A New Approach for the Performance Base Seismic Deisgn of Structure - A. G. Ayala

A New Approach for the A New Approach for the Performance Based Seismic Performance Based Seismic

Design of Structures Design of Structures

U.N.A.M.U.N.A.M.

A Gustavo AyalaA Gustavo Ayala

September 2003September 2003

Instituto de IngenieríaInstituto de Ingeniería

Performance Based Seismic Design

• Conjunction of the design, construction Conjunction of the design, construction and maintenance procedures necessary to and maintenance procedures necessary to reach, through engineering means, reach, through engineering means, predictable performances for multiple predictable performances for multiple design objectives.design objectives.

• Its purpose is to minimize the economic Its purpose is to minimize the economic losses after a seismic event during the losses after a seismic event during the useful life of the structures.useful life of the structures.

• Is it really new? NOIs it really new? NO

• Is it really good? YESIs it really good? YES

NOVEL or NOBLE?


Background• PBSD is not a new concept, however, with the PBSD is not a new concept, however, with the

current procedures of seismic design it is not current procedures of seismic design it is not possible to guarantee that the objectives of possible to guarantee that the objectives of the design philosophy are satisfied.the design philosophy are satisfied.

• The application of the PBSD implies the use of The application of the PBSD implies the use of methods and tools which emphasize a precise methods and tools which emphasize a precise characterization of the structures and lead to characterization of the structures and lead to predictions using a level of technology higher predictions using a level of technology higher than that currently used.than that currently used.

• The Computational Mechanics group of the The Computational Mechanics group of the Institute of Engineering at UNAM has Institute of Engineering at UNAM has developed various procedures for the developed various procedures for the evaluation and design of structures using the evaluation and design of structures using the philosophy of PBSD.philosophy of PBSD.

Needs• Procedures for the PBSD of structures Procedures for the PBSD of structures

validated with realistic performance validated with realistic performance indexes which guarantee for a given design indexes which guarantee for a given design level a better control of the performance level a better control of the performance objectivesobjectives. .

• Till now the design philosophy and the Till now the design philosophy and the theoretical basis which regulate the PBSD theoretical basis which regulate the PBSD of structure have been established. of structure have been established. However, more work on the development However, more work on the development of the procedures to implement the PBSD is of the procedures to implement the PBSD is required. required.

Objective• To develop a simplified method for the PBSD To develop a simplified method for the PBSD

which implicitly involves in its formulation the which implicitly involves in its formulation the non linear behaviour and be directly applicable non linear behaviour and be directly applicable to different criteria for the objectives of PBSD.to different criteria for the objectives of PBSD.

• Develop a methodology to determine design Develop a methodology to determine design spectra based on the concepts of PBSD and the spectra based on the concepts of PBSD and the control of damage. control of damage.

• Validate the simplified method of PBSD in plane Validate the simplified method of PBSD in plane frames, asymmetric buildings and bridges. frames, asymmetric buildings and bridges.


Seismic performance level.Seismic performance level.

Seismic design level.Seismic design level.

Seismic design objectives.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.


• ATC-33ATC-33• FEMA – 273, ATC 40FEMA – 273, ATC 40• SEAOC- Vision 2000SEAOC- Vision 2000• Euro Code 8Euro Code 8• Japanese codeJapanese code

EC8: Conventional Criterion

• Explicitly satisfy the level of performance “Life Explicitly satisfy the level of performance “Life safety” under a design level “rare”safety” under a design level “rare”

• Limit the economic losses through a check of Limit the economic losses through a check of

the damage limits for a “frequent” demandthe damage limits for a “frequent” demand

• Prevent the collapse under any imaginable Prevent the collapse under any imaginable demand through a “Capacity Design ”demand through a “Capacity Design ”

