Calculation method for bond-slip relationship between energy-dissipating steel bars and concrete in assembled bridge piers

Abstract

This invention belongs to the field of prefabricated bridges, specifically relating to a calculation method for the bond-slip relationship between energy-dissipating reinforcing bars and concrete in assembled bridge piers. The method includes the following steps: assembling the bridge pier; applying quasi-static loading to the assembled bridge pier; calculating the slip at the loading end of the energy-dissipating reinforcing bars; establishing an initial calculation model for the bond-slip relationship between the energy-dissipating reinforcing bars and concrete; calculating the average bond stress before and after yielding in the initial model based on measured and obtained data, thereby obtaining the final calculation models for the bond-slip relationship between the energy-dissipating reinforcing bars and concrete before and after yielding. This invention can be applied to measuring and calculating the bond-slip relationship between energy-dissipating reinforcing bars and concrete in different assembled bridge piers, and has engineering application value.

Description

Technical Field

[0001] This invention belongs to the field of prefabricated bridges, specifically relating to a method for calculating the bond-slip relationship between energy-consuming steel bars and concrete in assembled bridge piers. Background Technology

[0002] In recent years, with the continuous deepening of the "prefabricated construction" concept, segmental assembled bridge piers have rapidly developed in engineering practice due to their advantages of low environmental impact, high construction efficiency, and prefabrication of components. However, traditional segmental assembled bridge piers, lacking energy-dissipating components within the pier columns, have significantly weaker energy dissipation capacity compared to integral cast-in-place bridge piers. To effectively address this issue, energy-dissipating steel bars are commonly used as built-in energy-dissipating components in engineering practice to improve the overall energy dissipation capacity of the bridge pier, thereby enhancing the seismic performance of the bridge system. Existing research shows that the bond performance between energy-dissipating steel bars and concrete has a significant impact on the seismic performance of the bridge pier as a whole and its local components. The quality of the bond performance directly affects the deformation capacity, ultimate bearing capacity, and failure mode of the assembled bridge pier structural system. Especially under cyclic loading, the degradation of the bond performance between energy-dissipating steel bars and concrete leads to a significant increase in relative slip between them, and even pull-out failure, thus affecting the overall hysteretic energy dissipation performance of the bridge pier. Therefore, the bond-slip relationship between energy-dissipating steel bars and concrete has always been a focus of research both domestically and internationally.

[0003] Currently, most research on the bond-slip relationship between energy-dissipating steel bars and concrete focuses on the level of individual structural members, while research on the bond-slip relationship between energy-dissipating steel bars and concrete in the overall assembled bridge pier is still lacking. Although tests on individual structural members can obtain basic data on the bond performance between steel bars and concrete, this data is obtained under simplified test conditions. It is difficult to fully simulate the complex stress state and boundary conditions in actual bridge structures, so the results of tests on individual structural members may not be directly applicable to the analysis of the overall bridge structure. In overall tests of assembled bridge piers, since energy-dissipating steel bars are usually embedded inside the pier, it is difficult to directly measure the bond stress and relative slip between the energy-dissipating steel bars and concrete. Summary of the Invention

[0004] The purpose of this invention is to provide a method for calculating the bond-slip relationship between energy-consuming steel bars and concrete in assembled bridge piers.

[0005] The technical solution to achieve the purpose of this invention is: a method for calculating the bond-slip relationship between energy-dissipating steel bars and concrete in assembled bridge piers, comprising the following steps:

[0006] Step (1): Assemble the pier: Assemble the cap beam (1), pier column (2) and abutment (3). The energy-dissipating steel bars (4) arranged at the joint between the pier column (2) and the cap beam (1) or abutment (3) are fitted with steel strain gauges (8) and formed into a length of l by an outer PVC sleeve (5). un The unbonded section has an extended steel rod (6) on both sides of the end of the pier (2) for fixing the pressure rod displacement gauge (7). The position of the extended steel rod (6) is set according to the range of the pressure rod displacement gauge (7).

