structural design i · cantilever truss transfer truss. 8 terminology and nomenclature >>...

1http://www.block.arch.ethz.ch/eq/

Structural Design IIPhilippe Block ∙ Joseph Schwartz

2

6. Trusses 7. Beams 8. Frames 9. Slabs

1. IntroductionArchitecture and Structure

3. Cables 4. Arches 5. Arch-Cable Structures2. Graphic Statics

10. Columns 11. Spatial Structures

Structural Design II

Structural Design I

3

>> Terminology and nomenclature

Statical determinacy of trusses

Analysis of trusses

Trusses as a combination of arch-cable structures

Determination of internal forces

Influence of the position of external forces

Determination of the maximal member force

Geometrical variations of trusses

Different types of trusses

Additional types of trusses

Construction of trusses

Planar trusses

4Terminology and nomenclature

Renzo Piano, Richard Rogers, Peter Rice: Centre Pompidou, Paris, 1977

5Terminology and nomenclature

8m 2m

2m

2m

Depth or Rise

(statische Höhe)Diagonal (Strebe)

Diagonal member

Members:

Pile (Pfosten)

Vertical member

Column

(Stütze)

Node / Joint

(Knoten)

Top chord (Obergurt)

Horizontal member

Bottom chord (Untergurt)

Horizontal member

6Terminology and nomenclature

- All connections are pin joints

- All elements are straight

- Loads only apply on nodes

- Only axial forces occur

- Trusses consist out of stiff triangles

Assumptions

7Terminology and nomenclature

Trussed beam Trussed frame

Cantilever truss Transfer truss

8

Terminology and nomenclature

>> Statical determinacy of trusses

Analysis of trusses

Trusses as a combination of arch-cable structures

Determination of internal forces

Influence of the position of external forces

Determination of the maximal member force

Geometrical variations of trusses

Different types of trusses

Additional types of trusses

Construction of trusses

Planar trusses

9Statical determinacy of trusses

S = Number of members (Stäbe)

K = Number of nodes (Knoten)

A = Number of support restraints (Auflager)

S + A < 2 * K

S + A = 2 * K

S + A > 2 * K

The system is unstable/ a mechanism

The system is statically determinate

The system is statically indeterminate

10Statical determinacy of trusses

IV

III

I

II

IVI

II III

A

B

BV

BV

BH

A

BV

BH

A

H

II

I

III

IV

2

2

2

4

4

4

5

5

6 3

3

3

1

1

1

S + A = 7 < 2 * K = 8

The system is unstable/ a mechanism.

S + A = 8 = 2 * K = 8

The system is statically determinate.

S + A = 9 > 2 * K = 8

The system is statically indeterminate.

S = 4

A = 3

K = 4

S = 5

A = 3

K = 4

S = 6

A = 3

K = 4

11Statical determinacy of trusses

IV

III

I

II

IVI

II III

A

B

BV

BV

BH

A

BV

BH

A

H

II

I

III

IV

2

2

2

4

4

4

5

5

6 3

3

3

1

1

1I

II

III

IV

BV

BH

AV

AH

2

31

II

I

III

IV

BV

BH

AV

AH

2

31

S + A = 7 < 2 * K = 8

The system is unstable/ a mechanism.