Performance LevelPerformance Level

Seis

mic

Des

ign

Lev

elSe

ism

ic D

esig

n L

evel

Frequent (43 years)Frequent (43 years)50% in 30 years50% in 30 years

Ocassional (72 years)Ocassional (72 years)50% in 50 50% in 50 yearsyears

Rare (475 years)Rare (475 years)10% in 50 10% in 50 yearsyears

Very Rare (970 years)Very Rare (970 years)10% en 100 10% en 100 yearsyears

Fully Fully operationaloperational

Life safetyLife safetyOperationalOperationalCollapseCollapse

preventionprevention

Basic Objective

Basic Objective

Essential/Risk Objective

Essential/Risk Objective

Critical Safety Objective

Critical Safety Objective

Non acceptable

Non acceptable

performance in new

performance in new

construction

construction

Performance Level SEAOC- Vision 2000

Desempeño no aceptable


en construcciones

en construcciones

nuevas

nuevas

FullyFullyoperationaloperational

LifeLifeSafetySafetyOperationalOperational

CollapseCollapsepreventionprevention

LifeLifeSafetySafetyoperationaloperational

CollapseCollapsepreventionprevention



en construcciones

en construcciones

nuevas

nuevas

SEAOC- Vision 2000

Fully functionalFully functionalPerformance level where Performance level where essentially no damage occursessentially no damage occurs

•General damageGeneral damage•Vertical Elems. Vertical Elems. •Horizontal Elems. Horizontal Elems. •Non structural Non structural Elems. Elems. •Sanitary, electrical Sanitary, electrical and mechanical and mechanical systemssystems•ContentsContents

Performance Level

Fully OperationalFully Operational

LifeLifesafetysafetyOperationalOperational

Collapse Collapse preventionprevention

Non acceptable

Non acceptable

performance for new

performance for new

construction

construction

SEAOC- Vision 2000

Performance level where Performance level where essentially no damage occursessentially no damage occurs

•D max.D max.•Distortions Distortions 0.002-0.0050.002-0.005•Floor Accel. 0.10gFloor Accel. 0.10g•Strength Rel. <1Strength Rel. <1•Non structural Non structural behaviourbehaviour

Performance Level

FullyFullyOperationalOperational

LifeLifesafetysafetyOperationalOperational

Non acceptable

Non acceptable

performance for new

performance for new

construction

construction

SEAOC- Vision 2000

Collapse Collapse preventionpreventionExtreme state of damage in Extreme state of damage in

which the capacity of the which the capacity of the structure to sustain vertical structure to sustain vertical loads is significantly diminished.loads is significantly diminished.

Performance Level

•General damageGeneral damage•Vertical Elems. Vertical Elems. •Horizontal Elems. Horizontal Elems. •Non structural Non structural Elems. Elems. •Sanitary, electrical Sanitary, electrical and mechanical and mechanical systemssystems•ContentsContents


Life Life SafetySafetyOperationalOperational

Non accepotable

Non accepotable

performance for new

performance for new

construction

construction

SEAOC- Vision 2000 •D maxD max•Distortions 0.02-0.04Distortions 0.02-0.04•Rotactions 0.02-0.05Rotactions 0.02-0.05•Floor Accel 1.5gFloor Accel 1.5g•Strength Rel. f(Strength Rel. f())•Ductility and Ductility and dissipation of energy dissipation of energy (Damage indexes)(Damage indexes)

Performance Level

Collapse Collapse preventionpreventionExtreme state of damage in Extreme state of damage in

which the capacity of the which the capacity of the structure to sustain vertical structure to sustain vertical loads is significantly diminished.loads is significantly diminished.