[0007] Step (2): Perform quasi-static loading on the assembled pier: read the tensile h1 and compression h2 of the compression bar displacement gauge (7) during the loading process, the distances L1 and L2 from the two compression bar displacement gauges (7) to the center of the pier column, and measure the strain ε of each energy-dissipating steel bar through the steel strain gauge (8). s ;

[0008] Step (3): Calculate the slip S at the loading end of the energy-dissipating steel bar. l : Calculate the joint rotation angle θ based on the data measured by the column displacement gauge (7) in step (2), and then calculate the distance L from the energy dissipation steel bar to the center of the pier column based on the joint rotation angle θ and the distance L from the energy dissipation steel bar to the center of the pier column. ED The total elongation Δ of the energy-consuming steel bars was calculated. ti Based on the total elongation Δ of the energy-consuming steel bars ti Deformation of unbonded section of energy-consuming steel reinforcement △ un Determine the slip S at the loading end of the energy-dissipating rebar. l ;

[0009] Step (4): Establish the initial calculation model of bond-slip between energy-dissipating steel bars and concrete: The energy-dissipating steel bars adopt a bilinear constitutive model, assuming that the bond stress between the energy-dissipating steel bars and concrete is uniformly distributed along the stress development length of the steel bars, and set boundary conditions; establish the initial calculation model of bond-slip between energy-dissipating steel bars and concrete before and after yielding;

[0010] Step (5): Calculate the average bond stress τ before and after yielding in the initial model for calculating the bond-slip between the energy-dissipating steel bars and concrete before and after yielding, based on the data measured and obtained in step (3). E and τ Y Thus, the final calculation model of bond-slip between the energy-dissipating steel bars and concrete before and after yielding is obtained.

[0011] Furthermore, step (3) specifically includes the following steps:

[0012] Step (31): Calculate the joint angle θ according to the following formula:

[0013]

[0014] Step (32): Based on the joint angle θ obtained in step (31), and combined with the distance L from the energy-dissipating steel bar to the center of the pier column, ED The distance L1 from the corresponding lateral compression bar displacement gauge to the center of the pier and the elongation h1 of the corresponding lateral compression bar displacement gauge are used to calculate the total elongation Δ of the corresponding energy-dissipating steel bar using the following formula. ti :

[0015] △ ti =h1-θ·(L1-L ED )

[0016] Step (33): Calculate the deformation Δ of the unbonded section of the energy-consuming steel bar. un :

[0017] △ un =ε s ×l un

[0018] Step (34): Calculate the slip S at the loading end of the energy-dissipating steel bar. l :

[0019] S l =(△) ti -△ un ) / 2.

[0020] Furthermore, step (4) specifically includes the following steps:

[0021] Step (41): The bilinear constitutive model of the energy-dissipating reinforcement is calculated using the following formula:

[0022]

[0023] In the formula: E s E represents the elastic stiffness of the energy-dissipating reinforcing steel. h The tangential stiffness of the energy-dissipating steel bar after yielding; s y The yield strength of the energy-dissipating steel reinforcement;

[0024] Step (42): Assuming the bond stress between the energy-dissipating steel bar and the concrete is uniformly distributed along the length of the steel bar stress development, specifically:

[0025] According to the stress s of the energy-dissipating steel bars s Less than or greater than yield strength s y The bond stress is divided into the average bond stress τ before yielding. E and the average bond stress τ after yielding y ;

[0026] The boundary conditions are set as follows:

[0027] Energy-consuming steel reinforcement stress s s When the value is 0, the corresponding slip is also 0;

[0028] Step (43): Establish an initial model for calculating the bond-slip between the energy-dissipating steel reinforcement and concrete before yielding;

[0029] Step (44): Establish an initial model for calculating the bond-slip between the energy-dissipating steel bars and concrete after yielding.

[0030] Furthermore, step (43) specifically involves:

[0031] Step (431): Calculate the stress function of the energy-dissipating steel bars based on the mechanical equilibrium relationship:

[0032]

[0033] For the pre-yield bond-slip calculation model between the energy-dissipating steel reinforcement and concrete, the average bond stress between the energy-dissipating steel reinforcement and concrete is τ. E d0 is the diameter of the energy-consuming steel bar, l y A is the stress development length at which the energy-dissipating steel bar yields. s Let x be the cross-sectional area of ​​the energy-dissipating steel bar, and l be the stress development length of the energy-dissipating steel bar. s The length of the variable is denoted by .

[0034] Among them, the stress development length l at the yielding of the energy-dissipating steel bar y The calculation formula is as follows:

[0035]

[0036] Step (432): Ignoring concrete deformation, the slippage S between the energy-dissipating steel bar and the concrete represents the deformation of the energy-dissipating steel bar, and its calculation formula is as follows:

[0037]

[0038] Step (433): Substitute the bilinear constitutive model of the energy-dissipating steel bar and the stress function of the energy-dissipating steel bar obtained in step (431) into the slip amount S expression in step (432) to obtain the initial model for the bond-slip calculation of the energy-dissipating steel bar and concrete before yielding, as follows:

[0039]

[0040] Furthermore, step (44) specifically involves:

[0041] Step (441): Calculate the stress function of the energy-dissipating steel bars based on the mechanical equilibrium relationship:

[0042]

