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

Structural Design I

01.12.2016

Philippe Block ∙ Joseph Schwartz

http://www.block.arch.ethz.ch/eq/

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

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

Q/2

Q

Q

Q/2

Q/2 Q/2

Trusses as a combination of arch-cable structures

Combination

4

Q

Q

Q/2Q/2

Q/2Q/2


Combination

5

Q

Q

Q/2Q/2

Q/2Q/2


Combination

6

Trusses as a combination of arch-cable structures 7

R. Piano, R. Rogers, P. Rice: Centre Georges Pompidou, Paris, 1977


Ludwig Mies van der Rohe: Project, National theater, Mannheim, 1953

8

Q

Q

Q/2 Q/2

Q/2 Q/2


Force distribution

9

Q

Q

Q/2Q/2

Q/2Q/2


Force distribution

10

Q

Q

Q/2 Q/2

Q/2 Q/2


Force distribution

11

Planar trusses


12

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

-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



14

Planar trusses


15

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



16

800 kN 200 kN200 kN

300 kN

700 kN

800 kN

700 kN 300 kN




17

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




18

Planar trusses


19

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

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


3

700 kN

200 kN

2

N300 kN

800 kN

300 kN

N

N

N

1N

N

2

1

N

N

3

300 kN


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


Planar trusses


24

Q

Q

Q/2

Q/2

Q/2

Q/2

Q

Q/2 Q/2

Q/2Q/2

Q

Geometrical variations of trusses



25

Q

1A

A

A

B

Q

Q 2

Q 2

1

B

A

2Q Q1

1Q 2Q

B

B

h

2h




26

A

Q 2

1

Q Q 21

A

Q Q 2

A

A

B

1Q

2Q B

1Q

B

B

h

h/2




27

Planar trusses


28

A

Different types of trusses

Truss with V-shaped diagonals (System Warren)

29

A

Different types of trusses 30


R. Piano, R. Rogers, P. Rice: Centre Georges Pompidou, Paris, 1977

A

A

A

=

+



Joseph Paxton, Fox Henderson: Crystal palace, London, 1851

33

A


Truss with N-shaped diagonals (System Howe), patent 1840

34


Structure proposed by A. Palladio in 1570 („The four books of architecture“, 3. book, chapter VIII)

35

A


Truss with N-shaped diagonals (System Pratt), patent 1844

36


Ludwig Mies van der Rohe: Project, National theater, Mannheim, 1953

37

A

A

A +

=



Truss with X-shaped diagonals and posts (System Long), patents 1830 and 1839

39


Double decker Fairey Swordfish I, Great Britain, 1934

40

A/2

A/2

A

+

=Q/2

Q/2

Q/2

Q/2


Truss with X-shaped diagonals without posts

41

+

=Q/2

Q/2

Q/2

Q/2

A/2

A/2

A


=

+

Q/2

Q/2

Q/2

Q/2

A/2

A/2

A



A B

A B



Friedrich August von Pauli, Heinrich Gerber, Ludwig Werder: Isar bridge, Grosshesselohe, 1857

46

A B


BA


BA


B

BA

A


Truss system Polonceau

50


Jakob Ignatz Hittorf: Gare du Nord, Paris, 1865


Jakob Ignatz Hittorf: Gare du Nord, Paris, 1865

Planar trusses


53

100 kN100 kN100 kN

100 kN

100 kN

100 kN

100 kN

100 kN

RA

B

A

BR

R

Additional types of trusses



54

R

B

A

R

A

B




55

A

B

R

B

A




56

Q

A

A

1

QB

3

2

Q

QQ

3

Q

64

Q

4

5

Q 5

Q 6

QQ2

B

Q1

Q

A

A

1

QB

3

2

Q

QQ

3

Q

64

Q

4

5

Q 5

Q 6

QQ2

B

Q1




57

Spacial trusses 58

Skidmore, Owings & Merrill, F. Kahn: John Hancock Center, Chicago, 1969

180 kN

180 kN

180 kN

200 kN

180 kN

180 kN

200 kN

200 kN

180 kNR

BA

BR

A




59

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




60

0.5*l

l

l

l

1f 3 42 fff

Additional types of trusses 61

Additional types of trusses 62

Maurice Koechlin, Gustave Eiffel: La Tour Eiffel, Paris, 1889


Pier Luigi Nervi: Birgi airplane hangar, Marsala, Italy, 1940

63


Pier Luigi Nervi: Birgi airplane hangar, Marsala, Italy, 1940

64

Documents

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