Time Period Analysis of Reinforced Concrete Framed Buildings

International Research Journal of Engineering and Technology (IRJET) e ISSN: 2395 0056

Volume: 09 Issue: 07 | July 2022 www.irjet.net p ISSN: 2395 0072

Time Period Analysis of Reinforced Concrete Framed Buildings

N. Ravikumar1 , CH. Durgarao2

1PG Student, Department of civil Engineering, Velaga Nageswara Rao (VNR) College of Engineering, (Approved by AICTE and affiliated to JNTUK, Kakinada), G.B.C. Road, Ponnur 522124, GUNTUR, A.P (INDIA).

2Assistant Professor, Department of civil Engineering, Velaga Nageswara Rao (VNR)College of Engineering, (Approved by AICTE and affiliated to JNTUK, Kakinada), G.B.C. Road, Ponnur 522124, GUNTUR, A.P (INDIA). ***

Abstract The approximate fundamental natural period of vibration in seconds of a moment resisting frames building without brick infill panels may be estimated by the following empirical expressions of IS 1893:2016

Ta = 0.075h0.75 for R.C. frame building

Ta

= =

0.085h0.75 0.09 h /√d for steel frame building for all other buildings

Computation of seismic base shear requires the fundamental natural period of vibration (T of the building. However, for the building configuration adopted and the construction material chosen, it is not always possible to exactly determine T fromtheoretical considerations, that is, through detailed dynamic analysis. Hence, empirical formulae obtained through experimentally observed behavior of buildings are utilized. A number of experimental studies were performed by various agencies of different countries and proposed period vs. height relationship for the estimation of the fundamental natural period of the building. Efforts arestill being made by various researchers to improve the code based expressions, as current code equations are predicting period values on the lowerside, which ultimatelyproduce higherbase shear. The aim of this study is to produce a period equation in order to predict the fundamental period of vibration of reinforced concrete buildings with moment resisting frames. Such buildings are considered in this study by analytically modeling 3D frames. For bare RC buildings, these 3D frames can be used adequately to estimate the period of vibration of the whole building in the principle direction in which these frames act. However, in a real building with infill panels, some of the frames are bare, some are fully in filled and some have infill panels with openings for windows and doors and it has been observed that infill masonry provides additional stiffness to the structure, but after a few second of earthquake shaking stiffness degradation is observed. Hence, the influence of infill panels is not considered.

building.Thefundamentalperiodistheimportantproperty of the building/structure for determination of the elastic demandand,indirectly,therequiredinelasticperformanceof thestructure.Inthecalculationoflateralforcesanddesign baseshearofabuilding,itisanimportantparametertobe considered. In the evaluation of the expected seismic load affectingthebuilding,theestimatedfundamentalperiodisan essential parameter, that’s why its precise estimation is important for the safety of the design procedure and consequently for the performance of the structure in the future. The Indian seismic code IS 1893(Part 1) 2016 providestheempiricalexpressionsof T ofthebuildingtaking its parameters; vertical dimension (H; height), types of structure,lateralforce resistingsystem,andinfillwalls,into prime consideration. These expressions are based on the recorded period of vibration of real buildings during the earthquake. Initially, the expressions were presented in termsofthenumberofstories(N)orheightofthebuilding (H),butlateron,thesameweredevelopedintermsofother considerationsalsoasmentionedabove.

The use of an empirical expression, the rational method (referring to dynamic analysis) and the experimental techniquesappliedonsimilarbuildings(which isprobably notdoneinusualpractice)aretheprimlyavailablewaysto estimation the value of T. In other words, in current provisionsofseismiccodes,theestimationofseismicforces with the help of design spectra requires either the use of available empirical equations for the fundamental period determination or more specifically detailed dynamic analysis.

But, the study of research works shows that the earlier attempts of the deriving formula of T was made using the recordingsoftheearthquakesandperformingthestudyof vibration on a limited number of buildings of a set of locations.Thederivedempiricalexpressionsof T basedon thesedatawereadoptedbymanydesigncodesofdifferent countries.

