A New Approach for the Performance Based Seismic Design of Structures

1. U.N.A.M. Instituto de Ingeniería A New Approach for the Performance Based Seismic Design of Structures A Gustavo Ayala September 2003

2. Conjunction of the design, construction and maintenance procedures necessary to reach, through engineering means, predictable performances for multiple design objectives. • Its purpose is to minimize the economic losses after a seismic event during the useful life of the structures. Performance Based Seismic Design

3. Performance Based Seismic Design • Is it really new? NO • Is it really good? YES NOVEL or NOBLE?

4. Background • PBSD is not a new concept, however, with the current procedures of seismic design it is not possible to guarantee that the objectives of the design philosophy are satisfied. • The application of the PBSD implies the use of methods and tools which emphasize a precise characterization of the structures and lead to predictions using a level of technology higher than that currently used. • The Computational Mechanics group of the Institute of Engineering at UNAM has developed various procedures for the evaluation and design of structures using the philosophy of PBSD.

5. Procedures for the PBSD of structures validated with realistic performance indexes which guarantee for a given design level a better control of the performance objectives. • Till now the design philosophy and the theoretical basis which regulate the PBSD of structure have been established. However, more work on the development of the procedures to implement the PBSD is required. Needs

6. To develop a simplified method for the PBSD which implicitly involves in its formulation the non linear behaviour and be directly applicable to different criteria for the objectives of PBSD. • Develop a methodology to determine design spectra based on the concepts of PBSD and the control of damage. • Validate the simplified method of PBSD in plane frames, asymmetric buildings and bridges. Objective

7. Seismic performance level. • Seismic design level. • Seismic design objectives. Expression the maximum acceptable damage in a structure subjected to earthquake action. Seismic demand representing the hazard of a site where the structure would be located. Union of a performance level and a level of seismic design. Performance Based Seismic Design

8. Performance Based Seismic Design • ATC-33 • FEMA – 273, ATC 40 • SEAOC- Vision 2000 • Euro Code 8 • Japanese code

9. EC8: Conventional Criterion • Explicitly satisfy the level of performance “Life safety” under a design level “rare” • Limit the economic losses through a check of the damage limits for a “frequent” demand • Prevent the collapse under any imaginable demand through a “Capacity Design ”

10. Performance Level Life safety Collapse prevention Fully operational Operational Frequent (43 years) 50% in 30 years Ocassional (72 years) 50% in 50 years Basic Objective Rare (475 years) 10% in 50 years Essential/Risk Objective Critical Safety Objective Very Rare (970 years) 10% en 100 years Non acceptable performance in new construction Seismic Design Level

11. Life Safety Collapse prevention Fully operational Operational Desempeño no aceptable en construcciones nuevas Performance Level SEAOC- Vision 2000

12. Fully functional Performance level where essentially no damage occurs Performance Level SEAOC- Vision 2000 • General damage • Vertical Elems. • Horizontal Elems. • Non structural Elems. • Sanitary, electrical and mechanical systems • Contents Life Safety Collapse prevention operational Desempeño no aceptable en construcciones nuevas

13. Performance Level SEAOC- Vision 2000 • D max. • Distortions 0.002-0.005 • Floor Accel. 0.10g • Strength Rel. <1 • Non structural behaviour Fully Operational Performance level where essentially no damage occurs Life safety Collapse prevention Operational Non acceptable performance for new construction

14. Collapse prevention Extreme state of damage in which the capacity of the structure to sustain vertical loads is significantly diminished. Performance Level SEAOC- Vision 2000 • General damage • Vertical Elems. • Horizontal Elems. • Non structural Elems. • Sanitary, electrical and mechanical systems • Contents Life safety Fully Operational Operational Non acceptable performance for new construction

15. Collapse prevention Extreme state of damage in which the capacity of the structure to sustain vertical loads is significantly diminished. Performance Level SEAOC- Vision 2000 • D max • Distortions 0.02-0.04 • Rotactions 0.02-0.05 • Floor Accel 1.5g • Strength Rel. f(f,m) • Ductility and dissipation of energy (Damage indexes) Life Safety Fully Operational Operational Non accepotable performance for new construction

16. Seguridad de vidas Colapso incipiente Fully Operational Operational Frequent (43 years) 50% in 30 years Ocassional (72 years) 50% in 50 years Objetivo Básico Rare (475 years) 10% in 50 years Objetivo Esencial/Riesgo Objetivo Seguridad Crítica Very Rare (970 years) 10% in 100 years Design Level • Location of epicentres and identification of seismic sources • Frequency of events at each source • Distribution of the magnitude of the events and their number • Attenuation of seismic waves • Effects of local soil conditions • Determination of the seismic hazard

17. Seguridad de vidas Colapso incipiente Completamente Funcional Funcional Frequent (43 years) 50% in 30 years Ocassional (72 years) 50% in 50 years Objetivo Básico Rare (475 years) 10% in 50 years Objetivo Esencial/Riesgo Objetivo Seguridad Crítica Very Rare (970 years) 10% in 100 years Design Level

18. Seguridad de vidas Colapso incipiente Completamente Funcional Funcional Frequent (43 years) 50% in 30 years Ocassional (72 years) 50% in 50 years Objetivo Básico Rare (475 years) 10% in 50 years Objetivo Esencial/Riesgo Objetivo Seguridad Crítica Very Rare (970 years) 10% in years Design Level

