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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
3
Arches and cables - an inverted principle
Wilhelm Riphahn, Fritz Leonhardt: Mülheimer bridge, Cologne, 1951
4
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
7
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
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
Arches
Arches and cables - an inverted principleThrust lineStiffening of arches by using prestressConcepts for stabilization Construction of thrust linesSpacial profiling
13
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
17
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.“
Arches
Arches and cables - an inverted principleThrust lineStiffening of arches by using prestressConcepts for stabilization Construction of thrust linesSpacial profiling
20
A
B
Q
G
G
QQQ
A B
GG
Stiffening of arches by using prestress
Initital Case 2: Dead load + Equally distributed life load
22
-∆l+∆l
G G
BA
Q
Stiffening of arches by using prestress
Special Case: Dead load + Life load on one side
23
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
27
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
28
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
29
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
30
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
31
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
32
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
33
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
34
Arches
Arches and cables - an inverted principleThrust lineStiffening of arches by using prestressConcepts for stabilization Construction of thrust linesSpacial profiling
35
Concepts for stabilization
Additional load
Stiffness of the arch
Stiffness of the carried element
Prestress
Planar tension stiffening
Spatial cable net/Membrane as stabilization
36
Concepts for stabilization
gmp Architekten, Schlaich Bergermann and Partner: Museum for history, Hamburg, 1989
46
Concepts for stabilization
Frank Gehry Architects, Schlaich Bergermann and Partner: DZ Bank, Berlin, 2001
47
Arches
Arches and cables - an inverted principleThrust lineStiffening of arches by using prestressConcepts for stabilization Construction of thrust linesSpacial profiling
53
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.
57
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
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
93