TANQUES REFORZADOS

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REINFORCED CONCRETE TANKSPerformance and practice for earthquake resistance

By JAVEEO A. MUNSHI and WILLIAM C. SHERMAN

Historically, reinforced concrete tankshave performed very well againstearthquakes. Recent reports on theNorthridge earthquake of 1994 and theKobe earthquake of 1995 have givenminimal, if any, evidence of damage tothese structures. There are variousreasons why it is common that manytanks behave elastically during anearthquake, thus are not damaged. Thequestions then arise: Can there be asimple approach to designing these

structures against earthquakes? When dowe need to use more elaborateprocedures? This article addresses theseissues and provides an example of how toapply the current design code, ACI 350-01.

There are several reasons why thesestructures escape damage:

Concrete tanks are inherently rigidand are often partially or fully buried in

the ground. Because of this, they donot deform much with respect to theground. Research1 has shown that forburied structures subjected to groundexcitation up to 0.3 x acceleration dueto gravity g, nonseismic loadcombinations control the design. Thein-plane shear resistance of the wallsis generally adequate to resist seismicloads, with both the concrete and thereinforcement contributing to thestructure's strength. Out-of-plane wall

deformations are minimal due to therigidity of the concrete walls and thestructure's boundary conditions;

Concrete tanks have typically beendesigned using provisions similar tothose included in "Code Requirementsfor Environmental EngineeringConcrete Structures (ACI 350-01) andCommentary (350R-01). "Those

provisions require that concrete tanksminimally crack under static serviceload conditions.2 Section 21.2.1.6 of ACI 350-01 clearly indicates thatliquid-tightness should not becompromised as a result of inelasticaction. To achieve this, the load factorused with lateral fluid pressures isincreased from 1.4 to 1.7 and anadditional environmental durabilityfactor S ranging from 1.3 for flexureand shear to 1.65 for direct tension is

imposed on static load conditions toreduce the service level stresses andminimize crack widths and leakage.This results in the nonseismic loadcombinations governing over seismicload combinations in many cases; and

Concrete tanks are designed usinglow response modification factors R w to ensure that the structure is notsignificantly damaged during anearthquake. The responsemodification factor reduces the elastic

response spectrum to account for thestructure's ductility, energy-dissipatingproperties, and redundancy. Typically,R w values ranging from 2 to 3 areused, which are much smaller thanthose for building structures.

PRACTICEBackgroundThe seismic design of tanks varies fromthat of buildings in part due to the sloshingeffect of the contained fluid. Furthermore,

cracking, which may be permitted in thedesign of buildings, is avoided in liquid-containing structures to prevent leakage.Methods of seismic analysis of tanks,currently adopted by a number of industrystandards, have evolved from earlieranalytical work by Housner,3-5 Haroun andHousner,6 Haroun,7,8 Veletsos9, Vestosand Shivakumar,10 and others. Of these,



the best known is Housner's pioneeringwork published in the early 1960s in the Atomic Energy Commission's (now theU.S. Nuclear Regulatory Commission)Technical Information Document (TID)7024.5

It is interesting to note that while thedynamic modeling of the tank contents(impulsive and convective components)has remained pretty much as developedby Jacobsen and Housner, the modelingof the tank structure has undergonecertain modifications and refinements. Forexample, where Jacobsen and Housner'searly models (for example, in TID- 7024)were based on the impulsive componentof the liquid being rigidly attached to a

rigid tank structure, later studies (includingwork by Housner) introduced the conceptof wall and foundation flexibility. Accordingto this concept, the impulsive componentis still modeled as rigidly attached to thetank shell, but the shell itself is nowflexible. This has a significant effect on theresponse of the overall system to groundmotions.

Recent developmentsThe design of tanks, like building

structures, has to conform to theapplicable building codes such as the IBC200011, UBC 199712, UBC 199412, BOCA1996,13 and SBC 1997.14 Note thatalthough these codes do not containprovisions for detailed seismic analysisand design of liquid-containing structures,they allow the use of consensus industrystandards. The seismic design provisionsdeveloped by ACI Committee 350,Environmental Engineering ConcreteStructures, meets the requirement of

being a nationally recognized consensusstandard applicable to liquid-containingstructures. The committee recentlypublished the provisions "Seismic Designof Liquid-Containing Concrete Structures(ACI 350.3-01) and Commentary (ACI350.3R-01)" that give detailed proceduresfor determining the loading for the seismicanalysis and design of liquid-containing

structures.15 Furthermore, Chapter 21provisions of ACI 350-01 focus on theresistance of liquid-containing structuresto seismic loads (much the same wayChapter 21 of ACI 318 does for buildingstructures).

