A simplified method for vertical calculation model of brackets
By establishing a refined finite element model and simplifying the Douyin components, the difficulties of Douyin complex structure in the calculation and analysis of wooden structure buildings are solved, and more efficient and accurate calculation analysis is achieved, which significantly improves the calculation efficiency and model accuracy.
Patent Information
- Application Number
- CN202210251614.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-03-15
- Publication Date
- 2025-03-18
- Estimated Expiration
- 2042-03-15
AI Technical Summary
The existing technology is difficult to accurately consider the complex internal structure of Douzhang. In the calculation and analysis of the overall structural performance of traditional Chinese wooden buildings, it leads to difficulty in computing and analysis and inefficiency.
By establishing a refined finite element model of the bucket arch, the tension and compressive stress transmission paths are extracted, and the components in the bucket arch are simplified into beam units or rod units according to the stress transmission paths, and a reduction coefficient is introduced to ensure the consistency of vertical stiffness.
The accuracy and calculation efficiency of the simplified model are significantly improved, and the stress distribution and deformation consistency between the simplified model and the fine model is good. The numerical error is about 10%, and the vertical stiffness error is between 4% and 11%, and the calculation time can be reduced by 90% to 97%.
Smart Images
Figure CN114611192B_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the technical field of bracket analysis and calculation, and particularly relates to a method for simplifying a vertical calculation model of a bracket. Background Art
[0002] The majority of the ancient architectural remains in my country are wooden structures, including palaces, government offices, temples, houses, towers, etc., accounting for more than 60% of all ancient buildings. Among them, palaces, government offices, temples, towers, and other traditional buildings that embody the wisdom of ancient craftsmen mostly use brackets. Brackets are the essence of traditional Chinese wooden structures and are also extremely critical force-transmitting components. Roof loads often need to be transmitted to column heads through brackets, and are important structures in the main force-transmitting path of traditional wooden structures. In the Song and Yuan dynasties, the ratio of bracket height to column height even reached 1:3, and its huge size also shows its key role in the structure. A dougong is often composed of various dou, gong, ang, lining square head and shuatou. There are four types of dou: loudou, sandou, qixindou and jiaohuodou; there are five types of gong: huagong, nidaogong, guazigong, mangong and linggong. All of them are connected by mortise and tenon joints without any metal connectors. Its complex and exquisite internal structure is self-evident. However, the complex structure makes it difficult to calculate and analyze its structural performance. On the other hand, if the overall structural performance of traditional Chinese wooden buildings is to be numerically simulated, the complex internal structure of dougong itself is often not fully considered when modeling the overall building structure. Therefore, it is necessary to propose a reliable simplified calculation model that can accurately consider the structural performance of dougong in all aspects when calculating and analyzing the overall structural performance of traditional Chinese wooden buildings, based on the condition of understanding the stress conditions and force transmission mechanism of each dougong component under common load conditions. Summary of the invention
[0003] The purpose of the present invention is to provide a simplified method for the vertical calculation model of brackets, thereby improving the accuracy and efficiency of the finite element model analysis and calculation of the Chinese ancient architectural wood structure.
[0004] In order to solve the above technical problems, the present invention is achieved through the following technical solutions:
[0005] The present invention provides a method for simplifying a vertical calculation model of a bracket, comprising the following steps:
[0006] Establish a refined finite element model of the bracket and conduct stress analysis;
[0007] Extract the tensile and compressive stress transfer paths from the stress trace cloud diagram of the finite element model;
[0008] The components in the bracket are simplified into beam units or rod units according to the stress transfer path so that the load borne by the bracket is concentrated to the bottom bracket.
[0009] Furthermore, in the bracket, on the tensile and compressive stress transmission path, the components subjected to tensile force greater than compressive force are simplified to beam unit components, the rods subjected to compressive stress are all inclined in the overall space of the building, and the components mainly subjected to compression are simplified to rod unit components.
[0010] Furthermore, in the bracket, in the depth direction, the components that bear at least 2 / 3 of the force as bending force are simplified to beam unit components.
[0011] Furthermore, the inner head and the outer head are used as beam unit components.
