research paper - ijerst 1: comparative study of sdof and tdof model of water tank[1] ... forces as...

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Int. J. Engg. Res. & Sci. & Tech. 2017 Pronoy Roy Chowdhury and Partha Ghosh, 2017

A CRITICAL STUDY OF SEISMIC BEHAVIOR OFR.C ELEVATED WATER TANKS ON SHAFTS TYPE

OF STAGING SYSTEM

Elevated water tanks are top heavy structures. These structures have an inherent tendency tooverturn under earthquake induced lateral forces. However it is important to keep such life linefacilities functioning in the post earthquake scenario. Thus such structures should be designedas earthquake resistant. In recent years elevated water tanks are constructed both on annularshaft and frame type of staging as per judgment of the Structural Engineer. But fromreconnaissance studies post earthquake it was found that shaft structures have relatively inferiorseismic performance in comparison to frame type of staging due to lack of redundancy anddifficulty in implementing ductile detailing in the shaft portion. In this paper an attempt shall bemade to make a comparative study of seismic design of such elevated water tanks with shaftstaging against frame staging with special reference to seismic codes.

Keywords: Elevated water tanks, Shaft staging, Seismic design, Earthquake resistant design,Water tank

INTRODUCTIONElevated water tanks are top heavy invertedpendulum structures. These structures have aninherent tendency to overturn under earth quakeinduced lateral forces. However it is important tokeep such life line facilities functioning in the post-earthquake scenario. Thus such structuresshould be designed as earthquake resistant. Inrecent years R.C.C elevated water tanks aresupported on annular shaft has become popularamong water supply Engineers due to the relative1 Assistant Professor, Department of Construction Engineering, Jadavpur University, Saltlake campus, Kolkata, India.2 Ph.D. Student, Executive Engineer PHE Directorate, Govt. of W.B, 185/186 Shibpur Road Howrah, West Bengal, India, PIN-

711102.

Int. J. Engg. Res. & Sci. & Tech. 2017

ISSN 2319-5991 www.ijerst.comVol. 6, No. 1, February 2017

© 2017 IJERST. All Rights Reserved

Research Paper

ease of construction and lesser time involved inconstruction in comparison to frame type ofstaging. But shaft structures have relatively inferiorseismic performance in comparison to frametype of staging due to lack of redundancy anddifficulty to implement ductile detailing in the shaftstaging portion. Many of shaft type elevated watertanks have failed in recent earthquakes, at Killari,Jabalpur and Bhuj in India (see Figures 2a-2d). Inthis dissertation an attempt has been made tocritically study seismic design of such elevated

Partha Ghosh1 and Pronoy Roy Chowdhury2*

*Corresponding Author: Pronoy Roy Chowdhury [email protected]

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water tanks with shaft type staging against framestaging, with special reference to the Indianseismic code. Elevated tanks have either on shaftor frame staging which has failed due toearthquake at various places of India which hasbeen recorded in literature (Rai and Singh, 2004).Reinforced concrete shaft staging for water tanksare designed typically to sustain gravity loads andsome moderate lateral loads. Such shaft stagingsystems should be so designed so that theybehave elastically in the event of severeearthquakes. Since many such tanks has failedin the past due to earthquakes it has become acrying need of the hour to properly design suchstructures. It has been found (Rai, 2003) that themajor cause attributed to the failure of elevatedwater tank with shaft staging are circumferentialcracking of concrete near the base zone due toflexural tension. Whereas elevated water tankson frame staging may fail due to shear of beamand column members of the staging system underseismic jolts.

It is alarming to find that many elevated tankstructure actually designed for earthquake forceshave failed, raising eyebrows regarding thesanctity of the Indian Earthquake codes. This widecriticism has invited alternative suggestion fromvarious researchers (Rai, 2003). But certainresearchers (Vamshidhar and Jain, 2007) are ofthe opinion that elevated water tanks designedas per Indian codes in the past has performedsuccessfully in many cases under severeearthquake forces so the existing codes areadequate. To support their thought the otherschool has sited few example water tanks actuallyconstructed in at various places in India. TheSingle Degree of freedom (SDOF) model assuggested in the existing code is anoversimplification of the problem where all the

higher modes are neglected. The SDOF modelingsuggested in the relevant Indian earthquake designcode IS:1893-1984 forms such a structural modelso that the fundamental period of the structure is ashort period system. Hence the structure shallattract larger seismic forces. It is found that SDOFmodel actually overestimates the seismic forces,experimental verifications (Boyce, 1973) havesubstantiated the findings and it is also depicted inpaper (see Figure 1). But multi-degree freedommodel gives the effect of the higher modes and

Figure 1: Comparative Study of SDOFand TDOF Model of Water Tank[1]

Figure 2a: Collapsed 265 kL Water Tankin Chobari Village about 20 km from the

Epicenter, The Tank was Approx. Half FullDuring the Bhuj Earthquake (2001)

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hence ensures a more accurate analysis of lateralforces. Such modeling also gives an idea aboutflexibility of the structural system, in this case thestaging part. In fact the fundamental period beinglarger the structure shall represent a more flexiblesystem and response shall be much lower ascompared to SDOF model.

