MODELLING AND DYNAMIC ANALYSIS OF THREE-DIRECTION GRID PRESTRESSED RETICULATED MEGA-STRUCTURE

In this paper, the generation way of three-direction grid prestressed reticulated megastructure is studied, and the three-direction grid prestressed reticulated mega-structure composite joint specific formation ideas are proposed. The important control parameters of three-direction grid prestressed reticulated mega-structure are determined, and the geometric modelling method of hexagon across the middle joint and octagon across the side joint is proposed. Coordinate formula of hexagonal and octagonal joints are derived to ensure reasonable grid arrangement and uniform stress distribution of the structure. Combined with the geometric parameters of the mega grid, a new method for creating the geometric model of three-direction grid prestressed mega reticulated structure is realized. The quadrangular pyramid space grid structure with the same length, span, rise and grid size and the three-direction grid prestressed grid structure are calculated, and the advantages of three-direction grid prestressed grid structure in dynamic performance are compared and analyzed.


Composition of mega-member and establishment of composite joint
Through the comprehensive consideration of the characteristics of several commonly used flat grid forms, the inverted pyramid truss is finally selected as the lattice mega component of the three-direction grid prestressed grid structure, and the inverted pyramid truss is specifically shown in Figure1.

Fig. 1 -Inverted quadrangular pyramid truss
After the flat grid frame is evacuated, a three-direction grid type single-layer grid structure is formed, and the configuration is shown in Figure 2.

Fig. 2 -Evacuated Grid Structure
When a single bar is replaced by pyramid truss, the joint between mega components is complex. The joint of inverted pyramid truss structure is the key to form the geometric model of three-direction grid prestressed mega grid structure, which is called "composite joint" in this paper. Joints 1, 2 and 3 indicated in Figure 2 represent three types of connection forms respectively. Joint 1 with long direction indicates that five members are connected at the joint. Corner point 2 indicates that three members are connected at the joint. Joint 3 with cross direction indicates that four members are connected, indicating that the structure needs three different treatment methods to connect the inverted quadrangular pyramid trusses on the four edges. In order to make the modeling of the geometric model of the structure meet the connection of three different joints at the same time, eight groups of inverted quadrangular pyramid trusses are connected, and an inverted octagonal pyramid with an octagonal plane projection is formed at the cross connection. And that eight side on the upper part of the truss can simultaneously meet the form that the joints of the invert quadrangular pyramid truss are mutually crossed and connected in the three forms.

Formation of Composite Joint
The geometric model of three-direction grid prestressed reticulated mega-structure is essentially a flat plate-type space structure, so the establishment of the geometric model of the hexagonal mid-joint and the octagonal side joint is the key to generate the structural model. The above-mentioned "hexagon" refers to that projection of the inverted quadrangular pyramid truss in the interior of the structure on the intersect connecting plane, and the "octagon" refers to the projection of the inverted quadrangular pyramid truss on four out edges on the intersecting connecting plane. The specific connection mode is shown in Figure 4, wherein (A) is the connection mode of the internal inverted quadrangular pyramid;(B) is an inverted quadrangular pyramid connection with four outer edges.
(A) Cross structure projected as hexagon (B) Cross structure projected as octagon

Fig. 4 -Hexagonal and Octagonal Connections
As shown in the figure above, both the internal and external connection modes of the cross connection part are hollowed out, which will cause uneven force on the bar and adversely affect the overall stiffness. And therefore that diagonal line of the upper polygons of the hollow structure need to be mutually crossed and connected; As the octagonal protruding structure part on four sides is easy to be stressed and concentrated, the part protruding out of the outer edge of the quadrangular pyramid is cut off. The corner points of the hexagon and the trimmed octagon are respectively connected with the corresponding joints of the three-direction grid type single-layer grid structure to form partial web members of the three-direction grid type prestressed mega-grid structure. Finally, a composite joint is formed as shown in Figure 5.
(A) Hexagonal internal connection (B) Octagonal internal connection

Geometric parameter setting of mega-structure
According to the characteristics of the three-direction grid type prestress mega-grid structure, the geometric parameters of the mega-grid are set as shown in Figure 6, wherein Lx represents the length of the structural longitudinal mega-grid, Ly represents the length of the structural transversal mega-grid, and H represents the thickness of the structure; The number of long direction giant grids Nx, the number of span direction giant grids Ny, the number of long direction giant component interjoint grids N1, the numbers of span direction giant component interjoint grids N2, and the numbers of oblique direction giant component interjoint grids N3.  The single member of the three-direction grid single-layer reticulated structure is replaced by the inverted pyramid truss. In order to make the huge grid arrangement even, the overall structure stress reasonable, the member type reduces as far as possible, so the inverted quadrangular pyramid truss must be arranged reasonably. In the structure shown in Figure 8, the lines connecting the central point of the hexagon to the four corner points are equal, that is, the lengths of the four line segments are equal and are all e; The connecting lines of the central point of the hexagon and the remaining two corner points are equal, and the lengths of the two line segments are B; In order to ensure that the members are evenly distributed and properly stressed, l in the illustration must be perpendicular and bisect C. To sum up, in order to reduce the structural mega grid to the form as shown in Figure 7 (b), and ensure uniform bar specification and uniform stress, the triangle divided by the hexagon must be a regular triangle, that is, b = e, so the hexagon of the projection of the mid-span composite joint in the lower chord plane must be a regular hexagon.

