US3292315A - Shell structure for concrete roofs and the like - Google Patents

Description

Dec. 20, 1966 w. J. SILBERKUHL ETAL 3,292,315

SHELL STRUCTURE FOR CONCRETE ROOFS AND THE LIKE Filed Nov. 22, 1963 4 Sheets-Sheet 1 W/LHELM J. SILBERKUHL 322*# um KAS TL 4,? ERNST HAEUSSLER INVENTORS Dec. 20, 1966 w. J. SILBERKUHL ETAL 3,292,315

SHELL STRUCTURE FOR CONCRETE ROOF'S AND THE LIKE Filed Nov. 22, 1963 4 Sheets-Sheet 2 WILHELM J S/LBERKUHL UWE KASTL ERNST HAEUSSLEP INVENTORS Dec. 20, 1966 w. J. SILBERKUHL ETAL 3,292,315

SHELL STRUCTURE FOR CONCRETE ROOFS AND THE LIKE Filed Nov. 22, 1963 4 Sheets-Sheet 5 WILHELM J. S/LBERKUHL UWE KASTL ERNST HAEUSSLER INVENTORS 1966 w. J. SILBERKUHL-IE'IV'AL 3,292,315

SHELL STRUCTURE FOR CONCRETE ROOFS AND THE LIKE Filed Nov. 22, 1963 4 Sheets-Sheet 4 INVENTORS WILHELM J. S/LBERKUHL U WE KAS TL ERNST HAEUSSLER imam United States Patent Cfifice 3,292,315 Patented. Dec. '20, 1966 13 Claims. (Cl. 52-40 Our present invention relates to a shell structure of the general type disclosed in our copending application Ser. No. 168,700, filed January 25, 1962, now Patent No. 3,142,136 issued July 28, 1964, i.e. a concrete shell of substantially rectangular horizontal outline and upwardly concave transverse curvature.

Heretofore, as more particularly described in our abovementioned US. Patent, such shells were preferably designed as bodies with negative Gaussian curvature conforming, at least approximately, to a one-sheet hyperboloid with straightline generatrices extending substantially diagonally across the rectangle, the region of these generatrices representing a convenient site for the embedding of tensioned prestressing elements (e.g. steel cables) in the concrete. Other reinforcements, e.g. in the shape of suitably curved wires or rods without prestress, could be embedded close to the upper and lower surfaces of the shells.

Structures of this description, with a shell thickness of, say, 5-7 cm. or about 2-3", have been found satisfactory for use in various types of roof construction as disclosed, for example, in our copending application Ser. No. 133,754, filed July 21, 1961, now Patent No. 3,207,054, issued September 21, 1965, in which a plurality of such shells are disposed side by side on supporting walls or piers with interposition of curved connecting members such as plates of corrugated sheet material.

In these prior constructions, the shells were generally of uniform thickness so that both their upper and lower surfaces had substantially the same approximately hyperboloidal shape. This configuration, While simplifying the task of the designer, imposes certain limitations upon the load-carrying capacity of the shell structure. To increase this capacity, it would be necessary to deepen the upwardly concave curvature of the shells, to increase their overall thickness and/or to enlarge their width. The first of these measures is only limitedly feasible because of manufacturing difliculties in the pouring of concrete shells whose sides slope upwardly at an angle greater than about 30 with reference to the horizontal. The increase in thickness is frequently objectionable in that it also adds to the weight of the shell itself, thus entailing not only higher costs but also a less favorable ratio of live to dead weight. The width of the shell, finally, is limited in the case of precast structures by considerations of transportation and handling.

The general object of our present invention is, therefore, to provide an alternate solution for the problem of increasing the load-carrying capacity of such shell structures.

As has been explained in our aforementioned application Ser. No. 168,700, shells of negative Gaussian curvature develop inwardly or outwardly directed torques at their longitudinal edges, the magnitude and direction of the torques being determined by various forces due in part to the longitudinal upward arching of the structure.

torques.

With shells of uniform thickness a certain camber is required to overcome the stresses due to live and dead weight in order to prevent the occurrence of outward edge torques at least at the center of the structure. A more specific object of our present invention is to provide a shell of such shape that the same result, under given loading conditions, will be obtained with reduced camber.