[0043] Step (442): For the end slip of the energy-dissipating steel bar after yielding, substitute the bilinear constitutive model of the energy-dissipating steel bar and the stress function of the energy-dissipating steel bar in step (441) into the slip amount S expression in step (432) to establish the bond-slip calculation model between the energy-dissipating steel bar and concrete after yielding, as follows:

[0044]

[0045] Furthermore, step (5) specifically includes the following steps:

[0046] Step (51): Calculate the stress s of the energy-dissipating steel bar by taking the strain measured in step (2) according to the bilinear constitutive model of the energy-dissipating steel bar in step (41). s ;

[0047] Step (52): The energy-dissipating steel stress s obtained in step (51) s The energy-consuming steel bar loading end slip S calculated in step (3) l A relationship curve was established between the two, and after nonlinear fitting, the calculation expression for the bond-slip relationship curve between the energy-dissipating steel bars and concrete before yielding was obtained as follows:

[0048]

[0049] Step (53): Based on the calculation expression of the bond-slip relationship curve between the energy-dissipating steel bar and concrete obtained in step (52), and combined with the stress function of the energy-dissipating steel bar obtained in step (431), determine the average bond stress τ of the energy-dissipating steel bar before yielding. E ,as follows:

[0050]

[0051] In the formula: f c This is the design value for the compressive strength of concrete;

[0052] The average bond stress τ after the yielding of the energy-dissipating steel bar Y Based on the average bond stress τ of the energy-consuming steel bar before yielding obtained in step (53) E Simultaneously, based on the test results of the assembled bridge piers and the stress function of the energy-dissipating steel bars obtained in step (441), the average bond stress τ of the energy-dissipating steel bars before yielding is determined. Y ,as follows:

[0053]

[0054] Compared with the prior art, the significant advantages of this invention are:

[0055] (1) The calculation method of the present invention only requires setting up multiple compression bar displacement gauges at the corresponding positions, and there are no specific requirements for the device: by pre-embedding the extended steel rods at the top and bottom of the pier column and fixing the compression bar displacement gauges with the extended ends of the steel rods, the opening and closing amount of the joint of the assembled bridge pier under cyclic loading can be measured; by attaching strain gauges to the unbonded section of the energy dissipating steel bar, the strain data of the energy dissipating steel bar can be obtained; in summary, only two commonly used measuring devices, compression bar displacement gauges and energy dissipating steel bar strain gauges, are needed in the measurement process. These two devices are easy to install, have readily available data, and good stability, which fully reflects the simplicity of the measuring device.

[0056] (2) Simple method: The opening and closing amount of the joint of the pier column is measured by the displacement gauge, and it can be converted into the rotation angle at the joint of the assembled pier by a simple formula; Based on the strain plane section assumption of the pier column section, the total elongation of the energy dissipating steel at different positions is obtained. Combined with the strain of the energy dissipating steel measured by the strain gauge, the slip value of the loading end of the energy dissipating steel can be calculated by a simple formula; Finally, the bond-slip relationship between the energy dissipating steel and the concrete in the assembled pier is established. This method only requires the measured displacement and strain data to be converted into the bond-slip relationship between the energy dissipating steel and the concrete by a simple formula, which fully reflects the simplicity of the calculation method.

[0057] (3) Accurate results: Based on the bond-slip relationship curve between the energy-consuming steel bars and concrete obtained by the experiment, and based on the assumption of the average distribution of bond stress between the energy-consuming steel bars and concrete, the energy-consuming steel bars are divided into pre-yield and post-yield bond-slip calculation models according to whether the energy-consuming steel bars yield. At the same time, combined with the experimental data results and theoretical research results, the value of the average bond stress between the energy-consuming steel bars and concrete in the assembled bridge pier is determined, thereby constructing a complete bond-slip calculation model of the energy-consuming steel bars and concrete applicable to assembled bridge piers. Through the comparison and analysis of the calculation results and the experimental results, it can be seen that the two are in good agreement, which fully reflects the accuracy of the bond-slip calculation model of the energy-consuming steel bars and concrete. Attached Figure Description

[0058] Figure 1 This is a schematic diagram of the assembled bridge pier of the present invention.

[0059] Figure 2 for Figure 1 The cross-sectional view of AA pier in the diagram.

[0060] Figure 3 for Figure 1 The cross-sectional view of the BB bridge pier.

[0061] Figure 4 This is a schematic diagram for calculating the total elongation of energy-consuming steel bars in the assembled bridge pier.

[0062] Figure 5This is a schematic diagram for calculating the slippage of the loading end of the energy-consuming reinforcing bar.

[0063] Figure 6 This is a flowchart of the calculation method of the present invention.

