Analysis method, system, equipment and medium for shear lag of deteriorated concrete box beam

Abstract

The invention discloses an analysis method, system, equipment and medium for shear lag of a deteriorated concrete box girder, and relates to the technical field of deteriorated concrete box girders. The method comprises the following steps: performing scaled model tests on box girder bridges under different corrosion environments to obtain the distribution law of steel bars and concrete after time-deterioration; equating the deteriorated steel bars to an equivalent concrete cross-sectional area; establishing a shear lag displacement mode of a concrete box girder affected by material deterioration, and then obtaining the shear lag longitudinal displacement and stress of the box girder affected by material deterioration; adopting the energy variation principle to establish a control differential equation of a deteriorated concrete box girder affected by shear lag, and deriving a one-dimensional shear lag beam segment unit of a deteriorated concrete box girder; obtaining an analysis method for the shear lag beam segment unit of a concrete box girder bridge after deterioration; the analysis method takes into account the relationship between the concrete affected by material deterioration and the time-varying distribution of shear lag spatial stress, so that engineering personnel can accurately grasp the stiffness degradation law of a concrete box girder bridge and the changing state of spatial stress.

Description

Technical Field

[0001] The invention relates to the technical field of deteriorated concrete box girders, and in particular to an analysis method, system, equipment and medium for shear lag of deteriorated concrete box girders. Background Art

[0002] Shear lag effect is a spatial mechanical behavior that must be considered in the design practice of box girder bridges. It will cause uneven stress distribution and additional deformation in the cross section, and in severe cases will cause safety accidents.

[0003] At present, a lot of research work has been carried out on the shear lag analysis method of concrete box girders and the calculation of the effective width of the flange; the shear lag effect analysis method of single-chamber concrete or steel-concrete composite box girders, the analog rod analysis method of the shear lag effect of variable-section box girders, the shear lag analysis method of single-box multi-chamber box girders and the shear lag analysis method of curved box girders and obliquely supported box girders have been proposed, but the shear lag coupling analysis method with the maximum shear rotation difference as the generalized displacement is extremely inconvenient for engineers to understand and apply; in patent CN109252441B, a method for analyzing the shear lag effect of variable-section box girders is proposed. In view of the deficiency that the traditional analog rod method can only analyze the shear lag effect of equal-section box girders, the equivalent area of ​​the stiffener of the variable-section box girder and the shear lag effect control equation group are re-derived, and the influence of the changes in the box girder height and web thickness on the shear lag effect of the box girder is discussed.

[0004] However, although the currently used shear lag analytical method has carried out an assessment method for the degradation of concrete stiffness, elastic modulus and remaining life in terms of material performance degradation, the relationship between the time-varying distribution of spatial stress of concrete and shear lag affected by material degradation is not considered in its analytical process, resulting in inaccurate analysis of the shear lag of box girders, which affects the spatial effect assessment and health monitoring of existing concrete box girders. Summary of the invention

[0005] In view of the deficiency that the prior art does not consider the relationship between the time-dependent degradation of concrete materials and the time-varying distribution of shear lag spatial stress, the present invention proposes an analysis method, system, equipment and medium for the shear lag of deteriorated concrete box beams. Combined with the concept of converted section, the reinforced concrete section is equivalent to a concrete section beam. According to the concrete section of the deteriorated box beam, on the basis of considering the relationship between the time-dependent degradation of concrete materials and the time-varying distribution of shear lag spatial stress, an 8-degree-of-freedom beam segment unit affected by the degradation of concrete box beam materials is used to build the displacement column vector and load column vector of the box beam shear lag beam segment unit and the stiffness matrix, and the longitudinal stress of the deteriorated concrete box beam bridge is obtained. The shear lag of the deteriorated box beam is analyzed through the longitudinal stress, thereby solving the problems existing in the prior art.

[0006] An analysis method for shear lag of a deteriorated concrete box girder comprises the following steps:

[0007] Obtain the distribution law of material strength, elastic modulus and stress-strain relationship of steel bars and concrete after time-deterioration of box girders under different corrosion environments;

[0008] According to the distribution law of material strength, elastic modulus and stress-strain relationship between steel bars and concrete after time-deterioration, the cross-sectional area of ​​the deteriorated steel bars is equivalent to the equivalent concrete cross-section, so as to obtain the concrete cross-section of the deteriorated box girder; the concrete cross-section of the deteriorated box girder includes the concrete cross-section after the steel bar cross-section is equivalent and the original concrete cross-section of the box girder;

[0009] Determine the longitudinal stress of the concrete section of the deteriorated box girder, and analyze the shear lag of the deteriorated box girder based on the longitudinal stress of the concrete section of the box girder;

[0010] Wherein, the determining of the longitudinal stress of the concrete cross section of the box girder after deterioration specifically comprises the following steps:

[0011] A Cartesian coordinate system is established based on the concrete cross section of the box girder after degradation to obtain the shear lag distribution function on the x and y axes; the additional shear lag deflection of the box girder affected by time degradation is determined based on the warping inertia moment of the section obtained by differentiating the square of the shear lag distribution function and any vertically symmetrical load;

[0012] Using the 8-DOF beam segment unit affected by the deterioration of concrete box girder materials, the displacement column vectors and node load column vectors of the box girder shear lag beam segment unit containing the box girder shear lag additional deflection, the box girder bridge section warping moment of inertia, the section shear lag moment and the section bending moment are constructed respectively; according to the ratio of the moment of inertia of the box girder section around the x-axis to the beam segment unit length, the stiffness matrix corresponding to the beam segment unit is constructed;

[0013] The section bending moment and section shear lag moment are determined by the beam segment unit displacement column vector, the node load column vector and the corresponding stiffness matrix; the longitudinal stress of the concrete section of the deteriorated box girder is determined by the shear lag distribution function, the section shear lag moment and the section warping moment of inertia, as well as the section bending moment and the moment of inertia of the section around the x-axis.

