1. 2o Ciclo de Palestras em Engenharia Civil 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

2. 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

3. Seismic performance – Inelastic Types of analysis
Nonlinear dynamic analysis- time history (final solution)
Static Nonlinear analysis -Push-over Analysis (aproximative solution) UN F Vb Vb
Push-over Curve
Load vs Deflection UN

4. 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.

5. Inelastic analysis models
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 hinge
Plastic zones
Elastic

6. 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
Variation of reinforcement bars along the member
One element/
member

7. Inelastic analysis of cross-sectionsx
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

8. 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)

9. Case study (Six story RC frame building)
Elastic spectrum response: Type 1
Ground Type: A
Design ground acceleration: PGA=0.3g
Mass=40 (80) tones/level
Control node
60 x60
30 x50
Structural configuration

10. Seismic force evaluation
Pushover loads “mode 1 transv.”
Effective modal mass=65%
Pushover loads “mode 1-longit”
Effective modal mass=76%
T1=1.27s
T1=1.5s
Base shear forces:
Transversal (mode 1): Fz= 348 kN
Longitudinal (mode 1):Fx= 482 kN

11. Inelastic analysis data Plastic hinge analysis Plastic zone analysis
Interaction surface equation:
Stress-strain curves for concrete and steel bars (Eurocodes)
7 Gauss-Lobatto IP/member
1625
60x60cm
Unconfined concrete
Confined concrete
820
30x50cm

12. Pushover analysis: Longitudinal direction
Plastic zone analysis
Plastic hinge analysis
One element/physical member
Plastic hinge: CPU time: 1.5 min
(120 load cycles)
Plastic zone: CPU time: 8.3 min
(150 load cycles)

13. Pushover analysis: Transversal direction
Plastic zone analysis
Plastic hinge analysis

14. Plastic zone analysis: Longitudinal direction
Bending moments
Flexural rigidities

15. Plastic zone analysis: Transversal direction
Bending moments
Flexural rigidities

16. Modal vs Uniform force distribution

17. Modal vs Uniform force distribution

18. Equivalent SDOF and target displacement

19. Target displacements: transversal direction

20. Target displacements: transversal direction

21. Target displacements: longitudinal direction

22. Target displacements – longitudinal direction

23. Local seismic demands

24. Local seismic demands

25. Global seismic demands
PGA=0.15g
Dt=7.80 cm
PGA=0.3g
Dt=15.77 cm
PGA=0.6g
Dt=31.54 cm
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D=64.8 cm

26. Plastic performance: Transversal direction
Plastic zone analysis
PGA=0.15g
PGA=0.3g
PGA=0.6g
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27. Plastic performance: Transversal direction
Plastic hinge analysis
PGA=0.3g
PGA=0.6g
PGA=0.15g
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7 PH
10 PH
13 PH
2 PH

28. Plastic performance: Longitudinal direction
Plastic zone analysis
PGA=0.15g
PGA=0.3g
PGA=0.6g
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29. Plastic performance: Longitudinal direction
Plastic hinge analysis
PGA=0.15g
PGA=0.3g
PGA=0.6g
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7 PH
13 PH
15 PH
16 PH

30. 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