Method for determining shear stiffness of bolt shear connectors with reserved holes

Abstract

The present invention relates to a method for determining the shear stiffness of a bolt shear connector with a reserved hole. Based on test data, multiple load-slip curves of the bolt shear connector with a reserved hole are obtained; each load-slip curve is divided into a friction section, a slip section, and a curve section, and the shear stiffness of each section is determined respectively. In the determination of the fitting curve parameter β of the curve section, an initial value of the fitting curve parameter is preset, the average value of the maximum shear loads of all curve sections is calculated, and the average value of the maximum shear loads is used as the maximum shear load of the curve section. The average value of the maximum slips of all curve sections is calculated, and the average value of the maximum slips is used as the maximum load slip of the curve section. Based on energy balance, linear programming iteration is performed on the energy error obtained from the area difference to determine the fitting curve parameter β, which reduces the dependence on experience, has stronger applicability, and at the same time gives theoretical guidance, pointing out a new direction for corresponding research.

Description

Technical Field

[0001] The present invention relates to the technical field of determining the shear stiffness of shear connectors in bridge engineering, and particularly relates to a method for determining the shear stiffness of bolt shear connectors with reserved holes. Background Art

[0002] A steel-concrete composite beam refers to a beam structure that uses two materials, steel and concrete, and connects the steel beam and the concrete into a whole through shear connectors to jointly bear the load, making full use of the material properties of steel in tension and concrete in compression, and at the same time ensuring the effective utilization rate of the materials. Common forms of shear connectors are as Figure 1 shown. The shear connector 01 is a key component for the coordinated work of the steel beam 03 and the concrete slab 02, directly affecting the transfer of shear stress at the junction of the steel beam 03 and the concrete slab 02. The shear stiffness is defined as the stress required to cause a unit shear deformation of the shear connector 01, which directly reflects the ability of the shear connector to resist shear deformation. The shear connector 01 includes stud bolts, bolts, and punched plate (PBL) connectors. Please refer to Figure 2 , and the load-slip curves of the three are roughly the same. The vertical coordinate is the shear load P, and the horizontal coordinate is the slip s, where P u and s u respectively represent the maximum shear load and the maximum slip. The curve includes an approximately linear elastic stage 04, a plastic stage 05, and a descending stage 06. Currently, the methods for determining the shear stiffness of shear connectors at home and abroad are generally derived based on the load-slip curve. That is, the secant slope at a specific percentage of the ultimate shear load or the equivalent slip on the load-slip curve is used. For example, Eurocode 4 stipulates that the stiffness calculation method for shear connectors is the secant slope at 0.9 times the maximum load.

[0003] However, the prerequisite for applying this type of method is that the load-slip curve of the component is known, that is, a push-out test or a direct shear test needs to be carried out. Moreover, the characteristics of the load-slip curves of different shear connectors vary greatly. This method depends on the test conditions, experience, and subjective judgment of different researchers, lacks unified theoretical guidance, and can only generally calculate a shear stiffness as a reference, with poor applicability. The example provided by Eurocode 4 is a stud bolt connector. Before reaching the maximum load, the curve characteristic is a monotonically increasing line, and its relative slip is generally less than 9 mm. For bolt or PBL connectors, there are problems such as relatively large relative slip and a plateau in the rising stage. This type of formula is not universal. In addition, there is very little research on the shear stiffness of shear connectors at home and abroad, especially for bolt and PBL connectors. It is necessary to establish a more general and reasonable shear stiffness calculation method for shear connectors using a unified framework.

[0004] In current research, in terms of studying the load-slip behavior, in some solutions, through the non-linear regression analysis of the push-out test results and the theoretical analysis using the classical Ollgaard constitutive law, the exponential form load-slip relationship expressions for stud shear connectors and single shear connectors are obtained. In some solutions, a theoretical model of the load-slip relationship for assembled steel-ultra-high performance thin-layer concrete large-diameter group stud connectors is proposed. All these solutions are studies on the load-slip relationship of studs.

[0005] In some solutions, the mechanical properties of bolt connectors in steel-steel fiber concrete composite beams are studied by experiments and finite element models, and a design formula for predicting the load-slip relationship of high-strength bolt connectors is proposed. In some solutions, the characteristics of the three stages of the load-slip relationship of bolt shear connectors are analyzed, and a simplified load-slip model of 16-mm diameter bolt shear connectors is established. All these solutions are studies on the load-slip relationship of bolts.

