effect of sloping ground on structural ... of sloping ground on structural performance of rcc...
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EFFECTOFSLOPINGGROUNDONSTRUCTURALPERFORMANCEOFRCCBUILDING
UNDERSEISMICLOAD
1SUJITKUMAR,2Dr.VIVEKGARG,3Dr.ABHAYSHARMA
1PostGraduateStudent,StructuralEngineeringDepartmentofCivilEngineering,MANIT,Bhopal,MadhyaPradesh,India,Email:[email protected]
2AssistantProfessor,CivilEngineeringDepartment,MANIT,Bhopal,MadhyaPradesh,India,
Email:[email protected]
3AssociateProfessor,CivilEngineeringDepartment,MANIT,Bhopal,MadhyaPradesh,India,Email:[email protected]
ABSTRACT
Previous studies emphasize for proper planning and construction practices of multistoried buildings on sloping ground.However,innormaldesignpracticethedesignersgenerallyignoretheeffectofslopinggroundonthestructuralbehaviorofthe building. The seismic analysis of a G+4 storey RCC building on varying slope angles i.e., 7.50 and 150 is studied andcomparedwiththesameontheflatground.TheseismicforcesareconsideredasperIS:1893‐2002.Thestructuralanalysissoftware STAADPro v8i isused to study theeffect of sloping groundonbuildingperformanceduring earthquake. Seismicanalysis has been done using Linear Staticmethod. The analysis is carried out to evaluate the effect of sloping ground onstructural forces. The horizontal reaction, bending moment in footings and axial force, bending moment in columns arecriticallyanalyzedtoquantifytheeffectsofvariousslopingground.Ithasbeenobservedthatthefootingcolumnsofshorterheightattractmoreforces,becauseofaconsiderable increase intheirstiffness,whichinturnincreasesthehorizontalforce(i.e.shear)andbendingmomentsignificantly.Thus,thesectionofthesecolumnsshouldbedesignedformodifiedforcesduetothe effect of sloping ground. The present study emphasizes the need for proper designing of structure resting on slopingground.IndexTerms:Slopingground,Seismicforces,RCCBuilding,Structuralanalysis,STAADetc.1.INTRODUCTION
Earthquake is the most disastrous due to itsunpredictability and huge power of devastation.Earthquakes themselves do not kill people, rather thecolossal loss of human lives and properties occur due tothedestructionofstructures.Buildingstructurescollapseduringsevereearthquakes,andcausedirectlossofhumanlives. Numerous research works have been directedworldwide in last fewdecades to investigate thecauseoffailureofdifferenttypesofbuildingsundersevereseismicexcitations.Massivedestructionofhigh‐riseaswellaslow‐risebuildingsinrecentdevastatingearthquakeprovesthatindevelopingcountieslikeIndia,suchinvestigationistheneed of the hour. Hence, seismic behavior of asymmetricbuildingstructureshasbecomeatopicofworldwideactiveresearch. Many Investigations have been conducted onelastic and inelastic seismic behavior of asymmetricsystems to find out the cause of seismic vulnerability ofsuch structures. The purpose of the paper is to performlinear static analysis ofmedium height RC buildings andinvestigate the changes in structural behavior due toconsiderationofslopingground.
1.1SEISMICBEHAVIOUROFBUILDINGSONSLOPESININDIA
NorthandnortheasternpartsofIndiahavelargescalesofhilly region,whichare categorizedunderseismiczone IVand V. In this region the construction of multistory RCframedbuildingsonhillslopeshasapopularandpressingdemand, due to its economic growth and rapidurbanization. This growth in construction activity isaddingincreaseinpopulationdensity.Whileconstruction,itmustbenotedthatHillbuildingsaredifferentfromthoseinplainsi.e.,theyareveryirregularandunsymmetricalinhorizontal and vertical planes, and torsionally coupled.Since there is scarcity of plain ground in hilly areas, itobligatestheconstructionofbuildingsonslopes.
