peter fajfar - prota engineering sunumlar... · peter fajfar prota‘s 30th anniversary symposium...

On performance analysis procedures

in the next Eurocode-8

Peter Fajfar

Prota‘s 30th Anniversary Symposium

New generation of seismic codes and new technologies in earthquake engineering Ankara, 26. February 2015

Institute of Structural Engineering, Earthquake Engineering and Construction IT

University of Ljubljana Faculty of Civil and Geodetic Engineering

Disclaimer

In this presentation the ideas and the proposals of the author for the revised version of Eurocode 8 are presented

They will not necessarily be included in the revised version of Eurocode 8

Scope

Introduction

Pushover analysis

Demand versus capacity

Influence of higher modes in plane and elevation

Nonstructural elements – floor acceleration spectra

Probabilistic approach

Pushover curve

Nonlinear analysis

Static (pushover) in combination with inelastic response spectra

Dynamic

Nonlinear dynamic versus pushover

Nonlinear dynamic analysis

More general and accurate (if applied by a knowledgeable user)

Computationally demanding (analysis and postprocessing)

Additional data

Input ground motions

Hysteretic behaviour

Damping model

Less transparent

M.Sozen, A Way of Thinking

Quoted from EERI Newsletter, April 2002

"Today, ready access to versatile and powerful software enables the engineer to do more and think less."

Pushover-based methods

Based on pushover analysis of MDOF model and response spectrum analysis of SDOF model

Provide valuable information on inelastic structural behaviour

Are transparent

Appropriate for everyday design use for usual structures, for conceptual design and for checking the results

LIMITATIONS APPLY

Pushover-based methods

If presented graphically in the AD format, especially in conjunction with the “Equal displacement rule”, they help to better understand relations between seismic demand and capacity

stiffness, strength, deformation, and ductility

Equal displacement rule

For a system with given initial period (stiffness and mass) and damping,

maximum displacements are approximately equal in the case of linear

and nonlinear response.

2nd World Conference on Earthquake Engineering, Japan 1960

„One of the possibilities is to relate the spectrum for the elasto-plastic

system to that for the corresponding elastic system by considering the

maximum relative displacements for the two systems to be equal“

LIMITATIONS APPLY

Explanation of “ductility-factor method” in Clough,Penzien: Dynamics of Structures 1.edition, 1975.

Ductility-factor method

DisplacementSd=Sde

Acceleration

Sae

Sa=Say

Sdy

Elastic spectrum

Inelastic spectrum

T

Demand versus capacity

Seismic demand

Inelastic spectrum

Inelastic spectra – basic relations

Elastic demand: 2

aede ae2 2

S TS S

4

aea d de

SS S S

R R

Inelastic demand:

R - - T relation is needed

R = reduction factor

/ R = inelastic displacement ratio

R - - T relation

1

TC

R

TTC

T

1

/R

Simple

aea d de

SS S S

R R

Simple R - - T relation

Elastic spectrum

Inelasticspectra

Displacement

Acceleration

=1.5

2

346

Inelastic spectra

Infilled RC frame

0 2 4 6 8 10 12 140

100

200

300

400

500

600

700

800

Top Displacement (cm)

Ba

se S

hear

(kN

)

Pla

sti

cm

ech

an

ism

Base S

hear

(kN

)

Top displacement (cm)

R - - T relation

1

TC

R

TTC

T

1

/R

TD u2 r-TD u2 r-

r =0.5u

s=1.5

r =0.5u

s=1.5

Infilled frames

aea d de

SS S S

R R

N2 method

SUMMARY OF THE N2 METHOD as implemented in EC8

N2 method

Pushover analysis of a MDOF model

Transformation to an equivalent SDOF model

Idealization of the pushover curve

Displacement demand for the SDOF system from inelastic response spectrum

Displacement demand for the MDOF system (Target displacement)

Seismic demand for all relevant quantities

Comparison of demand and capacity

Data m3

m2

m1

m3

m2

m1 ag

TTC TD

Sae

ag

TTC TD

Sae

M

q

Plastic

hinge Elastic element

Dt

{P}

V

D t

V

Pushover analysis

m*

D*

F*

D *

F *

y

Dy *

F *

G * V

F

G * D

D

Equivalent idealized SDOF model

Seismic demand for SDOF model

Sd

Sa T* = TC

T*

> TCSae

= 1 (elastic)

Sd = Sde

Say

Sd

Sa T* = TCSae

= 1 (elastic)

Say

Sde

T*< TC

Sd

Equal displacement rule

Global and local demands

Gt dD S

Dt

Performance evaluation

Capacity Demand

Check: • plastic mechanism Dt

• displacements • storey drifts • ductilities • plastic rotations • stresses in brittle elements • accelerations for equipment • overstrength