[0064] Figure 7 This is a schematic diagram of the bond-slip relationship between the energy-dissipating steel bars and concrete before yielding.

[0065] Figure 8 This is a schematic diagram of the bond-slip relationship between the energy-dissipating steel bars and concrete after yielding.

[0066] Figure 9 This is a schematic diagram comparing the bond-slip test results of energy-consuming steel bars and concrete with the calculation model.

[0067] Explanation of reference numerals in the attached figures:

[0068] 1-Cap beam, 2-Pier column, 3-Bearing cap, 4-Energy dissipating steel bar, 5-PVC sleeve, 6-Extended steel bar, 7-Compression rod displacement gauge, 8-Strain gauge of steel bar, 9-Longitudinal reinforcement, 10-Spiral stirrup, 11-Prestressed tendon. Detailed Implementation

[0069] The present invention will now be described in further detail with reference to the accompanying drawings.

[0070] Step (1) Assemble the bridge piers: (See attached image) Figure 1 The composition of the assembled bridge piers and the arrangement of measuring instruments are described.

[0071] For the connection between the various components of the pier, unbonded prestressed tendons are used, which are sequentially inserted through the three components of the abutment, pier column, and cap beam from bottom to top. Fixed end anchorages are set at the bottom of the abutment, while low-retraction anchorages are used at the top of the cap beam. Prestressed tendons are tensioned at the top of the cap beam to compact the various components of the assembled pier into a whole.

[0072] For the arrangement of energy-consuming steel bars, one end of the energy-consuming steel bar is pre-embedded in the cap beam or pile cap, and the other end is inserted into the pier column and connected to the pier column by grouting to form an integral whole.

[0073] The distribution of energy-consuming steel bars in the piers is divided into inner energy-consuming steel bars and outer energy-consuming steel bars according to the distance of the energy-consuming steel bars from the center of the pier column, and the distance of the energy-consuming steel bars from different locations to the center of the pier column is recorded.

[0074] For the unbonded sections of the energy-dissipating steel bars, they are concentrated at the joints between the pier column and the cap beam or abutment. The energy-dissipating steel bars at the joints are wrapped with PVC sleeves as unbonded sections, with a length of 100mm. At the same time, steel strain gauges are applied to the surface of the energy-dissipating steel bars at the joints to record the strain patterns of the energy-dissipating steel bars at different positions inside the pier column during the loading process of the assembled pier.

[0075] Appendix Figure 2 The reinforcement details of section AA of the assembled bridge pier are described in detail. This pier section includes several longitudinal bars, spiral stirrups, energy-dissipating bars, and prestressed tendons. The prestressed tendons run through the entire pier, applying prestress to form the assembled pier into a single unit.

[0076] In the appendix Figure 3 In addition to the above-mentioned reinforcement arrangement, the BB section of the assembled bridge pier also uses PVC sleeves to wrap the energy-dissipating steel bars at the joints of the pier column as an unbonded section, which can prevent the energy-dissipating steel bars from breaking due to stress concentration. In addition, the BB section of the bridge pier also has compression bar displacement gauges installed on both sides of the pier column, which can be used to measure the opening and closing of the joints of the assembled bridge pier during loading.

[0077] Step (2) Quasi-static loading of the assembled pier: Quasi-static loading is applied to the assembled pier, and the tensile h1 and compression h2 of the displacement gauges on both sides of the pier column, the distances L1 and L2 from the displacement gauges on both sides of the pier column to the center of the pier column are read during the loading process. At the same time, the strain ε of each energy-dissipating steel bar is measured by the steel strain gauge. s ;

[0078] Step (3) Calculate the slip S at the loading end of the energy-consuming reinforcement. l Appendix Figure 4-5 Describes the slippage S at the loading end of the energy-dissipating rebar. l Complete calculation process; including, attached Figure 4 The total elongation of energy-consuming steel bars in the assembled bridge piers is △ ti The calculation diagram shows that, based on the tensile h1 and compression h2 of the displacement gauges on both sides of the pier measured in step (2), and the distances L1 and L2 from the displacement gauges on both sides of the pier to the center of the pier, the joint angle θ can be calculated. Based on the calculated joint angle θ, and combined with the distance L from the energy-dissipating steel bar to the center of the pier, the angle can be calculated. ED The distance L1 from the corresponding lateral compression bar displacement gauge to the pier center and the elongation h1 of the corresponding lateral compression bar displacement gauge are used to calculate the total elongation Δ of the energy-dissipating steel bars of the assembled pier under different loading displacements. ti The calculation process is as follows:

[0079] First, based on the tensile amount h1 and compression amount h2 measured by the displacement gauges on both sides of the pier, and the distances L1 and L2 from the displacement gauges on both sides of the pier to the center of the pier, the rotation angle θ at the joint of the assembled pier can be calculated. The calculation formula is as follows:

[0080]

[0081] Subsequently, based on the obtained joint angle θ, and combined with the distance L from the energy-dissipating steel bar to the center of the pier column, the calculation is performed. EDSubstituting the distance L1 from the corresponding lateral compression bar displacement gauge to the center of the pier and the elongation h1 of the corresponding lateral compression bar displacement gauge into formula (2), we obtain the total elongation Δ of the energy-consuming steel bar to be determined. ti The calculation formula is as follows:

[0082] △ ti =h1-θ·(LL) ED (2)

[0083] Appendix Figure 5 A schematic diagram for calculating the slippage of the energy-dissipating reinforcing bar at the loading end is given; based on the calculated total elongation Δ of the energy-dissipating reinforcing bar... ti Deformation of unbonded section of energy-consuming steel reinforcement △ un The total amount of slippage at the end of the energy-consuming reinforcing bar, Δ, is obtained. S The calculation formula is as follows:

[0084] △ S =△ ti -△ un (3)

[0085] In the formula, Δ represents the deformation of the unbonded section of the energy-consuming steel bar. un The strain ε of the energy-dissipating steel bar can be measured experimentally. s Length l of unbonded section un The result is obtained by multiplication, and the specific calculation formula is as follows:

[0086] △ un =ε s ×l un (4)

[0087] Considering that the energy-dissipating steel bars in the assembled bridge piers have two stress development lengths, the slippage S at the loading end of the energy-dissipating steel bars is... l Expressed as the total amount of slippage at the end of the energy-consuming reinforcing bar, Δ S Half of it; from this, the slippage S at the loading end of the energy-consuming steel bar can be derived. l The calculation formula is as follows:

[0088] S l =(△) ti -△ un ) / 2 (5)

[0089] The strain ε of the energy-dissipating steel bar measured in the experiment s Substituting into the bilinear constitutive model of the energy-dissipating steel reinforcement, the stress s of the energy-dissipating steel reinforcement is obtained. s Combined with the stress of the energy-dissipating steel reinforcement s s and its corresponding loading end slip S l A bond-slip curve between energy-consuming steel bars and concrete was constructed.

[0090] Appendix Figure 6The specific process of this invention is given, which is as follows: assembling the bridge pier, assembling the bridge pier under quasi-static loading, and calculating the slippage S of the energy-dissipating steel reinforcement loading end. l Establish an initial calculation model for the bond-slip between energy-dissipating steel bars and concrete, and determine the average bond stress τ of the energy-dissipating steel bars before and after yielding. E and τ Y .

[0091] Step (4) Establishment of the initial calculation model for the bond-slip between energy-dissipating steel bars and concrete: Appendix Figure 6-7 The bond-slip relationship between energy-dissipating steel bars and concrete is described in detail. The bond-slip calculation model between the energy-dissipating steel bars and concrete is based on an assumption and a boundary condition, which are described in detail below:

[0092] Assumption 1: The bond stress between the energy-dissipating steel bar and the concrete is uniformly distributed along the length of the steel bar stress development, according to the energy-dissipating steel bar stress s s Less than or greater than yield strength s y The bond stress is divided into the average bond stress τ before yielding. E and the average bond stress τ after yielding Y .

[0093] Boundary condition 1: Stress s in the energy-dissipating steel reinforcement s When the value is 0, the corresponding slip S is also 0.

[0094] The aforementioned bond-slip calculation model for energy-dissipating steel bars and concrete is based on the stress s of the energy-dissipating steel bars. s Less than or greater than yield strength s y The calculation models are divided into two categories: a pre-yield bond-slip calculation model for energy-dissipating steel bars and concrete, and a post-yield bond-slip calculation model for energy-dissipating steel bars and concrete.

[0095] Appendix Figure 7 The bond-slip relationship between the energy-dissipating steel reinforcement and concrete before yielding is given. When the stress s in the energy-dissipating steel reinforcement... s Less than yield strength s y The bond stress between the energy-dissipating steel bars and concrete extends along the stress development length l. s When the two are uniformly distributed, the average bond stress between them can be expressed as τ. E .

[0096] Appendix Figure 8 The bond-slip relationship between the energy-dissipating steel reinforcement and concrete after yielding is given. When the stress s in the energy-dissipating steel reinforcement... s Less than yield strength s y At that time, the bond stress between the energy-dissipating steel bars and concrete is calculated according to the average bond stress τ before yielding. E The calculation is sufficient, and when the stress s of the energy-dissipating steel reinforcement... s Greater than yield strength sy The bond stress between the energy-dissipating steel bars and the concrete extends along the stress development length l. p When the two are uniformly distributed, the average bond stress between them can be expressed as τ. Y .

