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Structural Design I
01.12.2016
Philippe Block ∙ Joseph Schwartz
http://www.block.arch.ethz.ch/eq/
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Structural design I+II
1. Introduction
2. Equilibrium and graphic static
3.+4. Cables
13. Cable-net and membrane structures
5.+7. Arches
14.+15. Vaults, domes and shells
16. Spatial arch-cable-structures
6.+8. Arch-cable-structures
12. Materials and dimensioning
9. +10. Trusses
17. Spacial trusses
11. Beams and frames
16. Shear walls and plates
20. Columns
19. Bending
Structural design I
Structural design II
Course overview
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Planar trusses
Trusses as a combination of arch-cable structuresDetermination of internal forcesInfluence of the position of external forcesDetermination of the maximal member forceGeometrical variations of trussesDifferent types of trussesAdditional types of trussesSpacial trusses
3
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Q/2
Q
Q
Q/2
Q/2 Q/2
Trusses as a combination of arch-cable structures
Combination
4
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Q
Q
Q/2Q/2
Q/2Q/2
Trusses as a combination of arch-cable structures
Combination
5
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Q
Q
Q/2Q/2
Q/2Q/2
Trusses as a combination of arch-cable structures
Combination
6
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Trusses as a combination of arch-cable structures 7
R. Piano, R. Rogers, P. Rice: Centre Georges Pompidou, Paris, 1977
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Trusses as a combination of arch-cable structures
Ludwig Mies van der Rohe: Project, National theater, Mannheim, 1953
8
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Q
Q
Q/2 Q/2
Q/2 Q/2
Trusses as a combination of arch-cable structures
Force distribution
9
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Q
Q
Q/2Q/2
Q/2Q/2
Trusses as a combination of arch-cable structures
Force distribution
10
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Q
Q
Q/2 Q/2
Q/2 Q/2
Trusses as a combination of arch-cable structures
Force distribution
11
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Planar trusses
Trusses as a combination of arch-cable structuresDetermination of internal forcesInfluence of the position of external forcesDetermination of the maximal member forceGeometrical variations of trussesDifferent types of trussesAdditional types of trussesSpacial trusses
12
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500 kN
500 kN
1000 kN
500 kN
500 kN
1000 kN
Determination of internal forces
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
13
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-375
kN -625
-375kN
-625kN
kN
kN-625 -625
-750
kN
kN
-625 kN
kN-750
kN -625
500 500
375
500
kN375
kN kN500
750 kN750kN 1125 kN
kN kN
kN
500 kNV
1000 kN
II
III
IX
VIII
XI
500 kNVIIXI
IX
IVXVIII
XVII
VI
V
IV
VI
III
II
I
I
1000 kN
500 kN 500 kN
Determination of internal forces
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
14
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Planar trusses
Trusses as a combination of arch-cable structuresDetermination of internal forcesInfluence of the position of external forcesDetermination of the maximal member forceGeometrical variations of trussesDifferent types of trussesAdditional types of trussesSpacial trusses
15
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200 kN 800 kN
R
R
200 kN
700 kN
300 kN
700 kN
300 kN
R
800 kN
Influence of the position of external forces
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
16
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800 kN 200 kN200 kN
300 kN
700 kN
800 kN
700 kN 300 kN
Influence of the position of external forces
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
17
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kN
-375 kN-375-900
-525
kN -375
kN kN
-875 kN
-900
kN
kN
kN
kN -450 -225
-300
kN
kN
900 300 kN
900
kN
kNkN
300
kN kN 675
kN
450 225525
375
800 kN
300 kN
700 kN
200 kN200 kN
700 kN
800 kN
300 kN
IV
I
XI
IXVIIVIII
I
VIII XVIII
III
II
IV
V
VI
VII
VIII
IX
X
XI
Influence of the position of external forces
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
18
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Planar trusses
Trusses as a combination of arch-cable structuresDetermination of internal forcesInfluence of the position of external forcesDetermination of the maximal member forceGeometrical variations of trussesDifferent types of trussesAdditional types of trussesSpacial trusses
19
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kN-225
kN
kN
-450-525
-900
kN
kN675
900
450 kN
kN225
kN525
kN
700 kN 300 kN
200 kN 800 kN
Determination of the maximal member force 20
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800 kN
700 kN
700 kN
800 kN
200 kN200 kN
300 kN
N
2N N
1N
3
200 kN 800 kN
700 kN
NN
3
1N2N
Determination of the maximal member force 21
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3
700 kN
200 kN
2
N300 kN
800 kN
300 kN
N
N
N
1N
N
2
1
N
N
3
300 kN
Determination of the maximal member force 22
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5 6
57 N
N
300 kN
NN
N
N
300 kN
700 kN
N
700 kN
6
7
4
800 kN
4
200 kN
N
Determination of the maximal member force 23
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Planar trusses
Trusses as a combination of arch-cable structuresDetermination of internal forcesInfluence of the position of external forcesDetermination of the maximal member forceGeometrical variations of trussesDifferent types of trussesAdditional types of trussesSpacial trusses
24
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Q
Q
Q/2
Q/2
Q/2
Q/2
Q
Q/2 Q/2
Q/2Q/2
Q
Geometrical variations of trusses
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
25
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Q
1A
A
A
B
Q
Q 2
Q 2
1
B
A
2Q Q1
1Q 2Q
B
B
h
2h
Geometrical variations of trusses
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
26
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A
Q 2
1
Q Q 21
A
Q Q 2
A
A
B
1Q
2Q B
1Q
B
B
h
h/2
Geometrical variations of trusses
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
27
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Planar trusses
Trusses as a combination of arch-cable structuresDetermination of internal forcesInfluence of the position of external forcesDetermination of the maximal member forceGeometrical variations of trussesDifferent types of trussesAdditional types of trussesSpacial trusses