Note that ACI 350-01 includes modifiedportions of ACI 318-95,16 while ACI 350.3-01 is compatible with UBC 1994 service-level (aIlowable stress) earthquake designmethodology. Thus, provisions of ACI350.3-01 are not presently compatiblewith IBC 2000, UBC 1997, BOCA 1996,and SBC 1997, all of which use thestrength-level earthquake force.Therefore, ACI 350.3-01 in its current formcannot be used directly with the seismic

provisions in these building codes.

A publication17 was recently developed tobridge the gap between ACI 350.3-01 andthe model codes indicated previously thatuse strength-level earthquake forces. Theconcepts of ACI 350-01 and ACI 350.3-01have been extended for use with the IBC2000, UBC 1997, BOCA 1996, and SBC1997 for the design of liquid containingstructures. Despite these developments,several issues related to the analysis,

design, and detailing of liquid-containingstructures remain unclear and need to beexplored in the interest of providing asimple design procedure.

ANALYSIS AND DESIGNDynamic modeling ACI 350.3-01 uses the previouslyindicated references, particularly theHousner method.3-5 This methodessentially assumes that hydrodynamiceffects due to seismic loading can be

approximated as the sum of the followingtwo parts:1. The impulsive part, which represents

the portion of the liquid that moves inunison with the structure in itsfundamental mode of vibration; and

2. The convective part, whichrepresents the effect of the sloshingaction of the liquid in its fundamental



mode of vibration.The equivalent mass of the impulsivecomponent of the stored liquid W i includesthe weight of tank shell and roof and theportion of fluid acting in unison with thetank shell. The impulsive and convective

equivalent masses create differentpressure distribution along the height ofthe tank wall.15,17

Figure 1 shows the typical schematic of arectangular tank with inside length L(parallel to the direction of the earthquakeforce [use the inside diameter D for

circular tanks]), inside width B(perpendicular to the direction of theearthquake force), and height of liquid H L.The equivalent mass of the impulsivecomponent of the stored liquid W i isassumed to be rigidly attached to thestructure at height hi , while the equivalentmass of the convective component of thestored liquid W c is attached to thestructure by springs of finite stiffness anddamping at height hc . For concrete tankswith rigid walls and roof, this results in a

two degree-of-freedom system (Fig. 1).Both the impulsive and the convectivecomponents have periods associated withthem that are gene rally far apart. Theimpulsive period is dependent on theinside wall dimensions, wall thickness,boundary conditions, and the amount ofcontained liquid. The convective period isdependent on the inside dimensions of thetank. Based on the ACI 350.3-01provisions, the total horizontal base shearV T is estimated by the square root of the

sum of squares (SRSS) combination ofthe impulsive and convective forces

V T = √V i 2 + V c

2

where V i and V c represent the base shearassociated with the impulsive andconvective equivalent masses,respectively.

The use of SRSS to combine modes ofvibration that are out-of-phase with eachother is not uncommon. It should benoted, however, that SRSS may not bethe best way to combine impulsive andconvective forces. The period ofconvective oscillations is typically muchlonger than the impulsive period, as

shown in Fig. 2. This could mean thatthere is a greater likelihood that responsedue to impulsive and convective forceswould be additive to give the maximumresponse. Furthermore, because of therelatively small magnitude of theconvective force, the SRSS combinationnegates much of the influence of theconvective force on the total response,which may be unconservative. It isrecommended that because of the near-static nature of convective forces, the

impulsive and convective forces should bealgebraically added together to get themaximum design forces. In fact, theoriginal method developed by Housnercombined impulsive and convective forcesby algebraic sum. This would also beconsistent with the reasoning behind the ACI 350.3-01 recommendation to use an



R w value of 1.0 for convective forces (referto the section in this article on theresponse modification factor).