[0006] In some solutions, the normalization method is used to analyze the influence of the shear stiffness of concrete tenons and the tensile capacity of penetrating steel bars on the load-slip relationship at each working stage of PBL connectors, and a load-slip relationship formula for the whole loading process is proposed, and it is considered that the load-slip curve can be divided into an elastic section, an elastic-plastic section, and a strengthening section. In some solutions, the mechanical mechanism of the PBL shear key in the hybrid structure and its important influencing factors are deeply analyzed, a calculation formula for the ultimate bearing capacity of the PBL shear key in the hybrid structure is proposed, the characteristic loads and corresponding slips under the elastic limit and yield limit of the PBL shear key are given, and finally the load-slip characteristic curve of the PBL shear key for the whole loading process is obtained. All these solutions are studies on the load-slip relationship of PBL.

[0007] In terms of studying the shear stiffness, in some solutions, through the data analysis of 116 push-out test results, the tangent modulus method at 0.5 times the shear ultimate load on the load-slip curve is proposed. In some solutions, through 40 push-out tests, the deformation characteristics and mechanical mechanism of studs are analyzed, and through zero-intercept linear regression analysis, a calculation formula for the shear stiffness of stud shear connectors regarding the elastic modulus of concrete, the elastic modulus of studs, and the diameter of studs is proposed. In some solutions, with the aperture of the perforated plate, the concrete strength and elastic modulus, and the diameter, strength, and elastic modulus of the steel bars in the holes as variable parameters, a shear stiffness model test of 60 perforated plate connectors is carried out; the variation relationship of the ratio of the slope of the tangent line to the secant line of the shear relative slip curve of each model specimen with relative slip is analyzed, and a method for obtaining the shear stiffness of perforated plate connectors is proposed; the elastic foundation beam method is used to analyze the shear mechanism of the concrete and steel bars in the holes, and the theoretical calculation formula for the shear stiffness of perforated plate connectors is derived; based on theoretical analysis and 123 model tests from various countries, a calculation formula for the shear stiffness of PBL connectors with and without steel bars in the holes is proposed.

[0008] However, although in the current schemes for determining the shear stiffness of shear connectors, most are obtained based on experimental experience, with a stronger dependence on experience and a lack of theoretical guidance. Especially for the determination of the shear stiffness of bolted shear connectors with pre - drilled holes, due to the complexity of their force - bearing, the dependence on experience is even stronger, and it needs to be obtained based on each experiment, making it difficult to give a determination scheme applicable to various situations. Summary of the Invention

[0009] The technical problem to be solved by this application is to provide a method for determining the shear stiffness of bolted shear connectors with pre - drilled holes, which has the characteristic of stronger applicability of the shear stiffness confirmation method for connectors.

[0010] In a first aspect, in one embodiment, a method for determining the shear stiffness of bolted shear connectors with pre - drilled holes is provided, including:

[0011] Obtaining multiple load - slip curves of bolted shear connectors with pre - drilled holes based on experimental data;

[0012] Dividing each load - slip curve into a friction section, a slip section, and a curve section, and respectively determining the shear stiffness of the friction section, the slip section, and the curve section; wherein, the friction section is formed by frictional force resisting the shear load and is linear; the slip section consists of a nearly horizontal line formed after the frictional force fails and slip occurs; the curve section is formed by the interaction between the bolt and the concrete to resist the shear load and is non - linear;

[0013] For the curve section, solving the shear stiffness based on the load - slip curve corresponding to the curve fitting formula where P q represents the shear load of the curve section, P qu represents the maximum shear load of the curve section, P h represents the shear load corresponding to the end of the slip section, s represents the relative slip between the concrete slab and the steel beam, s h represents the relative slip corresponding to the end of the slip section, represents the fitting curve parameter, and e represents the base of the natural logarithm;

[0014] Among them, the determination method of the fitting curve parameter includes:

[0015] Presetting the initial value of the fitting curve parameter ;

[0016] Calculating the average value of the maximum shear loads of all curve sections in the multiple load - slip curves, and taking this average value of the maximum shear load as the maximum shear load P qu of the curve section;

[0017] Calculate the average value of the maximum slips of all curve segments in the multiple load-slip curves, and use this average value of the maximum slip as the maximum load slip s of the curve segment u ;

[0018] Calculate the area enclosed by each curve segment and the segment [s h,n , s u,n on the s-axis as the first area, where n represents the index of the load-slip curve;

[0019] Calculation formula The area enclosed by the curve where it is located and the segment [s h , s u on the s-axis as the second area;

[0020] Calculate the absolute value of the difference between the second area and each first area;

[0021] Calculate the energy error based on each of the absolute values;

[0022] Based on linear programming iterative solution, the solution of that minimizes the energy error is used as the fitting curve parameter value.

