US3280518A - Hyperbolic paraboloid roof structure and method of constructing the frame thereof - Google Patents

Description

W. S. WHITE, JR ABOLOID ROOF STRUCTURE AND 3,280,518 M THOD OF Oct. 25, 1966 HYPERBOLIC PAR 5 Sheets-Sheet 1 Filed Oct. 6, 1959 INVENTOR. MA TEE .5. WH/TE, Je.

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HYPERBOLIC PARABOLOID ROOF STRUCTURE AND ME CONSTRUCTING THE FRAME THEREOF 5 Sheets-Sheet 2 Filed Oct. 6, 1959 JNVENTOR. M475? 5. WwrE /fe.

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3,280,518 HOD OF W. 8. WHITE, JR

Oct. 25, 1966 HYPERBOLIC PARABOLOI 00F STRUCTURE AND MET CONSTRUCTING THE FRAME THEREOF :5 Sheets-Sheet 5 Filed Oct. 6, 1959 IN V EN TOR. M1. 752 5. W075, (I.

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United States Patent 3,280,518 HYPERBOLIC PARABOLOID ROOF STRUCTURE AND METHOD OF CONSTRUCTING THE FRAME THEREOF Waiter S. White, Jr., Palm Desert, Calif. (R0. Box 310, Colorado Springs, Colo.) Filed Oct. 6, 1959, Ser. No. 844,744 9 Claims. (Cl. 52-80) This invention relates to building construction and particularly to a hyperbolic paraboloid roof structure of the type disclosed and claimed in my copending application Ser. No. 749,882, filed July 21, 1958 and now abandoned and entitled Curved Roof Structure of which this application is a continuation in part.

The hyperbolic paraboloid is a geometric configuration defined by a straight line generatrix translated about a transverse normal line and angularly moved about that line as an axis during the course of such translation.

The essential problem encountered in constructing such a structure is that the horizontal projection of a roof structure is desirably polygonal, that is, having sides that are straight. Strips of wood or metal that are uniform in cross-section cannot be used economically because the area described by the generatrix is obviously greater, the farther away it is from the axis along which the generatrix is translated.

In my copending application I described and claimed the use of a transversely flexible decking strip made of uniform cross sections whereby hand fitting methods may be avoided. The primary object of this invention is to improve in general upon the structure as shown in said copending application.

In hyperbolic par-aboloid roof structures of the character discussed herein, essentially a two-point suspension or support is provided at diagonal corners of the structure. The opposite or diagonal corners are elevated. By virtue of the fact that only two points of support are required, substantial freedom and versatility of plan design is achieved within or beneath the roof structure.

Heretofore the angle of inclination to the horizontal from a point of support to the quadrature point high above the support has been kept rather substantial in order to minimize the cantilever type torque imposed on the roof. The lower the angle, the greater the torque. From the standpoint of savings in material it is obviously advantageous to maintain the lowest possible angle to the horizontal. An object of this invention is to make possible for the first time a very low arid graceful angular inclination of the entire roof structure, yet maintaining the desired two-point suspension.

It has been heretofore understood that there is a substantial stress tending to move the two points of the support outwardly and this is by virture of the very characteristic of the hyperbolic paraboloid structure. In other words, the arch that exists in a vertical plane passing through both support points tends, under the weight of the roof, to flatten. This means that the support points of the arch tend to move apart. An object of this invenion is to provide a new hyperbolic paraboloid roof structure of this character that adds an extra dimension of strength thereto, whereby no special reinforcements what soever need be provided in order to restrain the roof from such movement. Accordingly, one of the principal problems heretofore encountered in hyperbolic paraboloid roof structures is now overcome.

In order to achieve the foregoing results use is made of a double decking structure, each deck or layer isformed by joining a plurality of transversely flexible decking elements in side-by-side relationship. The decking elements in each layer extend transversely of those of the other vlayer.

3,280,518 Patented Oct. 25, W66

In structuresof this character, it is no small problem to provide an adequate peripheral support for the decking elements. The reason for this is that the plane of the decking element changes drastically along the length of the peripheral support. Thus at the support points of the roof structure, the plane slants downwardly in an outward direction, whereas at the elevated corners, the plane of the roof slants upwardly in a corresponding direction. In my prior application I utilized tubing at the peripheral supporting structure.