It is also an object of our invention to provide a shell structure of the general type set forth which retains its load-carrying capacity even when provided with a flattened underside at its supported ends (i.e. in the region of the minor sides of the rectangle) so as to be more conveniently deposited on building walls or other types of piers.

We have found, in accordance with this invention, that a substantial increase in the load-carrying capacity of an upwardly concave shell can be obtained by only a partial enlargement of the shell thickness, particularly in the central transverse zone, advantageously with a gradual change in shell thickness from the middle of its central cross-section toward the ends thereof. The increased thickness enhances both the shear strength and the bending resistance of the shell but, by being confined to selected locations, does not involve a commensurate increase in weight.

In principle, the change in thickness from the middle of the central cross-section to its ends may be either positive or negative, this cross-section thus assuming the shape of either a diverging or a converging meniscus. A shell with a converging meniscus, i.e. with a crescentshaped central cross-section, is claimed in our copending application Ser. No. 325,704, filed on even date herewith. The present disclosure, besides setting forth the overall concept, is therefore more specifically directed to shells whose upper surface has a smaller radius of transverse curvature than its lower side, at least in the central region of the structure.

The relative enlargement of the shell edges in the central region elevates the center of gravity of the crosssection of the shell and effectively increases the lever arm of the forces which are due to the upward camber of the structure and which counteract the outward edge It thus follows that edge torques of substantially zero magnitude or, if desired, of inverted sign (i.e. directed inwardly) can be realized with less arching than in the case of shells of uniform thickness.

Since the elimination or reversal of edge torques is of primary importance only at the center of the structure, it is possible to reduce the edge thickness in a progressive manner from the center toward the supported sides of the shell. This measure enables a gradual increase in the thickness of the shell from its central section toward the minor sides of the rectangle, i.e. along the median longitudinal plane of the structure, to strengthen the shell at its supported ends without adding to its weight.

Another possibility afforded by our present invention is the flattening of the underside of the shell, either throughout its length or only in the region of the supports. According to a further feature, the upper shell surface may also be flattened in such manner that the edges of the shell progressively converge toward the median plane upon approaching the supported sides, again with a concomitant gradual increase in the median shell thickness.

The several modifications referred to above afford a variety of choices for the disposition of the generally longitudinal prestressing elements. As long as the curvature of at least the upper surface approximates that of a onesheet hyperboloid, the prestressing means may extend substantially diagonally as in the previously disclosed shells of uniform thickness. With a flat-bottomed shell, on the other hand, the direction of prestress may be parallel to the longitudinal edges, if desired. With hybrid structures, the prestressing elements may run at some intermediate angle. These elements may be constituted by various elongated elastic members, preferably of structural steel, e.g. in the form of one or more parallel cables or of flat ribbons.

The invention will be described in greater detail with references to the accompanying drawing in which:

FIG. 1 is a perspective view of a shell embodying the invention, parts broken away;

FIG. 2 is a longitudinal sectional view taken on the line IIII of FIG. 1;

FIG. 3 is a side-elevational view of the shell shown in FIGS. 1 and 2;

FIGS. 4 and 5 are, respectively, a cross-sectional view and an end view taken on the lines IVIV and VV of FIG. 2 but drawn at a larger scale;

FIG. 6 is a bottom view of the shell shown in FIGS. 1-5;

FIG. 7 is a perspective view '(parts broken away) similar to FIG. 1, of a modified shell embodying the invention;

FIG. 8 is a longitudinal sectional view taken on the line VIII-VIII of FIG. 7;

FIGS. 9-12 are cross-sectional and end views taken, respectively, on the lines ]X-1X, XX, XI-XI, and XIIXII of FIG. 8;

FIG. 13 is a bottom view of the shell shown in FIGS. 7-12;

FIG. 14 is a perspective view (parts broken away) of still another shell embodying the invention;

FIG. 15 is a longitudinal sectional view taken on the line XVXV of FIG. 14;

FIGS. 16, 17 and 18 are cross-sectional and end views taken, respectively, on the lines XVI-XVI, XVII-XVH and XVIII-XVIII of FIG. 15; and

FIG. 19 is a bottom view of the shell shown in FIGS. 14-18.

