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When using preformed slots, vertical bending moments induced in the wall by shear should be considered. The roof-to-wall joint is subject to earthquake shear from the horizontal acceleration of the roof. Where dowels are provided to transfer this shear, the distribution will be the same as shown in Fig. For tanks with roof overhangs, the concrete lip can be designed to withstand the earthquake force. Because the roof is free to slide on top of the wall, the shear transfer will take place over that portion of the circumference where the lip overhang comes into contact with the wall.

The maximum reaction force will be given by 2. The vertical distribution, per foot of wall height, of the dynamic forces acting perpendicular to the plane of the wall may be assumed as shown below adapted from NZS [], Section 2. Superimposed on these lateral unbalanced forces shall be the lateral hydrodynamic force resulting from the hydrodynamic pressure due to the effect of vertical acceleration pvy acting on each wall.

Where applicable, the effect of the dynamic earth and groundwater pressures against the buried portion of the walls shall be included. The horizontal distribution of the dynamic pressures across the wall width B is. The dynamic force on the leading half of the tank will be additive to the hydrostatic force on the wall, and the dynamic force on the trailing half of the tank will reduce the effects of the hydrodynamic force on the wall.

For circular tanks, the vertical distribution of the impulsive and convective forces is identical to that shown above for rectangular tanks, while the horizontal distribution varies along the tank circumference as shown in Fig. The vertical distribution, per foot of wall height, of the dynamic forces acting on one half of the wall may be assumed as shown below and in Fig.

Superimposed on these lateral unbalanced forces shall be the axisymmetric lateral hydrodynamic force resulting from the hydrodynamic pressure pvy acting on the tank wall. The horizontal distribution of the dynamic pressure across the tank diameter D may be assumed as follows. Typical earthquake force distributions in walls of rectangular and circular tanks are presented in R5. The vertical bending stresses and shear stresses in the wall and at the wall base due to lateral earthquake forces shall be computed on the basis of shell action using an acceptable pressure distribution.

For free-base circular tanks Type 2. Hydrodynamic membrane hoop forces in the cylindrical wall corresponding to any liquid level y above the tank base shall be determined by 2. Similarly, the terms in Eq. Provisions shall be made to accommodate the maximum wave oscillation dmax generated by earthquake acceleration. The horizontal earthquake acceleration causes the contained fluid to slosh with vertical displacement of the fluid surface. The amount of freeboard required in design to accommodate this sloshing will vary.

Where overtopping is tolerable, no freeboard provision is necessary. Where site-specific response spectra are used, the maximum vertical displacement dmax may be calculated from the following expressions: Rectangular tanks 0. Dynamic earth pressures shall be taken into account when computing the base shear of a partially or fully buried liquid-containing structure and when designing the walls. The lateral forces due to the dynamic earth and groundwater pressures are combined algebraically with the impulsive forces on the tank as in Eq. The effects of groundwater table, if present, shall be included in the calculation of these pressures.

The coefficient of lateral earth pressure at rest Ko shall be used in estimating the earth pressures unless it is demonstrated by calculation that the structure deflects sufficiently to lower the coefficient to some value between Ko and the active coefficient of lateral earth pressure Ka. In a pseudostatic analysis, the resultant of the seismic component of the earth pressure shall be assumed to act at a point 0.

The dynamic characteristics of ground-supported liquidcontaining structures subjected to earthquake acceleration shall be computed in accordance with Sections 9. The lateral seismic pressures and forces determined in accordance with this Standard are based on vertical tank walls and vertical wall elements, and the pressures and forces may need to be modified for sloping surfaces. The dynamic characteristics of pedestal-mounted liquid-containing structures shall be computed in accordance with Section 9. The following commentary is adapted from Housner : The design procedures described in Chapter 4 recognize that the seismic analysis of liquid-containing structures subjected to a horizontal acceleration should include the inertia forces generated by the acceleration of the structure itself; and the hydrodynamic forces generated by the horizontal acceleration of the contained liquid.

The impulsive pressures are not impulses in the usual sense but are associated with inertia forces produced by accelerations of the walls of the container and are directly proportional to these accelerations. The convective pressures are those produced by the oscillations of the fluid and are therefore the consequences of the impulsive pressures.

