Shear calculation method suitable for grouting sleeve connection area of prefabricated assembly compression-bending member

Abstract

This invention discloses a method for calculating the shear strength of the grouting sleeve connection zone in precast assembled compression-bending components, relating to the technical field of shear strength calculation in grouting sleeve connection zones. The method includes the following steps: S100, inputting relevant parameters of the isolator, where the isolator is the grouting sleeve connection zone; S200, determining the yield moment of the isolator section based on the shear span ratio λ. When λ < 1.5, the yield moment of the isolator section is set to zero; when λ ≥ 1.5, the yield moment of the isolator section is determined to be Mu based on the column section nonlinear analysis module; S300, based on the determined yield moment of the isolator section, obtaining the strain value at the centerline of the corresponding isolator cross-section, and setting the strain value equal to the average longitudinal strain of the isolator; S400, calculating the shear capacity of the isolator section according to different failure modes. This method allows for the quantitative calculation of the shear strength of the grouting sleeve connection zone in precast assembled compression-bending components.

Description

Technical Field

[0001] This invention relates to the technical field of shear calculation, and more specifically, to a method for calculating shear resistance in the grouting sleeve connection zone of precast assembled bending members. Background Technology

[0002] Grouting sleeves, as stable and reliable steel bar connectors, have been widely used in prefabricated buildings. The connection area of ​​grouting sleeves has the characteristics of high rigidity and high strength.

[0003] The length of the grouting sleeve is limited by the anchorage length of the reinforcing bars, making continuous connection along the column height impossible. This results in high stiffness in localized areas where the reinforcing bars are connected by the grouting sleeve. In precast columns with grouting sleeves, the deformation of the member under bending conditions is inconsistent, affecting the energy dissipation of the structure under seismic loading. Under low-cycle cyclic loading, plastic hinges easily form on both sides of the sleeve in precast columns connected by grouting sleeves, while the damage in the grouting sleeve area is relatively small. The grouting sleeve area is difficult to damage in experiments, making it even more difficult to measure its shear strength in vertical compression-bending members. Currently, existing codes do not provide corresponding shear calculation methods for grouting connection areas. To apply the high-strength characteristics of the grouting sleeve area to practical engineering, this invention proposes a shear calculation method suitable for the grouting sleeve connection area of ​​precast assembled compression-bending members. Summary of the Invention

[0004] To address the aforementioned technical problems in related technologies, this invention provides a shear calculation method applicable to the grouting sleeve connection zone of prefabricated assembled bending components, which can solve the above problems.

[0005] To achieve the above-mentioned technical objectives, the technical solution of the present invention is implemented as follows:

[0006] A method for calculating the shear strength of the grouting sleeve connection zone of precast assembled bending members includes the following steps:

[0007] S100. Input the relevant parameters of the isolator, where the isolator is the grouting sleeve connection area;

[0008] S200. Determine the yield moment of the isolation body section based on the shear span ratio λ. When λ < 1.5, set the yield moment of the isolation body section to zero. When λ ≥ 1.5, determine the yield moment of the isolation body section to Mu based on the column section nonlinear analysis module.

[0009] S300. Based on the determined yield moment of the isolated body section, obtain the strain value at the centerline of the corresponding isolated body cross section. And set the strain value Equal to the average longitudinal strain of the isolated body ;

[0010] S400. Calculate the cross-sectional shear capacity of the isolation body according to different failure modes. The failure modes include failure mode one and failure mode two. Failure mode one is when the stirrups in the grouting sleeve splice area reach the yield strength, and failure mode two is when the concrete in the grouting sleeve area reaches the ultimate compressive bearing capacity state and the concrete exhibits a failure state.

[0011] S410. Under failure mode one conditions, calculate the cross-sectional shear capacity of the isolated body according to the following specific steps;

[0012] S411, Initial angle of principal compressive stress for the isolated concrete element and initial principal tensile strain Assign values ​​and according to the formula. Calculate the principal compressive strain of the isolated concrete element ;

[0013] S412. Assuming the stirrups reach the yield state, then ,in This represents the normal stress in the transverse stirrups. The yield strength of the stirrup is represented by the formula. Calculate the principal tensile strain of the new isolated concrete element. ,in This represents the average transverse strain in the grouting sleeve region. Satisfy the formula Then determine If convergent, e takes a value below 0.0001. If convergent, return to S411 and recalculate with a new initial value.

[0014] S413, Calculation and And according to the formula Calculate the principal stress angles of the new isolated concrete element. ,in This represents the normal stress in the transverse stirrups. For the principal tensile stress in concrete, This refers to the shear stress in concrete. The reinforcement ratio of the transverse stirrups, if Satisfy the formula Then determine If convergence is achieved, e takes a value below 0.0001. If convergence is not achieved, return to S411, reset the initial value, and perform interval search calculation using the bisection method until convergence is achieved.

