Structural Design II - ETH Z frames_ER...Notation - Force Diagram Cremona- Construction without notation only external forces..full arrow head Cremona- Construction without notation

Structural Design II

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

Philippe Block ∙ Joseph Schwartz

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

>>

Bending frames

Rotational equilibrium

Bending moments in systems

Introduction

Shaping Frames

3

Introduction 4

Introduction 5

Introduction 6

Introduction

Design intent

Where the forces want to go

7

RR

R = w • l

B

A

w

h

h

l

BA

Introduction 8

B

A

R = w • l

RR

A Bl

w

Introduction 9

l

R

= w • l

i

Ri i

C

A

A

w

C

i

i

Introduction

Free body diagram

10

>>

Bending frames



Introduction

Shaping Frames

11


In equilibrium Not in equilibrium

12

M

F

F F

y

M

x

y

x

F

Rotational equilibrium 13

∑ Fx = 0 ∑ Fx = 0

∑ M ≠ 0∑ M = 0

∑ Fy = 0 ∑ Fy = 0

M = F • d

F

FF

F

F

F

F

F

F

F e

d d d d

d


Moment

Force (couple)

moment arm

14

M = F • d

M

F

d

=

=

=

=

M = F • d

F

FF

F

F

F

F

F

F

F e

d d d d

d M = F • d

F

FF

F

F

F

F

F

F

F e

d d d d

d


M = F • 0 + F • d

M = F • d

=

M = F • d

F

FF

F

F

F

F

F

F

F e

d d d d

d M = F • d

F

FF

F

F

F

F

F

F

F e

d d d d

d


M = F • 0 + F * d M = F • d + F • 0

M = F • d M = F • d

=

M = F • d

F

FF

F

F

F

F

F

F

F e

d d d d

d M = F • d

F

FF

F

F

F

F

F

F

F e

d d d d

d


M = F • 0 + F • d M = F • d + F • 0 M = F • d/2 + F • d/2

M = F • d M = F • d M = F • d

=

M = F • d

F

FF

F

F

F

F

F

F

F e

d d d d

d


M = F • 0 + F * d M = F • d + F • 0 M = F • d/2 + F • d/2 M = F • (d+e) - F • e

M = F • d M = F • d M = F • d M = F • d

=

eQ Moment from force pair

http://www.block.arch.ethz.ch/eq/drawing/view/49


= F • d1 1

1

M1

F

F 1

d1


Not in equilibrium

20

∑ M = - M1 ≠ 0

= F • dM21 1MF

F12

2= F • d1

1F

F

22

d21d


In equilibrium

21

∑ M = - M1 + M2 = 0

>>

Bending frames



Introduction

Shaping Frames

22

l

R

= w • l

i

Ri i

C

A

A

w

C

i

i


Free body diagram

23

V

R

CH

C

Ri

l

i

C

A

CH

CV

A

w

i

i

Bending moments in systems 24

∑ Fx = 0

∑ Fy = 0

C'

C

A

iR

CV

R

l

i

HC

C'

C

C

V

H

H

w

A

V

i

i


∑ Fx = 0

∑ Fy = 0

∑ M ≠ 0

C'

C

A

iR

CV

R

l

i

HC

C'

C

C

V

H

H

w

A

V

i

i


∑ Fx = 0

∑ Fy = 0

∑ M ≠ 0

M

M

R11

R1

1

R

C

R = w • l

R

R

w

1

A

R

R

H

C

R

x

C

F

1

8

1

y

F

1

1 M

9

C

C

H

H

CV

i

1

w

i

H

i

v

w

= F • d

M

= F • d

H H

1

F

F

H

F

C

i

H

R = w • l

A = F

R

H

H

A

H

A

R

R

1

F

A B

l

R

FB

F

R

C'

R

i

i

C

l

i

N

C'

V

V

H

i

C

R

V

N

R

M

i

2

i

MM = B • x

C'

i

AA

Q

Q

R

H

A

V

w

C

C

R

R

C

H

A

l

2

v

= F • d1

M

w

A

F

V

F

A B

w

A

R

HC

2

A

9

M

i

l

3

F

A = F

i

l

R

Step 3: separate the line of the dimension from drawing line a distance of 3.6 mm.