During past earthquakes, reinforced concrete (RC) framebuildingsthathavecolumnsofdifferentheightswithinonestorey, suffered more damage in the shorter columns ascompared to taller columns in the same storey. Oneexampleofbuildingswithshortcolumnsinbuildingsonaslopinggroundcanbeseeninthefigure(1)given
SUJIT KUMAR et al. DATE OF PUBLICATION: SEPTEMBER 01, 2014
ISSN: 2348-4098 VOLUME 2 ISSUE 6 AUGUST 2014 (VER II)
INTERNATIONAL JOURNAL OF SCIENCE, ENGINEERING AND TECHNOLOGY- www.ijset.in 1310
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SUJIT KUMAR et al. DATE OF PUBLICATION: SEPTEMBER 01, 2014
ISSN: 2348-4098 VOLUME 2 ISSUE 6 AUGUST 2014 (VER II)
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Balaji K.V.G.D (2011) studied the non‐linear analysis ofvarioussymmetricandasymmetricstructuresconstructedon plain as well as sloping grounds subjected to variouskinds of loads. Different structures constructed on planegroundand inclined groundof30o slope is considered inthe study. Various structures are considered in plansymmetryandalsoasymmetrywithdifferenceinbaysizesin mutual directions. The analysis has been carried outusingSAP‐2000andETABSsoftware.
Mohammed U. and Farooque P. (2012) studied thebuildings on hill differ from other buildings. The variousfloors of such building steps back towards the hill slopeand at the same time buildings may have setbacks also.Buildingssituatedinhillyareasaremuchmorevulnerabletoseismicenvironment.Inthisstudytheeffectofvaryingheightofcolumnsingroundstoreyduetoslopinggroundand the effect of shear wall at different positions duringearthquake. Seismic analysis has been done using LinearStatic, Linear Dynamic method and evaluated usingpushoveranalysisEightStoriedbuilding.
KeyvanRamin(2013) studiedtheexperimentalmodelingand numerical modeling for a four‐story reinforcedconcretebuildingthattheanalysisofsimple3‐Dframesofvarying floor heights and varying number of bays withdifferent slope angles using a very popular software toolSTAADPro.onbothaslopingandaflat lot.AlsoSap2000softwarehadbeenusedtoshowthat thedisplacementoffloors is greater for a flat lot building than a sloping lotbuilding.
PradeepKumarRamancharla(2013)studiedthebehaviorofabuildingonvaryingslopeanglesi.e.,15°,30°and45°isstudied using shear wall in different location andcompared with the same on the flat ground. Building isdesignedasper IS456and latersubjected toearthquakeloads.
The salient objectives of the present study have been tostudy the effect of sloping groundon structural forces incriticalhorizontalreaction,bendingmomentinfootingandcriticalaxialforce,bendingmomentincolumns.2.METHODOLOGY
Thispresentworkdealswithstudyofbehaviorofslopingground building frames considering different inclination(7.5o, 15o) under earthquake forces. The comparison ofsloping ground and plane ground building under seismicforcesisdone.HereG+4storeyistakenandsameliveloadis applied in three the buildings for its behavior andcomparison.
The framedbuildingsaresubjected tovibrationsbecauseof earthquake and therefore seismic analysis is essentialfor these building frames. The fixed base system isanalyzedbyemployinginthreebuildingframesinseismiczoneIVbymeansofSTAADPro.Software.Theresponseofthree the building frames is studied for usefulinterpretationofresults.
2.1STEPSFORCOMPARISON
Comparisons of results in terms of horizontal reaction,
bendingmoments,axialforce.Followingstepsareadoptedinthisstudy
Step‐1 Selection of building geometry and Seismic zone:The behavior of three the models is studied for seismiczone IV of India as per IS code 1893 (Part 1):2002 forwhichzonefactor(Z)is0.24.
Step‐2Formationofloadcombination
Types of Primary Loads and Load Combinations: ThestructuralsystemsaresubjectedtoPrimaryLoadCasesasper IS 875:1987 and IS 1893:2002.Six primary load caseandthirteenloadcombinationsusedforanalysis.
Step‐3 Modelling of building frames using STADD Pro.Software
Step‐4 Analysis of three the building frames are doneunderseismiczoneIVforeachloadcombination.
