Simply supported new and old concrete superposed beam deformation calculation method considering interface slippage

Abstract

The invention discloses a simply supported new and old concrete superposed beam deformation calculation method considering interface slippage. The method comprises the following steps: constructing a mechanical assumption model; the physical condition of the simply supported new and old concrete superposed beam is preset, a second-order ordinary differential equation of the interface relative slippage is constructed according to the support boundary condition of the simply supported new and old concrete superposed beam and the specific external load, the second-order ordinary differential equation is calculated, and a function of the interface relative slippage distributed along the beam length is obtained. Calculating an additional curvature based on a function of distribution of the interface relative slip along the beam length, performing double integration on the additional curvature function along the beam length of the simply supported new and old concrete superposed beam, and calculating deflection completely caused by the interface relative slip effect; and finally, superposing the deflection with the conventional deflection calculated based on the traditional complete shear connection theory to obtain the total deflection of the superposed beam finally considering the interface relative slip effect. The method has the advantage of calculating the deformation degree of the superposed beam.

Description

Technical Field

[0001] This invention relates to the field of composite beams, and more specifically, to a method for calculating the deformation of simply supported composite beams of old and new concrete that takes into account interface slip. Background Technology

[0002] Composite concrete beam structures, which involve pouring a new layer of concrete onto an existing precast concrete beam to create a unified load-bearing structure, are a widely used technique in structural reinforcement and new construction projects. Their deformation (deflection) is a key indicator for measuring the structural safety and serviceability.

[0003] Currently, the calculation of composite beam deformation in engineering mainly relies on two extreme assumptions. The first is the theory of perfect shear connection, which assumes that the shear connectors (such as shear keys and rebar) at the interface between the old and new concrete layers have infinite stiffness, and that no relative slippage occurs at the interface. Under this assumption, the composite beam is calculated as a single integral section. This method overestimates the overall stiffness of the structure, resulting in calculated deflection values ​​that are usually smaller than the actual values, leading to an unsafe assumption. The second is the theory of no shear connection: this theory assumes that the interface is completely smooth, with no shear capacity, and that the old and new concrete layers are subjected to bending independently, with deformation being compensated by curvature. This method completely ignores the role of interface connection, underestimates the structural stiffness, and results in calculated deflections far greater than the actual values, leading to material waste.

[0004] In reality, interface connections in engineering are all "partial shear connections," meaning that there is a certain degree of relative slip at the interface. This slip effect causes additional deformation, which is an important component of the total deformation. Although some scholars have proposed complex numerical models or nonlinear analysis methods that consider partial shear connections, these methods are often complex, difficult to determine parameters, and cumbersome in calculation, making them unsuitable for widespread application in engineering design. Therefore, there is an urgent need for a practical engineering calculation method that can accurately reflect the core mechanical behavior of interface slip, while also being simple in form, easy to calculate, and with clear physical meaning. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, such as the discrepancy between theory and actual engineering conditions, and the fact that existing analytical methods considering partial shear connections are complex in model selection, difficult in parameter determination, cumbersome in calculation process, and difficult to promote and apply in engineering design, this invention provides a method for calculating the deformation of simply supported composite beams of old and new concrete that considers interface slip.

[0006] The technical solution of this invention is as follows:

[0007] A method for calculating the deformation of a simply supported composite beam of old and new concrete considering interface slip includes the following steps:

[0008] S1. Construct a mechanical assumption model to presuppose the physical conditions of a simply supported composite beam of old and new concrete.

[0009] S2. Based on the preset conditions of step S1, and according to the support boundary conditions of the simply supported new and old concrete composite beam and the specific external load, the interface of the beam is relatively slipped. The second-order ordinary differential equation is used to calculate the relative slip of the interface. A function distributed along the beam length;

[0010] S3, Based on the relative sliding of the interface The additional curvature is calculated by a function distributed along the beam length. The additional curvature function is then double-integrated along the beam length of the simply supported composite beam of old and new concrete to calculate the deflection caused entirely by the relative slip effect of the interface.

