4 - seismic analysis procedures
DESCRIPTION
Analisis gempaTRANSCRIPT
Seismic Perfomance Assessment
Performance based Earthquake Engineering
Slide: 2/55
• Conjunction of the design, constructionand maintenance procedures necessary toreach, through engineering means,predictable performances for multipledesign objectives.
• Its purpose is to minimize the economiclosses after a seismic event during theuseful life of the structures.
Performance Based Seismic Design
• Limit permissible drifts under
specified forces
• Require buildings have complete
structural systems
Code Procedures
• Require systems have sufficient
strength to resist specified forces
• Require members and connections
be “detailed” prescriptively
2003
Building Codes Imply Performance
> Ability to resist frequent, minor earthquakes without damage
> Ability to resist infrequent, moderate earthquakes with limited structural and nonstructural damage
> Ability to resist worst earthquakes ever likely to occur without collapse or major life safety endangerment
100 yrs
500 yrs
2,500 yrs
Performance is not guaranteed
2003
Slide: 5/53
Building Codes & Peformance Warranties
> If a building is affected by an extreme event and performs poorly:
• There is an expectation of how the building
should have performed but no implied
warranty> The only warranty is that the engineer complied with
the standard of care
• For most buildings, demonstration that a
design was performed in accordance with
the building code will provide adequate
proof of conformance to the standard of
care
Slide: 6/55
To transform earthquake engineering assessment and design ...
Perform.-Based Approach
• Scientifically-defined seismic hazard
• Direct design
approaches
• Defined outcomes with probabilities of achieving them
Traditional Approach
•Non-scientifically defined seismic hazard
•Indirect design approaches
•Undefined and uncertain outcomes
Performance-Based Earthquake Engineering
Slide: 7/53
Performance Based Seismic
Design
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.
Slide: 8/53
Performance Based Seismic Design
•ATC-33
• FEMA – 273, ATC 40
• SEAOC- Vision 2000
• Euro Code 8
• Japanese code
Slide: 9/53
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 ”
Slide: 10/55
Selecting PerformancePresent Generation
Joe’s
Beer!Beer!
Food!Food!
Operational
Operational – negligible impact on building
Beer!Beer!
Food!Food!
Joe’s
Beer!Beer!
Food!Food!
Beer!Beer!
Food!Food!
Joe’sJoe’s
Immediate
Occupancy
Immediate Occupancy – building is safe to occupy but
possibly not useful until cleanup and repair has occurred
Beer!Beer!
Food!Food!
Beer!Beer!
Food!Food!
Beer!Beer!
Food!Food!
Life
Safety
Life Safety – building is safe during event but possibly not
afterward
Collapse
Prevention
Collapse Prevention – building is on verge of
collapse, probable total loss
Slide: 11/53
Performance LevelS
eism
ic D
esig
n L
evel
Frequent (43 years)
50% in 30 years
Ocassional (72 years)
50% in 50 years
Rare (475 years)
10% in 50 years
Very Rare (970 years)
10% en 100 years
Fully
operationalLife safety
Operational
Collapse
prevention
Slide: 12/55
Code-equivalent Performance
Beer!Beer!
Food!Food!
Joe’s
Beer!Beer!
Food!Food!
Beer!Beer!
Food!Food!
Joe’sJoe’s
Immediate
Occupancy
Frequent event (varying between
50- and 100- year return periods)
Beer!Beer!
Food!Food!
Beer!Beer!
Food!Food!
Beer!Beer!
Food!Food!
Life
Safety
DBE
Collapse
Prevention
MCE
Slide: 13/55
Structurally
Stable
Assessment by Static Pushover Analysis (FEMA 273/356 and ASCE 41)
Life Safe
Beer!
Food!
Rare events
(10%/50yrs)
Very rare events
(2%/50yrs)
Operational
Frequent events
(50%/50yrs)
Lateral Deformation
Base
Shear
DemandJoe’s
Beer!
Food!
