Method for calculating maximum crack width of section-increased secondary reinforcement reinforced concrete beam

Abstract

The invention relates to the technical field of building structure engineering, in particular to a method for calculating the maximum crack width of a secondary reinforced concrete beam with an increased cross section. The method comprises the steps of firstly determining parameters of an original beam and a reinforced beam, and then substituting the parameters into a formula to calculate the maximum crack width. On the basis of theoretical parameter analysis and a large number of tests, in combination with the balance condition of steel bar and steel plate force and the balance condition of the moment of the resultant force point of the concrete compression area when the crack is about to occur, the steel bar stress and the average crack width are calculated, and the non-uniform strain coefficient of the tensile steel bar between the cracks is calculated. And the actual calculation method for the maximum crack width of the secondary reinforced concrete beam with the increased cross section is obtained. According to the method, the crack condition of the beam can be well reflected, the calculation steps are clear, the calculation method is simple, and the defect that a reliable calculation method for the maximum crack width of the section-enlarged secondary reinforcement reinforced concrete beam is lacked is overcome.

Description

Technical Field

[0001] This invention relates to the field of building structure engineering technology, and in particular to a method for calculating the maximum crack width of a reinforced concrete beam that has been reinforced with a larger cross-section for secondary strengthening. Background Technology

[0002] In the field of building structural engineering, reinforced concrete beams are key load-bearing components, and the calculation of their maximum crack width is a major research focus. The secondary reinforcement technique of increasing the cross-section involves further strengthening the beam by increasing its cross-section, building upon the initial reinforcement with bonded steel plates. This increases the component's cross-sectional dimensions, thereby improving its load-bearing capacity. The construction process is relatively simple, and the reinforcement and repair capabilities are strong.

[0003] At present, secondary reinforcement projects for structural members are gradually increasing, but research on secondary reinforcement of reinforced concrete members is still in its initial stage. In particular, the bending performance of beams after secondary reinforcement has not been studied in depth, and the bending mechanism is still unclear. There is a lack of research on the calculation method of the maximum crack width of reinforced concrete beams after secondary reinforcement with increased cross-section. Summary of the Invention

[0004] To overcome the deficiency in the prior art of lacking a reliable method for calculating the maximum crack width of reinforced concrete beams with enlarged cross-sections and secondary reinforcement, this invention proposes a method for calculating the maximum crack width of reinforced concrete beams with enlarged cross-sections and secondary reinforcement, which can simply, quickly, and reliably reflect the crack condition of the beam.

[0005] This invention proposes a method for calculating the maximum crack width of a reinforced concrete beam that has undergone secondary reinforcement with an enlarged cross-section. The method is applicable to concrete beams that have been raised from the bottom, where a steel plate is bonded to the bottom of the original beam. The method first determines the parameters of the original beam and the reinforced beam, and then calculates the maximum crack width using the following formula. : ; The component's overall influence coefficient; The coefficient of non-uniform strain of tensile reinforcement in the crack; This is the equivalent stress of the tensile reinforcement; The equivalent tensile reinforcement elastic modulus; This represents the average crack spacing.

[0006] Preferably, the coefficient of uniform strain of tensile reinforcement between cracks The calculation formula is: ; in, To add a new standard value for the axial tensile strength of concrete; For the equivalent area of ​​the tensile reinforcement, A is the effective tensile concrete cross-sectional area.p Let be the cross-sectional area of ​​the steel plate. pp For the tensile stress of the steel plate; , , All of these are experimental fitting parameters, and The distance is the axial distance from the resultant force point of the equivalent tensile reinforcement to the resultant force point of the concrete compression zone. The distance between the resultant force point in the tension zone of the concrete and the resultant force point in the compression zone of the concrete is axial distance. denoted as , where is the axial distance from the resultant force point of the steel plate to the resultant force point of the concrete compression zone, and h is the height of the reinforced beam.

[0007] Preferred: ; in, This is the sum of the cross-sectional areas of the newly added tensile reinforcement. E is the sum of the cross-sectional areas of the original tensile reinforcement. s0 For the original tensile reinforcement elastic modulus, E sm For the addition of elastic modulus for tension reinforcement.