[0023] In one embodiment, calculate the average value of the maximum shear loads of all curve segments in the multiple load-slip curves, and use this average value of the maximum shear load as the maximum shear load P of the curve segment qu , including:

[0024] (7)

[0025] where P qu,n represents the maximum shear load of the curve segment of the nth load-slip curve, N represents the total number of load-slip curves, and 1 ≤ n ≤ N;

[0026] Calculate the average value of the maximum slips of all curve segments in the multiple load-slip curves, and use this average value of the maximum slip as the maximum load slip s of the curve segment u , including:

[0027] (8)

[0028] where s u,n represents the maximum load slip of the curve segment of the nth load-slip curve;

[0029] The calculation of the absolute value of the difference between the second area and each first area includes:

[0030] (9)

[0031] Wherein, represents the absolute value corresponding to the nth load-slip curve, represents the second area, represents the first area corresponding to the nth load-slip curve.

[0032] In one embodiment, calculating the energy error based on each of the absolute values includes:

[0033] (10)

[0034] Wherein, E represents the energy error, represents the absolute value corresponding to the nth load-slip curve, n represents the index of the load-slip curve, and N represents the total number of load-slip curves, where 1 ≤ n ≤ N.

[0035] In one embodiment, for the maximum shear load of the friction section, it is calculated based on the average value of the maximum shear loads of the friction sections of all load-slip curves; for the maximum load slip of the friction section, it is calculated based on the average value of the maximum load slips of the friction sections of all load-slip curves; based on the maximum shear load and the maximum load slip of the friction section, the shear resistance stiffness of the friction section is calculated.

[0036] In one embodiment, for the maximum shear load of the slip section, it is calculated based on the average value of the maximum shear loads of the slip sections of all load-slip curves; for the maximum load slip of the slip section, it is calculated based on the average value of the maximum load slips of the slip sections of all load-slip curves; based on the maximum shear load and the maximum load slip of the slip section, the shear resistance stiffness of the slip section is calculated.

[0037] In one embodiment, for the curve section, solving the shear resistance stiffness based on the load-slip curve corresponding to the curve fitting formula includes:

[0038] Dividing the curve section into a first broken line segment before the shear connector yields and a second broken line segment after yielding, where the slope of the first broken line segment is greater than the slope of the second broken line segment;

[0039] Obtaining the bilinear models of the first broken line segment and the second broken line segment;

[0040] Based on the principle of equal area of energy balance and the bilinear models, calculating the ordinate of the mathematical yield point when and the abscissa of the mathematical yield point when ; wherein, represents the shear resistance stiffness before the shear connector yields, represents the shear resistance stiffness after the shear connector yields;

[0041] Based on the ordinate of the mathematical yield point when and the abscissa of the mathematical yield point when calculate the abscissa and ordinate of the turning point between the first broken line segment and the second broken line segment;

[0042] Based on the abscissa and ordinate of the turning point between the first broken line segment and the second broken line segment, calculate the shear stiffness before yield and the shear stiffness after yield of the curve segment.

[0043] In one embodiment, the obtaining of the bilinear model of the first broken line segment and the second broken line segment includes:

[0044] (11)

[0045] Wherein, represents the bilinear model fitted for the curve segment, , , represents the slip when the shear connector yields, represents the shear load when the shear connector yields.

[0046] In one embodiment, based on the principle of equal area of energy balance and the bilinear model, calculating the ordinate of the mathematical yield point when and the abscissa of the mathematical yield point when includes:

[0047] (14)

[0048] Wherein, P A represents the ordinate of the mathematical yield point when in the bilinear model, represents the abscissa of the mathematical yield point when in the bilinear model.

[0049] In one embodiment, based on the ordinate of the mathematical yield point when and the abscissa of the mathematical yield point when calculate the abscissa and ordinate of the turning point between the first broken line segment and the second broken line segment, including:

[0050] (15)

[0051] Wherein, s y and P y respectively represent the abscissa and ordinate of the turning point between the first broken line segment and the second broken line segment.

[0052] In one embodiment, calculating the shear stiffness before yielding and the shear stiffness after yielding of the curve segment based on the abscissa and ordinate of the turning point between the first broken line segment and the second broken line segment includes:

[0053] (16)

[0054] Among them, represents the change in shear load of the fitted curve segment, represents the load-slip change of the fitted curve segment, represents the shape characteristic parameter of the fitted curve; , , .

[0055] The beneficial effects of the present invention are:

[0056] In the determination of the fitted curve parameters of the curve segment, a general value is obtained based on energy balance, reducing the dependence on experience and having stronger applicability. At the same time, a clear theoretical guidance is given from the energy perspective, pointing out a new direction for corresponding research and can also be used for reference in the determination of the stiffness of other types of shear connectors. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 is a schematic diagram of a common form of the shear connector;

[0058] Figure 2 is a schematic diagram of the common load-slip curve of the shear connector;

[0059] Figure 3 is a schematic diagram of the flow of the method for determining the shear stiffness of the bolt shear connector with reserved holes according to an embodiment of the present application;

[0060] Figure 4 is a schematic diagram of three load-slip curves of the bolt shear connector with reserved holes obtained based on three groups of test data according to an embodiment of the present application;

[0061] Figure 5 is a schematic diagram of the flow of the method for determining the fitted curve parameter according to an embodiment of the present application;

[0062] Figure 6 is a schematic diagram of the flow of the method for determining the shear stiffness of the curve segment based on energy balance according to an embodiment of the present application;

[0063] Figure 7 is a schematic diagram of the shear stiffness analysis model based on energy balance according to an embodiment of the present application.

[0064] In the illustration, 01 is the shear connector; 02 is the concrete slab; 03 is the steel beam; 04 is the approximate linearly elastic stage; 05 is the plastic stage; 06 is the descending stage. Specific embodiments

[0065] The present invention will be further described in detail below in conjunction with the accompanying drawings through specific embodiments. Similar elements in different embodiments are labeled with related similar element numbers. In the following embodiments, many detailed descriptions are provided to enable a better understanding of the present application. However, those skilled in the art can easily recognize that some of the features can be omitted in different situations, or can be replaced by other elements, materials, or methods. In some cases, some operations related to the present application are not shown or described in the specification, which is to avoid the core part of the present application being overwhelmed by excessive descriptions. For those skilled in the art, it is not necessary to describe these related operations in detail, and they can fully understand the related operations based on the descriptions in the specification and general technical knowledge in the art.

[0066] In addition, the features, operations, or characteristics described in the specification can be combined in any appropriate manner to form various embodiments. At the same time, the steps or actions in the method description can also be reordered or adjusted in an obvious manner by those skilled in the art. Therefore, the various sequences in the specification and drawings are only for clearly describing a certain embodiment and do not mean that they are the necessary sequences, unless it is stated that a certain sequence must be followed.

[0067] The serial numbers assigned to the components herein, such as "first", "second", etc., are only used to distinguish the described objects and do not have any sequential or technical meaning.

[0068] A method for determining the shear stiffness of a bolted shear connector with pre - drilled holes based on the present invention application, please refer to Figure 3 , including:

[0069] Step S10, obtaining multiple load - slip curves of the bolted shear connector with pre - drilled holes based on test data.

[0070] Please refer to Figure 4 , in the figure, three load - slip curves of the bolted shear connector with pre - drilled holes obtained based on three groups of test data are shown. Those skilled in the art can understand that this is only an illustration, and in order to obtain more accurate results, this solution can be implemented based on more load - slip curves.

[0071] From Figure 4It can be seen that the slip broken line of the bolt shear connector with reserved holes can be roughly divided into three segments. The first segment is the linear part where the shear load is resisted by friction. The second segment is the nearly horizontal line generated by slip after the friction fails. The third segment is the non-linear part in the shape of a curve where the shear load is resisted by the interaction between the bolt and the concrete.

[0072] Step S20: Divide each load-slip curve into a friction segment, a slip segment, and a curve segment, and determine the shear stiffness of the friction segment, the slip segment, and the curve segment respectively.

[0073] Among them, the friction segment is formed by the friction resisting the shear load and is linear; the slip segment is composed of the nearly horizontal line generated by slip after the friction fails; the curve segment is formed by the interaction between the bolt and the concrete resisting the shear load and is non-linear.

[0074] For the friction segment and the slip segment, the specific values of the fitting curve can be directly determined by the average values of each load-slip curve in the friction segment and the slip segment. Thus, in one embodiment, for the maximum shear load of the friction segment, it is calculated based on the average value of the maximum shear loads of all load-slip curves in the friction segment and can be expressed as:

[0075] (1)

[0076] Where, P l represents the maximum shear load of the friction segment, n represents the index of the load-slip curve, P l,n represents the maximum shear load of the friction segment of the nth load-slip curve, N represents the total number of load-slip curves, and 1 ≤ n ≤ N.

