Calculation method of maximum crack width of reinforced concrete beam with enlarged cross section and secondary reinforcement

Abstract

The present application relates to the technical field of building structure engineering, especially to a calculation method of maximum crack width of reinforced concrete beam with secondary reinforcement by increasing section. The present application firstly determines the parameters of the original beam and the reinforced beam, and then brings them into the following formula to calculate the maximum crack width. Based on theoretical parameter analysis and a large number of tests, combined with the force balance condition of steel and steel plate and the balance condition of the moment of the force point of the compressed area of the concrete when the crack appears, the present application calculates the steel stress and the average crack width, and calculates the uneven coefficient of the tensile steel strain between cracks, so as to obtain the calculation method of the maximum crack width of the reinforced concrete beam with secondary reinforcement by increasing section, which conforms to the actual situation. The present application can well reflect the crack situation of the beam, the calculation steps are clear, the calculation method is simple, and the defect of lacking reliable calculation method of the maximum crack width of the reinforced concrete beam with secondary reinforcement by increasing section is overcome.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of building structure engineering, and particularly relates to a calculation method of maximum crack width of reinforced concrete beam reinforced by enlarging section twice. BACKGROUND

[0002] In the technical field of building structure engineering, reinforced concrete beam is a key load-bearing component, and the calculation of the maximum crack width thereof is a research focus. The reinforced concrete beam reinforced by enlarging section twice is reinforced by enlarging section on the basis of the beam reinforced by sticking steel plate for the first time, that is, the section size of the component is enlarged to improve the bearing capacity thereof, and the construction process is relatively simple, and the reinforcing and repairing capacity is relatively strong.

[0003] At present, the component reinforced twice gradually increases, but the research on the reinforced concrete component reinforced twice is still in the initial stage, especially the flexural performance of the beam reinforced twice is not deeply researched, the flexural mechanism thereof is not clear, and the calculation method of the maximum crack width of the reinforced concrete beam reinforced by enlarging section twice is lacked. SUMMARY

[0004] In order to overcome the defect that the reliable calculation method of the maximum crack width of the reinforced concrete beam reinforced by enlarging section twice is lacked in the prior art, the present application provides a calculation method of the maximum crack width of the reinforced concrete beam reinforced by enlarging section twice, which can simply, quickly and reliably reflect the crack condition of the beam.

[0005] The calculation method of the maximum crack width of the reinforced concrete beam reinforced by enlarging section twice provided by the present application is characterized in that it is suitable for the concrete beam with the bottom increased, and the original beam has a steel plate bonded at the bottom. The method firstly determines the parameters of the original beam and the reinforced beam, and then brings the parameters into the following formula to calculate the maximum crack width :

[0006] ;

[0007] is a component comprehensive influence coefficient; is a crack interval tensile steel bar strain uneven coefficient; is equivalent stress of tensile steel bar; is equivalent tensile steel bar elastic modulus; is average value of crack interval.

[0008] Preferably, the calculation formula of the crack interval tensile steel bar strain uneven coefficient is as follows:

[0009] ;

[0010] wherein, is a new concrete axial tensile strength standard value; Aeff Aeff p Aeff pp σs , , are experimental fitting parameters, and Ls Lc Lsc h

[0011] Preferably,

[0012] ;

[0013] wherein, As As s0 Es sm Es

[0014] Preferably,

[0015] ;

[0016] wherein, , and are experimental fitting parameters; d is the diameter of the new reinforcement, and c is the thickness of the concrete cover, t and are proportional coefficients, , ; b t

[0017] Preferably, the constraint of

[0018] ;

[0019] wherein, σct sm σt l is the average bond stress between the concrete and the new tensile reinforcement within the length , are experimental fitting parameters, and is the distance from the force point of the equivalent tensile reinforcement to the force point of the concrete compression zone, is the distance from the force point of the concrete tensile zone to the force point of the concrete compression zone, and h is the height of the reinforced beam.

[0020] Preferably, The constraint is:

[0021] ;

[0022] wherein, are experimental fitting parameters, and is the distance from the force point of the steel plate to the force point of the concrete compression zone, pm is the length from the crack as the starting point l The average bond stress between the concrete and the steel plate.

