Squaroid type liquid storage tank

July 9, 1963 _{c ARNE} 3,096,901

SQUAROID TYPE LIQUID STORAGE TANK

Filed May 12, 1960 3 Sheets-Sheet 1

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July 9, 1963

C. ARNE 3,096,901

SQUAROID TYPE LIQUID STORAGE TANK

Filed May 12, 1960

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July 9, 1963

C. ARNE

SQUAROID TYPE LIQUID STORAGE TANK

3,096,901

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3,096,901

Patented July 9, 1963

United States Patent Office

3,096,901

SQUAROID TYPE LIQUID STORAGE TANK Christian Arne, Chicago, III., assignor to Chicago Bridge &amp; Iron Company, Chicago, III., a corporation of Illinois

Filed May 12,1960, Ser. No. 28,719 ⁵

Claims. (CI. 220—18)

This invention relates to improvements in large capacity liquid storage tanks. It is more particularly concerned with storage tanks of the so-called “squaroid” 10 type.

In general a squaroid tank comprises a flat bottom resting on a prepared grade or foundation, a substantially flat roof supported by columns and girders from the bottom, and sidewalls which are straight in plan and curved 15 in elevation. A squaroid type tank can be either square or rectangular in plan, although it may in unusual cases be triangular, pentagonal or otherwise polygonal. One of the chief advantages of the squaroid type tank over the more conventional cylindrical storage tank is that, in 20 areas of extremely high land values, a rectangular squaroid type tank makes more efficient use of the land on which it is built because most parcels of land are rectangular and therefore less land in any parcel is wasted when a squaroid is used than is the case when a cylindrical tank ²⁵is used.

The present state of the squaroid tank art is as shown in Boardman United States Patent No. 2,593,408 in which there is described and claimed a simple squaroid having mitered corners, and with sidewalls having a ³θ curvature as determined by a formula therein given.

It has been found that more efficient utilization can be made of material going into the construction of a squaroid tank by making changes in the curvature of the sidewalls, the design of the corners, the relative dimensions of the roof and bottom, and other changes, for the purpose of effecting a more efficient distribution of stresses in the squaroid tank structure. According to this invention there is provided an improved squaroid tank, design which, among other things, distributes a ⁴⁰relatively greater proportion of the total horizontal tension-stresses to the tank roof than previously, and correspondingly reduces the proportion of the total horizontal tension stresses carried by the bottom. In the tank of this invention there is provided a means for distributing ⁴⁵portions of the total horizontal stresses formerly carried by the roof and bottom to the sidewalls, thereby reducing the amount of material necessary to be used in the bottom and roof and also increasing the strength of the sidewalls. The vertical curvature of the sidewalls of the ⁵instant tank is such that the strength of the vertical trusswork extending from the bottom to the roof and located generally in the space between the vertical sidewall curve and the chord of such curve is more efficiently utilized. These and further improvements in squaroid type storage ⁵⁹tank design will be related in more detail in the succeeding portions of this specification.

In the drawings:

FIGURE 1 is a plan view of an illustrative embodi- 60 ment of a squaroid storage tank of this invention, illustrating in the lower left quadrant a fragmentary view of the vessel in its completed condition; in the upper left quadrant is shown the tank without roof plates in place in order to illustrate the layout of the bottom plates and 65 the vertical columns supporting the roof trusses; the upper right quadrant shows the column and roof truss layout; and in the lower right quadrant the roof truss and purlin layout is seen;

FIGURE 2 is an elevation view taken along line 2__2 ⁷⁰ in FIGURE 1 the left portion of which shows the com- pleted tank in elevation; and the right portion presents a cut away sectional view;

FIGURE 3 is a graphical presentation of the horizontal force pattern exerted by a contained liquid;

FIGURE 4 is a schematic representation of the force moment which is created in the tank sidewall by the liquid contained within the tank;

FIGURE 5 illustrates the general equation of this invention for the curve (shown in solid lines) at any point along the sidewall in comparison with the curvature (shown in dotted lines) of the sidewall of squaroid type tanks constructed in accordance with Boardman’s teachings in United States Patent 2,593,408;

FIGURE 6 graphically represents the factors “H,” “A,” and “h” shown for a point “P” on the curve of the sidewall in juxtaposition with the curve of a sidewall constructed in accordance with Boardman’s teachings;

FIGURE 7 shows a sidewall curvature that includes, in addition to the improvement of this invention, a curvature having greater overhang in an amount necessary to make the tension in the roof plates equal to the tension in the bottom plates;

FIGURE 8 is a fragmentary view of a section of the sidewall showing details of the heel structure employed at the tank base; and

FIGURE 9 is a cross-sectional side view of the sidewall taken along line 9—9 of FIGURE 8.

