7'. In such mgnnet EiA fo be able to resist the pressure. of the piuars and being anchored at a suffleierit depth for resisting the traction that is exerted on these pillars under certain conditions of partial filling. 5 Of course, the supporting means for pillars 3 is not necessarily constituted by a plurality of elements such as said blocks 4. It might consist of a single annular element suitably embedded in the ground. I 10 Concerning the construction of the reservoir proper, supposed to be constituted by metal sheets, I advantageously proceed by assembling (through riveting, welding or equivalent methods) developable elements, of sufficiently small 15 dimensions for making practically negligible the difference between the shape obtained after assembly and the theoretical shape, the assembled elements being themselves fixed to belt 2. For instance, as shown in plane view at 9 on 20 Fig. 3, these elements are made of substantially triangular shape. Advantageously, according to a feature of my invention, the struettire obtained after assembly of these elements is subjected to the action of an 25 inner pressure (liquid pressure or gas pressure) sufficiently high for deforming the whole into a shape sufficiently close to the theoretical shape. The tank wall is advantageously made of metal, but my invention does not exclude the use of 30 other materials such as concrete, wood, etc. Also, while, in the above description, the tank has been supposed to be in the shape of a body of revolution about a vertical axis, my invention also applies to tanks the horizontal sections 35 of which are of non-circular shape, for instance ovoid or elliptic. Tanks made according to my invention have many advantages the most interesting of which are the following ones: 40 Their construction is cheap, owing to the possibility of dispensing with external reinforcing elements, and also owing to the fact that the material of which the walls are made are caused to work under the best Possible conditions. 45 Their flat shape reduces the action of wind thereon when they are built above the ground and is particularly advantageous in the case of buried tanks. Furthermore, it permits of building tanks on grounds of relatively low resistance. 50 In a general manner, while I have, in the above description, disclosed what I deem to be practical and efficient embodirnents of my invention, it should be well understood thst I do not wish to be liniited thereto as there rnight be changes gB made in the arrangerhent, disposition and form of the parts without departing from the principle of the present invention as comprehended within the scope of the accompanying claims. What I claim is, 60 1. A reservoir for holding a liquid at a variable level and under pressure of a gas, the pressure resisting part of said reservoir being constituted exclusively by a thin wall defining a space in the shape of a flattened spheroid and resting on the 65 ground, a rigid belt spaced above the ground con7 nected on the outside of said wall substantially at the plane of maximum horizontal cross-section ' thereof, and anchoring means connecting said belt to the ground and assuring the immovabilit,y lo thereof under all conditions of filling of the reservoir. @ 2. A reservoir for.holding a liquid at-a vari . able level and under.Pressure.of a gas, comprising a houow-body formed essentially of:a thin woil in theiforrii 6f a flattened spheroid with its bottom resting on the ground, a rigid ring above the g@roiind and connected on the outside of the said @vall substantially in the plane of maximum horizontal cross-section thereof means between the ring and the ground to anc@or the ring with respect to the ground, the ring dividing the waU into upper and lower parts, the mean radius of curvature of the wall at each point being such that the compression forceq which can arise in the wall under various filling conditions of the reservoir never exceed the resistance of the waR to buckling at such point, calculated from the wall thickness and the radius of curvature. 3. A reservoir for holding a liquid at a variable level and under pressuke of a gas, comprising 9, hollow body formed essentially of a thin wall in the form of a flattened spheroid with its bottom resting on the ground, a rigid ring above the ground and connected on the outside of the said wall substantially in the plane of maximum horizontal cross-section thereof, nieans between the ring and the ground to anchor the ring with respect to the ground, the ring dividing the wall into upper and lower parts, the mean radius of curvature of the W,@ll Cm at each point being such that the horizontal compression force Nm which can arise in the wall under various con-@ ditions of filling never exceeds aB e2 -r3 (17 b2) where E is Hooke's modulus, b is Poisson's coefficient, e is the thickness of the wall and a is a safety factor. 