Ocassional (72 years)Ocassional (72 years)50% in 50 years50% in 50 years

Rare (475 years)Rare (475 years)10% in 50 years10% in 50 years

Very Rare (970 years)Very Rare (970 years)10% in 100 years10% in 100 years

Objetivo Esencial/Riesgo


Objetivo Seguridad Crítica



•Location of epicentres and Location of epicentres and identification of seismic sources identification of seismic sources •Frequency of events at each Frequency of events at each source source •Distribution of the magnitude of Distribution of the magnitude of the events and their number the events and their number •Attenuation of seismic wavesAttenuation of seismic waves•Effects of local soil conditionsEffects of local soil conditions•Determination of the seismic Determination of the seismic hazardhazard

Design Level









CompletamenteCompletamenteFuncionalFuncional

10

100

1000

0 10 20 30 40 50 60 70 80 90 100Periodo de exposición (vida útil años)

Perio

do d

e R

etor

no (a

ños)

Pe(50%)Pe(20%)Pe(10%)Pe(5%)Pe(2%)

Design Level




Very Rare (970 years)Very Rare (970 years)10% in years10% in years





CompletamenteCompletamenteFuncionalFuncional

0.001

0.01

0.1

0 100 200 300 400Aceleración (gal)

Tasa

de

exce

denc

ia (1

/yr)

T=0.15 s

T=0.3 s

T=0.5 s

T=1.0 s

T=2.0 s

T=3.0 s

A max

Design Level

0

200

400

600

800

1000

1200

0 0.5 1 1.5 2 2.5 3T sec

Ace

lera

ción

gal

.

43 años72 años475 años970 años









Fully Fully OperationalOperational FuncionalFuncional

Design Level

0

200

400

600

800

1000

1200

0 0.5 1 1.5 2 2.5 3T sec

Ace

lera

ción

gal

.

43 años72 años475 años970 años




Very Rare (970 Very Rare (970 years)years)

10% in 100 years10% in 100 years





FullyFullyOpertionalOpertional FuncionalFuncional

Design Level

• Design process that relates a performance Design process that relates a performance level with a seismic design level.level with a seismic design level.

Procedures of PBSD

Moehle 1992; Priestley 1998, Moehle 1992; Priestley 1998, 2000; Kowalsky 1994, 1997; 2000; Kowalsky 1994, 1997; Paulay 2000; Fajfar 1999, CalviPaulay 2000; Fajfar 1999, Calvi

a) Displacementsa) Displacements

b) Energyb) Energy

c) Distortionsc) Distortions

a),b) o c) + a),b) o c) + d) Damage d) Damage distribution distribution

Mander 1996Mander 1996

Heidebrecht Heidebrecht 20002000

Ayala, Sandoval, Vidaud, Ayala, Sandoval, Vidaud, Basilio, Torres and Avelar Basilio, Torres and Avelar 1999->20021999->2002

Work Assumptions

• Based on concepts of structural Based on concepts of structural dynamics extended to systems with dynamics extended to systems with non linear behaviour it is possible to non linear behaviour it is possible to transform the capacity curve in the transform the capacity curve in the behaviour curve of an equivalent SDFS. behaviour curve of an equivalent SDFS.

• The behaviour curve of an equivalent The behaviour curve of an equivalent SDFS can be idealized as bilinear.SDFS can be idealized as bilinear.

Procedure for the Procedure for the Performance Based Seismic Performance Based Seismic

Design.Design.

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

0

0.1

0.2

0.3

0.4

0.5

0 10 20 30 40 50Sd (cm)

Sa (

g)

T=0.5s T=1.0s T=1.5s T=2.0s

T=3.0s

T=4.0s

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

0

0.1

0.2

0.3

0.4

0.5

0 10 20 30 40 50Sd (cm)

Sa (

g)

T=0.5s T=1.0s T=1.5s T=2.0s

T=3.0s

T=4.0s

• Based on the stiffnesses for the elastic and Based on the stiffnesses for the elastic and ultimate state, calculate the strength spectrum ultimate state, calculate the strength spectrum corresponding to the chosen performance index.corresponding to the chosen performance index.

• Relationship of the demand with the required Relationship of the demand with the required state of functionality.state of functionality.