[0008] Preferred: ; in, , and All parameters are experimental fitting parameters; d is the diameter of the newly added reinforcing bar, and c is the thickness of the concrete cover. The thickness of the steel plate; and This is the proportionality coefficient. , ; The width of the steel plate; This refers to the thickness of the steel plate.

[0009] Preferred, The constraints are: ; in, To add a new standard value for the axial tensile strength of concrete; sm The length starting from the crack l The average bond stress between the inner concrete and the newly added tensile reinforcement; , All of these are experimental fitting parameters, and The distance is the axial distance from the resultant force point of the equivalent tensile reinforcement to the resultant force point of the concrete compression zone. denoted as , where is the axial distance from the resultant force point in the tensile zone of the concrete to the resultant force point in the compressive zone of the concrete, and h is the height of the reinforced beam.

[0010] Preferred, The constraints are: ; in, The parameters are the fitting parameters for the experiment, and The distance is the axial distance from the resultant force point of the steel plate to the resultant force point of the concrete compression zone. pm The length starting from the crack l The average bond stress between the inner concrete and the steel plate.

[0011] Preferably, the beam reinforcement method includes the following steps: The original beam was first reinforced by attaching steel plates to its bottom, and then U-shaped hoops were installed for anchoring. Two rows of studs are welded longitudinally along the steel plate to anchor the new concrete. New stirrups are installed in the gaps of the U-shaped stirrups and inserted into the original beam. The new stirrups overlap with the original stirrups, and new tensile reinforcement is installed on the inner circumference of the new stirrups. The new stirrups are filled with concrete inside and outside, aligned with the original beam, to increase the beam's structural height.

[0012] The present invention proposes an application method for calculating the maximum crack width of a reinforced concrete beam with enlarged cross-section secondary reinforcement. The method is characterized by first designing a secondary reinforcement scheme with enlarged cross-section for the beam structure to be reinforced, extracting parameters from the design scheme and substituting them into the method for calculating the maximum crack width of the reinforced concrete beam with enlarged cross-section secondary reinforcement, and then selecting the design scheme by comparing the maximum crack width with the set upper limit of allowable crack width.

[0013] The present invention proposes a system for calculating the maximum crack width of a reinforced concrete beam with enlarged cross-section and secondary reinforcement, comprising a memory and a processor. The memory stores a computer program, and the processor is connected to the memory. The processor is used to execute the computer program to realize the method for calculating the maximum crack width of the reinforced concrete beam with enlarged cross-section and secondary reinforcement.

[0014] The present invention proposes a storage medium storing a computer program, which, when executed, is used to implement the method for calculating the maximum crack width of a reinforced concrete beam with increased cross-section and secondary reinforcement.

[0015] The advantages of the present invention are: This invention proposes a method for calculating the maximum crack width of secondary reinforced concrete beams with enlarged cross-sections. Based on theoretical parameter analysis and extensive experiments, and combining the equilibrium conditions of the forces between the reinforcing bars and the steel plate, as well as the equilibrium conditions of the resultant moment at the compressive point of the concrete when cracks are about to appear, the method calculates the reinforcing bar stress and average crack width, and calculates the non-uniformity coefficient of tensile reinforcing bar strain between cracks, thus obtaining a practical method for calculating the maximum crack width of secondary reinforced concrete beams with enlarged cross-sections. This invention can accurately reflect the cracking situation of the beam, with clear calculation steps and a simple calculation method, providing a convenient, effective, and rapidly scalable solution for calculating the maximum crack width of secondary reinforced concrete beams with enlarged cross-sections. Attached Figure Description

