Anti-shear-slip constitutive calculation method for J-shaped hook in double-steel-plate shear wall

Abstract

The invention relates to an anti-shear-slip constitutive calculation method for J-shaped hooks in a double-steel-plate shear wall, the double-steel-plate shear wall comprises a pair of steel plates and a concrete plate, the steel plates are respectively located on two sides of the concrete plate, and a plurality of corresponding J-shaped hooks are fixedly installed at the joints of the steel plates and the concrete plate at intervals. Wherein every two corresponding J-shaped hooks are connected together, and the method comprises the following steps: calculating an elastic point slip value and a bearing capacity of the J-shaped hooks; calculating the yield point slip value and the bearing capacity of the J-shaped hook; the peak point slip value and the bearing capacity of the J-shaped hook are calculated; and calculating the limit point slip value and the bearing capacity of the J-shaped hook. According to the calculation method, a mechanical analysis model of the J-shaped hook at an elastic point, a yield point, a peak point and a limit point is established, and key points on a shear-slip resistance constitutive model are determined according to geometric parameters and material performance parameters of the J-shaped hook, so that the complete shear-slip resistance constitutive model is constructed; and a shearing force transmission mechanism between the J-shaped hook and concrete can be fully considered.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of shear wall construction, and relates to a double-steel-plate shear wall, in particular to a shear-slip constitutive calculation method of a J-shaped hook in a double-steel-plate shear wall. BACKGROUND

[0002] In a double-steel-plate-concrete combined shear wall structure, due to the low bonding strength of the interface between the steel plate and the concrete, a mechanical shear-resistant connecting piece needs to be arranged to improve the bonding strength of the steel plate and the concrete, so as to ensure the cooperative work of the two. Among them, the J-shaped hook connecting piece is widely used in the double-steel-plate-concrete combined shear wall structure because it has the advantages of simple structure, flexible arrangement, adaptation to ultra-thin structure, and convenient construction.

[0003] However, in the prior art, the calculation method of the shear-slip relationship of the J-shaped hook connecting piece is completely obtained based on the regression of test results, which cannot accurately reflect the shear force transmission principle between the J-shaped hook and the concrete, and lacks theoretical basis and interpretability. SUMMARY

[0004] The purpose of the present application is to overcome the shortcomings of the prior art and provide a shear-slip constitutive calculation method of a J-shaped hook in a double-steel-plate shear wall, which is comprehensive and complete.

[0005] To solve the above problems, the technical scheme of the present application is as follows:

[0006] A shear-slip constitutive calculation method of a J-shaped hook in a double-steel-plate shear wall, the double-steel-plate shear wall comprising a pair of steel plates and a concrete plate, the pair of steel plates being located on both sides of the concrete plate, and a plurality of corresponding J-shaped hooks being fixedly installed at intervals at the connection between the steel plate and the concrete plate, wherein each two corresponding J-shaped hooks are connected together, comprising:

[0007] calculating the elastic point slip value and the bearing capacity of the J-shaped hook;

[0008] calculating the yield point slip value and the bearing capacity of the J-shaped hook;

[0009] calculating the peak point slip value and the bearing capacity of the J-shaped hook;

[0010] calculating the limit point slip value and the bearing capacity of the J-shaped hook.

[0011] In a further embodiment, the elastic point slip value and the bearing capacity of the J-shaped hook are calculated, specifically comprising:

[0012] calculating the elastic point bearing capacity of the J-shaped hook:

[0013] ;

[0014] ;

[0015] wherein, is the elastic point bearing capacity value of the J-hook; is the diameter of the J-hook; is the maximum shear stress in the cross section of the J-hook; is the yield strength of the J-hook.

[0016] In further embodiments, calculating the elastic point stiffness value and the slip value of the J-hook further comprises:

[0017] establishing a mechanical model of the J-hook;

[0018] establishing a deflection curve differential equation of the J-hook:

[0019] ;

[0020] wherein, is the elastic modulus of the J-hook; is the cross-sectional moment of inertia of the J-hook; is the concrete reaction force per unit length of the J-hook; is the coordinate value along the length direction of the J-hook; is the deflection deformation value perpendicular to the length direction of the J-hook.

[0021] solving the deflection curve differential equation in combination with the equivalent spring stiffness of the concrete:

[0022] ;

[0023] ;

[0024] ;

[0025] ;

[0026] wherein, is the characteristic coefficient; is the coordinate value along the length direction of the J-hook; is the deflection deformation value perpendicular to the length direction of the J-hook; is the constant of the general solution in the differential equation; is the constant of the general solution in the differential equation; is the constant of the general solution in the differential equation; is the constant of the general solution in the differential equation; is the equivalent spring stiffness of the concrete; is the elastic modulus of the J-hook; is the cross-sectional moment of inertia of the J-hook; is the diameter of the J-hook; is the elastic modulus of the concrete; Poisson's ratio of concrete Depth of influence of concrete under compression at the lower part of J-hook.

[0027] Where A, B, C, D can be solved according to boundary conditions:

[0028] ;

[0029] ;

[0030] ;

[0031] ;

[0032] Where, Elastic point slip value of J-hook; Characteristic coefficient; Height of J-hook;

[0033] Calculate the elastic stage stiffness of J-hook:

[0034] ;

[0035] ;

[0036] ;

[0037] ;

[0038] Where, Strain energy generated by deformation of J-hook; Elastic modulus of J-hook; Moment of inertia of cross section of J-hook; Coordinate value along the length direction of J-hook; Deflection deformation value perpendicular to the length direction of J-hook; Height of J-hook; Strain energy generated by deformation of concrete; Equivalent spring stiffness of concrete; Total energy; Diameter of J-hook; Process variable for solving; Process variable for solving; Characteristic coefficient; Elastic point slip value of J-hook; Elastic stage stiffness of J-hook.