This model has been accepted by the profession since the early s. In this model, Wi represents the resultant effect of the impulsive seismic pressures on the tank walls. Wc represents the resultant of the sloshing convective fluid pressures. In the model, Wi is rigidly fastened to the tank walls at a height hi above the tank bottom, which corresponds to the location of the resultant impulsive force Pi. Wi moves with the tank walls as they respond to the ground shaking the fluid is assumed to be incompressible and the fluid displacements small. The impulsive pressures are generated by the seismic accelerations of the tank walls so that the force Pi is evenly divided into a pressure force on the wall accelerating into the fluid, and a suction force on the wall accelerating away from the fluid.

During an earthquake, the force Pi changes direction several times per second, corresponding to the change in direction of the base acceleration; the overturning moment generated by Pi is thus frequently ineffective in tending to overturn the tank. Wc is the equivalent weight of the oscillating fluid that produces the convective pressures on the tank walls with resultant force Pc, which acts at a height of hc above the tank bottom. In the model, Wc is fastened to the tank walls by springs. The sloshing pressures on the tank walls result from the fluid motion associated with the wave oscillation.

The period of oscillation of the sloshing depends on the ratio of fluid depth to tank diameter, and is usually several seconds. The overturning moment exerted by Pc Fig. The forces Pi and Pc act independently and simultaneously on the tank. The force Pi and its associated pressures primarily act to stress the tank wall, whereas Pc acts primarily to uplift the tank wall. The vertical vibrations of the ground are also transmitted to the fluid, thus producing pressures that act on the tank walls.

They act to increase or decrease the hoop stresses. The pressures and forces on a cylindrical tank are similar to, but not the same as, those acting on a rectangular tank. The rapid fluctuations of the force Pi mean that the bending moments and stresses in the wall of a rectangular tank also vary rapidly the effect is not like a constant force acting on the wall. The duration of the fluctuations is 10 to 15 seconds for earthquakes of magnitude 6.

The force Pc fluctuates sinusoidally with a period of vibration that depends on the dimensions of the tank, and can be several seconds or longer. The duration of sloshing can be 20 to 40 seconds for earthquakes of magnitude 6. Note that the damping of the sloshing water is small: approximately 0. The sloshing increases and decreases the fluid pressure on the wall. Normally, this is smaller than the impulsive effect, but if there is not enough dead load, the tank will tend to uplift.

All equations in Section 9. Equations , , and were adapted from NZS H cosh 3.

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For all tanks H cosh 3. The following equations are provided as examples for the special case of a wall of uniform thickness. Note that mass is equal to weight divided by the acceleration due to gravity. For walls of nonuniform thickness, special analysis is required to determine mw, mi, and h. For fixed-base, free-top cantilever walls, such as in open-top tanks, flexural stiffness for a unit width of wall k may be approximated using the following equation. Such spring constants will generally fall within the low period range less than about 0.

As an alternative to computing the natural period of vibration, particularly for end conditions other than cantilever, it is reasonable to assume the wall rigid. In such a case, Eq. A plot of the seismic response coefficient Ci is shown in the design response spectrum in Fig. SS and S1 are the mapped spectral response accelerations at short periods Ss and 1 second S1 , respectively, and shall be obtained from the seismic ground motion maps in Fig.

This mode of vibration is relevant only to circular tanks, and does not apply to rectangular tanks. While the derivation of Tv for circular tanks has been the subject of several technical papers, the committee is not aware of any work devoted to the derivation of this parameter for rectangular tanks.

Therefore, for rectangular tanks, Ct is taken independent of the period of vibration. When site-specific procedures are used, the maximum considered earthquake spectral response accelerations SaM and ScM shall be obtained from the site-specific acceleration spectrum as follows:. The seismic response coefficients Ci, Cc, and Ct shall be determined from Eq. Equation and are adapted from ASCE Housner , Haroun and Ellaithy , and ACI Committee provide additional guidelines on the dynamic analysis of pedestal-mounted tanks. The dynamic properties, including periods of vibration and lateral coefficients, shall be permitted to be determined on the basis of generally acceptable methods of dynamic analysis.

L tanh 0. D tanh 0. Housner, G. Atomic Energy Commission. John A. Bertero, V. D-1 to D Haroun, M. Medearis, K. Newmark, N. Scarlat, A. Uang, C. Veletsos, S. Engineering, Vol. Mononobe, N. The de"'lgn ot some of the components.. In the absence 1t u more refined analvsis, approxi mate method.. Figure ::;-1 shows the hvdrodx narnic forces on walls and ha Besides hydrodynamic lorn's, the t. Hydrodynamic Pressures Due to Ground Motion.

