understanding the complexities of designing diaphragm 155

56
Understanding the Complexities of Designing Diaphragms in Buildings for Earthquakes Des K. Bull Holmes Consulting Group Ltd

Upload: antonio-henry

Post on 14-Apr-2017

218 views

Category:

Documents


5 download

TRANSCRIPT

Page 1: Understanding the Complexities of Designing Diaphragm 155

Understanding the Complexities of Designing Diaphragms in Buildings for Earthquakes

Des K. BullHolmes Consulting Group Ltd

Page 2: Understanding the Complexities of Designing Diaphragm 155

2

Function of Diaphragms

1. Relatively thin but stiff horizontal structural systems which transmit in-plane lateral forces to, or between, vertical lateral force resisting elements.

2. The diaphragms tie the whole structure together.

Page 3: Understanding the Complexities of Designing Diaphragm 155

3

Page 4: Understanding the Complexities of Designing Diaphragm 155

4

Forces in diaphragms under earthquakes

• ‘Inertia’ forces– Inertia at a particular floor

• ‘Transfer’ forces– Forces develop between primary lateral

force resisting structures– These forces are often very large.

Force distribution in a floor diaphragm = Inertia + Transfer forces

Page 5: Understanding the Complexities of Designing Diaphragm 155

5

Forces in diaphragm (cont.)

• Inertia and “transfer” forces are COUPLED in the analysis.

– through stiffness and deformation compatibility of the diaphragms and vertical structural systems.

• CAN’T determine distribution of “transfer” forces or inertia in isolation.

Page 6: Understanding the Complexities of Designing Diaphragm 155

6

Floor plan configuration issues

Page 7: Understanding the Complexities of Designing Diaphragm 155

7

• Plan configurations

Page 8: Understanding the Complexities of Designing Diaphragm 155

8

• Plan configurations

Page 9: Understanding the Complexities of Designing Diaphragm 155

9

Pretensioned, precast concrete floors with cast-in-place topping

• Are these more of a concern than cast-in-place slabs ?

Page 10: Understanding the Complexities of Designing Diaphragm 155

10

Pretensioned, precast concrete floors with cast-in-place topping

Page 11: Understanding the Complexities of Designing Diaphragm 155

11

Structural Behaviour of Diaphragms

Page 12: Understanding the Complexities of Designing Diaphragm 155

12

Beam Analogy

Page 13: Understanding the Complexities of Designing Diaphragm 155

13

Openings in diaphragms and “Strut & Tie” methods

• “Strut & Tie”– Advantages over the simple Beam or

Tied Arch approach

Page 14: Understanding the Complexities of Designing Diaphragm 155

14

Openings in diaphragms and “Strut & Tie” methods

Diagonal compression fields

Page 15: Understanding the Complexities of Designing Diaphragm 155

15

Openings in diaphragms and “Strut & Tie” methods

Load paths in a section of floor: “micro strut & tie” solution

Page 16: Understanding the Complexities of Designing Diaphragm 155

16

Openings in diaphragms and “Strut & Tie” methods

Diagonal tension fields

Page 17: Understanding the Complexities of Designing Diaphragm 155

17

“Beam” or “Tied Arch” or “Strut & Tie” ?

– simple model– Provision of “tie” reinforcement

Page 18: Understanding the Complexities of Designing Diaphragm 155

18

“Drag Bars” or “Collectors”

Page 19: Understanding the Complexities of Designing Diaphragm 155

19

“Strut & Tie” with “drag” bars

A bit complex?