[0016] Figure 1 Schematic diagram of a reinforced concrete beam structure with secondary reinforcement to increase cross-section; Illustration: 1-Original beam; 11-Original stirrups; 12-Original tensile reinforcement; 13-Top beam reinforcement; 21-New stirrups; 22-New tensile reinforcement; 23-Steel plate; 24-U-shaped stirrup plate; Figure 2 A schematic diagram of the overall calculation model for crack derivation; Figure 3 This is a schematic diagram of the equivalent calculation model for reinforcing bars; Figure 4 This is a schematic diagram of the equivalent calculation model for the steel plate. Figure 5 This is a schematic diagram of the equivalent reinforcement and steel plate isolation body analysis; Figure 6 This is a flowchart illustrating a method for calculating the maximum crack width of a reinforced concrete beam with increased cross-section, as proposed in this invention. Detailed Implementation

[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0018] Reference Figure 1This invention relates to a method for secondary reinforcement of reinforced concrete beams by increasing the cross-section of the original beam 1 from the bottom. The reinforcement process specifically involves: firstly reinforcing the original beam 1 by attaching a steel plate to the bottom, then anchoring it with U-shaped stirrups 24; welding two rows of studs longitudinally along the steel plate 23 to anchor the newly added concrete; inserting new stirrups 21 into the original beam 1 at the gaps in the U-shaped stirrups 24, with the new stirrups 21 overlapping the original stirrups 11; and adding new tensile reinforcement 22 around the inner circumference of the new stirrups 21; filling the inside and outside of the new stirrups 21 with concrete, aligning them with the original beam 1, thereby increasing the beam's structural height. The reinforced beam structure is described below. Figure 1 The bottom inner circumference of the original stirrup 11 is provided with two original tensile steel bars 12, and the top inner circumference is provided with beam top support bars 13.

[0019] Determine the basic parameters of the reinforced concrete beam and steel for secondary reinforcement with enlarged cross-section, including beam height. h That is, the beam height after secondary reinforcement by increasing the cross-section; the original beam height. h 0 That is, the height of the beam structure before the secondary reinforcement of the cross-section is increased; the width of the beam cross-section b; and the sum of the cross-sectional areas of the original tensile reinforcement. A s0 The sum of the cross-sectional areas of the newly added tensile reinforcement bars A s steel plate area A p ; original perimeter of tensile reinforcement s 0; Perimeter of newly added tensile reinforcement s ; width of steel plate b p Large-section, secondary-strengthened reinforced concrete beam structures are shown in [reference needed]. Figures 1 to 5 In the figure, the original tensile reinforcement stress s0 , stress of newly added tensile reinforcement s and tensile stress of steel plate pp These are the measured parameters.

[0020] Assuming the average crack spacing is l : Let the distance between the cracks l The original tensile stress of the reinforcing steel after length is denoted as s10 The stress of the newly added tensile reinforcement is recorded as s1 The tensile stress of the steel plate is denoted as p1 And this distance from the crack l The tensile stress in the concrete section after the length increase rises to the standard value of the axial tensile strength of the newly added concrete. f tk , f tkThe inherent parameters of the newly added concrete material can be obtained by referring to the table.

[0021] Assuming a length starting from the crack l The average bond stresses between the inner concrete and the original tensile reinforcement, between the concrete and the newly added tensile reinforcement, and between the concrete and the steel plate are respectively denoted as . sm0 , sm , pm .

[0022] For secondary reinforcement of reinforced concrete beam structures with increased cross-section, see [link / reference]. Figure 1 The overall calculation model for crack derivation is shown in [link to calculation]. Figure 2 The equivalent calculation model for reinforcing bars is shown in [link to model]. Figure 3 The equivalent calculation model for the steel plate is shown in [link to model]. Figure 4 .

[0023] The tensile stress in the concrete at the crack section is zero. The derivation process of the formula for calculating the maximum crack width is shown in steps S1-S4.

[0024] S1. Taking the reinforcing bars and steel plates as isolated bodies respectively, calculate the equivalent stress of the tensile reinforcing bars. The tensile stress in the concrete rises to f tk Equivalent stress of tensile reinforcement at time And the tensile stress in concrete rises to f tk Equivalent shear stress of tensile reinforcement at time ; and Based on the experiment.

[0025] The calculation process for this step is as follows: First, establish the equilibrium conditions for the forces: (1); (2); (3); Then, the reinforced tensile steel bars are treated as a whole, and the equivalent stress of the tensile steel bars is solved by the force equilibrium condition. , the formula is as follows: (4); in: For the equivalent area of ​​the tensile reinforcement, ; For the original tensile reinforcement elastic modulus, The elastic modulus of the added tension reinforcement for secondary reinforcement can be determined according to the "Tensive Testing of Metallic Materials" (GB / T228.1-2010); This is the equivalent stress of the tensile reinforcement; The tensile stress in the concrete rises to f tk Equivalent stress of tensile steel bars at that time; The tensile stress in the concrete rises to f tk The equivalent shear stress of the tensile reinforcement at that time; The equivalent perimeter of the tensile reinforcement is given by the equivalent area of ​​the tensile reinforcement. Calculated; that is , r is the equivalent radius; and Based on experimental measurements; then substituting into formula (4), and combining equations (1), (2), (3), and (4), the result can be calculated. .

[0026] S2. Calculate the bending moment of the crack section that will appear at the crack. Taking the moment at the resultant force point in the compression zone of the concrete, we can obtain the following from the moment equilibrium condition: (5); in, The distance between the equivalent tensile reinforcement resultant point and the concrete compression zone resultant point along the axis. This is the axial distance from the point of resultant force on the steel plate to the point of resultant force on the concrete compression zone. This refers to the resistance to bending moment in the tension zone of concrete. (6); in, For the effective tensile concrete cross-sectional area, b represents the width of the concrete section; The newly added standard value for the axial tensile strength of concrete is an inherent parameter of concrete material and can be obtained by referring to a table. It is the axial distance between the resultant force point in the tension zone of the concrete and the resultant force point in the compression zone of the concrete.

[0027] S3. Calculate the average crack spacing. l ; Solving equations (3), (4), (5), and (6) simultaneously yields: (7); in, and This is the proportionality coefficient. , d is the diameter of the reinforcing bar; The width of the steel plate; This refers to the thickness of the steel plate.

[0028] Numerous experimental studies have shown that and Proportional and It is also directly proportional, according to experimental data. and It can be taken as a constant. Related to the shape of the reinforcing bar; when the shape of the reinforcing bar is given, It can be taken as a constant. l With the thickness of the concrete protective layer c Regarding this, referring to the concrete structure design code, equation (7) is rewritten as: (8); (9); (10); Analysis of the experimental data shows that: =0.08, =1.9, =0.05.

[0029] S4. Calculate the coefficient of non-uniform strain in tensile reinforcement between cracks. and maximum crack width ; The average stress of the equivalent reinforcement is: (11); in, This represents the average stress of the equivalent reinforcing steel. According to the experimental data: (12); (13); The equivalent reinforcement resists the bending moment as follows: The tensile stress generated by the concrete resists the bending moment as The bending moment resisted by the steel plate is Combining equation (5), we can obtain: (14); Therefore: (15); In subsequent embodiments, based on experimental data... , This further simplifies equation (15) to: (16); The formula for calculating the maximum crack width of a reinforced concrete beam with an enlarged cross-section, derived from the relevant specifications, is as follows: (17); The comprehensive influence coefficient of the component includes factors such as experimental randomness, steel bar type and stress characteristics, and is determined based on experimental data. It is set to 2.2 based on the experimental data. This is the equivalent stress of the tensile reinforcement; Equivalent tensile reinforcement elastic modulus: Among them, E s0 For the original tensile reinforcement elastic modulus, E sm For the addition of elastic modulus for tension reinforcement.

[0030] The following specific embodiments verify the method for calculating the maximum crack width of the above-mentioned reinforced concrete beam with enlarged cross-section and secondary reinforcement.

[0031] In this embodiment, the original tensile reinforcement stress s0 , stress of newly added tensile reinforcement s Tensile stress in steel plates pp Original tensile reinforcement elastic modulus Secondary reinforcement adds elastic modulus of tension reinforcement The value is determined according to the "Tensive Testing of Metallic Materials" (GB / T228.1-2010); In this embodiment, three reinforced concrete beam specimens with enlarged cross-sections and secondary reinforcement were selected from a laboratory of a research institute. The specimen numbers were LA-1, LA-2, and LA-3, respectively. Static failure tests and finite element numerical simulations were conducted on the reinforced concrete beam specimens with enlarged cross-sections and secondary reinforcement to explore the rationality and practicality of the calculation method for the maximum crack width of reinforced concrete beams with enlarged cross-sections and secondary reinforcement.