D

w

Free-Body diagram

In case you draw a free body diagram, make the lines of the bars manually thicker--> 0.35 mm

C

A

R

A

w

F

F

l

C

w

A

A B

w

C

1

1

R

lBA

Q

8

E

5

6

C'

w

l

A

R

S

C

R

F

V

i

A

R

R

Q

F

w

l

F

SC IC

= w • l

IISC

F

2

N 4

A

R

A

N

C

H

8

x

R

N

9

F

i

N7

C

A

P

V

N

P

3

A

w

H

9

w

A

C

B

A

P

F

H

H

Ri

C

C

l

A

F

C

B

i

A

C

A

f

B

F

A

F

A

F

C

A

H

F

C

V

V

F

H

l

l

i

CV

mmm

22

F

i

A

1

F

1

1 1

F

R

w

D2

1D

C 8

9C

C 7

C 6

5C

C 4

3C

C 2

1C

B9

8

cable

F

A

2

C

w

5

6

B4

B2

B7

B

B

B

B

A

B

A 6

A 5

4

F

A 3

A 2

1A

3D

4

Step 4: Pick the text box from the library which fits to the text you wish to write and modify the text

E

2E

3E

E 4

1

1

2F

F3

4

F

G1

G 2

3G

G 4

1H

H2

3H

4H

A C D

l

G

1

1R

1

F

1

8D

9D

5E

6E

7E

1

E

R

9

R

F

N

F

II

w

IV

C

C

AH

V

A

VIII

C'

H

IX

d

M = F • d

B

H

A

H6

7

D

VIIVI

A h

Bv

hB

IIII

hCv

Dh

Q

Q

C

Q

Q

Q

A

3

4

5

6

7

8

9

5N N5

M = F • d

1

2R

R3

4R

III

1

i

N

N

4

3 3

N

C'

N

N2

1NR N

C

5

6

7R

H

R

9

H

6

1

N

N

N

5

9N

N8

N

parallel lines

6

8

7

P

P

P

P

P

P

P

P

G

1

F

9

4

5

6

7

8

9

G 8

7

6

5

4

3

2

1

PP

P

P

P

P

P

F

P

P

Step 6: Copy the perpendicular line and place it through the corner of the text margin which is more near to the dimension line. Then, move the text box to the dimension line keeping the center of the box on the first perperdicular. Then group the text and the dimension line.

8

Ri

B

F

y

C'

F

R

G

w

2

F

Q

w

Text for dimensions 2 mm Arial Narrow

2.3 mm text Arial Narrow

generic security factormeaning unitssymbol 3.4 mm text Arial Narrow / subscript 2.3 mm

γγ = 1,35

= 1,5γsecurity factor materialsecurity factor external loadsecurity factor self-weight

M

EthblA

CBR

I

A'A

hinge

chosen point by the designerresulting point (intersection etc.)

44m /mmmoment of inertia

direction of rotation in cremona

section mark

symmetry

sliding support

hinge support

density kg/m3ρ

2N/mmgeneric strength of material

Elastic/Young’s modulus 2N/mmmthickness

depth mmwidth

length

7

2

G

2marea

subsystems (force elements where necessary)III III IV nodes in diagrams (where necessary)

support reaction force kNkNresultant force

area dead load kN/m2

kN/mlinear dead loadgarea life load kN/m2

q linear life loaddead load kN

kN/mG

kNlife loadQprestress force kNP

kNinternal compression force

N kNinternal tension forceF generic force kN

εσ 2kN/cmMPa2N/mm

mm/mmgeneric straingeneric stress

MγExternal force, 1 mm distance to structure / forces

Support forces, use margin symbol support

support force is 1.5 cm long, but in case it its represented in horizontal and vertical components it is relatively related to the magnitude

Uniformly distributed load: 0.5 cm and arrowhead 2mm

Resultant Force: 2 cm long and arrowhead 4.5 mm

External point force and support force: 1.5 cm long and arrowhead 3.5 mm

node numbers (Roman) (I,II, etc) from the library.if possible, place the node number to the right of the nodealso if possible below the nodeotherwise use your eye.

