Calculation method of interfacial bond slip of reinforced concrete components under cyclic loading

Abstract

The present invention relates to a method for calculating the interfacial bond slip of rebar-anchored concrete components under cyclic loads, and belongs to the technical field of engineering structure reinforcement and reconstruction. The method comprises three parts, namely, analysis of rebar bond stress, correction of bond slip calculation under static loads, and calculation of bond slip under cyclic loads. The present invention takes into account the influence of the main factors of rebar bonding, such as the rebar diameter and the rebar anchoring depth, and accurately describes the influence of the key factors affecting the pull-out bearing capacity of rebar-anchored components, such as the rebar diameter and the rebar anchoring depth, on the bond force, thereby providing a theoretical basis for calculating the internal force and deformation of rebar-anchored components and improving the design of rebar reinforcement and reconstruction projects.

Description

Technical Field

[0001] The invention relates to a calculation method for the interface bond slip of a reinforced concrete component under cyclic load, and belongs to the technical field of engineering structure reinforcement and reconstruction. Background Art

[0002] my country's construction industry is currently in a phase where both new construction and maintenance are equally important. Numerous buildings constructed in the last century will face extensive repair, reinforcement, and renovation tasks over their service lives. Anchor bolting technology relies on the bond between rebar and adhesive, and between adhesive and concrete, to transfer loads. Holes of a certain diameter and depth are drilled into the original concrete substrate. Anchor bolting adhesive is injected into the holes, and rebar is then embedded into the original component. After the adhesive in the overlapped section of the anchor bolts cures, stirrups are added to the newly added component, and concrete is poured. This allows the new and existing concrete components to bear the load as a whole, making it ideal for reinforcement, renovation, and maintenance of various buildings.

[0003] Good bond-slip properties ensure effective force and deformation transfer between embedded rebar and concrete. They are the foundation and prerequisite for the coordinated operation of rebar and concrete. Stress transfer occurs through the mutual adhesion between the different materials, ensuring they function as a single unit and withstand external loads. Extensive research has been conducted on the bond-slip properties between concrete and rebar in cast-in-place components with rebar directly embedded in concrete, and corresponding technical specifications have been issued. However, due to the presence of adhesive-rebar and adhesive-concrete interfaces in cast-in-place components, the bond-slip calculation principles for cast-in-place components are not fully applicable. Furthermore, structures such as bridges and industrial plants are constantly subjected to multiple, high-amplitude cyclic loading during operation, making them susceptible to sudden fatigue failure. Compared to extensive engineering practice, research on the fatigue failure mechanisms of rebar components lags behind. my country's "Code for Design of Reinforcement of Concrete Structures" (GB50367-2013) also lacks theoretical calculations for fatigue failure in rebar components.

[0004] Structures such as bridges and industrial plants are constantly subjected to multiple and large-amplitude cyclic loads during use. Although rebar planting technology is a reinforcement and renovation technology with broad application prospects, there is little research on its working performance in such buildings.

[0005] In the prior art:

[0006] (1) The "Standard for Test Methods of Physical and Mechanical Properties of Concrete" (GB / T 50081-2019) provides a calculation method for the bond strength (bond strength) between concrete and steel bars in cast-in-place components, as shown below:

[0007] The bond strength between concrete and steel bars should be calculated according to the following formula:

[0008] (Formula 1)

[0009] (Equation 2)

[0010] Where, is the bond strength between concrete and steel bars (MPa); is the load when the slip deformation is 0.01 mm (N); is the load when the slip deformation is 0.05 mm (N); is the load when the slip deformation is 0.10 mm (N); is the surface area of steel bars embedded in concrete (mm 2 ); is the nominal diameter of the steel bar; is the embedded length of the steel bar.