For purposes of providing an appropriately oriented plate for attachment to the decking elements of the roof, I provided a channel that was twisted along the length of the tubing, the tubing by its very nature providing a support appropriately operable irrespective of the angular orientation of the channel about the axis of the tubing. The tubing as such is not a particularly strong section for present purposes. Furthermore, it is not particularly simple to weld the channel into position after the peripheral support member are elevated.

Accordingly, an object of this invention is to provide an improved method of peripheral support whereby the appropriate changing orientation of the support is automatically achieved. For this purpose I utilize channel elements as the primary peripheral support members, and by the aid of a unique process, cause it to be appropriately oriented by an automatic process as the support members are placed in position.

This invention possesses many other advantages and has other objects which may be made more clearly apparent from a consideration of several embodiments of the invention. For this purpose there are shown a few forms in the drawings accompanying and forming part of the present specification. These forms will now be described in detail, illustrating the general principles involved; but it is to be understood that this detailed description is not to be taken in a limiting sense since the scope of the invention is best defined by the appended claims.

Referring to the drawings:

FIGURE 1 is a pictorial view of a roof structure incorporating the present invention;

FIG. is a top plan view thereof;

FIG. 3 is an enlarged fragmentary sectional view taken along a plane indicated by line 3-3 of FIG. 2;

FIG. 4 is an enlarged fragmentary sectional view taken along a plane indicated by line 44 of FIG. 2;

FIG. 5 is an enlarged side elevation of the roof structure;

FIG. 6 is an enlarged sectional view in fragmentary form taken along a plane indicated by line 66 of FIG.

FIG. 7 is a sectional view taken along a plane indicated by line 7-7 of FIG. 6; 7

FIG. 8 is a diagrammatic view illustrating how the peripheral support members are elevated;

FIG. 9 is a fragmentary side elevation view similar to FIG. 5 but illustrating another embodiment of the present invention;

FIG. 10 is a sectional view similar to FIG. 7, taken along the plane indicated by line 1l10 of FIG. 9, but illustrating an alternate peripheral support member; and

FIG. 11 is a view similar to FIGS. 7 and 10 showing a modified roof structure in which four layers of decking elements instead of two are provided. 7

In FIG.--1 thr''i's' illustrated a hyperbolic paraboloid roof structure that is characterized by the provision of two bearing devices 12 and 14, located at two of the four cornersthereof, upon which the entire roof rests. The corners 16 and 18 of the roof are located at the bearings 12 and 14. The opposite corners 20 and 22 (see also FIG. 2) are located substantially above the bearings 12 and 14. In the present example, the horizontal projection of the roof structure is a parallelogram other than a rectangle. While this is a matter of choice, an equilateral rhombus has a recognized capacity of uniquely fitting with like structures.

The bearings 12 and 14 each consists of a concrete foundation 11 (FIG. and a generally inverted U- shaped leg 13 made of I-beam or other suitable structure. The angularity of the central connecting, portions 13a conforms to the orientation of the roof at the corners 16 and 18. A gusset plate 17 is interposed between each corner and the leg 13 to provide an increased area for support and for welding.

The roof comprises four composite peripheral support members 24, 26, 28 and 30 (FIG. 2) of virtually identical construction. These peripheral support members define a framework between which decking members 32 are suspended in side by side relationship.

The decking elements are elongate and are uniform in cross section. At one side of each of the decking elements 32, and as illustrated in FIG. 3, a socket 34 is formed and at the opposite side of a depending flange 35 is provided. The socket 34 at the right hand side of one decking element 32 (FIG. 3) receives the flange 35 of the next adjoining decking element 32. The socket and flange arrangement serves as a means whereby the decking elements can be secured together to form a unitary whole, the-re being suitable welding at the area of the flanges 35 and sockets 34. The decking elements are similar to those illustrated in my copending application.

The decking members by virtue of their longitudinal fluting, are transversely flexible so that the ends thereof may be bent out and the central portions thereof squeezed together, whereby the number of decking elements is uniform despite the changing width or dimension of the roof. In this connction it must be noted that FIG. 2 represents a horizontal projection of the roof; in other words, the dimension along the roof between the corners 20 and 18 is greater than the dimension of the roof along the mid-length indicated by the line 1.

