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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
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
Lecture 2ARK-A3001
3.11.2020
3
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
Lecture 2ARK-A3001
3.11.2020
4
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
Lecture 2ARK-A3001
3.11.2020
5
Toni Kotnik, Professor of Design of Structures
R
F1F2
Lecture 2ARK-A3001
3.11.2020
6
Toni Kotnik, Professor of Design of Structures
R
F1
F2
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
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
Lecture 2ARK-A3001
3.11.2020
9
Toni Kotnik, Professor of Design of Structures
tensionforce pulling away from subsystem
Inner Force
Lecture 2ARK-A3001
3.11.2020
10
Toni Kotnik, Professor of Design of Structures
compressionforce pushing towards the subsystem
Inner Force
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
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
Lecture 2ARK-A3001
3.11.2020
13
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.
Lecture 2ARK-A3001
3.11.2020
14
Toni Kotnik, Professor of Design of Structures
R
location plan
force plan
S1
S2
R
Equilibriumcable
S2
S1
Lecture 2ARK-A3001
3.11.2020
15
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
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
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
Lecture 2ARK-A3001
3.11.2020
18
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
Lecture 2ARK-A3001
3.11.2020
19
Toni Kotnik, Professor of Design of Structures
Equilibriumcable
Lecture 2ARK-A3001
3.11.2020
20
Toni Kotnik, Professor of Design of Structures
Equilibriumcable
Alvaro Siza: Expo-PavilionLisbon, Portugal, 1998
Lecture 2ARK-A3001
3.11.2020
21
Toni Kotnik, Professor of Design of Structures
Alvaro Siza: Expo-PavilionLisbon, Portugal, 1998
Lecture 2ARK-A3001
3.11.2020
22
Toni Kotnik, Professor of Design of Structures
Alvaro Siza: Expo-PavilionLisbon, Portugal, 1998
Lecture 2ARK-A3001
3.11.2020
23
Toni Kotnik, Professor of Design of Structures
Eero Saarinen: Dulles AirportWashington, USA, 1962
Lecture 2ARK-A3001
3.11.2020
24
Toni Kotnik, Professor of Design of Structures
Eero Saarinen: Dulles AirportWashington, USA, 1962
Lecture 2ARK-A3001
3.11.2020
25
Toni Kotnik, Professor of Design of Structures
Principle of Duality
cable
arch
only tension as inner foces
only compression as inner foces
Lecture 2ARK-A3001
3.11.2020
26
Toni Kotnik, Professor of Design of Structures
Principle of Duality
cable
arch
only tension as inner foces
only compression as inner foces
Lecture 2ARK-A3001
3.11.2020
27
Toni Kotnik, Professor of Design of Structures
Antoni Gaudi: hanging modelSagrada Familia, Barcelona, Spain
around 1889
Principle of Duality
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
Lecture 2ARK-A3001
3.11.2020
29
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
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
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
Lecture 2ARK-A3001
3.11.2020
32
Toni Kotnik, Professor of Design of Structures
Heinz Isler: study of variations
Principle of Duality
Lecture 2ARK-A3001
3.11.2020
33
Toni Kotnik, Professor of Design of Structures
Heinz Isler: Wyss Garden CenterSolothurn, Switzerland, 1962
Principle of Duality
Lecture 2ARK-A3001
3.11.2020
34
Toni Kotnik, Professor of Design of Structures
Heinz Isler: GasstationDeitingen, Switzerland, 1968
Principle of Duality
Lecture 2ARK-A3001
3.11.2020
35
Toni Kotnik, Professor of Design of Structures
Heinz Isler: Sicli FactoryGeneva, Switzerland, 1969
Principle of Duality
Lecture 2ARK-A3001
3.11.2020
36
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
Lecture 2ARK-A3001
3.11.2020
37
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
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