[0014] Furthermore, by conducting scaled model tests on box girder bridges under different corrosion environments, the distribution laws of material strength, elastic modulus and stress-strain relationship of steel bars and concrete after time-deterioration are obtained; the specific process of the scaled model test is to keep the cross-sectional size and material strength of the box girder bridge unchanged, and accelerate the corrosion test by changing the corrosion concentration, corrosion time and electrochemistry.

[0015] Furthermore, the method of converting the cross-sectional area of ​​the deteriorated steel bar into an equivalent concrete cross-section according to the distribution law of the material strength, elastic modulus and stress-strain relationship of the steel bar and concrete after time-deterioration to obtain the cross-sectional area of ​​the deteriorated concrete box girder specifically includes the following steps:

[0016] The cross-sectional area of ​​the longitudinal reinforcement in the upper and lower flange plates of the box girder is converted into the concrete cross-sectional area according to the cross-sectional conversion method, which specifically includes:

[0017] Convert the steel bars of the upper flange of the box girder into the cross section of concrete, and its cross-sectional area A c ' is expressed as:

[0018] A c ′=α Es A s ′,

[0019] Convert the steel bars of the lower flange of the box girder into the cross section of concrete, and its cross-sectional area A c It is expressed as:

[0020] A c =α Es A s ,

[0021] Among them, A s ' is the cross-sectional area of ​​the longitudinal reinforcement in the upper flange plate of the box girder; A s is the cross-sectional area of ​​the longitudinal reinforcement in the lower flange plate of the box girder; α Es is the elastic modulus ratio of steel and concrete, i.e. α Es =E s / E c , E s is the elastic modulus of the deteriorated steel bar, E c is the elastic modulus of degraded concrete.

[0022] Furthermore, by establishing a Cartesian coordinate system according to the concrete cross section of the deteriorated box girder, the shear lag displacement mode of the deteriorated concrete box girder is established, and the shear lag distribution function on the x and y axes is obtained, which is expressed as:

[0023] The longitudinal displacement u of the box girder affected by shear lag is:

[0024] u(x,y,z)=u0(x,y,z)+u ω (x,y,z)=-yw′(z)-ω(x,y)f′(z),

[0025] Among them, u is the longitudinal displacement of the box girder affected by shear lag; a Cartesian coordinate system is established based on the converted concrete cross section, with o as the origin, x as the transverse axis, y as the vertical axis, and z as the longitudinal axis; u0 is the longitudinal displacement of the elementary beam, u ω is the shear warping longitudinal displacement; f' is the first-order derivative of the additional deflection of the box girder shear lag; w' is the first-order derivative of the elementary beam deflection of the box girder; ω is the shear lag distribution function; wherein the shear lag distribution function ω(x,y) is:

[0026]

[0027] Among them, h u h is the distance from the top plate of the box girder to the centroid of the cross section, b is the distance from the bottom plate to the centroid of the cross section; 2b1 is the width of the top plate, 2b2 is the width of the bottom plate, and b3 is the width of the cantilever plate on one side; β1, β2 and are the correction coefficients of the warping displacement functions corresponding to the top plate, bottom plate and cantilever plate, β1=(b2·h b ) / (b1·h u ), β2=b3 / b1, η is the warping self-balancing coefficient, and its expression is:

[0028]

[0029] Where I1, I2 and I3 are the moments of inertia of the top plate, bottom plate and cantilever plate around the x-axis, respectively. x is the moment of inertia of the box girder section about the x-axis.

[0030] Further, the determination of the shear lag additional deflection of the box girder affected by time degradation based on an arbitrary vertically symmetrical load and the cross-sectional warping inertia moment obtained by differentiating the square of the shear lag distribution function comprises the following steps:

[0031]

[0032] Where: q is any vertical symmetrical load, k c is the Reissner parameter considering the effect of material degradation, and its expression is A ω is the shear hysteresis warping area, A ω =∫ A ω′ 2 dA,I ω is the shear hysteresis warping moment of inertia, I ω =∫ A ω 2 dA,G c and E c are the shear modulus and elastic modulus of deteriorated concrete, respectively, f″″ and f″ are the fourth-order derivative and second-order derivative of the shear lag additional deflection;

[0033] f=C1+C2z+C3sinh(k c z)+C4cosh(k c z),

[0034] Where: C1, C2, C3, and C4 are all solved by the corresponding boundary conditions, z is the ordinate, f is the shear lag additional deflection of the box girder considering the influence of material degradation, sinh is the hyperbolic sine function, and cosh is the hyperbolic cosine function.

[0035] Furthermore, the section bending moment and section shear lag moment are determined by the beam segment unit displacement column vector, the node load column vector and the corresponding stiffness matrix, specifically including the following steps:

[0036] Calculate the shear lag generalized shear force Q of the box girder after degradation ω , expressed as:

[0037]

[0038] Where, f″′ is the third-order derivative of the shear lag additional deflection;

[0039] By using the 8-DOF beam segment element affected by the material degradation of the concrete box beam Shift it by column vector δ e and the node load column vector F e It is expressed as:

[0040]

[0041] F e =[Q i M i Q ωi M ωi Q j M j Q ωj M ωj ] T ,

[0042] Where: w i and w j is the elementary beam deflection at the i-end and j-end of the beam element; θ i and θ j is the elementary beam deflection rotation at the i-end and j-end of the beam element; f i and f j is the shear lag additional deflection at ends i and j of the beam element; and is the shear lag additional flexural rotation at the i and j ends of the beam element; Q i and Q j is the elementary beam shear force at ends i and j of the beam element; M i and M j is the elementary beam bending moment at ends i and j of the beam element; Q ωi and Q ωj is the shear lag generalized shear force at the i-end and j-end of the beam element; M ωi and M ωj is the shear lag generalized moment at ends i and j of the beam element, T is the matrix transpose;

[0043] The stiffness matrix K corresponding to the beam segment element e for:

[0044]

[0045] Among them, sinh is the hyperbolic sine function, cosh is the hyperbolic cosine function, sym is the diagonal element of the 8*8 matrix, ψ is the intermediate variable, ψ=k c lsinh(k c l)-2cosh(k c l)+2, l is the length of the beam unit;

[0046] The nodal load column vector F of the beam segment element is:

[0047]

[0048] Among them, ζ is the global variable,

[0049] Then we get:

[0050] F=K e ·δ e ,

[0051] According to the equivalent node load array and stiffness matrix of the beam segment unit, the corresponding box beam section bending moment M is obtained. x and section shear lag moment M ω .