Seismic capacity Local / Global

Local capacity

Eurocode 8 – Part 3

Annex A provides empirical formulas for RC beams, columns and walls under flexure and shear

Chord rotation capacity at NC, SD and DL limit states

Shear strength at NC limit state

based on work by Fardis and coauthors

Capacity

Deformation

Fo

rce

20%

drop

ultimate displacement

Deformation

Fo

rce

Element level

Ultimate chord rotation (EC8-3)

radLfc

P

el

**

25),01.0max(

),01.0max(3.0016.0

1 35.0*

225.0

''

δ chord rotation P* axial load index fc‘ concrete compressive strength L* shear span index αρ* index related to confinement ω’ , ω reinforcement ratio (tensional and compressional) γel importance factor

Capacity

SERIES database

Within the FP7 project SERIES, a database of RC structural elements has been assembled from

existing databases

experimental data from literature

Sources

Univ. Patras (Fardis et al.) (beams, columns, walls)

PEER (columns)

Univ. Stanford (Lignos, Krawinkler) (beams)

Univ. Ljubljana (Peruš, Fajfar) (walls)

Literature

http://www.dap.series.upatras.gr/

Peruš et al., 2. ECEES, Istanbul 2014

Capacity - global

PEER

Near Collapse

NC Limit State

NC limit states

Element level Structure level

Global ultimate (NC) limit state

Possible definition:

Global ultimate (NC) limit state is reached when in the first important vertical structural element (column or wall) the ultimate (NC) limit state is reached.

Local vs global NC limit state

Low-rise buildings (up to 4 stories): NC LS of the structure ≈ NC LS of the critical element

Higher buildings NC LS of the structure more critical than NC LS of the critical element (due to P-Δ effect)

Rejec and Fajfar, 2014

Performance evaluation of a complex existing building

Kreslin and Fajfar, BEE, 2010

FGG building

Designed in 1962

Hor. Force = 2% Weigth

FGG building

FGG building

T= 1.8 s, Design force: F = 0.02 W EC8 demand: ag = 0.345 g, Type C soil Capacity: Shear failure: ag = 0.09 g, Flexural failure: ag = 0.31 g – 0.49 g

0.07

0.06

0.05

0.04

0.03

0.02

0.01

Ba

se

sh

ea

r /

Weig

ht

0.4 0.8 1.2 1.6 2.0 2.4 2.8

Top displacement / Height [%]

0.3

2

1.1

6

1.2

4

1.7

6

Shear

failure

Flexural

failure

NC – flexural capacity EC8-3

Upper bound

Lower bound

NC – shear capacity EC8-3

Displacement demand EC8

Design force

FGG building

Locations of the plastic hinges and

the demand/capacity ratios (for chord rotations) for selected elements

Limitation

Simplified (pushover-based) nonlinear methods

Basic assumption: structure vibrates predominantly in a single mode

Problem – influence of higher modes Elevation (medium- and high-rise buildings)

Plan (plan-asymmetric buildings)

Higher modes (torsion) in EC8-1

Higher modes in EC8-3

Extensions

“ The nonlinear static pushover analyses were introduced as simple methods … Refining them to a degree that may not be justified by their underlying assumptions and making them more complicated to apply than even the nonlinear response-history analysis … is certainly not justified and defeats the purpose of using such procedures.”

(Baros and Anagnostopoulos 2008)

Extension – higher modes

Proposed approach

Combination (envelope) of results of two standard analyses

Basic pushover (in two directions)

Elastic spectral analysis (scaled)

Beneficial effects of torsion are not considered

Higher modes in elevation

9-storey LA building (SAC) Kreslin and Fajfar, EESD, 2011

SPEAR building

SPEAR building

Torsion (Higher modes in plan)

Y - direction X - direction

u/u

CM

Stiff CM Flex. Stiff CM Flex.