[0023] Preferably, the beam reinforcement method comprises the following steps:

[0024] Firstly, the steel plate is adhered to the bottom of the original beam for reinforcement, and then the U-shaped hoop plate is arranged for anchoring;

[0025] Two rows of studs are welded along the longitudinal direction of the steel plate to anchor the new concrete, and the new stirrups are arranged in the gap between the U-shaped hoop plates and implanted into the original beam, the new stirrups are overlapped with the original stirrups, and the new tensile reinforcement is arranged in the inner circumference of the new stirrups;

[0026] The concrete is filled in and outside the new stirrups, and the beam structure height is increased by aligning with the original beam.

[0027] The application method of the maximum crack width calculation method of the increased section secondary reinforced concrete beam is characterized in that, firstly, the increased section secondary reinforcement scheme is designed for the beam structure to be reinforced, and the parameters are extracted from the design scheme and brought into the maximum crack width calculation method of the increased section secondary reinforced concrete beam to calculate the maximum crack width; the design scheme is screened through the comparison result of the maximum crack width and the upper limit of the allowable crack width.

[0028] The application method of the maximum crack width calculation method of the increased section secondary reinforced concrete beam is characterized in that, firstly, the increased section secondary reinforcement scheme is designed for the beam structure to be reinforced, and the parameters are extracted from the design scheme and brought into the maximum crack width calculation method of the increased section secondary reinforced concrete beam to calculate the maximum crack width; the design scheme is screened through the comparison result of the maximum crack width and the upper limit of the allowable crack width.

[0029] The application method of the maximum crack width calculation method of the increased section secondary reinforced concrete beam is characterized in that, firstly, the increased section secondary reinforcement scheme is designed for the beam structure to be reinforced, and the parameters are extracted from the design scheme and brought into the maximum crack width calculation method of the increased section secondary reinforced concrete beam to calculate the maximum crack width; the design scheme is screened through the comparison result of the maximum crack width and the upper limit of the allowable crack width.

[0030] The present application has the advantages of:

[0031] The application provides a calculation method for the maximum crack width of a reinforced concrete beam with enlarged section and secondary reinforcement, which is based on theoretical parameter analysis and a large number of tests, combines the force balance conditions of the steel bars and the steel plate and the moment balance condition of the force point of the compressed area of the concrete when a crack is about to occur, calculates the stress of the steel bars and the average crack width, and calculates the uneven strain coefficient of the tensile steel bars between cracks to obtain a calculation method for the maximum crack width of the reinforced concrete beam with enlarged section and secondary reinforcement, which is in line with the actual situation. BRIEF DESCRIPTION OF DRAWINGS

[0032] Figure 1 A structural schematic diagram of a reinforced concrete beam with enlarged section and secondary reinforcement is shown in the figure.

[0033] The figure shows: 1, original beam; 11, original stirrup; 12, original tensile steel bar; 13, beam top frame vertical bar; 21, new stirrup; 22, new tensile steel bar; 23, steel plate; 24, U-shaped stirrup plate.

[0034] Figure 2 A schematic diagram of a whole calculation model for crack derivation is shown in the figure.

[0035] Figure 3 A schematic diagram of an equivalent calculation model for steel bars is shown in the figure.

[0036] Figure 4 A schematic diagram of an equivalent calculation model for steel plates is shown in the figure.

[0037] Figure 5 A schematic diagram of an equivalent steel bar and steel plate isolation body analysis is shown in the figure.

[0038] Figure 6 A flowchart of the calculation method for the maximum crack width of the reinforced concrete beam with enlarged section and secondary reinforcement is shown in the figure. DETAILED DESCRIPTION

[0039] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the present application.

[0040] REFERENCE Figure 1The application is applicable to the method for increasing section secondary reinforcement of reinforced concrete beam from the bottom, and the reinforcement process is as follows: firstly, the original beam 1 is reinforced by sticking a steel plate at the bottom, and then the U-shaped hoop plate 24 is arranged for anchoring; two rows of studs are welded along the longitudinal direction of the steel plate 23 so as to anchor the newly added concrete; the newly added hoop 21 is arranged in the original beam 1 at the gap of the U-shaped hoop plate 24, the newly added hoop 21 is overlapped with the original hoop 11, and the newly added tensile steel bars 22 are arranged in the inner periphery of the newly added hoop 21; the concrete is filled in the inner and outer peripheries of the newly added hoop 21, and the beam structure height is increased in alignment with the original beam 1. Figure 1 The bottom inner periphery of the original hoop 11 is provided with two original tensile steel bars 12, and the top inner periphery is provided with the beam top frame vertical reinforcement 13.