[0011] (2) The design value of anchor bearing capacity for planted reinforcement in my country's Code for Design of Reinforcement of Concrete Structures (GB50367-2013) is calculated based on the tensile bearing capacity of a single planted reinforcement under static load and unidirectional pullout, as shown below:

[0012] The design value of the anchorage depth and tensile bearing capacity of a single rebar should be calculated according to the following formula:

[0013] (Formula 3)

[0014] (Formula 4)

[0015] Where, is the design value of the tensile bearing capacity of the embedded steel bar; is the design value of tensile strength of the steel bar used for planting reinforcement; is the cross-sectional area of the steel bar; is the design value of the anchoring depth of the rebar; is the basic anchoring depth of the rebar; In order to consider the influence of various factors on the tensile bearing capacity of the planted reinforcement, the correction factor of the anchoring depth needs to be increased; It is a correction factor to take into account the displacement ductility coefficient. When the concrete strength is not higher than C30, for the first and second type sites in the 6 degree zone and the 7 degree zone, 1.10; for the third and fourth types of sites in the 7-degree zone and the 8-degree zone, When the concrete strength grade is higher than C30, take The basic anchorage depth is 1.0. For details on the value of basic anchorage depth, refer to the Code for Design of Reinforcement of Concrete Structures (GB50367-2013).

[0016] (3) Shu Ruibin, Zhang Jianrong, Zhang Chun. Analysis of bond-slip stress mechanism of free-pullout anchoring system [J]. Structural Engineer, 2008, 05: 64-70.

[0017] Based on the steel sleeve method and concrete block restrained pullout tests, the paper establishes a constitutive relationship for the bond-slip behavior of rebar in a rebar-anchored system under static pullout. The formula presented here uses statistically derived proportional coefficients from the test results, presented in a mathematical analysis format. However, it fails to account for the role of parameters influencing rebar bond. Furthermore, the paper lacks a detailed description of the interfacial bond-slip behavior of rebar-anchored concrete components under cyclic loading.

[0018] (4) For details on the pull-out bearing capacity test of planted rebar, see: Yan Xikang, Liang Linxiao, Liang Chen. Slip performance of planted rebar anchor bond under fatigue load [J]. Chinese Journal of Civil and Environmental Engineering, 2020, 42(02): 149-156.

[0019] The paper describes the experimental phenomena and uses numerical analysis to fit some calculation formulas based on the experimental data, but does not conduct theoretical analysis on the parameters that affect the bonding of rebars, such as the rebar diameter and the rebar anchoring depth. 、 Only possible influencing factors are given, and no theoretical calculation method is given. Due to the limited number of specimens, the accuracy of the parameter values in the formula needs to be optimized.

[0020] Compared with cast-in-place components where steel bars are directly embedded in concrete, the bonding force in rebar-embedded components is no longer between the steel bars and concrete, but between the steel bars and the rebar-embedded adhesive, and between the rebar-embedded adhesive and concrete. The adhesive-rebar and adhesive-mixed bonding interfaces are added, and the load transfer path is changed. The bond-slip calculation principles of cast-in-place components are not fully applicable to rebar-embedded components.

[0021] The "Code for Design of Reinforced Concrete Structures" (GB50367-2013) provides a macroscopic formula for the tensile bearing capacity of anchored rebar under static, unidirectional pullout. The key to transmitting tensile bearing capacity lies in reliable bond strength. However, the code does not provide specific formulas for the main factors influencing bond strength or how to describe bond-slip performance.

[0022] The bond strength calculation results in existing literature are obtained by fitting experimental data using numerical analysis, without theoretical analysis of the main factors affecting the bond of rebars, such as rebar diameter and rebar anchoring depth; some parameters only provide possible influencing factors, without providing theoretical calculation methods.

[0023] As a key factor in ensuring the stability and safety of rebar structures, the research on the bonding and anchoring mechanism of rebar is still insufficient. It is necessary to propose a calculation method for the interfacial bond slip of rebar-cemented concrete components under cyclic loads to provide a theoretical basis for engineering design. Summary of the Invention

[0024] In response to the above-mentioned defects of the above-mentioned prior art, the present invention proposes a method for calculating the interfacial bond slip of rebar-anchored concrete components under cyclic loads, so as to accurately describe the influence of key influencing factors of the pull-out bearing capacity of rebar-anchored components, such as the rebar diameter and the rebar anchoring depth, on the bond strength, thereby providing a theoretical basis for calculating the internal force and deformation of rebar-anchored components and improving the design of rebar reinforcement and renovation projects.

