structural design i - eth z · pdf filearches and cables - an inverted principle wilhelm...
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Structural Design I
05.11.2015
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Course overview
Structural design I Structural design II
Structural design I+II
1. Introduction
2. Equilibrium and graphic static
3.+4. Cables
5. Cable-net and membrane struc-tures
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
Arches
Arches and cables - an inverted principleThrust lineStiffening of arches by using prestressConcepts for stabilization Construction of thrust linesSpacial profiling
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Arches and cables - an inverted principle
Wilhelm Riphahn, Fritz Leonhardt: Mülheimer bridge, Cologne, 1951
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Arches and cables - an inverted principle
Robert Maillart: Valtschielbachbridge, Donath, 1925
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B
Q
A
Q Q Q Q Q Q Q Q Q Q Q Q Q
BA
Q Q Q Q Q Q Q Q Q Q Q Q
Arches and cables - an inverted principle 6
Arches and cables - an inverted principle
Gerd Lohmer, Fischer, Fritz Leonhardt: Severin bridge, Cologne, 1959
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A B
B
A BB
F
AF
A
F
F
Arches and cables - an inverted principle 8
1
B
1
1 2
2
22
1
A
Q
Q
Q
Q
Q
Q Q Q Q
QQQQQ
B
A
Q
Q
Q
Q
Q
A B
BA
Q
Arches and cables - an inverted principle 9
Q Q
Q
Q
Q1B
A
2
2 1Q
AQ
Q
B
2
Q
2
A B1
A
Q
B
1
Q
Arches and cables - an inverted principle 10
Q Q Q Q
Q
2
Q
v1B
B2A
1A
Q
QQQQ
2H
H1
v2
v1
H
H1
Q
Q
Q
Q
Q
Q
Q
Q
QA 1
A 2
B
Bv2
Arches and cables - an inverted principle 11
2
F1A
F
A
B
1F
2F
F 2
21
B1
22
11
A
2F1F
B
1F 2
BA
Arches and cables - an inverted principle 12
Arches
Arches and cables - an inverted principleThrust lineStiffening of arches by using prestressConcepts for stabilization Construction of thrust linesSpacial profiling
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Thrust line 14
Robert Hooke, 1675
abcccddeeeeefggiiiiiiiillmmmmnnnnnooprrsssttttttuuuuuuuux
Thrust line 15
Robert Hooke, 1675
abcccddeeeeefggiiiiiiiillmmmmnnnnnooprrsssttttttuuuuuuuux
ut pendet continuum flexile, sic stabit contiguum rigidum inversum
Thrust line 16
Robert Hooke, 1675
„As hangs the flexible line, so but inverted will stand the rigid arch.“
abcccddeeeeefggiiiiiiiillmmmmnnnnnooprrsssttttttuuuuuuuux
ut pendet continuum flexile, sic stabit contiguum rigidum inversum
Thrust line
Giovanni Poleni, 1748: Hooke’s guiding principles
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Robert Hooke, 1675
abcccddeeeeefggiiiiiiiillmmmmnnnnnooprrsssttttttuuuuuuuux
ut pendet continuum flexile, sic stabit contiguum rigidum inversum
„As hangs the flexible line, so but inverted will stand the rigid arch.“
Thrust line 18
BA
BA
q
q
g
g
Thrust line
Different behavior of cables and arches for changeable life loads
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Arches
Arches and cables - an inverted principleThrust lineStiffening of arches by using prestressConcepts for stabilization Construction of thrust linesSpacial profiling
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G
G
B
AG G
BA
Stiffening of arches by using prestress
Initital Case 1: Dead load
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A
B
Q
G
G
QQQ
A B
GG
Stiffening of arches by using prestress
Initital Case 2: Dead load + Equally distributed life load
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-∆l+∆l
G G
BA
Q
Stiffening of arches by using prestress
Special Case: Dead load + Life load on one side
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GG
G
QG
Q
Q
A
B
Q
Q
G
GB
G
Q
Q
Q
A
A
B
A G
G
G
B G
A
Q
BQ
B
G
B
A
A
G
G
+
=
Stiffening of arches by using prestress 24
G
G G
Q
G
G
QA
B
G
Q
Q
G
A
B QQA
BG
A G
A BG
GG
BA
B
+
=
Stiffening of arches by using prestress 25
Q
G
G
Q
GB
A
B
B
A
Q
BA
G
Q
B
Q
Q
Q
Q
G
Q
Q
G
Q
B
A
A
G
Q
G A
-
=
Stiffening of arches by using prestress 26
I
I
GG
Q
Q
G G
A B
Q
2
2
1
1
Stiffening of arches by using prestress
Form diagram
Free body diagram Force diagram
scale 1:200
no scale scale 1cm = 200kN
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I
G
G
G
A
G
Q
I
Q
B
Q
2
2
2
1 1
1
Stiffening of arches by using prestress
Form diagram
Free body diagram Force diagram
scale 1:200
no scale scale 1cm = 200kN
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I
G
Q
Q
Q
I
G G
B
G
A
2
2
2
1
1
1
Stiffening of arches by using prestress
Form diagram
Free body diagram Force diagram
scale 1:200
no scale scale 1cm = 200kN
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I
Q
Q
G
I
Q
G
BA
GG
2
2
2
1
11
Stiffening of arches by using prestress
Form diagram
Free body diagram Force diagram
scale 1:200
