calatrava: Stadelhofen Railway Station, Zurich, Switzerland, Toni Kotnik, Professor of Design of Santiago Calatrava Stadelhofen Railway Station Zurich, Switzerland, 1990 Flow Transformation Santiago Calatrava: Stadelhofen Railway Station, Zurich, Switzerland, Toni Kotnik, Professor of Design of Santiago Calatrava Stadelhofen Railway Station Zurich, Switzerland,

21 Flow Transformation Santiago Calatrava: Stadelhofen Railway Station, Zurich, Switzerland, Toni Kotnik, Professor of Design of Santiago Calatrava Stadelhofen Railway Station Zurich, Switzerland, 1990 Flow Transformation 42 Toni Kotnik, Professor of Design of 21

22 Material Accumulation 43 Toni Kotnik, Professor of Design of Material Accumulation Logic of Force Flow redirection material accumulation as metabolic process 44 Toni Kotnik, Professor of Design of 22

23 Design of Form, Force, Matter force material redistribution metabolic process funicular shape form & matter activation of matter amount of material variablity of form spectra of possible shapes amount of material variablity of form activation of form principles of redirection & distribution 45 Toni Kotnik, Professor of Design of Design of Toni Kotnik Professor of Design of Aalto University Department of Architecture Department of Civil Engineering 23

24 Equilibrium the forces add up to zero the line of action of the forces intersect in one point 47 Toni Kotnik, Professor of Design of Equilibrium the forces add up to zero the line of action of the forces intersect in one point force diagram check condition 1 location diagram check condition 2 48 Toni Kotnik, Professor of Design of 24

25 from external loads to inner forces how do forces travel through the building structure? tension force pulling away from subsystem 49 Toni Kotnik, Professor of Design of from external loads to inner forces how do forces travel through the building structure? compression force pushing towards the subsystem 50 Toni Kotnik, Professor of Design of 25

26 geometric logic of the flow of inner forces principle of duality similar pattern of force flow but different structural behaviour! 51 Toni Kotnik, Professor of Design of Solid Material Buckling F F ball-and-spring model of transmission of forces in solid materials -F -F compression tension 52 Toni Kotnik, Professor of Design of 26

27 Solid Material Buckling F F t t ball-and-spring model of transmission of forces in solid materials -F -F buckling of column compression unstable tension stable 53 Toni Kotnik, Professor of Design of Solid Material thick thin F F F F -F -F -F -F compression tension Kenneth Snelson: Needle Tower Washington, USA, 1968 unstable equilibrium stable equilibrium 54 Toni Kotnik, Professor of Design of 27

28 Bending 55 Toni Kotnik, Professor of Design of Redirection move mirror the force flow is a flexible pattern that can be adapted to design ideas From Cantilever to Redirection 56 Toni Kotnik, Professor of Design of 28

29 Redirection 57 Toni Kotnik, Professor of Design of Design of Form, Force, Matter force material redistribution metabolic process funicular shape form & matter activation of matter amount of material variablity of form spectra of possible shapes amount of material variablity of form activation of form principles of redirection & distribution 58 Toni Kotnik, Professor of Design of 29

30 Bracing 59 Toni Kotnik, Professor of Design of Bracing Grimshaw Architects: Airside Center, Zurich Airport, Switzerland, Toni Kotnik, Professor of Design of 30

31 Bracing Norman Foster: Renault Distribution Centre, Swindon, UK, Toni Kotnik, Professor of Design of Bracing Norman Foster: Renault Distribution Centre, Swindon, UK, Toni Kotnik, Professor of Design of 31

32 Stabilization of Form Distribution of forces Why can a beam not be of any length? 63 Toni Kotnik, Professor of Design of EMBT: Renovation, Santa Caterina Market Barcelona, Spain, Toni Kotnik, Professor of Design of 32

33 EMBT: Renovation, Santa Caterina Market Barcelona, Spain, Toni Kotnik, Professor of Design of EMBT: Renovation, Santa Caterina Market Barcelona, Spain, Toni Kotnik, Professor of Design of 33