[0077] From Figure 4 it can be known that the maximum shear load of the friction segment of the nth load-slip curve is the shear load at the end of the friction segment of the nth load-slip curve. Therefore, the maximum shear load of the friction segment is the shear load at the end of the friction segment.

[0078] In one embodiment, for the maximum load slip of the friction segment, it is calculated based on the average value of the maximum load slips of all load-slip curves in the friction segment and can be expressed as:

[0079] (2)

[0080] Where, s l represents the maximum load slip of the friction segment, n represents the index of the load-slip curve, s l,n represents the maximum load slip of the friction segment of the nth load-slip curve, N represents the total number of load-slip curves, and 1 ≤ n ≤ N.

[0081] Thus, the end point L (sl , P l ).

[0082] Then, based on the maximum shear load and maximum load slip of the friction section, the shear stiffness of the friction section can be calculated and expressed as:

[0083] (3)

[0084] Wherein, represents the shear stiffness of the friction section.

[0085] In one embodiment, for the maximum shear load of the slip section, it is calculated based on the average value of the maximum shear loads of the slip sections of all load-slip curves and can be expressed as:

[0086] (4)

[0087] Wherein, P h represents the maximum shear load of the slip section, n represents the index of the load-slip curve, and P h,n represents the maximum shear load of the slip section of the nth load-slip curve, N represents the total number of load-slip curves, and 1 ≤ n ≤ N.

[0088] It can be seen from Figure 4 that the maximum shear load of the slip section of the nth load-slip curve is the shear load at the end of the slip section of the nth load-slip curve. Therefore, the maximum shear load of the slip section is the shear load at the end of the slip section.

[0089] In one embodiment, for the maximum load slip of the slip section, it is calculated based on the average value of the maximum load slips of the slip sections of all load-slip curves and can be expressed as:

[0090] (5)

[0091] Wherein, s h represents the maximum load slip of the slip section, n represents the index of the load-slip curve, and s h,n represents the maximum load slip of the slip section of the nth load-slip curve, N represents the total number of load-slip curves, and 1 ≤ n ≤ N.

[0092] Thus, the end point H (s h , P h ) of the slip section can be obtained.

[0093] Then, based on the maximum shear load and maximum load slip of the slip section, the shear stiffness of the slip section can be calculated and expressed as:

[0094] (6)

[0095] Among them, represents the shear stiffness of the slip section.

[0096] For the curved section, based on the curve fitting formula the shear stiffness is solved for the corresponding load-slip curve. Among them, P q represents the shear load of the curved section, P qu represents the maximum shear load of the curved section, s represents the relative slip between the concrete slab and the steel beam, s h represents the relative slip corresponding to the end of the slip section, represents the fitting curve parameter, and e represents the base of the natural logarithm. This curve fitting formula is a classical curve fitting formula.

[0097] However, for the fitting curve parameter in the formula, at present, it is a value directly determined based on respective tests. The values determined by each test are different and cannot be applied to all situations, and it has a strong dependence on experience.

[0098] In view of this, the present application provides a method for determining the fitting curve parameter . In this determination method, a general value is obtained based on energy balance, which has stronger applicability. At the same time, theoretical guidance is given, pointing out a new direction for corresponding research.

[0099] Please refer to Figure 5 , in an embodiment, the method for determining the fitting curve parameter includes:

[0100] Step S100, preset the initial value of the fitting curve parameter.

[0101] Here, assume an initial value of a fitting curve parameter.

[0102] Step S200, calculate the average value of the maximum shear loads of all curve sections in multiple load-slip curves, and use this average value of the maximum shear load as the maximum shear load P qu of the curve section.

[0103] In an embodiment, step S200 may include:

[0104] (7)

[0105] Among them, P qu,n represents the maximum shear load of the curve section of the nth load-slip curve, N represents the total number of load-slip curves, and 1 ≤ n ≤ N.

[0106] Step S300: Calculate the average value of the maximum slips of all curve segments in multiple load-slip curves, and use this average value of the maximum slip as the maximum load slip s of the curve segment. u .

[0107] In one embodiment, step S300 may include:

[0108] (8)

[0109] where s u,n represents the maximum load slip of the curve segment of the nth load-slip curve.

[0110] Step S400: Calculate the area enclosed by each curve segment and the segment [s h,n , s u,n on the s-axis as the first area. Here, n represents the index of the load-slip curve.

[0111] For each load-slip curve, calculate the area enclosed by the segment from s h to s u on the s-axis and the curve segment as the corresponding first area.