[0039] Calculate the elastic point slip value of J-hook:

[0040] ;

[0041] wherein, is the elastic point slip value of the J-hook; is the elastic point load carrying capacity value of the J-hook; is the elastic stage stiffness of the J-hook.

[0042] In further embodiments, calculating the yield point slip value and the load carrying capacity of the J-hook specifically comprises:

[0043] calculating the load carrying capacity value of the J-hook:

[0044] constructing a static equilibrium equation for the root length portion of the J-hook:

[0045] ;

[0046] ;

[0047] wherein, is the yield point load carrying capacity value of the J-hook; is the shear force on the J-hook; is the equivalent resultant force of the concrete in the range between the two yield hinges of the J-hook; is the corresponding moment when the J-hook reaches full section yielding; is the corresponding moment when the J-hook reaches full section yielding; is the distance between the two yield hinges of the J-hook section;

[0048] calculating the load carrying capacity value of the J-hook according to the static equilibrium equation:

[0049] ;

[0050] wherein, is the yield point load carrying capacity value of the J-hook; is the diameter of the J-hook; is the coefficient of simplifying the stress pattern of the concrete in the compression zone into an equivalent rectangular stress pattern; is the stress amplification factor of the concrete under multi-axial state; is the uniaxial compressive strength of the concrete prism; is the yield strength of the J-hook.

[0051] In further embodiments, calculating the yield point slip value and the load carrying capacity of the J-hook further comprises:

[0052] calculating the yield point slip value of the J-hook;

[0053] obtaining the bending moment of the J-hook;

[0054] establishing the rotation angle equation and the deflection curve equation of the J-hook;

[0055] obtaining a yield point slip value of the J-hook.

[0056] In further embodiments, a bending moment of the J-hook is obtained, specifically comprising:

[0057] ;

[0058] ;

[0059] wherein, is a bending moment expression of the J-hook in the range of ; is a bending moment expression of the J-hook in the range of ; is a yield strength of the J-hook; is a diameter of the J-hook; is a coordinate value along a length direction of the J-hook; is a yield point bearing capacity value of the J-hook; is a stress amplification factor of concrete in a multi-axial state; is a uniaxial compressive strength of a concrete prism; is a distance between two yield hinges of a cross section of the J-hook; is a height of the J-hook.

[0060] In further embodiments, an angle equation and a deflection equation of the J-hook are established, specifically comprising:

[0061] In the range of , the angle equation and the deflection equation of the J-hook (1) are:

[0062] ;

[0063] ;

[0064] ;

[0065] wherein, is an angle equation of the J-hook in the range of ; is an intermediate variable of the angle equation of the J-hook in the range of ; is a deflection equation of the J-hook in the range of ; is an elastic modulus of the J-hook; is a moment of inertia of a cross section of the J-hook; is a diameter of the J-hook; is a stress amplification factor of concrete in a multi-axial state; is a uniaxial compressive strength of a concrete prism; is a coordinate value along the length direction of the J-hook; is a yield point bearing capacity value of the J-hook; is a height of the J-hook; is a distance between two yield hinges of a cross section of the J-hook; is a yield strength of the J-hook.

[0066] In range, the angle equation and the deflection equation of the J-hook (1) are:

[0067] ;

[0068] ;

[0069] wherein, is a yield point bearing capacity value of the J-hook in the range; is a yield point bearing capacity value of the J-hook in the range; is a yield point bearing capacity value of the J-hook; is a diameter of the J-hook; is a distance between two yield hinges of a cross section of the J-hook; is a stress amplification coefficient of concrete in a multi-axial state; is a uniaxial compressive strength of a concrete prism; is a height of the J-hook; is a yield strength of the J-hook; is an elastic modulus of the J-hook; is a cross-sectional moment of inertia of the J-hook.

[0070] In further embodiments, a yield point slip value of the J-hook is obtained, specifically comprising:

[0071] In combination with the angle equation and the deflection equation of the J-hook, the yield point slip value of the J-hook is calculated:

[0072] ;

[0073] wherein, is a slip value of the J-hook at section; is a yield point bearing capacity value of the J-hook; is a diameter of the J-hook; is a distance between two yield hinges of a cross section of the J-hook; is a height of the J-hook; is a yield strength of the J-hook; is an elastic modulus of the J-hook; is a cross-sectional moment of inertia of the J-hook; To consider the stress amplification factor of concrete in multi-axial state; To consider the uniaxial compressive strength of concrete prism.

[0074] In further embodiments, calculating the peak point slip value and the bearing capacity of the J-hook specifically includes:

[0075] ;

[0076] wherein, is the peak point slip value of the J-hook; is the diameter of the J-hook; is the uniaxial compressive strength of concrete prism; is the elastic modulus of concrete; is the height of the J-hook.

[0077] ;

[0078] wherein, is the peak point bearing capacity value of the J-hook; is the cross-sectional area of the J-hook; is the diameter of the J-hook; is the ultimate strength of the J-hook; is the height of the J-hook; is the elastic modulus of concrete; is the uniaxial compressive strength of concrete prism.

[0079] In further embodiments, calculating the limit point slip value and the bearing capacity of the J-hook specifically includes:

[0080] ;

[0081] wherein, is the limit point slip value of the J-hook; is the uniaxial compressive strength of concrete prism; is the elastic modulus of concrete; is the diameter of the J-hook; is the height of the J-hook.

[0082] ;

[0083] wherein, is the limit point bearing capacity value of the J-hook; is the peak point bearing capacity value of the J-hook.