[0012] Furthermore, in the bracket, in the width direction, the single bracket and the double bracket serve as diagonal components of the rod unit.
[0013] Furthermore, the vertical force transmission path on the central axis of the bracket should be simplified into a vertical beam unit component in the simplified model.
[0014] Furthermore, the simplified manner of the finite element model component is constructed based on the length, direction, and end face center point of the component as features.
[0015] Furthermore, the cross-sectional dimensions of the beam unit components are taken according to the actual cross-sectional dimensions, and the diagonal components of the rod units are reduced by introducing reduction coefficients to reduce their cross-sectional areas. The cross-sectional shape of the beam unit components simplified by the vertical force transmission path is a square, and the cross-sectional dimensions are the material width or the inner width of the bucket.
[0016] Furthermore, the vertical stiffness of the cantilever beam model of the Huagong in the depth direction and the single Gong in the width direction is obtained by the displacement method, and the vertical component of the diagonal bar stiffness is obtained according to the deformation theory, so that the vertical stiffness of the simplified model and the refined complete model are equal, and the cross-sectional area reduction coefficients k1 and k2 of the simplified model of the diagonal bar of the Huagong in the depth direction component and the single Gong in the width direction component can be obtained;
[0017] When the Huagong is simplified into an oblique member of a bar unit, the reduction factor of its cross-sectional area is k1, and the calculation formula is: a t The distance is half of the length of the Huagong, s t is the length of the line connecting the position of the force bearing point of the scattered bucket or the interactive bucket on the Huagong and the center point of the Huagong, θ t for a t and t When the single bracket is an oblique member of the rod unit, the reduction factor of the cross-sectional area of the single bracket member is k2, and the calculation formula is: h1 is the cross-sectional height of the bracket component, h2 is the height from the center of the force bearing point of the single bracket to the center of the single bracket, and a n is the horizontal distance from the center point of the force of the bucket on the single bracket to the center point of the single bracket, s nis the length of the line connecting the position of the force bearing point of the scattered bucket or the interactive bucket on the Huagong and the center point of the Huagong, θ n for a n and n Angle.
[0018] Furthermore, the heavy arch structure is simplified into two cantilever beams of unequal lengths, and the two cantilever beams are connected by a rigid chain rod;
[0019] When analyzing structural deformation, remove the chain rod. Assuming that the axial force of the chain rod is P, the simplified structure of the heavy bracket can be split into two cantilever beams. The lower short cantilever beam is only subjected to the concentrated force P transmitted by the chain rod at the end, and the upper longer cantilever beam is subjected to a downward displacement load δA at the end, and the middle is subjected to the upward concentrated force P transmitted by the chain rod; the vertical stiffness of this simplified structure of the heavy bracket is the sum of the vertical reaction forces of the two cantilever beam supports, and the vertical stiffness of the simplified structure of the double cantilever beam is equal to the vertical stiffness component of the simplified model of the diagonal rod, and the cross-sectional area reduction coefficient k3 of the simplified model of the diagonal rod of the heavy bracket in the width direction is obtained; when the heavy bracket is simplified as an oblique member of the rod unit, the reduction coefficient of its member cross-sectional area is k3, and the calculation formula is where a n is the horizontal distance from the center point of the force of the scattered bucket on the lower bracket to the center point of the single bracket, am is the horizontal distance from the center point of the force of the scattered bucket on the upper bracket to the center point of the single bracket, s m is the length of the connecting line between the position of the force bearing point of the scattered bucket or the interactive bucket on the upper arch and the center point of the lower arch, θm is a m and m The angle between the two, where 2h2≈a m , then Therefore, k3 can also simplify the calculation:
[0020] described.
