ark-a3001 design of structures basics form & force toni …...heinz isler: new shapes of shells....
TRANSCRIPT
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Lecture 2ARK-A3001
3.11.2020
1
Toni Kotnik, Professor of Design of Structures
ARK-A3001 Design of Structures_BasicsForm & Force
Toni KotnikProfessor of Design of Structures
Aalto UniversityDepartment of Architecture
Department of Civil Engineering
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Lecture 2ARK-A3001
3.11.2020
2
Toni Kotnik, Professor of Design of Structures
ARK-A3001 Design of Structures_BasicsEquilibrium
Toni KotnikProfessor of Design of Structures
Aalto UniversityDepartment of Architecture
Department of Civil Engineering
Load cases
dead load
live load
environmental load
distributed load
point load
equilibrium
location plan
force plan
resultant force
lever principle
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Lecture 2ARK-A3001
3.11.2020
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Toni Kotnik, Professor of Design of Structures
Basic Operation with Forces
two forces can be addedinto one resulting force
F1
F2R
one force can be separated into two force
R F1
F2
Load cases
dead load
live load
environmental load
resultant force distribute forces to specific points
basic idea: building structure as a possibility to guideforces in space according to design interest
compress expand
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Lecture 2ARK-A3001
3.11.2020
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Toni Kotnik, Professor of Design of Structures
location plan force plan
F1
F2
distribute forces to specific points
R
R
F1
F2
R
F1
F2
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Lecture 2ARK-A3001
3.11.2020
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Toni Kotnik, Professor of Design of Structures
R
F1F2
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Lecture 2ARK-A3001
3.11.2020
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Toni Kotnik, Professor of Design of Structures
R
F1
F2
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Lecture 2ARK-A3001
3.11.2020
7
Toni Kotnik, Professor of Design of Structures
R
F2
F1
F2
-F2
F2
the forces add up to zerothe line of action of the forces intersect in one point
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Lecture 2ARK-A3001
3.11.2020
8
Toni Kotnik, Professor of Design of Structures
R
F1F2
F2
-F2
For a building structure to be in equlibrium means that every part of the structure is in equilibrium
each load is producing forces inside the material of the structure, so-called inner forces
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Lecture 2ARK-A3001
3.11.2020
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Toni Kotnik, Professor of Design of Structures
tensionforce pulling away from subsystem
Inner Force
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Lecture 2ARK-A3001
3.11.2020
10
Toni Kotnik, Professor of Design of Structures
compressionforce pushing towards the subsystem
Inner Force
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Lecture 2ARK-A3001
3.11.2020
11
Toni Kotnik, Professor of Design of Structures
R
F1F2
F2
-F2
each load is producing forces inside the material of the structure, so-called inner forces
tensionforce pulling away from subsystem
Inner Force
![Page 12: ARK-A3001 Design of Structures Basics Form & Force Toni …...Heinz Isler: New Shapes of Shells. IASS Conference, Madrid, 1955. Principle of Duality. Lecture 2 ARK-A3001 3.11.2020](https://reader035.vdocument.in/reader035/viewer/2022070216/611e4473a81ee73e1578881d/html5/thumbnails/12.jpg)
Lecture 2ARK-A3001
3.11.2020
12
Toni Kotnik, Professor of Design of Structures
R
Inner Force
location plan
force plan
F1
F2
R
F2y
F2x
F2
F2x
F2y
at 1
2
1
at 2
F1
F2
R
F2x
F2y
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Lecture 2ARK-A3001
3.11.2020
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Toni Kotnik, Professor of Design of Structures
single / double load
single / double deviation
uneven load condition
skewed load condition
Equilibriumcable
The form of a building structure is closely tight to the magnitude and direction of forces in the structure.
