structural design i - eth z
TRANSCRIPT
1
Structural Design I
2
Course overview
Structural design I Structural design II
Structural design I+II
1. Introduction
2. Equilibrium and graphic static
3.+4. Cables
5. Cablenets and membranes
7. Arches
8.+9. Vaults, domes and shells
11. Spatial arch-cable-structures
10. Arch-cable-structures
6. Materials and dimensioning
12. +13. Trusses 15.+16. Beams and frames
17. Spatial beams14. Spatial trusses
19. Columns
18. Bending
3Structural design I
Cable structures
A cable’s reaction to a single loadRelation between form and forces in cablesResultant of a set of forces A cable’s reaction to a set of nonconcurrent loadsA cable’s reaction to uniformly distributed loads
4A cable’s reaction to a single force
L/2L/2
BA
F
B
F
A2
2 1
1
5A cable’s reaction to a single force
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
L/2 L/2
h
B
v Bh
BA
h
F
BA
A
v v
B
F
B
h
A
A
A v2
2
1
1
6A cable’s reaction to a single force
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
7
Cable structures
A cable’s reaction to a single loadRelation between form and forces in cablesResultant of a set of forces A cable’s reaction to a set of nonconcurrent loadsA cable’s reaction to uniformly distributed loads
L/2L/2
L/2 L/2
F
F
A BB
A
2F
BA
2F
A
B
2
2
2
2
1
1
1
1
8Relation between form and forces in cables
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
L/2
L/2
L/2
L/2
A
B
F
A
B
F
A B
F
A B
F
2
2
2
2
1
1
1
1
9Relation between form and forces in cables
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
1/4 L
L/2L/2
3/4 L
F
A
B
A
B
F
A B
F
AB
F
2
22
2
1
1
1
1
10Relation between form and forces in cables
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
L/2L/2
F
B
A
F
BA
A
B
F
A B
F
2
2
2
2 1
1
1
1
1
11Relation between form and forces in cables
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
H
F1
F2A
B
1F2F
B
A
2
3
4
5
2
4
3
5
1
1
12Relation between form and forces in cables
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
H
F2
F1
B
A
A
B
F2 F1
24
3
5
1
13Relation between form and forces in cables
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
H
A
R
B
1F
2F
1F2F
B
A
24
3
5
1
14Relation between form and forces in cables
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
H
R
B
A
FF
B
2 1
A
R
24
3
5
1
15Relation between form and forces in cables
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
eQ
16Relation between form and forces in cables
H 1
A
B
F
F
F
F
F
V
IV
III
II
I
A B
IIIIIIIV
V
FFFFF
17Relation between form and forces in cables
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
18Relation between form and forces in cables
Schlaich Bergermann: Factory building, Dachwig, 1993
2
1
H
H
I
IIIIIIV
V
A BV
IV
III
II
I
A
B
F
F
F
F
F
F F F F F
19Relation between form and forces in cables
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
20Relation between form and forces in cables
Schlaich Bergermann: Pedestrian bridge, Bad Windsheim, 1988
H
1
3
H
V
IV
III
II
I
F
F
F
F
A
B
F
I
IIIII
IV
V
A B
F
FF
F
F
21Relation between form and forces in cables
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
22Relation between form and forces in cables
Julia Bohn: Pedestrian bridge, München, 1992
23Relation between form and forces in cables
Lord Norman Foster: Renault Center, Swindon, 1983
24Relation between form and forces in cables
Lord Norman Foster: Renault Center, Swindon, 1983
25
Cable structures
A cable’s reaction to a single loadRelation between form and forces in cablesResultant of a set of forces A cable’s reaction to a set of nonconcurrent loadsA cable’s reaction to uniformly distributed loads
R
Q
G R
Q
G
26Resultant of a set of forces
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
2
5F
F6
F4
F3
F
1F
R
3F
5F1F
6F
F4
F2
R
F4
5F
6F
1FF2 3F
R
27Resultant of a set of forces
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
F
1-2
1-2
F3F21
R
2F
F1
R
28Resultant of a set of forces
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
1-2
1-2
R1-2-3 = R
F
1-2
3F21F
R
2F
F1
R
R
3F
R
29Resultant of a set of forces
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
1F F3F2
30
Form diagramScale 1 : 100
Resultant of a set of forces
1F
F2
3F
R
1F F32F
31
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
Resultant of a set of forces
o' R
F3
2F
F1
3FF1 F2
32
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
Resultant of a set of forces
1F F2
o'
1F
F2
3F
R3F 3
4
2
1
33
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
Resultant of a set of forces
1F F32F
o'
1F
F2
3F
R
3
3
4
4
2
2
11
34
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
Resultant of a set of forces