[0021] The present invention has the following beneficial effects:
[0022] 1. When simplifying the compression components in the bracket into oblique rod unit compression components, the difference in vertical stiffness between the real components and the compression rod model is fully considered, and the reduction factor of the simplified component area is introduced, which significantly improves the accuracy of the simplified model;
[0023] 2. In terms of stress, the overall stress distribution of the simplified model and the refined model is consistent;
[0024] 3. In terms of deformation, the overall deformation of the simplified model and the original model is consistent, and the error of the estimated value is about 10%;
[0025] 4. In terms of vertical stiffness, the vertical stiffness of the simplified model and the original model is consistent, and the numerical error between the simplified model and the refined model is between 4% and 11%;
[0026] 5. In terms of calculation time, the calculation time of the simplified model is much shorter than that of the original model, which can be reduced by 90% to 97%, greatly improving the calculation efficiency.
[0027] Of course, any product implementing the present invention does not necessarily need to achieve all of the advantages described above at the same time. BRIEF DESCRIPTION OF THE DRAWINGS
[0028] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for describing the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.
[0029] Figure 1 It is a schematic diagram of Jixin’s bracket and the roof load condition;
[0030] Figure 2 This is a cloud diagram of the principal stress direction of Jixin-made brackets under roof loads;
[0031] Figure 3 A schematic diagram of a simplified model establishment method of a beam-type bracket based on stress distribution and force transmission path provided by the present invention;
[0032] Figure 4 The calculation diagram of the present invention is simplified to the equivalent diagonal brace by calculating the Huagong and the single Gong;
[0033] Figure 5 The calculation diagram of the present invention is to simplify the heavy bracket into an equivalent diagonal brace. DETAILED DESCRIPTION
[0034] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.
[0035] A simplified method for the vertical calculation model of dougong includes a refined finite element modeling analysis of the target dougong. The typical geometric features of the dougong and the detailed structures such as the grooves and dou ears need to be considered during the modeling. The stress direction cloud map calculated by the finite element calculation is analyzed to extract the main tensile and compressive stress transmission paths. When analyzing the stress cloud map and the tensile and compressive stress transmission paths, the depth direction and the width direction of the model should be analyzed respectively.
[0036] Secondly, based on the main tensile and compressive stress transfer paths, the main components of the bracket are simplified into beam units or rod units.
[0037] The components subject to bending and tension are simplified into beam unit components, and the components subject to compression are simplified into rod unit components. Among them, the compression rods are all oblique in space, and the compression rods are used to realize the structural function of the upper end of the real bracket bearing multiple vertical loads and finally converging to the bottom bracket and then to the wooden column.
[0038] Among the components in the depth direction, the outer head and the lining square head are mainly subjected to bending, and are simplified to beam unit components; the inner head is simplified to a beam unit component considering the structure and is connected to the outer head; the ang plays the role of both tensile force transmission and pressure transmission, and is simplified to a beam unit component; the huagong is mainly subjected to compression, and mainly transmits the pressure from the end dou obliquely to the louver dou, so it is simplified to a rod unit oblique component.
[0039] In the components in the width direction, for a single bracket, it is mainly responsible for transmitting pressure diagonally downward, and is simplified into two rod unit diagonal components; for a heavy bracket, because they jointly bear the work of transmitting pressure diagonally downward, they are simplified into two rod unit diagonal components. If the bracket is a double bracket, it is considered to act together and simplified into a beam unit component, and the cross section of the simplified component is kept as the cross section area of the double bracket.
[0040] The vertical force transmission path on the central axis of the real bracket should be simplified into a vertical beam unit component in the simplified model. The simplified beam model should have the characteristics of no disconnection in the force transmission path, and the force converges at the bottom of the model to meet the characteristics of the real bracket engineering, where the roof load is collected to the bracket through multiple force transmission paths and transmitted to the wooden column.
[0041] Finally, the position and connection relationship of these simplified beam-rod unit components are determined by considering the actual structure of the bracket and the dimensional relationship of the material system.
[0042] The length of the components and the direction characteristics of the oblique components of the simplified method. The components that act as connecting nodes in the bracket are called dou (divided into scattered dou, interactive dou, concentric dou and qiang dou, and the component at the bottom of the bracket is lou dou). The length and direction of the simplified components are determined by connecting the plane center points of the dou at the top of the component end. The components should satisfy the mechanical connection relationship between the real bracket components. The front end of the lou simplified component is the center point of the top surface of the qiang dou, and the rear end is the plane center point of the lou tail. When the single bracket is simplified to an oblique pressure rod, the upper end is the center point of the top surface of the bracket top dou, and the lower end is the center point of the top surface of the lower dou or the center point of the lou dou; when the double bracket is simplified to an oblique pressure rod, the upper end is the center point of the top surface of the upper bracket top dou, and the lower end is the center point of the lower dou or the center point of the lou dou.