Define the demand spectrum for the target performance index

2

222 1

2 21 2

1

2

2

mTk T

k Tm

T

Define the strength spectrum for the target performance index

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6

T seg

R/m

(g)

=1

=2=3

=40

0.2

0.4

0.6

0.8

1

0 20 40 60 80 100 120

Sd (cm)

R/m

(g)

=1

=2=3

=4

T=0.5s T=1.0s T=1.5s T=2.0s

T=3.0s

T=4.0s

Uniqueness of the solution

0

0.05

0.1

0.15

0 5 10 15Sd (cm)

R/m

(g)

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

0

0.05

0.1

0.15

0 5 10 15Sd (cm)

R/m

(g)


0

0.05

0.1

0.15

0 5 10 15Sd (cm)

R/m

(g)


Ductility – Performance Index

• Locus of the performance points which Locus of the performance points which satisfy the target ductilitysatisfy the target ductility

• Uniqueness of the solutionUniqueness of the solution

2 2

1 2

2

2

2

1 112 T T

Sa SdT

0

0.05

0.1

0.15

0 5 10 15

Sd (cm)

R/m

(g)

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

0

0.05

0.1

0.15

0 5 10 15Sd (cm)

Sa (g

)

T1

T2

Behaviour curve for a design satisfying several performance levels

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

seismic conditions

Strength and corresponding displacement spectra

0

50

100

150

200

250

300

0 1 2 3 4 5 6T (s)

R/m

gal

0

10

20

30

40

50

60

Sd (c

m)

Sdy

R/my

f f Sdy=(R/Sdy=(R/my)/my)/

Acceleration and corresponding displacement spectra

0

50

100

150

200

250

300

0 1 2 3 4 5 6T (s)

R/m

gal

0

10

20

30

40

50

60

Sd (c

m)

u ySd Sd

Sdy

R/my

Sdu

1T

Sa

Sd

1T

Sa

Sd

2T

2

222 1

21 2

1

2

2

mTk T

k Tm

T

0

20

40

60

80

100

120

140

160

0.0 1.0 2.0 3.0 4.0 5.0

T (seg)

R/m (gals)

[T1, (R/m)1]

, , , 1/R m

2 1

1 1R Rm m

Sd

1/R m

2/R m

ySd uSd

Sa

Sd

1/R m

Sa

PBSD Procedure - Fundamental Mode

1T

Sa

Sd

1T

Sa

Sd

2T

2

222 1

21 2

1

2

2

mTk T

k Tm

T

0

20

40

60

80

100

120

140

160

0.0 1.0 2.0 3.0 4.0 5.0

T (seg)

R/m (gals)

[T1, (R/m)1]

, , , 1/R m

2 1

1 1R Rm m

PBSD Procedure - Modal Spectral Analysis

0.0

2.0

4.0

6.0

8.0

10.0

0.0 1.0 2.0 3.0 4.0 5.0

T (s)

Sa (m/s2)

SCT-EW (erep1)

SCT-EW (ereo)

Sao / Sa1

Sa1 = (R/m)1

(T1, Sa1)

(T1, Sao)

0.0

2.0

4.0

6.0

8.0

10.0

0.0 1.0 2.0 3.0 4.0 5.0

T (s)

Sa (m/s2)

SCT-EW (erep2)

SCT-EW (ereo)

(T2, Sao )

(T2, Sa2 )

Sao / Sa2

Sa2 = (R/m)2 - (R/m)1

dy du

desplazamiento

Vy

Vu

VCapacity curve

Fundamental Mode PBSD Procedure

Sd

1/R m

2/R m

ySd uSd

SaBehaviour curve

Behaviour Curve

Capacity Curves for 1 mode and for many modes

V

azotea

T1

T2V1

VN

Vy N

Curva de mgdlCurva de 1gdl

VuN

Curva de comportamiento

0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0

180.0

200.0

220.0

240.0

260.0

0 5 10 15 20 25 30 35 40 45

desplazamiento (cm)

R/m (gals)

Many Modes PBSD Procedure

Determinaton of PBSD Spectra

Existing Approaches for the Design Level

•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.