[0112] Step S500: Calculate the area enclosed by the curve where formula is located and the segment [s h , s u on the s-axis as the second area.

[0113] Next, based on energy balance, implement steps S600 to S800.

[0114] Step S600: Calculate the absolute value of the difference between the second area and each first area.

[0115] In one embodiment, step S600 includes:

[0116] (9)

[0117] where represents the absolute value corresponding to the nth load-slip curve, represents the second area, represents the first area corresponding to the nth load-slip curve.

[0118] Step S700: Calculate the energy error based on each absolute value.

[0119] In one embodiment, step S700 includes:

[0120] (10)

[0121] where E represents the energy error, represents the absolute value corresponding to the nth load-slip curve, n represents the index of the load-slip curve, N represents the total number of load-slip curves, and 1 ≤ n ≤ N.

[0122] Step S800, based on iterative solution of linear programming, take the initial value of the solution that minimizes the energy error as the fitting curve parameters value.

[0123] Based on steps S100 to S800, a general value is obtained based on energy balance, which has stronger applicability. At the same time, theoretical guidance is given, pointing out a new direction for corresponding research.

[0124] Above, based on the fitting formula with the value determined, a definite fitting curve can be obtained. Based on this fitting curve, the shear stiffness can be determined in the manner of the existing technology. In the embodiments of the present application, a method for determining the shear stiffness based on energy balance is provided. Please refer to Figure 6 , including:

[0125] Step S1000, divide the curve segment into a first broken line segment before the shear connector yields and a second broken line segment after yielding. The slope of the first broken line segment is greater than that of the second broken line segment.

[0126] Please refer to Figure 7 , according to energy balance, the area enclosed by the first broken line segment and the second broken line segment should be equal to . Geometrically, there are countless possibilities for the two broken lines that satisfy this relationship. Figure 7 In, the area of triangle HCF is equal to the area enclosed by curve HF and straight line HF. As long as point C is located on AB parallel to HF, moving point C arbitrarily satisfies the area equality requirement. From a design perspective, point C cannot be too close to point A because this will result in too large a stiffness before yielding and cannot truly reflect the load-slip response characteristics of the shear connector. Similarly, point C cannot be too close to point B because when it is too close to point B, the shear stiffness after yielding approaches 0, which does not conform to the actual situation. Therefore, take the midpoint C of AB as a compromise treatment, which not only ensures that the stiffness before yielding is not too large but also ensures that the stiffness after yielding is not too small and distorted. Taking point C as the decomposition point, the HC segment is the first broken line segment and the CF segment is the second broken line segment. Let the position of point C on the s-axis be s y , then [s h , s y range can be regarded as the stage before the shear connector yields, that is, the first broken line segment, with a larger slope, that is, a larger stiffness. [s y , s uThe range can be regarded as the post-yield stage of the shear connector, that is, the second broken line segment, with a smaller slope, that is, a smaller stiffness.

[0127] Step S2000: Obtain the bilinear models of the first broken line segment and the second broken line segment.

[0128] Based on Step S1000, the bilinear models of the first broken line segment and the second broken line segment can be expressed by Equation (11), including:

[0129] (11)

[0130] Where, represents the bilinear model fitted for the curve segment; represents the shear stiffness before the shear connector yields, that is, the shear stiffness during the serviceability limit state (kN / mm), ; represents the shear stiffness after the shear connector yields (kN / mm), ; represents the slip (mm) when the shear connector yields; represents the shear load (kN) when the shear connector yields.

[0131] Based on the above analysis of point C in the figure, to solve the position of point C, it is necessary to first solve the positions of points A and B.

[0132] Step S3000: Based on the principle of equal area of energy balance and the bilinear model, calculate the ordinate of the mathematical yield point when and the abscissa of the mathematical yield point when in the bilinear model.

[0133] Based on energy balance, the relationship of equal area can be expressed as:

[0134] (12)

[0135] Where, represents the area difference between the idealized two-segment broken line bilinear model and the fitted actual load-slip curve, represents the fitted actual load-slip curve.

[0136] Substitute Equation and Equation (11) into Equation (12), then the formula (13) for calculating the ordinate P A of point A and the abscissa of point B can be obtained, which can be expressed as:

[0137] (13)

[0138] Among them, P A represents the ordinate of the mathematical yield point in the bilinear model when ; represents the abscissa of the mathematical yield point in the bilinear model when . Then, in Figure 7 , s A represents the abscissa of the mathematical yield point in the bilinear model when ; represents the ordinate of the mathematical yield point in the bilinear model when .