34 Louis Kahn Kimbell Art Museum Fort Worth, USA, Toni Kotnik, Professor of Design of Louis Kahn Kimbell Art Museum Fort Worth, USA, Toni Kotnik, Professor of Design of 34

35 Louis Kahn Kimbell Art Museum Fort Worth, USA, Toni Kotnik, Professor of Design of Louis Kahn Kimbell Art Museum Fort Worth, USA, Toni Kotnik, Professor of Design of 35

36 Louis Kahn Kimbell Art Museum Fort Worth, USA, Toni Kotnik, Professor of Design of Louis Kahn Kimbell Art Museum Fort Worth, USA, Toni Kotnik, Professor of Design of 36

37 Louis Kahn Kimbell Art Museum Fort Worth, USA, Toni Kotnik, Professor of Design of OOPEAA: Kärsämäki Church Kärsämäki, Finland, Toni Kotnik, Professor of Design of 37

38 OOPEAA: Kärsämäki Church Kärsämäki, Finland, Toni Kotnik, Professor of Design of OOPEAA: Kärsämäki Church Kärsämäki, Finland, Toni Kotnik, Professor of Design of 38

39 OOPEAA: Kärsämäki Church Kärsämäki, Finland, Toni Kotnik, Professor of Design of OOPEAA: Kärsämäki Church Kärsämäki, Finland, Toni Kotnik, Professor of Design of 39

40 Horizontal Load 79 Toni Kotnik, Professor of Design of Generic Solution for Building Structure structural grid 80 Toni Kotnik, Professor of Design of 40

41 Generic Solution for Building Structure structural grid with infill 81 Toni Kotnik, Professor of Design of Generic Solution for Building Structure structural grid with infill as column-plate combination 82 Toni Kotnik, Professor of Design of 41

42 Generic Solution for Building Structure people snow furniture self-weight Every physical being, living and nonliving, has to support its materiality against the various forces that are imposed upon it by its environment. Kotnik, T. & Weinstock, M. Material, Form and Force vertical loads horizontal loads wind earthquake structural grid with infill as column-plate combination 83 Toni Kotnik, Professor of Design of Lateral Stability distribution of horizontal forces in space 84 Toni Kotnik, Professor of Design of 42

43 Lateral Stability distribution of horizontal forces in space: cross-bracing 85 Toni Kotnik, Professor of Design of Lateral Stability distribution of walls in plan 86 Toni Kotnik, Professor of Design of 43

44 Typical Solutions for Lateral Stability 87 Toni Kotnik, Professor of Design of Typical Solutions for Lateral Stability 88 Toni Kotnik, Professor of Design of 44

45 Typical Solutions for Lateral Stability 89 Toni Kotnik, Professor of Design of Typical Solutions for Lateral Stability Five Points Towards A New Architecture Le Corbusier, 1924 The supports The roof gardens The free design of the ground plan The horizontal window The free design of the façade 1. The supports. To solve a problem scientifically means in the first place to distinguish between its elements. Hence in the case of a building a distinction can immediately be made between the supporting and the non-supporting elements. The earlier foundations, on which the building rested without a mathematical check, are replaced by individual foundations and the walls by individual supports. Both supports and support foundations are precisely calculated according to the burdens they are called upon to carry. These supports are spaced out at specific, equal intervals, with no thought for the interior arrangement of the building. They rise directly from the floor to 3, 4, 6, etc. meters and elevate the ground floor. Le Corbusier: Dom-Ino House, prototype, Toni Kotnik, Professor of Design of 45

46 Thinking in First Principles Le Corbusier: Villa Savoye, Poissy, France, Toni Kotnik, Professor of Design of Thinking in First Principles Le Corbusier: Villa Savoye, Poissy, France, Toni Kotnik, Professor of Design of 46