Step‐5 Comparative study of results in terms of bendingmomentsandhorizontal force in footings, axial forceandbendingmomentincolumns.
3.MODELLING
STAAD Pro. Software is used in modeling of buildingframes. STAAD stands for Structural analysis and designProgramanditisgeneralpurposesoftwareforperformingtheanalysisanddesignofawidevarietyofstructures.Thebasicactivitieswhicharetobecarriedouttoachievethisgoal:
a.Geometryofthestructure
b.Providingmaterialandmemberproperties
c.Applyingloadsandsupportconditions
3.1NOMENCLATUREOFSTRUCTURALMODELS
Apropernomenclatureforjointandmembersnumberingis very important as it gives the exact idea where thejoint/memberislocatedintheentirestructure.Thenodes,beams and columns numbering is according to the floornumbergivenintables.
Table‐1Numberingofnodesinstructure
NodeNo. Location
1‐25 Belowplinthlevel
51‐90 plinthlevel
101‐125 1ststorey
201‐225 2ndstorey
301‐325 3rdstorey
401‐425 4thstorey
Table‐2Numberingofcolumnsinstructure
ColumnsNo Location
1‐25Below plinthlevel
101‐125 1ststorey
SUJIT KUMAR et al. DATE OF PUBLICATION: SEPTEMBER 01, 2014
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4.ST
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SUJIT KUMAR et al. DATE OF PUBLICATION: SEPTEMBER 01, 2014
ISSN: 2348-4098 VOLUME 2 ISSUE 6 AUGUST 2014 (VER II)
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4.1LOADINFollowinglo(a)DeadLoConsideringSelf wt. of s25=3.125kFloorFinishTotalfloorloMasonry wa12.4kN/mMasonrywaParapetwall(b)LiveLoaLiveLoadon(c)EarthQuAll thebuild(IV)
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5.RESULTS
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SUJIT KUMAR et al. DATE OF PUBLICATION: SEPTEMBER 01, 2014
ISSN: 2348-4098 VOLUME 2 ISSUE 6 AUGUST 2014 (VER II)
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Theresultsofvariousanalysesfordifferentgroundslopes(0o, 7.5o, 15o) are presented and a comparative studybetween results of different slopes and plane ground ismadetoanalysestheeffectofslopinggroundonstructuralforces. In the present work horizontal reaction andbendingmoment in footingofstructure,bendingmomentin columns are compared for different ground slopesunder different seismic loads. The analysis resultsobtained in Staad Pro. are shown below in the form oftablesandgraphs.
5.1FOOTINGREACTIONINTHEBUILDINGFRAME
The footing reaction in the building frame systemdue tovarious analyses in terms of horizontal reaction, andComparison of horizontal reaction Fx (kN) in footing forvariousgroundslopesunderseismicloadsinX‐direction.
Table‐7ComparisonofhorizontalreactionFx(kN)infootingforvariousanalysesinX‐direction
FootingNo. Loadcase
Groundslope(indegree) Comparisonofvariousanalyses0 7.5 15
1 2 3 2/1 3/1
