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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
22oo Ciclo de Palestras em Engenharia Civil-2003 Ciclo de Palestras em Engenharia Civil-200312 de Novembro de 200312 de Novembro de 2003
Universidade Nova de Lisboa-Centro de Investigaçao em Estruturas e Construção-UNICUniversidade Nova de Lisboa-Centro de Investigaçao em Estruturas e Construção-UNIC
Push-over analysis for seismic Push-over analysis for seismic performance evaluation of RC frame performance evaluation of RC frame
structures. Computer programsstructures. Computer programs
22oo Ciclo de Palestras em Engenharia Civil-2003 Ciclo de Palestras em Engenharia Civil-200312 de Novembro de 200312 de Novembro de 2003
Universidade Nova de Lisboa-Centro de Investigaçao em Estruturas e Construção-UNICUniversidade Nova de Lisboa-Centro de Investigaçao em Estruturas e Construção-UNIC
Push-over analysis for seismic Push-over analysis for seismic performance evaluation of RC frame performance evaluation of RC frame
structures. Computer programsstructures. Computer programs Dr. C. G. ChioreanDr. C. G. Chiorean
Technical University of Cluj-Napoca, RomaniaTechnical University of Cluj-Napoca, RomaniaBolseiro na UNL/FCT, Lisboa, PortugalBolseiro na UNL/FCT, Lisboa, Portugal
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
Part II. Part II. Computer programsComputer programsNEFCAD NEFCAD Computer program for large deflection elasto-plastic Computer program for large deflection elasto-plastic
analysis of spatial frame structuresanalysis of spatial frame structures
ASEPASEP Computer program for inelastic analysis of arbitrary Computer program for inelastic analysis of arbitrary reinforced and composite concrete sectionsreinforced and composite concrete sections
OutlineOutlineOutlineOutline
Part I. Part I. Push-over analysis for seismic Push-over analysis for seismic
performance performance evaluation of spatial RC evaluation of spatial RC frame structuresframe structures
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
Static NonlinearStatic Nonlinear analysis - analysis -Push-over AnalysisPush-over Analysis (aproximative solution) (aproximative solution)
Seismic performanceSeismic performance – – Inelastic Inelastic Types of Types of analysisanalysis
Seismic performanceSeismic performance – – Inelastic Inelastic Types of Types of analysisanalysis
Nonlinear dynamic analysis- time history (final solution)Nonlinear dynamic analysis- time history (final solution)
Vb
UN
Push-over CurveLoad vs Deflection
UN F
Vb
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
• 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, ELF force distribution
• Estimation of the target displacement: elastic or inelastic response spectrum for equivalent SDOF system
• Performance evaluation: global and local seismic demands with capacities of performance level.
Key elements of the push-over analysisKey elements of the push-over analysisKey elements of the push-over analysisKey elements of the push-over analysis
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
Concentrated plasticity Distributed plasticity
• Dimensionless plastic hinge
• Interaction surface
• Return mapping plasticity algorithms
• Computationally efficient but limited accuracy
• Plastic zones
• Force-strain curves: quasi plastic hinge approach
• Stress-strain curves: fiber element approach
• Plastic flow rules
• High accuracy but computational expensive
Plastic hingePlastic zones
Elastic Elastic
Inelastic analysis modelsInelastic analysis modelsInelastic analysis modelsInelastic analysis models
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
IP4 IP3
IP2
j=IP5
iPI1
L/2
L/2
x
z
y
Concrete Steel
Z
Y x
vi, Tiy
y
wi, Tiz
z
zj,Mzj
xj,Mxj
uj, Nj vj, Tjy
yi,Myi
xi,Mxi
ui, Ni
zi,Mzi
X wj, Tjz
Mz
My
N z
y
• Flexibility-based nonlinear beam column element
•Iterative method to compute inelastic response at cross-sectional level (inelasatic flexural and axial rigidity)
• Gradual yielding along the member length and within the cross sections
• Distributed loads
• Uniform or nonuniform (tapered) members
• Variation of reinforcement bars along the member
One element/
member
3D RC Fiber Beam Column Element3D RC Fiber Beam Column Element3D RC Fiber Beam Column Element3D RC Fiber Beam Column Element
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
(NA)
y
x
22
yx
yxuxyu
• Arbitrary cross-sections under biaxial bending moments and axial force
• Arc length icremental iterative method with tangent stiffness strategy
• Green´s theorem: domain integrals are evaluated in terms of boundary integrals
• M-N- curves, N-Mx-My interaction diagrams and axial force ultimate curvature
Inelastic analysis of cross-sectionsInelastic analysis of cross-sectionsInelastic analysis of cross-sectionsInelastic analysis of cross-sections
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
• Large deflection and large rotations
• Geometrical local effects (P-) including bowing effect, shear deformations
• Concentrated and distributed plasticity (fiber and M-N- aproaches)
• Consistency between linear and nonlinear models (one element/member)
• Local geometrical and material imperfections
• Flexible (semi-rigid) and finite joints
• Complete non-linear behavior (pre and post crtical response: snap-back and snap-through)
Model capabilitiesModel capabilitiesModel capabilitiesModel capabilities
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
Elastic spectrum response: Type 1
Ground Type: A
Design ground acceleration: PGA=0.3g
Mass=40 (80) tones/level
Case study (Six story RC frame building)Case study (Six story RC frame building)Case study (Six story RC frame building)Case study (Six story RC frame building)
60 x60
30 x50
Structural configuration
Control node
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 1 transv.”