28
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A
Different types of trusses
Truss with V-shaped diagonals (System Warren)
29
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A
Different types of trusses 30
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Different types of trusses 31
R. Piano, R. Rogers, P. Rice: Centre Georges Pompidou, Paris, 1977
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A
A
A
=
+
Different types of trusses 32
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Different types of trusses
Joseph Paxton, Fox Henderson: Crystal palace, London, 1851
33
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A
Different types of trusses
Truss with N-shaped diagonals (System Howe), patent 1840
34
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Different types of trusses
Structure proposed by A. Palladio in 1570 („The four books of architecture“, 3. book, chapter VIII)
35
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A
Different types of trusses
Truss with N-shaped diagonals (System Pratt), patent 1844
36
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Different types of trusses
Ludwig Mies van der Rohe: Project, National theater, Mannheim, 1953
37
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A
A
A +
=
Different types of trusses 38
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Different types of trusses
Truss with X-shaped diagonals and posts (System Long), patents 1830 and 1839
39
![Page 40: Structural Design I - ETH Zblock.arch.ethz.ch/eq/files/TU10_truss_eng_161201...Different types o trusses Truss with X-shaped diagonals and posts (System Long), patents 1830 and 1839](https://reader036.vdocuments.us/reader036/viewer/2022071507/6127b56275b9583717648c00/html5/thumbnails/40.jpg)
Different types of trusses
Double decker Fairey Swordfish I, Great Britain, 1934
40
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A/2
A/2
A
+
=Q/2
Q/2
Q/2
Q/2
Different types of trusses
Truss with X-shaped diagonals without posts
41
![Page 42: Structural Design I - ETH Zblock.arch.ethz.ch/eq/files/TU10_truss_eng_161201...Different types o trusses Truss with X-shaped diagonals and posts (System Long), patents 1830 and 1839](https://reader036.vdocuments.us/reader036/viewer/2022071507/6127b56275b9583717648c00/html5/thumbnails/42.jpg)
+
=Q/2
Q/2
Q/2
Q/2
A/2
A/2
A
Different types of trusses 42
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=
+
Q/2
Q/2
Q/2
Q/2
A/2
A/2
A
Different types of trusses 43
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Different types of trusses 44
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A B
A B
Different types of trusses 45
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Different types of trusses
Friedrich August von Pauli, Heinrich Gerber, Ludwig Werder: Isar bridge, Grosshesselohe, 1857
46
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A B
Different types of trusses 47
![Page 48: Structural Design I - ETH Zblock.arch.ethz.ch/eq/files/TU10_truss_eng_161201...Different types o trusses Truss with X-shaped diagonals and posts (System Long), patents 1830 and 1839](https://reader036.vdocuments.us/reader036/viewer/2022071507/6127b56275b9583717648c00/html5/thumbnails/48.jpg)
BA
Different types of trusses 48
![Page 49: Structural Design I - ETH Zblock.arch.ethz.ch/eq/files/TU10_truss_eng_161201...Different types o trusses Truss with X-shaped diagonals and posts (System Long), patents 1830 and 1839](https://reader036.vdocuments.us/reader036/viewer/2022071507/6127b56275b9583717648c00/html5/thumbnails/49.jpg)
BA
Different types of trusses 49
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B
BA
A
Different types of trusses
Truss system Polonceau
50
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Different types of trusses 51
Jakob Ignatz Hittorf: Gare du Nord, Paris, 1865
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Different types of trusses 52
Jakob Ignatz Hittorf: Gare du Nord, Paris, 1865
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Planar trusses
Trusses as a combination of arch-cable structuresDetermination of internal forcesInfluence of the position of external forcesDetermination of the maximal member forceGeometrical variations of trussesDifferent types of trussesAdditional types of trussesSpacial trusses
53
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100 kN100 kN100 kN
100 kN
100 kN
100 kN
100 kN
100 kN
RA
B
A
BR
R
Additional types of trusses
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
54
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R
B
A
R
A
B
Additional types of trusses
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
55
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A
B
R
B
A
Additional types of trusses
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
56
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Q
A
A
1
QB
3
2
Q
3
Q
64
Q
4
5
Q 5
Q 6
QQ2
B
Q1
Q
A
A
1
QB
3
2
Q
3
Q
64
Q
4
5
Q 5
Q 6
QQ2
B
Q1
Additional types of trusses
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
57
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Spacial trusses 58
Skidmore, Owings & Merrill, F. Kahn: John Hancock Center, Chicago, 1969
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180 kN
180 kN
180 kN
200 kN
180 kN
180 kN
200 kN
200 kN
180 kNR
BA
BR
A
Additional types of trusses
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
59
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180 kN
200 kN
180 kN
200 kN180 kN
180 kN
V
III
III A
I V
II
IV
A
BIVIII B
180 kN
113 kN
200 kN
447 kN
180 kN
kN308308
171
kN
kNkNkN
171
308 kN308
kN
171
kN247kN
300
171 kN300 kN
kN
247
Additional types of trusses
Force diagramScale 1 cm = 1 kN
Form diagramScale 1 : 100
60
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0.5*l
l
l
l
1f 3 42 fff
Additional types of trusses 61
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Additional types of trusses 62
Maurice Koechlin, Gustave Eiffel: La Tour Eiffel, Paris, 1889
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Additional types of trusses
Pier Luigi Nervi: Birgi airplane hangar, Marsala, Italy, 1940
63
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Additional types of trusses
Pier Luigi Nervi: Birgi airplane hangar, Marsala, Italy, 1940
64