[0015] S414. Based on the convergent principal stress compression angle and convergent principal tensile strain of the isolated concrete micro-element, first, according to the formula... Calculate the shear strain of the shear element in cracked concrete Then calculate the shear capacity V of the isolated section. n When λ≥1.5, if If the value is less than 0, then the cross-section of the isolated body is in a state of compressive-shear failure. ,like If the value is greater than 0, then the cross-section of the isolated body is in a state of bending-shear failure. When λ < 1.5, then ,in Indicates the width of the component's cross-section. The effective height of the component section. The spacing between adjacent stirrups. The cross-sectional area of ​​the stirrups at the stressed section is... The cross-sectional area of ​​the grouting sleeve is... The shear modulus of the grouting sleeve. Let be the shear strain of the cracked concrete shear element, where The height of the isolation body;

[0016] S420. Under failure mode two conditions, calculate the cross-sectional shear capacity of the isolated body according to the following specific steps;

[0017] S421, Initial angle of principal compressive stress for the isolated concrete element Assignment;

[0018] S422. Assuming the concrete reaches its peak compressive stress, then , It is the strain corresponding to the peak stress of concrete under constrained conditions;

[0019] S423, First, according to the formula Calculate the principal tensile strain of the isolated concrete element Then according to the formula Calculate the transverse strain of the stirrups ,judge Is it less than or equal to the stirrup yield strain? If yes, proceed to the next step; otherwise, return to S421 and resubmit. Value, registrable Value in the original Add 0.01° to the value;

[0020] S424, Calculation , and And according to the formula Calculate the principal stress angles of the new isolated concrete element. ,in This represents the normal stress in the transverse stirrups. For the principal tensile stress in concrete, This refers to the shear stress in concrete. The reinforcement ratio of the transverse stirrups, if Satisfy the formula Then determine If convergence is achieved, e takes a value below 0.0001. If convergence is not achieved, return to S421, reset the initial value, and perform interval search calculation using the bisection method until convergence is achieved.

[0021] S425. Calculation of principal stress pressure angles in convergent isolated concrete micro-elements. First, according to the formula Calculate the shear strain of the shear element in cracked concrete Then calculate the shear capacity V of the isolated section. n When λ≥1.5, if If the value is less than 0, then the cross-section of the isolated body is in a state of compressive-shear failure. ,like If the value is greater than 0, then the cross-section of the isolated body is in a state of bending-shear failure. When λ < 1.5, then ,in Indicates the width of the component's cross-section. The effective height of the component section. The spacing between adjacent stirrups. The cross-sectional area of ​​the stirrups at the stressed section is... This represents the normal stress of the transverse reinforcing steel. The cross-sectional area of ​​the grouting sleeve is... The shear modulus of the grouting sleeve. Let be the shear strain of the cracked concrete shear element, where The height of the isolation body.

[0022] Furthermore, the relevant parameters of the isolator in S100 include the material type, the axial force P on the isolator, the bending moment M on the isolator, the lateral load Fx, and the dimensional parameters of the cross-section of the isolator.

[0023] Furthermore, the concrete, reinforcing steel, and grouting sleeve in the connection area of ​​the precast assembled bending component are made of elasto-plastic materials.

[0024] Furthermore, Calculated using the following formula:

[0025] ;

[0026] in The axial compressive strength of unconfined concrete It is the elastic modulus of concrete. It is the principal strain under compression in concrete;

[0027] Calculated using the following formula:

[0028] ;

[0029] in Let be the cross-sectional shear stress of the column cracking element. This refers to the reinforcement ratio of the transverse stirrups. This refers to the shear stress at the stirrup section.

[0030] S424 Calculated using the following formula:

[0031] ;

[0032] in The transverse normal stress of the column cracking element. This refers to the reinforcement ratio of the transverse stirrups. This represents the transverse normal stress in the concrete.

[0033] The beneficial effects of this invention are that the shear strength of the grouting sleeve connection zone of prefabricated assembled bending components can be quantitatively calculated using the method of this application. Attached Figure Description

[0034] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0035] The present invention will now be described in further detail with reference to the accompanying drawings.

[0036] Figure 1 This is a flowchart illustrating a method for calculating the shear strength of a precast assembled bending member with a grouting sleeve connection zone, as described in an embodiment of the present invention. Detailed Implementation

[0037] 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. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention are within the scope of protection of the present invention.