[0011] S4. Compare the deflection with the conventional deflection calculated based on the traditional fully shear-resistant connection theory. By superimposing the values, the total deflection of the composite beam, taking into account the relative slippage effect at the interface, is obtained. .

[0012] Furthermore, in one embodiment, the physical condition of the simply supported composite beam of old and new concrete in step S1 is specifically preset as follows:

[0013] In the simply supported composite beam of old and new concrete, the horizontal shear intensity at the interface between the precast concrete beam and the newly poured concrete layer is... relative sliding of the interface They exhibit a linear proportional relationship, and their calculation expression is:

[0014] =

[0015] in, This indicates the shear stiffness of the interface;

[0016] During the bending deformation process, the newly poured concrete layer at the top of the simply supported composite concrete beam has the same cross-sectional curvature as the precast concrete beam at the bottom.

[0017] Furthermore, in one embodiment, the external load includes a single-point concentrated load, a two-point symmetrical single-point concentrated load, a uniformly distributed load, and an arbitrary load. The calculation of the second-order ordinary differential equation based on the single-point concentrated load specifically involves:

[0018] S21, Based on the horizontal shear intensity v and the relative slip The forces exhibit a linear proportional relationship. The calculation expression for balancing the horizontal forces on the newly poured concrete layer is as follows:

[0019]

[0020]

[0021] in, and These represent the axial compressive forces on the left and right sections of the newly poured concrete layer in the micro-element segment of the simply supported composite beam, respectively. Indicates the length of the micro-element segment;

[0022] S22. After simplifying and rearranging the calculation expression by taking the centroid of the newly poured concrete layer and the left cross-section of the precast concrete beam in the micro-element segment, the calculation expression is as follows:

[0023]

[0024] in, This represents the bending moment at the left section of the newly poured concrete layer within the micro-element segment. This represents the bending moment of the left section of the precast concrete beam within the micro-element segment. Indicates the load value. This represents the total height of the simply supported composite beam of old and new concrete.

[0025] S23. Based on the fact that the newly poured concrete layer described above and the precast concrete beam described below have the same cross-sectional curvature, calculate the cross-sectional curvature of the simply supported composite beam of old and new concrete. Its calculation expression is:

[0026]

[0027] in, This represents the ratio of the elastic modulus of the precast concrete beam to that of the newly poured concrete layer. This represents the elastic modulus of the newly poured concrete layer. This represents the effective moment of inertia of the precast concrete beam;

[0028] S24, Calculate the interface slip strain Its expression is:

[0029]

[0030] in, Represents the equivalent flexibility area. This represents the distance from the neutral axis of the precast concrete beam to the top of the simply supported composite beam of old and new concrete. This indicates the axial tensile force of the precast concrete beam;

[0031] S25, Define parameters Build a relatively sliding interface The expression for the second-order ordinary differential equation is:

[0032]

[0033]

[0034]

[0035] in, This represents the equivalent moment of inertia of the interface. This indicates the distribution of shear force.

[0036] Furthermore, in one embodiment, the relative slip of the interface is calculated based on the single-point concentrated load. The function distributed along the beam length is specifically as follows:

[0037] Calculate the second-order ordinary differential equation The general solution and the boundary conditions are given. , Substituting and simplifying, its expression is:

[0038]

[0039] in, This indicates the beam length of a simply supported composite beam of old and new concrete.

