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PORTLAND CEMENT

Rectangular Concrete Tanks

Section 1. lntroduction

While a cylindrical shape may be structurlñly best for tank construction, rectangular tanks frequently are pre-ferred for specific purposes. Special processes o r operations may make circular tanks inconvenient to use. Wlien several separate cells are required, rectangular tanks can be arranged in less space than circular tanks of the same capacity. Tanks or vats needed inside a building are therefore often made in rectangular or sqiiare shapes. For these and other reasons. breweries. tanneries. and paper mills generally use rectangular tanks.

Data presented here are for design of rectangular tanks wliere the walls are subject t o hydrostatic pressure of zero at tlie top and maxjmum at the bot tom Some of the data rnay be used for design of coiinterforted retaining walls subject to eartli pressure for wliich a hydrostatic type of loading may be substituted in the design calcrrlations. Data also may be applied t o design of circular reservoirs of large diameter where lateral stability depends on the action of counterforts built integrally with the wall.

Another article on tank construction. "Circular Concrete Tanks Without Prestressing," has been published by Port- land Cement Association.

Secrion 2. Moment Coefficients

Moinent coefficients wcre calciilated for individual panels considered f i e d along vertical edpes, and coefficients were subsequently adjristed t o allow for a certain rotation about tlie vertical edges. First. three sets of edge conditions were iiivestigated, in al1 o f which vertical edges were assumed f i e d wliile the ot tier edges were as follows:

1. T o p hinged- bottoiii liinged 2. T o p free--bottom Iiinged 3. T o p free-bottoni fixed*

Moment coefficients for tliese edge conditions are given in Tables 1, 11, and 111 resptctively. In al1 tahles. a denotes height and b width of the wall. In Taldes 1, 11, and 111. coefficients are given for nine r a ~ i o s of b/a, the liinits being b/a = 3.0 and 0.5. Tlie origin of tlie cooidinate system is at midpoinl of the tup edge; tlie Y axis is Iiorizontal; the X axis is vertical and its p s i t i v e direction downwaid. Coeffi-

:ients are @ven-except wliere they are known 1 1 ) he zero-at edges, quarter points, and midpoints both in ,\ illld Y directions.

The slab was assumed t o act as a tliin plate. for 1111ich equations are available in textbooks sucli as Thnv 1' ~f PIates and Shells b'), S. Timoshenko.** blit since (~ l l ! ' a small portion of the necessary calculations for rntjiill'nf coefficients for specific cases is available in tlie engiiir+'linE literature, tlicy Iiave been made especially for tlus artirlk'

Tabio I\ ' contains nioment coefficients fvr uniforiii I6';1d on a rectangular plate considered hiiiged on al1 four ~111~'~. The table is for use in desigriing cover slabs and b1~11l)m slabs for rectangular tanks with one cell. If cover sldl' is made coiitinuous over /ntermediate sirpports, the dg.slFn niay be niade in accordance witli procedures for the d*31.n of slabs supported on forir sides.t

Coefficients for iiidividual paiiels with fixed side r c i ~ c ~ apply without modificativn to continuous walls prc,tlllrd tliere is n o rotation about vertical edges. lri a sqiiare 1411k. 11-iei-efore. monicnt coefficients may be taken directly Ill)m Tables 1, 11, or 111. In a rectangular tank. howevci, 11"

adjustinent inust be made. as was done in Tables V a1111 VI> sjniilar t o the niodification of fixed-end iiioinents 1 1 1 a frame analyzed by moment distribution.

In this procedure the conirnon-side edge of two adiílk " ~ l f

panels is first considered artificially restrairied so ttiial 110

rotation can take place about the edge. Fixed-edpr III(''

inents taken froin Tables 1, 11. or 111 are usiially dissiiiiillll ti1

adjacent panels and tlie differences, wliich ccirrespoiill '0

unbalanced iiionients, tend t o iotate tlie cdge. Wlicii (I'c artificial restraint is removed they will inciuce additill1l"l moments in the panels Adding induced and fixetl l'lld moinents al the edge gives filial end nioinrnts3 wliicli ~~~~~~~ be idcntical oii citlier side of tlie coinmon edge.

hloment distribution cannot be applied as simply t ( 1 ~ l ' e case of contiiiiious tank walls as it can t o framed struc1111~'s- bccause nioments inust be distiibrited siniuli:ineously allll:6 the entire length of tlie side edge so tliat nionicnts b e c ~ l l l ~ c eqiial at botli sides at any poiiit o f tlie e d g e Ttie prc,llfl'lil

* A ~ p l i c ; i h l ein rasrs wlferr i r~ : i l l slah. roiintrrf<,;t. alid hiri. al""

:Irt. al1 huili intepr;illy. *'l'uhlislied by McGraw-Hil l Rook Co.,News Yor . 1940.

tSre S r c t i i ~ n 2 0 0 2 , ACI Sla i idard 318.63. "liiiilding i '"*e Rrquirernenls f t ) r Hrinforred Concrele." Americo Coilcretc III"". tu t e . I)elroil. Mi r l i . , J u i i e 1963.