There are two layers of decking elements. The decking elements of the upper layer, as indicated in FIG. 2, extend between the opposite peripheral support members 24 and 26. The decking elements of the lower layer.

extend transversely to the decking elements of the upper layer and between the other two peripheral support members 28 and 30. The manner in which the decking elements 32 are connected to the peripheral support members is illustrated most clearly in FIG. 3, wherein the peripheral support member 28 exemplifies the others.

The support member 28 comprises four angles 36, 37, 38 and 39. The angles 36 and 37 have two of their flanges 36a and 37a in opposed relationship, while the other two of their other flanges 36b and 37b lie in a common plane. Sandwiched between the opposing flanges 36a and 37a is an elongate mounting plate 40 that projects beyond the flanges 36a and 37a and inwardly of the roof. A series of nuts 41 and bolts 42 serve to secure the mounting plate 40 along the length of the support member 28. T he ends of the lower decking elements 32 are welded to the under side of the projecting portion of the mounting plate 40. The decking members 32 on the upper side are in asimilar manner secured to the upper side of the mounting plates of the quadrature peripheral support members 24 and 26. However, the sidemost element 32 of the upper layer of decking members and as illustrated in FIG. 3, is likewise welded to the upper surface of the mounting plate 40.

The unusual additional dimension of strength is added to the structure by virtue of the interponnection of the layers themselves. Thus the troughs of the'fluted decking elements 32 on the upper layer are secured tothe crests of the decking elements 32 of the lowerlayer. In this example, bolts 43 (FIG. 6) are illustrated at those areas where the mounting plate 40 is interposed between the layers, and welds as at 45 are illustrated at the central areas. The bolts 43 extends as an inner border along the support members, the welds as at 45 being located within this border of nuts and bolts.

The roof structure, under load, tends as previously stated, to flatten, the corners 16 and 18 tending to spread apart. As may be appreciated in connection with FIG. 2, this means that the angularity of the parallelogram structure tends to change, and the layers of decking members tend to rotate with respect to each other. This, in turn, puts a shear on the variou fastening elements 43 and 45. The ability of the fastening elements to resist shear gives the new added strength dimension to the structure. The interlacing of the decking elements in two or more layers means that the tendency of the roof to flatten under both static and dynamic conditions is internally resisted. Means external to the roof resisting movement of the corners 16 and 18 away from each other are not actually required. The corners, however, must be confined against movements beyond the tolerable limits of deflection of the structure. The corners may be anchored to the bearing structures 12 and 14 solely for this purpose.

In this case, the roof is permitted to assume whatever position it may under its normal loaded conditions.

The bearing structures 12 and 14 are tied together by a reinforced concrete beam 66) below the ground level to resist dynamic forces without requiring the bearings individually to be overly massive. Of course, a tie rod directly between either pair or roof corners could accomplish a similar function, but tie rods so located might not be esthetically pleasing, and might interfere with placement of other strucures. The grade beam 60 adds versaility.

The corners 16 and 18 can if desired be anchored so that they are closer together than they normally would be under their static load. In this case, the bearings 12 and 14 and the reinforced beam 69 will then resist both static and dynamic loading, will be largely in tension.

Since a reinforced concrete beam most effectively is used in compression, this operation may be achieved by spreading the corners 16 and 18 apart prior to their anchoring to the bearings 12 and 14.

By tensioning the roof beyond expected dynamic loading it can then be insured that the beam 60 is always under compression.

Any intermediate distribution of load also is possible. For example, one satisfactory arrangement to permit half the spreading of the corners as might result without restraint at the corners. An effective distribution of load between the roof itself and the bearings 12 and 14 thereby results.

The angle members 38 and 39 are welded in complementary fashion to the angles 36 and 37 to form box-like sections, thereby adding increased strength to the peripheral supporting members. The peripheral supporting member 28, as it extends from anchor corner 16 forms, in essence, one of two beams upon which half of the roof is cantilevered.

The peripheral supporting members are joined together at the corners 16, 18, 20 and 22. In FIG. 6 a mitered joint is disclosed between the support member 28 and the support member 24. The members 24 and 28 are welded at the mitered joint.