Simplified approachThrough a detailed parametric study using

the general seismic design parametersgiven in ACI 350.3-01, the authors foundthat the method of using all the fluid as animpulsive-type force at midheight is aconservative assumption when the sitecoefficient S is 1.0 and the responsemodification factor R wi is 2.75. As S andR wi increase, however, such anassumption would not always beconservative. As S increases, theconvective component becomes larger,and as R wi increases, the impulsive

component becomes less. Thus, when S> 1.0 and/or R wi > 2.75, the convectivecomponent becomes a greaterpercentage of the total force relative to theimpulsive component and the "simplified"method becomes less conservative.Generally, for at least a 10 ft (3 m) waterdepth and L/H L or D/H L greater than 3, thesimplified method is still conservative.

PeriodThe periods associated with impulsive and

convective weights T i and T e are used toestimate the response associated withthem that contributes to the base shear. Aparametric study conducted by theauthors (based on ACI 350.3-01)indicated that the majority of fixed-baserectangular and circular tanks have animpulsive period less than 0.3 s, which is

less than the characteristic period of soilTs, as shown in Fig. 3. Considering thespectrum shown in Fig. 3, it is obviousthat for T i < T s, the response will be basedon the upper bound shown as a plateau inFig. 3. This would simplify the design

procedure for situations where T i < T s,.For example, the parameter Ci per UBC1994 would be given by

C i . = 2.75 for T i < T s Impulsive

The convective period is given in ACI350.3 as

T c = 2π √L Rectangular tanks

λ

T c = 2π √D Circular tanks λ

where L is the inside length of a tank inthe direction of analysis, and D is theinside diameter (Fig. 1 (a)). Theparameter 2n/A for rectangular tanks isobtained from Fig. 4 (taken from ACI350.3).15

Response modification factorNot much research has be en performedto date with regard to response

modification factors for concrete tanks.Table 1 compares the R w values ofreinforced concrete bearing walls andtanks with a nonflexible base in variousmodel codes. These R w values for tankwalls are approximately 1/2 to 2/3 of thevalues used for the design of walls in



building structures. This, as indicatedpreviously, is consistent with the ACI 350recommendations to limit the extent ofinelastic deformation in tank walls toprevent excessive crack widths andleakage.

ACl 350.3-0115 recommends separate R w values for impulsive and convectiveportions of the base shear, as shown inTable 2. For the convective response, R wc of 1.0 is used for all tank types (Table 2).This is because the convective periodsare usually long and fall in thedescending/flat portion of the spectrum(Fig. 3). It is believed that the convectiveforce, because of its low frequency,should be treated as static such that an

R wc factor of 1.0 mar be appropriate. One

problem, however, is that if one were toconvert the R wc values given in ACI 350.3-01 for use with any strength-level buildingcode, the R wc value would become 0.7(1.0/1.4). This would mean that theconvective earthquake force would have

to be increased by 40%, which seemsrather conservative.

lt is recommended that R wc be increasedto 1.5 in Table 2, which would beconsistent with an over strength of 1.5generally associated with concretestructures. This would also eliminate thediscrepancy created by using R wc equal to0.7 with model codes that use strength-level earthquake forces.

It is also recognized that the damping ratiofor convective motion is small (0.5 to 2%)as compared with the impulsive force(5%). This requires that a scale factor of1.5 be applied to the acceleration valuesfor 0.5% damping over those for 5%damping ratio. For example, with UBC1994, the convective response at 5%damping is given by

Cc = 1.25 ST c

2/3

For 0.5% damping, the value would beincreased to

Cc = 1.5 1.25 ST c

2/3

For long periods (> 2.4 s), thisis further modified in ACl350.3-0115 to

Cc = 6 S

T c 2

Effect of dynamic earth andground water pressureThe effect of dynamic earthpressure is commonlyapproximated by theMononobe-Okabe theory.18-21



This involves the use of constanthorizontal and vertical acceleration fromthe earthquake acting on the soil masscomprising Coulomb's active or passivewedge. This theory assumes that wallmovements are sufficient to fully mobilize

the shear resistance along the backfillwedge. The dynamic pressure due to thesoil wedge will either increase or decreasethe static active and passive pressure onthe walls due to backfill, depending on thedirection of ground motion with respect tothe wall. For the wall moving into the soil,the passive dynamic pressure will opposethe impulsive force acting on the wall,while for the wall moving away from thesoil, the active pressure will add to theimpulsive force. Dynamic movement of

soil particles, however, may be out-of-phase with the tank wall movement. Thus,dynamic earth pressure should becombined with static earth pressure in aconservative manner (to increase activeearth pressure for wall deformations awayfrom the soil or to reduce passive earthpressure for wall deformations into thesoil).