[0025] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0026] The invention discloses a method for calculating the interfacial bond slip of planted reinforced concrete components under cyclic loads. The method comprises three parts: analysis of planted reinforcement bond stress, correction of bond slip calculation under static loads, and calculation of bond slip under cyclic loads.

[0027] Furthermore, the anchor bonding stress analysis specifically includes:

[0028] Set up the force analysis model of the rebar interface, take a microelement with a length of dx, and from the force balance we can know:

[0029] (Formula 5)

[0030] Where, is the diameter of the rebar; is the adhesive stress at the rubber reinforcement interface; The length of the microelement for force analysis; The diameter of the hole for embedding reinforcement; is the adhesive-mixed interface bonding stress; The rebar is subjected to tensile stress;

[0031] visible 、 There is a certain proportional relationship between them, so only the adhesive stress at the rubber reinforcement interface is Perform analysis and set the bonding stress = .

[0032] Furthermore, the calculation and correction of the bond slip under static load includes the following steps:

[0033] Assume that the bond-slip constitutive relation is:

[0034] (Equation 6)

[0035] Where, is the bonding stress; is the slip value; is the ultimate bonding strength; is the limit slip value; is the slip value in the elastic stage; is the residual slip value;

[0036] The coefficients of the bond-slip model under static load are modified, the anchorage depth is used as a parameter to represent the residual slip, and a three-stage linear function is used to represent the modified model.

[0037] Furthermore, the correction model is represented by a three-stage linear function, specifically:

[0038] Limiting bond stress of interfacial failure caused by pulling out anchor bars under static load for:

[0039] (Equation 7)

[0040] Where, is the ultimate bonding stress under static action; It is the bonding shear strength of the rebar rubber sleeve;

[0041] Initial slip bond stress Use the general calculation formula:

[0042] (Equation 8)

[0043] (Equation 9)

[0044] Where, is the initial slip bond stress; is the initial slip bond strength proportional coefficient;

[0045] Residual bond stress Use the general calculation formula:

[0046] (Equation 10)

[0047] (Equation 11)

[0048] Where, is the residual bonding stress; is the proportional coefficient of residual bond strength;

[0049] Initial slip bond stress , ultimate bond stress , residual bond stress The corresponding slip values are 、 、 ; The slip value is linearly related to the depth of the rebar, and the critical rebar depth is Calculated as follows:

[0050] (Equation 12)

[0051] Where, is the critical rebar planting depth; is the yield strength of the rebar;

[0052] Limit slip value Calculated based on the critical rebar planting depth:

[0053] (Equation 13)

[0054] Where, is the limit slip value;

[0055] Initial slip value and The relationship is:

[0056] (Equation 14)

[0057] Where, is the initial slip value;

[0058] Convert to The relationship is expressed as:

[0059] (Equation 15)

[0060] Residual slip value and The relationship is:

[0061] (Equation 16)

[0062] Where, is the residual slip value;

[0063] Convert to The relationship is expressed as:

[0064] (Equation 17)

[0065] The bond-slip relationship curve is defined as a three-stage model, which is divided into elastic stage, slip stage and failure stage. Each stage corresponds to a linear function, that is, a three-stage linear function.

[0066] The eigenvalues to be determined 、 、 、 、 、 Substituting the three-stage linear function, the bond-slip relationship is obtained.

[0067] Furthermore, the determined eigenvalues 、 、 、 、 、 Substituting the three-stage linear function, we get the bond-slip relationship, which is:

[0068] Elasticity stage:

[0069] (Equation 18)

[0070] Slip phase:

[0071] (Equation 19)

[0072] Destruction phase:

[0073] (Equation 20)

[0074] Where, 、 The diameter of the rebar , anchoring depth of rebar The correlation coefficient, It decreases with the increase of the diameter of the rebar and the anchoring depth. It increases with the increase of the diameter of the rebar and the anchoring depth.