The mounting plates 40 necessarily have changing orientation or inclination to the horizontal along the various peripheral support members 24, 26, 28, 30 in order to parallel those portions of the roof which they serve to attach. For this purpose the support members 24, 26, 28 and 30 are themselves warped. This may be seen most clearly in a perspective showing of FIG. 1, for example, in 'connection with the support of member 24. At the corner 16, a normal to the plane determined by the flanges 36b and 37b of the support member 24, slopes downwardly in an'outward direction. The support member 24 is twisted so that at the corner 22 the opposite angular orientation is perceived.

In order to warp the peripheral supporting members 24, 26, 28 and 30, a unique method is used. First, and as the initial step in the construction of the roof proper, the support members are positioned subtantially at a common level. At each of the corners 16, 18, 2-0 and 22, the support members are tied together (FIGS. 6 and 7) by a pair of straps 50 and 52. These straps engage the outer surfaces of the flanges 36a and 37a of the angles 36 and 37. Half of each strap extends along the corresponding support member 24 or 28.

A single bolt 54 for each support member passes through aperture in the straps 5i and 52 as well as the flanges 35a and 37a, and is held in position by the aid of a nut 56. The bolts 54 permit slight relative angular movement of the support members 24 and 28 with respect to each other about an axis normal to the plane defined by adjacent support members 24 and 28, at least to the extent permitted by slight spacing of the support member ends. In this specific example, the axis of movement In (PEG. 7) may be at either one of the bolts 54. Other devices, such as an actual hinge joint might be provided. The reason why the angular movement is necessary will appear hereinafter. The straps 5t and 52, while permitting the angular movement described, securely hold the flanges 36a and 37a of both support members in coplanar relationship. Thus the corner joint cannot break apart as by movements of the support members 24 and 28 angularly about an axis n (FIG. 6) lying in the common plane generally defined by the support members 24 and 28.

After all of the support members 24, 26, 28 and 30 are secured by straps such as 50 and 52, the diagonal corners 2G and 22 are moved upwardly. During the course of 1 this movement opposite halves of the roof actually rotate about a horizontal axis extending between the opposite diagonal corners 16 and 18, and which coincides with the axes n thereat. This rotation tends to break the joints at 16 and 18. Since the straps prevent this movement at all of the corners, the support members Warp automatically to the desired configuration.

The necessity for permitting angular movement about axes m may be explained with reference to FIG. 8. As the end of the member 24 for example, is raised, its horizontal projection tends to shorten towa d the corner 16, in proportion to the increasing angle of elevation. The magnitude of shortening is equivalent to a cosine function for the increasing angle of elevation. The end of the member 3%) likewise tends to recede, but towards the opposite corner 13. Since the ends of the members 24 and 30 are secured together, the resultant shortening is along the symmetry line p. Now it will be apparent that movement of the corners 26 and 22 together slightly changes the angles at the corners. These angles must be permitted freely to change in order to avoid bowing. Hence the degree of freedom for this purpose is provided.

After the support members are elevated, the members at the corners are securely welded together and the straps 5i) and 52 remain to provide an extra measure of strength.

The angles 38 and 39 are positioned on the roof after the angles 36 and 37 are elevated as heretofore described.

After the support members are in place, the decking members 32 of the lower layer are next positioned, as by the aid of appropriately located frame or scaffolding structure, following generally the contour of the roof. Finally, the lower layer forms a suflicient support for workmen on the top to place the upper layer in position. As the roof is built layer by layer and row by row, a final rigid construction ultimately results when the roof is completed. During the course of construction, as material is added on the roof, the corners 16 and 18, as indicated in FIG. 5, tend to spread apart and along the upper resting portions of the supports 12 and 14. Restraints may be provided prior to actual welding of the corners at a position appropriate for load distribution.

During the course of construction stabilizing rods 64 may be attached adjacent to the corners 20 and 22 and firmly anchored in order to hold the roof against tilting about an axis joining the corners 16 and 18, due to a symmetrical loading. The completed roof, however, is quite stable if the load is uniformly distributed. Nevertheless to provide a substantial safety factor, the stabilizing cables can remain.

In the forms illustratedin FIGS. 9 and 10 a different section for the peripheral support members is provided. In this instance two channels 101 and 163 are provided, the webs of which face outwardly in a common plane. The mounting plate 40 is clamped between the sides of the channels 101 and 103, substantially in the same manner as in connection With the angles 36 and 37 of the form previously described.