Position of arrowheads

element / subsystem numbers, from library. always in the center of the lineNotation - Form Diagram

Arrows & Arrowheads - Lengths

Notation - Force DiagramCremona- Construction without notationonly external forces..full arrow head

Cremona- Construction without notationinner forces always precise without arrowhead, external with an offset of 1.0 mm and with half arrow heads when internal eq is also shown

Cremona- Construction with notationexternal eq..corner point of name goes to the center of the line

Dimensioning

Cremona- Construction with notationinternal eq..offset from inner to external 1.5 mmNode number goes to barycenter of the triangle

Case 1: vertical forces --> name always on the right side of the force, in the centerpick text from the library!

Case 2: diagonal forces --> name always in the interior of the structure. Corner point in the center of the arrow. pick text from the library!

R

B7

H

6

H

8

F

w

A

I

G

A B

F

BA

F

arch

BA

F

I

I

F

A B

R

A

F

1

BA

F

I

F

A B

A

BF

5

A

A

B

I

1/32/3

I

line of the drawing

dimension from the library

9

Step 2: manually adapt it to the line of the drawing by rotating and streching one of its sides.

Step 1: Pick the dimension from the library

i

F

F

i

8

1

M

C

Step 5: Ungroup and erase the old text.Build a perpendicular line through the mid point of the dimension line and place the center of the text on it.

Point types - hinges / selected points / resulting pointsA hinge is a hinge --cicrle with no hatchA choosen geometric point is a thin black circle with grey hatchA resulting point is black point

---> take them from the library

7

A

C

F

H

Dimensioning

Please add the units (m) (mm) like in the following way.

25 m or 25.12 m250 mm or 25 cm25.1 cm or 251 mm

C

V

C

F

F

V

example:

III

II

I

R

R

B

A

3F

i

2

F1

F3

2F

1FIII

II

I

B

A

intersection point --> resultpoint selected on the closing string

Force 0.28 mm Bar 0.35 mm

Force- change line properties 0.28 mm

Bars - keep line properties

Drawing Conventions - Latest Update 17.09.2015

CS ISC closing string

nm

i intersection point of closing string and line of action of resultant

geometric planes

o' o'' o'''

r' r'' r''' rise point (form diagram)

trial pole (force diagram)o

E F

B

X

h

H

R

D

h

5

6

w

D

R

7

w

D

1R

R9

8

7

6

5

4

3

n

n

n

n

n

n

n

1

2n

n

i

i

80.2 kN

54.9 kN

54.9 kN

13 m

13 m

m88 m 13

kN8888 kN

kN88

i

0

1.50

i

yi

i

1.00

y

i

i

15.00

1.00

15.00

d

15.00

15.00

15.00

20.00

15.00

15.00

5.00

d

3

2

d

1

6f

m

y

cmmm

y

kNN

3

88.88 m

1

88 m

y

8.8 m

2

m8

d

m8.88

i

m88.8

d

m888

8 cm8.8 cm

8.88 cm88 cm

88.8 cm

888 cm88.88 mm

88 mm

8.8 mm

d

mm8

mm8.88

d

f

mm

f 1

88.8

f 2

kNf

f88.88

d

f

f

kN

f

f

88

3

4

kN

5

6

8.8

7

8

kN

f 9

8

8.88 kN

kN88.888.88 N

e

88 N

8.8 N

x

N8

N8.88

d

N88.8cm88.88

mm888

d

N888 888 kN888

kN88

kN88

i

f 6

i

88 kN kN88

88.8888.8

88

i

8.888.8

8

i

l

i i

i

i

i

d

i

i

2dd1

1d

l

d

d

2

5

2

2 3

322

4 9

1

5

2

6

1

7

2

3

4

2

81

1

1

1

1

1


MC

H

V

H

i

V

R

i

A

l

C

w

R

H

V

H

A

C

C

C

C'

