Towhatextenddoestheheightsofsquarebased buildingsaffecttheirassociatedresonantfrequency?
Towhatextenddoestheheightsofsquarebasedbuildingsaffecttheirassociatedresonant frequency?
Gautham Ramesh
001805 - 0021
EXTENDED ESSAY
To what extend does the heights of square based buildings affect their associated resonant frequency?
Session May2014
CandidateName GauthamRamesh
Subject Physics
Supervisor’sName Mr.JohnHeyworth
WordCount 3813
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Towhatextenddoestheheightsofsquarebasedbuildingsaffecttheirassociatedresonant frequency?
CONTENTS
Gautham Ramesh 001805 - 0021 2 | Page
-----------------------------------------------------------------------------------------------1. Abstract.............................................................................................................................2 2. Glossaryforkeyterms......................................................................................................3 3. Geophysics:MakingofanEarthquake.............................................................................4 4. Earthquake:CauseandEffect...........................................................................................5 5. CaseStudy 5.1. EarthquakeproneregioninIndia...............................................................................6 5.1.1. Himachal 5.2. NotanearthquakeproneregioninIndia....................................................................7 5.2.1. Pune 6. LabReport.........................................................................................................................8 6.1. ResearchQuestion 6.2. Variables 6.2.1. IndependentVariable 6.2.2. DependantVariable.........................................................................................9 6.2.3. ControlledVariable 6.3. Hypothesis..................................................................................................................10 6.4. Materials 6.5. Preparation 6.5.1. ConstructionofaShakeTable........................................................................11 6.6. Procedureforexperimentation 6.6.1. Lengthfactorof ruler.....................................................................................12 6.6.2. Heightfactorofbuilding 6.7. DataTableforRuler...................................................................................................13 6.7.1. RawDataTableforRuler 6.7.2. AnalysedDataTableforRuler........................................................................14 6.8. GraphforRuler 6.8.1. LengthagainstResonant FrequencyforRuler 6.8.2. 1/Length2 againstResonantFrequencyforRuler............................................15 6.9. DataTableforBuilding 6.9.1. RawDataTableforBuilding 6.9.2. AnalysedDataTableforRuler 6.10. GraphforBuilding 6.10.1.HeightagainstResonant Frequency.................................................................17 6.10.2.1/Height2 againstResonantFrequency 6.11. DataAnalysis 6.11.1.Describingthegraphs.......................................................................................18 6.12. ConclusionandEvaluation...............................................................................19 7. Bibliography.......................................................................................................................22
Towhatextenddoestheheightsofsquarebasedbuildingsaffecttheirassociatedresonant frequency?
Gautham Ramesh 001805 - 0021
Abstract
Thisessayexaminesthequestion,“Towhatextenddoestheheightsofsquarebased buildingsaffecttheirassociatedresonantfrequency?”Theessaybeginsbyintroducingthe mechanismofanearthquakewithallthedifferent forcesinvolved.It furtherdevelopsits pointofviewonthespecificeffectscausedbythisnaturaldisasterandhowitposesasa potentialthreattomankind.Asimplechangeinthestructuralcompositionoradaptionto particularearthquakesisthewaythroughwhichdamagecanbepreventedbyearthquakes. ThenextpartintroducesthecasestudiesIwillbereferringtoafteranalyzingthedatafrom theexperiment.HimachalandPunearethetwocasestudiesusedforcomparingtherelative magnitude3 ofearthquakesineachofthoseregions.
Afterthattheexperimentbeginsandadatatablewithallthedataoftheexperimentis recordedandthiswillhelp;howtheheightandlengthaspectsofastructureaffectthe magnitude,whichinthiscase,isresonantfrequency.Foundoutthataninversesquare relationshipexistsbetweentheheightandtheresonantfrequency- ∝f.Thereforearrived attheconclusionthattheregionwithlowfrequencyearthquake,Pune,shouldhaveshort structuresbuiltandtheearthquakeproneregion,Himachal,shouldhavetallstructuresbuilt.
WordCount:214
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Towhatextenddoestheheightsofsquarebasedbuildingsaffecttheirassociatedresonant frequency?
