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22ooCiclo de Palestras em Engenharia Civil-2003Ciclo de Palestras em Engenharia Civil-2003
12 de Novembro de 200312 de Novembro de 2003
niversidade Nova de !isboa-Centro de "nvestiga#ao em $struturas e Constru#%o-N"Cniversidade Nova de !isboa-Centro de "nvestiga#ao em $struturas e Constru#%o-N"C
Push-over analysis for seismicPush-over analysis for seismic
performance evaluation of RC frameperformance evaluation of RC framestructures. Computer programsstructures. Computer programs
Dr. C. G. ChioreanDr. C. G. Chiorean
Technical University of Cluj-Napoca, RomaniaTechnical University of Cluj-Napoca, Romania
Bolseiro na UNL!CT, Lis"oa, #ortu$alBolseiro na UNL!CT, Lis"oa, #ortu$al
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Part "".Part "".Computer programsComputer programs
N$&C'(N$&C'( Computer program for large deflection elasto-plasticComputer program for large deflection elasto-plastic
analysis of spatial frame structuresanalysis of spatial frame structures
')$P')$P Computer program for inelastic analysis of arbitraryComputer program for inelastic analysis of arbitrary
reinforced and composite concrete sectionsreinforced and composite concrete sections
OutlineOutline
Part ".Part ".Push-over analysis for seismic performancePush-over analysis for seismic performance
evaluation of spatial RC frame structuresevaluation of spatial RC frame structures
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)tatic Nonlinear)tatic Nonlinearanalysis -analysis -Push-over 'nalysisPush-over 'nalysis*apro+imative solution,*apro+imative solution,
Seismic performanceSeismic performance InelasticInelastic TypesTypes
of analysisof analysis
Nonlinear dynamic analysis- time history *final solution,Nonlinear dynamic analysis- time history *final solution,
Vb
!
Push-over Curve
"oadvs #eflection! $
Vb
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Nonlinear static procedure: constant gravitational loads and
monotonically increasing lateral loads Plastic mechanisms and P-effects: diplacement or arc length
control
Capacity curve: Control node displacement vs base shear force
Lateral load patterns: uniform, modal, SRSS, L! force
distribution
stimation of the target displacement: elastic or inelastic response
spectrum for e"uivalent S#$! system
Performance evaluation: global and local seismic demands %ith
capacities of performance level&
Key elements of the push-over analysisKey elements of the push-over analysis
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Concentrated plasticity #istributed plasticity
#imensionless plastic hinge
'nteraction surface
Return mapping plasticity
algorithms Computationally efficient but limitedaccuracy
Plastic (ones
!orce-strain curves: "uasi plastic hingeapproach
Stress-strain curves: fiber element approach Plastic flo% rules
)igh accuracy but computational e*pensive
Plastic hingePlastic (ones
lastic lastic
Inelastic analysis modelsInelastic analysis models
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IP4IP3
IP2
j=IP5
iPI1
L+,
L+,
x
z
y
ConcreteSteel
Z
Yx
vi, Tiy
wi, Tiz
zj,Mzj
xj,Mxj
uj, Njvj, Tjy
yi,Myi
xi,Mxi
ui, Ni
zi,Mzi
wj, Tjz
z
y
N
y
!le*ibility-based nonlinear beam column element
'terative method to compute inelastic response at cross-sectional level inelasatic
fle*ural and a*ial rigidity.
/radual yielding along the member length and %ithin the cross sections
#istributed loads
0niform or nonuniform tapered. members
1ariation of reinforcement bars along the member
$ne element+
member
3D RC Fier !eam Column "lement3D RC Fier !eam Column "lement
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N2
.
y
x
,,
yx
yxuxyu
+=
+=++=
2rbitrary cross-sections under bia*ial bending moments and a*ial force
2rc length icremental iterative method %ith tangent stiffness strategy/reen3s theorem: domain integrals are evaluated in terms of boundary integrals
4-N-curves, N-4*-4y interaction diagrams and a*ial force ultimate curvature
Inelastic analysis of cross-sectionsInelastic analysis of cross-sections
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Large deflection and large rotations
/eometrical local effects P-. including bo%ing effect, shear deformations
Concentrated and distributed plasticity fiber and 4-N-aproaches.
Consistency bet%een linear and nonlinear models one element+member.
Local geometrical and material imperfections
!le*ible semi-rigid. and finite 5oints
Complete non-linear behavior pre and post crtical response: snap-bac6
and snap-through.
#odel capailities#odel capailities
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lastic spectrum response: 7ype 8
/round 7ype: 2
Desi$n $roun% acceleration& #G'().*$
+ass() )/ toneslevel
Case study $Si% story RC frame uildin&'Case study $Si% story RC frame uildin&'
9 *9
; *
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Push-over analysis for seismic performance evaluation of RC frame structures. Computer programsPush-over analysis for seismic performance evaluation of RC frame structures. Computer programs
Pushover loads =mode 8 transv&>
ffective modal mass?9
ffective modal mass?A9@
Base shear forces:7ransversal mode 8.: !(? ;D 6N
Longitudinal mode 8.:!*? D 6N
78?8&
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Plastic hinge analysis Plastic (one analysis
'nteraction surface e"uation: Stress-strain curves for concrete andsteel bars urocodes.