• To use seismic design objectives consisting in pairs of performance level versus seismic design level corresponding to an exceedence rate of the performance level.

Vision 2000:

This work:

Nivel de Desempeño SísmicoNi

vel d

e Dise

ño S

ísmico

Completamente Funcional

Funcional Seguridad de Vidas

Cercano a Colapso

Frecuente

Ocasional

Raro

Muy Raro0 0.31 0.63 0.94 1.25 1.56 1.88 2.19 2.5 2.81 3.13 3.44 3.75 4. 06 4.38 4.69 5

17.22

34.44

51.67

68.89

86.11

103.33

120.56

137.78

155

T (seg.)

R /

m

For an chosed design objective, spectra with a

uniform rate of exceedence of the

proposed performance level

Design Objective:

Performance Based Design 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.

, lim1

,iMuN

ir i i

i Mo

d Mr P r r M L dM

dM

• Seismicity.

• Probability of exceedence of a performance level.

PBSD Spectra

• 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.

Mu

rMo

d MR P R e R M dM

dM

Considerations:

Observation: It is necessary to check the uniqueness of the relationship strength-ductility.

• Region under study, the lake zone of Mexico City

PBSD Spectra

• 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).

Evaluation of the seismic hazard

Probability of exceedence of a performance level

• Response of a SDFS to a set of seismic events.

PBSD Spectra

Performance level: Near to collapse, performance index μ = 4.

Design level: Very rare, rate of exceedence of the performance level of 1/1000.

0 0.31 0.63 0. 94 1.25 1.56 1.88 2.19 2.5 2.81 3.13 3.44 3.75 4.06 4.38 4.69 5

17.22

34.44

51.67

68.89

86.11

103.33

120.56

137.78

155

T (seg.)

R /

m

Basic Design Objective

Nivel de Desempeño Sísmico

Nive

l de D

iseño

Sísm

ico

Completamente Funcional

Funcional Seguridad de Vidas

Cercano a Colapso

Frecuente

Ocasional

Raro

Muy Raro

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 = 7.5F = 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)

80 7.5E M

Expected magnitude value:

7 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8 8.1 8.2 8.3 8.4 8.51 10 4

1 10 3

0.01

0.1TASA DE EXCEDENCIA DE MAGNITUDES

Magnitud

Tasa

de

exce

denc

ia (1

/año

) log

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

Exceedence rate of magnitudes λ(M)

00 max 0, * 00E M T M D F Ln T

Relationship of magnitude recurrence

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:

0

001

M

M E M TM k

0UM M M

0M uM M

00

1T

Characteristic earthquake model


rP R e R M

Earthquake simulations

Green Functions

Earthquake

M = 6.9

Registered 25 April 1989 at the SCT station

in Mexico City

Simulated earthquakes

7.2, 7.3, 7.4, 7.5, 7.6,7.7,

7.8, 7.9, 8.0, 8.1, 8.2

1000 simulations for each

magnitude

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

0.0 1.0 2.0 3.0 4.0 5.0

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.0 1.0 2.0 3.0 4.0 5.0

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

0.0 1.0 2.0 3.0 4.0 5.0

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

0.0 1.0 2.0 3.0 4.0 5.0

0.00

0.50

1.00

1.50

2.00

2.50

0.0 1.0 2.0 3.0 4.0 5.0

1T

2T

ySduSd

Sd

/R m

/ yR m

/ uR m

4 5% 23%


Probability density functions of strengths obtained for periods of 0.05 to 5 s and a M = 8.1 demand

4 5% 23% 8.1M

Strengths PDF

Distribución de probabilidad

R / m

f (R

/ m

)

0 40 80 120 160 2000

0.01

0.02

0.03

f (Re)

Re

f (R

e)

R_


P Re R

4 1P Re R F R

0 40 80 120 160 2000

0.5

1

P (Re > R)

R

1 - F

(R)

R_

8.1M 2 .T seg

1P Re R P Re R

Re

R

Uniform Hazard Spectra

8.4

7.0r

d MR P R e R M dM

dM

Seismic design objective: performance level (μ = 4) and design level very rare (rate of exceedence 1/1000).

