Peter Fajfar - Prota Engineering sunumlar... · Peter Fajfar Prota‘s 30th Anniversary Symposium...
Transcript of 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
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
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
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
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
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
Performance evaluation
Capacity Demand
Check: • plastic mechanism Dt
• displacements • storey drifts • ductilities • plastic rotations • stresses in brittle elements • accelerations for equipment • overstrength
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
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
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
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)
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
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
FEMA E-74
Contents
Nonstructural
Structural
Office Hotel Hospital
Typical investment in building construction
Nonstructural elements and contents
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
Floor acceleration spectra
SDOF structure elastic and µ=2 (Q model), 5% damping (primary and secondary
system), EC8 ground motion, soil type B
Floor acceleration spectra
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)
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
f TOT C TOT CP k H PGA k k PGA
Probability of “failure“
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
f TOT C TOT CP k H PGA k k PGA
Probability of “failure“
Example k = 3, βTOT = 0.4
Pf = 2 H(PGAC )
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
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.