Generally in earthquake analysis it iscustomary to consider that the structure isfounded on solid rock, but in actual practice thereis interaction of the structure with soil. It has beenfound (Dutta and Dutta, 2003) that if suchinteraction is taken into account then there islengthening in the fundamental period of the tankstructure. Circular Raft foundations are typicallyused for elevated reservoirs; in one of the worksattempt has been made to model the interactionbehaviour of the raft slab and the underlyingfoundation soil. Springs with three types ofstiffness are used to model three degrees offreedom namely translational, rocking andtorsional degrees of freedom. The relevantexpressions of such stiffness are given inliterature (Rai and Singh, 2004). R.C.C elevatedwater tanks of various capacities and differentheight of staging system both on shaft and frametype of staging shall be studied against seismicforces as per I.S codes for SDOF, two degree offreedom model (TDOF), multi-degree of freedom,ball and stick model and finite element model andthe cases shall be compared so as to identify therelative efficiency of each of the modellingscheme. The work may act as an elaborateguideline to Structural Engineers while designingsuch class of structures.

STRUCTURAL MODELINGAND ANALYTICALAPPROACHHousner (1963) proposed a two degree of

Figure 2c: Killery Earthquake Tank of KauthaCollapsed Straight Down into its Crumpled

Supports, Circumferential Displacementof about 0.5 m Suggests that Rotational

Vibration Led to its Collapse

Figure 2b: This Type of Failure Occurs Dueto High Shear Force in the End of Beams, 45°

Angle Shear Cracks Appear in the PlasticJoints, This Type of Failure is Observedin Chile Earthquake in South Americain 1960 with a Magnitude M = 8.5,

for Elevated Water Tank

Figure 2d: 200 kL Bhachau Water TankDeveloped Tension-Flexural Cracks Up toOne-Third Height of the Staging, Severe

Cracking at the Junctions of the First Two ‘Lift’

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freedom model where elevated water tank withits liquid content has been modeled as a twodegree of freedom system. These types of tanksare categorized under “inverted Pendulum” classof structure. When the surmounted tank filled withwater is subjected to seismic shaking,hydrodynamic pressure develops. Broadly thehydrodynamic pressure may be classified in twocategories (i) Impulsive pressure, and (ii)Convective pressure respectively. The portion ofthe liquid in the inner part of the tanks acts withthe body of the tank walls and creates theimpulsive pressure. The other part of the liquidwhich is near the liquid surface exhibits a sloshingmotion. The oscillatory motion developsconvective pressure on the walls and base of thetank. The two classifications of hydro-dynamicpressures have been represented by a simplemechanical analogy which is represented in theFigures 3a-3d. The impulsive pressure isrepresented as a liquid mass rigidly fixed to thewalls of the tank by rigid links as impulsive massmi and the convective pressure is representedby mass mc attached with a convective spring to

the impulsive mass of stiffness say Kc. Forelevated water tanks the mass of the stagingsystem is also to be taken into consideration asms. As per IS: 1893-1984 vide clause no. 5.2.4 l/3rd of the staging mass should act together withthe weight of the full tank container. The mass mi

is attached to the base of the staging system viaa vertical member of stiffness that of the stagingsystem.

The expressions of mi, mc and Kc are givenbelow (Newmark and Rosenblueth, 1971).

...(1)

...(2)

...(3a)

impulsive and convective masses are located ata distance hi and hc respectively from the bottomof the tank container, the expressions for whichare as follows

...(3b)

...(3c)

The time period for the impulsive mode ofvibration is given by

T0 = 2((mi + ms)/Ks) ...(4)

Time period should be calculated for tank fulland tank empty condition of the water tank.

In case of the convective mode of vibration thetime period is

Tc = 2((mc)/Kc) ...(5)

Analysis due to water sloshing induced impacton overhead liquid storage structures has been

Figure 3: Two Mass Idealization of ElevatedWater Tank[4]

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Lateral stiffness of the frame type staging isobtained in the similar way as for building frames.

The natural period for the SDOF model assuggested by IS: 1893-1984 vide clause no. 5.2.3is given by the formula.

T = 2(/g) ...(7)

where = the static horizontal deflection at thetop of the tank under a static horizontal force equalto a weight W acting at the centre of gravity of thetank.

and g = Acceleration due to gravity.

