GB2150169A

GB2150169A - Dome of shell elements

Info

Publication number: GB2150169A
Application number: GB08428367A
Authority: GB
Inventors: Istvan Szavav; Istvan Halasz; Ferenc Rencz
Original assignee: VEGYTERV VEGYIMUEVEKET TERVEZO
Current assignee: VEGYTERV VEGYIMUEVEKET TERVEZO
Priority date: 1983-11-21
Filing date: 1984-11-09
Publication date: 1985-06-26
Also published as: DE3437372A1; HUT36532A; GB2150169B; HU189778B; GB8428367D0

Abstract

The shell elements 2 are longitudinally convex and transversely concave, and are fixed to a lower ring 11, an upper cornice 9 and to one another by coupling elements 5. The shell element comprises of a central trough 3 and a rim 4 connected to the two lateral edges of the trough 3. The shell element 2 is bounded by two non-concentric spherical surfaces Gb, Gk of a common vertical axis and by the planes of two latitudinal circles A, H and two longitudinal circles of each spherical surface. The central generatrix 8 of the trough 3 falls in the plane of the longitudinal circle of the inner spherical surface Gb. The diameter of the latitudinal circle A of the inner spherical surface Gb bounding the shell element 2 at its upper end corresponds to the outer diameter of the upper cornice 9. The latitudinal circle H bounding the shell element 2 at its lower end is located between the upper bounding latitudinal circle A and the equatorial great circle K of the inner spherical surface Gb. The cross-section of the trough 3 is a circular arc of which the radius of curvature and the arc length increase continuously from the upper end of the shell element 2. At the upper end the shell element 2 has a rim 10 and at its lower end it has a sole-plate 12. <IMAGE>

Description

SPECIFICATION Dome made from shell elements, and a master-pattern and a process for the manufacture of such shell elements The invention relates to domes made from shell elements and a master-pattern and a process for the manufacture of such shell elements; the domes being of spherical segment shape for covering approximately circular spaces, and the master-pattern being a template or a mould pattern. The terms 'dome' and 'cupola' are used interchangeably.

The covering over of spaces of circular or nearly circular ground shape has been a preoccupation since the beginning of human building activity. The road of progress has led from primitive vaulting of stone arches without mortar to the domes and cupolas of monumental cathedrals in the Baroque style.

Thus e.g. the cupola or dome of St. Peter's Cathedral in Rome has a diameter of 42 m.

The current trends of contemporary building technology, which aim at the application of lightweight prefabricated building elements minimising on-site works to eliminate the need for extensive and complicated scaffolding systems, do not favour the application of dome or cupola covering despite their many advantages. For this reason a number of attempts are known to develop dome constructions assembled from lightweight building elements.

Due to their low weight and favourable tensile strength properties, shell elements of synthetic materials lend themselves to be applied to the covering over of circular spaces.

Although many shell constructions of calotte or spherical shape have already been erected, their maximum diameter was only 20 m, while that of corrugated shell-constructions only 7.5 m. These constructions were lifted to their place as one-piece structural elements.

The spherical shells of radomes, i.e. domes of buildings housing radar installations, are assembled from more or less complicated sections, often of planar pieces made of synthetic material with a wall thickness of 50-75 mm.

The spherical dome with a span-width of 15.25 m of a planetarium at Armagh is assembled of 24 sections made of synthetic material, each section weighing 350 kg and the specific weight of the whole dome related to the covered area is 46 kg/m2. The dome of a covered sports hall with a diameter of 68 m has been constructed of approximately 500 elements placed on an aluminium framework and has a specific weight of 55 kg/m2. (See Saechtling: 'Bauen mit Kunststoffen'; pages 207, 493, 499-502).

There are already known roof or dome constructions assembled from elements of double-curvature, e.g. hyperbolic-paraboloid or other arcuate surface. (Ibid: pages 503-504, 517-518). Their specific weight has been reduced to 1 5 kg/m2 but could not be reduced below this figure so far. The curvature of their elements is convex in both directions. therefore the joints of contiguous elements form the lowest part of the dome for drainage of rainwater and their packing and insulation poses difficulties.