Reference will first be made to the structure of FIGS. 1-6. This structure comprises a concrete shell 20. of rectangular horizontal outline and negative Gaussian curvature with an upwardly directed concavity, the entire shell being upwardly cambered as best seen in FIGS. 2 and 3. The major sides of the rectangle are defined by a pair of upwardly arched longitudinal edges 21, its minor sides being constituted by edges 22 which are supported on piers 23 shown diagrammatically, in dot-dash lines in FIG. 1.

The concrete of shell 20 is reinforced by steel- wire nettings 24 and 25, imbedded therein adjacent the lower and upper shell surfaces 27 and 28, respectively, and by prestressin g elements in the form of two fiat steel ribbons 26 which intersect at the center C of the shell and extend nearly diagonally across the rectangle. Each tensioned ribbon 26 may also be replaced, as illustrated in subsequent figures, by a bank of parallel cables numbering from one to about thirty or forty. I

When seen in transverse cross-section, shell 20 has the shape of a diverging meniscus, resembling a bow tie,

at its center (FIG. 4) while approximating .a crescent, or converging meniscus, at the supported ends 22 (FIG. 5). Thus, each transverse section of the shell is bounded by two nearly circular arcs, approximating sections of hyperbolas or parabolas, whose centers of curvature lie above the shell; at the central section, FIG. 4, the upper surface 28 has the smaller radius of curvature whereas at the end sections, FIG. 5, the converse is true. Thus, the central section increases in thickness from the middle toward the edges 21 whereas the opposite situation exists at the ends. Furthermore, as best seen in FIGS. 2 and 3, the edges 21 diminish in thickness from.

the profiles seen in FIGS. 2-5 as well as for the entire shell) ranging between approximately 1.6:1 and 2:1.

The thickening of the longitudinal edges 21 in the central zone of the shell, FIG. 4, raises the center of gravtiy G of its transverse section above the geometrical.

center C thereof by a distance d which is considerably greater than the distance d between corresponding points G and C at the end section seen in FIG. 5. The higher center of gravity G tends to give rise to inwardly directed transverse moments or edge torques M at the midpoints of the longitudinal edges 21, in contradistinction to the outwardly directed edge torques M at the corners due to the lower center of gravity G. The inward moments M oppose deformation of the shell under load at its vulnerable central cross-section whereas the outward moments M are directly absorbed by the supporting piers 23 and, in addition, effectively counteract the contractile transverse \force exerted by the crossed tension.

members 26 which is at its maximum in the region of these piers.

Although the prestressed ribbons 26 have been shown twisted so that their ends are inclined to the horizontal, it will be apparent that their longitudinal axes (or the central element of an equivalent array of wires or cables) extend in a horizontal plane (if the slight deviation due to their intersection is disregarded) so as to define straight-;

line generatrices of an imaginary hyperboloidal figure of revolution disposed between the upper and lower shell.

surfaces.

In FIGS. 7-13 we have illustrated a modified shell 30 with longitudinal edges 31 and transverse edges 32,1

defining a rectangular outline similar to that of shell 20 in the preceding figures. The central transverse section of the shell, seen in FIG. 9, is again substantially in the shape of a diverging meniscus with generally hyperbolical curvature while being slightly flattened at the center of its convex side, owing to the presence of a flat bottom surface 37 which widens from the center toward the minor sides 32 so as to extend over the full width of the shell at the supported ends thereof. T-hese ends, therefore, can rest on level-topped piers 33 (FIG. 7), representative of Walls, beams, girders and the like, in contrast to the specially shaped piers 23 of shell 20 (FIG. 1). In the median longitudinal plane, as shown in FIG. 8, the lower and upper shell surfaces 37, 38 are both slightly concave and converge at the center; the maximum thickness at the flared ends of the median shell sections, seen in FIGS. 8 and 9, again exceeds the minimum thickness at the midpoints of these sections by a factor ranging between, preferably, about 1.6 and 2.