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Lecture 2ARK-A3001
3.11.2020
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Toni Kotnik, Professor of Design of Structures
R
location plan
force plan
S1
S2
R
Equilibriumcable
S2
S1
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Lecture 2ARK-A3001
3.11.2020
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Toni Kotnik, Professor of Design of Structures
1
R
location plan
force plan
2
R
Equilibriumcable
F1
F2
F1
F2
S2
S1
S1
S2
1
2
in equilibrium in equilibrium
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Lecture 2ARK-A3001
3.11.2020
16
Toni Kotnik, Professor of Design of Structures
1
location plan
force plan
2
Equilibriumcable
F1
F2
F1
F2
S2
S1
S1
S2
1
2
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Lecture 2ARK-A3001
3.11.2020
17
Toni Kotnik, Professor of Design of Structures
1
location plan
force plan
2
Equilibriumcable
F1
F2
F1
F2
S2
S1
S1
S2R
R
Step 1: construct R in force plan and location planStep 2: construct support forces S1 & S2
Step 3: construct inner forces in force planStep 4: use this inner forces to construct inflection pointsStep 5: use inflection points to construct cable
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Lecture 2ARK-A3001
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Toni Kotnik, Professor of Design of Structures
the forces add up to zerothe line of action of the forces intersect in one point
( ∑x = 0 = ∑y ) ( ∑M = 0 )
Equilibriumcable
reciprocal relationship between form of cable and forces at support
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Lecture 2ARK-A3001
3.11.2020
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Toni Kotnik, Professor of Design of Structures
Equilibriumcable
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Lecture 2ARK-A3001
3.11.2020
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Toni Kotnik, Professor of Design of Structures
Equilibriumcable
Alvaro Siza: Expo-PavilionLisbon, Portugal, 1998
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Lecture 2ARK-A3001
3.11.2020
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Toni Kotnik, Professor of Design of Structures
Alvaro Siza: Expo-PavilionLisbon, Portugal, 1998
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Lecture 2ARK-A3001
3.11.2020
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Toni Kotnik, Professor of Design of Structures
Alvaro Siza: Expo-PavilionLisbon, Portugal, 1998
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Lecture 2ARK-A3001
3.11.2020
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Toni Kotnik, Professor of Design of Structures
Eero Saarinen: Dulles AirportWashington, USA, 1962
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Lecture 2ARK-A3001
3.11.2020
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Toni Kotnik, Professor of Design of Structures
Eero Saarinen: Dulles AirportWashington, USA, 1962
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Lecture 2ARK-A3001
3.11.2020
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Toni Kotnik, Professor of Design of Structures
Principle of Duality
cable
arch
only tension as inner foces
only compression as inner foces
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Lecture 2ARK-A3001
3.11.2020
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Toni Kotnik, Professor of Design of Structures
Principle of Duality
cable
arch
only tension as inner foces
only compression as inner foces
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Lecture 2ARK-A3001
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Toni Kotnik, Professor of Design of Structures
Antoni Gaudi: hanging modelSagrada Familia, Barcelona, Spain
around 1889
Principle of Duality
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Lecture 2ARK-A3001
3.11.2020
28
Toni Kotnik, Professor of Design of Structures
Antoni Gaudi: hanging modelSagrada Familia, Barcelona, Spain
around 1889
Principle of Duality
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Lecture 2ARK-A3001
3.11.2020
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Toni Kotnik, Professor of Design of Structures
Pneumatic Membrane Hanging Form Flow Form
Heinz Isler: New Shapes of ShellsIASS Conference, Madrid, 1955
Principle of Duality
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Lecture 2ARK-A3001
3.11.2020
30
Toni Kotnik, Professor of Design of Structures
Heinz Isler: experimental setup for form-finding of hanging forms
Principle of Duality
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Lecture 2ARK-A3001
3.11.2020
31
Toni Kotnik, Professor of Design of Structures
Heinz Isler: experimental setup for form-finding of hanging forms
Principle of Duality
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Lecture 2ARK-A3001
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Toni Kotnik, Professor of Design of Structures
Heinz Isler: study of variations
Principle of Duality
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Lecture 2ARK-A3001
3.11.2020
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Toni Kotnik, Professor of Design of Structures
Heinz Isler: Wyss Garden CenterSolothurn, Switzerland, 1962
Principle of Duality
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Toni Kotnik, Professor of Design of Structures
Heinz Isler: GasstationDeitingen, Switzerland, 1968
Principle of Duality
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Toni Kotnik, Professor of Design of Structures
Heinz Isler: Sicli FactoryGeneva, Switzerland, 1969
Principle of Duality
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Lecture 2ARK-A3001
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Toni Kotnik, Professor of Design of Structures
ARK-A3001 Design of Structures_BasicsForm & Force
Toni KotnikProfessor of Design of Structures
Aalto UniversityDepartment of Architecture
Department of Civil Engineering
Inner Forces
tension
compression
form & inner forces are coupled
inner forces act upon material
cable as tension-only structure
arch as compression-only structure
principle of duality
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Toni Kotnik, Professor of Design of Structures
Exercise 2.1
F1
F2
F3
Construct a cable (a) and an arch (b) as equilibrium solution for the given three forces F1, F2 and F3. How is the form changing if F1 is doubled?
location plan