Page 20: Understanding the Complexities of Designing Diaphragm 155

20

“Drag Bars” or “Collectors”

Page 21: Understanding the Complexities of Designing Diaphragm 155

21

Diaphragms: Force distribution and detailing

EQF i : floor, beams, columns and cladding

Floor plate

Page 22: Understanding the Complexities of Designing Diaphragm 155

22

EQF i : floor, beams, columns and cladding

Inertia effects, distributed across the floor

Diaphragms: Force distribution and detailing

Page 23: Understanding the Complexities of Designing Diaphragm 155

23

EQF i : floor, beams, columns and cladding

Compression fan develops

Diaphragms: Force distribution and detailing

Page 24: Understanding the Complexities of Designing Diaphragm 155

24

EQF i : floor, beams, columns and cladding

C C

C’

Sketch in the centres of compression: struts of a truss

Diaphragms: Force distribution and detailing

Page 25: Understanding the Complexities of Designing Diaphragm 155

25

Note: the tie T is connected at the mid points of the beams

• more later

EQF i : floor, beams, columns and cladding

C C

C’

T

Diaphragms: Force distribution and detailing

Page 26: Understanding the Complexities of Designing Diaphragm 155

26

EQF i : floor, beams, columns and cladding

C C

C’

T

Part of the floor (mauve) wants to “fall out” of the building

Diaphragms: Force distribution and detailing

Page 27: Understanding the Complexities of Designing Diaphragm 155

27

EQF i : floor, beams, columns and cladding

C C

C’

T

Must tie this part back in to the truss or arch (dotted red ties)

Diaphragms: Force distribution and detailing

Page 28: Understanding the Complexities of Designing Diaphragm 155

28

Alternatively: use secondary beams as ties/chords and make smaller struts to collect on these ties

EQF i : floor, beams, columns and cladding

C C

C’

T

Diaphragms: Force distribution and detailing

Page 29: Understanding the Complexities of Designing Diaphragm 155

29

Or, combine the secondary beams withthe floor reinforcement acting as ties

EQF i : floor, beams, columns and cladding

C C

C’

T

Diaphragms: Force distribution and detailing

Page 30: Understanding the Complexities of Designing Diaphragm 155

30

EQF i : floor, beams, columns and cladding

C C

C’

More struts, closer to the fan compression field

Diaphragms: Force distribution and detailing

Page 31: Understanding the Complexities of Designing Diaphragm 155

31

Diaphragms: Forces

EQF i : floor, beams, columns and cladding

C C

C’

T

Struts and ties

T is smallerTo get other ties, requires some cracking and yielding within the floor: “redistribution of actions”

Page 32: Understanding the Complexities of Designing Diaphragm 155

32

Issues for Diaphragms when resisting Earthquakes

Page 33: Understanding the Complexities of Designing Diaphragm 155

33

Page 34: Understanding the Complexities of Designing Diaphragm 155

34

Deformation modes with beam elongation

(a) Beam plastic hinge rotates to allow for beam elongation (10 – 50 mm)

Bea

m e

long

atio

n

Beam elongation

Loss

of

sup

por

t pos

sible

ove

r thi

s re

gio

n

Mode 1

Page 35: Understanding the Complexities of Designing Diaphragm 155

35

Deformation modes with beam elongation

(b) Entire beam rotates to allow for beam elongation (10 – 50 mm)

Beam elongation

Bea

m e

long

atio

n

Loss

o

f sup

po

rt p

oss

ible

ove

r thi

s re

gio

n

Mode 2

Page 36: Understanding the Complexities of Designing Diaphragm 155

36

Delamination of topping from hollowcore units

South

North

Plan View

Page 37: Understanding the Complexities of Designing Diaphragm 155

37

Diaphragms: Connections or Nodes of the Struts and Ties

Column-Beam Node: Traditional view• Higher compressive stress - smaller contact surface

Page 38: Understanding the Complexities of Designing Diaphragm 155

38

Diaphragms: Connections or Nodes of the Struts and Ties

Column-Beam Node

• Potentially large plasticity demands in Ties

Page 39: Understanding the Complexities of Designing Diaphragm 155

39

Diaphragms: Connections or Nodes of the Struts and Ties

Node locations (where the struts and ties meet):

• Mid-point of beams– these points are relatively undamaged by

ductile frame action– Keep TIE steel away from primary beams

because this steel can be included in the tension flange (negative moment, typ.)