[0075] Furthermore, the 、 They are expressed by the following formulas:

[0076] (Equation 21)

[0077] (Equation 22)

[0078] Where, is the diameter of the rebar, is the anchoring depth of the rebar;

[0079] The bond-slip relationship between the rubber reinforcement interface under static load is obtained as follows:

[0080] (Equation 23).

[0081] Furthermore, the bond slip calculation under the cyclic load is as follows:

[0082] because The distribution along the length of the rebar is irregular. When establishing the bond-slip constitutive relationship under cyclic loading, the average bond stress is used. The bond stress-slip curve follows the same law as the three-stage model. Three characteristic points can be determined from the distribution of the bond-slip relationship curve: the initial slip bond stress under cyclic loading, , initial slip value under cyclic loading ; Ultimate bond stress under cyclic loading , the limit slip value under cyclic loading ; Residual bond stress under cyclic loading , residual slip value under cyclic loading ;

[0083] Limiting bond stress of interfacial failure caused by pulling out anchor bars under static load As shown in (Equation 7);

[0084] Considering the decrease in bond strength caused by cyclic loading, the ultimate bond strength proportional coefficient is introduced ,

[0085] (Equation 24)

[0086] Where, is the ultimate bond strength proportional coefficient; is the ultimate bonding stress under static action; is the ultimate bond stress under cyclic loading;

[0087] With the diameter of the embedded steel bar There is a linear relationship. By analyzing the test data, we can get:

[0088] (Equation 25)

[0089] Obtain the ultimate bond stress of the rebar under cyclic loading for:

[0090] (Equation 26)

[0091] Initial slip bond stress under cyclic loading The calculation formula is:

[0092] (Equation 27)

[0093] (Equation 28)

[0094] Where, is the initial slip bond strength proportional coefficient;

[0095] Residual bond stress under cyclic loading Use the general calculation formula:

[0096] (Equation 29)

[0097] (Equation 30)

[0098] Where, is the proportional coefficient of residual bond strength.

[0099] Furthermore, in (Formula 26), (Formula 27) and (Formula 29), 、 、 The corresponding slip values under cyclic load are 、 、 ;

[0100] Limit slip value under cyclic loading Calculated based on the critical rebar planting depth:

[0101] (Equation 31)

[0102] Initial slip value under cyclic loading and The relationship is:

[0103] (Equation 32)

[0104] Convert to The relationship is expressed as:

[0105] (Equation 33)

[0106] Residual slip value under cyclic loading and The relationship is:

[0107] (Equation 34)

[0108] Convert to The relationship is expressed as:

[0109] (Equation 35)

[0110] Substituting the eigenvalues determined by (Equation 27)-(Equation 35) above into the three-stage linear function, the bond-slip relationship is obtained.

[0111] Furthermore, the eigenvalues determined by (Equation 27)-(Equation 35) above are substituted into the three-stage linear function, and the bond-slip relationship obtained is:

[0112] Elasticity stage:

[0113] (Equation 36)

[0114] Slip phase:

[0115] (Equation 37)

[0116] Destruction phase:

[0117] (Equation 38)

[0118] 、 is the correlation coefficient with the cyclic load;

[0119] (Equation 39)

[0120] (Equation 40)

[0121] The bond-slip relationship between the rubber-reinforced bar interface under cyclic loading is obtained:

[0122] (Equation 41)

[0123] After adopting the above technical solution, the present invention has the following beneficial effects compared with the prior art:

[0124] The present invention proposes a calculation method for the interfacial bond slip of a reinforced concrete component under cyclic load, which takes into account the influence of main factors of rebar bonding, such as rebar diameter and rebar anchoring depth.

[0125] According to the bond-slip relationship obtained in the previous test, the characteristic value points of the elastic stage, slip stage and failure stage were determined: initial slip bond stress , ultimate bond stress , residual bond stress , initial slip value , limit slip value , residual slip value , a three-stage calculation model is given, and the bond-slip calculation formula of the rebar in the reinforced concrete member under static load is revised.