[0084] Compared with the prior art, the beneficial effects of the present application are:

[0085] 1. The calculation method establishes mechanical analysis models of the J-shaped hook at the elastic point, yield point, peak point and limit point, determines the key points on the shear-slip constitutive model according to the geometric parameters and material performance parameters of the J-shaped hook, thereby constructing a complete shear-slip constitutive model, fully considering the shear transfer mechanism between the J-shaped hook and the concrete, making the calculation results have clear physical meaning, and meeting the actual engineering needs.

[0086] 2. The calculation method establishes mechanical models of the elastic point, yield point, peak point and limit point, realizes the shear-slip constitutive model calculation based on geometric parameters and material performance parameters, overcomes the limitation of relying on experimental data regression in the prior art, does not need to rely on a large amount of experimental data in the calculation process, has wide applicability and scene adaptation ability, significantly improves the universality of the method, and provides an efficient and flexible technical tool for engineering design.

[0087] 3. In the calculation of the elastic point slip and bearing capacity, the lower concrete of the J-shaped hook is simplified as a discrete spring unit, and based on the stress distribution characteristics of the concrete, the calculation depth of the lower concrete of the J-shaped hook is reasonably determined as 6 times the diameter of the J-shaped hook, which is in line with the mechanical response law of the concrete, avoids the errors caused by unreasonable parameters in the traditional simplified model, and makes the calculation results of the present application more in line with the actual stress condition of the engineering, thereby providing a powerful guarantee for the safety and reliability of subsequent structure design.

[0088] 4. In the calculation of the yield point slip, a segmented bending moment function is adopted based on the static equilibrium principle, the differential relationship between the bending moment and the deformation is established, and the integral constant is solved combined with the boundary conditions, so as to obtain the yield slip and ensure the rigor of the yield slip calculation; in the calculation of the yield bearing capacity, the influence of the multi-axial stress state of the concrete is considered, and the calculation accuracy is improved. BRIEF DESCRIPTION OF DRAWINGS

[0089] Figure 1 It is a shear-slip curve diagram of a shear-slip constitutive calculation method of a J-shaped hook in a double steel plate shear wall;

[0090] Figure 2 It is a schematic diagram of an elastic point calculation model of a shear-slip constitutive calculation method of a J-shaped hook in a double steel plate shear wall;

[0091] Figure 3 It is a schematic diagram of an elastic point calculation model of a shear-slip constitutive calculation method of a J-shaped hook in a double steel plate shear wall;

[0092] Figure 4 It is a schematic diagram of an elastic point calculation model of a shear-slip constitutive calculation method of a J-shaped hook in a double steel plate shear wall;

[0093] Figure 5It is a schematic diagram of the elastic point calculation model of a shear-slip constitutive calculation method of J hooks in a double steel plate shear wall;

[0094] Figure 6 It is a schematic diagram of the yield point calculation model of a shear-slip constitutive calculation method of J hooks in a double steel plate shear wall;

[0095] Figure 7 It is a schematic diagram of the yield point calculation model of a shear-slip constitutive calculation method of J hooks in a double steel plate shear wall;

[0096] Figure 8 It is a schematic diagram of the yield point calculation model of a shear-slip constitutive calculation method of J hooks in a double steel plate shear wall;

[0097] Figure 9 It is a flowchart of a shear-slip constitutive calculation method of J hooks in a double steel plate shear wall.

[0098] In the figure: 1, J hook; 2, concrete plate; 3, steel plate. DETAILED DESCRIPTION

[0099] In the description of the present application, it should be understood that the orientation or positional relationship indicated by the terms "center", "longitudinal", "transverse", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer" and the like is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the present application and simplifying the description, and therefore cannot be understood as indicating or implying that the devices or elements indicated must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as limiting the present application. In addition, the terms "first", "second" and the like are only for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the technical features indicated. Therefore, the features defined with "first", "second" and the like can explicitly or implicitly include one or more of the features. In the description of the present application, unless otherwise stated, the meaning of "a plurality of" is two or more.

[0100] Example 1:

[0101] A shear-slip constitutive calculation method of J hooks in a double steel plate shear wall, as shown in Figures 1 to 9 The double steel plate shear wall includes a pair of steel plates 3 and a concrete plate 2, the pair of steel plates 3 are respectively located on both sides of the concrete plate 2, a plurality of opposite J hooks 1 are fixedly installed at the connection between the steel plate 3 and the concrete plate 2, and the two corresponding J hooks 1 are hooked together. Figure 1 It is a shear-slip curve of the J hook 1, wherein the horizontal coordinate represents the slip value, and the vertical coordinate The shear-slip curve of the J-shaped hook 1 representing the shear strength can be divided into four stages, which are the first stage: elastic stage, the second stage: nonlinear stage, the third stage: strengthening stage and the fourth stage: degradation stage. The four stages correspond to the key points of the elastic point, the yield point, the peak point and the limit point respectively. In the figure: is the slip value corresponding to the elastic point, is the shear strength corresponding to the elastic point; is the yield slip value, is the shear strength of the yield point; is the slip value corresponding to the peak point, is the peak shear bearing capacity; is the limit point slip value, is the limit shear bearing capacity. Figure 2 in the formula represents that pressure is applied to the surface of the concrete slab 2 during loading.

[0102] Further comprising the following steps:

[0103] Step S101, calculating the elastic point slip value and bearing capacity of the J-shaped hook 1:

[0104] Figure 3 is a schematic diagram of the deformation of the J-shaped hook 1, is the length of the microelement, is the diameter of the J-shaped hook, is the height of the J-shaped hook, is the core concrete thickness of the J-shaped hook 1 test piece. Figure 4 is a schematic diagram of the elastic point calculation model of the J-shaped hook 1, is the equivalent elastic stiffness of the concrete. is the elastic point slip value of the J-shaped hook 1. is the coordinate value along the length direction of the J-shaped hook 1; is the deflection deformation value perpendicular to the length direction of the J-shaped hook 1; is the height of the J-shaped hook 1, is the core concrete thickness of the J-shaped hook 1 test piece; is the corner of the intermediate tie in the J-shaped hook 1. Figure 5 is a schematic diagram of the stress analysis of the microelement extracted from the J-shaped hook 1, in which is the cross-sectional shear force, is the cross-sectional bending moment, is the length of the microelement, is the concrete reaction force in the range of the microelement, is the differential increment of the shear force on the microelement, is the differential increment of the bending moment on the microelement.

[0105] The elastic point bearing capacity calculation of the J-shaped hook 1 includes:

[0106] (1)

[0107] (2)

[0108] wherein, is the elastic point bearing capacity value of the J-shaped hook; is the diameter of the J-shaped hook; is the maximum shear stress in the cross section of the J-shaped hook; is the yield strength of the J-shaped hook.

[0109] The elastic point slip value calculation of the J-shaped hook 1 includes:

[0110] Determine the basic assumptions: Set the J-shaped hook 1 to satisfy the plane section assumption; The lower surface of the J-shaped hook 1 is always in close contact with the concrete, and the deformation is one-to-one correspondence, consistent; Ignore the bonding force and friction between the concrete and the J-shaped hook 1.

[0111] Establish the mechanical model: Based on the Winkler foundation model, i.e. Winkler foundation model, the connection between the J-shaped hook 1 and the steel plate 3 is simplified as a fixed end, and the tie-in area of the J-shaped hook 1 is simplified as a semi-rigid support, and the lower concrete of the J-shaped hook 1 is simplified as a discrete spring unit.

[0112] Establish the deflection curve differential equation: The microelement of the J-shaped hook 1 is analyzed, combined with the Euler beam theory and the Winkler foundation model, the deflection curve differential equation of the J-shaped hook 1 is established, as shown in formula (3), formula (4):

[0113] (3)

[0114] (4)

[0115] wherein, is the elastic modulus of the J-shaped hook; is the sectional moment of inertia of the J-shaped hook; is the concrete reaction force per unit length of the J-shaped hook; is the coordinate value along the length direction of the J-shaped hook; is the deflection deformation value perpendicular to the length direction of the J-shaped hook; is the diameter of the J-shaped hook.

[0116] Determine the equivalent spring stiffness of the concrete slab 2: as shown in formula (5):

[0117] (5)

[0118] wherein, is the equivalent spring stiffness of the concrete; is the elastic modulus of the concrete; is the Poisson's ratio of concrete; is the height of the lower part of the J-hook 1 under compression.

[0119] Considering that the stress distribution of the lower part of the J-hook 1 under the action of external force in the push-out test is consistent with the distribution rule of the additional stress in the calculation of foundation settlement, the additional stress decreases with the increase of depth, and when the depth of the concrete exceeds 6 times the diameter of the J-hook 1, the vertical stress of the concrete decreases to 5% of the vertical stress value of the concrete at the root of the J-hook 1, therefore the height of the lower part of the J-hook 1 under compression can be taken as 6 wherein is the diameter of the J-hook 1.

[0120] Solving the differential equation: the boundary conditions are: , , , ; solving the deflection curve differential equation according to the boundary conditions to obtain the displacement function of the J-hook 1; substituting formula (6) into formula (3), the deflection curve equation is shown in formula (7):

[0121] (6)

[0122] (7)

[0123] wherein, is a characteristic coefficient, which is a comprehensive parameter for measuring the relative stiffness between the J-hook and the concrete; is the equivalent spring stiffness of the concrete; is the elastic modulus of the J-hook; is the sectional moment of inertia of the J-hook; is the coordinate value along the length direction of the J-hook; is the deflection deformation value perpendicular to the length direction of the J-hook; is the diameter of the J-hook;

[0124] The general solution of the deflection curve equation can be obtained as shown in formula (8):

[0125] (8)

[0126] wherein, is the general solution of the deflection curve equation; is the coordinate value along the length direction of the J-hook; is a characteristic coefficient, which is a comprehensive parameter for measuring the relative stiffness between the J-hook and the concrete; , , , are the general solution constants in the differential equation respectively.

[0127] In formula (8) , , , It can be determined from the boundary conditions: when tending to hour, Approaching 0, turning angle ;when When it approaches 0, the angle , ; , , , The expressions are shown in formulas (9), (10), (11), and (12):

[0128] (9)

[0129] (10)

[0130] (11)

[0131] (12)

[0132] In the formula, The characteristic coefficient is a comprehensive parameter that measures the relative stiffness between the J-hook and the concrete. These are the coordinate values ​​along the length of the J-hook; , , , These are the general solution constants in the differential equation; This represents the elastic point slip value of the J-shaped hook; The height of the J-hook.

[0133] Calculate the elastic stage stiffness of J-hook 1: Using the energy method, based on the principle of energy conservation in mechanics of materials, calculate the deformation energy of J-hook 1 and the deformation energy of concrete slab 2 respectively. Determine the elastic stage stiffness of the specimen by the energy balance relationship, as shown in formulas (12), (13), (14), and (15):

[0134] ; (13)

[0135] (14)

[0136] (15)

[0137] In the formula, The strain energy generated by the deformation of the J-shaped hook; The elastic modulus of the J-hook; The moment of inertia of the J-shaped hook section; The height of the J-hook; The strain energy generated by concrete deformation; The equivalent spring stiffness of concrete; Total strain energy; The diameter of the J-hook; The characteristic coefficient is a comprehensive parameter that measures the relative stiffness between the J-hook and the concrete. These are the coordinate values ​​along the length of the J-shaped hook; This represents the elastic point slip value of the J-shaped hook.

