1. Seismic Performance Assessment and Rehabilitation of Existing Buildings SPEAR International Workshop Joint Research Centre, Ispra, 4 th -5 th April 2005 An event to honour the memory of Jean Donea SPEAR International Workshop Pre- and post-test mathematical modelling of the SPEAR building M.Dolšek 1, D.Marušić 1, A.Stratan 2, P.Fajfar 1 1 University of Ljubljana, Slovenia 2 Technical University of Temisoara, Romania, formerly visiting researcher at the University of Ljubljana

2. SPEAR International Workshop An event to honour the memory of Jean Donea Ispra, 4 th -5 th April 2005 Overview of work Parametric study (Stratan and Fajfar, 2002)Parametric study (Stratan and Fajfar, 2002) Initial model (Stratan and Fajfar, 2003)Initial model (Stratan and Fajfar, 2003) Pre-test model (Marušić and Fajfar, 2003)Pre-test model (Marušić and Fajfar, 2003) Post-test model (Dolšek and Fajfar, 2005)Post-test model (Dolšek and Fajfar, 2005)

3. SPEAR International Workshop An event to honour the memory of Jean Donea Ispra, 4 th -5 th April 2005 Element Model One-component lumped plasticity elements based on moment-rotation relationship (the plastic hinge defined for uni-axial bending)One-component lumped plasticity elements based on moment-rotation relationship (the plastic hinge defined for uni-axial bending) Takeda’s hysteretic rulesTakeda’s hysteretic rules Elastic axial, shear and torsional behaviourElastic axial, shear and torsional behaviour Fiber elements in initial studies Element and joint shear strength checked

4. SPEAR International Workshop An event to honour the memory of Jean Donea Ispra, 4 th -5 th April 2005 Parametric study

5. SPEAR International Workshop An event to honour the memory of Jean Donea Ispra, 4 th -5 th April 2005 Common features of all models (with one-component elements)

6. SPEAR International Workshop An event to honour the memory of Jean Donea Ispra, 4 th -5 th April 2005 Modelling assumptions

7. SPEAR International Workshop An event to honour the memory of Jean Donea Ispra, 4 th -5 th April 2005 Conclusions - Initial model Damage to the structure dictated by weak columnsDamage to the structure dictated by weak columns Elements and joints not susceptible to shear failuresElements and joints not susceptible to shear failures Higher displacement demands in X directionHigher displacement demands in X direction Critical columns: C3, C1, C2, C4Critical columns: C3, C1, C2, C4 Intensity levelsIntensity levels  0.1g: damage starts  0.2g: cover concrete spalling for the C1-C4 columns  0.24g: significant global structural damage  0.3g: concrete in the most critical columns starts to crush

8. SPEAR International Workshop An event to honour the memory of Jean Donea Ispra, 4 th -5 th April 2005 Modelling assumptions

9. SPEAR International Workshop An event to honour the memory of Jean Donea Ispra, 4 th -5 th April 2005 Pre-test model 0.15 g test Top displacement in CM X direction X direction Y direction Y direction

10. SPEAR International Workshop An event to honour the memory of Jean Donea Ispra, 4 th -5 th April 2005 Pre-test model Top rotation in CM (0.15 g)

11. SPEAR International Workshop An event to honour the memory of Jean Donea Ispra, 4 th -5 th April 2005 Pre-test model Storey drift in CM (first and second storey, 0.15 g)

12. SPEAR International Workshop An event to honour the memory of Jean Donea Ispra, 4 th -5 th April 2005 Pre-test model Maximum storey drifts (0.15 g)

13. SPEAR International Workshop An event to honour the memory of Jean Donea Ispra, 4 th -5 th April 2005 Pre-test model - torsion Amplification due to torsion (Maximum storey drifts at the edge versus maximum average storey drifts)

14. SPEAR International Workshop An event to honour the memory of Jean Donea Ispra, 4 th -5 th April 2005 Conclusions – Pre-test model Intensity levelIntensity level  0.2g: substantial damage to C1, C2, C4 and C3  0.25g: local failure (crushing of concrete) of critical columns “…PGA = 0.20 g should be appropriate for testing. …such ground motion would lead to damage serious enough to apply desired retrofitting techniques …, yet it would not cause the collapse of any member.” (ULJ 2 nd year report)

15. SPEAR International Workshop An event to honour the memory of Jean Donea Ispra, 4 th -5 th April 2005 Pre-test model versus tests

16. SPEAR International Workshop An event to honour the memory of Jean Donea Ispra, 4 th -5 th April 2005 Stiffness and strength Pushover analysis

17. SPEAR International Workshop An event to honour the memory of Jean Donea Ispra, 4 th -5 th April 2005 Post-test model Open-Sees program (displacement – controlled analysis, P-Δ effect, envelope with degrading strength)Open-Sees program (displacement – controlled analysis, P-Δ effect, envelope with degrading strength) Determination of improved values of parametersDetermination of improved values of parameters  Rough estimates by displacement – controlled analysis (Dolšek and Fajfar,2002)  Fine tuning by trial and error procedure

18. SPEAR International Workshop An event to honour the memory of Jean Donea Ispra, 4 th -5 th April 2005 Modelling assumptions

19. SPEAR International Workshop An event to honour the memory of Jean Donea Ispra, 4 th -5 th April 2005 Moment - rotation