1 EQX ‐29.21 ‐89.91 ‐122.99 3.08 4.21
2 EQX ‐43.66 ‐50.88 ‐36.33 1.17 0.83
3 EQX ‐43.49 ‐25.15 ‐10.03 0.58 0.23
4 EQX ‐43.66 ‐12.24 ‐1.68 0.28 0.04
5 EQX ‐29.21 1.18 4.52 ‐0.04 ‐0.15
6 EQX ‐29.93 ‐92.14 ‐126.21 3.08 4.22
7 EQX ‐44.72 ‐52.14 ‐37.31 1.17 0.83
8 EQX ‐44.54 ‐25.78 ‐10.33 0.58 0.23
9 EQX ‐44.72 ‐12.56 ‐1.76 0.28 0.04
10 EQX ‐29.93 1.18 4.60 ‐0.04 ‐0.15
11 EQX ‐30.24 ‐93.04 ‐127.45 3.08 4.21
12 EQX ‐45.17 ‐52.65 ‐37.68 1.17 0.83
13 EQX ‐44.99 ‐26.04 ‐10.44 0.58 0.23
14 EQX ‐45.17 ‐12.69 ‐1.78 0.28 0.04
15 EQX ‐30.24 1.18 4.64 ‐0.04 ‐0.15
16 EQX ‐29.93 ‐92.14 ‐126.21 3.08 4.22
17 EQX ‐44.72 ‐52.14 ‐37.31 1.17 0.83
18 EQX ‐44.54 ‐25.78 ‐10.33 0.58 0.23
19 EQX ‐44.72 ‐12.56 ‐1.76 0.28 0.04
20 EQX ‐29.93 1.18 4.60 ‐0.04 ‐0.15
21 EQX ‐29.21 ‐89.91 ‐122.99 3.08 4.21
22 EQX ‐43.66 ‐50.88 ‐36.33 1.17 0.83
23 EQX ‐43.49 ‐25.15 ‐10.03 0.58 0.23
24 EQX ‐43.66 ‐12.24 ‐1.68 0.28 0.04
25 EQX ‐29.21 1.18 4.52 ‐0.04 ‐0.15Table‐7depicts thathorizontalreaction in footingsvariessignificantlyforvariousgroundslopesunderseismicloadinXdirection.SLOPE7.50providessignificantvariationof‐0.04 to3.08 times in the footingreaction (Fx) comparedtoSLOPE0o.Themaximumincreaseinratio3.08timesisfoundinfootingslocatedatlesserdepth(i.e.footingF1,F6,F11,F16andF21)whereasthemaximumdecreaseinratio
ofnearly‐0.04timesisfoundinfootingslocatedathigherdepth (i.e. footing F5, F10, F15, F20 and F25). Themaximumhorizontalreaction(Fx)infootingforSLOPE00is ‐45.17kN is found in footingF12andF14whereasthemaximumhorizontalreactioninfootingforSLOPE7.50is‐93.04 kN is found in footing F11. The sloping groundcausesincreaseoffootingreaction(Fx)forfootingslocated
SUJIT KUMAR et al. DATE OF PUBLICATION: SEPTEMBER 01, 2014
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atlesserdepthwhereasitdecreasesthisvalueforfootinglocatedathigherdepth.
SLOPE15o provides significant variation of 0.04 to 4.21times in the footinghorizontal reaction (Fx)compared toSLOPE 0o. The maximum increase in ratio 4.21 times isfoundinfootingslocatedatlesserdepth(i.e.footingF1,F6,F11,F16andF21)whereasthemaximumdecreasein
ratio of nearly 0.04 times is found in footings located athigher depth (i.e. footing F4, F9, F14, F19 and F24). Themaximumfootinghorizontalreaction(Fx)forSLOPE00is‐45.17 kN is found in footing F12 and F14 whereas the
maximumfootingreaction forSLOPE150 is ‐127.45kNisfound in footingF11.The slopinggroundcauses increaseoffootingreaction(Fx)forfootingslocatedatlesserdepthwhereas it decreases this value for footing located athigher depth. The maximum horizontal reaction (Fx) infootings value increases at lesser depth and maximumdeceases valueathigherdepth.Themaximumhorizontalreaction (Fx) in footings value significant change inearthquakeinZ‐direction.
