Structural Design I - Block Research Groupblock.arch.ethz.ch/eq/files/TU11_beams_eng_OO_161208_1481188947… · Structural design I Structural design II ... Structural behavior of

1

Philippe Block ∙ Joseph Schwartz

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

Structural Design I

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. Trusses

17. Spacial trusses

10.+11. Beams and frames

16. Shear walls and plates

20. Columns

19. Bending

Structural design I

Structural design II

Course overview

3

Beams

Structural behaviour of a simple beamReinforced concrete beamSteel beamBeam under concentrated and distributed loadsCantilever under concentrated and distributed loadsOverhanging beamGerber’s beam (Hinged girder system)Continuous beam

4

MembranwirkungMembran, SchaleBalken

Bogen, Seil

PlattenRaumfachwerk

Als äusseres Tragwerk

Beton, gerissen

Fachwerk

Als inneres Tragwerk

Stahl / Holz

BalkenrosteBogen-Seiltragwerk

Als äusseres Tragwerk Als inneres Tragwerk

Beton vorgespannt

Bogen, Seil,

Bogen-Seiltragwerk

Structural behavior of simple beam

Arch, cableas external structure

Arch, cable,membrane, Schale Membrane action

as external structureas internal structure as internal structure

Arch-cable structures

Arch-cable structures,truss,

space truss

Beam,beam grid,

slab

pre-stressed concrete

steel/ wood

cracked concrete

5

2

300

800

700

m

kN

kN

kN

200

kN

700

200

300

kN

kN

kN 800

kN


Force diagramScale 1 cm = 1 kN

Form diagramScale 1 : 100

6

kN

800

2

800

200

kN

300

300

kN

kN

700

m

200

700

kN

kN

kN

kN




7

kN

200

700 kN

200

kN

kN 800

300

kN

300

kN

kN

kN 800

700




8

Beams


9

300700

800

kN

kN

300

kN kN200

kN

700

kN

800

kN

200

kN

Reinforced concrete beam

10Reinforced concrete beam

11

300

700

kN

700

300

kN

800

800kN

kN

kN

kN

200

kN

200

kN

Reinforced concrete beam




15

Beams


16

kN

800

700

800 kN

kN

kN

200

300700

kN

300

kN

200

kN

kN

Steel beam

17Steel beam

18Steel beam

19Steel beam

20Steel beam

21Steel beam

22

Beams


23

A B

BA

F

F

Beam under concentrated and distributed loads

24

q

q

Q/2 Q/2

Q/2 Q/2


25

maximal belastetmaximal belastetDruckzone und Zugzone Schubzone

maximal belastetSchubzone

q

q

Q/2

Q/2 Q/2

Q/2Q/2

q

Q/2


Shear zonemaximum loading

Shear zonemaximum loading

compression and tension zonemaximum loading

26

MembranwirkungMembran, SchaleBalken

Bogen, Seil

PlattenRaumfachwerk

Als äusseres Tragwerk

Beton, gerissen

Fachwerk

Als inneres Tragwerk

Stahl / Holz

BalkenrosteBogen-Seiltragwerk

Als äusseres Tragwerk Als inneres Tragwerk

Beton vorgespannt

Bogen, Seil,

Bogen-Seiltragwerk


Arch, cableas external structure

Arch, cable,membrane, Schale Membrane action

as external structureas internal structure as internal structure

Arch-cable structures

Arch-cable structures,truss,

space truss

Beam,beam grid,

slab

pre-stressed concrete

steel/ wood

cracked concrete

27

Beams


28

B

A

A

B

F

F

A

BF

Cantilever under concentrated and distributed loads

29

A

B

q

q

A

B

B

A

F


30

maximal belastetSchubzone

q

A

B

A

B

q

q

B

A


31

BA

q


John Andrews & WMZ Architects, Nicolet, Dressel Associates & Bruno Thürlimann: CN Tower, Toronto, 1976

32Cantilever under concentrated and distributed loads










37

Beams


38Overhanging beam

Pier Luigi Nervi: project, airport terminal, Rom, 1957

39

A B

q

Overhanging beam

40

Beams


41

l' l'

l

0.5 f

l l

0.5 f

A B C D

F F

DCBA

F F

q

q

Gerber’s beam (Hinged girder system)

42Gerber’s beam (Hinged girder system)

Riccardo Morandi: Polcevera viaduct, Genoa, 1968

43

eQ

Gerber’s beam (Hinged girder system)

44

Beams


45

Schubzone

max. bel. maximal belastet max. bel.alle ZonenDruckzone und Zugzonealle Zonen

q

B

A

q

q

A

B

C

D

C

D

D

C

B

A

Continuous beam

every zonemax. loading

every zonemax. loading

Shear zone

compression and tension zonemaximum loading

46

0.33 f

l 0.79 l

0.66 f

0.21 l

l

0.58 l l0.21 l 0.58 l

0.79 l

0.21 l 0.79 l

q

EDCBA

q

Continuous beam

47Continuous beam

Arnold Bürkli: Quai bridge, Zurich, 1884

Documents

Structural Design I - Block Research Groupblock.arch.ethz.ch/eq/files/TU11_beams_eng_OO_161208_1481188947… · Structural design I Structural design II ... Structural behavior of