As will be apparent from FIG. 7, the transverse section of shell 30 changes froma bow-tie shape at the center to a .plano-convex shape at the supported ends 32 so that the curvature of its upper surface 38 is inverted in the vicinity of these ends. The region of inversion, in which the surface 38 flattens out, is seen in FIG. 11. The wire nettings extending close to these surfaces and conforming thereto have been omitted in FIGS.- 8-12 but the lower netting is visible at 34 in FIG. 7. Shell 30 also has prestressing means, disposed between these nettings, in the form of an array of rods or wires 36 of structural steel passing under tension along the longitudinal axis of the shell, thus in a direction parallel to its edges 31; it will be apparent that the shell would also accommodate horizontal wires or the like disposed at a small angle to this axial direction. Naturally, the

5, members 36 could also be replaced by one or more flat ribbons as in the first embodiment.

In FIGS. 14-19 we show a shell 40 whose longitudinally concave underside 47 flatens out toward the supported ends 42 (the supporting piers having been omitted in these figures) and which, in addition to unstressed steel-wire nettings (of which the lower one is visible at 44 in FIG. 14), incorporatesprestressing means in the form of two sets of cables 46 that are inclined to the longitudinal axis at somewhat smaller angles than the ribbons 26 of FIGS. l-6. The shell thickness again increases, at the aforestated ratio, from the center of the edges 41, 42 in the two median planes seen in FIGS. 15 and 16. In the longitudinal plane (FIG. 15) the top surface 48 is substantially horizontal; its transverse concavity, as shown in FIGS. 1618, becomes progressively shallower and narrower toward the minor sides 42 of the rectangular outline, owing to a flattening of the edges 41 which thus broaden horizontally as they approach these sides. The result, as seen in the end view of FIG. 18, is a considerable increase in cross-sectional areaat the ends, with corresponding strengthening of the shell in the region where the tensioned cables 46 (or equivalent ribbons) are anchored and the stresses due to the load are transferred to the supports. The central cross-section of shell 40 (FIG. 16) is similar to those of shells 20 and 30.

The raising of the center of gravity of the central shell section, described in conjunction with shell 20 but applicable to the other embodiments as well, also has the effect of shifting the moment line of that section toward the compression flange thereof, i.e., toward the upper shell surface. This is advantageous in many instances in which it has been observed that, in the case of prior structures, the upper flange reaches its permissible limit of compression while the stresses within the lower flange are still well below the maximum tension allowed under the building code. Because of this rather unexpected phenomenon, shells of constant thickness do not always have a loading capacity commensurate with the tensile strength of the material, yet with the shells herein described this drawback is obviated through a redistribution of stresses so that both the compressive and the tensile strength of the concrete are fully utilized.

Where the foregoing considerations do not apply, as where the conditions of use are such that stability rather than load-bearing capacity is the primarv requirement, the aforedescribed structures may be modified so that the central cross-section of the shell assumes the shape of a converging rather than diverging meniscus. With a shell of the general type shown in FIGS. l-6, for example, the cross-section may then remain constant throughout its length and have the shape illustrated in FIG. 5, the contours of the surfaces 27 and 28 being parallel to edge 21 in FIG. 2. The surfaces 37 and 38 of shell 30, similarly modified, would both appear horizontal in FIG. 8, whereas the upper surface 48 of shell 40 would become convex in FIG. 15 and approximately parallel to lower surface 47 under these circumstances. In all these instances, therefore, the center of gravity of the shell section would lie only slightly above the level of its geometrical center, as indicated at d in FIG. 5. These modifications have been specifically claimed in our copending application Ser. No. 325,704 referred to above.

What is claimed is:

1. A structure adapted to be used in .roof construction and the like, comprising a concrete shell of substantially rectangular horizontal outline with upwardly arched longitudinal edges at the longer sides of the rectangle, said shell being of upwardly concave transverse curvature at least over the major part of its surface and having a central cross-section substantially in the shape of a diverging meniscus, and reinforcing means imbedded within the body of said shell, said shell having a high center of 6 gravity and inwardly directed edge torques in the region of said central cross-section.

2. A structure as defined in claim 1 wherein the thickness of the shell at said longitudinal edges decreases gradually from the center to the minor sides of the rectangle.

3. A structure as defined in claim 1 wherein the thickness of the shell along its median longitudinal plane increases gradually from the center to said minor sides.