The channels 101 and 103 are capable of being twisted or warped readily. In place of other strengthening means, a series of gusset plates 105, 107, 109, 111, and 113 are provided, welded successively along the outer surfaces of the channels 191 and 193, and overlying them and each other. The width of the gusset plates conforms to that of the peripheral support member. The longest gusset plate 105 is first in contact with the channels of the support member. This plate 165 extends from the corner 15 to a place adjacent the corner 22, the end edge 195a of the gusset plate 105 appearing in FIG. 9. Similarly, the next longest gusset plate 107 extends from the corner 16 to a place spaced further from the corner 22, the edge 107a appearing likewise in FIG. 9. The gusset plates thus provide appropriate reinforcement and increased strength near the base of what is in essence a cantilever type beam.

In the form illustrated in FIG. 11, four layers of decking elements 120, 122, v124 and 126 are provided whereby the inherent strength of the roof may be further increased. By trapping air in the interstices a substantial measure of insulation is also provided. Pipes, conduits, and the like can easily be concealed in the channels of the roof.

The inventor claims:

1. In a hyperbolic paraboloid roof structure: a series of peripheral support members joined together to form a closed quadrilateral frame, each of the peripheral support members being elongate and rectilinear, any two contiguous support members defining a plane inclined to the plane defined by the remaining two of the peripheral support members; each peripheral support member comprising two parallel sections having opposed surfaces, each defined by a straight-line generatrix uniformly rotated angularly about the longitudinal axis of the correspondmg support member as the center of said generatrix is translated along said axis; the :generatrix at each position along said longitudinal axis being oriented to extend inwardly of the frame and toward corresponding portions of the opposite support member; each peripheral support member also having a mounting plate clamped between the said surfaces of said parallel sections and projecting inwardly of the frame, said mounting plate assuming a configuration corresponding to that of the surfaces of the corresponding parallel sections; a first set of decking members secured together in side-by-side relationship, and having ends fastened on the lower sides of the mounting plates at two of the peripheral support members; a second set of decking members secured together in side-by-side relationship, and having ends fastened to the upper side of the mounting plates at the other two of the peripheral support members so that the decking members of the second set extend transversely to and are superimposed on the first set of decking members; said decking mem bers being shaped to form a hyperbolic paraboloid structure; and fastening means joining the decking members of the sets of the areas of crossing.

2. The combination as set forth in claim 1 in which said decking members are longitudinally fluted to provide transverse flexibility as well as longitudinal reinforce ment; in which the end decking members of the first set are secured to the lower sides of the mounting plates at said other two peripheral support members; and in which the end decking members of the second set are secured to the upper sides of the mounting plates at said first two peripheral support members.

3. In a roof structure: elements forming a closed quadrilateral frame arrayed with respect to each other to define the boundary of an imaginary hyperbolic paraboloid surface, each of the elements of the frame being rectilinear, any two contiguous frame elements defining a plane inclined to the plane defined by the remaining two of the frame elements; the frame being capable of withstanding forces tending to alter the spacing of opposite frame elements; a first set of decking elements, each having transverse flexibility whereby the width of the decking element is variable along the length thereof to conform to various transverse dimensional requirements, each of said decking elements having a substantial resistance to longitudinal fiexure; means joining the decking elements of said first set in side-by-side relationship so that the end elements of said first set fall along two opposite frame elements, the ends of each decking element of said first set being secured respectively to the other two opposite frame elements to transmit the tension of said decking elements thereto; a second set of decking elements, each having transverse flexibility whereby the width of the decking element is variable along the length thereof to conform to various transverse dimensional requirements, each of said decking elements of said second set having a substantial resistance to longitudinal fiexure; means joining the decking elements of said second set in side-by-side relationship and in juxtaposed relationship to the decking elements of the first set so that the end elements of the second set fall along said other two opposite frame elements, the ends of each element of said second set being secured to said first two opposite frame elements to transmit the tension of said decking elements thereto; and means fastening the decking elements of the sets together at their areas of crossing to provide a shear type restraining force to assist in maintaining the decking elements of said sets in the shape of a hyperbolic paraboloid.

4. The combination as set forth in claim 3 together with a pair of bearings for opposite corners of the frame and fastened to the frame for transfer of seismic forces of the roof to said bearings.