S = 3

A = 4

K = 4

12

Terminology and nomenclature

Statical determinacy of trusses

>> Analysis of trusses

Trusses as a combination of arch-cable structures

Determination of internal forces

Influence of the position of external forces

Determination of the maximal member force

Geometrical variations of trusses

Different types of trusses

Additional types of trusses

Construction of trusses

Planar trusses

13Analysis of trusses

7 kN 7 kN 7 kN7 kN7 kN7 kN 7 kN

14Analysis of trusses

R

15Analysis of trusses

24.5 kN24.5 kN

R

A

B

R

BA

Form diagramScale 1 : 100

Force diagram

Scale 1 cm ≙ 1 kN

16Analysis of trusses

AForm diagram

Scale 1 : 100

Force diagram

Scale 1 cm ≙ 1 kN

17Analysis of trusses

Form diagramScale 1 : 100

Force diagram

Scale 1 cm ≙ 1 kN

18Analysis of trusses

Form diagramScale 1 : 100

Force diagram

Scale 1 cm ≙ 1 kN

19Analysis of trusses

Form diagramScale 1 : 100

Force diagram

Scale 1 cm ≙ 1 kN

20Analysis of trusses

Form diagramScale 1 : 100

Force diagram

Scale 1 cm ≙ 1 kN

21Analysis of trusses

Form diagramScale 1 : 100

Force diagram

Scale 1 cm ≙ 1 kN

22Analysis of trusses

Form diagramScale 1 : 100

Force diagram

Scale 1 cm ≙ 1 kN

23Analysis of trusses

Form diagramScale 1 : 100

Force diagram

Scale 1 cm ≙ 1 kN

24Analysis of trusses

Form diagramScale 1 : 100

Force diagram

Scale 1 cm ≙ 1 kN

25Analysis of trusses

R

R

26Analysis of trusses

27Analysis of trusses

28Analysis of trusses

eQ: Pratt / Howe truss

http://www.block.arch.ethz.ch/eq/drawing/view/37

29

Introduction

Terminology and nomenclature

Statical determinacy of trusses

Analysis of trusses

Construction of trusses

>> Trusses as a combination of arch-cable structures

Determination of internal forces

Influence of the position of external forces

Determination of the maximal member force

Geometrical variations of trusses

Different types of trusses

Additional types of trusses

Case study: Lufthansa maintenance hall

Planar trusses

30Trusses as a combination of arch-cable structures

Q/2

Q

Q

Q/2

Q/2 Q/2

Combination

31Trusses as a combination of arch-cable structures

Q

Q

Q/2Q/2

Q/2Q/2

Combination

32Trusses as a combination of arch-cable structures

Q

Q

Q/2Q/2

Q/2Q/2

Combination

33Trusses as a combination of arch-cable structures

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

34Trusses as a combination of arch-cable structures

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

35Trusses as a combination of arch-cable structures

Q

Q

Q/2 Q/2

Q/2 Q/2

Force distribution

36Trusses as a combination of arch-cable structures

Q

Q

Q/2Q/2

Q/2Q/2

Force distribution

37Trusses as a combination of arch-cable structures

Q

Q

Q/2 Q/2

Q/2 Q/2

Force distribution

38

Terminology and nomenclature

Statical determinacy of trusses

Analysis of trusses

Trusses as a combination of arch-cable structures

>> Determination of internal forces

Influence of the position of external forces

Determination of the maximal member force

Geometrical variations of trusses

Different types of trusses

Additional types of trusses

Construction of trusses

Planar trusses

39Determination of internal forces

500 kN

1000 kN

500 kN

1000 kN

500 kN

500 kN

