CN111350276B - Design method for initial prestress state of spoke type cable bearing grid steel structure - Google Patents
Design method for initial prestress state of spoke type cable bearing grid steel structure Download PDFInfo
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- CN111350276B CN111350276B CN202010220672.9A CN202010220672A CN111350276B CN 111350276 B CN111350276 B CN 111350276B CN 202010220672 A CN202010220672 A CN 202010220672A CN 111350276 B CN111350276 B CN 111350276B
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- E04B1/00—Constructions in general; Structures which are not restricted either to walls, e.g. partitions, or floors or ceilings or roofs
- E04B1/34—Extraordinary structures, e.g. with suspended or cantilever parts supported by masts or tower-like structures enclosing elevators or stairs; Features relating to the elastic stability
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Abstract
The invention relates to a design method of an initial prestress state of a spoke type cable bearing grid steel structure, which comprises the following steps: calculating to obtain the magnitude of load action borne by nodes of radial cables and ring cables according to the self-weight condition borne by the spoke type cable-bearing grid steel structure; obtaining the initial pretension estimated value of each radial cable under the self weight and the cable force distribution condition of the radial cables and the ring cables; determining the diameters of the radial cable and the ring cable according to the pretension, inputting the initial pretension obtained by comparison into a finite element structure model, and checking and adjusting the structure shape until the requirement of the building appearance is met after geometric nonlinear static calculation; determining the pretension of the radial cable and the ring cable, and obtaining the diameters of the new radial cable and the new ring cable at the same time, thereby determining the initial prestress state of the structure; the invention is suitable for the design of the spoke type cable bearing grid steel structure.
Description
Technical Field
The invention relates to the field of space structures, in particular to a construction design and a structural design of a spoke type cable-supported grid steel structure.
Background
The spoke type cable-supported grid steel structure generally comprises a rigid grid, a flexible cable system and vertical support rods, wherein the flexible cable system provides vertical support for the upper rigid grid through the vertical support rods; the rigid grid plays a role in pressing the ring, and the whole structure is a self-balancing system after the flexible inhaul cable system is tensioned, wherein the flexible inhaul cable system comprises radial cables and ring cables.
In the design of the spoke type cable bearing grid steel structure, the situation that the initial prestress state is difficult to determine is often encountered. The general conventional design method for initial pre-stress state has two types: one is calculus analysis; the other is a nonlinear finite element trial algorithm. The calculus analysis method generally requires that the structure has the characteristics of geometric dimension and load distribution which are biaxial symmetry, and the initial pretension of the inhaul cable is convenient to calculate and determine. In actual engineering, the spoke type cable-supported grid steel structure cannot be calculated and determined through an analytical method under the conditions that coordinates and loads can be asymmetric and the conditions are complex. The other nonlinear finite element trial algorithm is the most common method for determining the pretension of the stay rope by the spoke type cable bearing grid steel structure, but the adjustment iterative calculation needs to be carried out repeatedly for many times, so that the method is very tedious and consumes a lot of time. Therefore, a fast and simple method for determining the initial prestress state is needed to be invented to solve the problem of improving the design efficiency of the spoke type cable-supported grid steel structure.
Disclosure of Invention
The invention aims to provide a design method for quickly and simply determining the initial prestress state of a spoke type cable-supported grid steel structure.
In order to achieve the purpose, the invention provides a design method of an initial prestress state of a spoke type cable-supported grid steel structure, wherein the spoke type cable-supported grid steel structure comprises a rigid grid, radial cables, ring cables and vertical support rods, and the method comprises the following steps:
the method comprises the following steps: according to the self-weight (including the roof permanent load, the same below) of the spoke type cable-supported grid steel structure, the magnitude of the load acting on the node of the radial cable and the ring cable in the spoke type cable-supported grid steel structure and the vertical strut shaft force value N3 under the self-weight are obtained through statistical calculation. When both vertical struts and diagonal web members are present, it may be preferable to safely consider the load to be entirely concentrated on the vertical struts when determining the initial pre-tension phase.
Step two: determining an included angle alpha between a radial cable and a horizontal line at each node according to the building appearance, and preliminarily obtaining an initial pretension estimated value N2= N3/sin alpha of the radial cable at each node under the self weight by utilizing the vertical strut shaft force value N3 at each node obtained in the step one and the local static balance principle of the radial cable and the ring cable node; and after the radial cable force N2 at each node is obtained, multiplying the minimum radial cable force by 6.5 times is the looped cable force N1 at the corresponding node, multiplying the maximum radial cable force by 5.5 times is the looped cable force N1 at the corresponding node, and interpolating the rest nodes by 5.5-6.5 times to determine the looped cable force N1.
Step three: establishing a finite element structure calculation model, and when the structure is in a cable-free pretension state, the structure reaches a balance state through a static calculation structure under the action of dead weight, and then obtaining the cable force of the radial cable at each node
And cable force of the ring cable
And (4) distribution situation.
Step four: the results at the same node obtained in the second step and the third step are compared
、
、
、
N1 and N1 'in the system are respectively compared with N2 and N2', the pretension of the radial cable and the ring cable at each node is determined according to a larger value, the diameter of the radial cable and the ring cable at each node is determined according to the pretension, the initial pretension obtained by comparison is input into a finite element structure model, and after geometric nonlinear static calculation, whether the structure shape meets the requirement of the building appearance is checked.
Step five: and when the structural shape can not meet the requirement of the building appearance, gradually increasing the initial pretension obtained by comparison in the fourth step as a basic modulus, and repeatedly performing geometric nonlinear static calculation until the error with the building appearance is within two thousandth of the range, so that the pretension of the radial cable and the ring cable at each node can be determined, and the new diameters of the radial cable and the ring cable at each node can be obtained, thereby determining the initial prestress state of the structure.
And in the fifth step, if the initial pretension is increased more than 2 times step by step, the structural deformation and the building outline error still cannot be within two thousandth of a range, and the calculated structural shape and the building outline error reach the interval range by adjusting the included angle between the radial cable and the horizontal line, the rise of the cable-supported grid steel structure and the curvature of the ring cable.
Further, converting the pretension of the radial cable and the circular cable obtained in the step five into cable stress values
（
A is the effective cross-sectional area of the stay cable, and N =
Or
) If the stress value is 0.15-0.25 fptk，fptkThe diameter (and the effective cross-sectional area A) of the radial cable and the ring cable can be determined according to the standard value of the tensile strength of the stay cable.
The method initially obtains the initial pretension estimated value of each radial cable under the dead weight through the local static balance principle of the radial cable and the ring cable node, and is simple and easy to implement. And then, by establishing a structure finite element model, the structure reaches an equilibrium state under the self-weight action of the structure in a cable-free pretension state, and the cable force distribution condition of the radial cable and the ring cable is obtained at the moment, so that the complicated iterative calculation of a nonlinear finite element is avoided. The pretension of the radial cable and the annular cable is determined according to the results of the two methods according to a larger value, and the pretension is used as the basis of initial prestress state analysis to perform finite element analysis on the whole structure, so that the complexity and time consumption of the traditional method are saved.
Drawings
FIG. 1 is a schematic view of a spoke type cable-supported grid steel structure;
FIG. 2 is a schematic view of a typical local unit of a spoke type cable-supported grid steel structure;
FIG. 3 is a view of FIG. 2
The principle schematic diagram of local force balance of the radial cable and the ring cable node is shown;
in the figure: 1-prestressed ring cable, 2-prestressed radial cable and 3-vertical stay bar.
Detailed Description
Implementation mode one
The design method is explained by taking the design of a certain spoke type cable bearing grid steel structure as an example:
(1) the geometric shape of the spoke type cable bearing grid steel structure is determined according to the building modeling requirement, a fixed hinged support is arranged at the lower end of the vertical support rod 3 through structural analysis software, and support reaction force and a 3-axis force value N3 of the vertical support rod under the self-weight are obtained through load guiding calculation.
(2) Determining an included angle alpha between each radial cable 2 and a horizontal line according to the building shape, and initially obtaining an initial pretension estimated value N2= N3/sin alpha of each radial cable 2 under the self weight by utilizing the axial force N3 of the vertical stay bar 3 and the local force balance principle of the nodes of the radial cables 2 and the ring cables 1; and after the cable force N2 of each radial cable 2 is obtained, multiplying the minimum radial cable force by 6.5 times is the looped cable force N1 at the corresponding node, multiplying the maximum radial cable force by 5.5 times is the looped cable force N1 at the corresponding node, and interpolating the rest nodes by 5.5-6.5 times to determine the looped cable force.
(3) And deleting the fixed hinged support at the lower end of the vertical stay bar 3 of the structural calculation model, adding the radial cable 2 and the ring cable 1 models according to any cross section, and achieving a balance state through the static calculation structure under the action of dead weight, thereby obtaining the cable force (N1 'and N2') distribution conditions of the radial cable and the ring cable.
(4) Comparing the results N1, N2, N1 'and N2' obtained in the two steps, determining the pretension of the radial cable and the ring cable according to a larger value, using the pretension as the basis of the initial pretension of the radial cable and the ring cable, inputting the initial pretension obtained by comparison into a structural model, and checking whether the structural shape meets the requirement of the building appearance after geometric nonlinear static calculation.
(5) And when the structural shape can not meet the requirement of the building appearance, the initial pretension obtained by comparison in the previous step is taken as a basic modulus to be increased step by step (for example, 1.35 times, 1.7 times, 2.0 times and the like), and geometric nonlinear static calculation is repeatedly carried out until the error with the building appearance is within two thousandths of a range. If the initial pretension is increased by more than 2 times, the error between the structural shape and the building appearance still cannot be within two thousandth, the target is achieved by adjusting the building appearance parameters such as the included angle between the radial cable and the horizontal line, the rise of the cable-supported grid steel structure, the curvature of the looped cable and the like, and the pretension of the radial cable and the looped cable can be preliminarily determined at the moment.
(6) Converting the radial cable and ring cable pretension obtained in the last step into cable stress value (
A is the effective cross-sectional area of the stay cable), if the stress value is 0.15-0.25 fptk，fptkThe diameter (and the effective cross-sectional area A) of the radial cable and the ring cable can be determined according to the standard value of the tensile strength of the stay cable.
(7) And updating the structural calculation model according to the diameters of the radial cables 2 and the ring cables 1 determined in the previous step, adding the determined initial pretension to the structural calculation model, performing geometric nonlinear static calculation again, confirming that the error between the structural shape and the building appearance is within two thousandth, and determining the state as the initial prestress state with basically reasonable structure.
Second embodiment
To further illustrate the implementation of the method, the determination process of the initial pre-stress state of the steel structure of the spoke type cable-supported grid of a stadium is described by taking a certain steel structure as an example (only a typical axis is taken as an example for data).
Step 1: according to the building requirements, building an initial geometric model of the structure as shown in figures 1-3; and calculates the vertical strut axial force value N3 under the self weight.
Step 2: counting an included angle alpha between a radial cable and a horizontal line according to the building appearance, and preliminarily obtaining an initial pretension estimated value N2= N3/sin alpha of the radial cable by utilizing the axial force N3 of a vertical strut; after the cable force N2 of each radial cable 2 is obtained, the minimum radial cable force multiplied by 6.5 times is the looped cable force N1 at the corresponding node, the maximum radial cable force multiplied by 5.5 times is the looped cable force N1 at the corresponding node, and the looped cable force is determined at the rest nodes according to 5.5-6.5 times of interpolation, as shown in Table 1.
TABLE 1 exemplary axial radial and loop initial pretension estimates
And 3, step 3: a fixed hinged support at the lower end of a vertical stay bar 3 of the structural calculation model is deleted, a radial cable 2 model and a ring cable 1 model are added according to any cross section, the static calculation structure reaches a balance state under the action of dead weight, and the cable force (N1 'and N2') distribution conditions of the radial cable and the ring cable are obtained at the moment, as shown in Table 2.
TABLE 2 exemplary axial radial and cyclic cable force profiles
Step 4 and step 5: comparing the results N1, N2, N1 'and N2' obtained in the two steps, determining the pretension of the radial cable and the ring cable according to a larger value, using the pretension as the basis of the initial pretension of the radial cable and the ring cable, inputting the initial pretension obtained by comparison into a structural model, increasing the pretension step by step (for example, 1.35 times, 1.7 times, 2.0 times and the like), and repeating the geometric nonlinear static calculation until the geometric nonlinear static calculation is within two thousandths of the building shape error, as shown in Table 3.