[0138] Therefore, the elastic stiffness of each J-shaped hook 1 ejected from the specimen is given by formulas (16), (17), (18), (19), (20), (21), (22), (23), (24), and (25):

[0139] (16)

[0140] (17)

[0141] (18)

[0142] (19)

[0143] (20)

[0144] (twenty one)

[0145] (twenty two) (twenty three)

[0146] (twenty four)

[0147] (25)

[0148] In the formula, The elastic stage stiffness of the J-shaped hook; Total energy; This represents the elastic point slip value of the J-shaped hook; The elastic modulus of the J-hook; The moment of inertia of the J-shaped hook section; The height of the J-hook; The equivalent spring stiffness of concrete; The diameter of the J-hook; is a characteristic coefficient, is a comprehensive parameter for measuring the relative stiffness between the J-shaped hook and the concrete; is a coordinate value along the length direction of the J-shaped hook; 、 、 、 、 、 、 、 、 are process parameters in the solving respectively

[0149] The elastic point slip value of the J-shaped hook 1 is calculated as shown in formula (26):

[0150] (26)

[0151] In the formula, is the elastic point slip value of the J-shaped hook; is the elastic point bearing capacity value of the J-shaped hook; is the elastic stage stiffness of the J-shaped hook.

[0152] Step S103, calculating the yield point slip value and bearing capacity of the J-shaped hook 1:

[0153] Figure 6 is a schematic diagram of the force state of the J-shaped hook 1 at the yield point, and points A and C in the figure are yield hinges of the J-shaped hook 1, wherein point A is located at the connection between the J-shaped hook 1 and the steel plate 3, and point C is located at the middle of the J-shaped hook 1, and point B is the cantilever end of the J-shaped hook 1, which is used to connect the other J-shaped hook 1; is the distance between the two yield hinges of the J-shaped hook section, that is, the length of the AC segment; is the stress amplification coefficient of the concrete under the multi-axial state; is the uniaxial compressive strength of the concrete prism; is the yield point bearing capacity value of the J-shaped hook; and are the bending moments corresponding to the full-section yield of the J-shaped hook. Figure 7 is a force analysis diagram of the AC isolator of the J-shaped hook 1 at the yield point, wherein is the distance between the two yield hinges of the J-shaped hook section, that is, the length of the AC segment; is the yield point shear strength; and are the bending moments corresponding to the full-section yield of the J-shaped hook 1; is the equivalent force of the concrete acting on the AC length range of the J-shaped hook 1. Figure 8 is a concrete stress distribution cloud along the cross-sectional direction of the J-shaped hook 1, is the diameter of the J-shaped hook.

[0154] The yield point bearing capacity value calculation of the J-shaped hook 1 includes:

[0155] According to the stress state of the J-shaped hook 1, the yield state model is simplified: according to the stress state of the J-shaped hook 1, it is assumed that the welding position of the J-shaped hook 1 and the steel plate 3 and the root section of the J-shaped hook 1 reach the full-section yield state, and the root concrete of the J-shaped hook 1 reaches the ultimate bearing capacity.

[0156] The static equilibrium equation of the root length part of the J-shaped hook 1 is constructed, as shown in formulas (27), (28), (29), (30), (31), (32), (33), (34), and (35):

[0157] (27)

[0158] (28)

[0159] (29)

[0160] (30)

[0161] (31)

[0162] (32)

[0163] (33)

[0164] (34)

[0165] (35)

[0166] In the formula, is the yield point bearing capacity value of the J-shaped hook; is the shear force borne by the J-shaped hook, which is taken as 0 at the J-shaped hook C point section; is the equivalent force acting on the concrete in the J-shaped hook AC length range; and is the bending moment corresponding to the full-section yield of the J-shaped hook; is the distance between the two yield hinges of the J-shaped hook section, i.e., the distance between the sections AC; is the stress amplification coefficient of the concrete under multi-axial state; is the uniaxial compressive strength of the concrete prism; is the diameter of the J-shaped hook; is the concrete strength correction coefficient; is the yield strength of the J-shaped hook; is the confining pressure concrete strength; , coefficient for simplifying the stress pattern of the concrete in the compression zone into an equivalent rectangular stress pattern.

[0167] The yield load capacity of the J-hook 1 is calculated as shown in equation (36):

[0168] (36)

[0169] wherein, is the yield point load capacity value of the J-hook; is the stress amplification coefficient of the concrete in the multi-axial state; is the uniaxial compressive strength of the concrete prism; is the diameter of the J-hook; is the yield strength of the J-hook; coefficient for simplifying the stress pattern of the concrete in the compression zone into an equivalent rectangular stress pattern.

[0170] The yield point slip value of the J-hook 1 is calculated including:

[0171] Based on the stress state of the J-hook 1 and the concrete, the J-hook 1 is divided into two sections along the length direction. In the J-hook AC length range, based on the fact that the J-hook 1 is subjected to the distributed reaction force of the concrete, the bending moment expression is established by applying the static equilibrium principle . In the J-hook CB length range, based on the continuity of the bending moment distribution, the bending moment distribution is assumed to be a quadratic function form . The bending moment expressions are shown in equations (37) and (38) respectively:

[0172] (37)

[0173] (38)

[0174] wherein, is the bending moment expression in the J-hook AC length range, is the bending moment expression in the J-hook CB length range; is the yield strength of the J-hook; is the diameter of the J-hook; is the coordinate value along the length direction of the J-hook; is the yield point load capacity value of the J-hook; is the stress amplification coefficient of the concrete in the multi-axial state, and the value is taken as shown in equation (31); is the uniaxial compressive strength of the concrete prism; is the distance between the two yield hinges of the J-hook section, i.e. the distance between the sections AC; is the height of the J-hook.