4 . A r e s e r v o i r a c c o r d i n g t o c l a i m 3 , i n w h i c h a is at least 8. 5. A hollow structure for holding a liquid at variable level and a gas under pressure above said liquid, comprising a thin wall forming a container of curvilinear vertical and horizontal sections, a rigid belt secured to the outside of said container along the horizontal section of maxi-' mum dimension thereof, the part of said structure located above said belt being constituted exclusively by a dome-shaped portion of said thin wall and having a horizontal dimension substantially greater than twice its greatest vertical dimension, the bottom part of said waU resting on the ground, and means wholly outqide said wall anchoring said belt above the ground, the mean curvature of said wall, in the portions thereof adjoining said belt, being chosen to enable said wall to resist by itself such buckling stresses as may develop under particular filling conditions. 6. A structure according to claim 5 in which the means for anchoring -said belt include at least one support anchored in the ground and a plurality of bracing and supporting means interposed between said support and said belt adapted to oppose translatory displacements of said belt parallel to the ground. 7. A structure according to claim 5 in which the means for anchoring said belt include at least one support anchored in the ground and a plurality of triangulated rods interposed between said support and said belt adapted to oppose translatory displacements of said belt parauel to the ground. ALBERT IR]tNft CAQUOT. (iteferences on followhig page)

REFERENCES CffgD The following references are of record In the ffle of this patent: UNITED STATES PATENTS Number Name Date 1,517,006 Horton ------------ Nov. 25, 1924 1,622,787 Horton ------------ Mar. 29, 1927 10 I ITumber Name DiLte 1,670,024 Day --------------- May 15, 1928 1,885,601 Horton -------------- Nov. 1, 1932 2,094,589 Day ---------------- Oct. 5, 1937 52,156,400 Pechstein ----------- May 2, 1939 2,297,002 Larson ------------ Sept.29,1942 2,376,263 Marner ------------ May 15, 1945 2,417,053 Boardman ---------- Mar. 11, 1947

Patented JuIy 31, 1951 2 1 s i 6 2 , , 6 . 0 2 UNITED STATES,, PATENIT@ OFFICE 21562,602 TANK Albert lr6n6e Caguot, Paris, France Application October 2, 1946, Serial No. 700,775 in France August 23, il946 7.Claims. (Cl. 220-1) 2 The present invention relates to hollow bodies (having relatively thin walls and Gf relatively large size, such, as tariks for containing liquids or gases or both either simultaneously or successively. 'Such-bodies,andinparticulartaxiks,areknown@;5 in which@@the wall, Lgenerally a; nietallie, one, . is.re inforeed, either,on the inside or on the outside, by frarnes adapted to resist the more or less, variable stresses resulting: from. the combination of pressures du6 to the pressures ;exerted by the - 0 liquid and gas present iliside the tank On the other hand, tanks are - also known, as described in the French patent applications flled by Caquot and Dubois, on July 3, 1942 for: "ImStationary Tanks for Liquids". and on October .2, 1942, for: "Improvements Brought to Tanks, @in Particular for Liquids," in which the stresses oLpplied@ to.the wall. of the tank are transmitted to an@external,belt or bana carried by,@upports suit- @20 ably inclined for adapting themselves to expansion, both radial and vertical,, of the tank struc@!. ture and also arranged to be able to absorb the resultants of the distinct stresses applied to the two main portions of the tank, to wit the dome or @25 upper half and the cup-shaped portion ox lower half. In particular, these supports are adapted to resist the --action of the resultant of @ the tractive stresses @ that are created@ under -certain conditions of partial filling. by the liquid, when the 30 tank bottom resists directly upon the ground. In certain embodiments of the tanks described in these prior patent ap]@lications, the upper portion of the dome wall was free from any reinforcement on the in@ide, but this wall-was always 35 supported, on the outside, by frame elements or b@. a concrete cap adapted@ to receive the whole or a part of@ the cornprbssion @stresses and to transmit them to the belt or band. The object of the-present invention is to sim- 40 phfy the construction of the tanks or hollow ' bodies disclosed in these prior patents. A preferrcld embodiment of my invention will b6@-hereinafter @ described with ref6rence to the accompanying; dra;wings, given @ merely by Way of 45 e.tarnple, and in which: Fig. 1 is an elevational view of an ovoid'tank for liquid and gas (for instance inte-hded to contain gasoline or the like, under pressure) made according to my invention; 