Comparison of bending moment Mz (kN‐m) reaction infootingsinslopinggroundforvariousanalysesisdepictedintable8
Table‐8ComparisonofbendingmomentMzinfootingsforvariousanalyses(EQX)
FootingNo Loadcase
Groundslope(indegree) Comparisonofvariousanalyses0 7.5 15
1 2 3 2/1 3/1
1 EQX 83.31 145.44 176.64 1.62 2.12
2 EQX 89.76 99.49 82.40 1.11 0.92
3 EQX 89.66 68.76 43.02 0.77 0.48
4 EQX 89.76 48.90 23.92 0.59 0.27
5 EQX 83.31 28.46 8.29 0.34 0.10
6 EQX 85.30 148.95 181.12 1.62 2.12
7 EQX 91.90 101.89 84.51 1.11 0.92
8 EQX 91.80 70.42 44.14 0.77 0.48
9 EQX 91.90 50.09 24.57 0.59 0.27
10 EQX 85.30 29.17 8.55 0.34 0.10
11 EQX 86.16 150.39 182.88 1.62 2.12
12 EQX 92.82 102.87 85.33 1.11 0.92
13 EQX 92.71 71.10 44.58 0.77 0.48
14 EQX 92.82 50.58 24.81 0.59 0.27
15 EQX 86.16 29.46 8.64 0.34 0.10
16 EQX 85.30 148.95 181.12 1.62 2.12
17 EQX 91.90 101.89 84.51 1.11 0.92
18 EQX 91.80 70.42 44.14 0.77 0.48
19 EQX 91.90 50.09 24.57 0.59 0.27
20 EQX 85.30 29.17 8.55 0.34 0.10
21 EQX 83.31 145.44 176.64 1.62 2.12
22 EQX 89.76 99.49 82.40 1.11 0.92
23 EQX 89.66 68.76 43.02 0.77 0.48
24 EQX 89.76 48.90 23.92 0.59 0.27
25 EQX 83.31 28.46 8.29 0.34 0.10Table‐8depictsthatbendingmomentreactionin footingsvaries significantly for various ground slopes underseismicloadinXdirection.SLOPE7.50providessignificantvariationof0.34to1.62timesinthefootingreaction(Mz)compared to SLOPE 0o. The maximum increase in ratio1.62timesisfoundinfootingslocatedatlesserdepth(i.e.footingF1, F6, F11, F16 andF21)whereas themaximum
decrease inratioofnearly0.34times is found in footingslocatedathigherdepth(i.e. footingF5,F10,F15,F20andF25).
Themaximumfootingmomentreaction(Mz)forSLOPE00is92.82kN‐misfoundinfootingF12andF14whereasthemaximumfootingreactionforSLOPE7.50 is150.39kN‐misfoundinfootingF11.Theslopinggroundcausesincreaseoffootingreaction(Mz)forfootingslocatedatlesserdepth
SUJIT KUMAR et al. DATE OF PUBLICATION: SEPTEMBER 01, 2014
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whehigh
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of 0.10 toaredtoSLOPEmes is founting F1, F6,crease in ratiocated at hiand F25).E00is92.82easthemaximkN‐misfoun
iticalforcesin
Slopi
ueFootinNo.
47 11
25 14
77 11
reaction Fx) reaction inratioof2.85d(15o)compfverticalreacntgroundslop
ntalreactionunds(7.5o,15
oping ground 15
d at
2.12E0o.d inF11,ioofgherThe
2kN‐mumndin
nfootingfor
ingGround(7
2
ng Va
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226
(kN)n the5andaredctionpes.
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The slopingreaction(MzitdecreasesSeismic inmomentoffo
5.1 CRITICFRAME
Comparisonandbendingforvariousa
differentgro
7.50) Slo
alueFoogN
5.68 1
8.05 1
6.38 1
Figure14footingbe
5.2BENDIN
Thebendingtovariousan
0
50
100
150
200
250
300
Bending Moment (kN‐m
)
ground cauz)forfootingthisvaluefoZ‐directionootinginslop
CAL FORCES
of critical hgmomentinfanalyses
undslopesfo
opingGround
3
otinNo. V
1 1
4 8
1 2
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NGMOMENT
gmomentintnalysesisdep
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ses increasegslocatedatorfooting locsignificant
pinggrounds
S IN FOOT
orizontal forfootingfordi
orvariousan
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2Value
95.29 2
73.72 1
75.97 1
nofcriticalbandslopingbuildings
INTHECOLU
thecolumnsopictedinTabl
Sloping ground
of bendinglesserdepthcatedathighechange instructures.
TING OF BU
rces, verticalfferentgroun
alyses
Comparisonofvariousanalysis
2/1 3/1
.13 2.85
.01 1.01
.61 1.97
bendingmomgrounds(7.5
UMNS
ofslopinggrole‐10
d 7.5 Sloping gro
momentwhereaserdepth.bending
UILDING
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mentin5o,15o)
ounddue
und 15
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Comparison of bending moment Mz (kN‐m) in columnsbelowplinthlevelforvariousgroundslopesunderseismic
loadsinX‐direction.