0.05 0.43 0.81 1.19 1.57 1.95 2.33 2.72 3.1 3.48 3.86 4.24 4.62 5

16.5

33

49.5

66

82.5

99

115.5

132

148.5

165

Tasa de excedencia = 0.001 / año, Tr = 1000 años

ESPECTRO DE PELIGRO UNIFORME

T (seg.)

R /

m

4 5% 23%

Uniform Hazard Spectrum

0.05 0.43 0.81 1.19 1.57 1.95 2.33 2.72 3.1 3.48 3.86 4.24 4.62 5

16.5

33

49.5

66

82.5

99

115.5

132

148.5

165

Tasa de excedencia = 0.001 / año, Tr = 1000 añosTasa de excedencia = 0.002 / año, Tr = 500 añosTasa de excedencia = 0.005 / año, Tr = 200 añosTasa de excedencia = 0.01 / año, Tr = 100 años

ESPECTROS DE PELIGRO UNIFORME

T (seg.)

R /

m

4 5% 23%

Uniform Hazards Spectra

4 5% 23%

Exceedence curves for different vibration periods.

R/m ductility 4 (cm/sec2)

Exce

eden

ce ra

te(1

/year)

Illustrative ExamplesIllustrative Examples

Medium Height Plane FrameMedium Height Plane Frame

PlanPlan ElevationElevation

Rare (475 years)10% in 50 years

Life safety

-200

-100

0

100

200

0 20 40 60 80 100 120 140

t (Seg.)

Ace

l. (g

als)

SCT-EWSCT-EW

Force-Desplacements Spectra (Constant Ductility)

Curva de Curva de ComportamientoComportamiento

Ilustrative ExampleIlustrative Example

0

50

100

150

200

250

300

0 1 2 3 4 5 6T (s)

R/m

gal

0

10

20

30

40

50

60

Sd (c

m)

0

50

100

150

200

250

300

0 10 20 30 40 50 60

Sd cm

R/m

gal

SCT-EW, SCT-EW, =4, =4, =0.24=0.24

argC a gravitacionalVy Vu Vy

Strength demand in structural elements

Gravitational Loading Lateral elastic Lateral - elastic

Fyi Fui - Fyi

Table of Resisting Moments (t-m)Table of Resisting Moments (t-m)

LevelColumns

Beams

Left Central Right

I J I j I J

M+ M- M+ M- M+ M- M+ M- M+ M- M+ M- M+ M-

1 200 200 100 150 100 150 90 140 90 140 100 150 100 150

2 200 200 30 85 30 80 30 80 30 80 30 80 30 85

3 120 120 30 85 30 80 30 80 30 80 30 80 30 85

4 120 120 125 180 25 70 25 75 25 75 25 70 125 180

5 100 100 15 70 20 60 15 70 15 70 20 60 15 70

6 150 150 50 105 10 50 90 140 90 140 10 50 50 105

7 100 100 30 80 30 80 30 80 30 80 30 80 30 80

8 50 50 20 50 20 50 20 50 20 50 20 50 20 50

Illustrative ExampleIllustrative Example

Proposed Damage Proposed Damage DistributionDistribution

Obtained Damage Obtained Damage DistibutionDistibution

Evaluation MethodEvaluation Method

Obtained Damage Obtained Damage DistibutionDistibution

Step by Step AnalysisStep by Step Analysis

17 storey RC Frame17 storey RC Frame

8.0 m 8.0 m 8.0 m

8.0 m

8.0 m

8.0 m

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

110x110

90x90

75x75

60x60

@3.20 m

4.0 m

Design Forces (stage 2)Design Forces (stage 2)