Due to the rigidity of concrete tanks, thewall deformation and consequent

movement into the surrounding soil isusually small enough that the active orpassive soil wedge is not fully activated.For dense, medium-dense, and loosesands, a deformation equal to 0.1, 0.2,and 0.4%, respectively, of wall height isnecessary to activate the active soilreaction.18,19 Similarly, a deformationequal to 1, 2, and 4% of the wall height isrequired to activate the passive resistancefor these sands. Therefore, determinationof dynamic active and passive pressures

may not be necessary when walldeformations are small. Dynamic earthpressure at rest should be included,however, as given by the followingequation.18

F = k hγ sH s 2

where k h is the dynamic coefficient of

lateral earth pressure; γs is the density ofthe soil; and H s is the height of soil beingretained. This force, assumed to act at0.6H above the base, should be used toincrease or decrease the at-rest pressurewhen wall deformations are small, as

indicated previously.

Complexity of structural response andboundary conditionsCodes and design aids15,22 provideapproximate methods to evaluate forcesand stresses for the most simple tanksand boundary conditions. Computationscan get quite complicated, particularly formulticell and circular tanks. Therefore,unless there is a good reason to believethat an elaborate analysis is necessary,

simplified approaches should becombined with good engineering judgment. A finite element analysisapproach would be appropriate toaccurately account for the nature ofloading, boundary conditions, andstructure type in an elaborate analysis.

Load combinationsIt is not clear in the model building codesas to how load factors for earthquakesand fluid pressures should be combined.

ACI 318-99 and ACI 350-01 do not giveclear guidance in this matter. Section9.2.5 of ACI 318 indicates that fluidpressure F should be added to all loadcombinations that involve live load L. Noindication on how earthquake load Eshould be combined with F is provided.Section 9.2.5 of ACI 350-01 overrides thisrequirement by clarifying that F should beadded to all load combinations so that theeffect of L, W, or E does not reduce theeffect of F. Based on this, load

combinations consistent with theserequirements are given in Reference 17for different building codes. The loadfactor to be used for fluid pressure F, asrecommended in ACI 350-01, is 1.7 ratherthan 1.4 when ACI 318-99 basic loadcombinations are used. Based on Section21.2.1.7(a) of ACI 350-01, theenvironmental durability factor does not



apply to load combinations involvingseismic loads when designed inaccordance with the strength designmethod.

DETAILING

In the absence of clear guidelines forseismic detailing for liquid-containingstructures, ACI 318-9923 provides the bestdetailing requirements for reinforcedconcrete structures. The problem,however, arises because of incompatibledesign philosophies between buildingstructures and environmental structures.

Building structures are allowed to sustainsome damage during earthquakes,particularly in regions of high seismicity.

Accordingly, higher R w values areallowed, as indicated in Table 1. Tocontrol damage and prevent collapse,stringent detailing is required in thesebuilding structures, as shown in ACI 318-99.

Environmental structures, on the otherhand, are designed for minimal damage, ifany. Their R w values, as indicated inTable 2, are limited to between 2.0 and4.5, indicating that these structures are

not expected to have significant inelasticactivity during a design earthquake. Moreimportantly, to maintain serviceability,additional load factors and environmentaldurability factors are used that makethese structures behave almost elasticallyduring design earthquakes.

Accordingly, detailing requirements givenin ACI 318-99 for high levels of seismicity(Zone 3 and 4), Seismic PerformanceCategory (SPC) C and D, or Seismic

Design Category (SDC) C, D, and Eshould not be fully applicable toenvironmental engineering structures.Nevertheless, it would be prudent to usethe intermediate level of detailingassociated with moderate levels ofseismicity (Zone 2), SPC C, and SDC Cgiven in ACI 318-99 for these structures,unless severe inelastic deformations are

expected. This would eliminate specialrequirements for detailing of walls in mostcases. Special considerations should begiven to detailing of joints, however, toprevent distress, excessive deformation,and leakage.

