Slide 4_Static Nonlinear Analysis
-
Upload
lderradji59 -
Category
Documents
-
view
40 -
download
1
Transcript of Slide 4_Static Nonlinear Analysis
![Page 1: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/1.jpg)
STATIC NONLINEAR ANALYSISANALYSIS
Advanced Earthquake EngineeringCIVIL-706
Instructor:Amin KARBASSI, PhD
![Page 2: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/2.jpg)
By the end of today’s course…
You will be able to answer:
• What are NSA advantages • What are NSA advantages
over other structural
analysis methods?
• How to perform an NSA?
• What are the key elements
Static nonlinear analysis Advanced Earthquake Engineering CIVIL-706
• What are the key elements
when performing NSA?
![Page 3: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/3.jpg)
Earthquake Engineering Assessment
So
urc
e:
FE
MA
44
0
Advanced Earthquake Engineering CIVIL-706 Static nonlinear analysis
So
urc
e:
FE
MA
44
0
![Page 4: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/4.jpg)
Earthquake Engineering Assessment
Action
StructureStatic Dynamic
LinearEquivalent Force
method
Response
Spectrum method
Advanced Earthquake Engineering CIVIL-706
method Spectrum method
Non-linear PushoverNon-linear
Dynamic
Static nonlinear analysis
![Page 5: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/5.jpg)
Nonlinear time history analysis
• Advantage: considering the complexity of the
dynamic load + the dynamic behavior of structuredynamic load + the dynamic behavior of structure
• Disadvantage: time consuming
Advanced Earthquake Engineering CIVIL-706 Static nonlinear analysis
![Page 6: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/6.jpg)
Nonlinear static procedure
• How does it work? Capacity vs. Demand
Sa
Advanced Earthquake Engineering CIVIL-706 Static nonlinear analysis
Sd
![Page 7: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/7.jpg)
Nonlinear static procedure
• Necessary elements?
– Acceleration-displacement response spectrum (ADRS)– Acceleration-displacement response spectrum (ADRS)
Sa
T(sec.)
V (force)
Δ (disp.)
Sa
Advanced Earthquake Engineering CIVIL-706 Static nonlinear analysis
Sa
Sd
![Page 8: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/8.jpg)
Nonlinear static procedure
• Developing capacity curves:
– Displacement-based methods– Displacement-based methods
Advanced Earthquake Engineering CIVIL-706 Static nonlinear analysis
![Page 9: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/9.jpg)
Nonlinear static procedure
• Assumptions
– Response: maximum displacement– Response: maximum displacement
– Deformation: “most often” following the first mode
• Benefits
– Displacement-based analysis
– Nonlinear behavior of the structure
• Drawbacks
Advanced Earthquake Engineering CIVIL-706
• Drawbacks
– Simplified approach (static)
– Cyclic response resembled to monotonic response
– Damping difficult to represent
Static nonlinear analysis
![Page 10: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/10.jpg)
Content
• Pushover technique – capacity curve
• Seismic performance – damage• Seismic performance – damage
• Acceleration-Displacement Response Spectrum
(ADRS)
• Inelastic response spectrum and Performance Point
• Large-scale vulnerability assessment
Advanced Earthquake Engineering CIVIL-706
• Large-scale vulnerability assessment
Static nonlinear analysis
![Page 11: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/11.jpg)
Content
• Pushover technique – capacity curve
• Seismic performance – damage• Seismic performance – damage
• Acceleration-Displacement Response Spectrum
(ADRS)
• Inelastic response spectrum and Performance Point
• Large-scale vulnerability assessment
Advanced Earthquake Engineering CIVIL-706
• Large-scale vulnerability assessment
Static nonlinear analysis
![Page 12: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/12.jpg)
Capacity Curve
• Pushover: to estimate the capacity curve
Structural model
(FEM, AEM, etc.)
Advanced Earthquake Engineering CIVIL-706
• Objectives:
– Estimate the maximum horizontal displacement
– Estimate the (global) ductility of the structure
Static nonlinear analysis
(FEM, AEM, etc.)