19. Seguridad de vidas Colapso incipiente Fully Operational Funcional Frequent (43 years) 50% in 30 years Ocassional (72 years) 50% in 50 years Objetivo Básico Rare (475 years) 10% in 50 years Objetivo Esencial/Riesgo Objetivo Seguridad Crítica Very Rare (970 years) 10% in 100 years Design Level

20. Seguridad de vidas Colapso incipiente Fully Opertional Funcional Frequent (43 years) 50% in 30 years Ocassional (72 years) 50% in 50 years Objetivo Básico Rare (475 years) 10% in 50 years Objetivo Esencial/Riesgo Objetivo Seguridad Crítica Very Rare (970 years) 10% in 100 years Design Level

21. Procedures of PBSD • Design process that relates a performance level with a seismic design level. a) Displacements Moehle 1992; Priestley 1998, 2000; Kowalsky 1994, 1997; Paulay 2000; Fajfar 1999, Calvi b) Energy Mander 1996 c) Distortions Heidebrecht 2000 a),b) o c) + d) Damage distribution Ayala, Sandoval, Vidaud, Basilio, Torres and Avelar 1999->2002

22. Work Assumptions • Based on concepts of structural dynamics extended to systems with non linear behaviour it is possible to transform the capacity curve in the behaviour curve of an equivalent SDFS. • The behaviour curve of an equivalent SDFS can be idealized as bilinear.

23. Procedure for the Performance Based Seismic Design.

24. Determine the elastic stiffness of the structure and transform it to the space Sa vs Sd

25. For an assumed damage distribution calculate the slope of the second branch of the behaviour curve

26. Define the demand spectrum for the target performance index • Based on the stiffnesses for the elastic and ultimate state, calculate the strength spectrum corresponding to the chosen performance index. • Relationship of the demand with the required state of functionality.

27. Define the strength spectrum for the target performance index Uniqueness of the solution

28. Superpose the elastic and inelastic branches in the space of the demand spectrum

29. Superpose the elastic and inelastic branches in the space of the demand spectrum

30. Superpose the elastic and inelastic branches in the space of the demand spectrum

31. Ductility – Performance Index • Locus of the performance points which satisfy the target ductility • Uniqueness of the solution

32. Translate the second branch to the point the demand spectrum satisfies the target performance index

33. Behaviour curve for a design satisfying several performance levels

34. Carry out a static analysis with a distribution of lateral forces equivalent to those acting on the structure under seismic conditions

35. R/my Sdy Strength and corresponding displacement spectra Sdy=(R/my)/w2 f (a,m)

36. R/my Sdu Sdy Acceleration and corresponding displacement spectra

37. PBSD Procedure - Fundamental Mode

38. PBSD Procedure - Modal Spectral Analysis

39. Fundamental Mode PBSD Procedure Capacity curve Behaviour curve

40. Many Modes PBSD Procedure Behaviour Curve Capacity Curves for 1 mode and for many modes

41. Determinaton of PBSD Spectra

42. Existing Approaches for the Design Level Vision 2000: • To use as seismic design level demands corresponding to intensities with a given probability of exceedence. It does not give information on the rate of exceedence of the performance level. This work: • To use seismic design objectives consisting in pairs of performance level versus seismic design level corresponding to an exceedence rate of the performance level.

43. Performance Based Design Spectra Design Objective: For an chosed design objective, spectra with a uniform rate of exceedence of the proposed performance level

44. PBSD Spectra Rate of exceedence of a performance level Expected number of times per unit time in which the performance of the structure exceeds certain performance level when subjected to earthquakes of different magnitudes and seismic sources defining the seismic hazard of the site. • Seismicity. • Probability of exceedence of a performance level.

45. PBSD Spectra Considerations: • Region under study, the lake zone of Mexico City • The only source that contributes to the seismic hazards of Mexico City is the Guerrero gap. • The probability that the structural system develops a ductility > 4 is equal to the probability that the system has a strength less than that required to reach such ductility. Observation:It is necessary to checkthe uniqueness of the relationship strength-ductility.

46. PBSD Spectra • Evaluation of the seismic hazard • Identifify the earthquake generating zones that affect an specific site. • Evaluate the rate of seismic activity of the sourcers generators of earthquakes (rate of exceedence of magnitudes). • Probability of exceedence of a performance level • Response of a SDFS to a set of seismic events.

47. Basic Design Objective Performance level:Near to collapse, performance index μ = 4. Design level:Very rare, rate of exceedence of the performance level of 1/1000.

48. Seismicity parameters for the subduction zone of Guerrero T00 = 80 years(Elapsed time in years since the last occurrence of an earthquake with magnitude M>M0) M0 = 7.0 (Threshold magnitude) Mu = 8.4(Maximum magnitude) D = 7.5 F = 0.0(D, F, Parameter defining the variation od expected magnitude with time) σM = 0.27(Standard deviation of magnitudes) To = 39.7 years(Median of the time between events of magnitude M>M0) Expected magnitude value:

49. Exceedence rate of magnitudes λ(M) Exceedence rate of an earhquake of magnitude M or higher λ(M), for the seismic source of Guerrero

50. Relationship of magnitude recurrence Characteristic earthquake model In the model of a characteristic earthquake the rate of exceedence of the magnitude changes as a function of tme and it is given by: