CN111502098B - Suspended dome structure suitable for square boundary and calculation method thereof - Google Patents
Suspended dome structure suitable for square boundary and calculation method thereof Download PDFInfo
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- CN111502098B CN111502098B CN202010293737.2A CN202010293737A CN111502098B CN 111502098 B CN111502098 B CN 111502098B CN 202010293737 A CN202010293737 A CN 202010293737A CN 111502098 B CN111502098 B CN 111502098B
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- E—FIXED CONSTRUCTIONS
- E04—BUILDING
- E04B—GENERAL BUILDING CONSTRUCTIONS; WALLS, e.g. PARTITIONS; ROOFS; FLOORS; CEILINGS; INSULATION OR OTHER PROTECTION OF BUILDINGS
- E04B7/00—Roofs; Roof construction with regard to insulation
- E04B7/14—Suspended roofs
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/13—Architectural design, e.g. computer-aided architectural design [CAAD] related to design of buildings, bridges, landscapes, production plants or roads
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
Abstract
The invention discloses a suspended dome structure suitable for a square boundary and a calculation method thereof, wherein the suspended dome structure comprises an upper chord single-layer net shell and a lower chord cable rod structure, the lower chord cable rod structure comprises a vertical stay rod, a radial stay cable and a circumferential stay cable, and the analysis process comprises the processes of solving the vertical load requirement, the angle between the circumferential stay cable and the radial stay cable, generating a grid according to the angle between the circumferential stay cable and the radial stay cable, iterating the grid form, calculating the prestress of the circumferential stay cable and the like. The advantages are that: the blank that the suspended dome is adopted in the square boundary is filled, the explicit solution method for generating the suspended dome with the internal force such as the annular guy cable and the like by correcting the angle of the annular guy cable is provided, and the obtained suspended dome structure is ideal in stress performance.
Description
Technical Field
The invention relates to the field of buildings, in particular to a suspended dome structure suitable for a square boundary and a calculation method thereof.
Background
The suspended dome is a novel space structure system for realizing stress balance through the combined work of an upper chord single-layer latticed shell and a lower chord cable rod system, and has been researched for years and practiced in engineering in China. In recent years, domestic suspended dome structures are mainly applied to large-span space structures such as gymnasiums, conference halls, exhibition halls and the like, but due to the fact that the stress performance of the suspended dome is greatly related to the selection of the grid form of the single-layer latticed shell on the suspended dome, the unreasonable grid form can greatly reduce the structural efficiency of the suspended dome. When the suspended dome is applied to the square boundary, the square boundary and the circular annular stay cable are difficult to coordinate in stress, so that the cable rod shape and the shape and force finding of the upper chord single-layer latticed shell are difficult, and a unified and effective theoretical method is not available so far, so that the application boundary of the suspended dome at present is mainly a circular or quasi-elliptical boundary. The method for finding the shape and force of the suspended dome suitable for the square boundary is developed, the application range of the suspended dome structure can be greatly widened, and the method has a very positive significance for popularization and application of the suspended dome structure.
Disclosure of Invention
The purpose is as follows: aiming at the difficulty of applying the suspended dome structure on the square boundary, the suspended dome structure with better stress performance on the square boundary is provided.
The suspended dome structure comprises an upper chord single-layer latticed shell and a lower chord cable rod structure, wherein the lower chord cable rod structure comprises a vertical stay rod, a radial stay cable and an annular stay cable. The central point of the upper chord single-layer latticed shell is not provided with a vertical support rod, and other nodes provide prestress for the stay cable through the tensioning ring.
The method comprises the following steps: establishing a rib annular upper chord spherical reticulated shell within the square boundary, and establishing a lower chord cable rod structure corresponding to the upper chord spherical reticulated shell according to the preset height of the vertical strut, wherein the lower chord cable rod structure is used as an initial state of iterative computation;
taking an upper layer single-layer latticed shell as an isolator, guiding and calculating upper load into concentrated force at nodes of a grid, transmitting the load to the outside circle by circle according to the effect of an inner ring radial stay cable, accumulating the loads of all circles of nodes from inside to outside circle by circle in the radial direction to obtain the vertical load demand of each circle of nodes, calculating the horizontal load demand of each circle of nodes by force balance, and distributing the rotation angle of each node of the circumferential stay cable according to the size of the horizontal load demand.
Step two: and (3) calculating the angle of a radial stay cable passing through an outer ring node and capable of ensuring the internal force of the annular stay cable and the like one by one according to the calculated annular stay cable corner and starting from the outermost ring of the ring to a symmetrical shaft node of the stay cable, and enabling an upper-chord single-layer net shell annular rod to correspond to the position of the annular stay cable according to the conditions of the annular stay cable node, the outer ring dome node, the annular stay cable corner, the radial stay cable angle and the like to construct a new grid form, and repeating the step one from the new grid form to the stable state of the grid form, namely the shape of the upper-chord single-layer net shell and the lower-chord stay cable rod structure of the suspended dome.
Step three: after the final grid form is obtained, the prestress of each ring of circumferential inhaul cable can be obtained according to the horizontal load requirement of each ring of nodes and the rotation angle of the circumferential inhaul cable and the static balance condition of the nodes of the circumferential inhaul cable.
As a further improvement of the invention, the rotation angle of the annular inhaul cable node is distributed according to the calculated horizontal load demand.
As a further improvement of the invention, the grid form in the second step is derived from the rotation angle of the annular inhaul cable according to the geometric relationship, so that the internal force of the annular inhaul cable can be ensured to be equal.
The invention has the beneficial effects that:
(1) the invention provides a convenient and efficient calculation method for adopting the suspended dome on the square boundary, and fills the blank of the subdivision field of the application of the suspended dome on the square boundary;
(2) the annular stay cable of the obtained string-supported dome is not circular, but the internal force of the annular stay cable in the same circle among all the nodes is the same, the supporting force of the vertical stay rod of each node is balanced with the corresponding upper load (or the upper load reduced in proportion), and the structural stress performance is ideal;
(3) compared with other implicit form finding methods, the method adopts an explicit solution method, has simple process, quick convergence and convenient application.
Drawings
Fig. 1 is a schematic view of a suspended dome structure.
Fig. 2 is a schematic diagram of calculation of horizontal load demand of a suspended dome structure.
Fig. 3 is a schematic diagram illustrating an initial grid.
FIG. 4 is a schematic diagram illustrating the steady state of the final computational grid.
FIG. 5 is a flow chart for calculating a suspended dome structure according to the present invention.
Description of reference numerals:
1-radial rod, 2-annular rod, 3-vertical brace rod, 4-radial stay cable, 5-annular stay cable, 6-reticulated shell node,
Detailed Description
The present invention will be further illustrated with reference to the accompanying drawings and specific embodiments, which are to be understood as merely illustrative of the invention and not as limiting the scope of the invention.
As shown in fig. 1, the present invention is a suspended dome suitable for a square boundary and a calculation method thereof, and the suspended dome includes an upper chord single-layer reticulated shell and a lower chord system, the upper chord single-layer reticulated shell includes a radial rod 1 and a circumferential rod 2, and the lower chord system includes a vertical strut 3, a radial stay cable 4 (oblique cable) and a circumferential stay cable 5 (circumferential cable). The central node of the upper chord single-layer latticed shell is not provided with a vertical support rod, and the latticed shell node 6 applies prestress to the inhaul cable through a tensioning ring.
As shown in fig. 5, the analysis process of the method for calculating a suspended dome structure with a square boundary according to the present invention includes the following steps:
the method comprises the following steps: and in the square boundary, establishing a rib annular upper chord spherical reticulated shell, and establishing a lower chord cable-rod system corresponding to the position of the upper chord spherical reticulated shell according to the height of a preset vertical strut 3, wherein the lower chord cable-rod system is used as an initial state of iterative computation.
Taking an upper layer single-layer reticulated shell 1/4 structure as an isolator, leading the node rotation angle of each ring of circumferential guy cables to be pi/2, calculating the upper shell surface load into the node load of the grid, assuming that the 1/4 isolator structure grid has n rings, each ring has m nodes, transmitting the load from ring to outside according to the effect of the radial stay cable of the inner ring, accumulating the node load of each ring from inside to outside along the radial direction, and obtaining the vertical load VF requirement VF of each ring of nodesi,k。
Wherein, RFj,kNode load of the jth node of the jth circle
VFi,kVertical load demand of the ith circle of the kth node
Knowing the vertical load demand VF of each ring of reticulated shell nodes 6i,kObtaining the horizontal load requirement HF of each circle of the net shell node 6i,kAs shown in fig. 2, namely:
according to the ith circle horizontal load demand HFi,kSum of horizontal load requirements of i circle
Proportional distribution of the rotation angle theta of the annular stay 5 at each nodei,k。
Step two: according to the calculated 5 rotation angle theta of each section of the annular inhaul cablei,kStarting from the symmetric axis node of the outermost ring of the circumferential stay cable, the angle alpha of the radial stay cable passing through the outer ring node and capable of ensuring the equal internal force of the circumferential stay cable 5 is calculated one by onei,k。
According to the circumferential inhaul cable node, the outer ring dome node and the circumferential inhaul cable rotation angle thetai,kRadial stay cable angle alphai,kAnd (5) under the condition, enabling the positions of the circumferential rod 2 of the upper-chord single-layer reticulated shell to correspond to the positions of the circumferential inhaul cables 5, and constructing a new grid form. And (5) repeating the step one from the new grid form, and performing iterative computation to the stable state of the grid form, namely the shape of the upper chord single-layer grid shell and the lower chord cable rod of the suspended dome.