![Page 13: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/13.jpg)
Capacity Curve
• Load pattern: distribution of forces should represent
the dynamic behavior the dynamic behavior
– Triangular (if building regular enough)
– Following the first mode
– Other simplified distributions
depending on the building
Advanced Earthquake Engineering CIVIL-706
Base Shear
Static nonlinear analysis
![Page 14: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/14.jpg)
Capacity Curve
• Load pattern: IDARC practice
– Effect of lateral load pattern– Effect of lateral load pattern
Advanced Earthquake Engineering CIVIL-706 Static nonlinear analysis
![Page 15: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/15.jpg)
Capacity Curve
• Force/Displacement to spectral coordinates
Equivalent SDOF
V
Δ
Sa
Sd
V
Equivalent SDOF
Advanced Earthquake Engineering CIVIL-706 Static nonlinear analysis
1a
VWS
α=
1 1,( )droof
SPF
∆=×Φ
1
1,
1
(mod.1)
(mod.1)
(mod.1)roof
mass participation factor
roof level amplitude
PF Participation Factor
α =Φ =
=
![Page 16: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/16.jpg)
Content
• Pushover technique – capacity curve
• Seismic performance – damage• Seismic performance – damage
• Acceleration-Displacement Response Spectrum
(ADRS)
• Inelastic response spectrum and Performance Point
• Large-scale vulnerability assessment
Advanced Earthquake Engineering CIVIL-706
• Large-scale vulnerability assessment
Static nonlinear analysis
![Page 17: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/17.jpg)
Seismic Performance/Damage
Advanced Earthquake Engineering CIVIL-706 Static nonlinear analysis
![Page 18: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/18.jpg)
Seismic Performance/Damage
• Damage-based design/assessment:
– Related to social and economical costs of – Related to social and economical costs of
damage/mitigating measures
• Performance-based design/assessment:
– Related to life safety, reduce injuries, etc.
Advanced Earthquake Engineering CIVIL-706 Static nonlinear analysis
![Page 19: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/19.jpg)
FEMA 356 Performance levels
Advanced Earthquake Engineering CIVIL-706 Static nonlinear analysis
EMS98 damage grades
FEMA 356 Performance levels
![Page 20: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/20.jpg)
Example of damage grade estimation
RC building with FE modeling
– Pushover on the FE model: damage grade– Pushover on the FE model: damage grade
Advanced Earthquake Engineering CIVIL-706 Static nonlinear analysis
![Page 21: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/21.jpg)
Unreinforced masonry (URM)
Example
URM building in Yverdon-les-Bains
Advanced Earthquake Engineering CIVIL-706 Static nonlinear analysis
![Page 22: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/22.jpg)
Unreinforced masonry (URM)
Example
Architectural plan
Advanced Earthquake Engineering CIVIL-706 Static nonlinear analysis
![Page 23: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/23.jpg)
Unreinforced masonry (URM)
Example
Simplification for the modeling
Advanced Earthquake Engineering CIVIL-706 Static nonlinear analysis
![Page 24: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/24.jpg)
Unreinforced masonry (URM)
Key-parameter: Frame effect (coupling of horizontal/vertical elements)horizontal/vertical elements)
– flexible slab (w/o frame effect)
– Infinitely stiff lintels
0
2
3 totalh h= ×
Ze
ro m
om
en
t
Advanced Earthquake Engineering CIVIL-706
– Infinitely stiff lintels
(total frame effect)
Static nonlinear analysis
0
1
2 storeyh h= ×
![Page 25: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/25.jpg)
Unreinforced masonry (URM)
Example
Extreme case studies:
0
26.7
3 totalh h m= × =
Advanced Earthquake Engineering CIVIL-706 Static nonlinear analysis
0
11.25
2 storeyh h m= × =
![Page 26: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/26.jpg)
Unreinforced masonry (URM)
Example
Lateral strength – transverse direction
Lw (m) Nd (kN)w/o frame effect
(kN)
Complete frame
effect (kN)
2.0 180 22 96
5.0 360 117 216
6.0 1520 367 624
Advanced Earthquake Engineering CIVIL-706 Static nonlinear analysis
6.0 1520 367 624
total 690 1440
Too conservative Too optimistic
![Page 27: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/27.jpg)
Unreinforced masonry (URM)
Example
Lateral strength – transverse direction
Advanced Earthquake Engineering CIVIL-706 Static nonlinear analysis
![Page 28: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/28.jpg)
Content
• Pushover technique – capacity curve
• Seismic performance – damage• Seismic performance – damage
• Acceleration-Displacement Response Spectrum
(ADRS)
• Inelastic response spectrum and Performance Point
• Large-scale vulnerability assessment
Advanced Earthquake Engineering CIVIL-706
• Large-scale vulnerability assessment
Static nonlinear analysis
![Page 29: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/29.jpg)
Reminder: Response Spectrum
Advanced Earthquake Engineering CIVIL-706 Static nonlinear analysis
![Page 30: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/30.jpg)
Reminder: Response Spectrum
2a
d
SS
ω≈
Advanced Earthquake Engineering CIVIL-706 Static nonlinear analysis
