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IS CONSTRUCTIVE-TEHNOLOICHESKY FORMS OF MESH PRECAST SPHERICAL SHELLS ON THE BASIS OF SECTORS WITH FLAT HEXAGONAL AND TRIANGULAR PANELS.

Formation of a triangular geometrical network on sphere by criterion of a minimum of standard sizes of elements can be presented and solved placing of the correct and wrong hexagons entered in circles of minimum dimensions, for example, in spherical sectors, shown on drawings 2.8 and 2.9, and not just segments.

Innovative is constructive-technological forms of dome coatings in the form of spherical shells should provide realisation of all above the stated principles and approaches already at a stage geometrical razrezki spheres. Geometrical schemes of partitioning of a spherical shell razrayobotany by use as an initial basis spherical sektory 60о and 120о [5,14,132]. Each version razrezki as the geometrical basis, has the architectonic, technological and constructive possibilities and will be optimum only for a certain sort of domes or envelopments. From here follows, that parametres of several types razrezok that in a concrete design situation it was possible to select that variant which would be optimum for a concrete projected building or a construction should be offered and worked.

In work is constructive-technological methods of formation of triangular networks on sphere with hexagonal assembly panels which are named by system "Транер" (fig. 2.8) are investigated some.

The essence of the offered variants razrezok "Traner" consists that the precast spherical shell is made of the assembly hexagonal panels which polytypic marks equally are in full or in part located within the sectors having general vertex of sphere
On the panel executed in the form of a correct hexagon. Panels in the form of correct and wrong hexagons can have the decreasing sizes from the central panel to periphery. But panels in the form of correct hexagons can have and the identical sizes of the panels located on borders of sectors which are sphere symmetry axes.

For the first variant of decisions within the sectors making 60 ° in precast spherical shells hexagonal panels are executed with the corners described by circles with the radiuses from the centres of panels, laying on sphere. Between hexagonal panels triangular panels (bearing are located or not bearing), corners of hexagonal panels are described in the radiuses from the centres of panels, adjacent hexagonal panels are connected among themselves in points of intersection and in points of contact of the circles describing the panels. Panels, adjacent with the hexagonal panel at dome vertex, are executed one radius and also in the form of correct hexagons. Hexagonal panels can be executed also in turn from triangular panels with connection knot in the centre of the hexagonal panel (in the circle centre in which they are entered). In drawing 2.8 and the top view of the given national team of a spherical shell with six sectors in the plan, components 60 °, and in drawing 2.8 - a side view is represented.

In the second variant (fig. 2.9) for the sectors making 120 °, at sphere vertex the panel executed in the form of a correct triangle is located, and adjacent with the central triangular panel correct hexagonal panels are entered in circles of one radius. Panels, with the centres located on borders of sectors, are executed with decreasing from vertex to periphery in radiuses. In drawing 2.9, and the top view of a precast spherical shell with three sectors in the plan, components 120 ° is shown; in drawing 2.9, - a side view.

Fig.

2.8 - the Scheme of a precast spherical shell from 6 sectors with corners at vertex 60 ° with razrezkoj from hexagonal panels with triangular inserts between them: and - the top view; - a side view; 1 - panels in the form of flat hexagons; 2 - sectors; 3 - the panel at vertex of a dome in the form of a correct flat hexagon; 4 - panels in the form of correct hexagonal panels (are allocated by grey colour); 5 - panels in the form of a triangle; 6 - knots of connection of hexagonal panels; the centres shchestiugolnyh panels; 8 - borders of sectors; 9 - the residual triangular panel; 10 - a sector axis.

In these drawings schemes of distribution of the circles describing hexagons, in segments 2r, limited to lines «zenith - nadir», uniformly distributed concerning a line of one line of longitude of sphere and orthogonal are shown it in "zenith" of an auxiliary line of longitude.

Distribution represents a theoretical basis of placing of the maximum number of circles of one radius, taking into account a contact of three adjacent circles and formation between them a triangle. On schemes of drawings 2.1, 2.2 and 2.8 it is shown as by means of these segments it is possible to place circles in sector under a skew 60о to equator or under a skew 30о to equator. For use of methods of calculation by means of spherical trigonometry we will take advantage of dependences on a plane of diameter of a circle of the sphere, the polygons entered in it and radiuses.