[0126] Considering the decrease in bond strength caused by cyclic loading, based on the calculation formula of static pull-out bond slip under cyclic loading, the characteristic value points of the elastic stage, slip stage and failure stage under cyclic loading are determined: initial slip bond stress under cyclic loading , Ultimate bond stress under cyclic loading , residual bond stress under cyclic loading , initial slip value under cyclic load , limit slip value under cyclic load , residual slip value under cyclic loading A formula for calculating the interfacial bond slip of rebar-anchored concrete components under cyclic loading is presented, which can be used to calculate the bond stress during the entire tensile process of the rebar. This provides a theoretical basis for calculating the internal forces and deformations of rebar-anchored components and improves the design of rebar reinforcement and renovation projects. BRIEF DESCRIPTION OF THE DRAWINGS

[0127] Figure 1 This is the stress analysis model of the rebar planting interface of the present invention;

[0128] Figure 2 It is the three-stage bond-slip model of the present invention. DETAILED DESCRIPTION

[0129] The following is combined with Figure 1-2 The present invention will be further described in detail with specific implementations to facilitate a clear understanding of the present invention, but they do not constitute a limitation to the present invention.

[0130] In the description of the present invention, it should be noted that the terms "upper", "lower", "front", "back", "left", "right", "vertical", "inside", "outside", etc., indicating directions or positional relationships, are based on the directions or positional relationships shown in the accompanying drawings. They are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific direction, be constructed and operated in a specific direction. Therefore, they cannot be understood as limiting the present invention.

[0131] In the description of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "mounted," "connected," and "connected" should be understood broadly. For example, they may refer to fixed, detachable, or integral connections; mechanical or electrical connections; and direct or indirect connections through an intermediary. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on the specific circumstances.

[0132] The present embodiment provides a method for calculating the interfacial bond slip of rebar-anchored concrete components under cyclic loads. The method comprises three parts: analysis of rebar bond stress, correction of bond slip calculation under static loads, and calculation of bond slip under cyclic loads.

[0133] (1) Analysis of bonding stress of rebar.

[0134] Analysis of the rebar pull-out test shows that, under the condition of consistent rebar diameter, the bond stress at failure decreases as the rebar depth increases. As the rebar anchoring depth increases, the load will be evenly shared by the rebar within the entire anchoring depth range. In comparison, the bond stress per unit depth is smaller than that of specimens with smaller rebar depths, which helps to avoid local failure. At the initial loading stage, the stress peaks all appear close to the loading end, and the difference between the peaks and the average values is large, resulting in concrete cone failure at the peak stress. As loading continues, the larger value appears at the free end of the rebar. For rebars with the same depth, the larger the diameter, the closer the stress peaks in the later loading stage are to the average bond stress, and the more uniform the bond stress distribution of the rebar.

[0135] Analysis of the stresses on rebar-supported tension members reveals that, for a given anchor depth and drill hole diameter, the bond stress between the various materials is the key factor determining the failure morphology. During initial slip, the bond stress at the rubber-rebar interface has not yet been fully developed. Summarizing the failure characteristics of rebar-supported specimens, it is clear that, when the rebar reaches a certain depth, the bond stress at the rubber-rebar interface is the primary factor to consider in preventing specimen failure. Figure 1 For the force analysis model of the rebar interface, take a microelement with a length of dx. From the force balance, we can know that:

[0136] (Formula 5)

[0137] Where, is the diameter of the rebar; is the adhesive stress at the rubber reinforcement interface; The length of the microelement for force analysis; The diameter of the hole for embedding reinforcement; is the adhesive-mixed interface bonding stress; The rebar is subjected to tensile stress.

[0138] visible 、 There is a certain proportional relationship between them, so only the adhesive stress at the rubber reinforcement interface is Analyze, that is, the following .

[0139] (2) Correction of bond slip calculation under static load.

[0140] The existing literature "Analysis of Bond-Slip Stress Mechanism of Free Pullout Rebar System" gives the bond-slip constitutive relation as follows:

[0141] (Equation 6)

[0142] Where, is the bonding stress; is the slip value; is the ultimate bonding strength; is the limit slip value; is the slip value in the elastic stage; is the residual slip value.

[0143] Comparison with the experimental results revealed that the elastic stage coefficient in (Equation 6) was too high, resulting in high bond stress in the model. Furthermore, the original model uniformly set the residual slip for all specimens to 5 mm, while the actual measured residual slip value was not constant and varied with the anchorage depth. The coefficients of the bond-slip model under static load were modified, with the anchorage depth used as a parameter to represent the residual slip. A three-stage linear function was used to represent the modified model:

[0144] Limiting bond stress of interfacial failure caused by pulling out anchor bars under static load for:

[0145] (Equation 7)

[0146] Where, is the ultimate bonding stress under static action; It is the bonding shear strength of the rebar-embedded rubber sleeve.

[0147] Initial slip bond stress Use the general calculation formula:

[0148] (Equation 8)

[0149] (Equation 9)

[0150] Where, is the initial slip bond stress; is the initial slip bond strength proportional coefficient.

[0151] Residual bond stress Use the general calculation formula:

[0152] (Equation 10)

[0153] (Equation 11)

[0154] Where, is the residual bonding stress; is the proportional coefficient of residual bond strength.

[0155] Initial slip bond stress , ultimate bond stress , residual bond stress The corresponding slip values are 、 、 The slip value is linearly related to the depth of the rebar. The critical rebar depth is Calculated as follows:

[0156] (Equation 12)

[0157] Where, is the critical rebar planting depth; is the yield strength of the rebar.

[0158] Limit slip value It can be calculated based on the critical rebar planting depth:

[0159] (Equation 13)

[0160] Where, is the limit slip value.

[0161] Initial slip value and The relationship is:

[0162] (Equation 14)

[0163] Where, is the initial slip value.

[0164] Convert to The relationship is expressed as:

[0165] (Equation 15)

[0166] Residual slip value and The relationship is:

[0167] (Equation 16)

[0168] Where, is the residual slip value.

[0169] Convert to The relationship is expressed as:

[0170] (Equation 17)

[0171] The bond-slip relationship curve is defined as Figure 2 The three-stage model is divided into elastic stage, sliding stage and failure stage.

[0172] The above determined eigenvalues 、 、 、 、 、 Substituting the three-stage linear function, the bond-slip relationship is obtained.

[0173] Elasticity stage:

[0174] (Equation 18)

[0175] Slip phase:

[0176] (Equation 19)

[0177] Destruction phase:

[0178] (Equation 20)

[0179] Where, 、 The diameter of the rebar , anchoring depth of rebar The correlation coefficient, It decreases with the increase of the diameter of the rebar and the anchoring depth. It increases with the increase of the diameter of the embedded steel bar and the anchoring depth, and is expressed by the following formulas respectively.

[0180] (Equation 21)

[0181] (Equation 22)

[0182] Where, is the diameter of the rebar, The anchoring depth of the rebar.

[0183] The bond-slip relationship between the rubber-reinforced bar interface under static load is obtained (33).

[0184] (Equation 23)

[0185] (3) Calculation of bond slip under cyclic loading.

[0186] because The distribution along the length of the rebar is irregular. When establishing the bond-slip constitutive relationship under cyclic loading, the average bond stress is used. The bond stress-slip curve follows the same law as the three-stage model. Three characteristic points can be determined from the curve distribution: the initial slip bond stress under cyclic loading, , initial slip value under cyclic loading ; Ultimate bond stress under cyclic loading , the limit slip value under cyclic loading ; Residual bond stress under cyclic loading , residual slip value under cyclic loading .

[0187] Limiting bond stress of interfacial failure caused by pulling out anchor bars under static load for:

[0188] (Equation 7)

[0189] Where, is the ultimate bonding stress under static action; It is the bonding shear strength of the rebar-embedded rubber sleeve.

[0190] Considering the decrease in bond strength caused by cyclic loading, the ultimate bond strength proportional coefficient is introduced ,

[0191] (Equation 24)

[0192] Where, is the ultimate bond strength proportional coefficient; is the ultimate bonding stress under static action; is the ultimate bond stress under cyclic loading.