Effective modal mass=65%
Pushover loads “mode 1-longit”
Effective modal mass=76%
Base shear forces:
• Transversal (mode 1): Fz= 348 kN
• Longitudinal (mode 1):Fx= 482 kN
T1=1.5s T1=1.27s
Seismic force evaluationSeismic force evaluationSeismic force evaluationSeismic force evaluation
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
Plastic hinge analysis Plastic zone analysis
Interaction surface equation: Stress-strain curves for concrete and steel bars (Eurocodes)
7 Gauss-Lobatto IP/member
Interaction N-M
-2000
0
2000
4000
6000
8000
10000
12000
0 200 400 600 800 1000 1200
Bending moment (kNm)
-2000
0
2000
4000
6000
8000
10000
12000
0.00 0.01 0.02 0.03 0.04 0.05
Ultimate curvature
Axia
l fo
rce
(kN
)
-1000.00
0.00
1000.00
2000.00
3000.00
4000.00
5000.00
0.00 100.00 200.00 300.00 400.00
Bending Moment (kNm)
Major axisbending
Minor axisbending
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 axisbending
Minor axisbending
01
6.16.1
zp
z
py
y
M
M
M
M
820
30x50cm
Inelastic analysis dataInelastic analysis dataInelastic analysis dataInelastic analysis data
1625
60x60cm
Unconfined concrete
Confined concrete
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
Plastic zone analysis Plastic hinge analysisPushover curves-Longitudinal direction
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0.00 20.00 40.00 60.00 80.00 100.00 120.00Displacement X (cm)
Ap
lied
load
fac
tor
Plastic zone, Plim=1.12
Plastic hinge, Plim=1.11
Pushover analysis: Longitudinal directionPushover analysis: Longitudinal directionPushover analysis: Longitudinal directionPushover analysis: Longitudinal direction
Plastic hinge: CPU time: 1.5 min
(120 load cycles)
Plastic zone: CPU time: 8.3 min
(150 load cycles)
One element/physical member
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
Plastic hinge analysisPlastic zone analysisPushover curves-Transversal 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 80.00Displacement Z (cm)
Ap
lied
lo
ad f
acto
r Plastic zone, Plim=1.21
Plastic hinge, Plim=1.11
Pushover analysis: Transversal directionPushover analysis: Transversal directionPushover analysis: Transversal directionPushover analysis: Transversal direction
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
Bending moments Flexural rigidities
Plastic zone analysis: Longitudinal directionPlastic zone analysis: Longitudinal directionPlastic zone analysis: Longitudinal directionPlastic zone analysis: Longitudinal direction
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
Bending moments Flexural rigidities
Plastic zone analysis: Transversal directionPlastic zone analysis: Transversal directionPlastic zone analysis: Transversal directionPlastic zone analysis: Transversal direction
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 curves-Transversal 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 80.00Displacement Z (cm)
Ap
lied
loa
d f
ac
tor Plastic zone (modal pattern), plim=1.21
Plastic zone (uniform acceleration), plim=1.19
Modal vs Uniform force distributionModal vs Uniform force distributionModal vs Uniform force distributionModal vs Uniform force distribution
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 curves-Longitudinal 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 80.00 100.00 120.00Displacement X (cm)
Ap
lied
loa
d f
ac
tor
Plastic zone (modal pattern), Plim=1.12
Plastic zone (uniform pattern),Plim=1.28
Modal vs Uniform force distributionModal vs Uniform force distributionModal vs Uniform force distributionModal vs Uniform force distribution
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
Equivalent SDOF and target displacementEquivalent SDOF and target displacementEquivalent SDOF and target displacementEquivalent SDOF and target displacement
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
Target displacements (Plastic zone)-Transversal direction
Dt=7.80 cm
Dt=15.77 cm
Dt=31.54 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 80.00Displacement Z (cm)
Ap
lied
loa
d f
ac
tor Computed pushover curve (plastic zone)
Idealized elaso-perfectly plastic (EC8)
Target displacements: transversal directionTarget displacements: transversal directionTarget displacements: transversal directionTarget displacements: transversal direction