[0038] like Figure 1As shown, this invention proposes a shear strength calculation method for the grouting sleeve connection zone of precast assembled bending members. The grouting sleeve enhances the local stiffness of the structural member, but leads to uneven longitudinal stiffness distribution within the member. This unevenness causes a shift in the position of the plastic hinge, making the determination of the shear strength of the grouting sleeve connection zone in experiments complex and difficult. To solve this problem, this method isolates the grouting sleeve connection zone to form a grouting sleeve connection zone isolation body, and solves the problem using mechanical theory. Specifically, it includes the following steps:

[0039] Input the relevant parameters of the isolator, which is the grouting sleeve connection area, including material type, axial force P on the isolator, bending moment M on the isolator, lateral load Fx, dimensional parameters of the cross section of the isolator, etc., and the concrete, steel bars and grouting sleeve of the precast assembled bending component grouting sleeve connection area are selected as elastic-plastic materials.

[0040] The yield moment of the isolator section is determined based on the shear span ratio λ. When λ < 1.5, the yield moment is set to zero. When λ ≥ 1.5, the yield moment is determined to be Mu by the column section nonlinear analysis module. The column section nonlinear analysis module can determine the yield moment of the isolator section using the fiber strip method. A horizontal section of the grouting sleeve connection area is taken, and the concrete section is divided into strips with the centerline of the section as the x-axis origin. The centroid coordinates of the strip concrete are expressed as x... i This indicates the calculation of strain in the strip concrete micro-element and the grouting sleeve. According to Formula 1... The strain at any height of the concrete cross-section can be calculated; based on the balance of axial force and bending moment of the cross-section, Formula 2 can be obtained. ,in and These represent the stress functions of the concrete strip element and the grouting sleeve element, respectively. Represents the area of ​​the concrete strip. This represents the area of ​​the grouting sleeve. (Formula 1) Substitution function The independent variable in the equation, where x i For the centroid coordinates, and Given the known quantities, the only unknowns in the equation are... and The bending moment M gradually increases from 0, thus plotting the curve. The yield moment Mu is determined based on the yield point of the curve (the inflection point between linear and nonlinear modes).

[0041] When Mu is determined in the above steps, the corresponding section yield state can be determined accordingly. To obtain the strain value at the centerline of the cross-section of the grouting sleeve region when the calculated section reaches the yield bending moment Mu. And set the strain value Equal to the average longitudinal strain of the isolated body .

[0042] The shear capacity of the isolated section was calculated based on different failure modes. Tests showed that the grouting sleeve in the precast column shear test was largely elastic, not yet entering the plastic deformation stage. Therefore, there are two failure modes at the precast assembly location of the grouting sleeve: 1. The stirrups in the grouting sleeve splice area reach their yield strength; 2. The concrete in the grouting sleeve area reaches its ultimate compressive bearing capacity, and the concrete exhibits failure. Therefore, when calculating failure mode 1, it can be initially assumed that the stirrups have reached their yield strength. Similarly, in calculating failure mode 2, it is assumed that the concrete reaches its ultimate compressive strain. .

[0043] Under failure mode one conditions, the shear capacity of the isolated section is calculated according to the following specific steps:

[0044] Initial angle of principal compressive stress for isolated concrete micro-elements and initial principal tensile strain Assignment, setting =0.1, =0.0001, and according to the formula Calculate the principal compressive strain of the isolated concrete element ;

[0045] Assuming the stirrups reach the yield state, then ,in This represents the normal stress in the transverse stirrups. The yield strength of the stirrup is represented by the formula. Calculate the principal tensile strain of the new isolated concrete element. ,in This represents the average transverse strain in the grouting sleeve region. Satisfy the formula Then determine If convergent, e takes a value below 0.0001. If not convergent, return to S411 and recalculate with a new initial value (you can directly use the non-convergent value). (as a newly given initial value);

[0046] calculate and ,in , The axial compressive strength of unconfined concrete It is the elastic modulus of concrete. It is the principal compressive strain of concrete, among which Let be the cross-sectional shear stress of the column cracking element. This refers to the reinforcement ratio of the transverse stirrups. The shear stress at the stirrup section is given by the formula. Calculate the principal stress angles of the new isolated concrete element. ,in This represents the normal stress in the transverse stirrups. For the principal tensile stress in concrete, This refers to the shear stress in concrete. The reinforcement ratio of the transverse stirrups, if Satisfy the formula Then determine If convergence is achieved, e takes a value below 0.0001. If convergence is not achieved, return to S411, reset the initial value, and perform interval search calculation using the bisection method until convergence is achieved.