[0043] The cross-sectional dimension characteristics of the components determined by the simplified method are as follows: the cross-sectional dimension of the beam unit components is taken according to the actual cross-sectional dimension; the diagonal components of the rod units should be reduced by a reduction factor k to ensure the consistency of the vertical stiffness of the structure; the vertical beam unit components introduced due to the structure have a square cross-sectional shape and a cross-sectional dimension of the material width (or the inner width of the bucket).
[0044] The structure of the Huagong in the depth direction and the single Gong (Nidao Gong, Guazi Gong) in the width direction can be regarded as a cantilever beam with a concentrated force length a at the end. The vertical stiffness of this cantilever beam model can be obtained by the displacement method of structural mechanics, and the vertical component of the diagonal bar stiffness can be obtained according to the deformation theory. If the vertical stiffness of the two is equal, the cross-sectional area reduction coefficients k1 and k2 of the simplified model of the diagonal bar of the Huagong in the depth direction and the single Gong in the width direction can be obtained. When the Huagong is simplified to an oblique member of a bar unit, the reduction coefficient of its member cross-sectional area is k1, and the calculation formula is Where at is the distance of one jump (i.e. half the length of the Huagong), st is the length of the line connecting the position of the force-bearing point of the scattered dou or the interactive dou on the Huagong and the center point of the Huagong, and θt is the angle between at and st. When the single dou (mudway dou, melon seed dou) is simplified to an oblique member of a rod unit, the reduction factor of its member cross-sectional area is k2, and the calculation formula is: h1 is the cross-sectional height of the bracket component, h2 is the height from the position of the force center of the scattered bracket on the single bracket to the center point of the single bracket, an is the horizontal distance from the force center of the scattered bracket on the single bracket to the center point of the single bracket (i.e. half the length of the single bracket), sn is the length of the connecting line between the position of the force point of the scattered bracket or the interactive bracket on the Huagong and the center point of the Huagong, and θn is the angle between an and sn.
[0045] The heavy bracket structure can be simplified into two cantilever beams of unequal lengths, connected by a rigid chain rod in the middle (the rigid chain rod is connected vertically upward from the end of the short cantilever beam below to the long cantilever beam). When analyzing the deformation of the structure, the chain rod can be removed. Assuming that the axial force of the chain rod is P, the simplified structure of the heavy bracket can be split into two cantilever beams. The lower short cantilever beam is only subjected to the concentrated force P transmitted by the chain rod at the end, and the upper longer cantilever beam is subjected to a downward displacement load δA at the end and an upward concentrated force P transmitted by the chain rod in the middle; the vertical stiffness of this simplified structure of the heavy bracket is the sum of the vertical reactions of the two cantilever beam supports. By making the vertical stiffness of the simplified structure of the double cantilever beam equal to the vertical stiffness component of the simplified model of the diagonal rod, the cross-sectional area reduction factor k3 of the simplified model of the diagonal rod of the heavy bracket in the width direction can be obtained. When the heavy bracket is simplified as an oblique member of a rod unit, the reduction factor of its cross-sectional area is k3, and the calculation formula is Where an is the horizontal distance from the center of the force of the scattered bucket on the lower bracket (mudway bracket or melon seed bracket) to the center of the single bracket (i.e. half of the length of the lower bracket), am is the horizontal distance from the center of the force of the scattered bucket on the upper bracket (slow bracket) to the center of the single bracket (i.e. half of the length of the upper bracket), sm is the length of the line connecting the position of the force point of the scattered bucket or interactive bucket on the upper bracket and the center of the lower bracket, and θm is the angle between am and sm. In addition, considering that 2h2≈a m , then Therefore, k3 can also simplify the calculation:
[0046] Specifically,
[0047] Taking a typical Song and Yuan Dynasty dougong as an example, a single-beam double-lower-angled six-layer dougong (each jump is counted, the third jump of the outer eaves and the second jump of the inner turn use a single dougong, and the rest use a heavy dougong, with inner doutou, outer doutou and lining square head) as an example to introduce the specific implementation method of the present invention. The working condition is the roof load in daily use.