[0175] Solving integral constants, establishing displacement function: According to the principle of material mechanics, the differential relationship between the bending moment and the angle of rotation, deflection of J hook 1 is established, and the integral constants of each section are determined by the boundary conditions:

[0176] In the AC length range of J hook 1, the angle equation and deflection equation of J hook 1 are shown in formula (39) and formula (40):

[0177] (39)

[0178] (40)

[0179] In the formula, is the angle equation of J hook AC range; is the deflection equation of J hook AC range; is the elastic modulus of J hook; is the moment of inertia of J hook section; is the bending moment expression of J hook; , are integral constants, which can be solved by boundary conditions.

[0180] According to the boundary conditions, the boundary conditions are shown in formula (41) and formula (42):

[0181] (41)

[0182] (42)

[0183] In the formula, is the angle of J hook at A section; is the deflection of J hook at A section.

[0184] Substitute formula (41) and formula (42) into formula (39) and formula (40) to solve, as shown in formula (43) and formula (44):

[0185] (43)

[0186] (44)

[0187] In the formula, , are integral constants, which can be solved by boundary conditions; is the elastic modulus of J hook; is the moment of inertia of J hook section; is the height of J hook; is the yield strength of J hook; is the distance between two yield hinges of J hook section, that is, the distance between sections AC. The diameter of the J-hook; To account for the stress amplification factor of concrete under multiaxial conditions; The uniaxial compressive strength of a concrete prism; This represents the yield point bearing capacity value of the J-shaped hook.

[0188] Substituting formulas (43) and (44) into formulas (39) and (40), we obtain the rotation angle equation and deflection curve equation within the AC section of the J-shaped hook, as shown in formulas (45), (46), and (47):

[0189] (45)

[0190] (46)

[0191] (47)

[0192] In the formula, The equation for the turning angle within the AC range of the J-type hook; To solve the intermediate equations; The deflection equation within the AC range of the J-shaped hook; The elastic modulus of the J-hook; The moment of inertia of the J-shaped hook section; The diameter of the J-hook; To account for the stress amplification factor of concrete under multiaxial conditions; The uniaxial compressive strength of a concrete prism; These are the coordinate values ​​along the length of the J-shaped hook; This represents the yield point bearing capacity of the J-shaped hook. The height of the J-hook; The distance between the two yield hinges of the J-shaped hook section is the distance between sections AC; The yield strength of the J-shaped hook.

[0193] Within the section CB of J-hook 1, the rotation angle equation and deflection curve equation of J-hook 1 are shown in formulas (48) and (49):

[0194] (48)

[0195] (49)

[0196] In the formula, The equation for the turning angle within the CB range of the J-type hook; The deflection equation within the CB range of the J-shaped hook; The elastic modulus of the J-hook; The moment of inertia of the J-shaped hook section; Here is the expression for the bending moment of the J-shaped hook; , These are the integration constants, which can be solved using boundary conditions.

[0197] Solving based on boundary conditions, as shown in formulas (50) and (51):

[0198] (50)

[0199] (51)

[0200] In the formula, To determine the rotation angle at section C based on the rotation angle equation within the AC range of the J-type hook; To determine the rotation angle at section C based on the rotation angle equation within the CB range of the J-type hook; To determine the deflection at section C based on the deflection equation within the AC range of the J-type hook; The deflection at section C is determined based on the deflection equation within the CB range of the J-type hook.

[0201] Substituting formulas (50) and (51) into formulas (48) and (49) and solving, we get formulas (52) and (53):

[0202] (52)

[0203] (53)

[0204] In the formula, , These are the integration constants, which can be solved using boundary conditions; This represents the yield point bearing capacity of the J-shaped hook. The diameter of the J-hook; The distance between the two yield hinges of the J-shaped hook section is the distance between sections AC; To account for the stress amplification factor of concrete under multiaxial conditions; The uniaxial compressive strength of a concrete prism; The height of the J-hook; The yield strength of the J-shaped hook; The elastic modulus of the J-hook; The moment of inertia is the J-shaped hook section.

[0205] Substituting formulas (52) and (53) into formulas (48) and (49), we obtain the rotation angle equation and deflection curve equation of the J-type hook 1 within the cross section CB, as shown in formulas (54) and (55):

[0206] (54)

[0207] (55)

[0208] wherein, is the corner equation of the J-hook 1 in the range of the cross section CB; is the deflection equation of the J-hook 1 in the range of the cross section CB; is the yield point bearing capacity value of the J-hook; is the diameter of the J-hook; is the distance between two yield hinges of the cross section of the J-hook, i.e. the distance between the cross sections AC; is the stress amplification factor of the concrete under multi-axial state; is the uniaxial compressive strength of the concrete prism; is the height of the J-hook; is the yield strength of the J-hook; is the elastic modulus of the J-hook; is the moment of inertia of the cross section of the J-hook.

[0209] The yield point slip value of the J-hook 1 is calculated as shown in equation (56):

[0210] (56)

[0211] wherein, is the slip value of the J-hook 1 at the cross section B; is the yield point bearing capacity value of the J-hook; is the diameter of the J-hook; is the distance between two yield hinges of the cross section of the J-hook, i.e. the distance between the cross sections AC; is the height of the J-hook; is the yield strength of the J-hook; is the elastic modulus of the J-hook; is the moment of inertia of the cross section of the J-hook; is the stress amplification factor of the concrete under multi-axial state; is the uniaxial compressive strength of the concrete prism.