[0097] The establishment of a bond-slip calculation model for energy-dissipating reinforcing bars and concrete first requires determining the material constitutive relationship of the reinforcing bars. The energy-dissipating reinforcing bars are modeled using a bilinear constitutive model, and the calculation formulas are as follows:

[0098]

[0099] In the formula: E s E represents the elastic stiffness of the energy-dissipating reinforcing steel. h The tangential stiffness of the energy-dissipating steel bar after yielding; s y This represents the yield strength of the energy-dissipating steel reinforcement.

[0100] For the pre-yield bond-slip calculation model between the energy-dissipating steel reinforcement and concrete, the average bond stress between the energy-dissipating steel reinforcement and concrete is τ. E The stress function of the energy-dissipating steel bar before yielding is calculated based on the mechanical equilibrium relationship, as follows:

[0101]

[0102] In the formula: s s d0 is the stress in the energy-dissipating reinforcing bar; l is the diameter of the energy-dissipating reinforcing bar. y This is the stress development length at which the energy-dissipating steel bar yields.

[0103] When the energy-dissipating steel bar reaches its yield strength s y At that time, the stress development length of the energy-dissipating steel bar is l. y The calculation formula is as follows:

[0104]

[0105] Regarding the slippage S between the energy-dissipating steel bar and the concrete, considering that the stiffness of the pier concrete is much greater than that of the energy-dissipating steel bar, the slippage S between the energy-dissipating steel bar and the concrete can be expressed as the deformation of the energy-dissipating steel bar without considering concrete deformation. The calculation formula is as follows:

[0106]

[0107] Where: ε s S represents the strain of the energy-dissipating steel bar along the length of stress development; S represents the slippage of the energy-dissipating steel bar.

[0108] Substituting the material constitutive relation of the energy-dissipating steel bar in formula (6) and the stress function of the energy-dissipating steel bar before yielding in formula (7) into formula (9), an initial calculation model of bond-slip between the energy-dissipating steel bar and concrete before yielding is established as follows:

[0109]

[0110] For the post-yield energy dissipation steel bar bond-slip calculation model with concrete, based on the energy dissipation steel bar stress s s Less than or greater than yield strength s y The bond stress is divided into the average bond stress τ before yielding. E and the average bond stress τ after yielding Y The stress function of the energy-dissipating steel bar after yielding is calculated based on the mechanical equilibrium relationship:

[0111]

[0112] In the formula: s y τ is the yield strength of the energy-dissipating steel reinforcement. Y The average bond stress after the energy-dissipating steel bars yield.

[0113] For the slip S of the energy-dissipating steel bar after yielding, the material constitutive relation of the energy-dissipating steel bar in formula (6) and the stress function of the energy-dissipating steel bar after yielding in formula (11) are substituted into formula (9) to establish the initial calculation model of bond-slip between the energy-dissipating steel bar and concrete after yielding, as follows:

[0114]

[0115] Based on this, combining formulas (10) and (12), an initial calculation model for the bond-slip between energy-consuming steel bars and concrete is established as follows:

[0116]

[0117] Step (5) Determine the average bond stress τ before and after yielding. E and τ Y Based on the test data of the assembled bridge pier obtained in step (3), the average bond stress τ before and after yielding in the initial calculation model of bond-slip between the energy dissipation steel and concrete is obtained. E and τ Y Thus, the final calculation model of bond-slip between the energy-dissipating steel bars and concrete before and after yielding was obtained.

[0118] To determine the average bond stress τ before and after yielding E and τ Y An example was used to verify the assembly of bridge piers.

[0119] The assembled bridge pier consists of a pier cap, a cap beam, and two pier column segments. The pier column has a circular cross-section with a diameter of 350mm. The height of a single pier column segment is 800mm, and the total height of the pier column is 1600mm. The pier is compacted into a whole by using post-tensioned prestressed tendons for connection.

[0120] Eight HRB400 energy-dissipating steel bars with a diameter of 12mm are arranged at the bottom of the pier. Four of these energy-dissipating steel bars are 40mm away from the center of the pier, and the other four are 80mm away. A 100mm unbonded section is set at the joint at the bottom of the pier. Strain gauges are attached to the surface of the energy-dissipating steel bars in the unbonded section.

[0121] Two pressure bar displacement gauges were installed on both sides of the pier at a distance of 225mm from the center of the pier column.