[0048] (1) A refined finite element model of the bracket was established in the finite element software. Typical geometric features and detailed structures such as grooves and bracket ears were taken into consideration during modeling. Hard contact simulation was used between the components, and friction was considered, with a friction coefficient f of 0.3. The anisotropy of wood was taken into account in the analysis, the elastic modulus in the direction of the grain was taken as 9000MPa, the elastic modulus in the two directions of the transverse grain was taken as 1 / 10 of the elastic modulus in the direction of the grain, and the Poisson's ratio was taken as 0.3. Considering that most of the components of a general bracket are in the elastic stage, this paper only analyzes the force transmission characteristics of the bracket in the elastic stage without considering its plastic development. In this case, the finite element analysis was performed using the finite element analysis software ABAQUS. The specific model and load conditions are as follows. Figure 1 shown.
[0049] (2) Under the roof load condition, the force transmission mechanism of the bracket to the roof load is studied. The finite element model is calculated and analyzed, and the stress trace distribution diagram ( Figure 2 ), respectively, the model is processed in the depth direction Figure 2 (a) and width direction Figure 2(b) Analysis. Under the action of roof load, this bracket mainly transmits force to the column through the joint action of the gong and the plain beam, and then transmits force to the bracket through the cantilevered components in the depth direction. The roof load at the eaves beam is first gathered at the column axis through the top plain beam, and then transmitted downward in sequence through the components such as the lining beam head, the shua head, the ang and the hua gong at the column axis, and directly transmitted to the top of the column. The roof load at the eaves beam is transmitted to the column through the ang under bending, and then obliquely transmitted to the top of the column through the two jumps of the hua gong. Among them, the ang is the main bending component, the two jumps of the hua gong are mainly compressed, and the lining beam head and the outer shua head of the Jixin bracket are both bent and bear part of the load. Under the collapse condition, the two types of brackets mainly transmit force to both sides through the plain beam, and the plain beam and the bracket no longer work together. On the other hand, the components such as the lining beam heads and the ridgepole of the Jixin-made brackets effectively connect and tie the plain beams in different planes, so that these plain beams can share the load when they collapse.
[0050] (3) Based on the stress trace distribution diagram, the main tensile and compressive stress transmission paths in the depth and width directions of the bracket are extracted, and the stress conditions of each component in the force transmission path are analyzed. By considering the scale relationship of the material system, the corresponding beam units and rod units are simplified for different load-bearing components.
[0051] Figure 3 (a) shows how the components in the depth direction (lining square head, outer head, inner head, ang and huagong) transfer vertical loads. The lining square head and outer head share part of the roof load by bending, and the force transmission paths in the components are similar; at the lower edge of these components, a closed compressive stress path is formed between the eaves beam and the eaves beam, while a tensile stress zone is formed at the upper edge; therefore, the lining square head and outer head are simplified to beam unit components, and the cross-sectional dimensions are taken according to the width and thickness of the single material, taking b×h1. The inner head is considered to be simplified as a beam unit component, connected to the outer head, and the cross-sectional dimensions are taken according to the width and thickness of the single material, taking b×h1.
[0052] The force transmission path of the ang is more complicated, and there are multiple force transmission paths in the component: the load at the eaves beam is transmitted to the column through the front of the ang, while the load of the eaves beam is transmitted vertically through the middle part of the ang, and the two force flows converge at the bottom of the front side of the ang, and are transmitted obliquely to the louver through the front of the two jumping Huagong; another path is transmitted straight downward through the middle part of the ang to the louver; secondly, there is another path that is transmitted to the lower flat beam through the back side of the ang, and this force flow is also partially transmitted obliquely to the louver through the inner head and the rear tail of the Huagong; considering the structural conditions of the simplified model, the two angs are simplified into a beam unit component considering their joint effect, and the cross-section of the simplified component is one louver for two materials in height, and the width is the same as that of a single material, which is b×(h1+h2).