Gautham Ramesh 001805 - 0021
Glossary For Key Terms:
1. Criticalvalue:Thepointatwhichtheforcesholdingthestructuretogetherare overpoweredbytheforcestryingtobreakthestructure.
2. Elasticwaves:Thewavesproducedasaresultofanearthquakethatcarryhugeamounts ofenergyandtravellongdistances
3. (Earthquake)Magnitude:Ameasureofthesizeofanearthquakebasedonthequantityof energyreleased:specifiedontheRichterscale
4. Epicenter:The point on the earth'ssurfacedirectlyabovethefocusofanearthquake
5. (Earth’s)Crust:(geology)thesolid,rockyouterportionorshelloftheearth;lithosphere
6. CenterofGravity:thepointthroughwhichtheresultantofthegravitationalforcesona bodyalwaysacts
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All definition obtained from http://www.collinsdictionary.com/
Towhatextenddoestheheightsofsquarebasedbuildingsaffecttheirassociatedresonant frequency?
Gautham Ramesh
001805 - 0021
Geophysics: Mechanism of an Earthquake
TheouterlayeroftheEarth’scrustismadeup ofmanypieces,knownastectonicplates(Fig 1.1).Earthquakeshappenwhenenergyis releasedastheseplatesslippastoneanotheror collide(Physics.org,2013).Thisdiagramtomy rightisknownasthe'eggshellworld'model (Collins,2012).
TheEarth’sCrustisnaturallysubjectedtostress duetothefaultmotion.Whenthestressatapointinthecrustexceedsacriticalvalue1 a suddenfailureoccurs(PHYSICSOFEARTHQUAKES,2013,pp.2).Thesuddenfailure causesthedisplacement ofthecrust5 whichcauseselasticwaves2 toradiate.Thisgivesriseto anearthquake.
IwouldliketobasemystudyontheIndiansub-continent.Herethemainplatesresponsible fortheearthquakearetheIndianplateandtheEurasianplate.Sincedirectionofboththese plates(Fig1.1),istowardseachothersothereforeattheboundaryoftheseplatestherewasa hugecollisionmarginformedwhichgaveriseto mountains.Thesemountainsarenamedthe HimalayanrangeanditstretchesacrossallthewholenorthernboundaryofIndia(Fig1.2).
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Fig 1.1:
Fig 1.2:
Towhatextenddoestheheightsofsquarebasedbuildingsaffecttheirassociatedresonant frequency?
Gautham Ramesh
001805 - 0021
Earthquake:CauseandEffect
Earthquakesareresponsibleforhugedevastationsovertheyears,mostsignificantly impactingtheinfrastructureofaregion,whichinturnclaimsanddisruptsthelivesofpeople. Withtherapidgrowthofpopulationinmega-citiessuchasTokyoandMumbai, seismologistsarewarningthataquakemayclaimthelivesofupto3millionpeople. Millionsofdollarsarebeingspenteveryyeartorepairandreconstructthelossessuffered duringtheearthquake.Eventherecent 2011Sikkimearthquakein India,measuringa striking6.8magnitude3 ontheRichterscale,hastakenadeathtollof80peopleandabout1 lakhcrore(nearly22billiondollars)forrepairs(NDTV.com,2013).Theselivesandmoney canbesavedifsomesimplechangesaremadetotheinfrastructureoftheregion.Sothereis agrowingneedforearthquakeresistantorearthquakeproofinfrastructure.
Theextenttowhichanearthquakedamagesaregiondependsonthesize(magnitude3)ofthe earthquake,thedistancefromtheepicenter4,thelocalgeologicalconditionsandthe characteristicsofbuildings(EarthquakeHazardInformation–Hazard,Risk,Magnitude, Intensity,EarthquakeStatistics,2013,p.1).Sincethesize,distanceandgeologicalconditions arealldependantonnature,Iwilllookatinvestigatingthephysicalcharacteristicsof buildings.
Iwillbeginbylookingatsometraditionalexamplesinarchitecturehowtheproblemsof earthquakeswereaddressedinthem.Iwillthenlookatthelessonslearntfromaboveand understandtheiradaptioninthecontemporarycontext.
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Towhatextenddoestheheightsofsquarebasedbuildingsaffecttheirassociatedresonant frequency?
Gautham Ramesh
001805 - 0021
CaseStudy
EarthquakeProneRegioninIndia:
Himachal:
Himachalisaregionbasicallysituatedinanearthquakepronezoneanddoes experiencesomehighfrequencyquakes.Thereforesincetraditionaltimes,the houseshavebeenconstructedtocounteractthelateralforcesoftheearthquake. AtypicaltraditionalhouseinHimachal,Chamba,consistsofstoneandtimber walls,constructedinwhatisknownasKath-KonaStyle-anindigenousstyleof construction,inwhichthewallsaremadewithalternatecoursesofdrystone masonryandtimberwithoutanycementingmortar(TrainingandDemonstrationProgramme onEarthquakeResistantRuralHousing,2013,pp.2).