LevelLevel ForceForce112233445566778899101011111212131314141515161617 17

2.622.624.294.296.526.529.019.0111.5911.5914.0614.0615.7915.7917.3417.3419.4319.4321.7821.7823.8123.8125.8825.8827.5927.5928.3628.3628.4928.4928.7728.7728.2428.24

Design ForcesDesign Forces

Gravitational Loading

Stage 1

roof = 5.44 ton/m

floors = 6.33 ton/m

Base shearV = 408.64 ton

Base shearV = 313.57 ton

Stage 2

Asymmetric BuildingAsymmetric Building

8.0 8.0 8.00 8.00

7.0

7.0

7.0

A

B

C

D

CM

8.4

1 2 3 4 5

12.8 Secondary beams (0.6 X 0.25 m2) Columns (0.8 X 0.8 m2)

Principal beams (0.8 X 0.4 m2)

Intersorey DriftsIntersorey Drifts

012345678

0.0 0.2 0.4 0.6 0.8 1.0

ABCD12345

Design A, Dynamic Analysis Design A, Dynamic Analysis with 30% in X and 100% in Y of with 30% in X and 100% in Y of

SCT-EWSCT-EW Evaluation II

0

1

2

3

4

5

6

7

8

0.0 0.2 0.4 0.6 0.8 1.0Drifts (%)

Inte

rest

orey

0

1

2

3

4

5

6

7

8

0.0 0.2 0.4 0.6 0.8 1.0Drifts (%)

Inte

rest

orey

Frame

Design A, Dynamic Analysis withDesign A, Dynamic Analysis with 100% in X and 30% in Y of SCT-100% in X and 30% in Y of SCT-

EW EW

012345678

0.0 0.2 0.4 0.6 0.8 1.0

ABCD12345

0

1

2

3

4

5

6

7

8

0.0 0.2 0.4 0.6 0.8 1.0Drifts (%)

Inte

rest

orey

0

1

2

3

4

5

6

7

8

0.0 0.2 0.4 0.6 0.8 1.0Drifts (%)

Inte

rest

orey

Design B, Dynamic Analysis withDesign B, Dynamic Analysis with 100% in X of SCT-NS and 100% in Y 100% in X of SCT-NS and 100% in Y

of SCT-EWof SCT-EW

Design B, Dynamic Analysis withDesign B, Dynamic Analysis with 100%100% in X of SCT-EW and 100% in in X of SCT-EW and 100% in

Y of SCT-NSY of SCT-NS

Interstorey DriftsInterstorey Drifts

Analized BridgeAnalized Bridge

0.00

2.00

4.00

6.00

8.00

10.00

12.00

0.00 1.00 2.00 3.00 4.00 5.00

T (seg)

R /

m ID = 0ID = 0.1ID= 0.2ID = 0.3ID = 0.4

Strength Spectra

0.00

2.00

4.00

6.00

8.00

10.00

12.00

0.00 1.00 2.00 3.00 4.00 5.00

T (seg)

R /

m

ID = 0

ID = 0.4

1.871.87

0.41530.4153

Strength Spectra

0.00

1.00

2.00

3.00

0.000 0.005 0.010 0.015D (m)

R /

m

1.871.87

0.00840.0084 0.01140.0114

2.122.12

Behaviour Curve

Conclusions

► With this method it is possible to know if a given With this method it is possible to know if a given performance index can be reached for a structure performance index can be reached for a structure and a seismic demand.and a seismic demand.

► With this method it is possible to control With this method it is possible to control displacements and interstorey drifts and thus satisfy displacements and interstorey drifts and thus satisfy the design objectives.the design objectives.

► In general the method does not directly guarantee In general the method does not directly guarantee local performances e.g. it is not possible to control in local performances e.g. it is not possible to control in a direct manner the magnitude of plastic rotations in a direct manner the magnitude of plastic rotations in elements, only their distribution within the structure. elements, only their distribution within the structure.

► The results obtained with this method The results obtained with this method suggest the need to consider in the definition suggest the need to consider in the definition of design spectra the pos-yielding strength of design spectra the pos-yielding strength ratio of the capacity curve of the structure.ratio of the capacity curve of the structure.

