2o Ciclo de Palestras em Engenharia Civil-2003
12 de Novembro de 2003
Universidade Nova de Lisboa-Centro de Investigaçao em Estruturas e Construção-UNIC
Push-over analysis for seismic
performance evaluation of RC frame
structures. Computer programs
Dr. C. G. Chiorean
Technical University of Cluj-Napoca, Romania
Bolseiro na UNL/FCT, Lisboa, Portugal
Push-over analysis for seismic performance evaluation of RC frame structures. Computer programs
Outline
Part I.
Push-over analysis for seismic performance
evaluation of spatial RC frame structures
Part II.
Computer programs
NEFCAD Computer program for large deflection elasto-plastic
analysis of spatial frame structures
ASEP
Computer program for inelastic analysis of arbitrary
reinforced and composite concrete sections
Push-over analysis for seismic performance evaluation of RC frame structures. Computer programs
Seismic performance – Inelastic Types
of analysis
Nonlinear dynamic analysis- time history (final solution)
Static Nonlinear analysis -Push-over Analysis (aproximative solution)
UN
F
Vb
Push-over Curve
Load vs Deflection
UN
Vb
Push-over analysis for seismic performance evaluation of RC frame structures. Computer programs
Key elements of the push-over analysis
•
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.
Push-over analysis for seismic performance evaluation of RC frame structures. Computer programs
Inelastic analysis models
Concentrated plasticity
Distributed plasticity
Plastic zones
Elastic
Plastic hinge
Elastic
• 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
Push-over analysis for seismic performance evaluation of RC frame structures. Computer programs
3D RC Fiber Beam Column Element
• 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
One element/
member
• Variation of reinforcement bars along the member
Push-over analysis for seismic performance evaluation of RC frame structures. Computer programs
Inelastic analysis of cross-sections

y
x

(NA
)
  u   x y   y x  u  

 2x   2y
• 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
Push-over analysis for seismic performance evaluation of RC frame structures. Computer programs
Model capabilities
•
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)
Push-over analysis for seismic performance evaluation of RC frame structures. Computer programs
Case study (Six story RC frame building)
Elastic spectrum response: Type 1
Ground Type: A
Design ground acceleration: PGA=0.3g
Control node
Mass=40 (80) tones/level
60 x60
30 x50
Structural configuration
Push-over analysis for seismic performance evaluation of RC frame structures. Computer programs
Seismic force evaluation
Pushover loads “mode 1 transv.”
Pushover loads “mode 1-longit”
Effective modal mass=65%
Effective modal mass=76%
T1=1.5s
T1=1.27s
Base shear forces:
• Transversal (mode 1): Fz= 348 kN
• Longitudinal (mode 1):Fx= 482 kN
Push-over analysis for seismic performance evaluation of RC frame structures. Computer programs
Inelastic analysis data
Plastic hinge analysis
12000
Plastic zone analysis
Unconfined concrete
Axial force (kN)
10000
8000
1625
6000
4000
2000
0
0.00
-2000
0.01
0.02
0.03
0.04
0.05
Confined concrete
60x60cm
Ultim ate curvature
820
30x50cm
Interaction surface equation:
 My

M
py

1.6




 Mz

M
zp

1.6




1  0
Stress-strain curves for concrete and
steel bars (Eurocodes)
7 Gauss-Lobatto IP/member
Push-over analysis for seismic performance evaluation of RC frame structures. Computer programs
Pushover analysis: Longitudinal direction
Plastic zone analysis
Plastic hinge analysis
One element/physical member
1.20
Pushover curves-Longitudinal direction
1.00
Plastic zone, Plim=1.12
Aplied load factor
Plastic hinge, Plim=1.11
0.80
0.60
0.40
0.20
0.00
0.00
20.00
40.00
60.00
80.00
Displacem ent X (cm )
100.00
120.00
Plastic hinge: CPU time: 1.5 min
(120 load cycles)
Plastic zone: CPU time: 8.3 min
(150 load cycles)
Push-over analysis for seismic performance evaluation of RC frame structures. Computer programs
Pushover analysis: Transversal direction
Plastic zone analysis
1.40
Plastic hinge analysis
Pushover curves-Transversal direction
Aplied load factor
1.20
1.00
Plastic zone, Plim=1.21
Plastic hinge, Plim=1.11
0.80
0.60
0.40
0.20
0.00
0.00
20.00
40.00
60.00
Displacement Z (cm)
80.00
Push-over analysis for seismic performance evaluation of RC frame structures. Computer programs
Plastic zone analysis: Longitudinal direction
Bending moments
Flexural rigidities
Push-over analysis for seismic performance evaluation of RC frame structures. Computer programs
Plastic zone analysis: Transversal direction
Bending moments
Flexural rigidities
Push-over analysis for seismic performance evaluation of RC frame structures. Computer programs
Modal vs Uniform force distribution
1.40
Pushover curves-Transversal direction
1.20
Aplied load factor
1.00
Plastic zone (modal pattern), plim=1.21
Plastic zone (uniform acceleration), plim=1.19
0.80
0.60
0.40
0.20
0.00
0.00
20.00
40.00
60.00
Displacement Z (cm)
80.00
Push-over analysis for seismic performance evaluation of RC frame structures. Computer programs
Modal vs Uniform force distribution
1.40
Pushover curves-Longitudinal direction
1.20
Aplied load factor
1.00
0.80
Plastic zone (modal pattern), Plim=1.12
Plastic zone (uniform pattern),Plim=1.28
0.60
0.40
0.20
0.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00
Displacement X (cm)
Push-over analysis for seismic performance evaluation of RC frame structures. Computer programs
Equivalent SDOF and target displacement
Push-over analysis for seismic performance evaluation of RC frame structures. Computer programs
Target displacements: transversal direction
1.40
Target displacements (Plastic zone)-Transversal direction
1.20
Dt=31.54 cm
Aplied load factor
1.00
Computed pushover curve (plastic zone)
Idealized elaso-perfectly plastic (EC8)
0.80
Dt=15.77 cm
0.60
Dt=7.80 cm
0.40
0.20
0.00
0.00
20.00
40.00
60.00
Displacement Z (cm)
80.00
Push-over analysis for seismic performance evaluation of RC frame structures. Computer programs
Target displacements: transversal direction
1.20
Target displacem ents (plastic hinge)-Transversal direction
29.83
Aplied load factor
1.00
14.91
0.80
Computed pushover curve (plastic hinge)
Idealized elasto-perfectly plastic (EC8)
PGA=0.15g
0.60
7.45
PGA=0.3g
PGA=0.6g
0.40
0.20
0.00
0.00
10.00
20.00
30.00
40.00
Displacement Z (cm)
50.00
60.00
Push-over analysis for seismic performance evaluation of RC frame structures. Computer programs
Target displacements: longitudinal direction
1.20
Target displacem ents (plastic zone)-Longitudinal direction
1.00
Aplied load factor
46.64 cm
0.80
Computed pushover curve (plastic zone)
23.3 cm
Idealized elasto-perfectly plastic (EC8)
0.60
PGA=0.15g
11.65 cm
PGA=0.3g
0.40
PGA=0.6g
0.20
0.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00
Displacement X (cm)
Push-over analysis for seismic performance evaluation of RC frame structures. Computer programs
Target displacements – longitudinal direction
1.20
Target displacements (plastic hinge)-Longitudinal direction
1.00
45.08 cm
22.54 cm
Aplied load factor
0.80
Computed pushover curve (plastic hinge)
Idealized elasto-perfectly plastic (EC8)
PGA=0.15g
PGA=0.3g
0.60
PGA=0.6g
11.27 cm
0.40
0.20
0.00
0.00
20.00
40.00
60.00
80.00
100.00
Displacement X (cm)
Push-over analysis for seismic performance evaluation of RC frame structures. Computer programs
Local seismic demands
Curvatures along the member length
0.0200
PGA=0.15g
0.0150
PGA=0.3g
PGA=0.6g
Curvatures
0.0100
0.0050
0.0000
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
-0.0050
-0.0100
-0.0150
Member length (m)
Push-over analysis for seismic performance evaluation of RC frame structures. Computer programs
Local seismic demands
Curvatures along the member length
0.0010
Curvatures
0.0000
0.00
-0.0010
0.50
1.00
1.50
2.00
2.50
3.00
3.50
-0.0020
-0.0030
PGA=0.15g
-0.0040
PGA=0.3g
-0.0050
PGA=0.6g
-0.0060
-0.0070
Member length (m)
Push-over analysis for seismic performance evaluation of RC frame structures. Computer programs
Global seismic demands
PGA=0.15g
PGA=0.3g
PGA=0.6g
Dt=7.80 cm
Dt=15.77 cm
Dt=31.54 cm
Collapse
D=64.8 cm
Push-over analysis for seismic performance evaluation of RC frame structures. Computer programs
Plastic performance: Transversal direction
Plastic zone analysis
PGA=0.15g
PGA=0.3g
PGA=0.6g
Collapse
Push-over analysis for seismic performance evaluation of RC frame structures. Computer programs
Plastic performance: Transversal direction
Plastic hinge analysis
PGA=0.15g
2 PH
PGA=0.3g
7 PH
PGA=0.6g
Collapse
10 PH
13 PH
Push-over analysis for seismic performance evaluation of RC frame structures. Computer programs
Plastic performance: Longitudinal direction
Plastic zone analysis
PGA=0.15g
PGA=0.3g
PGA=0.6g
Collapse
Push-over analysis for seismic performance evaluation of RC frame structures. Computer programs
Plastic performance: Longitudinal direction
Plastic hinge analysis
PGA=0.15g
7 PH
PGA=0.3g
13 PH
PGA=0.6g
Collapse
15 PH
16 PH
Push-over analysis for seismic performance evaluation of RC frame structures. Computer programs
Concluding remarks
•
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
Push-over analysis for seismic performance evaluation of RC frame structures. Computer programs