0.8

0.9

1.0

1.1

1.2

1.3

1.4

0.7

PGA [g] 0.05 0.10 0.20 0.30 0.50

Pushover 0.30 g Elastic Spectral

N2 0.30 g

Nonstructural elements and contents

Floor acceleration spectra


FEMA E-74

Contents

Nonstructural

Structural

Office Hotel Hospital

Typical investment in building construction


Damage related to Displacements / drifts

Accelerations Floor acceleration spectra are needed

0

1

2

3

4

5

6

0 1 2 3 4

a

g

S

a S

a

1

T

T

z = 1.0

H

z = 0.5

H

z = 0

H

Floor acceleration spectra – Eurocode 8

No influence of

• damping of equipment

• nonlinear behavior of structure

• higher modes

As : floor acceleration spectrum (not applicable in resonance region Ts=Tp)

Tp, ξp : period, damping of the primary system

Ts, ξs : period, damping of the secondary system

Se : elastic acceleration spectrum (ground motion)

Rμ : reduction factor accounting for inelastic structural behaviour

Ts = large : As = Se(Ts, ξs) = acceleration spectrum (ground motion)

Ts = 0: As = Se(Tp, ξp) = max. acceleration of the primary structure

Vukobratović, Fajfar 2014

Approximate equation for floor acc. spectrum (based on theory)

AMP = max. acc. of the second. str. / max. acc. of the primary str.

Tp = period of the primary str., TC = characteristic period of ground motion

Amplification of floor spectra in resonance


SDOF structure elastic and µ=2 (Q model), 5% damping (primary and secondary

system), EC8 ground motion, soil type B

MDOF structure - Floor accelerations

Vukobratović, Fajfar 2015 (in preparation)


MDOF structure (3-storey wall, T1 = 0.3s)

elastic and µ=2 (Q model), 5% damping (primary and secondary system), EC8 ground motion, soil type B

1st floor 3rd floor

Vukobratović and Fajfar, 2015 (in preparation)

Probabilistic analysis

2 2 2 2

0exp 0.5 exp 0.5 k

f TOT C TOT CP k H PGA k k PGA

Probability of “failure“

Combination of the N2 method and SAC-FEMA probabilistic approach (Cornell et al.)

Fajfar, Dolšek, EESD 2012

Pf annual probability of “failure“ “Failure“ = economic failure = NC limit state

2 2 2 2

0exp 0.5 exp 0.5 k



H(PGAC) mean value of the hazard curve at PGAC

PGAC capacity in terms of PGA

determined by the N2 method

βTOT dispersion measure related to response (logaritmic standard deviation) k, k0 parameters of the hazard curve H(PGA) = k0 PGA-k

2 2 2 2

0exp 0.5 exp 0.5 k



Example k = 3, βTOT = 0.4

Pf = 2 H(PGAC )

SPEAR building

Typical cross-sections of the columns

l = 0,74 % l = 1,7 %

25

25

Column 25/25 cm

412

Stirrups

8/25 cm

1.5

Column 35/35 cm

Stirups

8/8.5 cm

3.0

35

416420 3

5

SPEAR building

Seismic loading

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

T [s]

Sa [

g] Elastic spectrum

Design spectrum

EC8, Soil type C

Pushover curves

Test

EC8 H

0

3

6

9

12

15

18

21

24

27

30

0.0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7

d n / H [%]

Fb /

W [

%]

Test1st yield of beam1st yield of columnNC

= 3.2

0

3

6

9

12

15

18

21

24

27

30

0.0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7

d n / H [%]

Fb /

W [

%]

TestEC8 H1st yield of beam1st yield of columnNCDesign force1. plast. grede1. plast. stebraNCt

= 3.2

= 6.5

X direction

Determination of seismic capacity (NC)

Test

EC8 H

Probability of “failure”

PGAC = 0.25 g (test building), PGAC = 0.77 g (EC8 building)

Pf = 0.65 x 10-2 or 28% in 50 years (test building)

Pf = 2.22 x 10-4 or 1.1% in 50 years (EC8 building)

Only randomness is considered

Discussion of results

Large increase of stiffness, strength, ductility and “failure” capacity of the code designed building compared to a building not designed for seismic resistance

Large decrease of the probability of “failure”

(1.1 % versus 28 % in 50 years)

Discussion of results

PGAC = 0.77 g

“The code is too conservative!?” (Design PGA = 0.29 g)

Pf = 1.1 % (in 50 years) “The probability is too high!?”

How high is the tolerable probability?

Survey (in Slovenia): less than 1 ‰ Engineers (217 respondents): economic failure 1 ‰, physical failure 0.6 ‰

Laymen (502 respondents): economic failure 0.8 ‰, physical failure 0.6 ‰

Conclusions – Revision of EC8

The basic tools for performance-based design of new buildings and assessment of existing buildings using pushover analysis are provided in the current version of EC8

• Some details have to be (better) defined • Definition of limit states at the global (structure) level

• Influence of higher modes in plan and elevation

The determination of acceleration demand needs a major revision (new floor acceleration spectra).

Quantification of probabilities is needed in performance-based engineering. In long term, a simplified probabilistic approach should be explicitly included in the standard.

Everything should be made as simple as possible, but not simpler

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