[0212] Step S105, the peak point slip value and the bearing capacity of the J-hook 1 are calculated:

[0213] The peak point slip value of the J-hook 1 is shown in equation (57):

[0214] (57)

[0215] wherein, is the peak point slip value of the J-hook; is the diameter of the J-hook; is the uniaxial compressive strength of the concrete prism; Econcrete is the elastic modulus of concrete; h is the J-hook height;

[0216] The peak point bearing capacity of the J-hook 1 is shown in equation (58):

[0217] (58)

[0218] In the equation, h is the J-hook height; A is the cross-sectional area of the J-hook; D is the diameter of the J-hook; fult is the ultimate strength of the J-hook; h is the J-hook height; Econcrete is the elastic modulus of concrete; fcr is the uniaxial compressive strength of the concrete prism.

[0219] Step S107, calculating the ultimate point slip value and the bearing capacity of the J-hook 1:

[0220] The ultimate point slip value of the J-hook 1 is shown in equation (59):

[0221] (59)

[0222] In the equation, h is the J-hook height; fcr is the uniaxial compressive strength of the concrete prism; Econcrete is the elastic modulus of concrete; D is the diameter of the J-hook; h is the J-hook height.

[0223] The ultimate point bearing capacity of the J-hook 1 is shown in equation (60):

[0224] (60)

[0225] In the equation, h is the J-hook height; h is the J-hook height.

[0226] In addition, it should be understood that although the present specification is described in terms of embodiments, not every embodiment contains only one independent technical solution, and the description of the specification is only for the sake of clarity, and those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can be appropriately combined to form other embodiments that those skilled in the art can understand.

Claims

1. A method for calculating the shear-slip constitutive relation of J hooks in a double-steel-plate shear wall, the double-steel-plate shear wall comprising a pair of steel plates (3) and a concrete plate (2), the pair of steel plates (3) being respectively located on the two sides of the concrete plate (2), a plurality of corresponding J hooks (1) being fixedly installed at intervals at the connection between the steel plates (3) and the concrete plate (2), wherein every two corresponding J hooks (1) are connected together, characterized in that, The method comprises the following steps: Calculating the elastic point slip value and the bearing capacity of the J-shaped hook (1); Calculating the yield point slip value and the bearing capacity of the J-shaped hook (1); Calculating the peak point slip value and the bearing capacity of the J-shaped hook (1); Calculating the limit point slip value and the bearing capacity of the J-shaped hook (1).

2. The method of claim 1, wherein the J-hook is a J-hook for a dual-steel-plate shear wall. The method for calculating the elastic point bearing capacity of the J-shaped hook (1) comprises the following steps: The method for calculating the elastic point bearing capacity of the J-shaped hook comprises the following steps: ； ； wherein is the elastic point load capacity value for a J-hook; is the diameter of the J-hook; is the maximum shear stress in the cross section of the J-hook; is the yield strength of the J-hook.

3. The method of claim 2, wherein the J-hook is a J-hook in a dual-steel-plate shear wall. The method for calculating the elastic point initial stiffness and the slip value of the J-shaped hook (1) further comprises the following steps: Establishing a mechanical model of the J-shaped hook (1); Establishing a deflection curve differential equation of the J-shaped hook (1); ； wherein is the J-hook elastic modulus; is the J-hook cross-sectional moment of inertia; is the J-hook concrete reaction per unit length; is the coordinate value along the J-hook length direction; is the deflection deformation value perpendicular to the J-hook length direction; Calculating the equivalent spring stiffness of the concrete: ； wherein K is the equivalent spring stiffness of concrete; E is the elastic modulus of concrete; v is the Poisson's ratio of concrete; d is the influence depth of the lower part of the J-hook under compression of concrete; Solving the deflection curve differential equation in combination with the equivalent spring stiffness of the concrete: ； ； In the formula, is a characteristic coefficient; is an equivalent spring stiffness of concrete; is a diameter of the J-hook; is a modulus of elasticity of the J-hook; is a cross-sectional moment of inertia of the J-hook; is a coordinate value in the length direction of the J-hook; is a deflection deformation value perpendicular to the length direction of the J-hook; The general solution of the deflection curve differential equation is: ； wherein is a characteristic coefficient; is a constant of the general solution of the differential equation; is a constant of the general solution of the differential equation; is a constant of the general solution of the differential equation; is a constant of the general solution of the differential equation; is a coordinate value in the length direction of the J-hook; is a deflection deformation value perpendicular to the length direction of the J-hook; In the formula, A, B, C, and D can be obtained according to boundary conditions: ； ； ； ； wherein is the characteristic coefficient; is the elastic point slip value of the J-hook; is the J-hook height; Calculating the elastic stage stiffness of the J-shaped hook (1): ； ； ； ； wherein is the energy developed by the J-hook deformation; is the J-hook elastic modulus; is the J-hook cross-sectional moment of inertia; is the J-hook height; is the energy developed by the concrete deformation; is the concrete equivalent spring stiffness; is the J-hook diameter; is the deflection deformation value perpendicular to the J-hook length direction; is the total energy; is the solution process variable; is the solution process variable; is the characteristic coefficient; is the J-hook elastic point slip value; is the J-hook elastic stage stiffness; Calculating the elastic point slip value of the J-shaped hook: ； wherein is the elastic point slippage value for a J-hook; is the elastic point load capacity value for a J-hook; is the elastic phase stiffness for a J-hook.