The horizontal component of the forces exerted by a contained liquid, such as water or oil, range from zero at the free liquid surface of the contained liquid to a maximum at the bottom of the liquid container, as is shown graphically in FIGURE 3. The centroid of such forces, therefore, is at the level one-third of .the distance above the bottom of the container, as represented by the large arrow designated “C” in FIGURE 3. In order for a straight, vertical-sided container wall to contain the horizontal components of the liquid pressure forces, it is necessary that the thickness of the wall be increased from a nominal thickness at the top to a substantial thickness at the bottom. This is the manner in which cylindrical liquid storage tanks are constructed. In such tanks, however, the liquid pressure is resisted by the hoop tension •of .the cylindrical walls, and .the cylindrical tank is designed so that the cylindrical walls carry the entire load resulting from the horizontal liquid pressures. In the cylindrical tank, therefore, the bottom and the roof may be constructed of light gauge materials, and it is quite generally the practice to use relatively thin steel plates for the top and bottom, and to weld them together by means of lap-welds because virtually no tension stresses exist in the plates, and the welded plate connections as a consequence need not be of great strength, the primary reason for connecting -them being to make the bottom liquid-tight.

In the design of a squaroid, however, it is impossible to develop hoop tension in the sidewalls, as is done in a cylindrical tank, because the sidewalls are polygonal in plan rather than circular. In order to resist the horizontal components of the liquid in the tank, therefore, it is necessary that the sidewalls be so designed as to develop tension in the vertical direction rather than in the horizontal direction as is the case with a cylindrical tank. When this is done, it can readily be seen that the sidewalls of the squaroid must, for efficient design, be of equal thickness from top to bottom, but because the horizontal components of the liquid pressure range from zero at the top to a maximum at the bottom, when the tank is full, it is necessary to select a curve in the vertical plane of such a shape that the sidewalls are in equilibrium, as taught by the Boardman patent above mentioned. The tension developed in the sidewalls must be transferred to other

3,096,901 members at the bottom edge of the sidewall and at the top edge of the sidewall. A strut is therefore provided, as taught in the Boardman patent which, when the tank is full, is subjected to high compressive stresses resisting the tensile stresses of the tank sidewalls, but it can readily be seen that there are uncompensated horizontal components of the tension transmitted from the sidewall at the top and bottom to the connecting members at each line of connection. It is therefore obvious that the unbalanced horizontal components must be carried by the roof and the bottom plates. Because the centroid of the horizontal forces, when the tank is full, is at the elevation one-third of the height between the bottom and the top, it becomes evident that the bottom plates must carry two-thirds of the total unbalanced horizontal forces transmitted from the sidewalls and that the top roof plates must carry only one-third of the total of such forces transmitted from the sidewall, when the sidewall curve taught by the Boardman patent is selected. This result can be seen by reference to FIGURE 4, in which the curve selected by the Boardman patent has been plotted in order to demonstrate the moment that is created by (a) the weight of the liquid in that portion of the Boardman curve which overhangs to the left of the vertical dotted line running through the sidewall to bottom connection and (Z&gt;) the vertical pressure acting against that portion of the sidewall to the right of the dotted line above mentioned. Since the sidewall tension at the bottom connection is equal to the sidewall tension at the top connection, and the connecting angles, Θ and Φ, are equal, it becomes obvious that if there were no moment the horizontal components of the tension transmitted through the bottom and top connections would be equal. The compression strut, extending between the top and bottom connection, not being vertical, therefore transmits horizontal components of the compressive stresses through the connection, and the net result is that at the bottom connection the sidewall tension and the strut compression transmit horizontal components of stress which are additive, while at the top the sidewall tension and the strut compression transmit horizontal components of the stress which are subtractive, and, as stated above, when the Boardman curve is used, the bottom carries up to two-thirds of the total horizontal component of the sidewall tension while the top carries only one-third.

Moreover, it will be seen that the Boardman design shows straight mitered corners, with a metal plate diaphragm extending vertically in the plane of the mitered joint as a reinforcing member. This construction effectively eliminates the possibility of working the sidewalls in tension in the horizontal direction. It has also been found in accordance with this invention that the sidewalls can be made to work in horizontal tension, thus increasing the stiffness of the sidewalls without increasing the thickness thereof, by substituting rounded corners in place of the mitered corners shown in the Boardman patent.