InsomepartsofHimachalPradesh,thereisapopularuseofthe Dhajji wallconstruction.In thisconstructionsystem,thewallsaremadeoftimberframeswithin-fillsof lightthinpanelsmadebyclosepackagingofmudmortar,stoneandballast (TrainingandDemonstrationProgrammeonEarthquakeResistantRural Housing,2013,pp.3).
Iwillbeusingthissimplealternatingstructureformymodelofthesquare building.SinceIamtryingtofindtheresonantfrequencyofthestructureIdidnotusestone tofillintheholesorgapsbetweenthealternatingwoodenblocks.
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Fig 3.1:
Fig3.2:
Fig 3.3:
Fig 3.4:
Towhatextenddoestheheightsofsquarebasedbuildingsaffecttheirassociatedresonant frequency?
Gautham Ramesh
001805 - 0021
NotanearthquakeproneregioninIndia:
Pune:
Althoughtheepicenter4 fortheearthquaketooccurmightbefarawayfromPune,therestill mightbeapossibilityoftheafter-effectsofthequakereachingPune,whicharebetween moderatetolowfrequencies.Thisisbecausethewavesemittedfromtheepicenterlose energyastheytravelandthiseffectcausesthewavestooscillatefaster.Thisisalsoknownas thedampingeffect.Astheytakemoretimetooscillatethefrequencyislow(F∝ )andso regionsfarawayfromtheearthquakepronezones,suchasPune,experiencelowfrequency quakes.
RecentlytherehasbeenalotofrealestatebusinessgoingoninPuneandeachcontractoris partofabiggerandbiggerdevelopingscheme.Thecompetitionhasbecomesointensefor landuseandmoneythatthecontractorsareconstructinghigherandlongerbuildings.The localsarediscussingthatPuneissoongoingtobeoverfilledwithskyscrapersandviewitasa positivechangetothecityinlocatedinmid-easternIndia.
PunehasbecometheIThub.Rightnexttomyschooltherehasbeenadevelopmentscheme fromoneofthefamousITcompanies,Cognizant(Fig4.2),whichfeaturesalongelongated structurestretchingparalleltotheroad. Peoplemightfeelitisabetteroptionthanthehigh risestructureshoweverbothstructureshaveanequalriskofcrumbinginearthquake.
SincePunereceivesmoderatetolowintensityearthquakes,theearthquakeisusually originatedfromadifferentregioninIndiaandspreadstoPune.Thisinvestigationwould determinehowviableistheoptionoftransformingPuneintoametropolitancityfeaturing hugeskyscrapersandlong,elongatedstructuresfromITcompanies.
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Fig 4.2: Fig 4.1:
Towhatextenddoestheheightsofsquarebasedbuildingsaffecttheirassociatedresonant frequency?
Gautham Ramesh
001805 - 0021
LabReport
ResearchQuestion:
Towhatextenddoestheheightsofsquarebasedbuildingsaffecttheirassociatedresonant frequency?
Variables:
IndependentVariable(s):
Iwouldfirstdoanexperimenttoseewhetherarelationshipexistsbetweenaphysicalaspect ofastructureandtheresonantfrequencybyinvestigatingthelengthfactoroftheruler.The rulercanhelpmeestablisharelationshipbetweenheightandresonantfrequencyofanobject andthroughthisrelationshipIcanputthebuildingtotestandseeifitagreeswiththis relationshipaswell.
Lengthoftheruler:
ThelengthsthatIwillbeusingare0.450m,0.500m,0.550m, 0.600m,0.650m,0.700m,0.750m,0.800m,0.850mand0.900m.I willfindtheassociatedfrequencyoftheselengthsandpossibly establisharelationshipforthesecondpartofmyexperiment.
Thestructureofthebuildingunderlateralforcesoftheearthquakewouldproveasan effectivetesttopredicthowthesestructureswillperformintherealscenario.Iwillcheckthe structureof Chamba byconstructingasimplemodelofthebuilding.Iwilltestthephysical aspectheightforthe Chamba structure.