[0041] The basic parameters of the reinforced concrete beam with increased section secondary reinforcement and steel material are determined, including the beam height h , i.e. the beam height after the increased section secondary reinforcement; the original beam height h 0 , i.e. the beam structure height before the increased section secondary reinforcement; the beam section width b; the sum of the section areas of the original tensile steel bars A s0 ; the sum of the section areas of the newly added tensile steel bars A s ; the area of the steel plate A p ; the periphery of the original tensile steel bars s 0; the periphery of the newly added tensile steel bars s ; the width of the steel plate b p ; the reinforced concrete beam structure with increased section secondary reinforcement is shown in Figures 1 to 5 , wherein the stress of the original tensile steel bar s0 , the stress of the newly added tensile steel bar s and the tensile stress of the steel plate pp are measured parameters.

[0042] The average value of the crack spacing is assumed to be l : the stress of the original tensile steel bar after the distance of l length is denoted as s10 , the stress of the newly added tensile steel bar is denoted as s1 , and the tensile stress of the steel plate is denoted as p1 ; and the tensile stress of the section concrete after the distance of l length 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.

[0043] 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 .

[0044] 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 .

[0045] 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.

[0046] 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.

[0047] The calculation process for this step is as follows:

[0048] First, establish the equilibrium conditions for the forces:

[0049] (1);

[0050] (2);

[0051] (3);

[0052] 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:

[0053] (4);

[0054] in: For the equivalent area of ​​the tensile reinforcement, ; The elastic modulus of the original tensile reinforcement, The elastic modulus of the newly added tensile reinforcement, both of which can be determined according to the Metallic Materials-Tensile Testing at Ambient Temperature (GB / T 228.1-2010);

[0055] The equivalent stress of the tensile reinforcement; The equivalent stress of the tensile reinforcement when the tensile stress of the concrete rises to f tk The equivalent stress of the tensile reinforcement when the tensile stress of the concrete rises to f tk The equivalent shear stress of the tensile reinforcement when the tensile stress of the concrete rises to The equivalent perimeter of the tensile reinforcement, which is calculated from the equivalent area of the tensile reinforcement ; that is, , r is the equivalent radius;

[0056] and According to the experimental measurement, formula (4) is substituted into formula (1), formula (2), formula (3), and formula (4), and .

[0057] S2, the bending moment of the crack section about to appear at the crack is calculated ; the moment is taken at the force point of the concrete compression zone, and the equilibrium condition of the moment can be obtained:

[0058] (5);

[0059] wherein, is the axial distance from the force point of the equivalent tensile reinforcement to the force point of the concrete compression zone;

[0060] is the axial distance from the force point of the steel plate to the force point of the concrete compression zone;

[0061] is the resisting bending moment of the concrete tensile zone;

[0062] (6);

[0063] wherein, is the effective tensile concrete sectional area, ; b is the concrete sectional width;

[0064] is the standard value of the newly added concrete axial tensile strength, which is an inherent parameter of the concrete material and can be obtained by table lookup;

[0065] ​The distance between the axis of the resultant force point in the tensile zone of the concrete and the resultant force point in the compression zone of the concrete.

[0066] S3, calculating the average crack spacing l ;

[0067] Solving formula (3), formula (4), formula (5) and formula (6) simultaneously can obtain:

[0068] (7);

[0069] wherein, and are proportional coefficients, , ; d is the diameter of the steel bar; is the width of the steel plate; is the thickness of the steel plate.

[0070] A large number of experimental studies show that, is proportional to , is also proportional to , according to the test data and can be taken as constants, is related to the shape of the steel bar, when the shape of the steel bar is given, can be taken as a constant, l is related to the thickness of the concrete protective layer c , formula (7) is rewritten as:

[0071] (8);

[0072] (9);

[0073] (10);

[0074] From the analysis of the test data, it can be known that: =0.08, =1.9, =0.05.

[0075] S4, calculating the strain non-uniformity coefficient of the tensile steel bar between cracks and the maximum crack width ;

[0076] The average stress of the equivalent steel bar is:

[0077] (11) ;

[0078] wherein, is the average stress of the equivalent steel bar;

[0079] According to the test data, it can be known that:

[0080] (12);

[0081] (13);

[0082] The resistance moment of the equivalent steel is , the resistance moment of the tensile stress of the concrete is , and the resistance moment of the steel plate is , and formula (5) can be obtained by combining formula (5):

[0083] (14);

[0084] Therefore, the following formula is obtained:

[0085] (15);

[0086] In the subsequent examples, the following formula is obtained according to the experiment: , , and formula (15) is further simplified to:

[0087] (16);

[0088] The calculation formula of the maximum crack width of the reinforced concrete beam of the secondary reinforcement by increasing the section according to the specification is as follows:

[0089] (17);

[0090] is a comprehensive influence coefficient of the component, including factors such as test randomness, steel type and stress characteristics, and is determined according to the test data, and is 2.2 according to the test data;

[0091] is the equivalent stress of the tensile steel; is the equivalent tensile steel elastic modulus: ; wherein, E s0 is the elastic modulus of the original tensile steel, and E sm is the elastic modulus of the new tensile steel.