C'

iy

i

i


M = C’H ∙ yi + C’V ∙ 0

= H ∙ yi

i

A

l

Ri

H

R

C

H

l

C

CV

w

B

A

i

2y

1

3

y1

2

3

y

0


M3 = H ∙ y3

M2 = H ∙ y2

M1 = H ∙ y1

M0 = H ∙ 0


>>

Bending frames



Introduction

Shaping Frames

31

A = F

F

d

∑ Fx = 0

∑ M ≠ 0

∑ Fy = 0

Shaping frames 32

F

M = F • d

A = F

d

Shaping frames 33

∑ Fx = 0

∑ M ≠ 0

∑ Fy = 0

A

FF

B

F

A

F

AA B

Shaping frames 34

C

CB A M

A

A

FF

A

B

A

F FF

F

A

F

A

ld

l

d d

Shaping frames 35

F • d = F • 0 = 0

A

FF

B

F

A

F

AA B

C

CB A M

A

A

FF

A

B

A

F FF

F

A

F

A

ld

l

d d

Shaping frames 36

F • d = F • 0 = 0

C

CB A M

A

A

FF

A

B

A

F FF

F

A

F

A

ld

l

d d

Shaping frames 37

F • d = F • 0 = 0 - F • d + B • l = 0

A

FF

B

F

A

F

AA B

C

CB A M

A

A

FF

A

B

A

F FF

F

A

F

A

ld

l

d d

Shaping frames 38

F • d = F • 0 = 0 - F • d + B • l = 0

C

CB A M

A

A

FF

A

B

A

F FF

F

A

F

A

ld

l

d d

Shaping frames 39

F • d = F • 0 = 0 - F • d + B • l = 0 - F • d + C • l = 0

A

FF

B

F

A

F

AA B

C

CB A M

A

A

FF

A

B

A

F FF

F

A

F

A

ld

l

d d

Shaping frames 40

F • d = F • 0 = 0 - F • d + B • l = 0 - F • d + C • l = 0

Shaping frames

Michael Jackson: Smooth criminal, 1987

41

A

FF

B

F

A

F

AA B

C

CB A M

A

A

FF

A

B

A

F FF

F

A

F

A

ld

l

d d

Shaping frames 42

F • d = F • 0 = 0 - F • d + B • l = 0 - F • d + C • l = 0

?

Shaping frames

Michael Jackson: Smooth criminal, 1987

43

F

B M = B • x

A

AM

B

dx

Shaping frames 44

∑ M = - F • d + M

= - F • d + B • x

Shaping frames 45

Shaping frames 46

Shaping frames 47

Shaping frames

Taq-i Kisra Palast (Ayvan-e Kasra), Asbanbar, near Baghdad, 550 n.Chr.

48

Shaping frames 49

Shaping frames 50

Shaping frames

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

51

Shaping frames

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

52

M

M

R11

R1

R

i

R

R = w • l

R

R

R

R

w

F

M

y

C

2

1

F

F

M = F • d

H

F

R

1

M 2= F • d

B

H

C

1

C

i

A

A

Ri

R

C

2

1

1

H

8

F

R

w

F

2

F

5

C

A

F

R = w • l

4

2

N

A

w

A

1

1

1

F

A

Q

C

H

A

C'

M = B • x

i

B

i

X

i

Ai

N

C'

C

i

C

H

H

i

l

R

A

i

i

l

C

i

N

x

w

R

A

F

i

C'

A

w

Q

V

H

y

R

A

A

V

V

i

l

R

H

V

l

= F • d

A

M

1

F

H

w

F

C

V

A B

w

A

R

1F

H

C

F

i

l

w

A

R

A = F

l

3

H

H



3

C

R

V

A

w

F

F

l

C

w

A

A

A

1

1

1

R

w

lBA

Q

E

9

F

R

C'

w

C

F

A

A

V

F

R

5

l

i

V

F

C

v

II

A

A

SC ICS IISC III

F

C

N

C

A

N

C

V

C'

C'