Referring now to FIGURES 1 and 2, the squaroid type storage tank shown therein is of large size being of the order of 310 feet square in overall dimensions and 42 feet high measured from the top of the foundations. Such a vessel has a capacity of 576,000 barrels. It will therefore be seen that the vessel is adapted for storage of extremely large quantities of liquid, having capacities well beyond the capacity of conventional cylindrical storage tanks.

The storage tank of this invention is constructed by initially preparing a foundation 1® which may be a well graded, oiled, sand or gravel pad on an earth subgrade. Flat bottom plates 12, thick are placed upon the foundation 10 and suitably connected together as by lap welding or butt welding.

Vertical columns 13 are erected at spaced intervals on the tank bottom 12, and sidewall trusses 14 are erected around the periphery of the tank bottom to which 14 thick sidewall plates 15 are attached. Roof support beams 16 are erected horizontally between adjacent columns 13, ⁴ roof purlins 17 extend in spaced relationship across the roof support beams 16, and the roof plates 18, which are s/_le thick, are placed over the purlins 17 and secured. For example, in the illustrative tank the columns are placed on 25' centers with the side trusses being placed on 5' centers.

In the rounded corners of the storage tank it will be noted that uniformity of the trusswork evident in the sidewall construction is carried through in the corner construction. With rounded corners there occurs a ring tension which puts horizontal tension in the side plates. Therefore, the side plates will expand elastically in harmony with the bottom plates. In the illustrative, embodiment a corner radius of 30' is employed.

The columns 13, roof support beams 16, purlins 17 and roof plates 18 are all of conventional design and construction, and are erected in the normal fashion. Preferably the center of the framing is held in fixed position. Temperature expansion of the framing is in a radial direction.

The curvature of the side wall 15, however, is unique, as is the co-registering curvature of the curved portion of the side trusses 14.

FIGURE 5 shows in larger scale, the design of the side trusses in accordance with the instant invention wherein the curve at any point along the sidewall is defined by the formula

Equation 1

T ^R2=jw(h-kH) in which the terms represent the following parts:

I?₃=thc radius of curvature of vertical curve, in inches. T—tension in the vertical direction in a 1 wide strip of the side plate, in lbs. per inch.

w=the actual weight of the liquid stored, lbs. per cubic inch.

j=a selective variable based upon the weight of the stored liquid.

77=the full height of the vessel measured from the bottom of the squaroid to the top capacity line, in inches. h=the distance in inches, from the top capacity line to any point P on the curved side plate.

A=a selective variable based upon the height of stored liquid.

A graphical representation of H, k and h is shown for a point P on the curve in FIGURE 6. The value AH is measured downward from the top capacity line.

FIGURES 5 and 6 also show by means of dashed lines the curve made according to the formula which is taught by Boardman.

The dashed curve ABCD in FIGURE 6 is in equilibrium when the squaroid type tank of this invention is full to D. The solid line curve ABCKD is in equilibrium between A and K when the squaroid type tank is only partially full to the level K, but when the liquid level is raised from K to D, the solid line tends to distort to resemble the shape of the dashed line, that is, to pull inwardly in the region of B and outwardly in the region of K. This tendency is manifested in loads which are transferred to the web members of the truss. Therefore, at the liquid level stage above K the web members will counteract the downward load from D an the strut and the strut will deliver a smaller downward load to A. This is reflected in the design by making the angle at which the side plate is connected to the bottom smaller than is the case in the Boardman design, as shown by comparing the solid ‘and the dashed curves at this point A.

When the liquid level is in the region of B it is, in both cases, necessary to have truss members which will carry the overhanging liquid load. The web members will

3,096,901 generally undergo a reversal of stress as the liquid rises above .them. On the dashed curve, these stresses are functions of the total height H, but on the solid curve they are functions of the height H—AH and are therefore smaller. After the liquid rises above K there is introduced in the truss a new set of stresses unknown in Boardman’s structure. ; In the instant structure lighter web members may be used than in Boardman’s structure for liquid stages from A to K and these lighter web members are still able to carry the loads imposed on them by liquid stages from K to D when the location of K is selected to the best advantage.

