Design method of ductile support frame structure and numerical analysis model based on beam unit fiber section

Abstract

The invention relates to the technical field of ductile structure system analysis and design, and provides a design method of a ductile supporting frame structure and a numerical analysis model based on a beam unit fiber section. By controlling the rigidity ratio of the frame to the support and the section parameter ratio of the connecting piece to the support, the section parameter design limit value of the ductility connecting piece is given, and the ductility of the structure is ensured. Secondly, based on an equivalent stiffness principle, a ductile support bilinear skeleton calculation model considering stiffness degradation is provided, then an existing buckling-restrained support calculation model is improved, and the mechanical behavior of the whole support is simulated by adopting plastic connection units and beam unit fiber sections; and forming a numerical calculation model of the ductile support steel frame structure based on the fiber section of the beam unit. The model can accurately simulate the mechanical characteristics of the overall support and the structural system thereof, the huge workload of multi-time iterative modeling is omitted, the analysis cost is low, and the efficiency and simulation precision are higher.

Description

Technical Field

[0001] The present invention belongs to the technical field of ductile structural system analysis and design, and particularly relates to a design method for a ductile support frame structure and a numerical analysis model based on a beam unit fiber section. Background Art

[0002] Previous major earthquakes have exposed the problem of centrally braced steel frame systems failing to fully realize their performance due to design and construction flaws, as well as residual stress and stress concentration generated by welds in the support end node plates. Furthermore, it has been observed that centrally braced steel frame structures can experience damage such as support buckling, fracture, and node plate failure under rare or extremely large earthquakes. Buckling of supports and fracture failure at the node plates and welds will limit the energy dissipation efficiency of the supports, reduce the low-cycle fatigue failure life of the centrally braced frame system and the overall seismic performance of the structure, and complicate damage detection, repair, and replacement of components after strong earthquakes. To further improve the ductility of centrally braced steel frame structures and optimize their seismic performance, a more economical, reasonable, and seismically effective support system has been established by increasing support ductility requirements to reduce bearing capacity requirements. This is referred to as the ductile centrally braced steel frame system.

[0003] Regarding ductile supports and their structural systems, both domestic and international research focuses on achieving long low-cycle fatigue life for their nodes and components through rigorous seismic calculations and restrictions on structural requirements, as well as optimizing and improving support and node structures and connection methods. This ensures that the components have sufficient ductility and the nodes have sufficient bearing capacity or deformation capacity, thereby giving the structural system good ductility and seismic energy dissipation capabilities. For example, the "Anti-buckling support for energy-dissipating components with ferrules constrained by an energy-dissipating component" disclosed by Yin Zhanzhong et al. in their Chinese authorized invention patent (authorization publication number CN109736465B) and the "Special central support steel frame structure" disclosed in their Chinese authorized invention patent (authorization publication number CN109736465B) have the following advantages:

[0004] 1) The braces in the traditional centrally braced steel frame are designed as buckling-restrained braces (CBRBs) with ductile standard connectors at both ends. That is, ductile standard connectors are installed at both ends of the brace, the gusset plates are removed, and the CBRBs are connected to the main frame using ductile connectors, forming a new type of ductile braced steel frame structure system (CBRBSF).

[0005] 2) In terms of the connection method between beams and columns and buckling-restrained braces, the welded gusset plates at the brace ends are designed as ductile standard connectors. This alleviates the residual stress and stress concentration caused by welding at the connection nodes, improves the reliability of the nodes and the low-cycle fatigue life of the structure, and fundamentally avoids the occurrence of brittle failure of the gusset plates.

[0006] 3) During earthquakes, the buckling-resistance braces and end ductile standard connectors both dissipate energy, improving the ductility of the braces. The ductile bracing members control the strength, stiffness, and ductility of the central support steel frame structure, maximizing the seismic performance of the ductile braces and the structural system.

[0007] 4) By rationally designing the ductile brace, inelastic deformation can be concentrated on the buckling-restrained brace and ductile standard connectors, allowing for rapid location of structural damage after an earthquake. Furthermore, the ductile standard connectors and buckling-restrained brace are both bolted together, allowing for rapid repair and replacement after an earthquake, reducing structural repair costs.

[0008] For traditional supports and their structural systems, my country's "Steel Structure Design Standard" (GB50017-2017) and "Code for Seismic Design of Buildings" (GB50011-2010) mainly design in accordance with the following regulations and requirements:

[0009] 1) Limiting structural details such as the support slenderness ratio, web height-to-thickness ratio, and flange extension width-to-thickness ratio to give full play to the plastic properties of the entire section and improve the ductility and low-cycle fatigue life of the support itself;

[0010] 2) Strengthen the design of connection nodes, calculate the strength of the node plate under the combined action of tension and shear, and require the connection to meet the requirements of linear clearance, so that the node remains in an elastic state and ensures the compressive stability of the node plate.