It is a common drawback of all known solutions of the problem that the geometry of the elements applied depends on the dimentions of the space to be covered, i.e. for different diameters individually manufactured elements of varying dimensions are necessary.

The aim of the invention is to provide a dome, cupola or curved roof constructed of shell elements wherein the shell elements for spans of variable dimensions differ only in arclength, therefore can be manufactured in the same master-pattern and the joining together of adjacent shell elements takes place on the outer enveloping surface of the shell cupola.

The invention is based on the recognition that the objective of the invention can be achieved if the various shell domes associated with spans of varying dimensions are constructed with spherical segmental surfaces of identical radii, but their latitudinal circles (parallel) are located such that the diameter should equal the diameter of the span bridging the space or opening to be covered by the dome. In this way the shell elements required for different domes or cupolas differ only in their arc length and can therefore be manfuactured in the same master-pattern. The maximum span-width is defined by the equatorial great circle of the spherical surface.

Furthermore, it has been recognised that a two-directional curvature of the shell elements ought to be developed in a mutually opposite sense. i.e. the longitudinal curvature should be convex. while the latitudinal curvature should be concave. In this way it can be achieved that the rims of adjacent shell elements to be linked to one another are located on the outer enveloping surface of the shellcupola while the troughs formed by the concave surfaces are positioned at the lowest parts of the shell elements. Consequently, atmospheric precipitation will flow along a continuous surface and not along the points where the elements are joined together.

The essence of the dome or vault or cupola according to the invention is that it consists of shell elements with bi-directional curvature.

e.g. longitudinally convex and latitudinally concave curved surfaces.

The shell elements are fastened to one another by linkage elements and to a lower cornice and to an upper uniting ring of the cupola or dome.

The shell element according to the invention consists of a central trough and a rim connecting the two edges of the trough. The shell element is bounded by two non-concen tric spherical surfaces with a common vertical axis and the two respective planes of its longitudinal and latitudinal circles. The rims form part of the spherical two-way angles of the outer spherical surface. The central generatrix of the trough falls in the plane of the longitudinal circle of the inner spherical sur- face.

The diameter of the latitudinal circle of the inner spherical surface bounding the shell element at its upper end corresponds to the outer diameter of the upper cornice. The latitudinal circle bounding the shell element at its lower end is positioned between the upper bounding latitudinal circle and the equatorial great circle of the inner spherical surface. The cross-section of the trough is a circular arc the radius and length of which increase continuously from the upper end to the lower end of the shell element. An upper rim is located at the upper end and a sole-plate at the lower end of the shell elements. The material of the shell element is preferably glassfibre-reinforced polyester (GRP).

The working surface of the master-pattern according to the invention corresponds to the shape of the shell element with the difference that its lower end is preferably bounded by the plane of the equatorial great circle or by a circle contiguous thereto.

The essence of the process for manufacturing the shell element accordng to the invention is that the shell element is prepared in a length, extending from the upper narrower end of the master-pattern, which is equal to the length of arc of the contour line of the spherical segment including the dome or cupola.

The dome or cupola, the master-pattern and the process for manufacturing the shell element according to the invention are further described purely by way of a preferred embodiment of the invention illustrated in the accompanying drawings, wherein: Figure 1 is a perspective view of a circular warehouse or rotunda; Figure 2 is a lateral view, not true to scale, of the shell element according to the invention; Figure 3 is a top plan view of the shell element according to the invention illustrated in Fig. 2; Figure 4 is an approximately true-to-scale side view of a shell element; Figure 5 shows a cross-section of two contiguous shell elements, and finally Figure 6 illustrates the covering over of a space bounded by straight lines and circular arcs.

Example 1 A rotunda or circular watehouse 1 (Fig. 1) is covered by a dome assembled from 48 pieces of prefabricated shell elements 2 (Figs.

2-4) made of GRP.