[0092] The calculation method of the maximum crack width of the reinforced concrete beam of the secondary reinforcement by increasing the section is verified by combining the specific examples.

[0093] In this example, the stress of the original tensile steel is s0 , the stress of the new tensile steel is s , and the tensile stress of the steel plate is pp , original tensile reinforcement elastic modulus , secondary reinforcement newly added tensile reinforcement elastic modulus , determined according to the metal material tensile test (GB / T228.1-2010);

[0094] In this embodiment, three reinforced concrete beam test pieces of the increased section secondary reinforcement are selected from a laboratory of an institute, and the test piece numbers are LA-1, LA-2 and LA-3 respectively. The increased section secondary reinforced concrete beam test pieces are respectively subjected to static failure test and finite element numerical simulation to explore the rationality and practicability of the calculation method of the maximum crack width of the increased section secondary reinforced concrete beam.

[0095] The test piece of the increased section secondary reinforced concrete beam in this embodiment is completed on the basis of the first reinforced beam with pasted steel plates, and the first reinforced beam with pasted steel plates is completed on the basis of the unreinforced beam. For details, refer to Figure 1 . In this embodiment, the test piece parameters are shown in Table 1.

[0096] Table 1: Basic parameters of the increased section secondary reinforced concrete beam test piece

[0097] ;

[0098] In this embodiment, the original beams (unreinforced beams) of the test pieces LA-1, LA-2 and LA-3 are the same, and are all poured with C30 concrete with a protective layer thickness of 30 mm; the newly added concrete strength grade is C40. The standard value of the axial tensile strength of the C30 concrete = 32.7 N / mm 2 , and the standard value of the axial tensile strength of the C40 concrete = 42.2 N / mm 2 .

[0099] In this embodiment, the steel bar types of the original tensile reinforcement, the original stirrup, the beam top frame vertical reinforcement, the newly added tensile reinforcement and the newly added stirrup are all HRB400; the steel plate material type is Q235B.

[0100] The original tensile reinforcement is configured as two HRB400 steel bars with a diameter of 20 mm, the beam top frame vertical reinforcement is configured as two HRB400 steel bars with a diameter of 14 mm, and the original stirrup is configured as HRB400 steel bars with a diameter of 8 mm; the newly added tensile reinforcement is configured as two HRB400 steel bars with a diameter of 18 mm, and the newly added stirrup is configured as HRB400 steel bars with a diameter of 8 mm. The interval of the original stirrup is 100 mm, and the newly added stirrup is overlapped with the original stirrup, i.e. the interval of the newly added stirrup is 100 mm.

[0101] The steel material parameters are shown in Table 2.

[0102] Table 2: Steel bar, steel plate mechanical property parameters

[0103] ;

[0104] In this embodiment, experiments, finite element simulation and Figure 6 The maximum crack width calculation method of the reinforced concrete beam with increased section secondary reinforcement given by the application is shown in the following formula (1) : w = 0. 2 fct / fyt (1) ω u、 ω fand ω t. The experimental results are shown in Table 3.

[0105] Table 3: Comparison of maximum crack width test value, finite element simulation value and theoretical value

[0106] ;

[0107] As shown in Table 3, the maximum crack width test value is very small compared with the finite element simulation value and the theoretical calculation value. The average value of the ratio of the maximum crack width test value to the theoretical calculation value is 1.01; the average value of the ratio of the maximum crack width finite element calculation value to the theoretical calculation value is 0.98, and the variation coefficient is 0.027. Overall, the parameters taken from the test and the finite element have certain reliability, the calculation formula can reflect the crack condition of the beam, has good accuracy and strong practicability.

[0108] Of course, for those skilled in the art, the application is not limited to the details of the above exemplary embodiments, but also includes the same or similar structures that can be realized in other specific forms without departing from the spirit or essential characteristics of the application. Therefore, from any point of view, the embodiments should be regarded as exemplary and non-limiting, and the scope of the application is defined by the appended claims rather than the above description, and therefore all changes falling within the meaning and scope of the equivalent elements of the claims are intended to be included in the application. Any reference signs in the claims should not be considered as limiting the claims involved.