[0122] By conducting a horizontal quasi-static loading test on the assembled bridge pier, the strain data ε of the energy-dissipating steel bars were obtained. s The tensile h1 and compression h2 data of the displacement gauges on both sides of the pier column are obtained. According to formulas (1)-(5), the bond-slip curves between the energy-dissipating steel bars and concrete in the assembled pier are calculated as shown in the attached figure. Figure 9 As shown.

[0123] The test results of the assembled bridge pier show that the stress s of the energy-dissipating steel bar before yielding is... s Its loading end sliding S l The relationship is proportional to the square root of the equation. Through fitting, the expression for the bond-slip relationship between the energy-dissipating steel reinforcement and concrete before yielding is determined as follows:

[0124]

[0125] Based on the stress function of the energy-dissipating steel bar before yielding (7) and the initial calculation model of bond-slip between the energy-dissipating steel bar and concrete before yielding (10), the average bond stress τ between the energy-dissipating steel bar and concrete before yielding can be obtained. E The calculation formula is as follows:

[0126]

[0127] In the formula: f c This is the design value for the compressive strength of concrete.

[0128] Similarly, based on the stress function of the energy-dissipating steel bar after yielding (11) and the initial calculation model of bond-slip between the energy-dissipating steel bar and concrete after yielding (12), and combined with the test results of the assembled pier obtained in step (3), the average bond stress τ between the energy-dissipating steel bar and concrete after yielding can be obtained. Y The calculation formula is as follows:

[0129]

[0130] The average bond stress τ before and after yielding E and τ Y Substituting into the initial calculation model of bond-slip between energy-consuming steel bars and concrete in formula (13), the final calculation model of bond-slip between energy-consuming steel bars and concrete is obtained.

[0131] By analyzing and comparing the experimental results and model calculation results of the bond-slip relationship between energy-consuming steel bars and concrete in assembled bridge piers, the two results showed good agreement and high goodness of fit, which fully demonstrated the accuracy of the bond-slip calculation model between energy-consuming steel bars and concrete established in this invention.

Claims

1. A method for calculating the bond-slip relationship between energy-dissipating reinforcing bars and concrete in assembled bridge piers, characterized in that, Includes the following steps: Step (1): Assemble the pier: Assemble the cap beam (1), pier column (2) and abutment (3). The energy-dissipating steel bars (4) arranged at the joint between the pier column (2) and the cap beam (1) or abutment (3) are fitted with steel strain gauges (8) and formed into a length of l by an outer PVC sleeve (5). un The unbonded section has an extended steel rod (6) on both sides of the end of the pier (2) for fixing the pressure rod displacement gauge (7). The position of the extended steel rod (6) is set according to the range of the pressure rod displacement gauge (7). Step (2): Perform quasi-static loading on the assembled pier: read the tensile h1 and compression h2 of the compression bar displacement gauge (7) during the loading process, the distances L1 and L2 from the two compression bar displacement gauges (7) to the center of the pier column, and measure the strain ε of each energy-dissipating steel bar through the steel strain gauge (8). s ; Step (3): Calculate the slip S at the loading end of the energy-dissipating steel bar. l : Calculate the rotation angle θ at the joint based on the data measured by the displacement gauge (7) in step (2), and combine it with the distance L from the energy-dissipating steel bar to the center of the pier column. ED The total elongation Δ of the energy-dissipating steel bar is calculated by taking the distance L1 from the corresponding lateral compression bar displacement gauge to the center of the pier and the elongation h1 of the corresponding lateral compression bar displacement gauge. ti Based on the total elongation Δ of the energy-consuming steel bars ti Deformation of unbonded section of energy-consuming steel reinforcement △ un Determine the slip S at the loading end of the energy-dissipating rebar. l ; Step (4): Establish the initial calculation model of bond-slip between energy-dissipating steel bars and concrete: The energy-dissipating steel bars adopt a bilinear constitutive model, assuming that the bond stress between the energy-dissipating steel bars and concrete is uniformly distributed along the stress development length of the steel bars, and set boundary conditions; establish the initial calculation model of bond-slip between energy-dissipating steel bars and concrete before and after yielding; Step (5): Calculate the average bond stress τ before and after yielding in the initial model for calculating the bond-slip between the energy-dissipating steel bars and concrete before and after yielding, based on the data measured and obtained in step (3). E and τ Y Thus, the final calculation model of bond-slip between the energy-dissipating steel bars and concrete before and after yielding is obtained; Step (4) specifically includes the following steps: Step (41): The bilinear constitutive model of the energy-dissipating reinforcement is calculated using the following formula: In the formula: E s E represents the elastic stiffness of the energy-dissipating reinforcing steel. h σ is the tangential stiffness of the energy-dissipating steel bar after yielding; y σ represents the yield strength of the energy-dissipating steel reinforcement. s For energy-dissipating steel reinforcement stress; Step (42): Assuming the bond stress between the energy-dissipating steel bar and the concrete is uniformly distributed along the length of the steel bar stress development, specifically: According to the stress σ of energy-dissipating steel bars s Less than or greater than the yield strength σ y The bond stress is divided into the average bond stress τ before yielding. E and the average bond stress τ after yielding Y ; The boundary conditions are set as follows: Energy-dissipating steel reinforcement stress σ s When the value is 0, the corresponding slip S is also 0; Step (43): Establish an initial calculation model for the bond-slip between the energy-dissipating steel bars and concrete before yielding; Step (44): Establish an initial calculation model for the bond-slip between the energy-dissipating steel bars and concrete after yielding; Step (43) is as follows: Step (431): Calculate the stress function of the energy-dissipating steel bar before yielding based on the mechanical equilibrium relationship: For the initial calculation model of bond-slip between the energy-dissipating steel bar and concrete before yielding, the average bond stress between the energy-dissipating steel bar and concrete is τ. E d0 is the diameter of the energy-consuming steel bar, l y A is the stress development length at which the energy-dissipating steel bar yields. s Let x be the cross-sectional area of ​​the energy-dissipating steel bar, and l be the stress development length of the energy-dissipating steel bar. s The length of the independent variable is l; where l is the stress development length at which the energy-dissipating steel bar yields. y The calculation formula is as follows: Step (432): Ignoring concrete deformation, the slippage S between the energy-dissipating steel bar and the concrete represents the deformation of the energy-dissipating steel bar, and its calculation formula is as follows: Step (433): Substitute the bilinear constitutive model of the energy-dissipating steel bar and the pre-yield stress function of the energy-dissipating steel bar obtained in step (431) into the slip amount S expression in step (432) to obtain the initial calculation model of bond-slip between the energy-dissipating steel bar and concrete before yielding, as follows: Step (44) is as follows: Step (441): Calculate the stress function of the energy-dissipating steel bar after yielding based on the mechanical equilibrium relationship: Step (442): For the slip of the energy-dissipating steel bar after yielding, substitute the bilinear constitutive model of the energy-dissipating steel bar and the stress function of the energy-dissipating steel bar after yielding in step (441) into the slip S expression in step (432) to establish the initial calculation model of bond-slip between the energy-dissipating steel bar and concrete after yielding, as follows:

2. The method according to claim 1, characterized in that, Step (3) specifically includes the following steps: Step (31): Calculate the joint angle θ according to the following formula: Step (32): Based on the joint angle θ obtained in step (31), and combined with the distance L from the energy-dissipating steel bar to the center of the pier column, ED The distance L1 from the corresponding lateral compression bar displacement gauge to the center of the pier and the elongation h1 of the corresponding lateral compression bar displacement gauge are used to calculate the total elongation Δ of the corresponding energy-dissipating steel bar using the following formula. ti : △ ti =h1-θ·(L1-L ED ) Step (33): Calculate the deformation Δ of the unbonded section of the energy-consuming steel bar. un : △ un =e s ×l un Step (34): Calculate the slip S at the loading end of the energy-dissipating steel bar. l : S l ＝(△ ti -△ un ) / 2。 3. The method according to claim 2, characterized in that, Step (5) specifically includes the following steps: Step (51): Calculate the stress σ of the energy-dissipating steel bar by taking the strain of the energy-dissipating steel bar measured in step (2) according to the bilinear constitutive model of the energy-dissipating steel bar in step (41). s ; Step (52): The energy-dissipating steel stress σ obtained in step (51) is... s The energy-consuming steel bar loading end slip S calculated in step (3) l A relationship curve was established between the two, and after nonlinear fitting, the calculation expression for the bond-slip relationship curve between the energy-dissipating steel and concrete before yielding was obtained as follows: Step (53): Based on the calculation expression of the bond-slip relationship curve between the energy-dissipating steel bar and concrete obtained in step (52), and combined with the stress function of the energy-dissipating steel bar before yielding obtained in step (431), determine the average bond stress τ of the energy-dissipating steel bar before yielding. E ,as follows: In the formula: f c This is the design value for the compressive strength of concrete; The average bond stress τ after the yielding of the energy-dissipating steel bar Y Based on the average bond stress τ of the energy-consuming steel bar before yielding obtained in step (53) E Simultaneously, based on the test results of the assembled bridge piers and the stress function of the energy-dissipating steel bars after yielding obtained in step (441), the average bond stress τ of the energy-dissipating steel bars after yielding is determined. Y ,as follows:

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