The horizontal seismic force as per the IS:1893-1984 is given by ahW

where ah = design horizontal seismic co-efficientwhich is given by

ah = ßIFo Sa/g ...(8)

where ß= A coefficient depending upon the soil-foundation system, I = A factor dependent uponthe importance of the structure = 1.5 for elevatedwater tanks, F0= Seismic Zone factor for averageacceleration spectra and Sa/g = Averageacceleration co-efficient as read from Figure 2 ofthe code for appropriate natural period anddamping of the structure.

Natural period of the SDOF model should beassessed for tank full and tank empty condition.

However from the recent version of the Indianseismic code IS: 1893-2002 part-(l) we have thatdesign seismic base shear as

VB= AhW ...(9)

where horizontal Seismic co-efficient is given by

Ah = Z/2 x Sa/g x I/R ...(10)

where Z = zone factor, I = importance factor andR = response reduction factor

recently done by researchers (Muthu Vijay andAmarprakash, 2014) elsewhere.

The behaviour of the shaft staging system ofthe elevated tank under lateral earthquake forceis like a flexural beam. Damage surveys have alsorevealed that the shaft staging system mainly failsby circumferential cracking near the base bytension flexure mode (Rai, 2003). Researchers(Sood and Singh, 1983) have insisted uponmodeling the shaft as a cantilever beam attachedas the base (Figure 4).

Thus Lateral stiffness of the shaft type staging

Kstg = 3EI/13 ...(6)

where 1 = length of the shaft, E = modulus ofelasticity, I = moment of inertia of the section. Incase of annular section we have

I = II(D14-D2

4)/64 where D1 and D2 are theoutside and the inside diameter of the annularshaft respectively.

Figure 4: BMD of Elevated Water Tankon Shaft[17]

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Sa/g = Average acceleration co-efficient asread from of IS: 1893 part (l)-2002 for appropriatenatural period and damping of the structure.

The importance factor selected I = 1.5 whichas per IS: 1893 part (l)-2002 is for importantstructures, which should remain in functionalcondition after an earthquake such as hospital,schools, etc. Elevated water tanks being a lifelinefacility and should remain in functional conditionto ensure water supply by gravity during the powercut period has been classified under this class ofimportance factor.

The parameter Response Reduction factor (R)represents the ratio of maximum seismic forceon a structure during specified ground motion if itwere to remain elastic to design seismic force.Thus actually (R) is used to reduce seismic forceto obtain design force. It has been found (Jaiswalet al., 2007) that the reduction is dependent onover strength, redundancy and ductility and it isidentified that shaft type elevated reservoir havecomparatively lower redundancy, than elevatedwater tanks with frame type of staging which is ahighly redundant space frame structure. Seismicdesign codes have specified different values ofResponse reduction factors for elevated watertanks like structure. However there is no specificprediction regarding shaft type of staging so lowerbound value has been suggested in view the lowerredundancy value of the structure. In thisconnection various international codes areavailable regarding seismic design of water tanks.Works on comparative discussions on suchcodes are available in literature (Jaiswal et al.,2007). Draft version of the Indian code forearthquake resistant design of water tanks arenow available (IITK- GSDMA August, 2005), thereinit has been suggested to adopt two mass modelof the elevated water tank (Housner, 1963). In the

above method the two mass idealized model ofthe elevated water tank is represented as anequivalent uncoupled system (Priestly et al.,1986). Both of this system now becomesequivalent SDOF system, which are shown infigure no.3. However such uncoupling is permittedwhen the period, for the impulsive and theconvective modes differ by at least 2.5 Sec. Thedraft code recommends response reductionfactor of Tank supported on RC shaft RC shaftwith two curtains of reinforcement, each havinghorizontal and vertical reinforcement as 1.8. Againfor Tank supported on RC frame and the framedoes not conform to ductile detailing, i.e., OrdinaryMoment Resisting Frame (OMRF) responsereduction factor is 1.8, for frames conforming toductile detailing, i.e., Special Moment ResistingFrame (SMRF) the response reduction factor is2.5. The Indian seismic code recommendsresponse spectrum analysis of a SDOF modelas a cantilever fixed at the base. Stiffness of theshaft staging is relatively higher so it is expectedthat SDOF model as per IS: 1893-1984 versionshall yield a relatively short period system. Suchshort period systems, generally pertains toacceleration sensitive region of the responsespectra. Also IS: 1893-1984 neglects theconvective component of hydrodynamicpressure. Again the Indian standard for stagingsystem of elevated water tanks IS: 11682-1985recommends the following for calculation ofseismic forces “wherever required the effect ofsurge due to wave formation due to water shouldbe considered” which is mutually contradictory.In the acceleration sensitive region of thespectrum lengthening of fundamental period ofthe structure may sometime cause increase inresponse, however in many other casesresponse may also reduce if the periodlengthening is very large. Some researchers have

