Non linear seismic analysis of masonry buildings - 1

Non-linear Seismic Analysis of Masonry Buildings

S.T.A. DATA srl - C.So Raffaello, 12 10126 Torino Italy+39 011 6699345 fax + 39 011 6699375 email: comm@stadata.com www.3muri.com

Non linear seismic analysis of masonry buildings - 2

Global response of masonry buildings: wall in-plane behaviour

Local devices resist to out-of-plane

mechanisms and favour a global

behaviour governed by wall in-plane

response Piers and spandrel beams

Non linear seismic analysis of masonry buildings - 3

In plane modelling

T

N

Non linear seismic analysis of masonry buildings - 4

Damage and failure modes

Non linear seismic analysis of masonry buildings - 5

The non-linear macro-element

Bending-rocking

Shear-sliding (friction)

Non linear seismic analysis of masonry buildings - 6

3D masonry building modelHypotheses:Hypotheses:Hypotheses: Earthquake Resistant Structure: walls + floors

Walls are bearing elements

Floors share vertical loads to the walls and are planar stiffening elements (orthotropic membranes)

Walls out-of-plane behaviour and flexural floors response negligible with respect to global one

Wall in-plane model:Wall inWall in--plane model:plane model: Frame-type model

2 nodes macro-elements: piers and lintels

Joints: rigid bodies

Tie-rods (no compression spar) and stringcourses (beam) elements included

Non linear seismic analysis of masonry buildings - 7

Macro-element wall models

Earthquake Damage ObservationFEM Non-linear Continuum Model

RigidNode

Spandrel

Pier

Non linear seismic analysis of masonry buildings - 8

3D MODEL

2D NODE

(3 d.o.f.)

3D NODE

(5 d.o.f.)

Z

z

xloc

X X

Y I J

K

Z

X

Y

Non linear seismic analysis of masonry buildings - 9

Pushover analysis

Base shear

F1

Fi

Fi+1

Fn

= n ib FT1

dtop

Non linear seismic analysis of masonry buildings - 10

Capacity curve

DTOP

TB

SASD

SA

SD

SA

SD

Non linear seismic analysis of masonry buildings - 11

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80

D [cm]

A [g]

Bilinear Approximation

Pushover analysis

81 82

83 84

85 86 87

88

89

90 91

n16 n17

N21

N25

N29

N33

N37

N41

N45

N49

N53

51 52 53

54 55 56

57 58 59

60 61

62 63

64 65

n10 n11 n12

N23

N27

N31

N35

N39

N43

N47

N51

N55

51 52 53

54 55 56

57 58 59

60 61

62 63

64 65

n10 n11 n12

N23

N27

N31

N35

N39

N43

N47

N51

N55

36 37 38

39 40 41

42 43 44

45 46

47 48

49 50

n7 n8 n9

N24

N28

N32

N36

N40

N44

N48

N52

N56

3D Pushover Analysis

= 2

ii

ii

mm

D = d/ A = V/

Capacity Curve:Base shear vs.Displacement

36 37 38

39 40 41

42 43 44

45 46

47 48

49 50

n7 n8 n9

N24

N28

N32

N36

N40

N44

N48

N52

N56

S.d.o.f. Equivalent System

( )2*2

i i

i i

mm m

m= =

m

Displacement demand

yy ADT /2* =

** ( )e

y

S Tqa

=

max (1 ( * 1) / *)C yD q T T D= + (Fajfar, 1999; EC8)

WALL 1

WAL

L 4

WALL 2

WAL

L 3

3D Pushover Analysis

3D Pushover Analysis

P1

P2

P3 P4

0

50000

100000

150000

200000

250000

300000

350000

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016

Parete 1Parete 2Globale

Rigid floors

P1

P2

P3 P4

0

50000

100000

150000

200000

250000

300000

350000

0 0.002 0.004 0.006 0.008 0.01 0.012

T

a

g

l

i

o

a

l

l

a

b

a

s

e

[

N

]

Parete 1Parete 2Globale

Flexible floors

Model validation: numerical simulation of experimental testing on a full-scale URM building

(University of Pavia Magenes, Calvi & Kingsley, 1995)

25 20 15 10 5 0 5 10 15 20 25

Numerical results

Damage pattern

n1 n2 n3

n4

n5

n6 n7

n8 n9

1 2 3

4 5 6

7 8

9 10

1 2

3 4

Non linear seismic analysis of masonry buildings - 16

Seismic Code Analyses by 3muri

P1

P2

P3

P4

P5 P6 P7 P8P1

P2

P3

P4

P5 P6 P7 P8

0

500

1000

1500

2000

2500

3000

3500

0 0.5 1 1.5 2 2.5 3 3.5 4

Drift ultimo

No Drift

N9 N10 N11 N12

N109 N110 N111 N112

N209 N210 N211 N212

N309 N310 N311 N312

N409 N410 N411 N412

300

301

302

303

304

305

306

307

308

309

310

311

312

313

314

315

316 317

318 319 320

321 322 323

324 325 326

237

38

39

40

41

42

43

44

45

46

47

48

Element expiration at ultimate drift

Bilinear element force- displacement curve

Non-linear 3D pushover analysis Automatic calculation of

rectangular and triangular force distribution

Automatic additional eccentricity Non-linear 3D time-history

analysis Spatial variability of ground

motion (bridges) Mixed structures Automatic mesh generation

Non linear seismic analysis of masonry buildings - 17

0

20

40

60

80

100

120

140

160

180

200

220

240

260

280

300

0.000 20.000 40.000 60.000 80.000 100.000 120.000 140.000 160.000 180.000 200.000

Seismostruct dxTremuri dxTremuri sxSeismostruct sx

1 2 3

4 5 6

7 8 9

10 11 12 13

14 15 16 17

18 19 20 21

n2 n3

n6 n7

n10 n11

n14 n15

N1 N4

N5 N8

N9 N12

N13 N16

1 2 3

4 5 6

7 8 9

10 11 12 13

14 15 16 17

18 19 20 21

n2 n3

n6 n7

n10 n11

n14 n15

N1 N4

N5 N8

N9 N12

N13 N16

1 2 3

4 5 6

7 8 9

10 11 12 13

14 15 16 17

18 19 20 21

n2 n3

n6 n7

n10 n11

n14 n15

N1 N4

N5 N8

N9 N12

N13 N16

1 2 3

4 5 6

7 8 9

10 11 12 13

14 15 16 17

18 19 20 21

n2 n3

n6 n7

n10 n11

n14 n15

N1 N4

N5 N8

N9 N12

N13 N16

Element expiration at ultimate drift

Bilinear element force- displacement curve

Non-linear 3D pushover analysis Automatic calculation of

rectangular and triangular force distribution

Automatic additional eccentricity Non-linear 3D time-history

analysis Spatial variability of ground

motion (bridges) Mixed structures Automatic mesh generation

Seismic Code Analyses by 3MURI

Non linear seismic analysis of masonry buildings - 18

Element expiration at ultimate drift

Bilinear element force- displacement curve

Non-linear 3D pushover analysis Automatic calculation of

rectangular and triangular force distribution

Automatic additional eccentricity Non-linear 3D time-history

analysis Spatial variability of ground

motion (bridges) Mixed structures Automatic mesh generation

Seismic Code Analyses by 3muri

Non linear seismic analysis of masonry buildings - 19

Seismic assessment of existing structures

Diapositive numro 123D Pushover AnalysisDamage pattern