Actual physical conditions, including both the height of the tank and the weight of the liquid stored, will influence the values selected for j and k. The “A” value is used to effect economy in .the web members and the “j” value is used to effect economy in the strut member. If j is given the value . ^H^J H—kH which may be done advantageously, Equation 1 is modified into .the expression:

„ T(l—k) τη x. „ ^R^h-kH) Equation 2

In Equation 2, the most advantageous values for k range from a minimum of .05 to a maximum of .25. This equation is favored because it gives at point A a radius equal to that taught by Boardman but at points above A the radii are greater with the result that the amount of truss webbing is decreased.

With respect to the design of the truss portion of the curve, the “A” value represents a percentile of the full height of the tank at which liquid level the stresses in the web members reverse. The stress reversal, excepting stability of the web members, allows the web members to do two jobs instead of one. This procedure also gives a depth of truss which allows the designer to use a smaller inclined strut member. It is not only the stress situation in the web members with which it is necessary to work in order to determine a “A” value; but also, in the case Where the member is in compression, the stability of the member in question can dictate its size. For design purposes the value of “A” will vary in accordance with the following schedule:

Tank height: 20 feet 0 feet0.05 feet0.25 feet0.10

Above a certain height, it becomes more economical to curve the shell according to some relatively small radius. It is not desirable to use a large radius having a center at 16 H and tying in not only at the bottom but at the top because the triangular shaped liquid load resultant acts below the halfway point and would unbalance the shell stress situation. This type of stress pattern would be contrary to the objectives of this invention. Accordingly, one radius is used to carry the load around -the bottom part and a flat configuration is used at the top. When this is done, it becomes necessary to find a radius which will provide the most economical solution with regard to the size of the web members and strut. If the factor “j” were not used and a large radius were used, the tension in the plate would be greater and the strut would therefore be a rather heavy compression member. If a factor “j” is used in the equation, then the radius becomes smaller and .the depth of the truss will be, of course, somewhat larger (up to a practical maximum of 12 feet for transportation purposes). In effect, the “j” value is changing the weight of the design liquid to give a more advantageous distribution of stress between the strut and the side plates. The side plates are never under very high stresses, but 14 minimum thickness plates are used in fabricating the storage tank of this invention.

The foregoing Equations 1 and 2 produce a curvature of the truss and of the co-registering sidewall plates which differs from the curvature shown in the Boardman patent in that the curvature shown in the Boardman patent is designed to produce zero stress in the truss web members when the tank is full, whereas the curvature obtained by the foregoing formula produces zero stress in the web members of the truss at a liquid level that is always less than the full condition provided, as is usually the case, that the curve is a straight line above K. By selecting a height somewhat less than the total height of the tank for the location of point K, it is possible to fit the web members of the truss through a reversal of stress and thereby to utilize them more effectively.

For example, where the point K is selected at height of 0.8H, where H is the total height of the vessel, a web member stressed in tension when the liquid level is below 0.8H will reach zero stress when the liquid level reaches 0.8H and then will be stressed in compression as the liquid level rises above that point. Similarly, a web member normally in compression at liquid levels below 0.8H will be reversed and go into tension as the liquid vessel rises above 0.8H. Inasmuch as the web members of the truss are relatively short, they are all capable of taking compression stresses and for that reason their cross section may be reduced from the cross section necessary if this reversal of stresses did not take place.

By way of an example, a comparison between the maximum compressive stress in a compression member of the truss web in a vessel built in accordance with the Boardman patent and one built in accordance with this invention where point K is located at 0.8H reveals that the maximum compressive force in the Boardman structure would be 10,000 pounds compared with 8,000 pounds or less for the instant invention. The difference is accounted for by the facts that, first, the truss sustains a smaller height of liquid AK, and secondly, at liquid levels from K to D an entirely new system of loads are imposed on the truss web members and these new loads can be sustained by the same web members when the location of K is selected to the best advantage.

It is also possible to achieve further economies by varying the .amount of overhang of the curved sidewalls of the vessel from that shown in the Boardman patent. FIGURE 7 shows a sidewall curvature that includes, in addition to the improvement shown in FIGURE 5, a curvature having greater overhang in an amount necessary to make the tension in the roof plates equal to the tension in the bottom plates. Normally, because of requirements for corrosion allowance, stiffness, etc., the minimum thickness of plates to be used in a vessel of this type is 'A As explained above, the tensile forces applied to the bottom plates are normally double those applied to the top plates because the centroid of the liquid forces in the vessel occurs at a point Vsh above the bottom. The sizeable force in the bottom plates may require that the thickness of the bottom plates be increased from Ά to or perhaps %. On the other hand, the roof plates made of a minimum thickness of W may not be stressed to their full working capacity, and by changing the shape of the curvature of the sidewalls, and also, of course, the shape of the supporting trusses, a more nearly equal distribution of tensile forces is achieved, thus enabling the designer to construct both the bottom plates and the roof plates of 14 thick steel.