47 Thinking in First Principles Christian Kerez: House with one wall, Zurich, Switzerland, Toni Kotnik, Professor of Design of Thinking in First Principles Christian Kerez: House with one wall, Zurich, Switzerland, Toni Kotnik, Professor of Design of 47

48 Thinking in First Principles Shigeru Ban: Paper House, Lake Yamanaka, Yamanashi, Japan, Toni Kotnik, Professor of Design of Thinking in First Principles Shigeru Ban: Paper House, Lake Yamanaka, Yamanashi, Japan, Toni Kotnik, Professor of Design of 48

49 Thinking in First Principles Toyo Ito: Mediatheque, Sendai, Japan, Toni Kotnik, Professor of Design of Thinking in First Principles Toyo Ito: Mediatheque, Sendai, Japan, Toni Kotnik, Professor of Design of 49

50 Thinking in First Principles Toyo Ito: Mediatheque, Sendai, Japan, Toni Kotnik, Professor of Design of Thinking in First Principles Toyo Ito: Mediatheque, Sendai, Japan, Toni Kotnik, Professor of Design of 50

51 Thinking in First Principles Michael de Haas: Aluminum Center of Netherlands, Houten, Netherlands, Toni Kotnik, Professor of Design of Thinking in First Principles Michael de Haas: Aluminum Center of Netherlands, Houten, Netherlands, Toni Kotnik, Professor of Design of 51

52 Cantilever Frank Lloyd Wright: Kaufman House Bear Run, USA, Toni Kotnik, Professor of Design of Cantilever ideal cantilever real cantilever stiffening of cantilever 104 Toni Kotnik, Professor of Design of 52

53 Stabilization by Material Accumulation 105 Toni Kotnik, Professor of Design of Stabilization by Form 106 Toni Kotnik, Professor of Design of 53

54 Structural Form The resistant virtues of the structures that we make depend on their form. It is through their form that they are stable and not because of an awkward accumulation of materials. There is nothing more noble and elegant from an intellectual point of view than this, resistance through form. Eladio Dieste 107 Toni Kotnik, Professor of Design of Form in 3d Gaussian Curvature Κ = Κ 1 Κ 2 Gaussian curvature is the product of the principal curvature and is a measurement of the local behaviour of the surface Κ < 0 hyperbolic point curves in opposite direction Κ = 0 parabolic point at least one curve is flat Κ > 0 elliptic point curves in same direction Κ > 0 elliptic point prototype: sphere Κ = 0 parabolic point prototype: cylinder 108 Toni Kotnik, Professor of Design of Κ < 0 hyperbolic point prototype: hyperboloid 54

55 Form in 3d Gaussian Curvature Κ = Κ 1 Κ 2 Gaussian curvature is the product of the principal curvature and is a measurement of the local behaviour of the surface Κ < 0 hyperbolic point curves in opposite direction Κ = 0 parabolic point at least one curve is flat Κ > 0 elliptic point curves in same direction Κ > 0 elliptic point prototype: sphere Κ > 0 elliptic point collection of arches Κ > 0 elliptic point collection of cables 109 Toni Kotnik, Professor of Design of Form in 3d Gaussian Curvature Κ = Κ 1 Κ 2 Gaussian curvature is the product of the principal curvature and is a measurement of the local behaviour of the surface Κ < 0 hyperbolic point curves in opposite direction Κ = 0 parabolic point at least one curve is flat Κ > 0 elliptic point curves in same direction Κ = 0 parabolic point prototype: cylinder Κ = 0 parabolic point collection of arch & beam Κ = 0 parabolic point collection of cable & beam 110 Toni Kotnik, Professor of Design of 55

56 Form in 3d Gaussian Curvature Κ = Κ 1 Κ 2 Gaussian curvature is the product of the principal curvature and is a measurement of the local behaviour of the surface Κ < 0 hyperbolic point curves in opposite direction Κ = 0 parabolic point at least one curve is flat Κ > 0 elliptic point curves in same direction Κ < 0 hyperbolic point prototype: hyperboloid Κ < 0 hyperbolic point combination of arch & cable 111 Toni Kotnik, Professor of Design of Form in 3d Gaussian Curvature bracing effect cable & arch stabilize each other in a hyperbolic point hyperbolic points stiffen a surface Κ < 0 hyperbolic point prototype: hyperboloid 112 Toni Kotnik, Professor of Design of 56