[0109] In addition, it should be understood that although the present specification is described in terms of embodiments, not every embodiment contains only one independent technical solution, and the description manner of the specification is only for the sake of clarity, and those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be properly combined to form other embodiments that those skilled in the art can understand.

[0110] The technologies, shapes and structural parts not described in detail in the application are well-known technologies.

Claims

1. A method for calculating the maximum crack width of a reinforced concrete beam with increased cross section and secondary reinforcement, characterized in that, The method is suitable for increasing the concrete beam from the bottom, and the original beam bottom is bonded with a steel plate; the method first determines the original beam and the reinforcement beam parameters, and then brings into the following formula to calculate the maximum crack width : is a member comprehensive influence coefficient; is a crack-to-crack tensile reinforcement strain non-uniformity coefficient; is an equivalent tensile reinforcement stress; is an equivalent tensile reinforcement elastic modulus; is an average crack spacing; Coefficient of uniformity of tensile reinforcement strain in cracks The calculation formula is: wherein, is the new standard value of the axial tensile strength of concrete; is the equivalent area of the tensile reinforcement, is the effective tensile concrete sectional area; A p is the sectional area of the steel plate, pp is the tensile stress of the steel plate; , , are all experimental fitting parameters, and is the axial distance from the equivalent tensile reinforcement force point to the concrete compression zone force point, is the axial distance from the concrete tensile zone force point to the concrete compression zone force point, is the axial distance from the steel plate force point to the concrete compression zone force point, and h is the height of the reinforced beam. wherein, , and are experimental fitting parameters; d is the diameter of the new reinforcement, c is the thickness of the concrete cover, is the thickness of the steel plate; and are proportionality coefficients, , ; is the width of the steel plate; is the thickness of the steel plate; Wherein, is the sum of the cross-sectional area of the newly added tensile reinforcement, is the sum of the cross-sectional area of the original tensile reinforcement; E s0 is the elastic modulus of the original tensile reinforcement, E sm is the elastic modulus of the newly added tensile reinforcement; The beam reinforcing method comprises the following steps: Firstly, the original beam is reinforced by pasting steel plates at the bottom of the original beam, and then U-shaped hoop plates are arranged for anchoring; Secondly, two rows of studs are welded along the longitudinal direction of the steel plates to anchor the newly added concrete, and in the gap between the U-shaped hoop plates, newly added stirrups are arranged to be embedded in the original beam, the newly added stirrups are overlapped with the original stirrups, and the inner periphery of the newly added stirrups is provided with newly added tensile steel bars; Finally, the original beam is filled with concrete inside and outside the newly added stirrups, and the height of the beam structure is increased.

2. The method of calculating the maximum crack width of a reinforced concrete beam with enlarged cross section and secondary reinforcement according to claim 1, wherein 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.

3. The method of calculating the maximum crack width of a reinforced concrete beam with enlarged cross-section and secondary reinforcement according to claim 2, wherein, The constraints are: wherein, is the experimental fitting parameter, and is the distance between the steel plate resultant point and the concrete compression zone resultant point axis, pm is the length from the crack as a starting point l is the average bond stress between the inner concrete and the steel plate.

4. A method of using the method of calculating the maximum crack width of a reinforced concrete beam with enlarged cross section and secondary reinforcement according to any one of claims 1 to 3, characterized in that, Firstly, a design scheme of increasing the cross section for reinforcing the beam structure is designed, parameters of the design scheme are brought into the maximum crack width calculation method of the reinforced concrete beam with increased cross section for secondary reinforcement according to any one of claims 1-3 to calculate the maximum crack width; and the design scheme is screened through comparison of the maximum crack width with the upper limit of the allowable crack width.

5. A system for calculating the maximum crack width of a reinforced concrete beam with increased cross section and secondary reinforcement, characterized in that, The device comprises a memory and a processor, the memory stores a computer program, the processor is connected to the memory, and the processor is used to execute the computer program to realize the maximum crack width calculation method of the reinforced concrete beam with increased cross section for secondary reinforcement according to any one of claims 1-3.

6. A storage medium, characterized by The computer program is stored and is used to realize the maximum crack width calculation method of the reinforced concrete beam with increased cross section for secondary reinforcement according to any one of claims 1-3 when the computer program is executed.

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