Occasional events
(20%/50yrs)
Ref: R.O. Hamburger
Slide: 14/55
Deformatio
n
Damage
Threshold
Collaps
e
Onset
OPEN
OPEN
OPEN
FEMA 356 Performance
Levels
IO LS CP
Performance-Based Earthquake Engineering
PBEE today
$, % replacement0 25% 50% 100%
Downtime, days0
1 7 30 180
Casualty rate0.0
0.0001 0.001 0.01 0.25
PBEE tomorrow
Slide: 15/53
Damage Assessment: Nonstructural Fragilities
0.0
0.2
0.4
0.6
0.8
1.0
0 0.005 0.01 0.015 0.02 0.025
EPD (IDR)
P(DM|EPD) 5/8" Gypsum partition wall with 3-5/8" Wall Frame
Small cracks
only
0.0
0.2
0.4
0.6
0.8
1.0
0 0.005 0.01 0.015 0.02 0.025
EPD (IDR)
P(DM|EPD) 5/8" Gypsum partition wall with 3-5/8" Wall Frame
Small cracks
only
Wide cracks in gypsum
boards
0.0
0.2
0.4
0.6
0.8
1.0
0 0.005 0.01 0.015 0.02 0.025
EPD (IDR)
P(DM|EPD) 5/8" Gypsum partition wall with 3-5/8" Wall
Frame
Small cracks
only
Wide cracks in gypsum boards
Severe damage to gypsum board and distorsion of metal frame(Replace partition)
(Replace gypsum boards)
(Patch, Retape & Paint)
Ref: E. Miranda
Interstory Drift Ratio
Pro
bab
ilit
y o
f
Dam
ag
e S
tate
Slide: 16/55
Engineering Demand
Parameter
Intensity Measure
Damage Measure
Performance-Based Methodology
Decision Variable• Collapse &
Casualties
• Direct Financial
Loss
• Downtime
drift as an EDP
Slide: 17/55
0 0.05 0.1 0.150
0.5
1
1.5
2
2.5
3
3.5
4
Sa
g.m
.(T=
1.0
s)[
g]
Maximum Interstory Drift Ratio
Incremental Dynamic Analysis –Collapse
STRUCTURAL RESPONSE (DRIFT)
GR
OU
ND
MO
TIO
N IN
TE
NS
ITY
44 Ground Motion Records
EQ: 11111, Sa: 2.06g EQ: 11112, Sa: 2.19g
EQ: 11121, Sa: 2.86g EQ: 11122, Sa: 2.32g
Slide: 19/53
Nonstructural Damage and Losses (Caltech)
Slide: 20/53
PBEE Methodology: IM-EDP-DM-DV
> Ground Motion Hazard Characterization
• IM Definition (Sa, …)
• Selection and Scaling of Ground Motions
> Simulation: IM – EDP
• Choice of EDPs (Drift, Floor Accel., other …)
• Fidelity of simulations to model collapse
> Damage Modeling: EDP – DM
• Taxonomy of components
• Definition of conditional EDP-DM “damage function”
> Loss Modeling: DM – DV
• Definition of conditional DM-DV loss functions
• Downtime and injuries/fatalities are a challenge
Slide: 21/53
Performance Assessment Components
Decision
Variable
Intensity
Measure
Damage
Measure
Engineering
Demand
Parameter
Relating Performance to Risk Decision Making
Quantifying Damage Measures
Simulation of System Response
Earthquake Hazard Characterization
Slide: 22/53
Performance Assessment Components
Decision
Variable
Intensity
Measure
Damage
Measure
Engineering
Demand
Parameter
DV: $ loss, functionality, downtime, casualties
DM: physical condition & consequences/ramifications
EDP: Drift Ratio (peak, residual), Floor Acceleration, Local Indices (Qp, strain, …)
IM: Sa(T1), multiple Sa’s, epsilon, Sdinelastic, duration
Slide: 23/53
• Linear static analysis • Equivalent static analysis
• Linear dynamic analysis • Modal analysis
• Direct time-history analysis
• Nonlinear static analysis - Nonlinear static procedures (NSPs)
• Capacity spectrum analysis (ATC-40, FEMA-440)
• Displacement coefficients method (FEMA-273-274,356,440)
- Improved NSPs• Modal pushover analysis (MPA) (Chopra & Goel, 2002)
• Adaptive Modal Combination (AMC) (Kalkan & Kunnath, 2006)
• Nonlinear dynamic analysis
Seismic Analysis Methods of Structures
Most common in
routine applications
Slide: 24/53
Nonlinear Static Analysis
Conceptual Theory&
Current Practice
Slide: 25/55
Multi-degree-of-freedom (MDF) system seismic behavior can be approximated
with certain accuracy by
equivalent SDF systems.
Equivalent SDF (ESDF) system properties are computed by conducting pushover analyses…
Slide: 26/53
Conventional Nonlinear Static (Pushover) Analysis
Choose height-wise distribution of lateral forces
Monotonically increase lateral forces till the “control node” reaches a
“target displacement” i.e., increasing load factor while fixing load
pattern.
Develop pushover (capacity) curve: Plot of base shear vs. roof
displacement
ur
Vb
Slide: 27/55
Summary of Nonlinear Static Analysis
V
D
D
V
Inelastic
SDF System
Target Displacement
of MDF System ut
ut
uj
dj
Capacity estimation at
target displacement
Pushover Analysis
Participation
Factor, Gn
Dn
Fsn/Ln
ESD System
Force-Deformation Relation
Slide: 28/53
Fundamental Assumptions:
• The response of the multi-degree-of-freedom (MDF) structure can be related to the response of an equivalent SDF system, implying that the response is controlled by a single mode and this mode shape remains unchanged even after yielding occurs.
• The invariant lateral force distribution can represent and bound the distribution of inertia forces during an earthquake.