[0052] Furthermore, the longitudinal stress σ of the concrete section of the box girder after degradation is determined by the shear lag distribution function, the section shear lag moment and the section warping moment of inertia, as well as the section bending moment and the moment of inertia of the section about the x-axis. z , expressed as:

[0053]

[0054] Among them, σ z is the longitudinal stress of the box girder section affected by shear lag, M x is the section bending moment, M ω is the cross-sectional shear lag moment, σ0 is the primary beam normal stress of the box girder section considering the influence of material degradation, σ ω is the shear lag warping normal stress of the box girder considering the influence of material degradation, ω is the shear lag distribution function, I x is the moment of inertia of the box beam section around the x-axis, I ω is the warping inertia moment of the box girder bridge section; according to elementary beam theory M ω =∫ A σ ω ωdA=-E c I ω f″,I ω =∫ A ω2 dA, f″ is the second-order derivative of the additional deflection, and A is the equivalent cross-sectional area of ​​the deteriorated concrete box girder.

[0055] The present invention also includes an analysis system for shear lag of a deteriorated concrete box girder, comprising:

[0056] An acquisition module is used to obtain the distribution law of material strength, elastic modulus and stress-strain relationship of steel bars and concrete after time-deterioration of box girders under different corrosion environments;

[0057] A cross-section transformation module is used to convert the cross-sectional area of ​​the deteriorated steel bar into an equivalent concrete cross-sectional area according to the distribution law of the material strength, elastic modulus and stress-strain relationship of the steel bar and concrete after time-deterioration, so as to obtain the concrete cross-sectional area of ​​the deteriorated box girder; the concrete cross-sectional area of ​​the deteriorated box girder includes the concrete cross-sectional area after the steel bar cross-sectional area is equivalent and the original concrete cross-sectional area of ​​the box girder;

[0058] The shear lag analysis module is used to determine the longitudinal stress of the concrete section of the deteriorated box girder and analyze the shear lag of the deteriorated box girder based on the longitudinal stress of the concrete section of the box girder;

[0059] Wherein, the shear lag analysis module includes:

[0060] The shear lag additional deflection determination unit is used to establish a Cartesian coordinate system based on the concrete cross section of the box girder after deterioration, and obtain the shear lag distribution function on the x and y axes; according to any vertically symmetrical load and the cross-sectional warping inertia moment obtained by differentiating the square of the shear lag distribution function, the shear lag additional deflection of the box girder affected by time deterioration is determined;

[0061] Build units for the 8-DOF beam segment units affected by the deterioration of concrete box girder materials, and build the displacement column vectors and node load column vectors of the box girder shear lag beam segment units containing the additional deflection of the box girder shear lag, the warping moment of inertia of the box girder bridge section, the section shear lag moment and the section bending moment; build the stiffness matrix corresponding to the beam segment unit according to the ratio of the moment of inertia of the box girder section around the x-axis to the length of the beam segment unit;

[0062] The section longitudinal stress calculation unit is used to determine the section bending moment and section shear lag moment through the beam segment unit displacement column vector, the node load column vector and the corresponding stiffness matrix; the longitudinal stress of the concrete section of the box girder after deterioration is determined through the shear lag distribution function, the section shear lag moment and the section warping moment of inertia, as well as the section bending moment and the moment of inertia of the section around the x-axis.

[0063] The present invention also includes a computer device for analyzing shear lag of a deteriorated concrete box girder, comprising: a memory, a processor, and a computer program stored in the memory, wherein the processor implements the steps of the method for analyzing shear lag of a deteriorated concrete box girder when executing the computer program.

[0064] The present invention also includes a readable storage medium, wherein the readable storage medium stores a computer program, wherein the computer program includes program instructions, and when the program instructions are executed by a processor, the steps of the analysis method of shear lag of deteriorated concrete box beams are executed.

[0065] The present invention provides a method, system, device and medium for analyzing shear lag of a deteriorated concrete box girder, which has the following beneficial effects:

[0066] In order to explore the influence of reinforced concrete deterioration on the bending spatial stress of box beams, the present invention conducts scaled model tests of box beam bridges in different corrosion environments, obtains the distribution law of material strength, elastic modulus and stress-strain relationship of steel bars and concrete after time-deterioration of box beam bridges, and enhances the relationship between concrete affected by material deterioration and time-varying distribution of shear lag spatial stress; combined with the concept of converted section, the reinforced concrete section is equivalent to a concrete section beam, and the calculation accuracy of shear lag analysis of deteriorated box beams is further improved; on the basis of considering the relationship between concrete material deterioration and time-varying distribution of shear lag spatial stress, a concrete box beam is adopted. The 8-DOF beam segment unit affected by material degradation builds the displacement column vector, load column vector and stiffness matrix of the box girder shear lag beam segment unit, and obtains the shear lag beam segment unit analysis method of the deteriorated concrete box girder bridge. The shear lag spatial stress of the deteriorated box girder can be directly output. Compared with the three-dimensional finite element analysis method, this method considers the relationship between the concrete affected by material degradation and the time-varying distribution of the shear lag spatial stress, improves the accuracy of the shear lag analysis, and facilitates engineering personnel to accurately grasp the stiffness degradation law of the concrete box girder bridge and the changing state of the spatial stress, providing technical means for the spatial effect evaluation and health monitoring of the existing concrete box girders. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 It is a flow chart of the analysis method of shear lag of deteriorated concrete box girder in an embodiment of the present invention;

[0068] Figure 2 It is a schematic diagram of the original cross section of reinforced concrete in an embodiment of the present invention;

[0069] Figure 3 A schematic diagram of a steel bar concrete conversion cross section in an embodiment of the present invention;