9

6

N

V

F

6

P

R

V

M

1

3

5

H

9

i

w

M

A

P

B

M = F • d

R

C

C'

ii

A

w

l

F

H

F

l

B

R

A

C

A

C

B

w

R

F

A

C

C

F

H

C

C

F

V

C

H

F

l

F

length

A

2area

i

2M

VII

F

= F • d11

kN/m

i

w

H

D2

1D

C 8

9C

generic force

7

C 6

5C

C 4

3C

C 2

1C

B9

8

C

7A

8

A

A 9

A

6

B4

B2

B7

B

B

B3

1B

A 6

A

5

4

R

A 3

A 2


A = F


D


1

i

Free-Body diagram


H

E


1

1

2F

F3

4F

G1

G 2

3G

G 4

1H

H2

3H

4H

A C D

H

R

B

R1

R

1

D

8D

9D

5E

6E

7E

8

1

E

1

5

A

6

I

C

A

B

V

C

w

C

VI

R

VIII IX

B

9

H

H

1

d

H

H

6

7

Dv

A h

w

v

h

IV

v

III

hC

C

Dh

Q

Q

Q

Q

Q

Q

w

2

3

4

5

6

7

8

9

5N N5

R1

2R

R3

4

R

N1

2N

N

4N3 3

H4

N

N2

1NR

H

N

A

R

6

7

parallel lines

8R

5

R

1

N

N

N

F

9 9N

N8

N

N

G

7

8

7

P

P

F

P

P

P

P

P

PP

9

2

x

4

G

6

7

88

9

8

7

6

5

4

3

2

1

M

P

P

P

P

P

P

P

P

P


= w • l

F

F

B

R

G

R

F

C

w

C

1

Q




γγ = 1,35


fEthblA

CB

I

A'A

hinge




section mark

symmetry

sliding support

hinge support

density kg/m3ρ



depth mmwidth

7

m

2mm

i

m

G




6

linear dead loadgarea life load kN/m2


kN/mG



N kNinternal tension forceF

i

kN

εσ 2kN/cmMPa2N/mm















Dimensioning




cable

B

H

G

C F

C

H

A

H

I

5

R

B

F

BA

F

arch

BA

F

I

I

F

A B

BA

F

9

BA

F

I

F

F

B

A

BF

F

A

A

B

I

1/32/3

I

line of the drawing

R

1A


F


A

R

8

F

B

D

M

H

E


7F

E

C

C

H

Dimensioning


w

E 4

F

V

F

example:

III

II

I

R

R

B

A

3F

F2

F1

F3

2F

1FIII

II

I

B

A







nm


geometric planes

o' o'' o'''



E

B

F

l

G

R

H

h

D5

h

6

R

D

w

7

R

1R

R9

8

7

6

5

4

3

n

n

n

n

n

n

n

1

2n

n

i

i

80.2 kN

54.9 kN

54.9 kN

13 m

13 m

m88 m 13

kN88

0

88 kN

i

kN88

i

1.50

yi

i

1.00

y

i

i

d

15.00

1.00

15.00

15.00

d

15.00

15.00

20.00

15.00

15.00

5.00

3

2

d

1

6f

y

mcm

y

mmkN

3

N

88.88

1

m

88

y

m

8.8

2

d

mm8

m

i

d

8.88

m88.8

m888

8 cm8.8 cm

8.88 cm88 cm

88.8 cm

888 cm88.88 mm

88

d

mm

8.8 mmmm

d

8

mm8.88

mm

f

f

88.8

1

f

kN

d

2

f88.88

f

f

kN

f

f

88

f

3

kN

4

5

8.8

6

7

kN

8

f

8

9

8.88 kN

kN

e

88.888.88 N

88 N

8.8

x

NN8

N

d

8.88

N88.8cm88.88

mm

d

888N888 888 kN888

kN88

kN88

f

i

6

i

88

i

kN kN88

88.8888.8

888.888.8

8

i

l

i i

i

i

d

ii

i

2d

l

d1

1d

d

d

2

5

2

2 3

322

4 9

1

5

2

6

1

7

2

3

4

2

81

1

1

1

1

1

Shaping frames 53

M

M

R11

R1

R

i

R

R = w • l

R

R

R

R

w

F

M

y

C

2

1

F

F

M = F • d

H

F

R

1

M 2= F • d

B

H

C

1

C

i

A

A

Ri

R

C

2

1

1

H

8

F

R

w

F

2

F

5

C

A

F

R = w • l

4

2

N

A

w

A

1

1

1

F

A

Q

C

H

A

C'