[0032] In this embodiment, the secondary reinforcement of the reinforced concrete beam using the cross-section enlargement method was completed based on the initial reinforcement of the beam with bonded steel plates, which in turn was completed on the basis of an unreinforced beam; see details below. Figure 1 As shown in Table 1, the specimen parameters in this embodiment are as follows.

[0033] Table 1: Basic parameters of reinforced concrete beam specimens with enlarged cross-section and secondary strengthening ; In this embodiment, the original beams (unreinforced beams) of specimens LA-1, LA-2, and LA-3 have the same structure, all cast with C30 concrete and a protective layer thickness of 30mm; the newly added concrete strength grade is C40. The standard value of the axial tensile strength of C30 concrete is... =32.7 N / mm 2 Standard value of axial tensile strength of C40 concrete =42.2 N / mm 2 .

[0034] In this embodiment, the original tensile reinforcement, original stirrups, beam top reinforcement, newly added tensile reinforcement, and newly added stirrups are all of type HRB400; the steel plate material is type Q235B.

[0035] The original tensile reinforcement consisted of two 20mm diameter HRB400 steel bars, the beam top stirrups consisted of two 14mm diameter HRB400 steel bars, and the original stirrups consisted of 8mm diameter HRB400 steel bars. The newly added tensile reinforcement consists of two 18mm diameter HRB400 steel bars, and the newly added stirrups consist of 8mm diameter HRB400 steel bars. The original stirrup spacing was 100mm, and the new stirrups lapped over the original stirrups, meaning the new stirrup spacing was also 100mm.

[0036] The steel parameters are shown in Table 2.

[0037] Table 2: Mechanical property parameters of reinforcing bars and steel plates ; In this embodiment, experiments, finite element simulations, and [other methods] were performed on each specimen separately. Figure 6 The present invention provides a method for calculating the maximum crack width of a reinforced concrete beam with enlarged cross-section and secondary reinforcement. The maximum crack width obtained is denoted as follows: ω u、 ω f and ω The experimental results are shown in Table 3.

[0038] Table 3: Comparison of experimental values, finite element simulation values, and theoretical values ​​for maximum crack width ; Table 3 shows that the experimental value of the maximum crack width is very close to the finite element simulation value and the theoretical calculation value. The average ratio of the experimental value to the theoretical calculation value of the maximum crack width is 1.01; the average ratio of the finite element calculation value to the theoretical calculation value of the maximum crack width is 0.98, and the coefficient of variation is 0.027. Overall, the parameters obtained from the experiment and finite element method have a certain degree of reliability, and the calculation formula can reflect the crack condition of the beam with good accuracy and strong practicality.

[0039] Of course, those skilled in the art will recognize that the present invention is not limited to the details of the exemplary embodiments described above, but also includes the same or similar structures that can be implemented in other specific forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be considered illustrative and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0040] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

[0041] The technologies, shapes, and structures not described in detail in this invention are all known technologies.

Claims

1. A method for calculating the maximum crack width of a reinforced concrete beam with enlarged cross-section and secondary reinforcement, characterized in that, This method is applicable to concrete beams that are raised from the bottom, where a steel plate is bonded to the bottom of the original beam. First, the parameters of the original beam and the reinforced beam are determined, and then the maximum crack width is calculated using the following formula. : The component's overall influence coefficient; The coefficient of non-uniform strain of tensile reinforcement in the crack; This is the equivalent stress of the tensile reinforcement; The equivalent tensile reinforcement elastic modulus; This represents the average crack spacing.