Slide: 29/55
Two Important Components of Nonlinear Static Analysis
• Construct loading vector shape
• Determine target roof displacement
Slide: 30/55
*
*1
*
*
Uniform:
First Mode :
ELF : 1 2
SRSS : from story shears
j j
j j j
kj j j
j
s m
s m
s m h k to
s
ELF and SRSS distributions
intended to consider higher mode
responses
Height-wise Distribution of Lateral Forces: FEMA Recommendations
Slide: 31/53
FEMA Recommended Force Distributions
Each force distribution pushes all floors in same direction
Slide: 32/53
Higher Mode Response
Initial Yielding Initial Yielding
Initial Yielding Initial Yielding
Slide: 33/55
Two Important Components of Nonlinear Static Analysis
• Construct loading vector shape
• Determine target roof displacement
Slide: 34/53
Target Displacement Estimation(Displacement Coefficient Method)
2
0 24e
t inel A
Tu C C S u
f
Elastic SDF System
u
f
Inelastic SDF System
u
f
Inelastic MDF System
C0 = Constant to relate elastic deformation of SDF and MDF system
Slide: 35/55
Displacement Coefficient Method
FEMA-356: Cinel =C1C2C3
• C1 = Ratio of inelastic and
elastic SDF systems
• C2 = Constant to account for
effects of pinching, stiffness
degradation, and strength
deterioration
• C3 = Constant to account for P-
Delta effects
ASCE-41: Cinel = C1C2
• C1 = Ratio of inelastic and
elastic SDF systems
• C2 = Constant to account for
cyclic degradation of stiffness
and strength
• Upper limit on R to avoid
dynamic instability
Slide: 36/53
Capacity Spectrum Method
0 ( , )t D eq equ C S T
u
f
Inelastic MDF System
u
f
Equivalent Linear Elastic SDF System
Teq, zeq
u
f
Inelastic SDF System
Slide: 37/55
Capacity Spectrum Method –Equivalent Damping Concept
z
1
1 110.05
1
eq o
eq
T T
For bilinear systems
Requires iterations to compute Teq and zeq
because of unknown ductility (uinel / uelas)
10.05
4D
eq
So
E
E
Teq= Tsec
Sd
Sa
ESo
ED
Slide: 38/55
FEMA-440 Capacity Spectrum Method
z z
z
z
2 3
2
2
1 1 ; 4.0
1 ; 4.0 6.5
1 1; 6.5
1
eq o
o
eq
o
o
A B
C D
F TE
TF
A to K = Constants that depend on hysteretic behavior and post-
yield stiffness ratio
2 31 1 1 ; 4.0
1 1 ; 4.0 6.5
-1K 1 1 ; 6.5
1+L 2
eq o
o
o
T G H T
I J T
T
Slide: 39/53
Limitations of Conventional (FEMA & ATC) Nonlinear Static Analysis Procedures
> Restricted to single mode response, can be reliably apply to 2D response of low-rise structures in regular plan.
> Gives erroneous results in case of:
Higher Mode Effects
Plan Irregularities (i.e., Torsion, Vertical Irregularities)
> No established procedure for 3D pushover analysis yet.
Slide: 40/53
Energy-based ESDF system representation of nth-mode MDF system capacity curve
Roof Displacement, u r,n
Base S
hear,
V b
,n
F 1(i)
F 2(i)
F 3(i)
Dd 3(i)
Dd 2(i)
Dd 1(i)
Forces
(sn(i))
( ) ( ) ( ) ( )
, , , ,
1,3 1,3
( ) / ( )i i i i
d n n n j n j n j
j j
S D F d F
D D
Dd 3(i)
Capacity
curve
(i-1)
(i)
(i)(i-1)
ur,n(i)ur,n
(i-1)
Spectral Displacement, S d,n
Sp
ectr
al
Accele
rati
on
, S
a,n
DD n(i)
wn(i)
zn(i)
,
,
b n
a n
n
VS
W
DD n(i)
Tn(elastic)
wn(i)) 2
Capacity
spectrum
MDF
Level
SDF
Level
Slide: 41/53
Performance point evaluation using system ductility through a set of inelastic spectra
Spectral Displacement, S d,n
Sp
ectr
al A
ccele
rati
on
, S
a,n
wn(i)
zn(i)
wn(ip)) 2
Global
Yield
( )
,
yield
d nS ( )
,
ip
d nS
With computed system ductility, ( )ip
n
Tn(elastic)
Tn(ip)
( )
,( )
( )
,
ip
d nip
n yield
d n
S
S
Spectral Displacement, S d,n
Sp
ectr
al A
ccele
rati
on
, S
a,n
( )ip
n
Dynamic Target
Point
Inelastic phase,
period elongation
Tn(elastic)
Tn(ip)
Inelastic Demand Spectra
plotted at different
ductility levels
M odal Capacity
Curve
Capacity
Side
Demand
Side
Slide: 42/55
Thank You