► As the nominal strengths obtained with this As the nominal strengths obtained with this method need to be modified to standardize method need to be modified to standardize the design of a structure, it is necessary to the design of a structure, it is necessary to check that the modified design satisfies the check that the modified design satisfies the performance levels under these new performance levels under these new conditions.conditions.

Conclusions

► The proposed method has the advantage to be able to The proposed method has the advantage to be able to control the damage in the structure. This characteristic control the damage in the structure. This characteristic makes it possible that a single design may satisfy different makes it possible that a single design may satisfy different performance levels.performance levels.

► The modal spectral version of the method can be applied to The modal spectral version of the method can be applied to more general cases in which the contribution of higher more general cases in which the contribution of higher modes is important. modes is important.

► The recursive application of this method allows to control the The recursive application of this method allows to control the economic implications of seismic design when varying the economic implications of seismic design when varying the intensity and distribution of damage, balancing the initial intensity and distribution of damage, balancing the initial costs with those of repairing the damage and colateral costs with those of repairing the damage and colateral losses due to the lack of functionality after a design losses due to the lack of functionality after a design earthquake occurs.earthquake occurs.

Conclusions

► It is shown that it is possible to reach sismic design objectives It is shown that it is possible to reach sismic design objectives considering as design level the corresponding to a rate of considering as design level the corresponding to a rate of exceedence of a proposed performance level. exceedence of a proposed performance level.

► Different damage configurations correspond to different slopes Different damage configurations correspond to different slopes of the secon (inelastic) branchof the behaviour curve and, as a of the secon (inelastic) branchof the behaviour curve and, as a consequence, different design spectra.consequence, different design spectra.

► From a practical point of view it is not possible to exactly satisfy From a practical point of view it is not possible to exactly satisfy with a single design more than two design levels.with a single design more than two design levels.

Conclusions

► Validate this method for other performance indexes, for Validate this method for other performance indexes, for which it is necessary to develop the design spectra for which it is necessary to develop the design spectra for these performance indexes.these performance indexes.

► Investigate further the definition and validation of the Investigate further the definition and validation of the performance levels.performance levels.

► Investigate seismic design levels with different Investigate seismic design levels with different probabilities of exceedence of other design levels.probabilities of exceedence of other design levels.

► Considered the assumed relationship of the Considered the assumed relationship of the parameter in the Park y Ang damage index with the parameter in the Park y Ang damage index with the stiffness degradation of the structure evaluate the stiffness degradation of the structure evaluate the range of values of this parameter in real structures.range of values of this parameter in real structures.

Recommendations

Recommendations► Investigate the relationship strength – ductility as Investigate the relationship strength – ductility as it is possible that a given ductility is reached with it is possible that a given ductility is reached with more than one strength.more than one strength.

► Develop and validate a methodology which allows Develop and validate a methodology which allows to satisfy with a single design different performance to satisfy with a single design different performance levels.levels.

►Calculate design spectra for other ductilities and Calculate design spectra for other ductilities and for other performance indexes. for other performance indexes.

► Obtain design spectra for different Obtain design spectra for different values and values and from them reduction factors, funtion of from them reduction factors, funtion of , to difine , to difine design spectra based on a reference nominal design spectra based on a reference nominal spectrum. spectrum.

► Consider for the calculation of nominal Consider for the calculation of nominal design strengths for the elements realistic design strengths for the elements realistic behaviour models for the concrete and steel.behaviour models for the concrete and steel.

► Whenever it is impossible to reach a Whenever it is impossible to reach a performance index associated to the global performance index associated to the global behaviour of the structure, it is necessary to behaviour of the structure, it is necessary to modify the structure accordingly and repeat modify the structure accordingly and repeat the procedure. the procedure.

Practical Considerations

Documents

A New Approach for the Performance Base Seismic Deisgn of Structure - A. G. Ayala