4. A structure as defined in claim 1 wherein the thickness of the shell progressively increases along its median longitudinal plane and progressively decreases at said longitudinal edges from the center of said minor sides, with inversion of its transverse curvature in the region of said minor sides.

5. A structure as defined in claim 4 wherein said shell is upwardly camhered in longitudinal direction.

6. A structure as defined in claim 1 wherein said shell has a flat underside at least in the region of the minor sides of the rectangle.

7. A structure as defined in claim 6 wherein said shell has fiat upper surfaces extending inwardly from its longitudinal edges in the region of said minor sides.

8. A structure as defined in claim 6 wherein said flat underside extends substantially horizontally over the full length of the shell and widens from the center to said minor sides.

9. A structure as defined in claim 8 wherein said reinforcing means includes an elongated elastic member extending under tension substantially along the longitudinal median plane of the shell.

10. A structure as defined in claim 1 wherein said reinforcing means includes steel-wire nettings extending close to the upper and lower shell surfaces over the full length and width of the shell.

11. A structure as defined in claim 10 wherein said reinforcing means further includes at least one steel ribbon extending under tension in generally longitudinal direction between said nettings from one of the minor sides of the rectangle to the other.

12. A structure adapted to be used in roof construction and the like, comprising a concrete shell of substantially rectangular horizontal outline with upwardly arched longitudinal edges at the longer sides of the rectangle, said shell being of upwardly concave transverse curvature at least over the major part of its surface and having a central cross-section substantially in the shape of a diverging menisous, and elongated prestressing means extending under tension in generally longitudinal direction from one of the minor sides of the rectangle to the other minor side within the body of said shell, said shell having a high center of gravity and inwardly directed edge torques in the region of said central cross-section.

13. A structure adapted to be used in roof construction and the like, comprising a concrete shell of substantially rectangular horizontal outline with upwardly arched longitudinal edges at the longer sides of the rectangle, said shell being of upwardly concave transverse curvature at least over the major part of its surface and having a central cross-section substantially in the shape of a diverging meniscus, and elongated prestressing means extending under tension in generally longitudinal direction from one of the minor sides of the rectangle to the other minor sides within the body of said shell, the thickness of the shell varying between the middle and the ends of said central cross-section by a factor of substantially 1.6 to 2, said shell having a high center of gravity and inwardly directed edge torques in the region of said central cross-section.

References Cited by the Examiner UNITED STATES PATENTS 830,483 9/1906 Luten 5288 852.202 4/1907 Russell 52-80 2,257,153 9/1941 Blaski 52-86 (Other references on following page) 7 8 UNITED STATES PATENTS OTHER REFERENCES 2,425,079 8/1947 Billig 5288 Article, Structural Applications of Hyperbolic Para- 3,142,136 7/1964 Silberkuhl et a1. 5281 boloidical Shells, pages 397-414. 3,207,054 9/1965 Silberkuhl et a1. 5281 Article, Hyperbolic Paraboloid, Civil Engineering,

5 pages 70-72, October 1961. FOREIGN PATENTS 838,294 12/1938 France HARRISON R. MOSELEY, Primary Examiner. 869,717 6/1961 Great Britain. A. I. BREIER, Assistant Examiner.

Claims (1)

1. A STRUCTURE ADAPTED TO BE USED IN ROOF CONSTRUCTION AND THE LIKE, COMPRISING A CONCRETE SHELL OF SUBSTANTIALLY RECTANGULAR HORIZONTAL OUTLINE WITH UPWARDLY ARCHED LONGITUDINAL EDGES AT THE LONGER SIDES OF THE RECTANGLE, SAID SHELL BEING OF UPWARDLY CONCAVE TRANSVERSE CURVATURE AT LEAST OVER THE MAJOR PART OF ITS SURFACE AND HAVING A CENTRAL CROSS-SECTION SUBSTANTIALLY IN THE SHAPE OF A DIVERGING MENISCUS, AND REINFORCING MEANS IMBEDDED WITHIN THE BODY OF SAID SHELL, SAID SHELL HAVING A HIGH CENTER OF GRAVITY AND INWARDLY DIRECTED EDGE TORQUES IN THE REGION OF SAID CENTRAL CROSS-SECTION.

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