[0070] Figure 4 Schematic diagram of a box girder segment unit considering the influence of shear lag in an embodiment of the present invention. DETAILED DESCRIPTION

[0071] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0072] The present invention proposes an analysis method for shear lag of deteriorated concrete box girder. The distribution law of basic parameters such as strength, elastic modulus, stress-strain relationship, Poisson's ratio, etc. of steel and concrete deteriorated over time is obtained based on material mechanical property test and probability method. Combined with the concept of converted section, the reinforced concrete section is equivalent to the concrete section beam. The energy variation principle is used to establish the control differential equation of the deteriorated concrete box girder considering the influence of shear lag. The one-dimensional beam theory is used to establish the shear lag beam segment finite element method of the deteriorated concrete box girder. The energy variation principle and the one-dimensional beam theory can be used to obtain the shear lag beam segment unit analysis method of the concrete box girder bridge after deterioration. The method specifically comprises the following steps:

[0073] S1. Analysis of the degradation laws of steel bars and concrete.

[0074] According to different corrosion environments, the scaled model test of the box girder bridge is carried out to obtain the distribution law of the material strength, elastic modulus and stress-strain relationship of the steel bars and concrete after time-deterioration; for example, the cross-sectional size and material strength of the box girder are kept unchanged, the corrosion concentration and corrosion time are changed, and the stress-strain relationship and elastic modulus of the steel bars and concrete after deterioration are obtained through electrochemical accelerated corrosion test; at the same time, the strength expression of the mechanical properties of concrete and steel bars after deterioration under conventional corrosion environment can also be given by referring to the reliability analysis theory of concrete structure, as follows:

[0075] ① Calculation formula for concrete strength degradation:

[0076]

[0077] Where: c (t) is the concrete strength after time degradation; f cd is the design value of concrete strength (taken from specification JTG3362-2018), e is the base of the exponential function, and ln(t) is the logarithmic function with time t as the independent variable.

[0078] ② Calculation formula for steel bar strength degradation:

[0079]

[0080] in:

[0081]

[0082] Where: f s(t) is the strength of the steel bar after deterioration over time; f sd is the design value of steel bar strength (according to specification JTG3362-2018); δ e (t) is the corrosion depth of the steel bar; d is the diameter of the steel bar, η s (t) is the corrosion rate of deteriorated steel bars.

[0083] S2. Combine the concept of converted section to convert the deteriorated reinforced concrete section into a concrete section.

[0084] According to the concept of converted section, the cross-sectional area of ​​the longitudinal reinforcement in the upper and lower flange plates of the box beam is converted into the concrete section. The original cross-sectional area of ​​the box beam is as follows: Figure 2 The converted cross section is shown as Figure 3 As shown, the details are as follows:

[0085] ① The cross section of the steel bars in the compression zone (upper wing plate) converted into concrete is:

[0086] A c ′=α Es A s '(4);

[0087] ② The cross section of the steel bars in the tension zone (lower wing plate) converted into concrete is:

[0088] A c =α Es A s (5);

[0089] Where: A c ' and A c A is the cross-sectional area of ​​the steel bars in the upper and lower flange plates of the box girder converted into concrete; s ' and A s is the cross-sectional area of ​​the longitudinal reinforcement in the upper and lower flange plates of the box girder; Es is the elastic modulus ratio of steel and concrete, i.e. α Es =E s / E c , E s is the elastic modulus of the deteriorated steel bar, E c is the elastic modulus of degraded concrete.

[0090] S3. Shear lag displacement model of concrete box girder considering the influence of material degradation.

[0091] The longitudinal displacement u of the box girder considering the influence of shear lag is:

[0092] u(x,y,z)=u0(x,y,z)+u ω (x,y,z)=-yw′(z)-ω(x,y)f′(z)(6);

[0093] Where: u0 is the longitudinal displacement of the elementary beam, u ω is the shear-warping longitudinal displacement; f' is the first-order derivative of the shear lag additional deflection considering the influence of material degradation; w' is the first-order derivative of the elementary beam deflection of the box girder considering the influence of material degradation; ω is the shear lag distribution function.

[0094] like Figure 3 In the Cartesian coordinate system shown in Figure 1, o is the origin, x is the horizontal axis, y is the vertical axis, and z is the longitudinal axis. The shear lag distribution function ω(x,y) is:

[0095]

[0096] Where: h u h is the distance from the top plate of the box girder to the centroid of the cross section, b is the distance from the bottom plate to the centroid of the cross section; 2b1 is the width of the top plate, 2b2 is the width of the bottom plate, and b3 is the width of the cantilever plate on one side; β1, β2 and is the correction coefficient of the warpage displacement function corresponding to each plate, β1=(b2·h b ) / (b1·h u ), β2=b3 / b1, η is the warping self-balancing coefficient, and its expression is:

[0097]

[0098] Where: I i is the moment of inertia of each plate of the box girder about the x-axis.

[0099] Longitudinal stress σ of box girder section considering shear lag z for:

[0100]

[0101] Where: σ0 is the normal stress of the primary beam of the box girder section considering the influence of material degradation, σ ω is the shear hysteresis warping normal stress of the box girder considering the influence of material degradation; M x and I x M is the bending moment and moment of inertia of the box beam section around the x-axis; ω is the shear lag moment of the box girder section, M ω =∫ A σ ω ωdA=-E c I ω f″,I ω is the warping inertia moment of the box beam section, I ω =∫ A ω 2 dA.

[0102] S4. Shear lag control differential equation and beam segment unit of concrete box girder considering the influence of material degradation. Specifically, it includes the following steps:

[0103] S4.1. Using the energy variation principle, the shear lag control differential equation of the concrete box girder considering the influence of material degradation is obtained as follows:

[0104]

[0105] Where: q is any vertical symmetrical load, k c is the Reissner parameter considering the effect of material degradation, and its expression is A ω is the shear hysteresis buckling area, A ω =∫ A ω′ 2 dA,G c and E c are the shear modulus and elastic modulus of concrete material considering the influence of material degradation, and f″″ is the fourth-order derivative of the shear lag additional deflection.

