Architectuur en constructie: bouwsystemen
Inhoudstafel
1) Equilibrium
1. What is a structure?
2. What is a load?
3. What is equilibrium?
I. Equilibrium of many forces
II. Inner forces
2) Cables
1. Cremona diagram
2. Form and forces
3. Cable form
4. Variations
5. Stabilisation
6. Cables/arches
I. Cable design
II. Cable design variation
III. Cable nets and membranes
IV. Arch duality
3) Arches
1. Arch development
2. Stabilisation
I. Stability with irregular loads
II. Stability measures
III. Force control through hinges
IV. Circular arches
3. Barrel vaults
4. Groined & cloister vaults
5. Domes
6. Shells
I. Descrete spacial arch structures
4) Arch-cables
1. Arch-cables
2. Load distribution
3. Arch-cable form
4. Cantilever
I. Introduction
II. Variation
5. Combinations
6. Spatial arch-cables
5) Trusses
1. Introduction
2. Types
3. Asymmetrical load
4. Spatial trusses
6) Beams and frames
1. Beams
2. Frames
3. Spatial beams
4. Slabs
5. Walls
I. Walls and horizontal loads
7) Combined systems
1. Forces in surface elements
2. Combinations
1
, 1) Equilibrium
1.1 What is a structure?
o System of physical components organised to take all loads of a building safely to the ground and to always
ensure stability
– Components: part of the architecture, silently in the background, …. Always different options
Arches, beams, cables, walls, …
– Loads: something acting on our building and need to take it down to the ground
1.2 What is a load
o Free vectors, not bound, orientation and direction, intensity (length)
o Bound vectors: forces acting on a specific point
– Point and line of action
o Gravitational forces: from the centre of planet earth
– Attractive forces: for example the moon
– We have our own mass and centre point
Relationship between any object with a mass and the centre of the earth
o External forces: example balcony
– Permanent load: self-weight of balcony (dead load)
– Not permanent: people, furniture, … (live load)
– Snow load, wind load, earthquake loads, impact loads, …
1.3 What is equilibrium
o Two forces are working on each other
– External support force for a subsystem
– Action = reaction (Newton)
o In force diagram forces graphically summed neglecting point of action
o Equilibrium if:
– forces have same intensity and opposite direction in form diagram i.e. vectors neutralise each other
– forces are on the same line of action in form diagram
o No equilibrium if:
– no reaction force (translation) lines of action not matching (rotation)
1.3.1 Equilibrium of many forces
o Example: tree being pushed by the wind
– Wind and gravity meet in one point
– End of one force is starting point of other force -> resultant connects point of action from the first force
with ending point of last force
o Example: two parallel forces
– Sum them up
F2 a
– Position resultant unknown: follows relation between intensity of force =
F1 b
2
, o Example: 3 forces
– Crossing each other but not in one point
– Resultant of F1 and F2
– Total resultant in intersection of R12 and F3
o Example: 3 parallel forces
– First R12 and choose a arbitrary point for geometrical relations (P1)
– Bring in F3 and R12 together for P2
– Or choose one arbitrary point for all forces
Connect all force lines and cross the first and last inclination
1.3.2 Inner forces
o Reactions to external forces
o Tension or compression
2) Cables
2.1 Cremona diagram
o Implementation of all the forces
o Equilibrium requires closed force diagram
o Subsystems
– Node of load: closed force diagram
– Cables
3
Inhoudstafel
1) Equilibrium
1. What is a structure?
2. What is a load?
3. What is equilibrium?
I. Equilibrium of many forces
II. Inner forces
2) Cables
1. Cremona diagram
2. Form and forces
3. Cable form
4. Variations
5. Stabilisation
6. Cables/arches
I. Cable design
II. Cable design variation
III. Cable nets and membranes
IV. Arch duality
3) Arches
1. Arch development
2. Stabilisation
I. Stability with irregular loads
II. Stability measures
III. Force control through hinges
IV. Circular arches
3. Barrel vaults
4. Groined & cloister vaults
5. Domes
6. Shells
I. Descrete spacial arch structures
4) Arch-cables
1. Arch-cables
2. Load distribution
3. Arch-cable form
4. Cantilever
I. Introduction
II. Variation
5. Combinations
6. Spatial arch-cables
5) Trusses
1. Introduction
2. Types
3. Asymmetrical load
4. Spatial trusses
6) Beams and frames
1. Beams
2. Frames
3. Spatial beams
4. Slabs
5. Walls
I. Walls and horizontal loads
7) Combined systems
1. Forces in surface elements
2. Combinations
1
, 1) Equilibrium
1.1 What is a structure?
o System of physical components organised to take all loads of a building safely to the ground and to always
ensure stability
– Components: part of the architecture, silently in the background, …. Always different options
Arches, beams, cables, walls, …
– Loads: something acting on our building and need to take it down to the ground
1.2 What is a load
o Free vectors, not bound, orientation and direction, intensity (length)
o Bound vectors: forces acting on a specific point
– Point and line of action
o Gravitational forces: from the centre of planet earth
– Attractive forces: for example the moon
– We have our own mass and centre point
Relationship between any object with a mass and the centre of the earth
o External forces: example balcony
– Permanent load: self-weight of balcony (dead load)
– Not permanent: people, furniture, … (live load)
– Snow load, wind load, earthquake loads, impact loads, …
1.3 What is equilibrium
o Two forces are working on each other
– External support force for a subsystem
– Action = reaction (Newton)
o In force diagram forces graphically summed neglecting point of action
o Equilibrium if:
– forces have same intensity and opposite direction in form diagram i.e. vectors neutralise each other
– forces are on the same line of action in form diagram
o No equilibrium if:
– no reaction force (translation) lines of action not matching (rotation)
1.3.1 Equilibrium of many forces
o Example: tree being pushed by the wind
– Wind and gravity meet in one point
– End of one force is starting point of other force -> resultant connects point of action from the first force
with ending point of last force
o Example: two parallel forces
– Sum them up
F2 a
– Position resultant unknown: follows relation between intensity of force =
F1 b
2
, o Example: 3 forces
– Crossing each other but not in one point
– Resultant of F1 and F2
– Total resultant in intersection of R12 and F3
o Example: 3 parallel forces
– First R12 and choose a arbitrary point for geometrical relations (P1)
– Bring in F3 and R12 together for P2
– Or choose one arbitrary point for all forces
Connect all force lines and cross the first and last inclination
1.3.2 Inner forces
o Reactions to external forces
o Tension or compression
2) Cables
2.1 Cremona diagram
o Implementation of all the forces
o Equilibrium requires closed force diagram
o Subsystems
– Node of load: closed force diagram
– Cables
3