[0011] The new ductile braced steel frame structure (CBRBSF) primarily utilizes buckling-resisted braces (BRBs) and standard ductile end connectors for plastic energy dissipation. This changes the deformation and energy dissipation mechanism of the braces, the internal force transmission of the ductile end connectors, and the failure mode. This leads to a mismatch between the design of this new ductile braced structure and the methods recommended by my country's seismic design code. Problems exist, such as the determination of ductile brace design parameters, the contribution of ductile connectors to structural stiffness and energy dissipation, and unclear ductile brace performance parameters and skeleton calculation models. These issues hinder the promotion of this new structure. Furthermore, currently available structural design software fails to provide effective solutions to these issues, further limiting the engineering application of this structure. Therefore, it is necessary to propose a numerical simulation method for structural design that can be used to address the unique energy dissipation mechanism of this type of structure, thereby further promoting the widespread application of ductile structures. Summary of the Invention

[0012] In order to solve the above technical problems, the present invention provides a design method for a ductile braced frame structure and a numerical analysis model based on the fiber cross-section of a beam unit.

[0013] The technical solution adopted in the present invention is as follows:

[0014] A design method for a ductile braced frame structure, characterized in that the ductile braced frame structure comprises a frame and a ductile bracing system; the ductile bracing system comprises a buckling-restrained brace and ductile connectors located at both ends of the buckling-restrained brace;

[0015] The design method comprises the following steps:

[0016] S101: Determine the structural height H of the frame, the angle θ between the buckling restraint brace and the horizontal plane, and the elastic modulus E of the buckling restraint brace. b , the length of the buckling restraint brace l, the cross-sectional area of ​​the buckling restraint brace A b , elastic modulus E of ductile connector c , the length of the ductile connector l c , cross-sectional area A of the ductile connector c , the cross-sectional width b of the ductile connector, the cross-sectional thickness t of the ductile connector;

[0017] S102: Calculate the lateral stiffness K of the frame F , calculate the lateral stiffness K of the ductile support system B ;

[0018] S103: Calculate the lateral stiffness ratio k of the ductile bracing system to the frame; calculate the area ratio λ of the ductile connector to the buckling-restrained brace A , the axial stiffness ratio of the ductile connector to the buckling-restrained brace λ K ; Through finite element analysis and experimental verification, k, λ are determined A ,λ K limit;

[0019] S104: Calculate the flexural buckling load and stress of ductile connectors based on the small deflection theory; calculate the torsional buckling load and stress of ductile connectors using the equilibrium method;

[0020] S105: Make the flexural buckling stress and torsional buckling stress greater than or equal to the yield strength f of the ductile connector y , and the slenderness ratio λ l ≤200, the design parameters of the ductile connector satisfy the following equations (10)(11)(19):

[0021]

[0022] l c / b≤40.4 (11)

[0023]

[0024] Preferably, in S102, the lateral stiffness K of the frame is F The calculation formula is:

[0025]

[0026] Among them, E F and I F are the elastic modulus and moment of inertia of the frame column respectively; α is the correction coefficient, for the bottom layer of the structure, α=(0.5+K) / (2+K), K=i b / i c ,i b and i c are the linear stiffness of the frame beams and columns, respectively;

[0027] The lateral stiffness K of the ductile support system B The calculation formula is:

[0028]

[0029] Preferably, in S103, the calculation formula of the lateral stiffness ratio k of the support system to the frame is: k=K B / K F ;

[0030] The area ratio of the ductile connector to the buckling-restrained brace is λ A The calculation formula is: A =A c / A b ;

[0031] The axial stiffness ratio of the ductile connector to the buckling-restrained brace is λ K The calculation formula is:

[0032] Determine λ A =4,λ K =19, k=2.

[0033] Preferably, in S104, under the premise of satisfying the plane section assumption and Hooke's law, based on the small deflection theory and considering the constraints at both ends of the ductile connector, the bending buckling load of the ductile connector is obtained: Flexural buckling stress of ductile connectors: Among them, μ is 0.7, E c is the elastic modulus of the ductile connector;

[0034] The torsional buckling load of the ductile connector is: The torsional buckling stress is:

[0035] Among them, I c is the moment of inertia of the ductile connector section, i is the extreme radius of gyration of the section to the shear center; I t is the cross-sectional torsional constant or torsional moment of inertia; I ωis the warping moment of inertia of the cross section. For a biaxially symmetric cross section, I ω ≈0; G is the shear modulus; E c is the elastic modulus of the ductile connector; μ ω The length factor for torsional buckling is calculated and taken as 0.7.

[0036] Preferably, in S105, the slenderness ratio λ l The calculation formula is λ l =μl c / i.

[0037] The ductile support frame structure obtained by the design method of the present invention.