Heightofsquarebuilding:
Thebuildingsputtotestwillbeasquareshapedbuildingwithvarying height, 0.075m, 0.15m,0.30mand0.40m.Iamusingtheseheights tofindtheresonantfrequencyso thereforeIwilltaketheheightofthebuildingasmyindependentfactor.
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Fig 5.1:
Towhatextenddoestheheightsofsquarebasedbuildingsaffecttheirassociatedresonant frequency?
Gautham Ramesh 001805 - 0021
DependentVariable(s):
Resonancefrequencyofbuilding: Thefrequencyatwhicheachbuildingvibratesmaybedifferentduetotheheightof thebuilding.Findingtheresonanceofthebuildingwouldhelpdeterminewhetherthe structurewouldstandinanearthquakesincetheresonancefrequencyofan earthquakeoccursbetween0.5-20Hz.
ControlledVariable(s):
Thematerialsusedinconstructingthebuildings: Icannotallowonebuildingtobemadeofbricks andtheothertobemadeofsteel sinceIwillbefocusingonthestructureaspectofthebuildingmorethanitsmaterial. Allthedifferentheightsofthebuildingswillbemadeoutofwood.
Foundation:
Iwillusedoublesidedtapeunderallthestructuresto stickittotheshaketablesothatitwillnothavean effectorwillremainconstantthroughoutthe experiment.
Themeasuringdevicesused: Iwillbeusingamotionsensorwhichwoulddetectthe movementofanyobjectinfrontofthesensorwould beusedagainandagainsoifthereisanysystematic errorinanyoneofthereadings,thesameerrorwillbe carriedforwardtoallofthereadingssotherewill bea consistencyandtheprecisionofthereadingswhencomparedtoeachotherwillbe maintainedalthoughthismightaffecttheaccuracyofthereadings.
TemperatureandPressure:
Theexperimentwillbecarriedoutinroomtemperatureandpressure.This is importantbecausethewoodwouldnotundergothermalexpansionwhichmight changeitsresonantfrequency.
Anyreinforcementsusedinanybuilding:
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Fig.5.2
Towhatextenddoestheheightsofsquarebasedbuildingsaffecttheirassociatedresonant frequency?
Gautham Ramesh
001805 - 0021
IfIhadprovidedanyreinforcementstoanyofthestructuretomaintainitsintegrity thenIwoulddothesameintherestofthestructurealthoughIwilltrytoprevent reinforcementsasfaraspossible.Forexample,reinforcethebuildingwith steelrods ontheedgesofthebuilding.Thiswouldgivemetheresonantfrequencyofthesteel andthewoodsothereforeahugeuncertaintyintheexperiment.
OtherVariables:
IwouldmakesurethatwhenIamperformingtheexperimentontheheight factorI wouldkeepthesurfaceareaofthesquarebaseofthestructureaconstant(i.e.at3cm x2cm).
Hypothesis:
Ipredictthattherewouldbeaninverselyproportionalrelationshipbetweentheheightofthe buildinganditsassociatedresonantfrequency.Ithinkthetalleststructurewouldstart resonatingatthelowestfrequencysinceithasalargerheight-to-baseratiothanallother buildingsandtheinertiaforceswillmakeitswaythemostthuscausingittoresonateatlower frequencies.
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Motionsensor(0.010Hz) x1
Loggerpro x1
Woodpieces(5cmx2cmx1cm) x235
Cardboard(100cmx200cm) x5
Fevicol(typeofglue) x1
Double-sidedtape(roll) x2 ShakeTable x1 Exhaustmotorwithoutthefans(240V) x1 Ruler x1
Materials:
5.3:
Fig
Towhatextenddoestheheightsofsquarebasedbuildingsaffecttheirassociatedresonant frequency?
Gautham Ramesh
001805 - 0021
ConstructionofShakeTable:
TheshaketableworksonabasicprincipleofshiftingtheCoG(CenterofGravity)asthe exhaustfanrotatesaround.Ithasfourspringsonthefouredgesoftheshaketablewhichalso hasawoodensupportcomingupfromthespringstotaketheweightoftheboard.
Onlythemotorwasusedfromtheexhaustfan.Iuseditscircular motiontocreatethevibrationsandcuttheaxleintohalfsothebalance wouldshifteachtimemakingtheshaketablemechanicallyoscillate. Themotorisconnectedtoaswitch/variableresistorinordertoincrease ordecreasethevibrationtomatchtheresonantfrequencyofthe structureonit.