4. The method of claim 3, wherein the J-hook is a J-hook of a double-steel-plate shear wall. The method for calculating the yield point slip value and the bearing capacity of the J-shaped hook (1) comprises the following steps: Calculating the bearing capacity value of the J-shaped hook (1): Constructing a static equilibrium equation for the root length part of the J-shaped hook (1): ； ； wherein is the yield point load capacity of the J-hook; is the shear force of the J-hook cross-section; is the equivalent resultant force of the concrete acting in the range between the two yield hinges of the J-hook; is the corresponding bending moment when the J-hook reaches full cross-section yield; is the corresponding bending moment when the J-hook reaches full cross-section yield; is the distance between the two yield hinges of the J-hook cross-section; Calculating the bearing capacity value of the J-shaped hook (1) according to the static equilibrium equation: ； wherein is the yield point load capacity value for the J-hook; is the diameter of the J-hook; is the coefficient for simplifying the stress pattern of the concrete in the compression zone into an equivalent rectangular stress pattern; is the stress amplification factor of the concrete under multi-axial state; is the uniaxial compressive strength of the concrete prism; is the yield strength of the J-hook.

5. The method of claim 4, wherein the J-hook is a J-hook of a double-steel-plate shear wall. The method for calculating the yield point slip value and the bearing capacity of the J-shaped hook (1) further comprises the following steps: Calculating the yield point slip value of the J-shaped hook (1); Obtaining the bending moment of the J-shaped hook (1); Establishing a rotation angle equation and a deflection curve equation of the J-shaped hook (1); Obtaining the yield point slip value of the J-shaped hook (1).

6. The method of calculating the shear-slip constitutive relation of the J-hook in the dual-steel-plate shear wall according to claim 5, wherein, The method for obtaining the bending moment of the J-shaped hook (1) comprises the following steps: ； ； wherein, is the yield strength of the J-hook; is the bending moment expression in the range of is the yield strength of the J-hook; is the bending moment expression in the range of is the yield strength of the J-hook; is the diameter of the J-hook; is the height of the J-hook; is the coordinate value along the length of the J-hook; is the yield point load capacity value of the J-hook; is the stress amplification factor of concrete in the multi-axial state; is the uniaxial compressive strength of the concrete prism; is the distance between the two yield hinges of the J-hook section.

7. The method of claim 6, wherein the J-hook is a J-hook of a double-steel-plate shear wall. The method for establishing a rotation angle equation and a deflection curve equation of the J-shaped hook (1) comprises the following steps: In Within the scope of the present application, the corner equation and the flexion equation of the J-hook (1) are: ； ； ； wherein J-hook intermediate variable of the corner equation within the range; J-hook intermediate variable of the corner equation within the range; J-hook deflection equation within the range; elastic modulus of the J-hook; moment of inertia of the J-hook; diameter of the J-hook; is the stress amplification factor of concrete in the multi-axial state; uniaxial compressive strength of the concrete prism; is the coordinate value along the length direction of the J-hook; yield point bearing capacity value of the J-hook; height of the J-hook; distance between the two yield hinges of the J-hook section; yield strength of the J-hook; In The corner equation and the flexion equation of the J-hook (1) are within the range of: ； ; wherein is the J-hook is the corner equation within the range of is the J-hook is the deflection equation within the range of is the yield point load value of the J-hook is the diameter of the J-hook is the distance between two yield hinges of the J-hook cross section is the stress amplification factor of concrete in multi-axial state is the uniaxial compressive strength of concrete prism is the height of the J-hook is the yield strength of the J-hook is the elastic modulus of the J-hook is the moment of inertia of the J-hook cross section 8. The method of claim 7, wherein the J-hook is a J-hook for a dual-steel-plate shear wall. The method for obtaining the yield point slip value of the J-shaped hook (1) comprises the following steps: Calculating the yield point slip value of the J-shaped hook (1) in combination with the rotation angle equation and the deflection curve equation of the J-shaped hook (1): ； wherein is the yield point load capacity value of the J-hook; is the slippage value at the cross section; is the yield point load capacity value of the J-hook; is the diameter of the J-hook; is the distance between the two yield hinges of the J-hook cross section; is the height of the J-hook; is the yield strength of the J-hook; is the elastic modulus of the J-hook; is the moment of inertia of the J-hook cross section; is the stress amplification factor of the concrete in the multi-axial state; is the uniaxial compressive strength of the concrete prism. 9.The method of calculating the shear-slip constitutive relation of the J-shaped hook in the dual-steel plate shear wall according to claim 8, wherein, The method for calculating the peak point slip value and the bearing capacity of the J-shaped hook (1) comprises the following steps: ； wherein is the peak point slippage value for the J-hook; is the diameter of the J-hook; is the uniaxial compressive strength of the concrete prism; is the elastic modulus of the concrete; is the J-hook height; ； wherein is the peak point load capacity value for a J-hook; is the cross-sectional area of the J-hook; is the diameter of the J-hook; is the ultimate strength of the J-hook; is the height of the J-hook; is the modulus of elasticity of concrete; is the uniaxial compressive strength of the concrete prism. 10.The method of calculating the shear-slip constitutive relation of the J-shaped hook in the dual-steel plate shear wall according to claim 9, wherein, The method for calculating the limit point slip value and the bearing capacity of the J-shaped hook (1) comprises the following steps: ； wherein is the limit point slip value for J-hooks; is the uniaxial compressive strength of the concrete prism; is the modulus of elasticity of the concrete; is the diameter of the J-hook; is the height of the J-hook; ； wherein is the ultimate point load capacity value for a J-hook; is the peak point load capacity value for a J-hook.

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