[0038] A numerical analysis model for a ductile braced frame structure based on a fiber cross section of a beam element, characterized by comprising the following steps:

[0039] S201: Determine the following parameters: initial stiffness K y , yield displacement △ y , yield load P y , post-yield stiffness K p , limit displacement △ u , Ultimate load P u , unloading stiffness K d ;

[0040] S202: Determine a bifold skeleton model of ductile support based on the parameters of S201;

[0041] S203: Finite element modeling based on beam element fiber cross-sections:

[0042] Buckling-restrained brace modeling: nonlinear plastic Wen element simulation is used, and parameters are input according to the results of S201-S202;

[0043] Modeling of ductile connectors: Divide the cross-section into fiber units and calculate the cross-section parameters according to equations (10), (11), (19) as described in claim 1;

[0044] Frame beam and column modeling: Use beam elements to define frame beams and column components;

[0045] S204: Combine the buckling-resisting braces, ductile connectors, and frame beams and columns to obtain a numerical analysis model of the ductile support structure based on the fiber section of the beam element.

[0046] Preferably, in S203, the model calculation formula of Wen unit simulation in the buckling-restrained brace modeling is: P = αK b △+(1-α)P y z;

[0047] In the formula, K bis the initial stiffness of the anti-buckling support, i.e. the slope of the elastic stage; P y is the yield load; α is the ratio of the stiffness after yielding to the initial stiffness, α=K p / K b ; z is the internal hysteresis variable, the value range is |z|≤1; e is the yield index, the value is ≥1;

[0048] In the frame beam-column modeling, the beam-column is set as a rigid connection, the beam-column node rigidity coefficient is defined as 0.5, and moment hinges and axial moment hinges are respectively specified for both ends of the frame beam and the bottom of the frame column.

[0049] Preferably, in S201, the initial stiffness K y Calculated according to the series stiffness formula:

[0050] The yield displacement Δ y The calculation formula is Among them, σ y is the yield strength of steel, l b is the length of the BRB energy consumption section;

[0051] The yield load P y The calculation formula is P y =K y △ y ;

[0052] The ultimate load P u The calculation formula is P u =ω·β·P y , where ω is the strain hardening coefficient when considering the combined effect of BRB and ductile connectors, which is set to ω = 1.5, and β is the tension and compression non-uniformity coefficient, which is set to β = 1.1;

[0053] The limit displacement Δ u The calculation formula is Where L is the span of the structure; tgα is the frame's limit inter-story drift angle, which is tgα = 1 / 30;

[0054] The post-yield stiffness K p The calculation formula is

[0055] The unloading stiffness K d The process is divided into two stages: forward unloading and reverse unloading:

[0056]

[0057] Preferably, in S202, the double-fold line skeleton model expression is:

[0058]

[0059] Compared with the existing technology, the present invention can accurately simulate the mechanical properties of the overall support and its structural system, eliminating the huge workload of multiple iterative modeling, with lower analysis costs and higher efficiency and simulation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1a This is a schematic diagram of the ductile support frame structure before assembly according to an embodiment of the present invention.

[0061] Figure 1b This is a schematic diagram of the assembled ductile support frame structure according to an embodiment of the present invention.

[0062] Figure 2a This is a simplified diagram of the deformation mechanics calculation of the ductile support frame structure according to an embodiment of the present invention.

[0063] Figure 2b Schematic diagram of ductile support calculation according to an embodiment of the present invention.

[0064] Figure 3 Schematic diagram of torsional deformation of the fiber cross section when the ductile connector is subjected to axial force according to an embodiment of the present invention.

[0065] Figure 4 Schematic diagram of a simplified double-broken-line skeleton model for ductile support according to an embodiment of the present invention.

[0066] Figure 5a Schematic diagram of the fiber cross-section division of the ductile connector according to an embodiment of the present invention.

[0067] Figure 5b Schematic diagram of the ductile support calculation model according to an embodiment of the present invention.

[0068] Figure 6 Schematic diagram of the calculation model of the ductile support steel frame structure according to an embodiment of the present invention.

[0069] Figure 7a Schematic diagram of the analysis results and test comparison of the ductile support model of an embodiment of the present invention.

[0070] Figure 7b Schematic diagram of the analysis results and test comparison of the ductile braced steel frame model according to an embodiment of the present invention.

[0071] Figure 8a Schematic diagram comparing the analysis results of the ductile brace model according to an embodiment of the present invention with those of a traditional buckling-restrained brace test.

[0072] Figure 8b Schematic diagram comparing the analysis results of the ductile braced steel frame model according to an embodiment of the present invention with the test results of a traditional buckling-restrained braced frame. DETAILED DESCRIPTION

[0073] The technical solution of the present invention is further described below in conjunction with specific implementation methods and drawings.

[0074] Based on the working energy consumption mechanism of the new ductile support steel frame structure, the present invention further proposes a numerical analysis model of the ductile support structure based on the fiber section of the beam unit that can be applied to seismic design. As shown in Figure 1, an example of such a structural system is given. In order to facilitate the calculation of the deformation and stiffness requirements of the ductile support steel frame structure, the present invention proposes a mechanical calculation diagram of the ductile support and its structural system as shown in Figure 1, and adopts the following analysis method: 1. Determination of the ductile connector and BRB section parameters

[0075] (1) Calculation of frame lateral stiffness:

[0076] The high ductility braced steel frame structure produces a displacement of △ under the action of horizontal force F, such as Figure 2a shown.