Key

Words: ReinforcedConcrete,Steelbuildings,Moment ResistingFramedBuildings

1.INTRODUCTION

Theearthquakedesignandanalysisofanyreinforced concrete structure requires an essential procedure of the estimation of the fundamental period of vibration of the

1.1 Objective of the study

 ThecharacterizationofthestructuralparametersofRC MRF buildings, affecting the fundamental period of reinforcedconcretemomentresistingframebuilding(RC MRF) comes under the preliminary objective of the study.

International Research Journal of Engineering and Technology (IRJET) e ISSN: 2395 0056

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The detailed analysis of the effect of the different parameters of structure including the characterized parametersistheintermediategoalofthestudy. 



The final objective of the work is to develop the expression of the time period(T) of the reinforced concreteframedbuildingsothattheexpressionmaybe capable enough to express the relation of T with the different structural members of the buildings in close vicinityoftheresultsofthedynamicanalysis.

2. METHODOLOFY



The sensitivity analysis has also been presented in the work to identify the weightage of the intensity of the effectoftheconsideredparametersontimeperiod. 

The validation analysis of the result of the developed expressionisalsoperformedbycomparingthemwith theresultsofdynamicanalysis.

In the previous study of literature, it has been already discussed thatthereisthescopeofconsiderationof thestructuralelementsotherthantheheightofthebuilding as the parameters in the analysis of ‘T’ of building. The presentcodeequationof ‘T’ givesitsconservativevalue,due towhich,thebaseshearcalculationsproduceitshighervalue, which tends for uneconomic construction due to higher sections of structural elements. The structural parameters discussed under the objectives of the study have been considered in the analysis of their effect on ‘T’ to fulfil the objective of the development of a period formula incorporating these parameters along with ‘H’. To achieve this aim, the analysis has been done as per the following adoptedmethodology.





The comparative study of the results of the developed equation and the proposed equations of different researchershasalsobeenpresented.

Based on the study of available research literature, the dependency of a fundamental time period (T) of the reinforcedconcrete(RC) momentresistingframed(MRF) building on other structural parameters(other than height ornumberof storey)can easily be observed.

1.2 Factors on the fundamental period of the building 

Slabthickness 

Dimensionsofthebuilding planorwidthofthe buildinginconsidereddirection 

Planareaofthebuilding. 

Stiffnessintermsofthetotalcross sectionalarea ofthecolumns 

Dimensionsofbeam 

Theratioofbeamwidthtodepth 

The number of panels in the longitudinal and transversedirection. 

Length of panel/bay in longitudinal and transversedirectionetc. 

Theratioofbaylengthtothetotalplandimension intheconsidereddirection 

Theratioofthetotalcross sectionalareaofthe columns to the base area of thebuilding.

Fig -1:Typicalplansofconsideredbuilding

Figure 1representthetypicalplansoftheconsidered buildingmodelswithbaysizes4×4,5×5,6×6,7×7, and8×8. L and B represent the dimension of the plan in respective directions,and, Lb isthelengthofthebay(m)inthecondered directionoftheplan.

2.1 Parameters consideration for analysis

Theconsidered RC framebuildingshavingsquare shapedintheplanareanalyzedusingtheanalysisanddesign software of structure STAAD.Pro V8i with the following assumptionmentionedinTables3.1.

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Table -2: Materialpropertiesanddesignparameters

Specifications Details

Fig 2:Typicalplanswith8×8gridsize

Table 1: Structuralconfigurations

Specifiions Details

Typeofstructure Multi storeyrigid jointedframes

No. of storey GFtoG+5, G+6toG+10

Floor height 3.6m

No. of grids 8×8,7×7,6×6, 5×5,4×4

Thickness of slab 150mm, 175mm, 200mm, 225mm, 250mm Bay length 4m,5m,6m,8m 0.3m×0.3m,0.4m×0.4m,

Size of columns 0.5m×0.5m,0.6m×0.6m, 0.7m×0.7m,0.8m×0.8m, Walls

(a) External 200mm100mm

(b) Internal Beamwidth 300mm Beam depth 600mm

Equivalent static lateral force method. Static analysis

Dynamic Usingresponsespectrum analysis method.

