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puchover analysis
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STR 614: Seismic StructuralAnalysis
(Pushover Analysis)
CUFE, Postgraduate studies2014/ 2014, Spring Semester
STR 614: Seismic Structural Analysis Spring Semester (2014/2015) 2
Evaluation of seismic designHistorical Approach:
Traditional Code Basis:
Current Trend:Design based on displacement
RVVbase max
weight theof%10~5baseV
PushoverAnalysis
In-between thetwo procedures ofanalysis
Only concern withthe maximumdisplacement.
Time HistoryAnalysis
Accurate andconsider strengthdegradation
Can take intoaccount highermode effect
PerformanceBased seismic
Long Time
STR 614: Seismic Structural Analysis Spring Semester (2014/2015) 3
Seismic Structural AnalysisResponseSpectrum
Simple and Quick Only consider thefirst mode
Inaccurate due tothe stiffness
SeismicDemand
STR 614: Seismic Structural Analysis Spring Semester (2014/2015) 4
Seismic Structural Analysis
CapacitySpectrum
PushoverAnalysis
Capacity is a representationof the structural ability.Demand is a representation ofthe EQ ground motion
STR 614: Seismic Structural Analysis Spring Semester (2014/2015) 5
Capacity Vs. Demand As displacements increase, the period of the structure lengthens. Inelastic displacements increase damping and reduce demand.
At the performance point,capacity and demand are equal.
The maximumdisplacement implies aunique damage state forthe building relateddirectly to a specific EQ.
Life SafetyDS-III
STR 614: Seismic Structural Analysis Spring Semester (2014/2015) 6
Building Performance LevelsPerformance
Point
OperationalDS-I
The post-EQdamage is limitedand safe.Cosmeticrepairing isneeded
ImmediateOccupancyDS- IIMost widely used
criteria foressential facilitiesReasonableusable
CollapsePreventionDS-IV
STR 614: Seismic Structural Analysis Spring Semester (2014/2015) 7
Capacity Curve Capacity Spectrum is derivate from an approximate nonlinear,
inelastic static analysis for the structure. In the process of performing this incremental nonlinear static
analysis, a capacity curve is developed for the building.DS
-I
DS-II
DS-II
I
DS-IV
STR 614: Seismic Structural Analysis Spring Semester (2014/2015) 8
Factors affecting Capacity CurveLateral Load Pattern Uniform *
Equivalent lateral force pattern
First (or any other) mode shape*
ii mf
kiii hmf
2.5sec.for0.20.5sec.for0.1
T
Tk
Mf iii mf
STR 614: Seismic Structural Analysis Spring Semester (2014/2015) 9
Developing Capacity curve1. Develop a nonlinear computer model of the structure.
Dimensioning and reinforcement of the beams and columnsare input in the section properties.
Stress-strain relationships are input in the materialdefinitions.
Moment-curvature and moment-axial plastic hinges aredefined and assigned.
Soil-structure interaction can be accounted in the analysis.
STR 614: Seismic Structural Analysis Spring Semester (2014/2015) 10
Developing Capacity curve (cont)2. Apply lateral story force in the proportion to the product the
mass and fundamental mode shape. (first mode shape loadpattern is used herein) This analysis should include gravity loads. The result from this step is the capacity curve (pushover
curve).
STR 614: Seismic Structural Analysis Spring Semester (2014/2015) 11
Developing Capacity curve (cont)2. Apply lateral story force in the proportion to the product the
mass and fundamental mode shape. (first mode shape loadpattern is used herein) This analysis should include gravity loads. The result from this step is the capacity curve (pushover
curve).
STR 614: Seismic Structural Analysis Spring Semester (2014/2015) 12
Transforming the capacity curve toAcceleration Displacement ResponseSpectrum (ADRS)The capacity spectrum is obtained by transforming the capacitycurve from base shear (VBase) vs. lateral displacement (d)coordinates to spectral acceleration (Sa) vs. spectral displacement(Sd)
STR 614: Seismic Structural Analysis Spring Semester (2014/2015) 13
Pushover analysis in seismicregulations
N2 (FEMA-365) and Capacity Spectrum methods (ATC 40)FEMA 365:
https://www.wbdg.org/ccb/DHS/ARCHIVES/fema356.pdf
ATC 40: chapters 6 and 8http://www.civil.iitb.ac.in/~p0saurabhrs/ATC-40.pdf
Capacity Spectrum is a method that allows a graphical comparisonbetween the lateral structural capacity of the building and theseismic demand of the EQ ground motion.
STR 614: Seismic Structural Analysis Spring Semester (2014/2015) 14
Capacity Spectrum Method
Totalbasea
MVS
TotalM
top
roofdS
Ni
ii
N
iii
m
m
12
1
Modal Mass
Participation factor
STR 614: Seismic Structural Analysis Spring Semester (2014/2015) 15
Capacity Spectrum Methodad STS 2
2
4
STR 614: Seismic Structural Analysis Spring Semester (2014/2015) 16
Calculating the Demand usingCapacity Spectrum MethodThe location of the performance point must satisfy tworelationships:
The point must lie on the capacityspectrum curve in order to representthe structure at a given displacement.
The point must lie on the spectraldemand curve, reduced from theelastic and 5% damping isconsidered, to represent thenonlinear demand at the samestructural displacement
STR 614: Seismic Structural Analysis Spring Semester (2014/2015) 17
Fragility In order to design a certain structure
to withstand seismic loads, thestructure is modeled to obtain itscapacity spectrum.
On the other hand, a specific Earth-Quake ground motion (or a designresponse spectrum) is used for theanalysis.
This is Not accurate
STR 614: Seismic Structural Analysis Spring Semester (2014/2015) 18
Fragility For numerous EQ, with the same PGA, there is a lot of
performance points.
There is a mean (average) and astandard deviation for all thesepeak displacements.
In accordance to these twovalues, the probability ofexceeding a certain roof driftvalue can be obtained.
STR 614: Seismic Structural Analysis Spring Semester (2014/2015) 19
Fragility
STR 614: Seismic Structural Analysis Spring Semester (2014/2015) 20
FragilityProbabilit
y of ex
ceedin
g Dam
age St
ate
Peak Ground Acceleration
DS - IDS - II
DS - III
DS - IV