[0077] The lateral stiffness of the frame can be calculated using the structural mechanics D-value method:

[0078]

[0079] Where: H is the structure height; E c and I c are the elastic modulus and moment of inertia of the frame column respectively; α is the correction coefficient, for the bottom layer of the structure, α=(0.5+K) / (2+K), K=i b / i c ,i b and i c are the linear stiffnesses of frame beams and columns, respectively.

[0080] (2) Ductile support lateral stiffness

[0081] Based on the small deformation assumption and ignoring the angle change between the support and the horizontal line, the lateral stiffness of the support is calculated as follows.

[0082] The supporting axial force is:

[0083]

[0084] The support horizontal force is:

[0085]

[0086] The lateral stiffness of the support is:

[0087]

[0088] Where: θ is the angle between the support and the horizontal plane; E is the elastic modulus of the support; l and l c are the lengths of supports and ductile connectors respectively; Ac and A b are the cross-sectional areas of the ductile connector and BRB, respectively.

[0089] (3) Ductile support to frame lateral stiffness ratio

[0090] Define the lateral stiffness ratio of the support to the frame as k, then:

[0091]

[0092] It can be seen from the above formula (5) that after the frame height and span, beam-column cross-sectional dimensions and lateral stiffness are determined, the structural lateral stiffness ratio is mainly related to the length and cross-sectional area of ​​the ductile connector and BRB.

[0093] (4) Cross-sectional dimensions of ductile connectors and buckling-restrained braces

[0094] Introducing the ductile connector and BRB area ratio λ A and the axial stiffness ratio of the ductile connector to the BRB, λ K Two parameters, namely:

[0095] λ A =A c / A b (6)

[0096]

[0097] Where: K c and K b are the axial stiffness of the ductile connector and the BRB, respectively. According to finite element analysis and actual test verification, when λ A =4,λ K =19, and the lateral stiffness ratio is k=2, the ductility performance of the overall support can be fully exerted.

[0098] (5) Ductile connector bending buckling load

[0099] In order to ensure the stability of the ductile connector under axial load and prevent flexural buckling and torsional buckling of the ductile connector, it is necessary to calculate the critical loads of torsional buckling and flexural buckling of the ductile connector and further obtain the critical design values ​​of the section parameters.

[0100] Under the premise of satisfying the plane section assumption and Hooke's law, based on the small deflection theory and considering the constraints at both ends of the ductile connector, the bending buckling load of the ductile connector is obtained:

[0101]

[0102] The flexural buckling stress of the ductile connector is:

[0103]

[0104] Where: μ is the length coefficient for flexural buckling calculation (take 0.7: one end fixed, one end simply supported), E is the elastic modulus (when the flexural buckling stress of the ductile connector section exceeds the proportional limit, the tangent modulus E can be simplified to t Replace E) in equations (8) and (9), where b is the cross-sectional width of the ductile connector.

[0105] In order to avoid flexural buckling of ductile connectors, it is necessary to ensure that σ cr ≥f y (f y is the yield strength of the ductile connector). Therefore, we can get:

[0106]

[0107] In addition, as the main axial compression member, the ductile connector must also meet the slenderness ratio requirement λ l =μl c / i≤200, simplifying to get:

[0108] l c / b≤40.4 (11)

[0109] (6) Torsional buckling load of ductile connector

[0110] The equilibrium method is used to solve the torsional buckling load of ductile connectors. The cross section is divided into fiber elements and the following two assumptions are met:

[0111] 1) Rigid perimeter assumption: The shape of the cross section before and after torsion is the same as the projection shape of the cross section perpendicular to the axis of the component;

[0112] 2) Assumption that shear strain is zero: When a member bends and torsions, the shear strain generated on the mid-surface of the plate has a very small effect on the stress of the member and can be ignored.

[0113] Based on the above assumptions, when the ductile connector is torsionally twisted, the non-uniform torque generated by the entire fiber cross section is (e.g. Figure 3 ):

[0114]

[0115] Where: P is the axial load, A is the cross-sectional area of ​​the fiber, ρ is the distance from the edge of the micro segment to the shear center of the section, The torsion angle is the torsion angle. When the fiber cross section is tilted due to torsion, the torsion formed by the component force in the cross section around the shear center of the cross section is called the Wagner effect. is the Wagner effect coefficient. For a biaxially symmetric section, ∫ A ρ 2 dA=I x +Iy =i 2 A.