Form diagramScale 1 : 100

Force diagram

Scale 1 cm ≙ 1 kN

40Determination of internal forces

Form diagramScale 1 : 100

Force diagram

Scale 1 cm ≙ 1 kN

41

Terminology and nomenclature

Statical determinacy of trusses

Analysis of trusses

Trusses as a combination of arch-cable structures

Determination of internal forces

>> Influence of the position of external forces

Determination of the maximal member force

Geometrical variations of trusses

Different types of trusses

Additional types of trusses

Construction of trusses

Planar trusses

42Influence of the position of external forces

200 kN 800 kN

700 kN

R

800 kN

R

200 kN

700 kN

300 kN

300 kN

R

Form diagramScale 1 : 100

Force diagram

Scale 1 cm ≙ 1 kN

43Influence of the position of external forces

800 kN 200 kN200 kN

700 kN

800 kN

300 kN

700 kN 300 kN

Form diagramScale 1 : 100

Force diagram

Scale 1 cm ≙ 1 kN

44Influence of the position of external forces

Form diagramScale 1 : 100

Force diagram

Scale 1 cm ≙ 1 kN

45

Terminology and nomenclature

Statical determinacy of trusses

Analysis of trusses

Trusses as a combination of arch-cable structures

Determination of internal forces

Influence of the position of external forces

>> Determination of the maximal member force

Geometrical variations of trusses

Different types of trusses

Additional types of trusses

Construction of trusses

Planar trusses

46Determination of the maximal member force

47Determination of the maximal member force

800 kN

700 kN

700 kN

800 kN

200 kN200 kN

300 kN

N3

N 2 N

N1

200 kN 800 kN

700 kN

N3

N

N1

N2

48Determination of the maximal member force

N3

700 kN

200 kN

N 2

300 kN

800 kN

300 kN

N N3

N 2

N1

N1N 300 kN

49Determination of the maximal member force

N5 N6

5 6

N7N N

300 kN

N4

700 kN

300 kN

N4

700 kN

N7

800 kN200 kN

Form diagramScale 1 : 100

Force diagram

Scale 1 cm ≙ 1 kN

50

Terminology and nomenclature

Statical determinacy of trusses

Analysis of trusses

Trusses as a combination of arch-cable structures

Determination of internal forces

Influence of the position of external forces

Determination of the maximal member force

>> Geometrical variations of trusses

Different types of trusses

Additional types of trusses

Construction of trusses

Planar trusses

51Geometrical variations of trusses

Q

Q/2

Q

Q/2

Q/2

Q

Q/2

Q/2 Q/2

Q/2Q/2

Q

Form diagramScale 1 : 100

Force diagram

Scale 1 cm ≙ 1 kN

52Geometrical variations of trusses

Q1

Q1

A

A

A

B

Q 2

Q 2 B

A

Q 2Q1

Q1 Q 2

B

B

h

2h

Form diagramScale 1 : 100

Force diagram

Scale 1 cm ≙ 1 kN

53Geometrical variations of trusses

A

Q 2

Q1

Q1 Q 2

A

Q 2

A

A

B

Q1

Q 2

B

Q1

B

B

h

h/2

Form diagramScale 1 : 100

Force diagram

Scale 1 cm ≙ 1 kN

54

Terminology and nomenclature

Statical determinacy of trusses

Analysis of trusses

Trusses as a combination of arch-cable structures

Determination of internal forces

Influence of the position of external forces

Determination of the maximal member force

Geometrical variations of trusses

>> Different types of trusses

Additional types of trusses

Construction of trusses

Trusses

55Different types of trusses

Truss with V-shaped diagonals (System Warren)