[0139] Then, from formula (13), the solutions of P A and can be obtained:

[0140] (14)

[0141] Step S4000: Based on the ordinate of the mathematical yield point when and the abscissa of the mathematical yield point when , calculate the abscissa and ordinate of the turning point between the first broken line segment and the second broken line segment.

[0142] Fully considering the stiffness change before and after yielding, select the compromise midpoint C as the ideal turning point. The midpoint C(s y , P y ) can be deduced from the calculation results of equation (14):

[0143] (15).

[0144] Step S5000: Based on the abscissa and ordinate of the turning point between the first broken line segment and the second broken line segment, calculate the shear stiffness before yielding and the shear stiffness after yielding of the curve segment.

[0145] Based on formula (15), there is:

[0146] (16)

[0147] Among them, represents the shear load change of the fitting curve segment, represents the load-slip change of the fitting curve segment, represents the shape characteristic parameter of the fitting curve; , , .

[0148] In this way, the shear stiffness of each stage of the bolt shear connector with a reserved hole is obtained.

[0149] In one embodiment of the present application, a computer-readable storage medium is provided. A program is stored on the storage medium, and the stored program includes methods that can be loaded and processed by a processor in any of the above embodiments.

[0150] Those skilled in the art can understand that all or part of the functions of the above methods can be implemented in a hardware manner or in a computer program manner. When all or part of the functions in the above embodiments are implemented in a computer program manner, the program can be stored in a computer-readable storage medium. The storage medium may include: read-only memory, random access memory, magnetic disk, optical disk, hard disk, etc. The above functions are implemented by a computer executing the program. For example, the program is stored in the memory of the device, and when the processor executes the program in the memory, all or part of the above functions can be implemented. In addition, when all or part of the functions in the above embodiments are implemented in a computer program manner, the program can also be stored in a storage medium such as a server, another computer, magnetic disk, optical disk, flash drive or mobile hard disk, downloaded or copied and saved to the memory of the local device, or the system of the local device is updated. When the processor executes the program in the memory, all or part of the functions in the above embodiments can be implemented.

[0151] The above uses specific examples to elaborate on the present invention, which is only used to help understand the present invention and is not intended to limit the present invention. For those skilled in the technical field to which the present invention belongs, based on the idea of the present invention, several simple deductions, deformations or substitutions can also be made.

Claims

1. A method for determining the shear stiffness of a shear connector of a bolt with a reserved hole, characterized in that, Including: Obtaining multiple load-slip curves of the bolt shear connectors with reserved holes based on test data; Dividing each load-slip curve into a friction section, a slip section, and a curve section, and respectively determining the shear stiffness of the friction section, the slip section, and the curve section; wherein, the friction section is formed by friction force resisting shear load and is linear; the slip section consists of a nearly horizontal line formed by slip occurring after the friction force fails; the curve section is formed by the interaction between the bolt and the concrete to resist shear load and is non-linear; For the curved segment, the shear stiffness is solved based on the load-slip curve corresponding to the curve fitting formula ; where P q represents the shear load of the curved segment, P qu represents the maximum shear load of the curved segment, P h represents the shear load corresponding to the end of the slip segment, s represents the relative slip between the concrete slab and the steel beam, s h represents the relative slip corresponding to the end of the slip segment, represents the fitting curve parameter, and e represents the base of the natural logarithm; Among them, the method for determining the fitting curve parameters includes: Initial values of preset fitting curve parameters ; Calculate the average value of the maximum shear loads of all curve segments in the multiple load-slip curves, and use this average value of the maximum shear load as the maximum shear load P of the curve segment qu ; Calculate the average value of the maximum slips of all curve segments in the multiple load-slip curves, and use this average value of the maximum slip as the maximum load slip s of the curve segment u ; Calculate the area enclosed by each curve segment and the segment on the s-axis from h,n , s u,n as the first area, where n represents the index of the load-slip curve; among them, s h,n represents the minimum load slip of the curve segment of the nth load-slip curve, and s u,n represents the maximum load slip of the curve segment of the nth load-slip curve; Calculation formula The area enclosed by the curve where it is located and the section [[s h , s u on the s-axis is taken as the second area; Calculating the absolute value of the difference between the second area and each first area; Calculating the energy error based on each of the absolute values; Based on iterative solution of linear programming, the solution that minimizes the energy error is used as the fitting curve parameter value.