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suggested to adopt multi-degree of freedommodel for seismic analysis of shaft supportedelevated water tanks, where the contributions ofthe various higher modes of vibration has beentaken into consideration. Dynamic analysis usingresponse spectrum analysis has been assortedto and the contribution of various modes has beencombined with SRSS method. Researchers(Memari and Ahmadi, 1992) has also studiedfailure of shaft supported R.C elevated watertanks during Manjil–Roudbar earthquake in 1990Iran. They have studied the behaviour of watertowers using finite element method. Thus itappears that structural models of elevated watertanks supported on shaft should be studiedthrough SDOF, TDOF, MDOF and FEM modelsto get a comprehensive idea about the seismicbehaviour and vulnerability of such structures.Design analysis and comparison of INTZ typewater tank for different wind speed and seismiczones as per Indian codes has also been doneby researchers (Singh and Mohammed, 2015)elsewhere.

STRUCTURES STUDIEDFive nos. R.C Elevated water tanks of Intz typeconstruction has been studied in this paper. Thecapacity of the tank container varies from 250Cum, 350 Cum, 600 Cum, 750 Cum and 1000Cum. It is assumed that the tanks are constructedof M30 grade concrete to ensure water tightnessand Fe 415 grade steel has been used. It isassumed that the tanks are constructed on shaftas well as frame type of staging. The heights ofthe staging are varied through 15 m, 20 m, and25 m respectively for all the tanks under study.SDOF model as suggested in the IS 1893-1984version shall be studied. Simultaneously Twodegree freedom model as proposed by Housnerand adopted by IITK-GSDMA guideline shall also

be studied. For shaft type of staging the lateralstiffness of the shaft has been modelled ascantilever, Kstg = 3EI/13 whereas for frame type ofstaging the lateral stiffness of the columns havebeen used as Kstg = 12EI/13. Where 1 = Length ofthe shaft, E = modulus of elasticity, I = momentof inertia of the section. It has been assumed thatthe horizontal bracings are very stiff and they donot undergo any deflection under lateral seismicload. Lumped mass model has been studiedusing response spectrum analysis in STAADPRO software. The shaft has been divided intofive small portions vertically and the mass of eachof the portions has been lumped, also the massof the tank container with and without water inthe tank has been lumped at appropriate locationsand free vibration analysis has been performedto take into account the contribution of the highermodes of vibration, which are neglected in theSDOF analysis. The lumped masses areconnected with beam elements which haveequivalent sectional area to that of the shaftstaging or the three dimensional frames. Theshaft and the frame elements are conceived assprings. The columns at a particular level ofbracing are conceived as springs connected inparallel. Whereas the lateral stiffness ofsubsequent bays of columns are conceived assprings connected in series. The tanks areassumed to be founded on hard rock, for thepurpose of the present study. Detailed sectionaldimensions of the tanks of five different capacitiesand staging systems are tabulated (Table 1) withthe lateral stiffness of their staging systems intabular form (Table 2) for ready reference. Besidethis tabular representation of fundamental timeperiod of the various tanks with different height ofthe staging are given for all the various analyticalmodels. The variation of Bending Moment (BM)at the base for all the five models, which the

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Table 1: Sectional Dimensions of the R.C Elevated Water Tanks of Five Different Capacitieson Shaft and Frame Type Staging

Top Dome 100 mm thick Top Dome 100 mm thick

Top Ring Beam 300 mm x 200 mm Top Ring Beam 300 mm x 200 mm

Cylindrical Wall 200 mm thick Cylindrical Wall 200 mm thick

Bottom Ring Beam 500 mm x 300 mm Bottom Ring Beam 500 mm x 300 mm

Circular Ring Beam 400 mm x 300 mm Circular Ring Beam 400 mm x 300 mm

Bottom Dome 150 mm thick Bottom Dome 150 mm thick

Conical Dome 250 mm thick Conical Dome 250 mm thick

Shaft Wall 150 mm thick Bracing 300mm x 300mm

Column 8 nos. 650 mm dia




Bottom Ring Beam 500 mm x 350 mm Bottom Ring Beam 500 mmx 350 mm




Shaft Wall 150 mm thick Bracing 300 mm x 300 mm

Column 8 nos. 660 mm dia








Shaft Wall 150 mm thick Braces 500 x 400 mm

Columns 8 nos. 670 mm dia

Component Details

Capacity of Tank = 600 cum

Shaft Type Staging

Component Details


Frame Type Staging

Component Details


Shaft Type Staging

Component Details


Frame Type Staging

Component Details


Shaft Type Staging

Component Details


Frame Type Staging

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Shaft Wall 150 mm thick Braces 500 x 400 mm



Top Ring Beam 300 x 300 mm Top Ring Beam 300 mm x 300 mm


Bottom Ring Beam 1200 x 600 mm Bottom Ring Beam 1200 mm x 600 mm

Circular Ring Beam 1200 x 600 mm Circular Ring Beam 1200 mm x 600 mm



Shaft Wall 200 mm thick Braces 500 mm x 500 mm


Component Details


Shaft Type Staging

Component Details


Frame Type Staging

Component Details


Shaft Type Staging

Component Details


Shaft Type Staging

Table 1 (Cont.)