APPLICATION OF ACI 350.3-0115,17 Partially buried nonflexible base tank

Specific weight of contained liquid γL

= 70 lb/ft3 (1000 kg/m3)

Specific weight of moist soil γS = 100

lb/ft3 (1600 kg/m3) Average wall thickness tw = 18 in.(460 mm)

Design depth of stored liquid H L= 8 ft

(2.4 m)

Concrete compressive strength f c´ =

4000 psi (30 MPa)

Specific weight of concrete γc = 150

lb/ft3 (2400 kg/m3)

Modulus of elasticity of concrete E c =

3834 ksi (26,400 MPa)Inside length, parallel to earthquakeforce direction L = 18.5 ft (5.6 m)Inside length, perpendicular toearthquake force direction B = 28.5 ft(8.7 m)Equivalent mass of the convective

component of the stored liquid W c Equivalent mass of the impulsive

component of the stored liquid W c

Total mass of the stored liquid W L

Mass of tank wall (shell) W w

Mass of tank roof W R

Height of tank walls H

Seismic load analysisWeightL=18.5=2.3 (For analysis in N-S direction)

H L 8

From Reference 17 for L = 2.3 forrectangular tanks H L

W i = 0.49 and W c = 0.51WL W L

WL = BxLxHLxγL



W L 1000 (79,800 kN/m)

=28.5x18.5x8x70=2.95 k (1310 kN) T i = 2π √ 369.7 = 0.008 s1000 32.2x6290x28.5

The period associated with the convective

component T can be determined asfollows

W i = 0.49 x 295.3 k

W i = 144.7 k (640 kN)W i = 144.7 k (640 kN)

W c = 0.51 x 295.3 kW c = 0.51 x 295.3 k T c = 2π √Lλ

W c = 150.6 k (670 kN)W c = 150.6 k (670 kN)From Reference 15 or 17,2π=0.66 for L=2.3

λ HL W w = 2([B+t W w = 2([B+t w ] +[L+tw ] ) x H x t w x γ c 1000 lb T c = 0.66 √18.5 = 2.8 s

kBase shear using UBC 1997For the tank located in Seismic Zone 4, Z

= 0.4 (Table 16-1)

W w = 2(20+30) x 10 x 1.5 x 150 =

1000Seismic Source Type (SST) = B with sitelocated225 k (1000 kN)10 km from a known seismic source

(Table 16-U)W R = 0Soil Profile Type (SPT) = D

(Table 16-J)PeriodSeismic Importance Factor = 1T i = 2π√ W

(Nonhazardous material)gkResponse Modification Factor R = 2.9

(Table 16-P)W =W w +W R +W i =225+0+144.7=For Z = 0.4 and SPT D

Ca = 0.44N a (Table 16-Q)369.7 k (1640 kN)C v = 0.64N v (Table 16-R)

K = E c (T w )3 From Tables 16-S and 16-T, the near-

source factors N a = 1 and N v = 1,respectively.

48 h

where h is the mean height at which theinertia force of the tank and its contents isassumed to act.

Ca = 0.44N a = 0.44Cv = 0.64N v = 0.64

Using Section 1634.3, for flat-bottom rigidtanks

h=(225x5+144.7 x 3) = 4.2 ft (1.3m) V= 0.7C a IW (225 + 144.7) =0.7x0.44x1x520.3=160.3k(713 kN)

Note that W includes the weight of tank

and contained liquid.t w = 18 in. (460 mm)UBC 1997 allows use of alternateprocedures such as the one given in ACI350.3-01. The guidelines for use of thismethod in conjunction with UBC 1997 aregiven in Reference 17.

E c = 3834 ksi (26,400 MPa)

g = 32.2 ft/s2 (9.81 m/s2)

K =3834(18)3=6290 k/ft per ft width Base Shear48 4.2 V i = C v I (Ww + W R + W i) Impulsive

RT i



V i=0.64x1(225+0+144.7)=302.2k(1340 kN) T s can be conservatively taken as 0.31S.

Because Ti < T s Ci = 2.752.9 x 0.27

In the short period range, the impulsivebase shear shall be limited by

Cc = 1.25 x 1.5 = 0.942.82/3

Vi = 0.4 x 1 x 2.75 (225+0+144.7)=V i = 2.5C aI (Ww + W R + W i) = 140.4k2.75R

<302.2k(1340kN) = 147.9 k (660 kN)

Use V i = 140.4 k (625 kN) V c = 0.4 x 1 x 0.94 (150.6) = 20.6 k (90 kN)2.75V c = C vI (W c) Conective

RT c Total base shear VT =√Vi

2 +V c2=149.3k (660 kN)