![Page 31: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/31.jpg)
Acceleration-Displacement Response
Spectrum (ADRS)
Advanced Earthquake Engineering CIVIL-706 Static nonlinear analysis
![Page 32: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/32.jpg)
Acceleration-Displacement Response
Spectrum (ADRS)
Advanced Earthquake Engineering CIVIL-706 Static nonlinear analysis
![Page 33: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/33.jpg)
Content
• Pushover technique – capacity curve
• Seismic performance – damage• Seismic performance – damage
• Acceleration-Displacement Response Spectrum
(ADRS)
• Inelastic response spectrum and Performance Point
• Large-scale vulnerability assessment
Advanced Earthquake Engineering CIVIL-706
• Large-scale vulnerability assessment
Static nonlinear analysis
![Page 34: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/34.jpg)
Inelastic Response Spectrum
Best linear SDOF which represents the nonlinear
structure? (examples covered here)structure? (examples covered here)
• Equivalent linearization (FEMA 440)
• Improved Spectrum Method of ATC40
• N2 method (equal displacement rule, EC8 approach)
Advanced Earthquake Engineering CIVIL-706
• N2 method (equal displacement rule, EC8 approach)
Static nonlinear analysis
![Page 35: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/35.jpg)
Equivalent Linearization Method
A little bit of background…
• First introduced in 1970 in a pilot project as a rapid evaluation tool (Freeman et al. 1975)
• Basis of the simplified analysis methodology in ATC-40 (1996)
Advanced Earthquake Engineering CIVIL-706
ATC-40 (1996)
• Improved later in FEMA 440 document (2005)
Static nonlinear analysis
![Page 36: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/36.jpg)
Equivalent Linearization Method
Optimal equivalent linear parameters (i.e.,
effective period, Teff, and effective damping, effective period, Teff, and effective damping,
βeff) are determined through a statistical
analysis that minimizes, in a rigorous manner,
the extreme occurrences of the difference (i.e.,
error) between the maximum response of an
actual inelastic system and its equivalent
Advanced Earthquake Engineering CIVIL-706
error) between the maximum response of an
actual inelastic system and its equivalent
linear counterpart.
Static nonlinear analysis
“FEMA 440”
![Page 37: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/37.jpg)
Equivalent Linearization
Basic equations…
Advanced Earthquake Engineering CIVIL-706 Static nonlinear analysis
![Page 38: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/38.jpg)
Equivalent Linearization-
Performance Point
So
urc
e:
FE
MA
44
0
Advanced Earthquake Engineering CIVIL-706 Static nonlinear analysis
So
urc
e:
FE
MA
44
0
![Page 39: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/39.jpg)
Equivalent Linearization
• Advantages:
– Linear computation– Linear computation
– Use of pushover analysis
• Drawbacks:
– Value of damping (through iterations)
Advanced Earthquake Engineering CIVIL-706
– Value of damping (through iterations)
– Not always conservative
Static nonlinear analysis
![Page 40: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/40.jpg)
N2 Method
A little bit of background…
• Started in the mid 1980’s (Fajfar and
Fischinger 1987, 1989)
• A variant of the Capacity Spectrum Method
(ATC-40)
Advanced Earthquake Engineering CIVIL-706
(ATC-40)
• Based on inelastic spectra rather than elastic
spectra
Static nonlinear analysis
![Page 41: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/41.jpg)
N2 Method Procedure (1)
Required tools:
Advanced Earthquake Engineering CIVIL-706 Static nonlinear analysis
Structural model (MDOF) Elastic response spectrum
![Page 42: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/42.jpg)
N2 Method Procedure (2)
,aea d de
SS S S
R Rµ µ
µ= =Reduction factorR Rµ µ
( 1) 1 CC
C
TR T T
T
R T T
µ
µ
µ
µ
= − + <
= ≥
Reduction factor
“Vidic et al. 1992”
Advanced Earthquake Engineering CIVIL-706 Static nonlinear analysis
Inelastic response spectrum (ADRS)
![Page 43: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/43.jpg)
N2 Method Procedure (3)-
Performance Point
:Cif T T≥
Basic equations…
:Cif T T≥
Advanced Earthquake Engineering CIVIL-706 Static nonlinear analysis
![Page 44: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/44.jpg)
N2 Method Procedure (3)-
Performance Point
d deS S=d deS S=
Advanced Earthquake Engineering CIVIL-706 Static nonlinear analysis
![Page 45: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/45.jpg)
N2 Method Procedure (3)-
Performance Point
:Cif T T<
Basic equations…
:Cif T T<
Advanced Earthquake Engineering CIVIL-706 Static nonlinear analysis
![Page 46: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/46.jpg)
N2 Method Procedure (3)-
Performance Point
1 ( 1)de Cd
S TS Rµ
= + − *1 ( 1)dS R
R Tµµ
= + −
Advanced Earthquake Engineering CIVIL-706 Static nonlinear analysis
![Page 47: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/47.jpg)
Content
• Pushover technique – capacity curve
• Seismic performance – damage• Seismic performance – damage
• Acceleration-Displacement Response Spectrum
(ADRS)
• Inelastic response spectrum and Performance Point
• Large-scale vulnerability assessment