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
Target displacements (plastic hinge)-Transversal direction
7.45
14.91
29.83
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 60.00Displacement Z (cm)
Ap
lied
loa
d f
ac
tor
Computed pushover curve (plastic hinge)
Idealized elasto-perfectly plastic (EC8)
PGA=0.15g
PGA=0.3g
PGA=0.6g
Target displacements: transversal directionTarget displacements: transversal directionTarget displacements: transversal directionTarget displacements: transversal direction
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
Target displacements (plastic zone)-Longitudinal 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 80.00 100.00 120.00Displacement X (cm)
Ap
lied
loa
d f
ac
tor
Computed pushover curve (plastic zone)
Idealized elasto-perfectly plastic (EC8)
PGA=0.15g
PGA=0.3g
PGA=0.6g
Target displacements: longitudinal directionTarget displacements: longitudinal directionTarget displacements: longitudinal directionTarget displacements: longitudinal direction
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
Target displacements (plastic hinge)-Longitudinal direction
11.27 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 80.00 100.00Displacement X (cm)
Ap
lied
loa
d f
ac
tor
Computed pushover curve (plastic hinge)
Idealized elasto-perfectly plastic (EC8)
PGA=0.15g
PGA=0.3g
PGA=0.6g
Target displacementsTarget displacements – – longitudinal directionlongitudinal directionTarget displacementsTarget displacements – – longitudinal directionlongitudinal direction
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
Local seismic demandsLocal seismic demandsLocal seismic demandsLocal 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 7.00
Member length (m)
Cur
vatu
res
PGA=0.15g
PGA=0.3g
PGA=0.6g
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
Local seismic demandsLocal seismic demandsLocal seismic demandsLocal seismic demands
Curvatures along the member length
-0.0070
-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 length (m)
Cur
vatu
res
PGA=0.15g
PGA=0.3g
PGA=0.6g
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
Global seismic demandsGlobal seismic demandsGlobal seismic demandsGlobal seismic demandsPGA=0.15g
Dt=7.80 cm
PGA=0.3g
Dt=15.77 cm
PGA=0.6g
Dt=31.54 cm
Collapse
D=64.8 cm
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
PGA=0.3g PGA=0.6gPGA=0.15g Collapse
Plastic zone analysis
Plastic performance: Transversal directionPlastic performance: Transversal directionPlastic performance: Transversal directionPlastic performance: Transversal direction
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
PGA=0.3g PGA=0.6gPGA=0.15g Collapse
Plastic hinge analysis
Plastic performance: Transversal directionPlastic performance: Transversal directionPlastic performance: Transversal directionPlastic performance: Transversal direction
2 PH 7 PH 10 PH 13 PH
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
CollapsePGA=0.15g PGA=0.3g PGA=0.6g
Plastic zone analysis
Plastic performance: Longitudinal directionPlastic performance: Longitudinal directionPlastic performance: Longitudinal directionPlastic performance: Longitudinal direction
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
PGA=0.15g PGA=0.3g PGA=0.6g Collapse
Plastic hinge analysis
Plastic performance: Longitudinal directionPlastic performance: Longitudinal directionPlastic performance: Longitudinal directionPlastic performance: Longitudinal direction
7 PH 13 PH 15 PH 16 PH
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
• A computational efficient 3-D RC fiber beam-column element was developed and implemented in a nonlinear inelastic analysis computer program
• Plastic hinge analysis: limited accuracy
• A pushover example for spatial model was presented in conjunction with EC8 provisions
• Pushover analysis: good estimates of global and local inelastic deformations demands
• Limitations: for structures that vibrate primarily in the fundamental mode
• Overcomes: adaptive force distribution and modal pushover analysis procedures
• Nonlinear dynamic analysis: final solution
Concluding remarksConcluding remarksConcluding remarksConcluding remarks