[0116] Formula (12) can be simplified as:

[0117]

[0118] Due to the various non-uniform torque components that bear torque, the non-uniform torque M z By free torque M s and warping torque M ω The torsional equilibrium equation of the section at a distance z from the origin is:

[0119] M z =M s +M ω (14)

[0120] Where: the free torque, warping torque and torsion rate derived from elastic mechanics and The relationship between them can be obtained: Substituting the combined formula (13) into the above formula (14), we get:

[0121]

[0122] Solving equation (15), the torsional buckling load of the connector is obtained as follows:

[0123]

[0124] For a biaxially symmetric cross section, I ω ≈0, then the above formula can be simplified to:

[0125]

[0126] The torsional buckling stress of the ductile connector is:

[0127]

[0128] Where: i is the extreme radius of gyration of the cross section to the shear center, I t is the cross-sectional torsional constant or torsional moment of inertia, I ω is the warping inertia moment of the cross section, G is the shear modulus, and E is the elastic modulus (when the torsional buckling stress of the ductile connector section exceeds the proportional limit, the tangent modulus E can be simplified to t Replace E) in formula (18), is the cross-sectional torsion angle, ν is the Poisson's ratio, l c , t and b are the length, section thickness and height of the ductile connector respectively ( Figure 3 ), μ ωCalculate the length factor for torsional buckling (take 0.7: one end fixed, one end simply supported).

[0129] In order to avoid torsional buckling of ductile connectors, it is necessary to ensure that σ cr ≥f y Therefore, we can get:

[0130]

[0131] In summary, the dimensions of ductile connectors should satisfy equations (10), (11), and (19) simultaneously.

[0132] 2. Determination of the bifold skeleton model considering stiffness degradation

[0133] According to the conclusion of the completed test analysis, the skeleton curve of the support was obtained, and it was proposed that the axial displacement and bearing capacity curve of the ductile support can be calculated using a bilinear model ( Figure 4 ), and divide the variation trend of the skeleton curve into the following two stages, and give the specific expression:

[0134] Elastic stage (OA / OA' segment): This is the process from the initial loading of the specimen to the occurrence of yield. During this stage, the load-displacement curve is linear, and the slope of the curve is the initial stiffness of the component. The specimen is in an elastic state during this stage.

[0135] Elastic-Plastic Stage (AB / A'B' Section): This is the process from yield to peak load. During this stage, as the loading displacement increases, the support yields, causing a significant degradation in support stiffness. The load growth rate is slower than in the elastic stage.

[0136] The expression is:

[0137]

[0138] The following parameters need to be determined for the bifold skeleton curve model: initial stiffness K y , yield displacement △ y , yield load P y , post-yield stiffness K p , limit displacement △ u , Ultimate load P u , unloading stiffness K d .

[0139] (1) Initial stiffness

[0140] Based on the stress characteristics of the support structure, the calculation is carried out according to the axial load-bearing components. The axial compressive stiffness can be calculated in series with the stiffness of the ductile connector and the BRB. The initial stiffness of the support as a whole is calculated as follows:

[0141]

[0142] Where: K C and K BRB are the axial stiffness of the ductile connector and the BRB core, respectively.

[0143] The ductile connector includes an end frame connection section l c1 、Middle section l c2 、Transition section l c3 and BRB connection segment l c4 ( Figure 2b ), therefore, the axial stiffness K of the ductile connector can be obtained from the elastic analysis c The calculation formula is:

[0144]

[0145] Where: They are the stiffness of the end frame connection section, middle section, transition section and BRB connection section of the ductile connector respectively.

[0146] Similarly, by Figure 2b As shown, the BRB kernel includes a connection segment l b1 、Transition section l b2 and energy consumption segment l b3 , then the axial stiffness of the BRB core K b The calculation formula is:

[0147]

[0148] Where: They are the stiffness of the BRB core connection section, transition section and energy dissipation section respectively.

[0149] The stiffness in equations (21) and (22) can be calculated using the formula K = EA / l, where E is the elastic modulus, A and l are the corresponding cross-sectional area and length, respectively.

[0150] (2) Yield displacement

[0151] When the support yields, the BRB first enters the plastic stage, and the ductile connector remains elastic. According to Hooke's law, the displacement caused by the axial deformation of the support is:

[0152]

[0153] Where: N is the supporting axial force, l is the length of the BRB energy dissipation section, E is the elastic modulus, A is the cross-sectional area of ​​the BRB core, σ y is the yield strength of steel.

[0154] (3) Yield load

[0155] Yield load P y is the initial stiffness Ky and yield displacement △ y The product of the support yield load P can be obtained according to the following formula y :

[0156] P y =K y △ y (twenty four)

[0157] Where: K y is the initial stiffness of the support, calculated by formula (20); y The yield displacement is calculated by formula (23).

[0158] (4) Ultimate load

[0159] The ultimate bearing capacity of the support must take into account the strain hardening of the BRB and the ductile connector, as well as the friction between the BRB core and the external constraints when under compression. Therefore, the ultimate bearing capacity of the support can be calculated as follows:

[0160] P u =ω·β·P y (25)

[0161] Where: ω is the strain hardening coefficient when considering the combined effect of BRB and ductile connector, that is, the ratio of the maximum bearing capacity of the support to the yield bearing capacity ω = P max / P y According to the pseudo-static test and referring to the provisions of the Technical Code for Steel Structures of High-rise Civil Buildings (JGJ99-2015), ω=1.5; β is the tension and compression unevenness coefficient, that is, the ratio of the maximum compressive bearing capacity of the support to the maximum tensile bearing capacity (β=P c,max / P t,max ), the American Seismic Code for Steel Structures (AISC341-16) stipulates that in order to avoid large unbalanced forces at the beam and column nodes, β should be less than 1.3. In this paper, combined with the results of the quasi-static test of the specimens, β = 1.1 is taken.