A /auss-Lobatto 'P+member
%nteraction !-&
-2000
0
2000
4000
6000
8000
10000
12000
0 200 400 600 800 1000 1200
Bendi ng moment (kNm)
-2000
0
2000
4000
6000
8000
10000
12000
0 .0 0 0. 01 0. 02 0. 03 0. 04 0 .0 5
ltimate curvature
'(ialforce)*!+
-1000.00
0.00
1000.00
2000.00
3000.00
4000.00
5000.00
0 .0 0 10 0.0 0 2 00 .0 0 3 00 .0 0 4 00 .0 0
Bending Moment (kNm)
ajor axis
bending
Minor axis
bending
0.00
50.00
100.00
150.00
200.00
250.00
300.00
350.00
400.00
0.00 0.05 0.10 0.15 0.20
Ultimate curvature
Major axis
bending
Minor axis
bending
:8
9&89&8
=
+
zp
z
py
y
M
M
M
M
D
;*
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Plastic (one analysis Plastic hinge analysis
Pushover curves-"ongitudinal direction
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0.00 20.00 40.00 60.00 80.00 100.00 120.00#isplacement , )cm+
'pliedloadfactor
Plastic zone, Plim1.12
Plastic !inge, Plim1.11
(ushover analysis) *on&itudinal direction(ushover analysis) *on&itudinal direction
Plastic hinge: CP0 time: 8&< min
8 load cycles.
Plastic (one: CP0 time: D&; min
8
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Plastic hinge analysisPlastic (one analysisPushover curves-ransversal direction
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
0.00 20.00 40.00 60.00 80.00#isplacement )cm+
'plied
load
factor Plastic zone, Plim1.21
Plastic !inge, Plim1.11
(ushover analysis) Transversal direction(ushover analysis) Transversal direction
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Bending moments !le*ural rigidities
(lastic +one analysis) *on&itudinal direction(lastic +one analysis) *on&itudinal direction
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Bending moments !le*ural rigidities
(lastic +one analysis) Transversal direction(lastic +one analysis) Transversal direction
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Pushover curves-ransversal direction
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
0.00 20.00 40.00 60.00 80.00#isplacement )cm+
'pliedloa
dfactor Plastic zone "modal #attern$, #lim1.21
Plastic zone "%ni&orm acceleration$, #lim1.1'
#odal vs ,niform force distriution#odal vs ,niform force distriution
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Pushover curves-"ongitudinal direction
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
0.00 20.00 40.00 60.00 80.00 100.00 120.00#isplacement , )cm+
'pliedloa
dfactor
Plastic zone "modal #attern$, Plim1.12
Plastic zone "%ni&orm #attern$,Plim1.28
#odal vs ,niform force distriution#odal vs ,niform force distriution
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"uivalent SDOF and tar&et displacement"uivalent SDOF and tar&et displacement
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arget displacements )Plastic /one+-ransversal direction
(t).80 cm
(t15.)) cm
(t31.54 cm
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
0.00 20.00 40.00 60.00 80.00
#isplacement . )cm+
'pliedlo
adfactor *om#%ted #%s!o+er c%r+e "#lastic zone$
dealized elaso-#er&ectl #lastic "*8$
Tar&et displacements) transversal directionTar&et displacements) transversal direction
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arget displacem ents )plastic hinge+-ransversal direction
).45
14.'1
2'.83
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0.00 10.00 20.00 30.00 40.00 50.00 60.00#isplacement )cm+
'pliedlo
adfactor
*om#%ted #%s!o+er c%r+e "#lastic !inge$
dealized elasto-#er&ectl #lastic "*8$
P/0.15g
P/0.3g
P/0.6g
Tar&et displacements) transversal directionTar&et displacements) transversal direction
T t di l t l it di l di ti
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arget displacements )plastic /one+-"ongitudinal direction
11.65 cm
23.3 cm
46.64 cm
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0.00 20.00 40.00 60.00 80.00 100.00 120.00#isplacement , )cm+
'pliedloadfactor
*om#%ted #%s!o+er c%r+e "#lastic zone$
dealized elasto-#er&ectl #lastic "*8$
P/0.15g
P/0.3g
P/0.6g
Tar&et displacements) lon&itudinal directionTar&et displacements) lon&itudinal direction
T t di l t l it di l di ti
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arget displacements )plastic hinge+-"ongitudinal direction
11.2) cm
22.54 cm
45.08 cm
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0.00 20.00 40.00 60.00 80.00 100.00#isplacement , )cm+
'pliedloa
dfactor
*om#%ted #%s!o+er c%r+e "#lastic !inge$
dealized elasto-#er&ectl #lastic "*8$
P/0.15g
P/0.3g
P/0.6g
Tar&et displacementsTar&et displacements lon&itudinal directionlon&itudinal direction
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*ocal seismic demands*ocal seismic demands
Curvatures along the member length
-0.0150
-0.0100
-0.0050
0.0000
0.0050
0.0100
0.0150
0.0200
0.00 1.00 2.00 3.00 4.00 5.00 6.00 ).00
Member lengt! "m$
*%r+at%res
P/0.15g
P/0.3g
P/0.6g
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*ocal seismic demands*ocal seismic demands
Curvatures along the member length
-0.00)0
-0.0060
-0.0050
-0.0040
-0.0030
-0.0020
-0.0010
0.0000
0.0010
0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50
Member lengt! "m$
*%r+at%res
P/0.15g
P/0.3g
P/0.6g
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.loal seismic demands.loal seismic demandsP/2?&8
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P/2?&;g P/2?&9gP/2?&8
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P/2?&;g P/2?&9gP/2?&8
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CollapseP/2?&8
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P/2?&8
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2 computational efficient ;-# RC fiber beam-column element %as
developed and implemented in a nonlinear inelastic analysis computer
program Plastic hinge analysis: limited accuracy
2 pushover e*ample for spatial model %as presented in con5unction
%ith CD provisions
Pushover analysis: good estimates of global and local inelastic
deformations demands
Limitations: for structures that vibrate primarily in the fundamental
mode
$vercomes: adaptive force distribution and modal pushover analysis
procedures
Nonlinear dynamic analysis: final solution
Concludin& remar/sConcludin& remar/s