Table 2: Lateral Stiffness of the Staging System of Tanks

15 m 20 m 25 m

Frame 44863.51 33647.64 26918.11

Shaft 249401.04 106261.25 54730.25

Frame 47688.71 35766.53 28613.23

Shaft 262669.06 112050.87 57754.69

Frame 50645.29 37983.97 30387.17

Shaft 313495.19 133895.3 69064.72

Frame 53737.26 40302.94 32242.36

Shaft 361348.43 155452.55 80535.47

Frame 56968.69 42726.52 34181.21

Shaft 476816.43 207072.94 107895.94

600

750

1000

Capacity of Tank (cum) Staging TypeStiffness (KN/m)

250

350

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structural staging shall be subjected to due to theapplication of seismic shear, shall also berepresented in a graphical form against height ofstaging system for both shaft and frame type ofstaging. This shall essentially indicate variationin seismic shear values, bending stress in thetank staging due to cantilever type bending withvariation in the staging height of tank.

RESULTS AND DISCUSSIONFrom the tabular representation (Table 2) of thelateral stiffness it is found that as the height of thetank staging increases from 15 m to 25 m both forshaft and the frame the lateral stiffness decreases.Drawing comparison between the two, lateralstiffness of the shaft is greater than frame type ofstaging. It is seen from the tabulated data on timeperiod (Tables 3, 4 and 5) that as the staging height

increase there is lengthening in the natural periodof the system. The period is much longer in thetank full condition than in tank empty condition. Forshaft type of staging system the period of thesystem is much shorter in comparison to the frametype of staging. The convective mode of the TDOFmodel is of much longer period in comparison tothe impulsive mode. It is also found that theimpulsive period is smaller in comparison to theperiod of the SDOF model. In the MDOF modeland the FEA model contribution of the highermodes are obtained (Figures 5a and 5b) and itprovides for a more elaborate structural analysis.The graphical representation showing variation inB.M at the base of the tank with variation in heightof the staging is given in graphs (1, 2, 3, 4, 5, 6, 7and 8) for tank full and tank empty condition for allSDOF, TDOF, MDOF and FEA models.

ImpulsiveMode

ConvectiveMode

Mode 1 Mode 2 Mode 3 Mode 1 Mode 2 Mode 3

Tank Full 0.261 0.224 0.344 0.027 0.011 0.405 0.055 0.038

Tank Empty 0.167 0.166 0.209 0.024 0.009 0.222 0.058 0.04

Tank Full 0.406 0.349 0.497 0.04 0.015 0.568 0.066 0.05

Tank Empty 0.265 0.264 0.307 0.036 0.013 0.32 0.069 0.05

Tank Full 0.574 0.496 0.67 0.056 0.02 0.751 0.077 0.064

Tank Empty 0.381 0.38 0.421 0.051 0.018 0.438 0.08 0.063

ImpulsiveMode

ConvectiveMode


Tank Full 0.615 0.526 0.807 0.059 0.202 1.443 0.472 0.148

Tank Empty 0.391 0.391 0.487 0.053 0.018 0.942 0.488 0.152

Tank Full 0.721 0.62 0.877 0.068 0.024 1.962 0.594 0.238

Tank Empty 0.468 0.468 0.541 0.062 0.021 1.29 0.606 0.24

Tank Full 0.817 0.706 0.95 0.078 0.027 2.441 0.704 0.343

Tank Empty 0.541 0.541 0.596 0.072 0.025 1.622 0.713 0.337

3.137

3.137

3.137

250 Frame

15

20

25

3.137

3.137

3.137

TankCondition

Time Period (sec)

SDOFModel

TDOF Model MDOF Model FEA Model

250 Shaft

15

20

25

Capacityof Tank(cum)

StagingType

Height ofStaging

(m)


StagingType

Height ofStaging

(m)

TankCondition

Time Period (sec)

SDOFModel


Table 3: (a) and (b) Showing Variation in Time Period for 250 cum Capacity of Tank with BothTypes of Staging System, Height of Staging has been Change from 15 m Through 25 m