[0047] Based on the convergent principal stress compression angle and the convergent principal tensile strain of the isolated concrete element, firstly according to the formula... Calculate the shear strain of the shear element in cracked concrete Then calculate the shear capacity V of the isolated section. n When λ≥1.5, if If the value is less than 0, then the cross-section of the isolated body is in a state of compressive-shear failure. V n Take V f and V m The maximum value in, if If the value is greater than 0, then the cross-section of the isolated body is in a state of bending-shear failure. V n Take V f and V m The minimum value in, when λ < 1.5, then ,in , Indicates the width of the component's cross-section. The effective height of the component section. The spacing between adjacent stirrups. The cross-sectional area of ​​the stirrups at the stressed section is... The cross-sectional area of ​​the grouting sleeve is... The shear modulus of the grouting sleeve. Let be the shear strain of the cracked concrete shear element, where The height of the isolation body.

[0048] Under failure mode two conditions, the shear capacity of the isolated section is calculated according to the following specific steps:

[0049] Initial angle of principal compressive stress for isolated concrete micro-elements Assignment, setting =0.1;

[0050] Assuming the concrete reaches peak compressive stress, then , It is the strain corresponding to the peak stress of concrete under constrained conditions;

[0051] First, according to the formula Calculate the principal tensile strain of the isolated concrete element Then according to the formula Calculate the transverse strain of the stirrups ,judge Is it less than or equal to the stirrup yield strain? If yes, proceed to the next step; otherwise, return to S421 and resubmit. Value, registrable Value in the original Add 0.01° to the value;

[0052] calculate , and ,in , The transverse normal stress of the column cracking element. This refers to the reinforcement ratio of the transverse stirrups. The transverse normal stress of concrete is given by... , The axial compressive strength of unconfined concrete It is the elastic modulus of concrete. It is the principal compressive strain of concrete, among which Let be the cross-sectional shear stress of the column cracking element. This refers to the reinforcement ratio of the transverse stirrups. The shear stress at the stirrup section is given by the formula. Calculate the principal stress angles of the new isolated concrete element. ,in This represents the normal stress in the transverse stirrups. For the principal tensile stress in concrete, This refers to the shear stress in concrete. The reinforcement ratio of the transverse stirrups, if Satisfy the formula Then determine If convergence is achieved, e takes a value below 0.0001. If convergence is not achieved, return to S421, reset the initial value, and perform interval search calculation using the bisection method until convergence is achieved.

[0053] Based on the convergence of the principal stress pressure angle of the isolated concrete micro-element and the calculation First, according to the formula Calculate the shear strain of the shear element in cracked concrete Then calculate the shear capacity V of the isolated section. n When λ≥1.5, if If the value is less than 0, then the cross-section of the isolated body is in a state of compressive-shear failure. ,like If the value is greater than 0, then the cross-section of the isolated body is in a state of bending-shear failure. When λ < 1.5, then ,in Indicates the width of the component's cross-section. The effective height of the component section. The spacing between adjacent stirrups. The cross-sectional area of ​​the stirrups at the stressed section is... This represents the normal stress of the transverse reinforcing steel. The cross-sectional area of ​​the grouting sleeve is... The shear modulus of the grouting sleeve. Let be the shear strain of the cracked concrete shear element, where The height of the isolation body.