no scale scale 1cm = 200kN
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G
G
II
II
B
I
Q
G G
A
2
1
1
3 4
34
1
Stiffening of arches by using prestress
Form diagram
Free body diagram Force diagram
scale 1:200
no scale scale 1cm = 200kN
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A
G
Q
I
G
B
II
G
II
G
2
1
43
43
1
4
31
Stiffening of arches by using prestress
Form diagram
Free body diagram Force diagram
scale 1:200
no scale scale 1cm = 200kN
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A
G
Q
G
III
G
II
G
B
2
13
4
1
3 4
34
1
Stiffening of arches by using prestress
Form diagram
Free body diagram Force diagram
scale 1:200
no scale scale 1cm = 200kN
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G
G
B
II
A
G
Q
I
II
G
2
1
43
43
1
4
31
Stiffening of arches by using prestress
Form diagram
Free body diagram Force diagram
scale 1:200
no scale scale 1cm = 200kN
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Arches
Arches and cables - an inverted principleThrust lineStiffening of arches by using prestressConcepts for stabilization Construction of thrust linesSpacial profiling
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Concepts for stabilization
Additional load
Stiffness of the arch
Stiffness of the carried element
Prestress
Planar tension stiffening
Spatial cable net/Membrane as stabilization
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Concepts for stabilization 37
Concepts for stabilization
Robert Maillart: Valtschielbachbridge, Donath, 1925
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Concepts for stabilization 39
Ralph Modjeski: San Francisco-Oakland Bay Bridge, San Francisco, 1936
Concepts for stabilization 40
Concepts for stabilization
A Pomerantsev, V. Shukhov: State warehouse GUM, Moscow, 1893
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Concepts for stabilization
A Pomerantsev, V. Shukhov: State warehouse GUM, Moscow, 1893
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Concepts for stabilization 43
Concepts for stabilization
R. Brosi & Obrist and Partner, Peter Rice: Bus station Chur, 1992
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Concepts for stabilization
R. Brosi & Obrist and Partner, Peter Rice: Bus station Chur, 1992
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Concepts for stabilization
gmp Architekten, Schlaich Bergermann and Partner: Museum for history, Hamburg, 1989
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Concepts for stabilization
Frank Gehry Architects, Schlaich Bergermann and Partner: DZ Bank, Berlin, 2001
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Concepts for stabilization 48
Peter Rice/ Arup: Pavilion of the Future, Sevilla, 1992
Concepts for stabilization 49
Peter Rice/ Arup: Pavilion of the Future, Sevilla, 1992
Concepts for stabilization 50
Peter Rice/ Arup: Pavilion of the Future, Sevilla, 1992
Concepts for stabilization 51
Peter Rice/ Arup: Pavilion of the Future, Sevilla, 1992
Concepts for stabilization 52
Peter Rice/ Arup: Pavilion of the Future, Sevilla, 1992
Arches
Arches and cables - an inverted principleThrust lineStiffening of arches by using prestressConcepts for stabilization Construction of thrust linesSpacial profiling
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Construction of thrust lines
Case 1 Case 2 Case 3
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Construction of thrust lines
Case 1
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min
maxf
f
A B
max
L min
B
A
B
min
q
H
max
max
maxB
max
min
H
max
minA
L
Aminmin
Construction of thrust lines 56
Construction of thrust lines
Taq-i Kisra Palast (Ayvan-e Kasra), Asbanbar, near Baghdad, 550 n.Chr.
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Construction of thrust lines 58
Renzo Piano, Arup: Padre Pio Pilgrim Church, San Giovanni rotondo, 2004
Construction of thrust lines 59
Renzo Piano, Arup: Padre Pio Pilgrim Church, San Giovanni rotondo, 2004
Construction of thrust lines 60
Renzo Piano, Arup: Padre Pio Pilgrim Church, San Giovanni rotondo, 2004
Construction of thrust lines 61
Renzo Piano, Arup: Padre Pio Pilgrim Church, San Giovanni rotondo, 2004
Construction of thrust lines 62
Renzo Piano, Arup: Padre Pio Pilgrim Church, San Giovanni rotondo, 2004
B
min
minA
max
BB
A
A Bmin
A
max
min
maxmax
Construction of thrust lines 63
EQ
Construction of thrust lines 64
A B
q
B
q
A
Construction of thrust lines 65
EQ
Construction of thrust lines 66
Construction of thrust lines
Vezelay Abbey, Burgundy, France, 11.Jh.
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Construction of thrust lines
Vezelay Abbey, Burgundy, France, 11.Jh.
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Construction of thrust lines
Vezelay Abbey, Burgundy, France, 11.Jh.