TABLE 3 exemplary axial radial and cyclic cable force and displacement control
6, 7: converting the radial cable and ring cable pretension obtained in the last step into cable stress value (
A is the effective cross-sectional area of the stay cable), if the stress value is 0.15-0.25 fptk，fptkThe diameter (and the effective cross-sectional area A) of the radial cable and the ring cable can be determined according to the standard value of the tensile strength of the stay cable. And updating the structural calculation model, adding the determined initial pretension to the structural calculation model, performing geometric nonlinear static calculation again, confirming that the error between the structural shape and the building outline is within two thousandth of the range, and determining the state as the initial prestress state with a basically reasonable structure at the moment, as shown in table 4.
TABLE 4 typical axial radial and hoop effective cross-sectional area and stress values
Claims (3)
1. A design method for an initial prestress state of a spoke type cable-supported grid steel structure comprises radial cables (2), ring cables (1) and vertical support rods (3), and is characterized by comprising the following steps:
the method comprises the following steps: according to the self-weight condition of the spoke type cable bearing grid steel structure, the load acting on the node of the radial cable (2) and the ring cable (1) in the spoke type cable bearing grid steel structure and the axial force value N3 of the vertical strut (3) under the self-weight are obtained through statistical calculation; when the vertical stay bar and the diagonal web member exist at the same time, the load can be safely considered to be totally concentrated on the vertical stay bar (3) in the initial pre-tension stage;
step two: determining an included angle alpha between the radial cable (2) at each node and the horizontal line according to the building appearance, and initially obtaining an initial pretension estimated value N2= N3/sin alpha of the radial cable (2) at each node under self weight by using the vertical strut shaft force value N3 at each node obtained in the first step and through the local force balance principle of the radial cable (2) and the ring cable (1); after the radial cable force N2 at each node is obtained, multiplying the minimum radial cable force by 6.5 times is the looped cable force N1 at the corresponding node, multiplying the maximum radial cable force by 5.5 times is the looped cable force N1 at the corresponding node, and interpolating the rest nodes by 5.5-6.5 times to determine the looped cable force N1;
step three: establishing a finite element structure calculation model, and when the structure is in a cable-free pretension state, achieving a balance state through a static calculation structure under the action of dead weight, and obtaining the distribution conditions of the cable force N2 'of the radial cable and the cable force N1' of the ring cable at each node;
step four: respectively comparing N1 and N1 'and N2 and N2' in the results N1, N2, N1 'and N2' at the same node obtained in the second step and the third step, determining the pretension of the radial cable and the ring cable at each node according to a larger value, determining the diameter of the radial cable and the ring cable at each node according to the pretension, inputting the initial pretension obtained by comparison into a finite element structure model, and checking whether the structure shape meets the requirement of the building appearance after geometric nonlinear static calculation;
step five: and when the structural shape can not meet the requirement of the building appearance, gradually increasing the initial pretension obtained by comparison in the fourth step as a basic modulus, and repeatedly performing geometric nonlinear static calculation until the error with the building appearance is within two thousandth of the range, so that the pretension of the radial cable and the ring cable at each node can be determined, and the new diameters of the radial cable and the ring cable at each node can be obtained, thereby determining the initial prestress state of the structure.
2. The design method of initial pre-stress state of spoke type cable-supported grid steel structure as claimed in claim 1, wherein in said step five, if the initial pre-tension is increased more than 2 times, the error between the structure shape and the building shape still can not be within two thousandth, the error between the structure shape and the building shape can reach the above range by adjusting the included angle between the radial cable (2) and the horizontal line, the rise of the cable-supported grid steel structure and the curvature of the ring cable (1).
3. The method for designing the initial prestress state of the spoke type cable-supported grid steel structure as claimed in claim 1, wherein the radial cable and ring cable pretensions at each node obtained in the fifth step are converted into cable stress values according to the following formula
：
A is the effective cross-sectional area of the stay cable, N = N1 or N2, if the stress value is 0.15-0.25 fptk，fptkThe diameter and the effective cross-sectional area A of the radial cable and the ring cable at each node can be determined according to the standard value of the tensile strength of the stay cable.
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| CN101630344A (en) * | 2009-07-31 | 2010-01-20 | 东南大学 | Gradual recursion method for determining initial equilibrium state of cable dome |
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