The shell element 2 of double curvature is bounded internally by an internal spherical surface Gb of radius Rb and externally by an external spherical surface Gk of radius Rk. The centre of the external spherical surface Gk coincides with the centre of the internal spherical surface Gb on a common vertical axis Z but the former lies more deeply, i.e. the two spherical surfaces Gb and Gk are not concentric. The cross-section (Fig. 5) of the shell element 2 consists of an arc-shaped circular trough 3 and rims 4. The length of shell element 2 is variable. In the dome, adjacent shell elements 2 are secured together by overlapping the rims 4 and joining them together by means of fastening elements 5.The rims 4 of shell elements 2 hug the spherical surface Gb. while its inside edges 6 and outside edges 7 coincide with the lines of longitude of the spherical surface Gk. The rim 4 forms part of a spherical two-way angle (double angle). The central generatrix 8 of the trough 3 is on the line of longitude of the internal spherical surface Gb.

The dome assembled of shell elements 2 is internally and externally bounded by respective spherical segments formed by intersections of the respective spherical surfaces Gb and Gk with respectively two lines of latitude (latitudinal circles). The uppermost boundary circle of latitude in plane A remains invariably the same, whatever are the dimensions of the space to be spanned, and its diameter corresponds to the diameter of the upper clamping ring or cornice 9 holding the shell elements 2 together at the top of the vault. The diameter of the lower boundary circle of latitude of spherical segment Gb internally covering or enveloping the shell element 2 corresponds to the diameter of the space to be spanned.In Example No. 1, Rb = 25 m; a dome bounded by a latitudinal circle in plane B the diameter of the space that can be spanned is 1 8 m; at plane C, 24 m; at plane E, 32 m; at plane F, 36 m; at plane H, 40 m; at plane J, 48 m and finally at plane K at the equatorial great circle, 50 m. The plane of the lower boundary circle of latitude circle may be freely selected and therefore the bridging of space may be of any diameter within the limiting value of 2Rb.

The master-pattern is dimensioned in such a way that it should permit the production of the largest desired shell element 2 between the latitudinal circle of plane A and the plane K of the equatorial plane. In the masterpattern shell elements 2 can be produced with an arc length corresponding to the actual requirement.

For the purpose of joining the shell element 2 to the cornice or ring 9, the upper end of the shell element is formed with an upper flange 10 while its lower end is formed with a sole-plate 1 2 to join it to cornice 11.

In this example the internal diameter of the circular warehouse building 1 is 36 m, for which purpose shell elements 2 extending between planes A and F are produced. The height of this dome is 7.60 m. The wall thickness of trough 3 of shell element 2 is 3 mm, the thickness of the rims 4 is 6 mm, the mass per unit area of the shell element 2 calculated on the basis of an element developed into a plane is 6.75 kg/m2. The developed or planispheric surface of a shell element of given dimensions is 31.5 m2 and its weight is 31.5 X 6.75 = 213 kg. The total weight of the dome consisting of 48 shell elements is: 48 X 213-10,200kg which, related to a unit covered area is 10.2 kg/m2.

Example 2 A dome was constructed for covering an effluent purification basin of circular ground plan and a diameter of 24 m, the dome consisting of 48 shell elements 2 made according to Example 1. Each shell element 2 is bounded at the top by the latitudinal circle of plane A and by a latitudinal circle of a diameter of 24 m at plane C at the bottom. The height of the cupola or dome is 3 m, the developed surface area of the shell element 2 is 12.6 m2; its weight is 12.6 x 6.75 = 85 kg. The total weight of the shell dome is 85 - 48 = 4080 kg and its specific weight related to the covered area of 452.4 m2 is 9 kg/m2.

Example 3 A cupola or dome with a diameter of 24 m was constructed for an exhibition hall of circular ground-plan supported by a pedestal of 2.50 m height, by a method similar to the one described in the preceding Examples but with the difference that the radius Rb of the spherical surface Gb internally enveloping the dome was 1 9 m. The dome was bounded at the bottom by a plane of a latitudinal circle with a diameter of 24 m. The height of the dome was 4.1 6 m, the developed surface area of a shell element 2 was 1 3.3 m2, its weight was 13.3 X 6.75 = 90 kg. The total weight of the shell dome was 90 X 48 = 4320 kg, the covered area is 452 m2 and specific weight related to the covered area was 9.56 kg/m2.

Example 4 A shell construction (Fig. 6) for covering a space for a sports hall for ball games was erected. The length of the pitch or playing field was 50 m, its width 32 m with semicircular boundaries at the two shorter sides.