Seismic code provisions AsperIS1893(Part1):2016

Software used STAAD.Pro V8i

Material used

ConcreteM 25and ReinforcementFe 415. Ec 5000√fckN/mm2 fcr 0.7√fckN/mm2 Specific weight 25kN/m3 (R.C.C.)

Floor finish 1kN/m2

Imposed load 4kN/m2

Type of soil

Type II,(mediumsoil) {as per IS1893 (Part1) : 2016}

Load of waterproofing 2.5kN/m2

Specific weight of infill 20.00kN/m3 Seismic zone III

Zone factor, Z 0.16,Asper IS1893(Part1) :2016. Importance 1 factor, I Response reduction factor, R 5 Damping 5%

2.2 Structural Parameters

432 building models have been analysed to characterizethedifferentconsideredstructuralparameters, which influence the fundamental period of the building. Three building plans with grid size 7×7, 5×5, 4×4 are analyzed with column sizes 0.3m×0.3m, 0.4m×0.4m, 0.5m×0.5m, 0.6m×0.6m, 0.7m×0.7m, 0.8m×0.8m. For above mentioned building plans and column sizes, considered the length of the bay are 4m, 5m, 6m and 8m. Heightofbuildingisalsovariedfrom5.6mto41.6m,andslab thickness variesfrom150mmto250mmattheintervalof 25mm. The variation of the ratio of depth to width of the beamisdonefrom1.5to2.0atinterval0.1.Thus,thetotal casesofbuildingsforcharacterizationstudycomeoutas432. Eachparameterhasbeenanalysed bringingvariationinit,

International Research Journal of Engineering and Technology (IRJET) e ISSN: 2395 0056

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keepingotherparametersconstantatthesametime,tostudy theeffectofthatparameteron ‘T’.

2.3 Assumptions for analysis



Itisconsideredforanalysisthatearthquakeis not likely to occur simultaneously with high wind, maximumflood.

Table 3: TimePeriod(T): GridSize7×7,SlabThickness= 150mm

ColumnsSize







Thesymmetricalsquare shapedbuildingplans havebeenconsideredtoperformtheanalysis.

RCbuildingshavebeenconsideredwithspecial moment resistingframe.

Thesymmetryisalsomaintainedinthevertical geometryofthebuildingmodelandtheappliedloadings.

Floors/ Height

0.6m×0.6m 0.3m×0.3m Baylength 5m 4m 5m 4m PlanArea

35m×35m 28m×28m 35m×35m 28m×28m T(sec)







Sizesofthestructuralelementslikebeamsand columnswerealsokeptconstantforaparticularmodel.

Thesoil structureinteractionhasnotbeentaken intoconsiderationofanalysis.

Thejointsofthebeamsandthecolumnsarekept asrigidjoints.

G+5/(23.6m) 1.227 0.988 2.617 2.181 G+4/(20m) 1.026 0.826 2.208 1.838 G+3/(16.4m) 0.826 0.665 1.802 1.497 G+2/(12.8m) 0.627 0.505 1.397 1.159 G+1/(9.2m) 0.432 0.348 0.995 0.823 G.F./(5.6m) 0.247 0.198 0.602 0.495

Table 4: TimePeriod(T): GridSize8×8,SlabThickness= 150mm

ColumnsSize 0.5m×0.5m 0.4m×0.4m







The nodes at the footing level are assigned as fixedsupports.

The gross moment of inertia of the sectionsis considered for performing theanalysis.

Theloadingofslabsisappliedusingfloorload commandofthesoftware.

Floors/Height

Baylength

5m 4m 5m 4m PlanArea

35m×35m 28m×28m 35m×35m 28m×28m T(sec)





Theuniformlydistributedloadofbrickmasonry isappliedasamemberloadonthebeams.

Intheframes,noinfillwallsaremodelledinthe softwarefortheanalysis.

3. STUDY OF STRUCTURAL PARAMETERS

In this study report 432 different models of building configurations have been analysed to characterize the differentconsideredstructuralparameterstoidentify them with capacity to affect the fundamental period (T) of the building. The elements of building frame; slab thickness, columnsize,gridsize,beamsize,planareaandbaylengthin considereddirectionofplanhavebeentakenasparameters intoanalysis.Theanalysishas been carried out as per the configurations described in parametric specification and adopted computational methodology as described The followings are the tabulated results of time period values.