50 Fig. 2 is a vertical section of this tank Fig. 3 is a sectional view on the line III-IU of Fig. 2. As above stated, the tank (or other hollow body) accbiding to my:invention includes a thin wall 55 (of steel, aluminium, copper, etc., and possibly of concrete), of flat ovoid shape, supposed to be supported on the one hand, either directly or indi etly,throughitsbottomi on thegroundXX', ,a@id on the other hand@ through its horizontal sec-@ 60 tion of maximum area, on a belt or band 2 SUPported by a plurality 6f pilla@@@ 3 capable of eventually resisting tractive stresses and anchored in the ground at 4. Up to the present time, it was considered that the wall of such a tank had to be fitted with external reinforcing means in, order to be able of resisting the - sire@sse@'iibve@loped under co@te@iri c6ii ditions. According to an esseritial feature of my invention, the wall of.a tank.of this kind, and especially the dome ppr tion tli6r6oi. is free from an'y such reinforcement @and is shaped to I resist by itself a.11 stresses as mety be api@lied the@eto. to utilize the matter u nder the best possible conditions, the dome 5 is given the general shape 6f a body of revolution about a vertical axis ZZ' and it is,calclilated in such manner that the maximum sire'sses are, tensile stresses limited. to the same value bo,th,on the meridians (sections by axial vertical planes) as on ttie tp@rallels (sections b@ horizontal planes), these stress maximums being not a sis c a ru e.simtiltaneous and re ' teiii e calculatio,iI@:@@eing effecl;ed-through the conventioiial methods relating to doiible 6iir@@ttire guifac@ -es.' But if i@@e desired re@ult can easily be obtained when the tank is whoily or nearly, wholly fwed with liquid,. the conditions are very different when' the tank is, only partly filled,, with a gas pressure above the liquid level.. in,this,case,!the wall of dome 5, supposed to be of the shape shown in veit.i@al s6- @tio@ a;t amb (Fig. 2), tends, under the,,effect of'th'e gaseotis pressure, to deform by @eing inflated at the top (for insta,nce,,,with a v,ery great exaggeration, toward the spherical surface amlib). In -.the top portion of the dome, th,e main stresses are ten.@. sions exerted on the parallels and the meridians. But the deformation of the,dome.produces a different eff ect.upon the portion of the dome closb to belt 2., In @ this ipq@tion of tlie tank the stresses on the meridians are compression,st@e@ses. Iii othe@ w6@d's,, iirid'er th6 eff@ci @f tli6 above mentioned deior -M-ation of, the dome, the parallels in this lower portion.thereof tend i6 shdrten. Th ese parallels, are located in a zone such as tliit between horizontal sections AB and CD (Tig.; 2), where, due to.th.e general ovoid shape that has I)een chosen, the curvatures of th6 m6ridians are maximum. At a point.such,.as x of this zone, I may therefore. have,,in the direction of the meridian and acting on. th parallel, tensible stresses Ti, 6,nd, on the contrar in tfle direction of the parallbl Y, and acting- on the ineridian, compression str6ss6@ T2 (Fig.,3). These compressions tend:to',produce a bu kli4g,Qffect,which would correspond to deformations, such as show-4 on an exaggerated scale,at 6 on Fig. 3. provements Brought to Tanks, in Particular to ;15 : In tanks of the type above set forth, in order

Thus, in the zone between AB and CD, a buck- might take place, same as in section plane ling effect is produced -which is due to the im- III-M, by compression on the meridian. portance,, of the meridian qur@vature. But, on This bizckling effect may also. be prpvented by the other hand, the, increa,@e 'of this meridian a suitable choide of the mean, curvature of porcurvat&6 tends to increase'-the resistance to r) 'tion 7, at'@ach' 6f th6 points olf 'its meridians. buckling. The principle of my invention consists In other words, it will be necessary suitably to in taking advantage of this circumstance for ob-' taining -a structure which is capable of supporting the stresses exerted thereon in service without requiring external reinforcements.10 As a matter of fact, the resistance to buekling of double curvature thin walls depends essentiglly upon the mean curvature Cm which is given by the fouowing formula: 15 11 (R@2 R,2 In *hlch 1 20 Rm i's the curvature along the meridians and 1 R, is the curvature along the paritllels. @ @ It is therefore possible, either by calcwgtion or by successive trials, or by experimenting on models, to determine the meridian curve, in its portions ae or bd corresponding to the zone in 30 question, in such manner that the mean curva@ure, along these portions, gives rise to a resistance to buckhng sufficient for enabling the wall tank to resist all stresses as rnay- be developed, even when the tank is but partly filled and sub- 35 jected