[0106] The general solution of the homogeneous linear differential equation corresponding to formula (9) is:

[0107] f=C1+C2z+C3sinh(k c z)+C4 cosh(k c z)(11);

[0108] Where: C 1～ The C44 parameters are solved by the corresponding boundary conditions, sinh is the hyperbolic sine function, and cosh is the hyperbolic cosine function.

[0109] S4.2. Shear lag generalized shear force Q of box girder considering the influence of material degradation ω for:

[0110]

[0111] Where: f″′ and f′ are the third-order derivative and first-order derivative of the shear lag additional deflection.

[0112] S4.3, if Figure 4 As shown, the present invention proposes an 8-DOF beam segment unit suitable for the influence of concrete box girder material degradation Its displacement column vector δ e and load F e The column vector is as follows:

[0113]

[0114] F e =[Q i M i Qωi M ωi Q j M j Q ωj M ωj ] T (14);

[0115] Where: w i and w j is the elementary beam deflection at the i-end and j-end of the beam element; θ i and θ j is the elementary beam deflection rotation at the i-end and j-end of the beam element; f i and f j is the shear lag additional deflection at ends i and j of the beam element; and Q is the additional flexural rotation due to shear lag at ends i and j of the beam element. i and Q j is the elementary beam shear force at ends i and j of the beam element; M i and M j is the elementary beam bending moment at ends i and j of the beam element; Q ωi and Q ωj is the shear lag generalized shear force at the i-end and j-end of the beam element; M ωi and M ωj is the shear lag generalized moment at ends i and j of the beam element.

[0116] S4.4, stiffness matrix K corresponding to beam segment element e for:

[0117]

[0118] Among them, sym is the diagonal element of the 8*8 matrix, ψ=k c lsinh(k c l)-2cosh(k c l)+2, l is the length of the beam unit.

[0119] S4.5. The equivalent node load vector F of the beam segment unit is:

[0120]

[0121] Where:

[0122] S4.6. Solution of displacement (shear lag generalized displacement) and internal force (shear lag generalized internal force):

[0123] F=K e ·δ e (16);

[0124] According to the unit node load and stiffness matrix, the corresponding elementary beam displacement and shear lag generalized displacement can be solved, and then the box beam section internal force and shear lag generalized internal force can be obtained. The result is substituted into formula (9) to obtain the box beam section longitudinal stress σ considering the influence of material degradation z The longitudinal stress expression was substituted into JTG3362-2018 (Design Specifications for Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts) to calculate the shear lag coefficient of concrete box girders with different degrees of deterioration, providing technical support for exploring the cracking mechanism of deteriorated concrete box girder bridges, rationalizing reinforcement and maintenance plans, and intelligent operation and maintenance of bridges.

[0125] Based on the same inventive concept, the present invention also proposes an analysis system for shear lag of deteriorated concrete box beams, comprising:

[0126] The acquisition module is used to obtain the distribution law of material strength, elastic modulus and stress-strain relationship of steel bars and concrete of box girder bridges after time degradation under different corrosion environments.

[0127] The cross-section transformation module is used to convert the cross-sectional area of ​​the deteriorated steel bar into an equivalent concrete cross-section according to the distribution law of the material strength, elastic modulus and stress-strain relationship of the steel bar and concrete after time-deterioration, so as to obtain the cross-sectional area of ​​the deteriorated concrete box girder.

[0128] The shear lag analysis module is used to determine the longitudinal stress of the deteriorated concrete box girder section and analyze the shear lag of the deteriorated concrete box girder bridge based on the longitudinal stress of the box girder section.

[0129] The shear lag analysis module includes:

[0130] The shear lag additional deflection determination unit is used to establish a Cartesian coordinate system according to the cross section of the concrete box girder after deterioration, and obtain the shear lag distribution function on the x and y axes; according to any vertically symmetrical load and the cross-sectional warping inertia moment obtained by differentiating the square of the shear lag distribution function, the shear lag additional deflection of the box girder affected by time degradation is determined.

[0131] Build units for the 8-DOF beam segment units affected by the material degradation of concrete box girders, and build the displacement column vector and load column vector of the box girder shear lag beam segment unit containing the additional deflection of the box girder shear lag, the warping moment of inertia of the box girder bridge section, the section shear lag moment and the section bending moment; build the stiffness matrix corresponding to the beam segment unit according to the ratio of the moment of inertia of the box girder section around the x-axis to the length of the beam segment unit.

[0132] The section longitudinal stress calculation unit is used to determine the section bending moment and section shear lag moment through the beam segment unit displacement column vector, load column vector and the corresponding stiffness matrix; the longitudinal stress of the box girder section affected by shear lag is determined through the shear lag distribution function, section shear lag moment and section warping moment of inertia, as well as the section bending moment and the moment of inertia of the section around the x-axis.

[0133] Based on the same inventive concept, the present invention also proposes a computer device for analyzing shear lag of deteriorated concrete box girders, comprising: a memory, a processor, and a computer program stored in the memory. When the processor executes the computer program, the steps of the method for analyzing shear lag of deteriorated concrete box girders are implemented.

[0134] Based on the same inventive concept, the present invention also proposes a readable storage medium, which stores a computer program. The computer program includes program instructions. When the program instructions are executed by a processor, they are used to execute the steps of the analysis method of shear lag of deteriorated concrete box beams.