20. SPEAR International Workshop An event to honour the memory of Jean Donea Ispra, 4 th -5 th April 2005 Moment - rotation Column C6 (C15) in strong direction C6 - 1 st storey C6 (C15) - 2 nd storey C6 (C15) – other positions Source: JRC Report

21. SPEAR International Workshop An event to honour the memory of Jean Donea Ispra, 4 th -5 th April 2005 Post-test model – Major changes Reduced strength (reduced strength of reinforcement at the bottom of columns)Reduced strength (reduced strength of reinforcement at the bottom of columns) Reduced energy dissipation (pinching and small unloading stiffness)Reduced energy dissipation (pinching and small unloading stiffness) Effective initial stiffness (different in different stories, locally reduced stiffness and strength of the strong column)Effective initial stiffness (different in different stories, locally reduced stiffness and strength of the strong column) Height of the 1st storey: 2.75 mHeight of the 1st storey: 2.75 m Higher values for ultimate rotation (empirical)Higher values for ultimate rotation (empirical) P-Δ effect and degrading strengthP-Δ effect and degrading strength

22. SPEAR International Workshop An event to honour the memory of Jean Donea Ispra, 4 th -5 th April 2005 Post-test model Pushover analysis

23. SPEAR International Workshop An event to honour the memory of Jean Donea Ispra, 4 th -5 th April 2005 Post-test model Top displacement in CM – X direction

24. SPEAR International Workshop An event to honour the memory of Jean Donea Ispra, 4 th -5 th April 2005 Post-test model Top displacement in CM – Y direction

25. SPEAR International Workshop An event to honour the memory of Jean Donea Ispra, 4 th -5 th April 2005 Post-test model Top rotation

26. SPEAR International Workshop An event to honour the memory of Jean Donea Ispra, 4 th -5 th April 2005 Post-test model Base shear (kN)

27. SPEAR International Workshop An event to honour the memory of Jean Donea Ispra, 4 th -5 th April 2005 Post-test model Storey drift in CM (first and second storey, 0.15 g)

28. SPEAR International Workshop An event to honour the memory of Jean Donea Ispra, 4 th -5 th April 2005 Post-test model Storey drift in CM (first and second storey, 0.20 g)

29. SPEAR International Workshop An event to honour the memory of Jean Donea Ispra, 4 th -5 th April 2005 Post-test model Storey shear vs. storey drift (second storey, 0.15 g)

30. SPEAR International Workshop An event to honour the memory of Jean Donea Ispra, 4 th -5 th April 2005 Post-test model Storey shear vs. story drift (second storey, 0.20 g)

31. SPEAR International Workshop An event to honour the memory of Jean Donea Ispra, 4 th -5 th April 2005 Post-test model Hysteretic energy (second storey)

32. SPEAR International Workshop An event to honour the memory of Jean Donea Ispra, 4 th -5 th April 2005 Post-test model Maximum story drifts in CM

33. SPEAR International Workshop An event to honour the memory of Jean Donea Ispra, 4 th -5 th April 2005 Post-test model Column C11 (corner, second storey, 0.15 and 0.20 g, analysis)

34. SPEAR International Workshop An event to honour the memory of Jean Donea Ispra, 4 th -5 th April 2005 Post-test model Column C11 (corner, second storey drifts in X and Y direction)

35. SPEAR International Workshop An event to honour the memory of Jean Donea Ispra, 4 th -5 th April 2005 Post-test model Column C11 (corner, second storey drifts)

36. SPEAR International Workshop An event to honour the memory of Jean Donea Ispra, 4 th -5 th April 2005 Post-test model Column C2, C11 (corner) - maximum storey drifts

37. SPEAR International Workshop An event to honour the memory of Jean Donea Ispra, 4 th -5 th April 2005 Capacity of columns Predicted capacity of columns in second storey

38. SPEAR International Workshop An event to honour the memory of Jean Donea Ispra, 4 th -5 th April 2005 Conclusions - Post-test model There are potential problems with the modelling of the initial damage in the strong column.There are potential problems with the modelling of the initial damage in the strong column. All basic response features observed in the tests were adequately simulated with the possible exception of larger damage at the top of the columns.All basic response features observed in the tests were adequately simulated with the possible exception of larger damage at the top of the columns. The correction of parameters was performed by displacement – controlled analysis (rough estimates) and by trial and error procedure (fine tuning).The correction of parameters was performed by displacement – controlled analysis (rough estimates) and by trial and error procedure (fine tuning). Pre-test model with corrected values of parameters was used.Pre-test model with corrected values of parameters was used.

39. SPEAR International Workshop An event to honour the memory of Jean Donea Ispra, 4 th -5 th April 2005 Conclusions Mathematical modelling of existing RC structures is difficult. Mathematical modelling of existing RC structures is difficult. Bar slippage and joint shear distortion have important effects.Bar slippage and joint shear distortion have important effects. Simple models with one-component lumped plasticity element models are robust and able to provide a fair assessment of response, provided that appropriate values of input parameters are used.Simple models with one-component lumped plasticity element models are robust and able to provide a fair assessment of response, provided that appropriate values of input parameters are used. Engineering judgement has to be used in modelling. It can be easily applied in robust simple models.Engineering judgement has to be used in modelling. It can be easily applied in robust simple models.