2. The method for determining the shear stiffness of the bolt shear connector with a reserved hole as claimed in claim 1, characterized in that, Calculate the average value of the maximum shear loads of all curve segments in the multiple load-slip curves, and use this average value of the maximum shear load as the maximum shear load P of the curve segment qu , Including: Among them, P qu,n represents the maximum shear load of the curve segment of the nth load-slip curve, N represents the total number of load-slip curves, and 1 ≤ n ≤ N; Calculating the average value of the maximum slips of all curve segments in the multiple load-slip curves, and taking the average value of the maximum slips as the maximum load slip s of the curve segment u , including: ； The calculating the absolute value of the difference between the second area and each first area includes: Wherein, represents the absolute value corresponding to the nth load-slip curve, represents the second area, represents the first area corresponding to the nth load-slip curve.

3. The method for determining the shear stiffness of the bolt shear connector with a reserved hole according to claim 1, characterized in that The calculating the energy error based on each of the absolute values includes: where E represents the energy error, represents the absolute value corresponding to the n-th load-slip curve, n represents the index of the load-slip curve, N represents the total number of load-slip curves, and 1 ≤ n ≤ N.

4. The method for determining the shear stiffness of the bolt shear connector with a reserved hole as claimed in claim 1, wherein For the maximum shear load of the friction section, it is calculated based on the average value of the maximum shear loads of the friction sections of all load-slip curves; for the maximum load slip of the friction section, it is calculated based on the average value of the maximum load slips of the friction sections of all load-slip curves; based on the maximum shear load and the maximum load slip of the friction section, the shear stiffness of the friction section is calculated.

5. The method for determining the shear stiffness of the bolt shear connector with a reserved hole as claimed in claim 1, wherein For the maximum shear load of the slip section, it is calculated based on the average value of the maximum shear loads of the slip sections of all load-slip curves; for the maximum load slip of the slip section, it is calculated based on the average value of the maximum load slips of the slip sections of all load-slip curves; based on the maximum shear load and the maximum load slip of the slip section, the shear stiffness of the slip section is calculated.

6. The method for determining the shear stiffness of the bolt shear connector with a reserved hole according to claim 2, characterized in that, For the curve segment, based on the curve fitting formula Solve the shear stiffness according to the corresponding load-slip curve, including: Dividing the curve section into a first broken line segment before the shear connector yields and a second broken line segment after yielding, wherein the slope of the first broken line segment is greater than the slope of the second broken line segment; Obtaining the bilinear models of the first broken line segment and the second broken line segment; Based on the principle of equal area of energy balance and the bilinear model, calculate the ordinate of the mathematical yield point in the bilinear model when and the abscissa of the mathematical yield point when ; wherein, represents the shear stiffness before the shear connector yields, represents the shear stiffness after the shear connector yields; Based on the ordinate of the mathematical yield point when and the abscissa of the mathematical yield point when calculate the abscissa and ordinate of the turning point between the first broken line segment and the second broken line segment; wherein, the turning point between the first broken line segment and the second broken line segment is when the shear connector yields, the abscissa represents the slip, and the ordinate represents the shear load; Based on the abscissa and ordinate of the turning point between the first broken line segment and the second broken line segment, calculating the shear stiffness before yielding and the shear stiffness after yielding of the curve section.

7. The method for determining the shear stiffness of the bolt shear connector with a reserved hole according to claim 6, characterized in that, The obtaining the bilinear models of the first broken line segment and the second broken line segment includes: Among them, represents the bilinear model for curve segment fitting, , , represents the slip when the shear connector yields, represents the shear load when the shear connector yields, represents the maximum shear load of the curve segment.

8. The method for determining the shear stiffness of the bolt shear connector with a reserved hole according to claim 7, characterized in that, Based on the area equality principle of energy balance and the bilinear model, calculate the ordinate of the mathematical yield point in the bilinear model when and the abscissa of the mathematical yield point when , including: Among them, P A represents the ordinate of the mathematical yield point when in the bilinear model, and represents the abscissa of the mathematical yield point when in the bilinear model.

9. The method for determining the shear stiffness of the bolt shear connector with a reserved hole according to claim 8, characterized in that, Based on the ordinate of the mathematical yield point at and the abscissa of the mathematical yield point at calculate the abscissa and ordinate of the turning point between the first broken line segment and the second broken line segment, including: 。 10. The method for determining the shear stiffness of the bolt shear connector with a reserved hole according to claim 9, characterized in that, The calculating the shear stiffness before yielding and the shear stiffness after yielding of the curve section based on the abscissa and ordinate of the turning point between the first broken line segment and the second broken line segment includes: Among them, represents the shear load change amount of the fitting curve segment, represents the load-slip change amount of the fitting curve segment, represents the shape characteristic parameter of the fitting curve; , , .

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