M = B • x

i

B

i

X

i

Ai

N

C'

C

i

C

H

H

i

l

R

A

i

i

l

C

i

N

x

w

R

A

F

i

C'

A

w

Q

V

H

y

R

A

A

V

V

i

l

R

H

V

l

= F • d

A

M

1

F

H

w

F

C

V

A B

w

A

R

1F

H

C

F

i

l

w

A

R

A = F

l

3

H

H



3

C

R

V

A

w

F

F

l

C

w

A

A

A

1

1

1

R

w

lBA

Q

E

9

F

R

C'

w

C

F

A

A

V

F

R

5

l

i

V

F

C

v

II

A

A

SC ICS IISC III

F

C

N

C

A

N

C

V

C'

C'

9

6

N

V

F

6

P

R

V

M

1

3

5

H

9

i

w

M

A

P

B

M = F • d

R

C

C'

ii

A

w

l

F

H

F

l

B

R

A

C

A

C

B

w

R

F

A

C

C

F

H

C

C

F

V

C

H

F

l

F

length

A

2area

i

2M

VII

F

= F • d11

kN/m

i

w

H

D2

1D

C 8

9C

generic force

7

C 6

5C

C 4

3C

C 2

1C

B9

8

C

7A

8

A

A 9

A

6

B4

B2

B7

B

B

B3

1B

A 6

A

5

4

R

A 3

A 2


A = F


D


1

i

Free-Body diagram


H

E


1

1

2F

F3

4F

G1

G 2

3G

G 4

1H

H2

3H

4H

A C D

H

R

B

R1

R

1

D

8D

9D

5E

6E

7E

8

1

E

1

5

A

6

I

C

A

B

V

C

w

C

VI

R

VIII IX

B

9

H

H

1

d

H

H

6

7

Dv

A h

w

v

h

IV

v

III

hC

C

Dh

Q

Q

Q

Q

Q

Q

w

2

3

4

5

6

7

8

9

5N N5

R1

2R

R3

4

R

N1

2N

N

4N3 3

H4

N

N2

1NR

H

N

A

R

6

7

parallel lines

8R

5

R

1

N

N

N

F

9 9N

N8

N

N

G

7

8

7

P

P

F

P

P

P

P

P

PP

9

2

x

4

G

6

7

88

9

8

7

6

5

4

3

2

1

M

P

P

P

P

P

P

P

P

P


= w • l

F

F

B

R

G

R

F

C

w

C

1

Q




γγ = 1,35


fEthblA

CB

I

A'A

hinge




section mark

symmetry

sliding support

hinge support

density kg/m3ρ



depth mmwidth

7

m

2mm

i

m

G




6



kN/mG




i

kN

εσ 2kN/cmMPa2N/mm















Dimensioning




cable

B

H

G

C F

C

H

A

H

I

5

R

B

F

BA

F

arch

BA

F

I

I

F

A B

BA

F

9

BA

F

I

F

F

B

A

BF

F

A

A

B

I

1/32/3

I

line of the drawing

R

1A


F


A

R

8

F

B

D

M

H

E


7F

E

C

C

H

Dimensioning


w

E 4

F

V

F

example:

III

II

I

R

R

B

A

3F

F2

F1

F3

2F

1FIII

II

I

B

A







nm


geometric planes

o' o'' o'''