[0135] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A method for analyzing shear lag of deteriorated concrete box beams, characterized in that: The following steps are involved: Obtain the distribution law of material strength, elastic modulus and stress-strain relationship of steel bars and concrete after time-deterioration of box beams under different corrosion environments; specifically: by conducting scaled model tests on box beam bridges under different corrosion environments, obtain the distribution law of material strength, elastic modulus and stress-strain relationship of steel bars and concrete after time-deterioration; the specific process of the scaled model test is to keep the cross-sectional size and material strength of the box beam bridge unchanged, and accelerate the corrosion test by changing the corrosion concentration, corrosion time and electrochemistry; According to the distribution law of material strength, elastic modulus and stress-strain relationship between steel bars and concrete after time-deterioration, the cross-sectional area of ​​the deteriorated steel bars is equivalent to the equivalent concrete cross-section, so as to obtain the concrete cross-section of the deteriorated box girder; the concrete cross-section of the deteriorated box girder includes the concrete cross-section after the steel bar cross-section is equivalent and the original concrete cross-section of the box girder; Specifically, the following steps are included: according to the conversion section method, the longitudinal steel bar cross-sectional area in the upper and lower flange plates of the box beam is converted into a concrete cross-sectional area, which specifically includes: Convert the steel bars of the upper flange of the box girder into the cross section of concrete, and its cross-sectional area A c ' is expressed as: A c ′=a Es A s ′, Convert the steel bars of the lower flange of the box girder into the cross section of concrete, and its cross-sectional area A c It is expressed as: A c =a Es A s , Among them, A s ' is the cross-sectional area of ​​the longitudinal reinforcement in the upper flange plate of the box girder; A s is the cross-sectional area of ​​the longitudinal reinforcement in the lower flange plate of the box girder; α Es is the elastic modulus ratio of steel and concrete, i.e. α Es =E s / E c , E s is the elastic modulus of the deteriorated steel bar, E c is the elastic modulus of deteriorated concrete; Determine the longitudinal stress of the concrete cross section of the box girder after deterioration, and analyze the shear lag of the box girder after deterioration according to the longitudinal stress of the concrete cross section of the box girder; wherein, the determining of the longitudinal stress of the concrete cross section of the box girder after deterioration specifically includes the following steps: A Cartesian coordinate system is established according to the concrete cross section of the deteriorated box girder to obtain the shear lag distribution function on the x and y axes; the shear lag additional deflection of the box girder affected by time degradation is determined according to the warping inertia moment of the section obtained by differentiating the square of the shear lag distribution function and the arbitrary vertically symmetrical load; specifically, a Cartesian coordinate system is established according to the concrete cross section of the deteriorated box girder, the shear lag displacement mode of the deteriorated concrete box girder is established, and the shear lag distribution function on the x and y axes is obtained, which is expressed as: The longitudinal displacement u of the box girder affected by shear lag is: u(x,y,z)=u0(x,y,z)+u ω (x,y,z)=-yw′(z)-ω(x,y)f′(z), Among them, u is the longitudinal displacement of the box girder affected by shear lag; a Cartesian coordinate system is established based on the converted concrete cross section, with o as the origin, x as the transverse axis, y as the vertical axis, and z as the longitudinal axis; u0 is the longitudinal displacement of the elementary beam, u ω is the shear warping longitudinal displacement; f' is the first-order derivative of the additional deflection of the box girder shear lag; w' is the first-order derivative of the elementary beam deflection of the box girder; ω is the shear lag distribution function; wherein the shear lag distribution function ω(x,y) is: Among them, h u h is the distance from the top plate of the box girder to the centroid of the cross section, b is the distance from the bottom plate to the centroid of the cross section; 2b1 is the width of the top plate, 2b2 is the width of the bottom plate, and b3 is the width of the cantilever plate on one side; β1, β2 and are the correction coefficients of the warping displacement functions corresponding to the top plate, bottom plate and cantilever plate, β1=(b2·h b ) / (b1·h u ), β2=b3 / b1, η is the warping self-balancing coefficient, and its expression is: Where I1, I2 and I3 are the moments of inertia of the top plate, bottom plate and cantilever plate around the x-axis, respectively. x is the moment of inertia of the box girder section about the x-axis; The method of determining the additional shear lag deflection of the box girder affected by time degradation based on an arbitrary vertically symmetrical load and the cross-sectional warping inertia moment obtained by differentiating the square of the shear lag distribution function comprises the following steps: Where: q is any vertical symmetrical load, k c is the Reissner parameter considering the effect of material degradation, and its expression is A ω is the shear hysteresis buckling area, A ω =∫ A ω′ 2 dA,I ω is the shear hysteresis warping moment of inertia, I ω =∫ A ω 2 dA,G c and E c are the shear modulus and elastic modulus of deteriorated concrete, respectively, f″″ and f″ are the fourth-order derivative and second-order derivative of the shear lag additional deflection; f=C1+C2z+C3 sinh(k c z)+C4 cosh(k c z), Where: C1, C2, C3, and C4 are all solved by the corresponding boundary conditions, z is the ordinate, f is the shear lag additional deflection of the box girder considering the influence of material degradation, sinh is the hyperbolic sine function, and cosh is the hyperbolic cosine function; Using the 8-DOF beam segment unit affected by the deterioration of concrete box girder materials, the displacement column vectors and node load column vectors of the box girder shear lag beam segment unit containing the box girder shear lag additional deflection, the box girder bridge section warping moment of inertia, the section shear lag moment and the section bending moment are constructed respectively; according to the ratio of the moment of inertia of the box girder section around the x-axis to the beam segment unit length, the stiffness matrix corresponding to the beam segment unit is constructed; The section bending moment and section shear lag moment are determined by the beam segment unit displacement column vector, the node load column vector and the corresponding stiffness matrix; the longitudinal stress of the concrete section of the deteriorated box girder is determined by the shear lag distribution function, the section shear lag moment and the section warping moment of inertia, as well as the section bending moment and the moment of inertia of the section around the x-axis; specifically including: calculating the generalized shear lag Q of the deteriorated box girder ω , expressed as: Where, f″′ is the third-order derivative of the shear lag additional deflection; By using the 8-DOF beam segment element affected by the material degradation of the concrete box beam, its displacement column vector δ e and the node load column vector F e It is expressed as: F e =[Q i M i Q ωi M ωi Q j M j Q ωj M ωj ] T , Where: w i and w j is the elementary beam deflection at the i-end and j-end of the beam element; θ i and θ j is the elementary beam deflection rotation at the i-end and j-end of the beam element; f i and f j is the shear lag additional deflection at ends i and j of the beam element; and is the shear lag additional flexural rotation at the i and j ends of the beam element; Q i and Q j is the elementary beam shear force at ends i and j of the beam element; M i and M j is the elementary beam bending moment at ends i and j of the beam element; Q ωi and Q ωj is the shear lag generalized shear force at the i-end and j-end of the beam element; M ωi and M ωj is the shear lag generalized moment at ends i and j of the beam element, T is the matrix transpose; The stiffness matrix K corresponding to the beam segment element e for: Among them, sinh is the hyperbolic sine function, cosh is the hyperbolic cosine function, sym is the diagonal element of the 8*8 matrix, ψ is the intermediate variable, ψ=k c lsinh(k c l)-2cosh(k c l)+2, l is the length of the beam unit; The nodal load column vector F of the beam segment element is: Among them, ζ is the global variable, Then the solution of shear lag generalized displacement and shear lag generalized internal force can be expressed as: F=K e ·d e , According to the node load column vector and stiffness matrix of the beam segment unit, the corresponding box beam section bending moment M is obtained. x and section shear lag moment M ω ; The longitudinal stress σ of the concrete section of the deteriorated box girder is determined by the shear lag distribution function, the section shear lag moment and the section warping moment of inertia, as well as the section bending moment and the section moment of inertia about the x-axis. z , expressed as: Among them, σ z is the longitudinal stress of the box girder section affected by shear lag, M x is the section bending moment, M ω is the cross-sectional shear lag moment, σ0 is the primary beam normal stress of the box girder section considering the influence of material degradation, σ ω is the shear lag warping normal stress of the box girder considering the influence of material degradation, ω is the shear lag distribution function, I x is the moment of inertia of the box beam section about the x-axis, I ω is the warping inertia moment of the box girder bridge section; according to elementary beam theory M ω =∫ A σ ω ωdA=-E c I ω f″,I ω =∫ A ω 2 dA, f″ is the second-order derivative of the additional deflection, and A is the equivalent cross-sectional area of ​​the deteriorated concrete box girder.