Advanced Earthquake Engineering CIVIL-706
• Large-scale vulnerability assessment
Static nonlinear analysis
![Page 48: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/48.jpg)
Large-scale vulnerability assessment
Steps for large-scale vulnerability assessment:
• Typology of the building stock with structural
characteristics
• Distribution of building classes in the area under
study
• Vulnerability assessment of each class including
Advanced Earthquake Engineering CIVIL-706
• Vulnerability assessment of each class including
variability (probabilistic assessment)
Fragility functions
Static nonlinear analysis
![Page 49: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/49.jpg)
Large-scale vulnerability assessment
Empirical methods (e.g. EMS98, GNDT, Risk-UE LM1,
Vulneralp) based on damage surveysVulneralp) based on damage surveys
• Relationship between ground motion (intensity)
and distribution of observed damage grades for
structures with a given vulnerability index
Advanced Earthquake Engineering CIVIL-706
Damage Probability Matrix
Static nonlinear analysis
![Page 50: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/50.jpg)
Empirical Methods
EMS98, GNDT, Risk-UE, Vulneralp) based on damage
surveyssurveys
• Relationship between ground motion (intensity)
and distribution of observed damage grades for
structures with a given vulnerability index
Advanced Earthquake Engineering CIVIL-706
Damage Probability Matrix
Static nonlinear analysis
![Page 51: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/51.jpg)
Empirical Methods
Empirical methods example
European Macroseismic Scale 98European Macroseismic Scale 98
• Calculate Vulnerability index
Advanced Earthquake Engineering CIVIL-706
• Calculate Vulnerability index
from vulnerability class
• Structural parameters is only
the structure class
Static nonlinear analysis
![Page 52: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/52.jpg)
Empirical Methods
EMS 98 (Empirical method):
So
urc
e:
Ris
k-U
E 2
00
3
Advanced Earthquake Engineering CIVIL-706 Static nonlinear analysis
So
urc
e:
Ris
k
![Page 53: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/53.jpg)
Empirical Methods
Example of EMS98 application: (Feriche et al. 2009)
b. Damage
grade from
intensity VI
a. Vulnerability
class in
downtown
Malaga
Advanced Earthquake Engineering CIVIL-706 Static nonlinear analysis
![Page 54: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/54.jpg)
Empirical Methods
• Application in large-scale assessment (engineering offices, insurance companies, etc.), real-time offices, insurance companies, etc.), real-time computations (WAPMERR) or risk-based seismic assessment in codes (SIA 2018)
BUT
• Not compatible with modern hazard assessment (site effect, etc.)
Only valid for large number of buildings (classification)
Advanced Earthquake Engineering CIVIL-706
• Only valid for large number of buildings (classification)
• No surveys available for areas with moderate seismic hazard
Static nonlinear analysis
![Page 55: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/55.jpg)
Mechanical Methods
• AKA as predicted methods (e.g., HAZUS, RISK-UE LM2)
• Based on computation (generally nonlinear static)• Based on computation (generally nonlinear static)
• Relation between ground motion (PGA, spectral
ordinate) and expected distribution of damage grade
Fragility curves
• Takes variability into account
Advanced Earthquake Engineering CIVIL-706
• Takes variability into account
Static nonlinear analysis
![Page 56: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/56.jpg)
Mechanical Methods
Fragility curves
So
urc
e:
HA
ZU
S 2
00
3
Advanced Earthquake Engineering CIVIL-706 Static nonlinear analysis
So
urc
e:
HA
ZU
S 2
00
3
![Page 57: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/57.jpg)
Mechanical Methods
RISK-UE LM2 method:
Advanced Earthquake Engineering CIVIL-706 Static nonlinear analysis
![Page 58: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/58.jpg)
Mechanical Methods
• Compatible with modern hazard definitions
• Independent of observed damage data (only verification)• Independent of observed damage data (only verification)
• Applicable to single buildings (capacity curves)
BUT
• Difficulties to build accurate models for existing buildings (lack of information)
• Crude approximation in computations
Advanced Earthquake Engineering CIVIL-706
• Crude approximation in computations
• Fragility curves only available for certain building classes
• Difficulties in estimating variability
Static nonlinear analysis
![Page 59: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/59.jpg)
Mechanical Methods
Example of RISK-UE application:
Advanced Earthquake Engineering CIVIL-706 Static nonlinear analysis
Probability of D4 and D5 in case of a 1887-type
scenario earthquake at 30 km (deterministic)
![Page 60: Slide 4_Static Nonlinear Analysis](https://reader030.fdocuments.in/reader030/viewer/2022020101/553262524a7959c5638b459d/html5/thumbnails/60.jpg)
Mechanical Methods
Example of RISK-UE application:
Advanced Earthquake Engineering CIVIL-706 Static nonlinear analysis
Probability of D4 and D5 for the 475-year return
period probabilistic scenario (probabilistic)