Step three: calculating the horizontal load demand VF of each circle of nodes according to the final grid formi,kAngle theta by pulling the cable in a circumferential directioni,k+1Can obtain the prestress T of each ring of the annular inhaul cableiThe size of (2).
The method of the invention is now validated using the ABAQUS finite element program. Setting the side length of a certain square boundary to be 80m, the height f to be 8.0m, adopting a spherical dome shape, dividing an upper chord single-layer latticed shell by using a rib ring type grid, and uniformly taking the mass density of a steel structure material to be 7850kg/m3The number of the loop bar turns is set to be 7, and the initial grid form and the final calculation grid form are shown in the figure. Calculating the prestress value T of the annular guy cableiAs shown in table 1:
TABLE 1 calculation error table for prestress of each loop of circumferential cable
The calculated prestress values of the circumferential stay cables of all the nodes in each circle are nearly equal, the error is only 6.16% at most, and the prestress of the circumferential stay cables in the final calculation grid form is considered to be equal, namely, the circumferential stay rods cannot deform circumferentially after the circumferential stay cables are prestressed.
The structural stress performance is verified by adopting a model at present, and the uniform load of the roof is 2kN/m2The elastic modulus of the cable structure is 1.8 multiplied by 105The MPa, the vertical stay bar and the latticed shell are made of Q345 steel, and the elastic modulus is 2.06 multiplied by 105And MPa, the sections of the reticulated shell rod pieces are uniformly made of rectangular steel pipes of 400 multiplied by 200 multiplied by 5mm, 7 circles of annular stay cables and radial stay cables are arranged on the lower chord cable rod structure, the included angle between each circle of vertical stay rods and the radial stay cables is equal, namely the preset initial height value of each circle of vertical stay rods is that the height difference between the current circle and the outer circle is increased by 3m, the vertical stay rods are made of phi 273 multiplied by 8 steel pipes, the outermost three circles of annular stay cables are made of phi 5 multiplied by 85 galvanized cold-drawn steel wire bundles, the rest annular stay cables are made of phi 5 multiplied by 55 galvanized cold-drawn steel wire bundles, and the radial stay cables are made of phi 5 multiplied by 55 galvanized cold-drawn steel wire bundles. The reticulated shell is simulated by a beam unit B31, the vertical stay bar is simulated by a truss unit T3D2, the guy cable and the circumferential guy cable are simulated by a truss unit T3D2, and meanwhile, the cable structural material is only capable of being pulled. The above material settings are only used for case explanation, and should be adjusted according to the calculation result in the actual engineering, fig. 3 is a schematic diagram illustrating the initial grid in this case, and fig. 4 is a schematic diagram illustrating the stable state of the final computational grid in this case.
The calculation result shows that under the action of uniformly distributed vertical loads, the maximum vertical displacement of the dome is 0.17m, the standard requirement is met, the maximum axial force of the rod piece is 1013kN, and the maximum bending moment is only 39 kN.m. The maximum axial stress ratio obtained by designing the components according to the internal force is 0.677, the maximum bending stress ratio is only 0.133, and the bending stress ratio of 90 percent of the rod piece is less than 0.100, which shows that the structure of the invention has good stress performance. If measures such as a small amount of chamfers at four corners are adopted, the stress performance can be further improved.
The above-mentioned embodiments of the present invention are not within the scope of the present invention, and the application of the present invention is not limited thereto, and other modifications and substitutions of the calculation method of the present invention can be made without departing from the technical scope of the present invention.