Table‐10ComparisonofbendingmomentMz(kN‐m)infootingcolumnsforvariousanalyses(EQX)
ColumnNo
Loadcase Nodes
Groundslope(indegree) Comparisonofvariousanalyses0 7.5 15
1 2 3 2/1 3/11 EQX 51 ‐39.49 ‐10.58 7.81 0.27 ‐0.20
1 83.31 145.44 176.64 1.75 2.122 EQX 52 ‐24.27 ‐2.82 1.14 0.11 ‐0.05
2 89.76 99.49 82.40 1.11 0.923 EQX 53 ‐24.43 ‐10.92 ‐11.94 0.45 0.49
3 89.66 68.76 43.02 0.77 0.484 EQX 54 ‐24.27 ‐15.85 ‐17.38 0.65 0.72
4 89.76 48.90 23.92 0.54 0.275 EQX 55 ‐39.49 ‐32.12 ‐29.52 0.81 0.75
5 83.31 28.46 8.29 0.34 0.106 EQX 56 ‐40.41 ‐10.75 8.17 0.27 ‐0.20
6 85.30 148.95 181.12 1.75 2.127 EQX 57 ‐24.83 ‐2.83 1.28 0.11 ‐0.05
7 91.90 101.89 84.51 1.11 0.928 EQX 58 ‐24.99 ‐11.13 ‐12.14 0.45 0.49
8 91.80 70.42 44.14 0.77 0.489 EQX 59 ‐24.83 ‐16.18 ‐17.72 0.65 0.71
9 91.90 50.09 24.57 0.55 0.2710 EQX 60 ‐40.41 ‐32.83 ‐30.16 0.81 0.75
10 85.30 29.17 8.55 0.34 0.1011 EQX 61 ‐40.79 ‐10.84 8.28 0.27 ‐0.20
11 86.16 150.39 182.88 1.75 2.1212 EQX 62 ‐25.06 ‐2.85 1.31 0.11 ‐0.05
12 92.82 102.87 85.33 1.11 0.9213 EQX 63 ‐25.23 ‐11.22 ‐12.24 0.44 0.49
13 92.71 71.10 44.58 0.77 0.4814 EQX 64 ‐25.06 ‐16.33 ‐17.88 0.65 0.71
14 92.82 50.58 24.81 0.54 0.2715 EQX 65 ‐40.79 ‐33.13 ‐30.44 0.81 0.75
15 86.16 29.46 8.64 0.34 0.10
Table‐10depicts thatbendingmoment in columnsvariessignificantlyforvariousgroundslopesunderseismicloadinXdirection.SLOPE7.50providessignificantvariationof0.11to1.75timesinthebendingmomentincolumn(Mz)compared to SLOPE 0o. The maximum increase in ratio1.75timesisfoundincolumnslocatedatlesserdepth(i.e.column C11) below plinth level. Whereas the maximumdecreaseinratio0.11timesisfoundincolumnslocatedatintermediate depth (i.e. column C2, C7 and C12) belowplinth level. The maximum bending moment in column(Mz) for SLOPE 00 is 92.82kN‐m is found in column (i.e.C12) whereas themaximum bendingmoment in columnforSLOPE7.50is150.39kN‐misfoundincolumnC11.Thesloping ground causes increase in bending moment forcolumns locatedat lesserdepthwhereas itdecreasesthis
value for column located at higher depth below plinthlevel.
SLOPE 150 provides significant variation of ‐0.05 to 2.12timesinthebendingmomentincolumn(Mz)comparedtoSLOPE 0o. The maximum increase in ratio 2.12 times isfoundincolumnslocatedatlesserdepth(i.e.columnC11)belowplinthlevelWhereasthemaximumdecreaseinratio‐0.05times is found in columns located at intermediatedepth(i.e.columnC2,C7andC12)belowplinthlevel.