[0053] Considering that the two-jump Huagong is mainly subjected to compression, it is simplified into an oblique rod unit component; considering the stiffness difference, the cross-sectional area of the simplified component needs to be reduced, and its cross-sectional area is taken as k1×b×h2, where k1 is the Huagong cross-sectional reduction coefficient.
[0054] Finally, the vertical force transmission path in the middle of the real bracket is simplified into a vertical square-section beam unit component with a cross-sectional size of b×b.
[0055] The positions and connection relationships of each component are as follows: Figure 3 (b) as shown.
[0056] akin, Figure 3 (c) and Figure 3 (d) shows how the components in the width direction (mudway gong, melon seed gong, slow gong and plain beam) transfer vertical loads. Since the components in the width direction are mostly arranged in two forms: single gong (mudway gong or melon seed gong combined with plain beam) and double gong (mudway gong, slow gong and plain beam combined), this example focuses on these two cases. Although some longer gongs also have tensile areas on their upper edges, forming a beam-like mechanism, considering the oblique force transmission of both and the calculation efficiency, they are still simplified into oblique rod unit components.
[0057] For a single bracket, the compressive stress of the plain beam is transmitted downward through three brackets, and the two ends of the mud road bracket are subjected to the compressive stress transmitted by the two brackets on both sides, and transmitted to the middle through the lower side of the bracket, and then to the lower component on the central axis; therefore, the mud road bracket (or melon seed bracket) is simplified into two diagonal braces. Also considering the difference in stiffness, the cross-sectional area of the simplified component must be reduced according to the actual cross-sectional area, and its cross-sectional area is taken as k2×b×h1, where k2 is the cross-sectional reduction coefficient of the single bracket.
[0058] The compressive stress transmitted by the middle bracket is directly transmitted vertically downward; based on the structural connection, the vertical force transmission path on the central axis of the actual bracket will be simplified to a vertical beam unit component with a cross-sectional area of b×b.
[0059] For the heavy bracket, the compressive stress of the plain beam is transmitted downward through the three brackets above the slow bracket. In the slow bracket, part of the compressive stress is transmitted to the middle through the lower side of the bracket, and then transmitted downward along the middle bracket after reaching the central axis. The other part of the compressive stress is transmitted to the mud bracket through the brackets on both sides below, and then continues to be transmitted to the central axis at the mud bracket, and is transmitted obliquely to the lower components. Therefore, the slow bracket and the mud bracket (or melon seed bracket) are simplified into two oblique braces. Also considering the difference in stiffness, the cross-sectional area of the simplified component must be reduced according to the actual cross-sectional area, and its cross-sectional area is taken as k3×b×h1, where k3 is the cross-sectional reduction coefficient of the heavy bracket.
[0060] Finally, the force transmission path on the central axis of the real bracket is also simplified into a vertical beam unit component with a cross-sectional area of b×b.
[0061] The positions and connection relationships of each component are as follows: Figure 3 (e) and Figure 3 (f).
[0062] in, Figure 3 The vertical line in the middle connects the components before and after simplification. The first letter B or T in the middle text indicates that the component is simplified to a beam or a rod, respectively, and the following text indicates the cross-sectional area of the simplified component. The meanings of the remaining letters are as follows: b is the width of the material; h1 is the height of a single material; h2 is the height of a full material; a t is the distance of one hop; a m It is half the length of the slow arch; a n It is half the length of the mud road arch; k1 is the cross-section reduction coefficient of the Hua arch; k2 is the cross-section reduction coefficient of the single arch; k3 is the cross-section reduction coefficient of the heavy arch
[0063] (4) Determine the cross-sectional area reduction coefficients of the simplified components of the Huagong in the depth direction and the single bracket in the width direction. The semi-structure can be regarded as a cantilever beam with a concentrated force of length a at the end. The vertical stiffness of this cantilever beam model can be obtained by the displacement method of structural mechanics. The vertical component of the diagonal bar stiffness can be obtained according to the deformation theory. If the vertical stiffness of the two is equal, the cross-sectional area reduction coefficients k1 and k2 of the simplified diagonal bar model of the Huagong in the depth direction component and the single bracket in the width direction component can be obtained. Figure 4 Schematic diagram of the analysis model.