Page 40: Understanding the Complexities of Designing Diaphragm 155

40

Diaphragms: Connections or Nodes of the Struts and Ties

Floor-Beam Node• Distributed node - keeps compressive stresses down

Page 41: Understanding the Complexities of Designing Diaphragm 155

41

Diaphragms: Connections or Nodes of the Struts and Ties

Floor-Beam Node• Distributed node - keeps compressive stresses down

Page 42: Understanding the Complexities of Designing Diaphragm 155

42

NZS 3101:1995 requires:

Tension component

Page 43: Understanding the Complexities of Designing Diaphragm 155

43

Alternative layout of reinforcement for column tie

Page 44: Understanding the Complexities of Designing Diaphragm 155

44

Detailing for integrity

Page 45: Understanding the Complexities of Designing Diaphragm 155

45

Detailing for integrity

Page 46: Understanding the Complexities of Designing Diaphragm 155

46

Determining forces in Diaphragms resulting from Earthquakes

Page 47: Understanding the Complexities of Designing Diaphragm 155

47

Diaphragms: Forces

‘Inertia’ & ‘Transfer’ forces are COUPLED– These can not be treated in isolation.

• Some analysis methods:

Equivalent Static Analysis (ESA)

• You have equilibrium (magnitudes and directions of the applied forces at the boundary of the diaphragm).

• If the TIES are connected correctly, this mitigates the coarseness of ESA.

Fi

Page 48: Understanding the Complexities of Designing Diaphragm 155

48

Diaphragms: Forces

Fi

Equivalent Static Analysis (ESA)

Maxima Envelope of Floor Accelerations

(DR 902 Parts)

Fi

Peak Ground Accn.

Page 49: Understanding the Complexities of Designing Diaphragm 155

49

Diaphragms: Forces

‘Inertia’ & ‘Transfer’ forcesModal Analysis

WON’T work

• you DO NOT have equilibrium.

– Or model the diaphragm in the analysis model ?

Page 50: Understanding the Complexities of Designing Diaphragm 155

50

Diaphragms: Introduced Forces

At each floor:• Using an ESA (?) :

– Determine the shear force distribution for walls, frames and columnsF2

Vbase i

He

ight

Shear in Wall i

• Calculate the storey forces Fi for each structural sub-system– It is these Fi that make

up the boundary conditions on each floor.

Page 51: Understanding the Complexities of Designing Diaphragm 155

51

Diaphragms: Introduced Forces

Actions on the diaphragm: ESA

1500 kN

FD = 2000 kN

500 kN

F i : floor, beams, columns and cladding

250 250 250

250 250 250Inertia = 165 kN

Page 52: Understanding the Complexities of Designing Diaphragm 155

52

Diaphragms: Introduced Forces

1500 kN

FD = 2000 kN

500 kN

F i : floor, beams, columns and cladding

250 250 250

250 250 250

≅ 500 kN≅ 1500 kN

Page 53: Understanding the Complexities of Designing Diaphragm 155

53

Diaphragms: Introduced Forces

Page 54: Understanding the Complexities of Designing Diaphragm 155

54

Conclusions: Issues

• Strut and Tie method is more versatile than the Beam or Tied Arch approach.

• Diaphragm will be damaged locally and may need some limited redistribution of internal forces.– Detailing of the floors to ensure integrity of the floor is

essential:• Maintenance of load paths• Continued support of gravity

Page 55: Understanding the Complexities of Designing Diaphragm 155

55

Conclusions: Issues

• Estimating magnitudes of the inter-related inertia and “transfer” forces requires further study:– A type of Equivalent Static Analysis that

generates the deformations of the structure (induces “transfer” forces) while producing reasonable magnitudes of inertia is highly desirable for desk-top design.

Page 56: Understanding the Complexities of Designing Diaphragm 155

56