For example, when 'A thick plates are used in bottom and roof which usually is the minimum plate thickness, on account of corrosion factors, the Boardman Squaroid can be built to a height of 34 feet with % the load in the bottom and Ά the load in the roof. When the overhang is increased to make the load equal in the bottom and the roof, the squaroid type tank of this invention can be built to a height of 39 feet without adding anything

3,099,901 to the roof or the bottom, thus increasing capacity by five feet of height without increasing the cost of either roof or bottom.

The above example is based on both roof and bottom being single lap welded. That is, in this case, welded from the top side only. The bottom is not ordinarily accessible for welding underneath because it is normally assembled directly on the ground. The roof, however, is accessible. Therefore, this invention makes it practical to increase the height of the -squaroid from 34 feet to 48 feet by welding the roof from both topside and underside and by increasing the overhang until the roof carries % of the total -load and the bottom carries Vs. This is still done with 14 thick plates in roof and bottom and with the bottom single lap-welded in all three cases.

By increasing the overhang still more, it is possible to put all of the load in the roof -and none in the -bottom. This is desirable where severe conditions of corrosion exist because the roof and sides can be given periodic inspection from both sides of the plate and the bottom can be inspected only from the topside.

If the -overhang is increased until -all the tension is in the roof, the bottom plates may be omitted. This would find practical application for ex-ample, in a water reservoir built on a foundation of impervious clay. Such a structure would normally have the sidewalls supported on a concrete ring wall.

It is obvious that -by increasing the -overha-nge still more, there would be created a condition where the bottom plates are in compression and the roof plates sustain a tension equal to the sum of the total liquid load plus the amount of the compression in the bottom. Moreover, the roof plates would be in tension when the tank is empty, a tension created by the -overhanging weight of steel. Such a condition is helpful in increasing the distance between roof supports and in keeping the roof plates from fluttering in the wind.

The overhanging liquid load creates a downward force which is exerted upon the foundation and spread evenly over the entire tank bottom, when the storage tank is constructed in accordance with the teachings of Boardman, by means of a strut-truss system in cooperation with an inwardly projecting -truss member. In accordance with one of the features of the instant invention, the overhanging liquid load can be reduced by providing a heel structure which, preferably, is continuous and extends peripherally around the base of the tank. This feature is shown in FIGURE 8 wherein is shown a fragmentary view of a section of a sidewall 15 and FIGURE 9 which is a profile view of -the sidewall taken along line 9—9 of FIGURE 8. A plurality of spaced side trusses 14 are assembled such that in cooperation with the sidewall 15 a heel structure 20 is formed at the bottom. The heel structure comprises a box girder comprising a bottom plate 21 which is connected -to a side plate 22. Plates 21 and 22 can be welded together to form the corner angle or a single plate can be formed into the desired configuration. The side plate 22 preferably depends tangentially from the sidewall 15 or it can be vertically attached thereto. Web members 23 are fitted into place and secured to -the side plate and bottom plate to complete the assembly. To permit the elimination of the inwardly projecting truss member employed by Boardman, the instant invention employs a continuous bottom plate 21, which extends from the side plate beyond the connection between the compression strut 24 and the tank bottom 12 to the point of connection with -the bottom proper.

The use of such a heel structure not only permits the tank to drain clean by eliminating any obstructions between the sidewall 15 and -the tank bottom 18 but also has the advantageous functional effect of reducing the earth pressure at the edge of the tank which is especially helpful when the tank is full. It also permits the use of a lighter -truss 14 because although under these conditions of load a moment exists in the truss at full load, the moment in the truss at part full stage is reduced. This construction also adapts itself to shop construction and assembly which is more economical and convenient than field erection. The extent to which bottom plate 21 extends outward of compression strut 24 depends upon required design considerations used in fabricating the -truss 14 to obtain maximum effectiveness with minimum weight.

The instant invention has special application in the storage of liquids such as water, liquid petroleum products, etc., at substantially atmospheric pressure where capacities about 300,000 barrels and upward are required. It can, however, be used for smaller installations if desired. Conventional materials of construction and API standards and AWS standards are used in the erection of the tanks of -this invention.

Although the instant invention has been described by reference to several illustrative embodiments, it is evident that various modifications will be suggested to those skilled in the art -to which this invention pertains without departing from the scope of -this invention.