57 Hyperbolic Surface in Nature Imogen Cunnigham: Calla Lilly, before Toni Kotnik, Professor of Design of Hyperbolic Surface in Architecture Hyperbolic paraboloid 114 Toni Kotnik, Professor of Design of 57

58 Hyperbolic Surface in Architecture Félix Candela: Lomas de Cuernavaca Chapel Morelos, Mexico, Toni Kotnik, Professor of Design of Hyperbolic Surface in Architecture Félix Candela: Lomas de Cuernavaca Chapel Morelos, Mexico, 1959 Félix Candela: Lomas de Cuernavaca Chapel, Morelos, Mexico, Toni Kotnik, Professor of Design of 58

59 Hyperbolic Surface in Architecture Félix Candela: Lomas de Cuernavaca Chapel Morelos, Mexico, 1959 Félix Candela: Lomas de Cuernavaca Chapel, Morelos, Mexico, Toni Kotnik, Professor of Design of Hyperboloid as Ruled Surface Carlo Aiello Design Studio The Parabolic Chair, Toni Kotnik, Professor of Design of 59

60 Hyperbolic Paraboloid Modularization 119 Toni Kotnik, Professor of Design of Hyperbolic Paraboloid Modularization 120 Toni Kotnik, Professor of Design of 60

61 Hyperbolic Paraboloid Modularization 121 Toni Kotnik, Professor of Design of Hyperbolic Paraboloid Modularization 122 Toni Kotnik, Professor of Design of 61

62 Hyperbolic Paraboloid Modularization 123 Toni Kotnik, Professor of Design of Hyperbolic Paraboloid Modularization 124 Toni Kotnik, Professor of Design of 62

63 Hyperbolic Paraboloid Modularization Félix Candela: Coyocán Market, Mexico City, Mexico, 1955 Félix Candela: High Life Textile Factory, Mexico City, Mexico, Toni Kotnik, Professor of Design of Hyperbolic Paraboloid Transformation Félix Candela: Factory Gate, Lederle Laboratories, Mexico City, Mexico, Toni Kotnik, Professor of Design of 63

64 Hyperbolic Paraboloid Transformation 127 Toni Kotnik, Professor of Design of Hyperbolic Paraboloid Transformation 128 Toni Kotnik, Professor of Design of 64

65 Félix Candela: Church of Our Lady of the Miraculous Medal, Mexico City, Mexico, Toni Kotnik, Professor of Design of Félix Candela: Church of Our Lady of the Miraculous Medal, Mexico City, Mexico, Toni Kotnik, Professor of Design of 65

66 Hyperbolic Paraboloid Transformation Félix Candela: Church of Our Lady of the Miraculous Medal Mexico City, Mexico, Toni Kotnik, Professor of Design of Félix Candela: Church of Our Lady of the Miraculous Medal, Mexico City, Mexico, Toni Kotnik, Professor of Design of 66

67 Hyperboloid as Ruled Surface Le Corbusier & Iannis Xenakis: Philips Pavilion, World s Fair Expo, Brussels, Toni Kotnik, Professor of Design of Hyperboloid as Ruled Surface Le Corbusier & Iannis Xenakis: Philips Pavilion, World s Fair Expo, Brussels, Toni Kotnik, Professor of Design of 67

68 Hyperboloid as Ruled Surface Le Corbusier & Iannis Xenakis: Philips Pavilion, World s Fair Expo, Brussels, Toni Kotnik, Professor of Design of Hyperboloid as Ruled Surface Edgrad Varèse: Poème électronique, score 136 Toni Kotnik, Professor of Design of 68

69 Thanks! 69