Thespringshelptoincreasetheeffectofvibration.Thespringscannottakethecomplete weightoftheboardsotherearewoodensupports attachedinsidethespringtillacertain height.Thereisdefinitelyacompromiseheresincethesesupportsrestrictthespringto magnifythevibrationstoalargerextentsothereforethisshaketablecanonlyobtainone resonantfrequencyofthebuildings.
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Fig 6.1:
Fig 6.2:
Towhatextenddoestheheightsofsquarebasedbuildingsaffecttheirassociatedresonant frequency?
Gautham Ramesh 001805 - 0021
Procedurefortestingthelengthfactoroftheruler:
1. Setuptherulerhorizontallyonthetablewithoneendof therulerprotrudingoutwardsfromthetable.(likeina cantileverstructure)
2. GClamptheotherendoftherulertothetableinaway thatexactlytherequiredheightorlengthinthiscaseis suspendedfreely.
3. Placethemotionsensorinthestandandadjustthestandinsuchawaythatitis exactly0.100mbelowtheruler. Nowthisheightshouldremainfixedthroughouttheexperiment.
4. Facethemotionsensorupwardstowardstherulerand connectittologgerprowhichinturnisattachedtothe laptop
5. Adjusttheloggerprosoftwaretotakethereadingsof heightandtimewiththeheightintheyaxisandthetime inthexaxis.
6. Pushtherulerdownwardsandstarttheloggerprototakereadingsimmediatelysince thereisalagtimeinvolvedwhichwouldcompensatefortheuncertaintyintheinitial readingforoscillation.
7. Makesurethatatleast10oftheoscillationsonthegraph occuratregularintervalsandthisisthereadingsforthisparticularheight.
8. Notethetimeittakesfor10oscillationsfromthegraphofthesoftwarewithits correspondingheightinadatatableandrecordall yourresults.
9. Afterthereadingsaretaken,changethepositionoftherulerwiththeprotrudingpart nowreading0.080m.
10.Repeatthesameprocedure1-6fortheotherlengthreadingsaswellandrepeateach readingtillyougetaconsistentoscillatingmotioninthesoftware.
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Fig 7.1:
Fig 7.2:
Towhatextenddoestheheightsofsquarebasedbuildingsaffecttheirassociatedresonant frequency?
Gautham Ramesh
001805 - 0021
Procedurefortestingtheheightfactorofthesquarebuildings:
1. Makeashaketablewithspringsattachedtothe4corners andanexhaustmotorwhichproducesthemechanicalmotion requiresforoscillatingtheboard,responsibleforvibrating theplate.
2. Useleadstoattachthemotoroftheshaketable.
3. Putthemotionsensorwhichisconnectedtologgerproinsuch awaythatitis5cmawayfromthebuildingwhichisrestingontheshaketable.
4. Constructawoodenstructurebyinterlockingwoodenblocksby stickingthemontoeachotherusingFevicol.
5. Makethestructuresofdifferentheights–0.40m,0.30m,0.25m, 0.20m,0.075m.
6. Takeoneofthestructuresandplaceitontheshaketablesecuredand fastenedwithdoublesidedtape.
7. Findthefrequencyatwhichthisstructurevibratesthemostby observingwhenthestructureoscillatesorresonatesatitsmaximum awayfromitsnormal.
8. Noteitdownintimefor10oscillationcolumnaccordingtoits respectiveheight.
9. Repeatthesameprocedurefrom1–8fortheotherheightsaswell.
RawDataTableforrulerexperiment:
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Fig 8.2:
LengthofRulerL(±0.020m) Timefor10oscillations(±0.005s) 0.900 5.50 0.800 4.70 0.750 4.40 0.700 3.70 0.650 3.50 0.600 3.10 0.550 2.60
Fig 8.1:
Towhatextenddoestheheightsofsquarebasedbuildingsaffecttheirassociatedresonant frequency?
Analysis: 60cmruler:
Equationofthisgraphwouldbeintheform:x=A*sin(B*t+C)+D
WhereA:Aisamplitude;B:( π)isperiod;C: isphaseshift;D:Disverticalshift(Stapel, 2013)
Theequationofthebestfitcurve=0.00910sin(24.4t+3.99)+0.250
SinceBhelpstogetthevaluefortheperiod,
π = . =0.258
Thereforefor60cmrulerlengththeperiodis0.258s
Gautham Ramesh 001805 - 0021 15 | Page 0.500 2.40 0.450 1.90
Towhatextenddoestheheightsofsquarebasedbuildingsaffecttheirassociatedresonant frequency?