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ImpulsiveMode

ConvectiveMode


Tank Full 0.349 0.314 0.548 0.038 0.013 0.613 0.084 0.047

Tank Empty 0.211 0.211 0.315 0.03 0.011 0.324 0.087 0.057

Tank Full 0.538 0.484 0.76 0.051 0.018 0.836 0.098 0.059

Tank Empty 0.329 0.329 0.442 0.043 0.015 0.446 0.101 0.066

Tank Full 0.754 0.68 0.994 0.068 0.024 1.083 0.111 0.073

Tank Empty 0.467 0.466 0.585 0.059 0.02 0.586 0.114 0.077

ImpulsiveMode

ConvectiveMode


Tank Full 0.868 0.782 1.353 0.087 0.025 1.527 0.564 0.15

Tank Empty 0.526 0.526 0.777 0.071 0.022 0.912 0.575 0.15

Tank Full 1.011 0.911 1.421 0.095 0.03 1.927 0.681 0.22

Tank Empty 0.621 0.621 0.827 0.081 0.026 1.154 0.689 0.215

Tank Full 1.039 1.029 1.498 0.104 0.034 2.298 0.785 0.295

Tank Empty 0.708 0.708 0.882 0.091 0.03 1.385 0.792 0.2843.365

600 Frame

15

20

25

3.365

3.365

3.365

3.365

3.365

TankCondition

Time Period (sec)

SDOFModel


600 Shaft

15

20

25


StagingType

Height ofStaging

(m)


StagingType

Height ofStaging

(m)

TankCondition

Time Period (sec)

SDOFModel



ImpulsiveMode

ConvectiveMode


Tank Full 0.293 0.249 0.4 0.029 0.011 0.468 0.064 0.04

Tank Empty 0.179 0.178 0.231 0.025 0.009 0.245 0.067 0.045

Tank Full 0.454 0.387 0.572 0.042 0.016 0.65 0.076 0.052

Tank Empty 0.282 0.281 0.336 0.037 0.013 0.348 0.079 0.054

Tank Full 0.639 0.548 0.765 0.058 0.021 0.855 0.087 0.066

Tank Empty 0.404 0.403 0.458 0.052 0.018 0.469 0.09 0.654

ImpulsiveMode

ConvectiveMode


Tank Full 0.689 0.586 0.932 0.065 0.022 1.279 0.451 0.144

Tank Empty 0.42 0.42 0.538 0.056 0.019 0.783 0.464 0.146

Tank Full 0.805 0.688 1.005 0.074 0.025 1.636 0.551 0.217

Tank Empty 0.501 0.501 0.591 0.066 0.224 1.008 0.561 0.214

Tank Full 0.911 0.782 1.085 0.084 0.029 1.967 0.643 0.296

Tank Empty 0.578 0.578 0.643 0.075 0.025 1.226 0.651 0.285

3.334

3.334

3.334

0.334

3.334

350 Frame

15

20

25

Capacityof Tank

(cum)


StagingType

Height ofStaging

(m)

TankCondition

Time Period (sec)

SDOFModel


FEA Model

350 Shaft

15

20

25

3.334

StagingType

Height ofStaging

(m)

TankCondition

Time Period (sec)

SDOFModel

TDOF Model MDOF Model

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ImpulsiveMode

ConvectiveMode


Tank Full 0.377 0.34 0.604 0.041 0.013 0.683 0.101 0.054

Tank Empty 0.242 0.242 0.369 0.032 0.011 0.371 0.104 0.062

Tank Full 0.578 0.521 0.832 0.054 0.018 0.923 0.118 0.066

Tank Empty 0.374 0.374 0.514 0.045 0.016 0.509 0.12 0.071

Tank Full 0.807 0.729 1.084 0.07 0.024 1.187 0.133 0.079

Tank Empty 0.526 0.526 0.676 0.06 0.021 0.665 0.135 0.081

ImpulsiveMode

ConvectiveMode


Tank Full 0.979 0.882 1.563 0.097 0.027 1.68 0.675 0.157

Tank Empty 0.63 0.63 0.955 0.079 0.024 1.041 0.68 0.151

Tank Full 1.138 1.027 1.628 0.104 0.032 2.107 0.809 0.225

Tank Empty 0.738 0.738 1.005 0.088 0.028 1.311 0.813 0.215

Tank Full 1.28 1.157 1.71 0.112 0.037 2.504 0.929 0.299

Tank Empty 0.838 0.838 1.066 0.098 0.032 1.567 0.932 0.2843.558

750 Frame

15

20

25

3.558

3.558

3.558

3.558

3.558

TankCondition

Time Period (sec)

SDOFModel


750 Shaft

15

20

25


StagingType

Height ofStaging

(m)


StagingType

Height ofStaging

(m)

TankCondition

Time Period (sec)