V c = 0.64 x 1 (150.6) = 11.8 k (50 kN)0.075ZIW= 0.075 x 0.4 x 1 x 520.3 =2.9 x 2.8

15.6 k < 149.3 k (660 kN)Total base shear V T = √Vi

2 + V c2 = 140.9 k

(630 kN) Note that ACI 350.3-01 recommendsusing Cc = 6S

TC2 Base shear using UBC 1994

for Tc2 ≥ 2.4 s and R = 1 for convective

motion. The provisions of ACI 350.3-01 wereessentially developed to be compatiblewith UBC 1994. Therefore, nointerpretations or extensions were madein application of ACI 350.3-01 with thisbuilding code.

Cc = 6 x 1.5 = 1.152.82

V c = 0.4x1x1.15 (150.6) = 69.2 k (310 kN)

For the tank located in Seismic Zone 4, Z= 0.4(Table 16-1)

1.0

Total base shear V T=√Vi2 +V c

2= 163.3 k (730 kN)Site Coefficient S = 1.5 (Table 16-J)Soil Profile Type = S3 (Table 16-J)Seismic Importance Factor = 1(Table 4-1,

Nonhazardous material)CONCLUDING REMARKS ACI 350.3-01, in combination with Chapter21 of ACI 350, fills a real need for thedesign profession. The new ACI350/350.R-Ol, "Code Requirements forEnvironmental Engineering ConcreteStructures," has greatly expanded theseismic design provisions of the previous

edition, ACI 350-89, in two ways: (1)through the adoption of Chapter 21 of ACI318 (“Special Provisions for SeismicDesign"); and (2) the drafting of detailedseismic analysis guidelines in a separateStandard, ACI 350.3/350.3R, "SeismicDesign of Liquid-Containing Structures."

Response Modification Factor R w = 2.75(Table 4-2 and Table 4(d) of ACI 350.3)

Base shearV i = ZICi (W w + W R + W i ) Impulsive

R w

V c = ZICc (W c ) ConvectiveR c

Ci = 1.25S for Ti< Ts ImpulsiveT1

2/3

Cc = 1.25S ConvectiveThe example shown illustrates the use of2.8c

2/3



the new provisions for UBC 1994 andextends the concepts of ACI 350.3-01 toUBC 1997. The base shears computedwith UBC 1994 and UBC 1997 are 149.3and 140.9 k, respectively, when ACIrecommended modifications for damping

ratio and response modification factor forlong period convective response are notincluded. When these modifications areapplied per ACI 350.3-01, the base shearincreases to 163.3 k for UBC 1994 design.The committee currently does not giveany recommendations on how to applysimilar modifications for tanks designedaccording to the UBC 1997 or IBC code.

Most concrete tanks, because of theirinherent rigidity and serviceability-based

design, can be designed using thesimplified approach outlined in this article.In many situations, it is the nonseismicload combinations that will govern thedesign. Therefore, it may be efficient to doa quick check using the simplified designmethod discussed in this paper assumingthat the tank will remain elastic for thedesign earthquake. lf the strengthrequirements exceed those undernonseismic load combinations, a closerlook using the appropriate R w factor may

be necessary.

lf the fundamental period can be assumedto be less than 0.3 s, one will not have tocompute the impulsive period. For certainconditions outlined in this article, it can befurther assumed that all the containedliquid acts at the tank's midheight to getthe total base shear. Separatecomputations for the impulsive andconvective weights, heights, periods, andbase shears are not required in this case.

Further, the response modification factorcan be assumed to be the same for bothimpulsive and convective components.Because of the rigidity of tank walls, onlyearth pressure at rest needs to beincluded for wall design. Designersshould, however, be cognizant of thelimitations of these simplifications.

REFERENCE1. MiIler, C. A, and Costantino, C. l,"Seismic Induced Earth Pressures onVaults," Natural Hazard Phenomena andMitigation, American Society ofMechanical Engineers, PVp-v. 271, 1994,

pp. 3-11.2. ACI Committee 350, "CodeRequirements for EnvironmentalEngineering Concrete Structures CACI350-01) and Commentary C350R-01)," American Concrete Institute, FarmingtonHills, MI, 2001, 387 pp.3. Housner, G. w., "The DynamicBehavior of Water Tanks," Bulletin of theSeismological Society of America, V. 53,No. 2, 1963, pp. 381-387.4. Housner, G. W, "Limit Design of