Gautham Ramesh
001805 - 0021
Iusedtheformula: =Frequency
=3.89Hz=ResonantFrequency
Iusedthesamemethodtofindouttheresonantfrequencyoftherulerfortheotherlengths.
AnalyzedDataTablefortherulergraphs:
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Lengthof RulerL(± 0.02m) Length L (±0.04m) (±0.04m) Periodof oscillation(±0.005 s) ResonantFrequency f(±0.005s) 0.900 0.810 1.23 0.537 1.86 0.850 0.723 1.38 0.473 2.11 0.800 0.640 1.56 0.429 2.33 0.750 0.563 1.78 0.374 2.67 0.700 0.490 2.04 0.339 2.95 0.650 0.423 2.37 0.286 3.50 0.600 0.360 2.78 0.257 3.89 0.550 0.303 3.31 0.221 4.52 0.500 0.250 4.00 0.183 5.46 0.450 0.203 4.94 0.145 6.90
Towhatextenddoestheheightsofsquarebasedbuildingsaffecttheirassociatedresonant frequency?
Gautham Ramesh 001805 - 0021
Graphsforruler:
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Equationofcurve: L=1.27f-0.540 0.40 0.46 0.52 0.58 0.64 0.70 0.76 0.82 0.88 0.94 1.501.802.102.402.703.003.303.603.904.204.504.805.105.405.706.006.306.606.907.20 Length L (m) Resonantfrequencyf(Hz) LengthagainstResonantFrequencyforruler Equationofgradient: L-2=0.755f-0.195 -1.00 -0.50 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 -0.500.000.501.001.502.002.503.003.504.004.505.005.506.006.507.007.50 1/Lenght 2 L -2 (m ) ResonantFrequencyf(Hz) 1/Lenght2againstResonantFrequency
Towhatextenddoestheheightsofsquarebasedbuildingsaffecttheirassociatedresonant frequency?
Gautham Ramesh
001805 - 0021
RawDataTableforthesquarebuildings:
*Thelefttop,leftbottom,middle,righttopandrightbottomrefertothepositionofthe buildingontheshaketable.
0.20mbuilding:
Analysis: 0.40mheightbuilding: 0.30mbuilding: 0.15mbuilding:
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HeightH (±0.02 m) Periodfor10oscillations(±0.20s) Left Top LeftBottom Middle Right Top RightBottom 0.15 1.58 1.44 1.06 1.11 1.52 0.20 1.92 1.59 1.98 1.91 1.76 0.30 2.07 - 1.77 1.940.40 2.85 1.85 1.88 1.86 1.92
Towhatextenddoestheheightsofsquarebasedbuildingsaffecttheirassociatedresonant frequency?
Gautham Ramesh
001805 - 0021
IuseddifferentplacesontheshaketableasmytrialsforthisexperimentsoIaveragedthem togetabettervalueforthetimeperiodofthe10oscillations.Ithencalculatedtheperiodby dividingtheaveragevalueby10forthe10oscillations.Ifoundtheresonantfrequencyusing theformula:
=Frequency
Icouldnotusethemathematicalsimulationtoobtaintheperiodfromthesegraphsbecause theoscillationswerenot aconstant.
AnalyzedDataTableforgraphsofsquarebuildings:
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Height (±0.02m ) Height2 H2 (±0.04 m2) 1/Height2 H-2 (±0.04m2) Periodfor10oscillations(±0.20s) Average (±0.20 s) Average for1 oscillatio n(±0.20 s) Resonant Frequenc y(Hz) (±0.20 Hz) Left Top Left Botto m Middle Right Top Right Botto m 0.15 0.023 44.4 1.58 1.44 1.06 1.11 1.52 1.34 0.134 7.45 0.20 0.040 25.0 1.92 1.59 1.98 1.91 1.76 1.83 0.183 5.46 0.25 0.063 16.0 1.9 1.76 2.01 1.91 1.79 1.87 0.187 5.34 0.30 0.090 11.1 2.07 - 1.77 1.94 - 1.93 0.193 5.19 0.40 0.16 6.3 2.85 1.85 1.88 1.86 1.92 2.07 0.207 4.83
Towhatextenddoestheheightsofsquarebasedbuildingsaffecttheirassociatedresonant frequency?