SDOFModel



ImpulsiveMode

ConvectiveMode


Tank Full 0.387 0.355 0.647 0.044 0.013 0.725 0.113 0.062

Tank Empty 0.255 0.255 0.406 0.034 0.011 0.398 0.116 0.07

Tank Full 0.59 0.542 0.888 0.057 0.018 0.97 0.132 0.073

Tank Empty 0.392 0.392 0.558 0.046 0.016 0.539 0.134 0.078

Tank Full 0.821 0.755 1.148 0.072 0.024 1.238 0.148 0.085

Tank Empty 0.548 0.548 0.727 0.06 0.021 0.698 0.151 0.087

ImpulsiveMode

ConvectiveMode


Tank Full 1.121 1.028 1.851 0.11 0.027 1.955 0.81 0.166

Tank Empty 0.739 0.739 1.161 0.088 0.025 1.23 0.813 0.155

Tank Full 1.3 1.194 1.93 0.118 0.034 2.451 0.972 0.233

Tank Empty 0.863 0.863 1.221 0.097 0.03 1.548 0.975 0.219

Tank Full 1.461 1.343 2.016 0.125 0.039 2.904 1.115 0.308

Tank Empty 0.976 0.976 1.286 0.106 0.035 1.843 1.117 0.2913.716

1000 Frame

15

20

25

3.716

3.716

3.716

3.716

3.716

TankCondition

Time Period (sec)

SDOFModel


1000 Shaft

15

20

25


StagingType

Height ofStag ing

(m)


StagingType

Height ofStag ing

(m)

TankCondition

Time Period (sec)

SDOFModel


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Figure 5b: Typical Mode Shapes of First ThreeModes for Elevated Tank with Finite Element

Model

Mode 1 Mode 2 Mode-3Fig. 5(a) Typical mode shapes of first threemodes for elevated tank with lumped massmodel

Figure 5a: Typical Mode Shapes of First ThreeModes for Elevated Tank with Lumped Mass

Model

Mode 1 Mode 2 Mode 3

From the limited scope of study followingdiscussions may be elaborated below.

1) The shaft type staging system generates amore rigid system in comparison to the frametype of staging system. As the shaft staging isa relatively shorter period system.

2) It is seen that as the height of the stagingsystem increases the fundamental period ofthe elevated tank system lengthens for boththe type of staging system.

3) As the shaft staging appears to be more rigid,the natural period of the system is in theacceleration sensitive zone of the responsespectrum. A slight variation in the fundamentalperiod may widely affect the design seismiccoefficient values.

4) As the tank container increases in capacity thefundamental period of the system alsoincreases.

5) With increase in height and mass of the tankcontainer the fundamental period alsoincreases. For longer period system, theseismic behavior is governed by thedisplacement sensitive character. Thus withlateral thrust of the seismic force there is

significant lateral displacement inducing P-effect.

6) The two degree of freedom model is animprovement as it takes into consideration theconvective component of vibration generateddue to seismic force induced by sloshing ofwater in the tank container. But the convectiveperiod is a much longer period and hence thecorresponding ordinate of the responsespectra is generally much lesser. Thus thecontribution of the convective mode isgenerally meager in comparison to theimpulsive mode. Thus it appears for smallercapacity tanks SDOF model may besufficiently used without any major error inanalysis (issue was more elaboratelydiscussed by Chandrasekaran and Jaikrishna,1965). The major lateral thrust is contributedby the impulsive mode. This lateral thrustinduces B.M at the tank base causing bothdirect and bending stresses in the shaft. Directstress in induced due to the vertical loading.This induced B.M generates circumferentialtension cracks. With load reversals duringseismic events this heavy B.M at the base ofthe shaft induces plastic hinge which opens

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Graph Showing Variation of B.M at the Base of Shaft Staging Due to Seismic Base Shearfor Elevated Water Tank with Variation in Staging Height Considering IS 1893-2002 Seismic

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Graph Showing Variation of B.M at the Base of Shaft Staging Due to Seismic Base Shearfor Elevated Water Tank with Variation in Staging Height Considering IS 1893-1984 Seismic

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Graph Showing Variation of B.M at the Base of Frame Type Staging Due to Seismic Base Shearfor Elevated Water Tank with Variation in Staging Height Considering IS 1893-2002 Seismic

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Graph Showing Variation of B.M at the Base of Frame Staging Due to Seismic Base Shearfor Elevated Water Tank with Variation in Staging Height Considering IS 1893-1984 Seismic

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up the circular ties which binds the longitudinalreinforcement in the shaft and may causecatastrophic failures by crushing of concreteand bulging out of reinforcements. For biggesttank capacities however the convectivesloshing of water induces considerable hydro-dynamic forces in the in the walls and base ofthe tank container. But the code allows thatfor transient loads such as wind andearthquakes a 331/3 % increase in permissiblestresses may be considered during design.Thus as the factor safety against hydro-dynamic stresses in tank walls and floorsincreases the designer may in general neglectthe convective component of vibration on thepremise of this additional factor of safety.