E

B

F

l

G

R

H

h

D5

h

6

R

D

w

7

R

1R

R9

8

7

6

5

4

3

n

n

n

n

n

n

n

1

2n

n

i

i

80.2 kN

54.9 kN

54.9 kN

13 m

13 m

m88 m 13

kN88

0

88 kN

i

kN88

i

1.50

yi

i

1.00

y

i

i

d

15.00

1.00

15.00

15.00

d

15.00

15.00

20.00

15.00

15.00

5.00

3

2

d

1

6f

y

mcm

y

mmkN

3

N

88.88

1

m

88

y

m

8.8

2

d

mm8

m

i

d

8.88

m88.8

m888

8 cm8.8 cm

8.88 cm88 cm

88.8 cm

888 cm88.88 mm

88

d

mm

8.8 mmmm

d

8

mm8.88

mm

f

f

88.8

1

f

kN

d

2

f88.88

f

f

kN

f

f

88

f

3

kN

4

5

8.8

6

7

kN

8

f

8

9

8.88 kN

kN

e

88.888.88 N

88 N

8.8

x

NN8

N

d

8.88

N88.8cm88.88

mm

d

888N888 888 kN888

kN88

kN88

f

i

6

i

88

i

kN kN88

88.8888.8

888.888.8

8

i

l

i i

i

i

d

ii

i

2d

l

d1

1d

d

d

2

5

2

2 3

322

4 9

1

5

2

6

1

7

2

3

4

2

81

1

1

1

1

1

Shaping frames 54

Shaping frames

Marcel Breuer, Bernhard Zehrfuss, Pier Luigi Nervi: Head quarters, UNESCO, Paris, 1957

55

Shaping frames

Marcel Breuer, Bernhard Zehrfuss, Pier Luigi Nervi: Headquarters, UNESCO, Paris, 1957

56

M

R

V

R

N

C

i

A

i

C

i

i

w

V

i

l

A

i

l

i

Ni

i

Shaping frames 57

Shaping frames

Sir Nicholas Grimshaw (Arch.) , Anthony Hunt (Eng.): Waterloo International Terminal, London UK, 1993

58

Shaping frames


59

Shaping frames


60

Shaping frames


61

Shaping frames


62

Shaping frames


63

Shaping frames

GMP Architects, Schlaich Bergermann und Partner (Eng.): Central Station, Berlin, 2006

64

Shaping frames


65

Shaping frames


66

Shaping frames


67

Shaping frames


68

Shaping frames


69

Shaping frames

Zaha Hadid Architects: Bergisel ski jump, Innsbruck, Austria, 2002

70

Shaping frames


71

Shaping frames


72

Shaping frames


73

Shaping frames


74

eQ Free-form thrust lines

http://www.block.arch.ethz.ch/eq/drawing/view/45

Shaping frames 75

ADD FORCE DIAGRAMS

Shaping frames 76

C

CB A M

A

A

FF

A

B

A

F FF

F

A

F

A

ld

l

d d

C

CB A M

A

A

FF

A

B

A

F FF

F

A

F

A

ld

l

d d

M

M

R11

R1

R

i

R

R = w • l

R

R

R

R

w

F

M

y

C

2

1

F

F

M = F • d

H

F

R

1

M 2= F • d

B

H

C

1

C

i

A

A

Ri

R

C

2

1

1

H

8

F

R

w

F

2

F

5

C

A

F

R = w • l

4

2

N

A

w

A

1

1

1

F

A

Q

C

H

A

C'

M = B • x

i

B

i

X

i

Ai

N

C'

C

i

C

H

H

i

l

R

A

i

i

l

C

i

N

x

w

R

A

F

i

C'

A

w

Q

V

H

y

R

A

A

V

V

i

l

R

H

V

l

= F • d

A

M

1

F

H

w

F

C

V

A B

w

A

R

1F

H

C

F

i

l

w

A

R

A = F

l

3

H

H



3

C

R

V

A

w

F

F

l

C

w

A

A

A

1

1

1

R

w

lBA

Q

E

9

F

R

C'

w

C

F

A

A

V

F

R

5

l

i

V

F

C

v

II

A

A

SC ICS IISC III

F

C

N

C

A

N

C

V

C'

C'