[0162] (5) Limit displacement

[0163] When ductile supports are placed in a steel frame structure, the ideal yield mechanism is that when the structure reaches the ultimate lateral displacement, the support forms a ductile failure mechanism. Since the lateral displacement caused by the axial deformation of the support is much larger than the lateral displacement caused by the deformation of the frame itself, based on the small deformation assumption and ignoring the deformation of the frame itself, the ultimate displacement of the support is:

[0164]

[0165] Where L is the span of the structure; tgα is the frame's ultimate inter-story drift angle (referring to the limit values ​​of the elastic-plastic inter-story drift angle of steel frame structures in the Code for Seismic Design of Buildings (GB50011-2010) and combined with the actual loading conditions of the test, tgα is taken as 1 / 30).

[0166] (6) Post-yield stiffness

[0167] After the support enters the elastic-plastic stage, according to Figure 4 The support post-yield stiffness K is obtained by using formulas (23) to (26): p , calculated as follows:

[0168]

[0169] (7) Unloading stiffness

[0170] The unloading process of the support can be divided into two typical stages: forward unloading and reverse unloading.

[0171] 1) When the load does not reach the yield displacement △ y When the ductile support is in the elastic stage, the loading and unloading stiffness is K y OAB and OA'B' are the unloading paths of the support under positive and negative loads, respectively. The bearing capacity is essentially symmetrical in the positive load direction.

[0172] 2) When the load exceeds the yield load, from the yield point A to B, the stiffness can be defined as the post-yield stiffness K p Then the unloading process is forward unloading, and the corresponding forward unloading stiffness is K d (positive). Similarly, the specimen moves from the negative yield point A' to B' and then unloads. The corresponding negative unloading stiffness is K d (burden).

[0173] 3) When the load exceeds the yield load of the ductile support, the unloading stiffness gradually decreases with the increase of displacement, which is mainly due to the sequential yielding of the BRB and the ductile connector. The unloading stiffness data of each hysteresis loop are fitted to obtain K d :

[0174]

[0175] Where: △ is the displacement corresponding to positive (negative) unloading (△ y ≤△≤△ u ).

[0176] 3. Analysis and verification of finite element model of ductile support structure based on fiber section of beam element

[0177] The SAP2000 finite element analysis program was used to establish a fiber-rod finite element analysis calculation model based on the double-broken-line skeleton model, and the model was compared and verified with the test.

[0178] (1) Simplified BRB calculation model

[0179] The plastic Wen element model in the nonlinear link element is used to define the BRB. This model is based on the support hysteresis behavior proposed by Wen. The model calculation formula is as follows:

[0180] P=αK BRB △+(1-α)P y z (29)

[0181] Where: K BRB is the initial stiffness, i.e. the slope of the elastic stage; P y is the yield load; α is the ratio of the stiffness after yielding to the initial stiffness (α=K p / K BRB ); z is an internal lag variable with a value range of |z|≤1. If otherwise e is the yield index, which has a value ≥ 1. Based on the theoretical calculation formulas (20) to (29), the model parameters of the plastic Wen unit in the above formula are defined.

[0182] (2) Simplified calculation model of ductile connectors

[0183] The ductile connector is designed as a cross-section. The fiber section beam element based on geometric linear small deformation and satisfying the plane section assumption is used to establish the model. The section is designed using the Section Designer (SD) to generate customized section properties. The section is divided into a certain number of fibers. The section parameters of the ductile connector (such as Figure 5a ).

[0184] Based on the above settings, a multi-scale model combining plastic connection elements and fiber sections is used to simulate the nonlinear behavior of the overall support (e.g. Figure 5b ).

[0185] (3) Simplified calculation model of frame beams and columns

[0186] Define frame beams and columns using beam elements that account for biaxial bending, torsion, axial deformation, and biaxial shear deformation. Set the beam-column connection to a rigid one, define the beam-column joint rigidity factor to 0.5, and assign moment hinges (M) and axial moment hinges (spatial-PMM) to the ends of the frame beams and the base of the columns. Modify the acceptable criteria and corresponding deformation values ​​for the corresponding components based on the requirements in Table 5-6 of FEMA 356.

[0187] According to the above setting method, a ductile support structure model based on the fiber section of the beam element is formed, such as Figure 6 .