5. The combination as set forth in claim 4 in which said roof is pre-stressed by altering the nominal working spacing of said corners by said fastening means, thereby distributing the seismic load of the roof between the decking elements and said bearings.

6. The combination as set forth in claim 5 together 7 with a grade beam between the bearings, and a floor structure above the grade beam; said fastening means lengthening the nominal working spacing of said corners whereby a nominal compressive load is transmitted to said grade beam.

7. A shell roof structure comprising a plurality of sheets in face to face contact and forming a hyperbolic paraboloid composite structure, each sheet having a plurality of undulations extending along one dimension thereof, one sheet having the undulations thereof at right angles to the undulations of the contacting sheet, and means rigidly securing said contacting sheets at a plurality of points along a plurality of contacting undulations of each sheet for retaining said sheets together in the shape of a hyperbolic paraboloid.

8. A shell roof structure including a pair of sheets having faces in opposed relationship to each other and forming a hyperbolic paraboloid composite structure, each sheet having a plurality of undulations extending along one dimension thereof, one sheet having the undulations thereof extending transverse and at a substantial angle to the undulations of the companion sheet, and means rigidly securing said sheets at a plurality of mutually opposed points along a plurality of adjacent undulations of each sheet for retaining said sheets together with each sheet in the shape of a hyperbolic paraboloid conforming to the shape of the other of the sheets.

9. The process of constructing a frame for a hyperbolic paraboloid roof structure, which comprises: attaching elongated support members together to form an open quadrilateral structure while the support members extend substantially in a common plane; each of said support members having parts extending along the length of said support members to form attachment surfaces, said attachment surfaces also extending substantially in a common plane when the support members extend substantially in a common plane; holding the members at each of the corners against angular movement out of the tangent planes at the corners While permitting angular movement of the members about the corners in their tangent planes, all while relatively raising two of the op posite corners twisting said support members about their longitudinal axes thereby automatically producing a longitudinal twist in the support members and causing said attachment surfaces to conform to the edges of a hyperbolic paraboloid.

References Cited by the Examiner UNITED STATES PATENTS 1,614,334 1/1927 Wright 52-48 2,034,383 3/1936 Bonsall 52-49 2,185,274 1/ 1940 Schoeniger 52-466 2,245,689 6/1941 Krueger 52-261 2,427,021 9/ 1947 Rapp 52-222 2,642,824 6/ 1953 McElhone 52-639 2,654,686 10/ 1953 Hansen 52-489 2,754,776 7/1956 Blaski 52-460 2,887,192 5/1959 Schaub 52-488 2,891,491 6/ 1959 Richter 52-81 2,912,940 11/1959 Baroni 52-80 FOREIGN PATENTS 124,525 9/ 1931 Austria.

781,162 8/1957 Great Britain.

753,204- 8/ 1933 France.

OTHER REFERENCES Architectural Record, p. 72, July 1943. House and Home Magazine, August 1955, p. 95, 96. House and Home, p. 97, August 1955.

EARL J. WITMER, Primary Examiner. WILLIAM L MUSHAKE, Examiner.

D. W. GRAVES, Assistant Examiner.

Claims (1)

1. 8. A SHELL ROOF STRUCTURE INCLUDING A PAIR OF SHEETS HAVING FACES IN OPPOSED RELATIONSHIP TO EACH OTHER AND FORMING A HYPERBOLIC PARABOLOID COMPOSITE STRUCTURE, EACH SHEET HAVING A PLURALITY OF UNDULATIONS EXTENDING ALONG ONE DIMENSION THEREOF, ONE SHEET HAVING THE UNDULATIONS THEREOF EXTENDING TRANSVERSE AND AT A SUBSTANTIAL ANGLE TO THE UNDULATIONS OF THE COMPANION SHEET, AND MEANS RIGIDLY SECURING SAID SHEETS AT A PLURALITY OF MUTUALLY OPPOSED POINTS ALONG A PLURALITY OF ADJACENT UNDULATIONS OF EACH SHEET FOR RETAINING SAID SHEETS TOGETHER WITH EACH SHEET IN THE SHAPE OF A HYPERBOLIC PARABOLOID CONFORMING TO THE SHAPE OF THE OTHER OF THE SHEETS.

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