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Dr. C. G. Chiorean Technical University of Cluj-Napoca, Romania

2 o 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

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Dr. C. G. Chiorean Technical University of Cluj-Napoca, Romania

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  1. 2o Ciclo de Palestras em Engenharia Civil-200312 de Novembro de 2003Universidade Nova de Lisboa-Centro de Investigaçao em Estruturas e Construção-UNICPush-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. UN F Vb Seismic performance – Inelastic Types of analysis Nonlinear dynamic analysis- time history (final solution) Static Nonlinear analysis -Push-over Analysis (aproximative solution) 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 Plastic zones Elastic Plastic hinge 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-sections y x (NA) • 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) 60 x60 30 x50 Elastic spectrum response: Type 1 Ground Type: A Design ground acceleration: PGA=0.3g Mass=40 (80) tones/level Control node 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 Unconfined concrete 1625 60x60cm 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 Collapse D=64.8 cm

  26. Plastic performance: Transversal direction Plastic zone analysis PGA=0.15g PGA=0.3g PGA=0.6g Collapse

  27. Plastic performance: Transversal direction PGA=0.15g PGA=0.3g PGA=0.6g Collapse Plastic hinge analysis 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 Collapse

  29. Plastic performance: Longitudinal direction Collapse PGA=0.15g PGA=0.3g PGA=0.6g Plastic hinge analysis 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

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