[0064] The expressions for the simplified reduction coefficient k1 of Huagong and the simplified reduction coefficient k2 of Dangong are:
[0065]
[0066]
[0067] The dimensions of Huagong, Nidaogong and Guazigong are clearly defined in the "Yingzaofashi": Huagong has a cross section of full material, 21 fen in height, 10 fen in width, and a jump of no more than 30 fen. This article uses a jump of 30 fen as the calculation; Nidaogong and Guazigong have cross sections of single material, 15 fen in height, 10 fen in width, and a total length of 62 fen. Therefore, h1 = 15, h2 = 21, and a = 2. t =30, a n =31, substituting into the formula, we can obtain k1≈0.441, k2≈0.227.
[0068] (5) Determine the cross-sectional area reduction factor of the simplified component of the heavy bracket unit in the width direction.
[0069] The semi-structure of the heavy arch can be simplified into two cantilever beams of unequal length, connected by a rigid chain rod in the middle (the rigid chain rod is connected vertically upward from the end of the short cantilever beam below to the long cantilever beam). When analyzing the deformation of the structure, the chain rod can be removed. Assuming that the axial force of the chain rod is P, the simplified structure of the heavy arch can be split into two cantilever beams. The lower short cantilever beam is only subjected to the concentrated force P transmitted by the chain rod at the end, and the upper longer cantilever beam is subjected to a downward displacement load δA at the end and an upward concentrated force P transmitted by the chain rod in the middle; the vertical stiffness of this simplified structure of the heavy arch is the sum of the vertical reaction forces of the two cantilever beam supports. By making the vertical stiffness of the simplified structure of the double cantilever beam equal to the vertical stiffness component of the simplified model of the diagonal rod, the cross-sectional area reduction factor k3 of the simplified model of the diagonal rod of the heavy arch in the width direction component can be obtained. Figure 5 Schematic diagram of the analysis model.
[0070] The expression of the simplified reduction factor k3 of the heavy bracket is:
[0071]
[0072] Based on the size regulations of Nidaogong, Guazigong and Mangong in "Yingzaofashi", Nidaogong and Guazigong are 15 fen high, 10 fen wide, and 62 fen in total length, while Mangong is 15 fen high, 10 fen wide, and 92 fen in total length. Therefore, h1=15, h2=21, a m =46, a n =31, substituting it into the formula, we can obtain k3≈0.141.
[0073] The above is only a specific simplified method given by the present invention for a single-beam, double-lower-angled, six-layer bracket set with a center (where each jump is a center, the third jump of the outer eaves and the second jump of the inner turn use a single bracket, and the rest use a double bracket, with an inner head, an outer head and a lining square head). It should be pointed out that for ordinary technicians in this technical field, it can be easily used for brackets of other structures; and, without departing from the principle of the present invention, several improvements and modifications can be made, and these improvements and modifications should also be regarded as the scope of protection of the present invention.
