04-Dynamic-Analysis-Methods jdsud cak.pdf

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1. Methods of
Dynamic Analysis
Dr. S. K. Prasad
Professor of Civil Engineering
S. J. College of Engineering, Mysore
[email protected]

2. Seismic shaking of structures -COMPLEX!!!!
Different structures behave differently during different
earthquakes. Material of structure, height of structure, seismic
weight, overburden soil, characteristics of earthquake force have
varied influence on shaking.

3. ANALYSIS TYPE
2D 3D

4. Seismic
Analysis
Linear
Equivalent
Static
Response
Spectrum
Time
History
Non-Linear
Pushover
Analysis
Time
History
Classification of Dynamic Analysis

5. Analysis Type Depends
Information needed
Complexity of the structure
Resources available e.g. time, money, skill etc.
Expected force level on the structure
Expected behaviour of the structure

6. Equivalent static force method
•Theequivalentstaticlateralforcemethodisa
simplifiedtechniquetosubstitutetheeffectof
dynamicloadingofanexpectedearthquakebya
staticforcedistributedlaterallyonastructurefor
designpurposes.
•ThetotalappliedseismicforceVisgenerally
evaluatedinhorizontaldirectionsparalleltothe
mainaxesofthebuilding.
•Itassumesthatthebuildingrespondsinits
fundamentallateralmode.Forthistobetrue,the
buildingmustbelowriseandmustbefairly
symmetrictoavoidtorsionalmovementunder
groundmotions.

7. •Thestructuremustbeabletoresisteffects
causedbyseismicforcesineitherdirection,
butnotinbothdirectionssimultaneously.
V = W * A
V = Base shear
W = Total weight of the structure
A = Basic horizontal seismic coefficient
•Also called Seismic Coefficient Method
Equivalent static force method

8. Equivalent lateral shear force along two
orthogonal axis

9. W
H
H = W * A
h
Pseudo Static or Seismic Coefficient Method
Zone
Designation
Zone Factor
Z
Zone II 0.10
Zone III 0.16
Zone IV 0.24
Zone V 0.36









g
S
R
ZI
A
a
h
2

10. When to use Equivalent static method?
•Alldesignagainstearthquakeeffectsmustconsider
thedynamicnatureoftheload.However,forsimple
regularstructures,analysisbyequivalentlinear
staticmethodsisoftensufficient.
•Thisispermittedinmostcodesofpracticefor
regular,low-tomedium-risebuildings.
•Tallbuildings(over,say,75m),wheresecondand
highermodescanbeimportant,orbuildingswith
torsionaleffects,aremuchlesssuitableforthe
method.
•Regularbuildingsuptoaround15storey'sinheight
canusuallybedesignedusingequivalentstatic
analysis.

11. Response Spectrum Method

12. Response Spectrum
Responsespectrumisaplotofpeakor
steadystateresponse(displacement,
velocityoracceleration)ofaseriesof
oscillators(SDoFsystems)ofvarying
naturalfrequencyatagivendampingand
forcedintomotionbythesamebase
vibration.

13. •Themethodinvolvesthecalculationofonlythe
maximumvaluesofthedisplacementsandforcesin
eachmodeofvibration.
•Responsespectraarecurvesplottedbetween
maximumresponseofSDOFsystemandtime
period(orfrequency).
•Responsespectrumcanbeinterpretedasthelocus
ofmaximumresponseofaSDOFsystemforgiven
dampingratio.
•Responsespectrahelpsinobtainingthepeak
structuralresponsesunderlinearrange.
Response Spectrum Method

14. •ResponseofaSDOFsystemisdeterminedbytime
domainorfrequencydomainanalysis,andfora
giventimeperiodofsystem,maximumresponseis
picked.
•Thisprocessiscontinuedforallrangeofpossible
timeperiodsofSDOFsystem.
•Finalplotwithsystemtimeperiodonx-axisand
responsequantityony-axisistherequired
responsespectra.
•Sameprocessiscarriedoutwithdifferent
dampingratiostoobtainoverallresponsespectra.
Response Spectrum Method

15. Response Spectrum Method

16. Response spectrum for El Centro ground motion plotted
with normalized scale for damping ratios of 0, 2, 5 & 10%

17. Design spectra for earthquakes originating from two
different faults

18. 0 1 2 3 4 5
0.0
0.5
1.0
1.5
2.0
2.5
Rock or Hard Soil
Medium Soil
Soft Soil
Sa/g
Time Period (secs)
Response Spectrum IS : 1893 :2002
R
I
g
SZ
A
WAV
a
h
hB
..
2


Structural Response Factor, Sa/g

19. The advantages of RSA, compared with time-history
analysis
•Thesizeoftheproblemisreducedtofindingonly
themaximumresponseofalimitednumberof
modesofthestructure,ratherthancalculatingthe
entiretimehistoryofresponsesduringthe
earthquake.
•Theuseofsmoothedenvelopespectramakesthe
analysisindependentofthecharacteristicsofa
particularearthquakerecord.
•RSAcanveryoftenbeusefulasapreliminary
analysis,tocheckthereasonablenessofresults
producedbytime-historyanalyses.

20. Disadvantages of RSA
•RSAisessentiallylinearandcanmakeonly
approximateallowancefornonlinear
behavior.
•Theresultsareintermsofpeakresponse
only,withalossofinformationon
frequencycontent,phaseandnumberof
damagingcycles,whichhaveimportant
consequencesforlow-cyclefatigueeffects.

21. Time history analysis
•Toperformsuchananalysis,arepresentative
earthquaketimehistoryisrequiredforastructure
beingevaluated.
•Inthismethod,themathematicalmodelofthe
buildingissubjectedtoaccelerationsfrom
earthquakerecordsthatrepresenttheexpected
earthquakeatthebaseofthestructure.
•Themethodconsistsofastep-by-stepdirect
integrationoveratimeinterval.
•Thetime-historymethodisapplicabletoboth
elasticandinelasticanalysis.

22. •Inelasticanalysisthestiffnesscharacteristicsofthe
structureareassumedtobeconstantforthewhole
durationoftheearthquake.
•Intheinelasticanalysis,however,thestiffnessis
assumedtobeconstantthroughtheincremental
timeonly.
•Themethodinvolvessignificantlygreater
computationaleffortthanthecorrespondingRSA
whichgivespreciseresults.
•Performancebaseddesign–bettermeansto
evaluateandunderstanddifferentperformance
levels.
Time history analysis

23. Time history analysis

24. What is Pushover Analysis?
V
B
Δ
roof
Δ
roof
V
B

25. What is Pushover Analysis?
Buildingispushedinonehorizontaldirection.
Proportionofappliedforceoneachfloorisconstant,
onlyitsmagnitudeisincreasedgradually.
Loadpatternmaybe1
st
modeshape,parabolic,
uniform,invertedtriangularetc.
Materialnonlinearityismodeledbyinsertingplastic
hingeatpotentiallocation.
Lateralloadisincreasedinstepandsequenceof
cracking,yielding,andfailureofcomponentis
recorded.

26. Why Pushover Analysis?
More accurate prediction of
Global displacement
Demand on individual members
Weakest link (“bad actors”)
Building do not respond as linearly elastic
during strong ground motion

27. How much information is needed?
Forces & displacement
Linear static
Modal properties & dynamic effects
(Elevation and plan irregularity)
Linear Dynamic
Post yield behavior & performance of
structure
Nonlinear Static (Pushover)

28. It is impossible to stop or predict
earthquake. As engineers, let us all
unite and move forward & work for
reducing calamities due to natural
and man made hazards