7) It has been found from the graphicalrepresentation that the response spectra of IS1893-1984 version generates relatively lesservalue of design seismic coefficient in comparisonto that what is obtained from 2002 version.

8) However of all the analytical model studied itis found from graphs that the SDOF modeladopting 2002 codal provisions are generallyon the higher side for all tank capacities in tankfull condition. Among the frame and the shafttype of staging system the B.M obtained is thehighest for the shaft staging type elevatedtanks. In most of the cases empty conditionsyields lesser B.M at the tank base than the tankfull condition. As the height of the tankincreases bending moment also increases atthe tank base due to greater lever arm of theover turning couple.

CONCLUSIONThe results obtained from such limited studythough not exhaustive but may be considered asindicative of the following conclusions.

• SDOF model of the elevated water tanks onshafts yields a short period system and henceattract more seismic forces in comparison tothe frame type staging system. Thus it is betterto adopt frame type staging for elevated watertanks because it is a three dimensional spaceframe and ductile detailing may beimplemented at the beam-column junction ofthe staging. But shaft is relatively easy toconstruct in lesser time using slip form thanbeam column staging. Thus R.C elevatedtanks on shafts are becoming popular choicefor Structural Engineers.

• TDOF model is structurally more accuratethan SDOF model. But for smaller tanksSDOF model may be sufficient as hydro-dynamic pressure on the tank walls shallconsiderable only for the largest capacitytanks.

• The structural engineers should preferably gofor all types of analytical models such asSDOF, TDOF, MDOF and FEA model and findthe worst possible B.M values at the base ofthe tank and logically decide the appropriatevalue of B.M which should be adopted fordesign. FEM approach naturally provides themost elaborate analytical model and the modeshapes gives a comprehensive idea about thedeflected shape of the structure under seismicjolts. Such deflected patterns give fairly goodopportunity to the structural designer toimplement appropriate detailing in the tankstaging to ensure protection against severeseismic jolts. MDOF model gives better ideaabout the flexural behavior of the tank stagingsystem.

• Structurally elevated water tanks on shafts faildue to circumferential tension cracks at thebase of the shaft where B.M due to lateral

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seismic jolt is maximum. A single plastic hingemay cause failure. Whereas frame stagingbeing a highly indeterminate structure sufficientnos. of plastic hinges should form to convert itinto a mechanism before failure. From thispoint of view frame staging system is usuallypreferred.

It is grossly concluded from discussion thatshaft type of staging is much more prone tocollapse under seismic forces thus elevated watertanks on shafts must be carefully designedconsidering all service loads and off courseincluding seismic forces. It must also be checkedfor wind forces.

ACKNOWLEDGMENTThe authors gratefully acknowledge, all thoseresearchers, whose papers and figures havebeen referred and adopted in this paper. Thedocument presented over here is purely in theacademic interest. The corresponding authorspecially acknowledges the kind guidance of hisPhD supervisor and senior author Dr. ParthaGhosh, and a Structural Engineer Sanku Mondalfor cross checking calculations and someinteractive discussion during the course of doingthe work.

REFERENCES1. Boyce W H (1973), “Vibration Test on a

Simple Water Tower”, Proceedings of 5th

World Conference on EarthquakeEngineering, Vol. I, pp. 220-225, Rome.

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5. IBC (2000), “International Building Code”,International Code Council, Falls Church, VA.

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8. IS: 1893 (Part-I) (2002), “Indian StandardCriteria for Earthquake Resistant Structures,Part-I, General Provisions and Buildings”,Bureau of Indian Standards, New Delhi, India.

9. IS: 1893-1984, “Indian Standard Criteria forEarthquake Resistant Design of Structures”,Bureau of Indian Standards, New Delhi, India.

10. IS: 11682-1985 (Reaffirmed in 1998), “IndianStandards Criteria for Design of RCCStaging for Overheard Water Tanks”, Bureauof Indian Standards, New Delhi, India.

11. Jain A and Vamsidhar S (2007), “Analysis ofWater Tanks in Accordance with IS: 1893-Part 2 Draft Code”, Indian Concrete Journal,January-March, pp. 21-26.

12. Jaiswal O R, Rai D and Jain S K (2007),“Review of Seismic Codes on LiquidContaining Tanks”, Earthquake Spectra,Earthquake Engineering Research Institute,Vol. 23, No. 1, pp. 239-260.

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13. Memari A M and Ahmadi M M (1992),“Behaviour of Reinforced Concrete WaterTowers During Manjil-Roudbar Earthquakeof June 1990”, Proceedings of the 10th WorldConference on Earthquake Engineering,Balkema, Rotterdam.

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