Fig. 2.9. The scheme of a precast spherical shell from 3 sectors with corners at vertex 120 ° with razrezkoj from hexagonal panels with triangular inserts between them: and - the top view; - a side view; 1 - panels in the form of flat hexagons; 2 - sectors; 3 - the panel at vertex of a dome in the form of a correct flat triangle; 4 - panels in the form of correct hexagonal panels (are allocated by grey colour); 5 - panels in the form of a triangle; 6 - knots of connection of panels; the centres of hexagonal panels; 8 - borders of sectors; 9 - the residual triangular panel; 10 - a sector axis.

By working out of algorithm of geometrical calculation razrezok, offered is constructive-technological systems, we will take advantage also of repeatability of parametres of a network on any spherical triangle) and, accordingly, on any compatible spherical triangle or in spherical sector. For geometrical construction of a mesh dome by means of program complex AutodeskAutoCad 2015, after program start it is necessary to pass in the Ze-modelling mode (fig. 2.10). We will break algorithm of construction into three basic stages. Points of intersection of axes of sectors from lines «zenith-nadir also will be a basic network of circles for vpisanija hexagons. Theoretically from hexagonal pyramids with triangles between them it is possible to cover with a network all sphere, anyway, below equator.

Fig. 2.10. The scheme of a basic network of circles and construction of a triangular network on sphere.

At the second stage we will take advantage of a basic network and we will construct circles without blanks (i.e. - compatible, concerning or crossed), but various radiuses (fig. 2.11). Sectors here go from orthogonal main lines-meridians with the centre to "zenith" to the uniform centre on sphere in a point "nadir". The axis At coincides on a plane of one of sector borders.

But for decrease in number of standard sizes it is better to place correct hexagons on axes of sectors, and all circles of the same kind to make one radius.

Therefore in constructions updating of radiuses with which construction on borders of sectors begins is possible; i.e. the radiuses intended for vpisanija of correct spherical pyramids. At the third stage on points
Crossings of circles we build the hexagons entered in circles, thereby receiving structure of a mesh dome (fig. 2.11). Despite nearness of a method because of distortions in a basic network, other ways of formation of a network from one vertex in height more than half of sphere have appeared more difficult and inexact.

Fig. 2.11. The scheme of distribution of circles from zenith to nadiru.

Taking into account restrictions which give razrezki on the basis of sectors 60о, we receive optimum by criterion of a minimum of standard sizes razrezku on sphere with five numbers of circles (fig. 2.12), consisting of assembly only hexagonal panels 9 standard sizes or from five correct hexagonal panels, four wrong hexagonal panels and twelve triangular panels-inserts (for rods - only 33 standard sizes).

Fig. 2.12. The scheme of a precast spherical shell in diameter of 100 m (60 m between

Bearers) from 6 sectors with corners at vertex 60 ° with razrezkoj from hexagonal panels with triangular inserts between them.

The basic contour of a precast envelopment is carried out in the form of six arches in radius of 46,1645 m (fig. 2.12 and,), executed on the circles which are passing through a point "nadir" and corners of basic hexagonal panels. Envelopment co-ordinates (fig. 2.12 and,) 100 m razrezki are resulted by diameter of the most effective in works [5, 14].

Taking into account restrictions which give razrezki on the basis of sectors 120о, we receive optimum by criterion of a minimum of standard sizes razrezku on sphere with three numbers of circles (fig. 2.13 see and,), consisting of assembly hexagonal panels of 4 standard sizes or from the correct hexagonal panel, one wrong hexagonal panel of the same radius, two wrong hexagonal panels of different radiuses and seventeen triangular panels-inserts (for rods - only 15 standard sizes).

Fig. 2.13. The scheme of a precast spherical shell in diameter of 50 m (36м between bearers) from 3 sectors with corners at vertex 120 ° with razrezkoj from hexagonal panels with

Triangular inserts between them.

Co-ordinates of an envelopment in diameter of the most effective of 50 m razrezki for sectors 120о (fig. 2.13 and,) are shown in work [14].

2.2.

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A source: Antoshkin Vasily Dmitrievich. is constructive-TECHNOLOGICAL DECISIONS of PRECAST SPHERICAL SHELLS. The dissertation on competition of a scientific degree of a Dr.Sci.Tech. Saransk - 2017. 2017

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