Claims (3)
1. The utility model provides a string dome structure suitable for square boundary, includes last string individual layer net shell and last string cable rod structure, it contains radial rod and hoop pole to go up string individual layer net shell, last string cable rod structure includes vertical brace, radial suspension cable and hoop cable, its characterized in that: the internal forces of the annular stay cables of all circles of the square boundary string dome are the same, and the supporting force of the vertical stay rods is suitable for the load requirements of the upper string single-layer latticed shell at different positions;
the calculation method of the suspended dome structure suitable for the square boundary comprises the following steps:
the method comprises the following steps: establishing a rib annular upper chord spherical reticulated shell within the square boundary, and establishing a lower chord cable rod structure corresponding to the upper chord spherical reticulated shell according to the preset height of the vertical strut, wherein the lower chord cable rod structure is used as an initial state of iterative computation;
taking an upper layer single-layer latticed shell as an isolator, guiding and calculating upper load into concentrated force at nodes of a grid, transmitting the load to the outside circle by circle according to the effect of an inner ring radial stay cable, accumulating the loads of all circles of nodes from inside to outside circle by circle in the radial direction to obtain the vertical load demand of each circle of nodes, calculating the horizontal load demand of each circle of nodes by force balance, and distributing the corners of the nodes of the circumferential stay cable according to the size of the horizontal load demand;
step two: calculating the radial stay cable angle which passes through an outer ring node and can ensure the internal force of the annular stay cable and the like one by one according to the calculated annular stay cable rotation angle and starting from a symmetrical shaft node of the outermost ring of the annular stay cable, and enabling an upper-chord single-layer net shell annular rod to correspond to the position of the annular stay cable according to the conditions of the annular stay cable node, the outer ring dome node, the annular stay cable rotation angle and the radial stay cable angle to construct a new grid form;
step three: after the final grid form is obtained, the prestress of each ring of circumferential cables is obtained according to the horizontal load requirement of each ring of nodes and the rotation angle of the circumferential cables and the static balance condition of the nodes of the circumferential cables.
2. A suspended dome structure adapted for use with a square boundary, as claimed in claim 1, wherein: in the first step, the rotation angle of the annular inhaul cable node is distributed according to the calculated horizontal load demand.
3. A suspended dome structure adapted for use with a square boundary, as claimed in claim 1, wherein: and the grid form in the second step is obtained by deducing the rotation angle of the annular inhaul cable according to the geometric relation.
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| CN101255749A (en) * | 2008-03-21 | 2008-09-03 | 河南大学 | Rectangle plane net shell structure and rectangle plane string supporting dome |
| JP2012007380A (en) * | 2010-06-24 | 2012-01-12 | Tokai Univ | Openable dome |
| CN104278782A (en) * | 2014-10-20 | 2015-01-14 | 天津大学建筑设计研究院 | Spherical suspended-dome structure applicable to non-circular buildings |
| CN204126098U (en) * | 2014-10-20 | 2015-01-28 | 天津大学建筑设计研究院 | A kind of sphere suspended-dome structure being suitable for not rounded building |
| CN104805903A (en) * | 2015-05-11 | 2015-07-29 | 东南大学 | Parallel annular rib suspendome structure suitable for elliptical planes |
| CN110145064A (en) * | 2019-05-17 | 2019-08-20 | 东南大学 | One kind is rib-ring-shaped to open up scissors central shoring cable dome structure |
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- 2020-04-15 CN CN202010293737.2A patent/CN111502098B/en active Active
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101255749A (en) * | 2008-03-21 | 2008-09-03 | 河南大学 | Rectangle plane net shell structure and rectangle plane string supporting dome |
| JP2012007380A (en) * | 2010-06-24 | 2012-01-12 | Tokai Univ | Openable dome |
| CN104278782A (en) * | 2014-10-20 | 2015-01-14 | 天津大学建筑设计研究院 | Spherical suspended-dome structure applicable to non-circular buildings |
| CN204126098U (en) * | 2014-10-20 | 2015-01-28 | 天津大学建筑设计研究院 | A kind of sphere suspended-dome structure being suitable for not rounded building |
| CN104805903A (en) * | 2015-05-11 | 2015-07-29 | 东南大学 | Parallel annular rib suspendome structure suitable for elliptical planes |
| CN110145064A (en) * | 2019-05-17 | 2019-08-20 | 东南大学 | One kind is rib-ring-shaped to open up scissors central shoring cable dome structure |
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