Article no. 14 THE CIVIL ENGINEERING JOURNAL 1-2021
Similarly, the octagon with side spans is also designed as a regular octagon, and the side length of the octagon is also C. The number of the long direction giant component interjoint grids is N1, the number of the cross direction giant component interjoint grids is N2, and the number of the oblique direction giant component interjoint grids is N3, and the length of each corresponding small grid is respectively L1, L2 and L3, which are respectively expressed by formulas (1), (2) and (3). Figure 9 (a) Length L2 and L3 of that transversal and oblique small grids, wherein L3 is divide into two parts which are respectively positioned between two hexagons and between a hexagon and an octagon, and are respectively denote by L3 and L3; Figure 9 (b) is the length L1 of the lengthwise small mesh; x y x y

Structural Geometric Parameter Scheme
In order to accurately express the relationship between the coordinate value of each point and the length of the polygon, this paper establishes the local coordinate origin at the center point of the hexagon and octagon, and stipulates the serial number of the corner points of the hexagon and octagon as shown in Figure 10.
Article no. 14 A hexagon on the upper chord of the mid-span joint is created according to the above method, and connected with the joint of the three-direction grid type single-layer grid structure to form a partial web member of the three-direction grid type prestressed giant grid structure. The schematic diagram is as shown in Figure 11, and the length is marked as L4. The length of L4 can be calculated by Formula (18):  Each corner point of the polygon after cutting is respectively connected with the joint of the three-direction grid type single-layer grid structure to form the web member of the three-direction grid type prestressed giant grid structure, and the joint connection schematic diagram is shown in Figure 13 below.

Fig. 13-Connection between octagon center and lower chord joints
The web member shown in the above figure is divided into two parts, one part is the corner point of the regular octagon connected with the three-direction grid type prestressed huge grid structure, and the length is marked as l5, the other part is the center point of the regular octagon connected with the joint of the three-direction grid type prestressed huge grid structure, and the length marked as l6 can be calculated by formula (19): After the webs are formed, the center points of the hexagons and the octagons are connected with the corner points of the hexagons and the octagons to form partial top chords. Thus, a three-direction grid type prestressed mega-grid structure is finally formed.

Calculation Model of Three-direction Grid Prestressed Reticulated Mega-structure
Determination of basic geometry size: This paper refers to the geometry size design of 306m × 90m hangar roof structure of Capital Airport [48], the control parameter of three-direction grid prestressed reticulated megastructure is set as follows: length 300m, span 150m, structural Replace the lower chords on the main diagonal and the middle span with prestressed cables, and finally form a three-direction grid type prestressed mega-grid structure as shown in Figure 14.

Orthogonal Pyramid Grid Structure
The modeling of square pyramid space truss structure can be obtained by inputting the corresponding parameters in MSTCAD software; The plane dimensions of square pyramid space grid structure are 300m in length direction, 150m in span direction, 31 grids in length direction, 19 grids in span direction and 6m in thickness. The load and constraint conditions are the same as those of the prestressed mega grid structure. The established model is shown in Figure 16 below:

Analysis of natural vibration characteristics of three-direction grid prestressed reticulated mega-structure
The steel grade of the members is Q345, the nominal diameter of the prestressed cable is 300mm, and the basic level of the selected pretension is 23000kN. The modal analysis of the three-direction grid type prestressed huge grid structure model is carried out by using sap2000 software, and 1. 0 dead load + 0. 5 times live load is considered as the representative value of gravity load. In order to compare and analyze the dynamic characteristics of two kinds of space truss structures, the orthogonal square pyramid space truss in chapter 4 and chapter 3 are used to compare and analyze the dynamic characteristics of the two kinds of space trusses. Table 1 is the first 30 natural frequencies of square pyramid space grid structure, and Table 2 is the first 30 natural frequencies of three-direction grid prestressed reticulated mega-structure.  From Figure 16, it can be found that the natural frequency of the three-direction grid prestressed mega-grid structure is lower than that of the square pyramid grid structure, and its basic period is larger than that of the grid structure. The main reason is due to the three-direction grid type prestressed reticulated mega-structure caused by the intmemberuction of cable, with cable element as the tension element. It can also be concluded that the high order modes cannot be ignored in the dynamic response of the structure for the large span structure. CONCLUSION 1. In this paper, the inverted pyramid truss is selected as the lattice mega-component of the three-direction grid prestressed reticulated mega-structure. By analyzing the connection form of the three-direction grid prestressed reticulated mega-structure, the specific ideas of "hexagon" and "octagon" cross connection composite joints are proposed, and the specific scheme of forming part of web members according to composite joints is proposed.
2. This paper determines the important control parameters of three-direction grid type prestressed reticulated mega-structure, and demonstrates the establishment of composite joints in the span and side composite joints, and finally chooses regular polygon to ensure that the mega-grid layout is uniform and the overall structure is reasonable.
3. According to the construction idea of three-direction grid type prestressed reticulated mega-structure, the hexagonal and octagonal joint coordinate schemes are deduced and formed, the geometric model establishment method of the hexagonal cross joint and the octagonal cross joint is proposed, and finally the specific scheme of threedirection grid type prestressed reticulated mega-structure geometric model construction is formed.
4. The quadrangular pyramid space grid structure with the same length, span, rise and grid size and the three-direction grid prestressed grid structure are calculated, and the