[0193] With the diameter of the embedded steel bar There is a linear relationship. By analyzing the test data, we can get:

[0194] (Equation 25)

[0195] Similarly, the initial slip bond strength proportional coefficient and the residual bond strength proportional coefficient can be obtained.

[0196] Obtain the ultimate bond stress of the rebar under cyclic loading for:

[0197] (Equation 26)

[0198] Initial slip bond stress under cyclic loading The calculation formula is:

[0199] (Equation 27)

[0200] (Equation 28)

[0201] Where, is the initial slip bond strength proportional coefficient.

[0202] Residual bond stress under cyclic loading Use the general calculation formula:

[0203] (Equation 29)

[0204] (Equation 30)

[0205] Where, is the proportional coefficient of residual bond strength.

[0206] and 、 、 The corresponding slip values under cyclic load are 、 、 .

[0207] Limit slip value under cyclic loading It can be calculated based on the critical rebar planting depth:

[0208] (Equation 31)

[0209] Initial slip value under cyclic loading and The relationship is:

[0210] (Equation 32)

[0211] Convert to The relationship is expressed as:

[0212] (Equation 33)

[0213] Residual slip value under cyclic loading and The relationship is:

[0214] (Equation 34)

[0215] Convert to The relationship is expressed as:

[0216] (Equation 35)

[0217] Substituting the above-determined eigenvalues into the three-stage linear function, the bond-slip relationship is obtained.

[0218] Elasticity stage:

[0219] (Equation 36)

[0220] Slip phase:

[0221] (Equation 37)

[0222] Destruction phase:

[0223] (Equation 38)

[0224] 、 is the correlation coefficient under cyclic loading.

[0225] (Equation 39)

[0226] (Equation 40)

[0227] The bond-slip relationship between the rubber-reinforced bar interface under cyclic loading was obtained.

[0228] (Equation 41)

[0229] The above is merely a preferred embodiment of the present invention and does not constitute any formal limitation on the structure of the present invention. The layout and number of the present invention are not limited to this example and can be optimized according to actual engineering practices. Any modifications, equivalent changes, and decorations to the above embodiment based on the technical principles of the present invention that do not depart from the content of the technical solution of the present invention are still within the scope of the technical solution of the present invention.