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A DB C
q
Construction of thrust lines 70
C DA
B
FF
C
B
D
F
A
Construction of thrust lines 71
Construction of thrust lines
Pont du Gard, Nimes, France, 1st century AD
72
Construction of thrust lines 73
L. Laurana: Palazzo Dcuale, Urbino, 1472
Construction of thrust lines
Case 2
74
minfmaxf
R'
R'
R''
R
R
R''
q2
q1
Construction of thrust lines 75
Construction of thrust lines
Eiffel, T. Seyring: Maria Pia bridge, Porto, 1877
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Construction of thrust lines 77
Gustave Eiffel, M. Koechlin: Viadukt Garabit, Ruynes, 1884
Construction of thrust lines 78
Gustave Eiffel, M. Koechlin: Viadukt Garabit, Ruynes, 1884
b
t
b
g
q
Construction of thrust lines 79
Construction of thrust lines
Case 3
80
R
A
R
1
R
R 2
B
B
2
A
RR
1
1
q2
q
Construction of thrust lines 81
Construction of thrust lines
Robert Maillart: Salginatobel bridge, Schiers, 1930
82
Construction of thrust lines
Robert Maillart: Salginatobel bridge, Schiers, 1930
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Construction of thrust lines
Robert Maillart: Salginatobel bridge, Schiers, 1930
84
Construction of thrust lines
Robert Maillart: Salginatobel bridge, Schiers, 1930
85
Construction of thrust lines
Robert Maillart: Salginatobel bridge, Schiers, 1930
86
Construction of thrust lines
Robert Maillart: Salginatobel bridge, Schiers, 1930
87
Construction of thrust lines
Robert Maillart: Salginatobel bridge, Schiers, 1930
88
Construction of thrust lines
Robert Maillart: Salginatobel bridge, Schiers, 1930
89
Construction of thrust lines
Robert Maillart: Salginatobel bridge, Schiers, 1930
90
EQ
Construction of thrust lines 91
Construction of thrust lines
Sir Horace Jones and Sir John Wolfe Barry: Tower Bridge, London, 1894
92
Arches
Arches and cables - an inverted principleThrust lineStiffening of arches by using prestressConcepts for stabilization Construction of thrust linesSpacial profiling
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Spacial profiling 94
Spacial profiling
Boston Public Library
95
Spacial profiling
McKim: National museum of natural History, Washington, 1910
96
Spacial profiling 97
B
BA L
g
A
Spacial profiling 98
Q
L
g *
A
B
BL
g *
Q
g *
1
g *
A
2
g
2
2
1
L
L
L
1
L
Spacial profiling 99
L 2A
A
B
B
g *Q
L 1
g *
g *
Q
g *
g
2
L
L
L 1
L 1
2
Spacial profiling 100
Spacial profiling 101
Spacial profiling 102
Spacial profiling 103
Spacial profiling 104
Spacial profiling 105
Spacial profiling
Eugène Freyssinet: Hangar d‘Orly, Orly, France, 1923
106
Spacial profiling
Eugène Freyssinet: Hangar d‘Orly, Orly, France, 1923
107
Spacial profiling
Pier Luigi Nervi: Main hall Expo Turino, Italy, 1949
108
Spacial profiling
Pier Luigi Nervi: Main hall Expo Turino, Italy, 1949
109
Spacial profiling
Pier Luigi Nervi: Main hall Expo Turino, Italy, 1949
110
13.60b
q g
Spacial profiling 111
Spacial profiling 112
Eladio Dieste: Cadyl Horizontal Silo, Young, Uruguay, 1978
15.15b
gq
Spacial profiling 113
Spacial profiling 114
Eladio Dieste: Cadyl Horizontal Silo, Young, Uruguay, 1978
Spacial profiling 115
Eladio Dieste: Cadyl Horizontal Silo, Young, Uruguay, 1978
Spacial profiling 116
Eladio Dieste: Cadyl Horizontal Silo, Young, Uruguay, 1978
Spacial profiling 117
Eladio Dieste: Cadyl Horizontal Silo, Young, Uruguay, 1978
Spacial profiling 118
Eladio Dieste: Gimnasio de Durazno, Durazno, Uruguay, 1975
Spacial profiling 119
Eladio Dieste: Gimnasio de Durazno, Durazno, Uruguay, 1975
Spacial profiling 120
Eladio Dieste: Gimnasio de Durazno, Durazno, Uruguay, 1975
Spacial profiling 121
Eladio Dieste: Gimnasio de Durazno, Durazno, Uruguay, 1975
Spacial profiling 122
Eladio Dieste: Gimnasio de Durazno, Durazno, Uruguay, 1975
Spacial profiling 123
Eladio Dieste: Gimnasio de Durazno, Durazno, Uruguay, 1975
Spacial profiling 124
Eladio Dieste: Gimnasio de Durazno, Durazno, Uruguay, 1975
Spacial profiling 125
Eladio Dieste: Gimnasio de Durazno, Durazno, Uruguay, 1975
Spacial profiling
Ildefonso Sanchez del Rio, Palacio de deportes, Oviedo, Spain, 1975
126
Spacial profiling
Ildefonso Sanchez del Rio, Palacio de deportes, Oviedo, Spain, 1975
127
Spacial profiling
Ildefonso Sanchez del Rio, Palacio de deportes, Oviedo, Spain, 1975
128