Structures to Resist Earthquakes,"Proceedings of the World Conference onEarthquake Engineering, University ofCalifornia, Berkley, CA, 1956, pp. 5-1 to 5-13.5. Housner, G. W, "Dynamic Pressure onFluid Containers," Technical information(TID) Document 7024, Chapter 6, Appendix F, U.S. Atomic EnergyCommission, 1963.6. Haroun, M. A, and Housner, G. w.,"Seismic Design of Liquid Storage Tanks,"

Joumal of the Technical Councils of the ASCE, Proceedings of the AmericanSociety of Civil Engineers, V. 107, No.TCI, 1994, pp. 191-207.7:Haroun, M. A., "Stress Analysis ofRectangular Walls Under SeismicallyInduced Hydrodynamic Loads," Bulletin ofthe Seismological Society of America, V.74, No. 3, June 1984, pp. 1031-1041.8. Haroun, M. A, and ElIaithy, H. M.,"Seismically Induced Fluid Forces onElevated Tanks," Journal of Technical

Topics in Civil Engineering, ASCE, V. 3,No. 1, Dec. 1985, pp. 1-15.9. Veletsos, A S., "Seismic Effects inFlexible Storage Tanks," Proceedings ofthe international Association forEarthquake Engineering, Rome, Italy,1974, pp. 630-639.10. Veletsos, S. A, and Shivakumar, P.,"Dynamic Response of Tanks Containing



Liquids or Solids," Computer Analysis andDesign of Earthquake ResistantStructures, Computational MechanicsPublications, Earthquake EngineeringSeries, D. E. Beskos and S. A Anagnostopoulos, eds., V. 3, 1997.

11. International Code Council,international Building Code, Falls Church,VA, Mar. 2000.12. International Conference of BuildingOfficials (ICBO), Uniform Building Code,Whittier, CA, 1994, 1997.13. Building Officials and Code Administrators International, The BOCANational Building Code, Country ClubHills, IL, 1996.14. Southern Building Code CongressInternational, Standard Building Code,

Birmingham, AL, 1997.15. ACI Committee 350, "Seismic Designof Liquid-Containing Concrete StructuresCACI 350.3-01) and CommentaryC350.3R-01),"American ConcreteInstitute, Farmington Hills, MI, 2001, 52pp.16. ACI Committee 318, "Building CodeRequirements for Structural ConcreteCACI 318-95) and Commentary C318R-95)," American Concrete Institute,Farmington Hills, MI, 1995, 369 pp.

17. Portland Cement Association, Designof Liquid-Containing Structures forEarthquake Forces, Skokie, IL, 2002.18. Ebeling, R. M., and Morrison, E. E.,"The Seismic Design of WaterfrontStructures," NCEL Technical Report, TR-939, Naval Civil Engineering Laboratory,Port Hueneme, CA, 1993.19. Clough, G. W., and Duncan, J M.,"Chapter 6: earth pressures,” FoundationEngineering handbook, 2nd Edition, NY1991, pp.223-235

20. Okabe, S., ·General Theory of EarthPressures”, Journal of the Japan Societyof Civil Engineering, V.12, No. 1, 192621. Mononobe, N., and Matsuo, H. “Onthe Determination of Earth PressuresDuring Earthquakes," Proceedings of theWorld Engineering Congress, 1929.22. AWWA Standard for CircularPrestressed Concrete Water Tanks With

Circumferential Tendons, ANSl/AWWADl15-95, 1995.23. ACI Committee 318, "Building CodeRequirements for Structural Concrete(ACI 318-99) and Commentary (318R-99)," American Concrete Institute,

Farmington Hills, MI, 1999, 391 pp.

Received and reviewed under Institute publicationpolicies.

ACI member Javeed A. Munshi is anassociate with STS Consultants, Ltd. Hehas authored several PCA publications ondesign of concrete tanks. He is an activemember of ACI Committee 350,Environmental Engineering ConcreteStructures. Munshi is a licensedprofessional engineer and a licensedstructural engineer.

WilIiam C. Sherman is a senior structuralengineer with Camp Dresser & McKee,lnc. He is an active member of ACICommittee 350, EnvironmentalEngineering Concrete Structures, and heis a licensed professional engineer and alicensed structural engineer.

FUENTE: Concrete International

Febrero, 2004g

TANQUES REFORZADOS

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