Claims

1. The calculation method of the interfacial bond slip of reinforced concrete components under cyclic loading is characterized by: The method for calculating the interfacial bond slip of reinforced concrete components under cyclic loads includes three parts: analysis of rebar bond stress, correction of bond slip calculation under static loads, and calculation of bond slip under cyclic loads. The anchor bonding stress analysis specifically includes: Set up the force analysis model of the rebar interface, take a microelement with a length of dx, and from the force balance we can know: (Formula 5) Where, is the diameter of the rebar; is the adhesive stress at the rubber reinforcement interface; The length of the microelement for force analysis; The diameter of the hole for embedding reinforcement; is the adhesive-mixed interface bonding stress; The rebar is subjected to tensile stress; visible 、 There is a certain proportional relationship between them, so only the adhesive stress at the rubber reinforcement interface is Perform analysis and set the bonding stress = ; The calculation and correction of the bond slip under static load includes the following steps: Assume that the bond-slip constitutive relation is: (Equation 6) Where, is the bonding stress; is the slip value; is the ultimate bonding strength; is the limit slip value; is the slip value in the elastic stage; is the residual slip value; The coefficients of the bond-slip model under static load are modified, the anchorage depth is used as a parameter to represent the residual slip, and a three-stage linear function is used to represent the modified model. The three-stage linear function is used to represent the correction model, specifically: Limiting bond stress of interfacial failure caused by pulling out rebar under static load for: (Equation 7) Where, is the ultimate bonding stress under static action; It is the bonding shear strength of the rebar sleeve; Initial slip bond stress Use the general calculation formula: (Equation 8) (Equation 9) Where, is the initial slip bond stress; is the initial slip bond strength proportional coefficient; Residual bond stress Use the general calculation formula: (Equation 10) (Equation 11) Where, is the residual bonding stress; is the proportional coefficient of residual bond strength; Initial slip bond stress , ultimate bond stress , residual bond stress The corresponding slip values are 、 、 ; The slip value is linearly related to the depth of the rebar, and the critical rebar depth is Calculated as follows: (Equation 12) Where, is the critical rebar planting depth; is the yield strength of the rebar; Limit slip value Calculated based on the critical rebar planting depth: (Equation 13) Where, is the limit slip value; Initial slip value and The relationship is: (Equation 14) Where, is the initial slip value; Convert to The relationship is expressed as: (Equation 15) Residual slip value and The relationship is: (Equation 16) Where, is the residual slip value; Convert to The relationship is expressed as: (Equation 17) The bond-slip relationship curve is defined as a three-stage model, which is divided into elastic stage, slip stage and failure stage. Each stage corresponds to a linear function, that is, a three-stage linear function. The eigenvalues to be determined 、 、 、 、 、 Substituting the three-stage linear function, we obtain the bond-slip relationship; The eigenvalues to be determined 、 、 、 、 、 Substituting the three-stage linear function, we get the bond-slip relationship, which is: Elasticity stage: (Equation 18) Slip phase: (Equation 19) Destruction phase: (Equation 20) Where, 、 The diameter of the embedded steel bar , anchoring depth of rebar The correlation coefficient, It decreases with the increase of the diameter of the rebar and the anchoring depth. It increases with the increase of the diameter of the rebar and the anchoring depth; described 、 They are expressed by the following formulas: (Equation 21) (Equation 22) Where, is the diameter of the rebar, is the anchoring depth of the rebar; The bond-slip relationship between the rubber reinforcement interface under static load is obtained as follows: (Equation 23) The bond slip calculation under the cyclic load is as follows: because The distribution along the length of the rebar is irregular. When establishing the bond-slip constitutive relationship under cyclic loading, the average bond stress is used, and the bond stress-slip curve follows the same law as the three-stage model. Three characteristic points can be determined from the distribution of the bond-slip relationship curve: the initial slip bond stress under cyclic loading, , initial slip value under cyclic loading ; Ultimate bond stress under cyclic loading , the limit slip value under cyclic loading ; Residual bond stress under cyclic loading , residual slip value under cyclic loading ; Limiting bond stress of interfacial failure caused by pulling out rebar under static load As shown in (Equation 7); Considering the decrease in bond strength caused by cyclic loading, the ultimate bond strength proportional coefficient is introduced , (Equation 24) Where, is the ultimate bond strength proportional coefficient; is the ultimate bonding stress under static action; is the ultimate bond stress under cyclic loading; With the diameter of the embedded steel bar There is a linear relationship. By analyzing the test data, we can get: (Equation 25) Obtain the ultimate bond stress of the rebar under cyclic loading for: (Equation 26) Initial slip bond stress under cyclic loading The calculation formula is: (Equation 27) (Equation 28) Where, is the initial slip bond strength proportional coefficient; Residual bond stress under cyclic loading Use the general calculation formula: (Equation 29) (Equation 30) Where, is the proportional coefficient of residual bond strength; In the above (Equation 26), (Equation 27) and (Equation 29), 、 、 The corresponding slip values under cyclic load are 、 、 ; Limit slip value under cyclic loading Calculated based on the critical rebar planting depth: (Equation 31) Initial slip value under cyclic loading and The relationship is: (Equation 32) Convert to The relationship is expressed as: (Equation 33) Residual slip value under cyclic loading and The relationship is: (Equation 34) Convert to The relationship is expressed as: (Equation 35) Substituting the eigenvalues determined by (Equation 27)-(Equation 35) into the three-stage linear function, the bond-slip relationship is obtained; Substituting the eigenvalues determined by (Equation 27)-(Equation 35) into the three-stage linear function, the bond-slip relationship is obtained as follows: Elasticity stage: (Equation 36) Slip phase: (Equation 37) Destruction phase: (Equation 38) 、 is the correlation coefficient with the cyclic load; (Equation 39) (Equation 40) The bond-slip relationship between the rubber-reinforced bar interface under cyclic loading is obtained: (Equation 41).

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