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15 th WORLD CONFERENCE ON EARTHQUAKE ENGINEERING Special Session SEISMIC RETROFIT OF MASONRY STRUCTURES September 24, 2012 - Lisbon, Portugal. Vulnerability assessment by macroseismic and mechanical-based models Seismic analysis of masonry buildings. Sergio LAGOMARSINO - PowerPoint PPT Presentation
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15th WORLD CONFERENCE ON EARTHQUAKE ENGINEERINGSpecial Session
SEISMIC RETROFIT OF MASONRY STRUCTURESSeptember 24, 2012 - Lisbon, Portugal
Sergio LAGOMARSINOUniversity of Genoa, Italy
sergio.lagomarsino@unige.it
Vulnerability assessment by macroseismic and mechanical-based models
Seismic analysis of masonry buildings
• Evaluation methods (at National scale)• Numerical simulation methods
Observational methods: DPM (Damage Probability Matrix), based on observed vulnerability. Implicitly contained in the macroseismic scaleSeismic input: IntensityDamage representation: 5 observed damage grades: D1 - D5
Class A I = VII
0510152025303540
0 1 2 3 4 5Damage Grade
Prob
abili
ty
Mechanical methods: Capacity Spectrum Method: vulnerability represented by a capacity curve; demand-capacity - performance evaluationSeismic input: Acceleration Displacement Response SpectraDamage representation: 4 Damage Limit States (performance levels)
Non-linear equivalent s.d.o.f. structure Capacity Curve
Sa
Sd
Au
Ay
Dy Du
LS1
LS2
LS3
LS4
Acceleration-Displacement Response Spectrum
Performance Point
0,670,470,201,3E-020,00183,2E-0950,280,380,389,2E-020,0237,8E-074
4,6E-020,120,2870,250,1177,6E-053
3,9E-032,0E-020,1080,340,2960,0382
1,6E-041,6E-032,0E-020,230,370,09212,7E-065,4E-051,5E-030,060,180,900
XIXVIIIVIIVIV
0,670,470,201,3E-020,00183,2E-0950,280,380,389,2E-020,0237,8E-074
4,6E-020,120,2870,250,117-3
3,9E-032,0E-020,1080,340,2960,0382
1,6E-041,6E-032,0E-020,230,370,09212,7E-065,4E-051,5E-030,060,180,900
XIXVIIIVIIVIV
Risk assessment of strategic masonry buildings at National scale
Macroseismic Method – vulnerability curves from EMS-98(Giovinazzi and Lagomarsino, 2006)
0
1
2
3
4
5
5 6 7 8 9 10 11 12I
m D
Bmin V=0.66Bmax V=0.82
mDmax= 2.88mDmin= 1.72
0
0.1
0.2
0.3
0.4
D0 D1 D2 D3 D4 D5
I=8 min
0
0.1
0.2
0.3
0.4
0.5
D0 D1 D2 D3 D4 D5
I=8 max
DI 6.25V -12.82.5 1 tanh
2.1 m
mean damage grade
PRIORITY LIST
Vulnerability index
Performance modifiers
DBV-masonry (Displacement Based Vulnerability model) (Cattari and Lagomarsino, 2008)
T fundamental period
Bilinear capacity curve defined by:
4T2
DDS1 DDS2 DDS3 DDS4
Entities directly defined on mechanical basis (the others are computed starting from these ones)
Ay
Sd
Sa
1,dir u,dir 1 2 3diry,dir * *
dir dir dir dir
A τ ξ ζ ζ ζFA =m Γ m Γ
* *dir dir
dir * *dir 4 5 dir(shear)
m mT =2π 2πk ζ ζ k
Du = DDS4 ultimate displacement capacity
Ay acceleration capacity
Geometrical features
h inter-storey height
bdir ratio between the resistant wall area at level i in the direction dir and the resistant wall area at top floor level in the same direction
adir ratio between the resistant wall area at top floor level in the direction dir and the total floor area A
Mechanical parameters and loads
tk shear strength
G shear modulus
g material density
du drift value
q floor load
Corrective factors
z1, z2, z3 which affect the evaluation of the yielding acceleration
z4, z5 which affect the evaluation of the period
DS4 udir
N hD = δΓ
dirDS4 u y,dir
ΓD = δ h + D 1-N
uniform soft - storey
OUT-OF-PLANE MECHANISMS(1st failure mode)
IN-PLANE MECHANISMS(2nd failure mode)
SEISMIC ANALYSIS OF MASONRY BUILDINGS
They can be prevented by proper interventions (tie-rods, connections)
H in
ters
tory
,i DISCRETIZION OF THE WALL BY FINITE ELEMENTSLofti and Shing 1991, Gambarotta and Lagomarsino 1997, Lourenço et al. 1997, Lourenço and Rots 1997, Luciano and Sacco 1997, Zhuge et al. 1998, Pietruszczak and Ushaksaraei 2003, Massart 2003, Schlegel 2004, Calderini and Lagomarsino 2008
SIMPLIFIED MODELS
STRONG SPANDREL –WEAK PIER
WEAK SPANDREL –STRONG PIER
(as proposed in FEMA 356 – FEMA 306 – POR Method) (Tomaževič and Weiss 1990, D’Asdia and Viskovic 1995, Brencich and Lagomarsino 1998, Magenes and Della Fontana 1998, Galasco et al. 2004)
EQUIVALENT FRAME MODEL
MODELLING STRATEGIES
Base
shea
r
Node
Pier
Spandrel
Assumed as rigid or linear elastic
Drift ratio
H in
ters
tory
,i
SIMPLIFIED MODELS EQUIVALENT FRAME MODEL
MODELLING STRATEGIES
STRONG SPANDREL –WEAK PIER
WEAK SPANDREL –STRONG PIER
(as proposed in FEMA 356 – FEMA 306 – POR Method) (Tomaževič and Weiss 1990, D’Asdia and Viskovic 1995, Brencich and Lagomarsino 1998, Magenes and Della Fontana 1998, Galasco et al. 2004)
TREMURI PROGRAMA.Galasco, S.Lagomarsino, A.Penna,
S.Cattari for research: ask to
tremuri@gmail.com Commercial version: www.stadata.com
TREMURI: 3D EQUIVALENT FRAME MODELLING
3-D equivalent frame is made of masonry walls, elastic floors, r.c. elements out-of-plane stiffness and strength of masonry walls are neglected floors are plane elements with only in-plane stiffness
Mixed masonry-r.c. buildings
CYCLIC PUSHOVER and NONLINEAR DYNAMIC ANALISYS
-3000000
-2000000
-1000000
0
1000000
2000000
3000000
-0,08 -0,06 -0,04 -0,02 0 0,02 0,04 0,06
V ba
se [N
]
U medio roof [m]
-3000000
-2000000
-1000000
0
1000000
2000000
3000000
-0,08 -0,06 -0,04 -0,02 0 0,02 0,04 0,06
V ba
se [N
]
U medio roof [m] with r.c. ring beams
without r.c. ring beams
PERFORMANCE-BASED APPROACH TO EARTHQUAKE PROTECTION OF CULTURAL HERITAGE IN EUROPEAN AND MEDITERRANEAN COUNTRIES
European Research Project funded by FP7
15th WORLD CONFERENCE ON EARTHQUAKE ENGINEERINGSpecial Session SS25.4
Earthquake Protection of Cultural HeritageResults from NIKER and PERPETUATE European FP7 Projects
Tuesday 25, 17:15-19:15 - Room P3a
Conveners: Claudio Modena and Sergio Lagomarsino
www.perpetuate.eu
www.perpetuate.eu
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