[0188] In order to verify the effectiveness of the simplified analysis model, the experimental results in literature 1 (Yin ZZ, Feng DZ, Yang B, Pan CC. The seismic performance analysis of double tube buckling-restrained brace with cast steel connectors. Advanced Steel Construction, 2022, 18 (1): 436-445) and literature 2 (Yin ZZ, Yang B, An S Z. Seismic performance analysis of buckling-restrained braced steel frames with ductile castings. KSCE Journal of Civil Engineering, 2021, 25 (10): 3879-3896) were verified, and a model consistent with the parameter information in literature 1 and 2 was established according to the method proposed in the present invention.

[0189] The finite element analysis model was established using SAP2000, and the parameter information and material properties of each component were consistent with the experiments in References 1 and 2. The load-displacement relationship curve was obtained through simulation analysis. Figure 7a The ductile support model analysis results and test comparison results are given. Figure 7b The analysis results of the ductile brace steel frame model and the experimental comparison results are presented. It can be seen that the simulation results of the analytical model proposed in this invention are in good agreement with the experimental results in existing literature. The simulated initial stiffness, ultimate load, and displacement have an error of less than 5% compared with the experimental results. This shows that the present invention can achieve reasonable predictions of the mechanical properties and load-displacement relationships of ductile braces and ductile brace steel frame structures, verifying the effectiveness of the present invention.

[0190] 4. Comparison of the ductile support structure model based on the fiber cross section of the beam element and the traditional buckling-restrained support structure model

[0191] In order to further verify the superiority of the ductile performance of the ductile brace and its structure, as well as the effectiveness of the analytical model proposed in this paper, its performance is compared with that of the traditional buckling-restrained brace and its structure. The plastic WEN model is used to simulate and analyze the buckling-restrained brace in Reference 3 (Chou CC, Chen SY, Subassemblage tests and finite element analyses of sandwiched buckling-restrained braces. Engineering structures, 2010, 32(8): 2108-2121.) and the buckling-restrained braced steel frame specimens in Reference 4 (Chou CC, Liu JH, Pham DH, Steel buckling-restrained braced frames with single and dual corner gusset connections: seismic tests and analyses. Earthquake engineering and structural dynamics, 2010, 41(7): 1137-1156.). According to the calculation method of the present invention, the end node plates of the buckling-restrained braces in References 3 and 4 are designed as ductile connectors. At the same time, the simulation method of the present invention is used to establish the ductile brace and its overall structural model. The load-displacement curve is obtained through analysis. Figure 8a and Figure 8b The comparison results of ductile braces and buckling-restrained braces, as well as ductile braced steel frames and buckling-restrained braced steel frames are given respectively.

[0192] As can be seen from the figure, the plastic WEN model can effectively simulate the mechanical properties of traditional buckling-restrained braces and their structural systems. The model is in good agreement with the experimental results and has high accuracy. After the ends of the buckling-restrained braces are designed as ductile connectors, the initial stiffness of the ductile braces and their overall structure is improved. At the same time, as the load increases, the ductile connectors contribute to the improvement of structural performance and participate in energy dissipation together with the buckling-restrained braces and the main frame. The ultimate bearing capacity and ductility are significantly higher than those of traditional buckling-restrained braces and buckling-restrained steel frame structures. In addition, in the later stage of loading, the buckling-restrained braces did not break, and the ductile connectors did not show any instability or failure, further verifying the superiority of the ductile brace and its structural system, as well as the effectiveness of the present invention.

[0193] In summary, the numerical analysis model of ductile support structures based on the fiber cross-section of beam elements proposed in the present invention not only has high simulation accuracy, but also can more reasonably consider the stiffness, energy dissipation and ductility contribution of the end ductile connectors compared to the plastic WEN model. It can be promoted and applied to the performance-based design of such structures, providing a practical analysis tool for engineering design.

Claims

1. A design method for a ductile braced frame structure, characterized in that: The ductile braced frame structure comprises a frame and a ductile bracing system; the ductile bracing system comprises a buckling-restrained brace and ductile connectors located at both ends of the buckling-restrained brace; The design method comprises the following steps: S101: Determine the structural height H of the frame, the angle θ between the buckling restraint brace and the horizontal plane, and the elastic modulus E of the buckling restraint brace. b , the length of the buckling restraint brace l, the cross-sectional area of ​​the buckling restraint brace A b , elastic modulus E of ductile connector c , the length of the ductile connector l c , cross-sectional area A of the ductile connector c , the cross-sectional width b of the ductile connector, the cross-sectional thickness t of the ductile connector; S102: Calculate the lateral stiffness K of the frame F , calculate the lateral stiffness K of the ductile support system B ; S103: Calculate the lateral stiffness ratio k of the ductile bracing system to the frame; calculate the area ratio λ of the ductile connector to the buckling-restrained brace A , the axial stiffness ratio of the ductile connector to the buckling-restrained brace λ K ; Through finite element analysis and experimental verification, k, λ are determined A ,λ K limit; S104: Calculate the flexural buckling load and stress of ductile connectors based on the small deflection theory; calculate the torsional buckling load and stress of ductile connectors using the equilibrium method; S105: Make the flexural buckling stress and torsional buckling stress greater than or equal to the yield strength f of the ductile connector y , and the slenderness ratio λ l ≤200, the design parameters of the ductile connector satisfy the following equations (10)(11)(19): l c / b≤40.4 (11) 2. The design method of a ductile braced frame structure according to claim 1, characterized in that: In S102, the lateral stiffness K of the frame F The calculation formula is: Among them, E F and I F are the elastic modulus and moment of inertia of the frame column respectively; α is the correction coefficient, for the bottom layer of the structure, α=(0.5+K) / (2+K), K=i b / i c ,i b and i c are the linear stiffness of the frame beams and columns, respectively; The lateral stiffness K of the ductile support system B The calculation formula is:

3. The design method of a ductile braced frame structure according to claim 2, characterized in that: In S103, the calculation formula of the lateral stiffness ratio k of the support system and the frame is: k = K B / K F ; The area ratio of the ductile connector to the buckling-restrained brace is λ A The calculation formula is: A =A c / A b ; The axial stiffness ratio of the ductile connector to the buckling-restrained brace is λ K The calculation formula is: Determine λ A =4,λ K =19, k=2.

4. The design method of a ductile braced frame structure according to claim 2, characterized in that: In S104, under the premise of satisfying the plane section assumption and Hooke's law, based on the small deflection theory and considering the constraints at both ends of the ductile connector, the bending buckling load of the ductile connector is obtained: Flexural buckling stress of ductile connectors: Among them, μ is 0.7, E c is the elastic modulus of the ductile connector; The torsional buckling load of the ductile connector is: The torsional buckling stress is: Among them, I c is the moment of inertia of the ductile connector section, i is the extreme radius of gyration of the section to the shear center; I t is the cross-sectional torsional constant or torsional moment of inertia; I ω is the warping moment of inertia of the cross section. For a biaxially symmetric cross section, I ω ≈0; G is the shear modulus; E c is the elastic modulus of the ductile connector; μ ω The length factor for torsional buckling is calculated and taken as 0.

7.

5. The design method of a ductile braced frame structure according to claim 2, characterized in that: In S105, the slenderness ratio λ l The calculation formula is λ l =μl c / i.

6. A ductile braced frame structure obtained by the design method according to any one of claims 1 to 5.

7. A numerical analysis model of the ductile support frame structure according to claim 6 based on the fiber cross-section of the beam unit, characterized in that: The following steps are involved: S201: Determine the following parameters: initial stiffness K y , yield displacement △ y , yield load P y , post-yield stiffness K p , limit displacement △ u , Ultimate load P u , unloading stiffness K d ; S202: Determine a bifold skeleton model of ductile support based on the parameters of S201; S203: Finite element modeling based on beam element fiber cross-sections: Buckling-restrained brace modeling: nonlinear plastic Wen element simulation is used, and parameters are input according to the results of S201-S202; Modeling of ductile connectors: Divide the cross-section into fiber units and calculate the cross-section parameters according to equations (10), (11), (19) as described in claim 1; Frame beam and column modeling: Use beam elements to define frame beams and column components; S204: Combine the buckling-resisting braces, ductile connectors, and frame beams and columns to obtain a numerical analysis model of the ductile support structure based on the fiber section of the beam element.

8. The numerical analysis model according to claim 7, characterized in that: In S203, the model calculation formula of the Wen unit simulation in the buckling-restrained brace modeling is: P=αK b △+(1-α)P y z; In the formula, K b is the initial stiffness of the anti-buckling support, i.e. the slope of the elastic stage; P y is the yield load; α is the ratio of the stiffness after yielding to the initial stiffness, α=K p / K b ; z is the internal hysteresis variable, the value range is |z|≤1; e is the yield index, the value is ≥1; In the frame beam-column modeling, the beam-column is set as a rigid connection, the beam-column node rigidity coefficient is defined as 0.5, and moment hinges and axial moment hinges are respectively specified for both ends of the frame beam and the bottom of the frame column.

9. The numerical analysis model according to claim 8, characterized in that: In S201, The initial stiffness K y Calculated according to the series stiffness formula: The yield displacement Δ y The calculation formula is Among them, σ y is the yield strength of steel, l b is the length of the BRB energy consumption section; The yield load P y The calculation formula is P y =K y △ y ; The ultimate load P u The calculation formula is P u =ω·β·P y , where ω is the strain hardening coefficient when considering the combined effect of BRB and ductile connectors, which is set to ω = 1.5, and β is the tension and compression non-uniformity coefficient, which is set to β = 1.1; The limit displacement Δ u The calculation formula is Where L is the span of the structure; tgα is the frame's limit inter-story drift angle, which is set to tgα = 1 / 30; The post-yield stiffness K p The calculation formula is The unloading stiffness K d The process is divided into two stages: forward unloading and reverse unloading:

10. The numerical analysis model according to claim 9, characterized in that: In S202, the double-fold skeleton model expression is:

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