[0054] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for calculating the shear resistance of a grout sleeve connection zone of a pre-fabricated assembled compression-bent member, characterized in that, The method comprises the following steps: S100, inputting related parameters of the isolation body, wherein the isolation body is a grouting sleeve connection area; S200, determining a cross-section yield bending moment of the isolation body according to a shear-span ratio λ of the isolation body, when λ < 1.5, setting the cross-section yield bending moment of the isolation body as zero, and when λ >= 1.5, determining the cross-section yield bending moment of the isolation body as Mu according to a column section nonlinear analysis module; S300, based on the determined isolated body cross-section yield bending moment, obtaining a strain value at the corresponding isolated body cross-section center line , and setting the strain value equal to the average longitudinal strain of the isolated body ; S400, calculating a cross-section shear capacity of the isolation body according to different failure modes, the failure modes including a failure mode one and a failure mode two, wherein the failure mode one is that a stirrup of the grouting sleeve splicing area reaches a yield strength, and the failure mode two is that concrete of the grouting sleeve area reaches a compressive ultimate bearing capacity state, and the concrete presents a failure state; S410, under the condition of the failure mode one, calculating the cross-section shear capacity of the isolation body according to the following specific steps; S411、give the initial angle of the principal compressive stress of the isolator concrete microelement and the initial principal tensile strain assignment, and according to the formula calculate the principal compressive strain of the isolator concrete microelement ; S412, if the stirrup reaches the yield state, then where represents the normal stress of the transverse stirrup, represents the yield strength of the stirrup, according to the formula the new main tensile strain of the concrete micro-element of the spacer is calculated where represents the average transverse strain of the grouting sleeve area, if the formula is satisfied, then it is determined that convergence, e takes a value below 0.0001, if not, return to S411 to reassign the initial value and bring it into calculation; S413, calculate and and according to the formula Calculate the new insulator concrete micro-element principal stress pressure angle wherein represents the normal stress of the transverse stirrup, is the principal tensile stress of the concrete, is the shear stress of the concrete, is the transverse stirrup reinforcement ratio, if satisfies the formula , it is determined that convergence, e is less than or equal to 0.0001, if not convergent, return S411 to reassign the initial value, and through the interval search calculation by bisection to convergence; S414, based on the convergence of the main stress pressure angle of the isolation body concrete micro-element and the convergence of the main tensile strain of the isolation body concrete micro-element, first according to the formula Calculate the shear strain of the cracked concrete shear element , then calculate the cross-section shear capacity V of the isolation body n When λ≥1.5, if <0, the cross section of the isolation body is in compression-shear failure, take , if >0, the cross section of the isolation body is in bending-shear failure, take When λ<1.5, then , wherein , Indicates the width of the member cross section, is the effective height of the member cross section, is the spacing between adjacent stirrups, is the cross-sectional area of the force cross-section stirrup, is the cross-sectional area of the grouting sleeve, is the shear modulus of the grouting sleeve, is the shear strain of the cracked concrete shear element, wherein is the height of the isolation body; S420, under the condition of the failure mode two, calculating the cross-section shear capacity of the isolation body according to the following specific steps; S421、Giving the initial angle of the principal compressive stress of the isolator concrete micro-element Assignment; S422, assuming that the concrete reaches a peak compressive stress, then , is the strain corresponding to the peak stress of the concrete under the constraint. S423、First, according to the formula Calculate the main tensile strain of the micro-element of the isolation concrete Then, according to the formula Calculate the transverse strain of the stirrup Determine Whether it is less than or equal to the yield strain of the stirrup If yes, proceed to the next step, otherwise return to S421 to reassign The value, the re-assigned Value is 0.01° added to the original Value; S424, calculate , and , and according to the formula Calculate the new isolation concrete micro-element principal stress pressure angle , wherein represents the normal stress of the transverse stirrup, is the principal tensile stress of the concrete, is the shear stress of the concrete, is the transverse stirrup reinforcement ratio, if satisfy the formula , it is determined convergence, e is less than or equal to 0.0001, if not convergent, return S421 to give the initial value, and through the interval search calculation by bisection to convergence; S425, based on the isolation body concrete micro-element principal stress pressure angle and the calculated , first according to the formula Calculate the shear strain of the cracked concrete shear element , then calculate the cross-section shear capacity V of the isolation body n When λ≥1.5, if <0, the cross section of the isolation body is in compression-shear failure, take If >0, the cross section of the isolation body is in flexural-shear failure, take When λ<1.5, then Where , Indicates the width of the member cross section, The effective height of the member cross section, The distance between adjacent stirrups, The cross-sectional area of the force cross-section stirrup, The normal stress of the transverse reinforcement, The cross-sectional area of the grouting sleeve, The shear modulus of the grouting sleeve, The shear strain of the cracked concrete shear element, where The height of the isolation body.

2. A method for calculating the shear resistance of the connection zone of a grout sleeve for precast segmental compression and bending members according to claim 1, characterized in that, The related parameters of the isolation body in S100 include a material type, an axial force P borne by the isolation body, a bending moment M borne by the isolation body, a lateral load Fx, and size parameters of a cross section of the isolation body.

3. A method of calculating the shear resistance of the connection zone of a grout sleeve for precast fabricated compression-bent members according to claim 2, wherein The concrete, the steel bars and the grouting sleeve of the grouting sleeve connection area of the prefabricated and assembled compression-bending member are selected as elastic-plastic materials.

4. A method of calculating the shear resistance of the connection zone of a grout sleeve for precast fabricated compression-bent members according to claim 3, characterized in that The calculation is made by the following formula:​ ； wherein is the unconfined concrete axial compressive strength, is the concrete elastic modulus, is the concrete compressive principal strain; Calculated by the formula: ； wherein is the cross-sectional shear stress of the column cracking unit, is the transverse stirrup reinforcement ratio, is the cross-sectional shear stress of the stirrup; In S424 By the following formula: ； wherein is the lateral normal stress of the column cracking element, is the lateral reinforcement ratio of the lateral tie, is the lateral normal stress of the concrete.

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