Claims
1. A simplified method for the vertical calculation model of brackets, characterized in that: The following steps are involved: Establish a refined finite element model of the bracket and conduct stress analysis; Extract the tensile and compressive stress transfer paths from the stress trace cloud diagram of the finite element model; Simplify the components in the bracket into beam units or rod units according to the stress transfer path so that the load borne by the bracket is concentrated to the bottom bracket; The vertical stiffness of the cantilever beam model is obtained by displacement method for the Huagong in the depth direction and the Dangong in the width direction, and the vertical component of the diagonal bar stiffness is obtained according to the deformation theory, so that the vertical stiffness of the simplified model and the refined complete model are equal, and the cross-sectional area reduction coefficients k1 and k2 of the simplified model of the diagonal bar of the Huagong in the depth direction component and the Dangong in the width direction component can be obtained; When the Huagong is simplified into an oblique member of a bar unit, the reduction factor of its cross-sectional area is k1, and the calculation formula is: , a t The distance is half of the length of the Huagong, s t is the length of the line connecting the position of the force bearing point of the scattered bucket or the interactive bucket on the Huagong and the center point of the Huagong, θ t for a t and t When the single bracket is an oblique member of the rod unit, the reduction factor of the cross-sectional area of the single bracket member is k2, and the calculation formula is: , h1 is the cross-sectional height of the bracket component, h2 is the height from the center of the force bearing point of the single bracket to the center of the single bracket, a n is the horizontal distance from the center point of the force of the bucket on the single bracket to the center point of the single bracket, s n is the length of the line connecting the position of the force bearing point of the scattered bucket or the interactive bucket on the Huagong and the center point of the Huagong, θ n for a n and n Angle.
2. The method for simplifying the vertical calculation model of bracket according to claim 1, characterized in that: In the bracket set, on the path of transmission of tensile and compressive stresses, the components subjected to tensile force greater than compressive force are simplified to beam unit components, and the rods subjected to compressive stress are all inclined in the overall space of the building, and the components mainly subjected to compressive force are simplified to rod unit components.
3. The method for simplifying the vertical calculation model of bracket according to claim 2 is characterized in that: In the bracket set, in the depth direction, the components that bear at least 2 / 3 of the force as bending force are simplified to beam unit components.
4. The method for simplifying the vertical calculation model of bracket according to claim 3 is characterized in that: The beam head and beam ridge are used as beam unit components.
5. A method for simplifying the vertical calculation model of bracket according to any one of claims 1 to 4, characterized in that: In the width direction of the bracket, the single bracket and the double bracket serve as diagonal components of the rod unit.
6. The method for simplifying the vertical calculation model of bracket according to claim 5 is characterized in that: The vertical force transmission path on the central axis of the bracket should be simplified into a vertical beam unit component in the simplified model.
7. The method for simplifying the vertical calculation model of bracket according to claim 6 is characterized in that: The simplified method of the finite element model component is to construct it based on the length, direction and end center point of the component.
8. The method for simplifying the vertical calculation model of bracket according to claim 5 is characterized in that: The cross-sectional dimensions of beam unit components are taken according to the actual cross-sectional dimensions. The diagonal components of the rod units are reduced by introducing reduction factors to reduce their cross-sectional areas. The cross-sectional shape of the beam unit components simplified by the vertical force transmission path is a square, and the cross-sectional dimensions are the material width or the inner width of the bucket.
9. The method for simplifying the vertical calculation model of bracket according to claim 8, characterized in that: The heavy arch structure is simplified into two cantilever beams of unequal length, which are connected by a rigid chain rod. When analyzing structural deformation, remove the chain rod. Assuming that the axial force of the chain rod is P, the simplified structure of the heavy bracket can be split into two cantilever beams. The lower short cantilever beam is only subjected to the concentrated force P transmitted by the chain rod at the end, and the upper longer cantilever beam is subjected to a downward displacement load δA at the end, and the middle is subjected to the upward concentrated force P transmitted by the chain rod; the vertical stiffness of this simplified structure of the heavy bracket is the sum of the vertical reaction forces of the two cantilever beam supports, and the vertical stiffness of the simplified structure of the double cantilever beam is equal to the vertical stiffness component of the simplified model of the diagonal rod, and the cross-sectional area reduction coefficient k3 of the simplified model of the diagonal rod of the heavy bracket in the width direction is obtained; when the heavy bracket is simplified as an oblique member of the rod unit, the reduction coefficient of its member cross-sectional area is k3, and the calculation formula is , where a n is the horizontal distance from the center point of the force of the scattered bucket on the lower bracket to the center point of the single bracket, am is the horizontal distance from the center point of the force of the scattered bucket on the upper bracket to the center point of the single bracket, s m is the length of the connecting line between the position of the force bearing point of the scattered bucket or the interactive bucket on the upper arch and the center point of the lower arch, θm is a m and m The angle of , then , so k3 can also simplify the calculation: .