to an internal pressure, without requiring any external reinforcement. This wM involve the choice, for the radius R .bf curvature Ri of the meridians in said zone, of a certain value or a'certsin law of variation ca- 40 pable of ensuring the desired resistance to buckling. Of course, these values may vary within a certain range. . It should be well understood that although the tank wall is capable of sup@orting by Itself any 45 stresses as rnay be produced, nly invention does 3:i6t exclude the provision of external reinforcements, intended for instance to ensure an increased rnargin of safety. @ There exists in the top portion of the dome 50 (portion c?nd) another cause of secondary compression 'stresses, resulting from negative pressures inside the tank, from the weight of the dome and from overloads due to climatic or aceidental conditions. This secondary effect is of 65 comparatively small importance and can easily be remedied if said portion cmd of the tank is given a shape approximateing that of a portion I of a sphere, with!a radiiig R2 equal to or smaller than the value corresponding to buckling@ 60 Concerning now the pbrtion of the tank located under the belt and more especially the zone 7 between said belt and the bottom proper 1, the phenomena th@at take place therein are analogous to those above referred to, but they are due to a& another cause, to wit the effect of the liquid alone during the fwing or emptying of the tank. If, for instance, it is supposed that the liquid level is at PQ, below the plane AB of belt 2, and . that the gas pressure is low or equal to atrnos 70 pheric pressure, zone aa'bb between AB and PQ tends to deform under the effect of the weight of the liquid, curvilinear arcs aal afid bbl tending to become straight lines so that in an interdetermine the radius or radii of curvature R3 of the curvilinear generatrix corresponding to this portion 7 of the tank. Thus, it is possible for someone skilled in the art, -by applying the principle of my invention and suitably determining pararneters Ri, R2, R3, etc., to obtain a thin waU tank capable of resisting aU the stresses that may be developed therein without requiring a reinforcement external frame, 'Me values found for these parameters will generauy lead to the choice of corresponding suitable values for the @ respective heights hi and h2 of the dome and of the lower portion of -the tank and also for the diameter d of the bottom in contact,with the ground. This last men'tioned value is preferably chosen large so as to reduce the effort aPPlied to belt 2 and pillars 3 by the weight of the liquid in the tank. Concerning the calculations leading to the choice of these values, the following indications are given, although it should be well understood that they have no limitative character. . These indications relate, for instance to portion -7 - oi@ the tank and concern the efforts in the vicinity of the belt (for instance in a plane such as PQ or EF) (Fig.i 2). I will call: v the annular volume per radian between the horizontal plane of the point that is being considered, the cylinder of a diameter d equal to that@ of the bottom proper coaxial with the tank, and the tank -wall, w the specific weight of the liquid, s the annual area per radian in the horizontal plane of the point that is being considered, and p pressure in this horizontal plane. The main effort Np per unit of length of the waR on the parallels, generauy a tension, will be given by the fouowing for-mula: Z;v+@p N,, = r COS a @(A) in the cL is the angle of the plane tangent to the WaR with. the vertical direction and r is the rg,dius of the parallel. On the other'hand, the main effort Nm on thO meridian is given by the following formula: (B) by way of examples, these forrnulas will be applied to @the case of a tank of a capacity of 10,000 cubic meters, in which I wiU consider a horizontal Plane deflned by the following values: R=17.5 meters RP=18.0-66 m. @'=46.7 M.2r--17.44 iii. Rln=4.09 m. P, 11.1,0 tons per sq. meter co@=0.9884 V@91.9 M.3 .-,Application of the@above formulas gives the fol]otving results Nl,=35.4 tons per meter Nni=43.8,tons.p@@r,meter ese are the; iii6,in tensions norinauy @supportmediate plane such as EF bucklingphenomena 15 ed@bS'r@'-pbrt'16i-i@;7' of-,the t@@nk in the Plane that is