2. The method for calculating the maximum crack width of a reinforced concrete beam with enlarged cross-section as described in claim 1, characterized in that, Coefficient of non-uniform strain of tensile reinforcement in cracks The calculation formula is: in, To add a new standard value for the axial tensile strength of concrete; For the equivalent area of ​​the tensile reinforcement, A is the effective tensile concrete cross-sectional area. p Let be the cross-sectional area of ​​the steel plate. pp For the tensile stress of the steel plate; , , All of these are experimental fitting parameters, and The distance is the axial distance from the resultant force point of the equivalent tensile reinforcement to the resultant force point of the concrete compression zone. The distance between the resultant force point in the tension zone of the concrete and the resultant force point in the compression zone of the concrete is axial distance. denoted as , where is the axial distance from the resultant force point of the steel plate to the resultant force point of the concrete compression zone, and h is the height of the reinforced beam.

3. The method for calculating the maximum crack width of a reinforced concrete beam with enlarged cross-section as described in claim 2, characterized in that: in, The sum of the cross-sectional areas of the newly added tensile reinforcement bars. E is the sum of the cross-sectional areas of the original tensile reinforcement. s0 For the original tensile reinforcement elastic modulus, E sm For the addition of elastic modulus for tension reinforcement.

4. The method for calculating the maximum crack width of a reinforced concrete beam with enlarged cross-section as described in claim 1, characterized in that: in, , and All parameters are experimental fitting parameters; d is the diameter of the newly added reinforcing bar, and c is the thickness of the concrete cover. The thickness of the steel plate; and This is the proportionality coefficient. , ; The width of the steel plate; This refers to the thickness of the steel plate.

5. The method for calculating the maximum crack width of a reinforced concrete beam with enlarged cross-section as described in claim 4, characterized in that, The constraints are: in, To add a new standard value for the axial tensile strength of concrete; sm The length starting from the crack l The average bond stress between the inner concrete and the newly added tensile reinforcement; , All of these are experimental fitting parameters, and The distance is the axial distance from the resultant force point of the equivalent tensile reinforcement to the resultant force point of the concrete compression zone. denoted as , where is the axial distance from the resultant force point in the tensile zone of the concrete to the resultant force point in the compressive zone of the concrete, and h is the height of the reinforced beam.

6. The method for calculating the maximum crack width of a reinforced concrete beam with enlarged cross-section as described in claim 5, characterized in that, The constraints are: in, The parameters are the experimental fitting parameters, and The distance is the axial distance from the resultant force point of the steel plate to the resultant force point of the concrete compression zone. pm The length starting from the crack l The average bond stress between the inner concrete and the steel plate.

7. The method for calculating the maximum crack width of a reinforced concrete beam with enlarged cross-section as described in claim 1, characterized in that, Beam reinforcement methods include the following steps: The original beam was first reinforced by attaching steel plates to its bottom, and then U-shaped hoops were installed for anchoring. Two rows of studs are welded longitudinally along the steel plate to anchor the new concrete. New stirrups are installed in the gaps of the U-shaped stirrups and inserted into the original beam. The new stirrups overlap with the original stirrups, and new tensile reinforcement is installed on the inner circumference of the new stirrups. The new stirrups are filled with concrete inside and outside, aligned with the original beam, to increase the beam's structural height.

8. An application method for calculating the maximum crack width of a reinforced concrete beam with enlarged cross-section as described in any one of claims 1-7, characterized in that, First, for the design of the secondary reinforcement scheme for the beam structure to be reinforced, the parameters are extracted from the design scheme and substituted into the calculation method for the maximum crack width of the reinforced concrete beam with increased cross section as described in any one of claims 1-7 to calculate the maximum crack width. The design scheme is selected by comparing the maximum crack width with the set upper limit of the allowable crack width.

9. A system for calculating the maximum crack width of a reinforced concrete beam with enlarged cross-section and secondary reinforcement, characterized in that, It includes a memory and a processor. The memory stores a computer program, and the processor is connected to the memory. The processor is used to execute the computer program to implement the method for calculating the maximum crack width of a reinforced concrete beam with increased cross-section as described in any one of claims 1-7.

10. A storage medium, characterized in that, The system contains a computer program that, when executed, implements the method for calculating the maximum crack width of a reinforced concrete beam with increased cross-section as described in any one of claims 1-7.

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