Gautham Ramesh 001805 - 0021 20 | Page Graphsforsquarebuildings: 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 4.504.704.905.105.305.505.705.906.106.306.506.706.907.107.307.507.70 Height h (m) ResonantFrequencyf(Hz) HeightagainstResonantFrequencyforsquare buildings
Towhatextenddoestheheightsofsquarebasedbuildingsaffecttheirassociatedresonant frequency?
Gautham Ramesh 001805 - 0021
Dataanalysis:
Describingthegraphs:
Idrewfourgraphs,twofortherulerandtwoforsquarebuildings,forinvestigatingthe relationshipbetweenheight/lengthandresonantfrequency.
IdrewtwographsforeachbecauseIwantedtolinearizetherelationshipsoIcanclearlysee anysystematicerrorfromthey-interceptorx-interceptdependingonhowfarawayisthe bestfitlinefromtheorigin.Alsolinearizingthegraphshelpstoseethescatterofthereadings andjustifythereliabilityofthebestfitline.
Thefirstgraphoflengthagainstresonantfrequencyoftherulershowsaninversepower relationshipwiththeequationofthebestfitcurvebeingL=1.27f
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-0.540 . H-2=0.066f+4.30 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 -10.0-5.00.05.010.015.020.025.030.035.040.045.050.0 1/Height 2 H -2 (m -2 ) ResonantFrequencyf(Hz) 1/Height2againstResonantFrequency
Towhatextenddoestheheightsofsquarebasedbuildingsaffecttheirassociatedresonant frequency?
Gautham Ramesh
001805 - 0021
ThereforetoconformthisIdrewanothergraphof againstresonantfrequency.Idid thisbecausebysquaringbothsidesandtheninversingitIwouldgetf1.08 whichisveryclose tof,theactualresonantfrequencyitselfandL-2.Itshowedabestfitlinewithminimum scatter.Althoughthevaluefortheyinterceptseemsprettyhigh,thereisminimumscatterin thegraphsoitdoesshowaproportionalrelationshipbutnotadirectlyproportional relationshipwhereinthevaluefortheyinterceptis(0,0)i.e.itpassesthroughtheorigin.
ThelasttwographsthatIdrewwerefortestingtheheightfactorofthesquarebuildings.I foundthatthegraphof1/Height2 againstresonantfrequencyhasmorescatterthanthegraph of1/Length2 againstresonantfrequencyfortherulersointhiscasethebestfitlineisnot justified.Neverthelesstheresonantfrequencydoesdecreasewithincreasinglength.The graphwasexpectedtohavelotsofscattersincethedifferencebetweeneachtrialandthehigh uncertaintyofthetime(s)weremajorfactorcontributingtowardsthescatter.
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Towhatextenddoestheheightsofsquarebasedbuildingsaffecttheirassociatedresonant frequency?
Gautham Ramesh 001805 - 0021
ConclusionandEvaluation:
Icanconcludethatthereisaninversesquarerelationshipbetweentheheightandlengthofa structureanditsassociatedresonantfrequency.Theequationforfrequency(f)andheight(h) wouldbe ∝f.
Thisrelationshipisdefinitelymoreapparentintherulerexperimentascomparedtothe squarebuildingexperimentduetothehugenumberoferrorsinvolvedinthesquarebuilding experiment.Thereforeinahugepartofmyevaluationrevolvesaroundresolvingtheseerrors. However,theexperimentdefinitelyhaselementswithresonantfrequencysothatcanalsobe concludedfromtheresults.
ForinstancetherulerwasoscillatinginitsnaturalfrequencywhenIleftit afterpushingit down.However,Ihadtomatchtheresonantfrequencygivenbytheshaketablewiththe naturalfrequencyofthesquarebuilding.Thereforetherewouldbelotsofhumanerror involvedinitsincetheresonantfrequencymightnotalwaysmatchthenaturalfrequencyof thebuilding.
Thereisalsoasystematicerrorinvolvedinthisexperimenttoo.Theshaketableshowed variationsinperiodofoscillationofthebuildingfromeachplaceoftheboardandthesewere notminorchangesinreadings.Theywouldoverlaporevengohigherthanthereadingfora differentheightforexample,for0.20mheightfromthemiddleoftheboard;Igotareading of1.98swhichisevenmorethantheaveragecalculatedvaluefor0.30mheight!Itwas prettysignificantandcouldbethereasonforthegreateramountofscatterinthesereadings ascomparedtothescatterfortherulerexperiment.