Themaximumbendingmomentincolumn(Mz)forSLOPE00is92.82kN‐misfoundincolumn(i.e.C12)whereasthemaximum bending moment in column for SLOPE 150 is182.88kN‐m is found in columnC11. The sloping groundcauses increase of bending moment in column (Mz) forcolumns locatedat lesserdepthwhereas itdecreasesthisvalue for column located at higher depth in belowplinth
SUJIT KUMAR et al. DATE OF PUBLICATION: SEPTEMBER 01, 2014
ISSN: 2348-4098 VOLUME 2 ISSUE 6 AUGUST 2014 (VER II)
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level. BendingmomentMz (kN‐m) in columnsbelowandaboveplinthlevelforvariousgroundslopesunderseismicloadsinZ‐directionisminutelyaffected.
5.2CRITICALFORCESINCOLUMNOFBUILDINGFRAME
Comparison of critical axial forces Fx (kN) and bendingmomentMz(kN‐m)incolumnsforvariousgroundslopesarediscussedforvariousanalyses.
Table11‐Comparisonofcriticalforcesincolumnfordifferentgroundslopesforvariousanalyses
Forces/
Component
PlaneGround SlopingGround(7.5o) SlopingGround(15o)Comparisonofvariousanalysis
1 2 3
3/1Column
No. Value
Column
No. Value
Column
No. Value
2/1
AxialForceFx(kN)
13 863.25 14 868.10 14 873.72 1.01 1.01
BendingMomentMz(kN‐m)
14 139.78 11 226.40 11 276.00 1.62 1.97
Table‐11depictsthatcriticalbendingmomentMz(kN‐m)in the column increases significantlywith change in ratioof1.97times forslopingground(15o)comparedtoplaneground. However critical value of vertical reaction incolumnremainsalmostsamefordifferentgroundslopes.
Figure 15: Comparison of critical bending moment incolumn between plane and sloping grounds (7.5o, 15o)buildings
Figure 16: Comparison of critical axial force in columnbetweenplaneandslopinggrounds(7.5o,15o)buildingsFigure 17 and figure18 shows the bending moment inplane ground and sloping ground (15o) building changesaccordinglyvaryingdepth.Graphsshowsclearthathigherbendingmomentinsmallerdepthsideanddecreaseswithincreaseindepth.0
50
100
150
200
250
300
Plane ground Sloping ground 7.5 Sloping ground 15
Bending moment (kN‐m
)
500
550
600
650
700
750
800
850
900
Plane ground Sloping ground 7.5 Sloping ground 15
Axial Force (kN
)
SUJIT KUMAR et al. DATE OF PUBLICATION: SEPTEMBER 01, 2014
ISSN: 2348-4098 VOLUME 2 ISSUE 6 AUGUST 2014 (VER II)
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F
Fi
6.C
The
a)
b)
Figure17:Ben
igure18:Bend
ONCLUSION
followingcon
Thecriticalhfootingincreslope. Howefooting remslopes.Thecriticalbsignificantlyplanegroundcolumn rem
ndingmomenbuilding
dingmoment(15o)build
NS
nclusionsma
horizontal foeasessignificaver critical v
main almost
bendingmomfor slopingd.However cmains almost
ntdiagramofgframe
tdiagramofsdingframe
aybedrawnf
orcesandbenantlywithinvalues of versame for d
ment in thecground (15
criticalvaluet same for d
f planegroun
slopinggroun
fromthestud
ndingmomenncreaseingrortical reactiodifferent gro
column incre5o) comparedeof axial forcdifferent gro
d
nd
dy:
nt inoundon inound
easesd toce inound
slopes.Ttoconta
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BIOGRAPH
HY
Sujit KGraduateStructuralDepartmenEngineerinBhopal, MIndia
Dr. VivAssistantPEngineerinMANIT, BPradesh,In
Dr.AbhaAssociateEngineerinMANIT,BhPradesh,In
Kumar, PStude
Engineernt of Cng MANMadhya Prade
vek GaProfessor,Civng DepartmBhopal, Madhndia
aySharma,Professor,CingDepartmenhopal,Madhyndia
Postent,ringCivilNIT,esh,
arg,vilmenthya
ivilntya
SUJIT KUMAR et al. DATE OF PUBLICATION: SEPTEMBER 01, 2014
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