G+5/(23.6m) 1.45 1.17 1.817 1.486 G+4/(20m) 1.218 0.982 1.531 1.251 G+3/(16.4m) 0.988 0.796 1.247 1.017 G+2/(12.8m) 0.758 0.61 0.964 0.785 G+1/(9.2m) 0.531 0.427 0.683 0.555 G.F./(5.6m) 0.311 0.249 0.408 0.33

Thevariationoftheratioofdepthtowidthofthebeamis donefrom1.5to2.0atinterval0.1.Thus,thetotalcasesof buildings for characterization. Each parameter has been analysed bringing variation in itself, keeping other parametersconstantat the sametime,tostudytheeffectof that parameter on ‘T’. The above characterization process confirms the significant contribution of considered parameters affecting ‘T’ of building. Hence it supports for further detailed analysis of building models to study the intensity of effect of all considered parameters and its pattern.

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3.1 Fundamental parameters

Variousparametersaffectingthefundamentalperiodof vibration in seismic analysis have been characterized in previouschapter,andithasbeenobservedthroughdynamic analysisonvariousbuildingconfigurations,that,theheightof the building is not only the parameter, but following parametersalsoinfluencetheperiodofvibration:  Planareaofthebuilding  Totalcrosssectionalareaofthecolumnsofthe structure  Baylength  Numberofbay  Slabthickness  Baysize  Beamsections

Toobservetheeffectsofthesevariousparameters,1768 variousbuildingconfigurationshavebeenanalyzedkeeping abovementionedparametersasvariables.

3.2 Effect of column size on time period

Table 5: TimePeriod(T): forgridsize8×8,planarea(m) =48×48,Slabthickness(mm)=150,baylength(m)=6m S. No Floors/ Building height

Tim e Peri od ColumnsSize as per IS18 93

0.5m×0 .5m 0.6m×0 .6m 0.7m×0 .7m 0.8m×0 .8m

T(sec)

1 G+10/(4 1.6m) 1.22 9 2.814 2.531 2.387 2.302 2 G+9 /(38m) 1.18 4 2.566 2.305 2.171 2.089 3 G+8/(34. 4m) 1.06 5 2.32 2.081 1.956 1.876 4 G+7/(30. 8m) 0.98 1 2.075 1.857 1.741 1.665 5 G+6/(27. 2m) 0.89 3 1.829 1.634 1.526 1.459

Chart 1:VariationofTforgridsize8×8

4. CONCLUSIONS

1. It can be concluded that the present work exploresthescopeofimprovisationinexpressionsof timeperiodofvibrationgiveninseismicdesigncode IS1893 2016andpresentsthestudytoshowthatthe height alone, as a primary factor, seems to be inadequate to evaluate the timeperiod of vibration accurately.

2. Further, it can be suggested that the different structural parameters other than the height of the building, also with respect to the parameters characterizedinthisanalysis.

3. Theaffecttheperiodandcanbeincorporatedin the simplified expressions of the time period of vibration illustrated in the design codes, which are commonlyusedinseismicanalysis.

4. In this work, the analysis has been done for buildingsconsideringdifferentbaysizes,columnsizes, slab thickness, bay length, plan area, beam sizes etc. This improvement can provide better assessment of the time period supporting to economy in the structuraldesign.

5. Multiple non linear regression analysis was performedover2200periodvaluesobtainedthrough dynamic analysis with various considered combinationsofdifferentparameters.

6. The different empirical expressions have been developed by non linear regressionand sensitivity analysishasalsobeenpresented.

7. Itissuggestedthatthereisscopetoincorporate theseconsideredstructuralparametersintimeperiod

International Research Journal of Engineering and Technology (IRJET) e ISSN: 2395 0056

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formula given in Indian Standard Code IS1893 to estimatethevalue of ‘T’ closerto results of dynamic analysis.

8. So, for the enhancement of the capacity of availableapproximateformula,theworkpresentswith theresultsofdynamicanalysis,whichcanbeusefulfor the researchers, academicians as well as for the professionals.

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