2. An analysis system for shear lag of deteriorated concrete box beams, characterized in that: include: The acquisition module is used to obtain the distribution law of the material strength, elastic modulus and stress-strain relationship of the steel bars and concrete after the box girder is degraded by time under different corrosion environments; specifically, by conducting scaled model tests on the box girder bridges under different corrosion environments, the distribution law of the material strength, elastic modulus and stress-strain relationship of the steel bars and concrete after the time deterioration is obtained; the specific process of the scaled model test is to keep the cross-sectional size and material strength of the box girder bridge unchanged, and accelerate the corrosion test by changing the corrosion concentration, corrosion time and electrochemistry; A cross-section transformation module is used to convert the cross-sectional area of ​​the deteriorated steel bar into an equivalent concrete cross-sectional area according to the distribution law of the material strength, elastic modulus and stress-strain relationship between the steel bar and the concrete after time-deterioration, so as to obtain the concrete cross-sectional area of ​​the deteriorated box girder; the concrete cross-sectional area of ​​the deteriorated box girder includes the concrete cross-sectional area after the steel bar cross-sectional area is equivalent and the original concrete cross-sectional area of ​​the box girder; Specifically, the following steps are included: according to the conversion section method, the longitudinal steel bar cross-sectional area in the upper and lower flange plates of the box beam is converted into a concrete cross-sectional area, which specifically includes: Convert the steel bars of the upper flange plate of the box girder into the cross section of concrete, and its cross-sectional area A c ' is expressed as: A c ′=a Es A s ′, Convert the steel bars of the lower flange of the box girder into the cross section of concrete, and its cross-sectional area A c It is expressed as: A c =a Es A s , Among them, A s ' is the cross-sectional area of ​​the longitudinal reinforcement in the upper flange plate of the box girder; A s is the cross-sectional area of ​​the longitudinal reinforcement in the lower flange plate of the box girder; α Es is the elastic modulus ratio of steel and concrete, i.e. α Es =E s / E c , E s is the elastic modulus of the deteriorated steel bar, E c is the elastic modulus of deteriorated concrete; The shear lag analysis module is used to determine the longitudinal stress of the concrete section of the box girder after deterioration, and analyze the shear lag of the box girder after deterioration according to the longitudinal stress of the concrete section of the box girder; Wherein, the shear lag analysis module includes: The shear lag additional deflection determination unit is used to establish a Cartesian coordinate system according to the concrete cross section of the box girder after deterioration, and obtain the shear lag distribution function on the x and y axes; determine the shear lag additional deflection of the box girder affected by time deterioration according to any vertically symmetrical load and the cross-sectional warping inertia moment obtained by differentiating the square of the shear lag distribution function; determine the longitudinal stress of the concrete cross section of the box girder after deterioration, and analyze the shear lag of the box girder after deterioration according to the longitudinal stress of the concrete cross section of the box girder; wherein, the determination of the longitudinal stress of the concrete cross section of the box girder after deterioration specifically includes the following steps: A Cartesian coordinate system is established according to the concrete cross section of the deteriorated box girder to obtain the shear lag distribution function on the x and y axes; the shear lag additional deflection of the box girder affected by time degradation is determined according to the warping inertia moment of the section obtained by differentiating the square of the shear lag distribution function and the arbitrary vertically symmetrical load; specifically, a Cartesian coordinate system is established according to the concrete cross section of the deteriorated box girder, the shear lag displacement mode of the deteriorated concrete box girder is established, and the shear lag distribution function on the x and y axes is obtained, which is expressed as: The longitudinal displacement u of the box girder affected by shear lag is: u(x,y,z)=u0(x,y,z)+u ω (x,y,z)=-yw′(z)-ω(x,y)f′(z), Among them, u is the longitudinal displacement of the box girder affected by shear lag; a Cartesian coordinate system is established based on the converted concrete cross section, with o as the origin, x as the transverse axis, y as the vertical axis, and z as the longitudinal axis; u0 is the longitudinal displacement of the elementary beam, u ω is the shear warping longitudinal displacement; f' is the first-order derivative of the additional deflection of the box girder shear lag; w' is the first-order derivative of the elementary beam deflection of the box girder; ω is the shear lag distribution function; wherein the shear lag distribution function ω(x,y) is: Among them, h u h is the distance from the top plate of the box girder to the centroid of the cross section, b is the distance from the bottom plate to the centroid of the cross section; 2b1 is the width of the top plate, 2b2 is the width of the bottom plate, and b3 is the width of the cantilever plate on one side; β1, β2 and are the correction coefficients of the warping displacement functions corresponding to the top plate, bottom plate and cantilever plate, β1=(b2·h b ) / (b1·h u ), β2=b3 / b1, η is the warping self-balancing coefficient, and its expression is: Where I1, I2 and I3 are the moments of inertia of the top plate, bottom plate and cantilever plate around the x-axis, respectively. x is the moment of inertia of the box girder section about the