R
1 23F FF
R
F3
2F
F1
o'3
3
4
4
2
2
11
35
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
Resultant of a set of forces
1F2F
R
1-2R
2F
F1
o'
1-2
3
3
4
4
2
2
36
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
Resultant of a set of forces
R
1F F
1-2
R
32F
1-2
o'
1F
F2
3F
R
R
3
3
4
4
2
2
1 1
37
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
Resultant of a set of forces
eQ
38Resultant of a set of forces
39
Cable structures
A cable’s reaction to a single loadRelation between form and forces in cablesResultant of a set of forces A cable’s reaction to a set of nonconcurrent loadsA cable’s reaction to uniformly distributed loads
r'''
Ro'''o''
R
3F
2F
F1
r''
40
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
A cable’s reaction to a set of nonconcurrent loads
F
F1
R
F3
2F
F1
r''
R
3F
r'''
o'' o'''
2
41
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
A cable’s reaction to a set of nonconcurrent loads
o'''1
o''
r''
R
CS
F3
2
F
1
F
R
F
F
r'''
CS
i
3
F
2
42
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
A cable’s reaction to a set of nonconcurrent loads
3 o'''
F
F
R
F
2
F
r'''
r''
o''
CS
CS i
1
R
3
2F
F1
43
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
A cable’s reaction to a set of nonconcurrent loads
o'''
o''CS II
F F
R
1
F
R
3
r''
r'''
R
CS I
CS II
iCS I
2
44
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
A cable’s reaction to a set of nonconcurrent loads
F
o''
o'''
CS II
1
R
F
r'''
r''
CS I
CS I
CS II
i
3F
F3
2F
F1
R
2
45
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
A cable’s reaction to a set of nonconcurrent loads
eQ
46A cable’s reaction to a set of nonconcurrent loads
47
Cable structures
A cable’s reaction to a single loadRelation between form and forces in cablesResultant of a set of forces A cable’s reaction to a set of nonconcurrent loadsA cable’s reaction to uniformly distributed loads
L/4
L/8
L/4L/4
L/8L/8
L/2
L/4
L/8
L/2
L/8 L/8
L
L/8 L/8
B A
A B
A AB
A
B
AA
B
B
B
B
A
F
F
F/2
F/2
F/4
F/8
F/4
F/8
48A cable’s reaction to uniformly distributed loads
L/8 L/8
h
L/8
h
L/8
L
L/8 L/8L/8 L/8
F/8
B
B A
A
B
A B
A
q = F/L
F/8
F
49A cable’s reaction to uniformly distributed loads
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
Eero Saarinen: Dulles International Airport, Washington, 1962
50A cable’s reaction to uniformly distributed loads
Eero Saarinen: Dulles International Airport, Washington, 1962
51A cable’s reaction to uniformly distributed loads
Eero Saarinen: Dulles International Airport, Washington, 1962
52A cable’s reaction to uniformly distributed loads
Eero Saarinen: Dulles International Airport, Washington, 1962
53A cable’s reaction to uniformly distributed loads
x
L
x
s
xx x xx x x
L
x
A B BA
54A cable’s reaction to uniformly distributed loads
ParabolaCatenary
LL
55A cable’s reaction to uniformly distributed loads
Parabola
Parabola
Catenary
Catenary
„same length“
xx x
L
xxx x xxx
BA
A
B
56A cable’s reaction to uniformly distributed loads
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
L
xxx xx xx xx x
BA
B
A
57A cable’s reaction to uniformly distributed loads
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
eQ
58A cable’s reaction to uniformly distributed loads
L/2x
f
x
f
L/2
R
A
B
q
R
A
B
SC
59A cable’s reaction to uniformly distributed loads
eQ
60A cable’s reaction to uniformly distributed loads
61A cable’s reaction to uniformly distributed loads
62A cable’s reaction to uniformly distributed loads
Alvaro Siza: Expo Pavillion of Portugal, Lissabon, 1998
63
Suspension bridge, Zanskar, India
A cable’s reaction to uniformly distributed loads
64
Inka Q‘eswachaka bridge, Peru, 2010
A cable’s reaction to uniformly distributed loads
65
Inka Q‘eswachaka bridge, Peru, 2010
A cable’s reaction to uniformly distributed loads
66
Inka Q‘eswachaka bridge, Peru, 2010
A cable’s reaction to uniformly distributed loads
67
Inka Q‘eswachaka bridge, Peru, 2010
A cable’s reaction to uniformly distributed loads
68A cable’s reaction to uniformly distributed loads
Othmar Ammann: Golden Gate Bridge, San Francisco, 1937
69A cable’s reaction to uniformly distributed loads
70A cable’s reaction to uniformly distributed loads
71A cable’s reaction to uniformly distributed loads
72A cable’s reaction to uniformly distributed loads
73A cable’s reaction to uniformly distributed loads
Othmar Ammann: Golden Gate Bridge, San Francisco, 1937
74A cable’s reaction to uniformly distributed loads
L
b
b bL
L
L
b
L
= q * bqq
Q = q * L * 1/2Q
75A cable’s reaction to uniformly distributed loads
Area load[kN/m2]
Line load[kN/m]
Point load[kN]
eQ
76A cable’s reaction to uniformly distributed loads