The static loads include the dead load, live load, hydrostatic pressure and earth pressure. TI,e d narnic load include the inertia of the elements, the h d rodynarnic forces impulsive and convectix e components of fluid motion and d narnic earth pressure. The inertia, impulsive and convective forces on the walls of rectangular and ci rcular tanks can be determined for d i ffL'ff'n t codes as follows: IBC Method. It is assumed that the impulsive and convective forces '1r1' equally resisted by the leading and the trailing walls perpendicular to the direction of till' earthquake force.

Thus, half of the total irnpulsiv l' and convective force is ,lssigned to each wall. Since earthquake forces arc reversible, both the leading and the lrai linh walls should be designed for the maximum effects, If Ihest' torces, Section 5.


The dynamic ea rth press me ca n be d eterrni ned using Reference Therefore, square root of the sum of squares SRSS method should be used to combine the lrnpulsive and convective torccs. The dynamic earth pressure caused b the movemerit of the tank can be directly added to the impulsive effects for design purposes.

The vertica I and horizontal bending and shear stresses in the walls rna be determined using plate analysis given in Rd. Walls parallel to the earthquake force are designed for in-plane forces due to a their own inertia and, b reactions from the roof and abutting walls. The remaining 20"u will be transferred through vertica I bending. Section "i. The horizon tal distribu ticn of the dynamic pressures ,1! Shear Transfer at Base Adapted from Ref. The hoop torces in cylindrical walls at allY lcvel t, from the base C,1n be determined by SRSS combination of the inertia, impulsive and convective stresses,.

The wcight of lilt uid per Ii neil! Tank Motton Trailing Half Fig. This torn' is dirccllv addcd to the hvdrodv namic force lind can be determined a.. The ox l'r,lll inlcgrih pt till' tank shall be ensured b prm id Lng. Fill" unanchored and contained flexible tanks, the strength of Ihe containment pad, its support structure and the t. In such situatlons. For both anchored and unanchored and uncontained flexible base t,1I1k.

S the computed horizontal displacement of the tank base lor hydrostatic and earthquake loading. The "ei..


In order to determine the necessarv detailins tor a - " structure, till' dl'sibJ1el" m. Thus Table should be used In. HISl' of their inherent ['Jgidity and to pres ern le,lj. The overriding requirments uf ACI Me shown wherever applicable. Provide two curtains of reinforcement Anchor and splice bars per Where special boundary elements are not required by Acv Jf;. Standard hook at ends of horizontal reinforcement engaging edge reinforcement or U-stlrrups spliced to horizontal reinforcement with same size and spacing as honzontal reinforcement x r tw. Be Sectum CI " 2tJ"i. For cum ective torn.

Bultumui II all rJ. Maximum hydrodynamic moments from fable , Vl'rtitai direction, Md. Ide flection in. Steel provided No. S7[j LIP J 'I 7. J2 1m the horizontal di rcction. OIl2 in, 7.

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Iowev cr, based on the SOC 0 associa ted to this structure, detailing correspond ing to high seismic risk will apply per Table 6-] sec Chapter 6. These l'nmpu ta ti uns are shown in Ref. The req uirerncnts of Table are ;' 1 tisfied for in. The steel prov ided along with spacing ""ltisrief, Section 2! I Figure Detailing of Wall 7. I",' III! I1k k "lll'd In Seisrru.. FlC lY'l7 and SllC! Hl' multiplied bv a tactor otLtt iothl' load corn bi n,1 tions.

Ihc 1E Top 13 It :-Jo 61 1 12 ill. L' arul hingl'd connection betw een th.. Ui III public utility facility 8. Irom tilt' direction It earthquake,.

Design of liquid-containing concrete structures for earthquake forces ( edition) | Open Library

U02 j 11 til e h onzon ta I direction , Id combinations: L. For deterrn i ning the ou t-of-p lane 11llcn t d u e to ea rthquake force Other Titles Liquid-containing concrete structures for earthquake forces. Classifications Dewey Decimal Class The Physical Object Pagination iv, 54 p. Download for print-disabled. Check your local library WorldCat Library. Buy this book Amazon.

Seismic Analysis Lecture #2 - Dirk Bondy, S.E.

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