9

6

N

V

F

6

P

R

V

M

1

3

5

H

9

i

w

M

A

P

B

M = F • d

R

C

C'

ii

A

w

l

F

H

F

l

B

R

A

C

A

C

B

w

R

F

A

C

C

F

H

C

C

F

V

C

H

F

l

F

length

A

2area

i

2M

VII

F

= F • d11

kN/m

i

w

H

D2

1D

C 8

9C

generic force

7

C 6

5C

C 4

3C

C 2

1C

B9

8

C

7A

8

A

A 9

A

6

B4

B2

B7

B

B

B3

1B

A 6

A

5

4

R

A 3

A 2


A = F


D


1

i

Free-Body diagram


H

E


1

1

2F

F3

4F

G1

G 2

3G

G 4

1H

H2

3H

4H

A C D

H

R

B

R1

R

1

D

8D

9D

5E

6E

7E

8

1

E

1

5

A

6

I

C

A

B

V

C

w

C

VI

R

VIII IX

B

9

H

H

1

d

H

H

6

7

Dv

A h

w

v

h

IV

v

III

hC

C

Dh

Q

Q

Q

Q

Q

Q

w

2

3

4

5

6

7

8

9

5N N5

R1

2R

R3

4

R

N1

2N

N

4N3 3

H4

N

N2

1NR

H

N

A

R

6

7

parallel lines

8R

5

R

1

N

N

N

F

9 9N

N8

N

N

G

7

8

7

P

P

F

P

P

P

P

P

PP

9

2

x

4

G

6

7

88

9

8

7

6

5

4

3

2

1

M

P

P

P

P

P

P

P

P

P


= w • l

F

F

B

R

G

R

F

C

w

C

1

Q




γγ = 1,35


fEthblA

CB

I

A'A

hinge




section mark

symmetry

sliding support

hinge support

density kg/m3ρ



depth mmwidth

7

m

2mm

i

m

G




6



kN/mG




i

kN

εσ 2kN/cmMPa2N/mm















Dimensioning




cable

B

H

G

C F

C

H

A

H

I

5

R

B

F

BA

F

arch

BA

F

I

I

F

A B

BA

F

9

BA

F

I

F

F

B

A

BF

F

A

A

B

I

1/32/3

I

line of the drawing

R

1A


F


A

R

8

F

B

D

M

H

E


7F

E

C

C

H

Dimensioning


w

E 4

F

V

F

example:

III

II

I

R

R

B

A

3F

F2

F1

F3

2F

1FIII

II

I

B

A







nm


geometric planes

o' o'' o'''



E

B

F

l

G

R

H

h

D5

h

6

R

D

w

7

R

1R

R9

8

7

6

5

4

3

n

n

n

n

n

n

n

1

2n

n

i

i

80.2 kN

54.9 kN

54.9 kN

13 m

13 m

m88 m 13

kN88

0

88 kN

i

kN88

i

1.50

yi

i

1.00

y

i

i

d

15.00

1.00

15.00

15.00

d

15.00

15.00

20.00

15.00

15.00

5.00

3

2

d

1

6f

y

mcm

y

mmkN

3

N

88.88

1

m

88

y

m

8.8

2

d

mm8

m

i

d

8.88

m88.8

m888

8 cm8.8 cm

8.88 cm88 cm

88.8 cm

888 cm88.88 mm

88

d

mm

8.8 mmmm

d

8

mm8.88

mm

f

f

88.8

1

f

kN

d

2

f88.88

f

f

kN

f

f

88

f

3

kN

4

5

8.8

6

7

kN

8

f

8

9

8.88 kN

kN

e

88.888.88 N

88 N

8.8

x

NN8

N

d

8.88

N88.8cm88.88

mm

d

888N888 888 kN888

kN88

kN88

f

i

6

i

88

i

kN kN88

88.8888.8

888.888.8

8

i

l

i i

i

i

d

ii

i

2d

l

d1

1d

d

d

2

5

2

2 3

322

4 9

1

5

2

6

1

7

2

3

4

2

81

1

1

1

1

1

Documents

Structural Design II - ETH Z frames_ER...Notation - Force Diagram Cremona- Construction without notation only external forces..full arrow head Cremona- Construction without notation