eonsid6red. It is found that the conditions thus -curvature @of for 'instance 21.40 in all dir6ctions obtained are much more favorable than for a cylindrical tank of the same radius R, for @wllich calculation. shows thot tension Nm wowd be equal to 194 tons per meter. . I viill now examine, according to the above explanations, the case in which these efforts N.,) and Nm, or at least Nml ri'lay be compressions. In order to calculate the maximum compression that may take place in the plane that is@considered (PQ or EF), it must be@ supposed that, the pressure becomes zero; in this case, in the:above example, I have: N.p=5.32 tons per meter, rtnd Nm=23.5 tons per meter. Thus, while Np is still positive, Nm is negative. It corresponds to a compression which:may involve a buckling effect. Now, in order for the whole to resist buckling, the following condition must be complied with: E -. -e2C@ N-<I-b2 @3- in which E is Hooke's modulus, b Poisson's, coefficient, e the thickness of the waU and,Cra the al?ove defined means curvature., For a wall of 8.5 mm., this condition is:. , Nm<187 tons per meter. So that, for a -wall of a thickness of 8.5 mm., I have a safety coefficient equal to 187 @3-.-5 1. e. approximately 8. It would be possible to calculate in the samo rnanner the resistance to buckling of the dome. For instance, for a point of the dbme close to the belt (in a plane such as III-M of Fig. 2), in which. r=17.10 Rin--6.40 Rp=18.42 and with a gas pressure of 1.75 tons per squore meter, I have: Np= 16.1 tons per meter Nm=14.2 tons per ir-eter. Therefore, in this case, Nni corresponds to a compression. . Now, resistance to buckling, according to the above formula, is sufficient when Nm is smaller than 159.4 tons per meter. Therefore, the safety coefficient is 159.4 -f4.-2 7 or 11.2 On the other hand, the dome should, of course, b6 capable of resisting the maximum main ten-@ sions corresponding to the case where liquid alone would fill the t-anlc to the maximum level, with, in '@d@ition, the gas pressure. In the case above ref6@ied to, it would be found, by app . lying Foriiiulas A and B, that these maximum tensions Nm and Np would not exceed 90 tons per meter, a value which caii be support d, without any risk, by a wall 8.5 mm thick. Finally, there would remain to verify, still'by means of the conventional formulas relating to buckling that the dome can resist buckling under the effe@t of its own @veight and of an overload. @ a@ It would be easy@ to show that, for@ radius of and an overload of 0.65 ton per meter, the compression effort would average 6.95 tons per minute, corresponding to a safety coefficient of about 6. 6 These exa@-nplc-s show that it is @possible, either through the calculation method above set forth or@ through any other.'suitable method, to pro@ vide a thin wall tank the meridian of which is so shaped as to enable it to resist all stresses, 10 both compression and tensile ones, that may be exeirted thereon, without requiring any external reinforcement. It seems that, concerning the above mentioned parameters Ri, R2, R3, and ratios 15 hi d and 2 2R they should advantageously be chosen inside thp following liriiits, which are given merely by @way 20 'ndication but should not be considered @as of i having an@ limitativb character. h, F- should preferably range from 1.5 to 4 2 25 d from 0.5 to 0.5,, 2R RI f 0 r m 0.15,to 0.5@ : R@ 30 R, froiia 1 to @.5; @R@ from 0.12 to 0.4. 35 R My. invention further includes the following features@ relating more especially to the belt and its@supports, on the one hand, and the construe-, t-lon of the ovoid wall, on the other hand. 40 Concerning tile belt, it has already been stated that its essential function is to act as a rigid support for the @thin wall of the tank proper. But it further contributes in protecting the tank against buckling!and against deformation in the 4 @-) plane of its maximum horizontal section, in partigular under @the effect of a lateral wind (if the reservior is not buried in the ground). The transverse section of this belt will therefore;be chosen sufficiently rigid and sufficiently strong for 50 preventing any such deformation. O@n the other hand, it is necessaxy, while permitting displacements due to thermalexpansion; to prevent,any translatory movement of the belt (in ])articular under the action of wind). 55 In order to ensure expansion, the pillars such as 3, may be given a sufficient inclination, as al@ ready mentioned in the ;above mentioned prior pplications, said pillars being arranged in such m anner as to be able to move with respect to 60 their base or to deform elastically. It is thus possible to guide the belt in such manner as to permit vertical displacements and radial deformations thereof, In order to prevent horizon-tal displacements 65 of the center of the belt in its own plane,, I provide bracing means, consisting for instance in a triarigulation @system i8 extending between the successive pillars 3 or at least some of them. The bracing means may be constitut@d by the pillars 70 themselves, digposed in V arrangement in elevatioli. In the embodiment shown by the drawings, pil-@ lars 3 are anchored, at the bases thereof, in concrete or metal blocks 4 (in which,they niay be i 75 pivotallymounted) these blocks being calculated