At the end of the pitch two domes of semicircular ground plan were erected. The halfdomes were built of 24-27 pieces of shell elements 2 according to Example 3, and made in the same master pattern. The shell elements 2 were bounded at the bottom by a plane of a latitudinal circle of diameter of 32 m. The developed surface area of the shell elements 2 was 26.98 m2, the weight was 1 82 kg/m2 and the specific weight of the two half-domes was 10.9 kg/m2. The oblongshaped part, of a length of 1 8 m, was covered by a staved (thin shell barrel) construction, e.g. consists of stave-shells according to the Hungarian Patent No. 176632.

The main advantage of the invention can be summarised in that the shell dome and its elements are lightweight and self-supporting.

The shell dome or cupola solves the problems of load-bearing and of the shell formation.

Due to the fact that the central generatrix of the trough is located on the internal enveloping spherical surface, proper water exclusion is assured without the need for special arrangements. Architecturally the dome is of high standard, pleasing and expressive, and it renders the covering of spaces of large diameter with low cost specific material use possible.

The shell dome may consist of one layer or several layers. In this latter case it permits the application of any randomly selected mode or material for heat insulation. The assembly of the shell dome is simple; depending on its dimensions it can be lifted into its position and assembled together section-by-section or element-by-element, utilising purpose-built equipment; it can be dismantled and re-assembled to be used at another building site even under difficult road conditions and extreme circumstances. The shell elements of the dome for covering different dimensions can be produced in the same master pattern.

The preferred material of the shell dome is GRP which is corrosion-resistant, light-weight and rigid. The specific material consumption and the total energy used to produce it are very small. Related to the covered area the specific weight of the cupola is only 9-11 kg/m2.

Claims

1. A spherical segment-shaped dome or cupola structure for covering spaces bounded by circular or nearly-circular arcs, comprising shell elements of double curvature each of which is of lengthwise convex and transversely concave surface, each shell element being secured to an upper cornice. a lower uniting ring or cornice as well as to one another by means of coupling elements.

2. A structure according to claim 1, wherein the shell element consists of a central trough and rims attached to the two outside edges of the trough, the shell element being bounded by two, outer and inner, non-concentric spherical surfaces with a common vertical axis as well as by the common plane of two lines of latitude of said surfaces and by the common plane of two lines of longitude of said surfaces; and the rims form part of a spherical double-angle of the external spherical surface, while the central generatrix of the trough falls in the plane of the line of longitude of the internal spherical surface.

3. A structure according to claim 1 or 2, wherein the diameter of the circle or line of latitude located on the spherical surface bounding the shell element at its upper end corresponds to the outer diameter of upper cornice and the circle or line of latitude is positioned between the upper bounding circle or line of latitude and the equatorial great circle of the said spherical suface.

4. A structure according to claim 2 or claims 2 and 3, wherein from the upper end towards the lower end of the shell element the cross-section of the trough is of continuously increasing radius of curvature and is a circular arc, and wherein the shell element is provided at its upper end with an upper rim and at its lower end with a sole plate.

5. A structure according to any preceding claim, wherein the material of the shell element is a synthetic resin, preferably glass fibre-reinforced polyester.

6. A master-pattern (matrix, mould, etc.) for the manufacture of the shell element of the dome or cupola according to any of claims 1 to 5, comprising a working surface corresponding in shape to the shape of the shell element but with the difference that the plane bounding its lower end is the plane of the equatorial latitudinal circle of the inner spherical surface or is adjacent to it.

7. A process for manufacturing shell elements of the dome or cupola according to any of claims 1 to 5 in the master-pattern according to claim 6, wherein each shell element is produced with a length, calculated from the upper narrower end of the master-pattern, which is equal with the length of arc of the contour of spherical segment enveloping the dome or cupola.

8. A structure according to claim 1, substantially as herein described with reference to any one of the Examples and/or the accompanying drawings.

9. A master pattern according to claim 6, substantially as herein described with reference to any one of the Examples and/or the accompanying drawings.

10. A process according to claim 7, substantially as herein described with reference to any one of the Examples and/or the accompanying drawings.

11. Shell elements, or a structure assembled therefrom, whenever made by the master pattern according to claim 6 or 9, or by the process according to claim 7 or 10.