x-axis; The method of determining the additional shear lag deflection of the box girder affected by time degradation based on an arbitrary vertically symmetrical load and the cross-sectional warping inertia moment obtained by differentiating the square of the shear lag distribution function comprises the following steps: Where: q is any vertical symmetrical load, k c is the Reissner parameter considering the effect of material degradation, and its expression is A ω is the shear hysteresis warping area, A ω =∫ A ω′ 2 dA,I ω is the shear hysteresis warping moment of inertia, I ω =∫ A ω 2 dA,G c and E c are the shear modulus and elastic modulus of deteriorated concrete, respectively, f″″ and f″ are the fourth-order derivative and second-order derivative of the shear lag additional deflection; f=C1+C2z+C3 sinh(k c z)+C4 cosh(k c z), Where: C1, C2, C3, and C4 are all solved by the corresponding boundary conditions, z is the ordinate, f is the shear lag additional deflection of the box girder considering the influence of material degradation, sinh is the hyperbolic sine function, and cosh is the hyperbolic cosine function; Build units for the 8-DOF beam segment units affected by the deterioration of concrete box girder materials, and build the displacement column vectors and node load column vectors of the box girder shear lag beam segment units containing the additional deflection of the box girder shear lag, the warping moment of inertia of the box girder bridge section, the section shear lag moment and the section bending moment; build the stiffness matrix corresponding to the beam segment unit according to the ratio of the moment of inertia of the box girder section around the x-axis to the length of the beam segment unit; The cross-section longitudinal stress calculation unit is used to determine the cross-section bending moment and cross-section shear lag moment through the beam segment unit displacement column vector, the node load column vector and the corresponding stiffness matrix; through the shear lag distribution function, the cross-section shear lag moment and the cross-section warping moment of inertia, as well as the cross-section bending moment and the cross-section moment of inertia around the x-axis, the longitudinal stress of the concrete cross-section of the deteriorated box girder is determined; specifically including: calculating the shear lag generalized shear force Q of the deteriorated box girder ω , expressed as: Where, f″′ is the third-order derivative of the shear lag additional deflection; By using the 8-DOF beam segment element affected by the material degradation of the concrete box beam, its displacement column vector δ e and the node load column vector F e It is expressed as: F e =[Q i M i Q ωi M ωi Q j M j Q ωj M ωj ] T , Where: w i and w j is the elementary beam deflection at the i-end and j-end of the beam element; θ i and θ j is the elementary beam deflection rotation at the i-end and j-end of the beam element; f i and f j is the shear lag additional deflection at ends i and j of the beam element; and is the shear lag additional flexural rotation at the i and j ends of the beam element; Q i and Q j is the elementary beam shear force at ends i and j of the beam element; M i and M j is the elementary beam bending moment at ends i and j of the beam element; Q ωi and Q ωj is the shear lag generalized shear force at the i-end and j-end of the beam element; M ωi and M ωj is the shear lag generalized moment at ends i and j of the beam element, T is the matrix transpose; The stiffness matrix K corresponding to the beam segment element e for: Among them, sinh is the hyperbolic sine function, cosh is the hyperbolic cosine function, sym is the diagonal element of the 8*8 matrix, ψ is the intermediate variable, ψ=k c lsinh(k c l)-2cosh(k c l)+2, l is the length of the beam unit; The nodal load column vector F of the beam segment element is: Among them, ζ is the global variable, Then the solution of shear lag generalized displacement and shear lag generalized internal force can be expressed as: F=K e ·d e , According to the node load column vector and stiffness matrix of the beam segment unit, the corresponding box beam section bending moment M is obtained. x and section shear lag moment M ω ; The longitudinal stress σ of the concrete section of the deteriorated box girder is determined by the shear lag distribution function, the section shear lag moment and the section warping moment of inertia, as well as the section bending moment and the section moment of inertia about the x-axis. z , expressed as: Among them, σ z is the longitudinal stress of the box girder section affected by shear lag, M x is the section bending moment, M ω is the cross-sectional shear lag moment, σ0 is the primary beam normal stress of the box girder section considering the influence of material degradation, σ ω is the shear lag warping normal stress of the box girder considering the influence of material degradation, ω is the shear lag distribution function, I x is the moment of inertia of the box beam section about the x-axis, I ω is the warping inertia moment of the box girder bridge section; according to elementary beam theory M ω =∫ A σ ω ωdA=-E c I ω f″,I ω =∫ A ω 2 dA, f″ is the second-order derivative of the additional deflection, and A is the equivalent cross-sectional area of ​​the deteriorated concrete box girder.

3. A computer device for analyzing shear lag of deteriorated concrete box beams, characterized in that: include: A memory, a processor, and a computer program stored in the memory, wherein when the processor executes the computer program, the steps of the method for analyzing shear lag of a deteriorated concrete box girder according to claim 1 are implemented.

4. A readable storage medium, characterized in that: The readable storage medium stores a computer program, and the computer program includes program instructions. When the program instructions are executed by a processor, they are used to execute the steps of the method for analyzing shear lag of a deteriorated concrete box girder according to claim 1.

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