56Different types of trusses

57Different types of trusses

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

58Different types of trusses

A

A

A

=

+

59Different types of trusses

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

60Different types of trusses

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

61Different types of trusses

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

62Different types of trusses

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

63Different types of trusses

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

64Different types of trusses

A

A

A +

=

65Different types of trusses

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

66Different types of trusses

Double decker Fairey Swordfish I, Great Britain, 1934

67Different types of trusses

Truss with X-shaped diagonals without posts

68Different types of trusses

69Different types of trusses

70Different types of trusses

71Different types of trusses

A B

A B

72Different types of trusses

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

73Different types of trusses

A B

74Different types of trusses

BA

75Different types of trusses

BA

76Different types of trusses

B

BA

A

Truss system Polonceau

77Different types of trusses

Jakob Ignatz Hittorf: Gare du Nord, Paris, 1865

78Different types of trusses

Jakob Ignatz Hittorf: Gare du Nord, Paris, 1865

79

Terminology and nomenclature

Statical determinacy of trusses

Analysis of trusses

Trusses as a combination of arch-cable structures

Determination of internal forces

Influence of the position of external forces

Determination of the maximal member force

Geometrical variations of trusses

Different types of trusses

>> Additional types of trusses

Construction of trusses

Trusses

80Additional types of trusses

100 kN100 kN100 kN

100 kN

100 kN

100 kN

100 kN

100 kN

RA

A

BB

R

R

Form diagramScale 1 : 100

Force diagram

Scale 1 cm ≙ 1 kN

81Additional types of trusses

RA

A

B

R

B

Form diagramScale 1 : 100

Force diagram

Scale 1 cm ≙ 1 kN

82Additional types of trusses

RA

A

BB

Form diagramScale 1 : 100

Force diagram

Scale 1 cm ≙ 1 kN

83Additional types of trusses

A

B

Q 2

Q1

Q 3 Q 4 Q 5 Q 6Q1 Q 2

A

Q 3

Q 5

Q 4

Q 6

B

Form diagramScale 1 : 100

Force diagram

Scale 1 cm ≙ 1 kN

84Additional types of trusses

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

85Additional types of trusses

180 kN180 kN

200 kN

180 kN

180 kN

200 kN

180 kN

180 kN

200 kN

R

BA

R

B

A

Form diagramScale 1 : 100

Force diagram

Scale 1 cm ≙ 1 kN

86Additional types of trusses

180 kN

200 kN

180 kN

200 kN

180 kN

180 kN

V

IV

III

II

I A

I V

II

IV

A

BIII B

180 kN

171 kN

113 kN

200 kN

447 kN

180 kN

171 kN

308 kN 247 kN 308 kN

308 kN 308 kN

300 kN

171 kN

247 kN

171 kN

300 kN

Form diagramScale 1 : 100

Force diagram

Scale 1 cm ≙ 1 kN

87Additional types of trusses

0.5*l

l

l

l

f 1

f 3 f 4f 2

88

Terminology and nomenclature

Statical determinacy of trusses

Analysis of trusses

Trusses as a combination of arch-cable structures

Determination of internal forces

Influence of the position of external forces

Determination of the maximal member force

Geometrical variations of trusses

Different types of trusses

Additional types of trusses

>> Construction of trusses

Planar trusses

89Construction of trusses

Gustav Eiffel, Theophile Seyring: Maria Pia bridge, Porto, 1877

90Construction of trusses

Gustav Eiffel, Theophile Seyring: Maria Pia bridge, Porto, 1877

91Construction of trusses

Gustav Eiffel, Theophile Seyring: Maria Pia bridge, Porto, 1877

92Construction of trusses

Squire Whipple, Cairo Rail Bridge, Illinois, USA, 1899

93Construction of trusses

Ceiling tile

Lighting fixture

Air-conditioning slit

Minoru Yamasaki, John Skilling, Leslie Robertson: World Trade Center, New York, 1973, destroyed 2001

Concrete Floor tiles

Telephone and power outlets

Corrugated steel truss covering

Heating , ventilation, air-conditioning

94Construction of trusses

Squire Whipple, Cairo Rail Bridge, Illinois, USA, 1899

95Construction of trusses

Sir John Fowler, Benjamin Baker, Firth of Forth Bridge, Edinburgh, 1890

96Construction of trusses

Sir Horace Jones, Sir John Wolfe Barry: Tower Bridge, London, 1894

97Construction of trusses

Office Eiffel, Maurice Koechlin: Eiffel tower, Paris, 1889

98Construction of trusses

Frederic-Auguste Bartholdi, Gustave Eiffel: Statue of Liberty, New York, 1886

99Construction of trusses

100Construction of trusses

Lifschutz, Techniker: Royal Victoria Dock Bridge, London, 1996

101Construction of trusses

Schulhaus Leutschenbach Zürich, 2009, Architekt: C. Kerez, Bauingenieur: J. Schwartz

102Construction of trusses

Schulhaus Leutschenbach Zürich, 2009, Architekt: C. Kerez, Bauingenieur: J. Schwartz

103Construction of trusses

Schulhaus Leutschenbach Zürich, 2009, Architekt: C. Kerez, Bauingenieur: J. Schwartz