Amechanicaloscillatorwouldbeabetterdevicetouseinsteadoftheexhaustmotorinorder tomaketheshaketablevibratewithoutallowingfortheshaketable’sresonantfrequencyto betakenintoconsideration.
Ialsouseddoublesidedtapewhichperhapsactedasadamperinthesquarebuilding experimenttoattachthebuildingstotheshaketable.Thiswouldbeanothersystematicerror incalculatingthevaluefortheresonantfrequency.Additionallythedoublesidedtapewould affecttheresonantfrequencyofthestructureaswellsinceitismadeofadifferentmaterial
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Towhatextenddoestheheightsofsquarebasedbuildingsaffecttheirassociatedresonant frequency?
Gautham Ramesh
001805 - 0021
andthereforethestructure’sresonantfrequencywouldhavewoodaswellasthematerialthe doublesidedtapeismadewith-rubberbasedadhesiveEVA(Indiamart.com,2013)
Icanreducethiserrorbyattachingittotheshaketablewithnailssothatonlytheresonant frequencyofthebuildingistakenintoconsideration.
Thisexperimentprovestheinversesquarerelationshipoftheheightandlengthofthe buildingsagainstitsassociatedresonantfrequency.Eventhoughallofthestructurestestedin theexperimentfallintotherangeof0.5to20Hzwhichistherangefortheresonant frequencyofanearthquakethereissomethingusefulwecanstillgleanout ofthis.
TheinverselysquareproportionalshowsthatinHimachalwherethereishighfrequencyof earthquakestallerstructuresshouldbebuiltsincetallerstructureswouldonlyresonateatlow frequencies.
However,theresonantfrequencyisnottheonlyfactoraffectingthebuildinginanearthquake. As mentioned earlier, the extent ofdamageof an earthquake depends on the size(magnitude3) oftheearthquake,thedistancefromtheepicenter4,thelocalgeologicalconditionsandthe characteristicsofbuildings(Pg5).Althoughthroughthisexperimentitwouldbeidealto buildtallstructuresinHimachalforthehighfrequencyearthquakes,itwouldprobablybe damagedmorebytheotherfactors.
AndinPune,wherepeoplearebusybuildingskyscrapers,shouldinsteadbuiltshortheight structurestoresistthemoderatetolowfrequencies.ThereforetheplanofPunebuilding skyscrapersdoesnotsoundlikeagoodoption.Thereforetheyneedtotakethisinto considerationwhenimplementingskyscrapersintoPune.
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Towhatextenddoestheheightsofsquarebasedbuildingsaffecttheirassociatedresonant frequency?
Gautham Ramesh
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Collins,B.2012.Whatcausedtherecent earthquakesinAustralia?InterviewedbyAnnie Hastwell[inperson]SchoolofEnvironmentalandLifeSciencesattheUniversityof Newcastle,01May.
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PHYSICSOFEARTHQUAKES.2013.[e-book]E.Brodsky.pp.2.Availablethrough:
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NDTV.com.2013.Sikkimquake:Deathtollrises;lossesestimatedatRs 1lakhcrore.[online]
Availableat:http://www.ndtv.com/article/india/sikkim-quake-death-toll-rises-lossesestimated-at-rs-1-lakh-crore-135377[Accessed:1Oct2013].
Stapel,E.2013.GraphingTrigonometricFunctions.[online]Availableat:
http://www.purplemath.com/modules/grphtrig.htm[Accessed:22Oct2013].
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Towhatextenddoestheheightsofsquarebasedbuildingsaffecttheirassociatedresonant frequency?
Gautham Ramesh
001805 - 0021
Indiamart.com.2013.DoubleSidedFoamTapes-DoubleSidedFoamTapes(PEFoam SolventAdhesive),DoubleSidedFoamTapes(PEFoamHotMeltAdhesive),DoubleSided FoamTapes(EVAFoamRubberBased)andDoubleSidedFoamTapes(EVAFoamHot Melt)Manufacturer&Exporterfrom Wadhwan,India.[online]Availableat: http://www.indiamart.com/onetape/double-sided-foam-tapes.html[Accessed:1Dec2013].
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