[0040] Furthermore, in one embodiment, calculating the additional curvature and deflection in step S3 based on the single-point concentrated load specifically involves:

[0041] Based on the cross-sectional strain distribution of the interface relative slip effect, the interface slip strain can be obtained. Additional curvature caused for:

[0042]

[0043] Based on additional curvature With additional deflection Existing structural mechanical relationships For additional curvature By performing a double integral, the mid-span deflection can be obtained. for:

[0044]

[0045] Furthermore, in one embodiment, the function for the relative slip distribution along the beam length of the calculation interface based on the two-point symmetrical single-point concentrated load is specifically:

[0046] Based on two-point symmetry, only the left half span [0, ] of the pre-defined simply supported composite beam of old and new concrete is analyzed. Shear force distribution for:

[0047]

[0048]

[0049] The second-order ordinary differential equation in the interval [0, / 3] and [ / 3, / 2] are respectively:

[0050]

[0051]

[0052] Calculate the general solution of the second-order ordinary differential equation, substitute the boundary conditions, and simplify and rearrange. Its expression is:

[0053]

[0054]

[0055] Furthermore, in one embodiment, the deflection calculation based on the two-point symmetrical single-point concentrated load specifically involves:

[0056] right By performing a double integral, the mid-span deflection can be obtained as follows:

[0057]

[0058] Furthermore, in one embodiment, the calculation of the second-order ordinary differential equation based on the uniformly distributed load specifically involves:

[0059] Assume uniformly distributed load strength Total load Then the shear force distribution of uniformly distributed load The second-order ordinary differential equation is expressed as:

[0060]

[0061]

[0062] in, The x-coordinate of the infinitesimal segment is represented.

[0063] Furthermore, in one embodiment, the deflection calculation based on the uniformly distributed load specifically involves:

[0064] Calculate the general solution of the second-order ordinary differential equation, substitute the boundary conditions, and simplify and rearrange. Its expression is:

[0065] ,

[0066]

[0067] right By performing a double integral, the mid-span deflection can be obtained as follows:

[0068]

[0069] Furthermore, in one embodiment, the deflection calculation based on the general non-ideal load specifically involves:

[0070] Since the relative slip of the composite surface depends on the shear force, the shear force at the support section is equivalent to a uniformly distributed load. :

[0071]

[0072] in, This represents the sum of the loads on the simply supported composite beam of old and new concrete;

[0073] The calculation of mid-span deflection is as follows:

[0074]

[0075] in, This represents the load correction factor.

[0076] The present invention, based on the above scheme, has the following advantages: it breaks through the limitations of traditional composite beam deformation relying on the extreme assumptions of fully shear-resistant connections or shear-resistant connections. With the core assumptions of a linear correlation between interface shear force and relative slip, and the same curvature between the old and new concrete layers, it establishes a differential equation controlling interface slip through rigorous mechanical derivation. For the first time, it provides an analytical calculation formula for additional deflection under typical load conditions, achieving precise fit for actual conditions of partial shear-resistant connections. The calculation process is simple in form, the physical meaning of the parameters is clear, and they are easy to obtain, eliminating the need for complex numerical modeling or nonlinear analysis, significantly reducing the complexity of engineering applications. This method not only quantitatively separates the additional deformation caused by interface slip and clearly reveals the contribution of slip to the total deformation, but also enables performance analysis of different interface treatment methods by adjusting the interface shear stiffness parameters. This provides strong support for refined structural design, optimized interface construction, and avoidance of over- or under-design. At the same time, its calculation results are in high agreement with measured values. It is applicable to typical working conditions such as concentrated loads and uniformly distributed loads, as well as arbitrary load forms (equivalent uniformly distributed load method). With a wide range of applications, it can provide a reliable theoretical basis and practical calculation tool for the reinforcement design, long-term performance evaluation, and safety monitoring of composite beam structures. Attached Figure Description

[0077] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the description of the embodiments or the prior art 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.

[0078] Figure 1 This is a flowchart illustrating the calculation method in this embodiment;

[0079] Figure 2 This is a schematic diagram of a simply supported composite beam of old and new concrete in this embodiment;

[0080] Figure 3 This is a schematic diagram of the single-point concentrated load case in this embodiment;

[0081] Figure 4 This is a schematic diagram of the two-point symmetrical concentrated load case in this embodiment;

[0082] Figure 5 This is a schematic diagram of the uniformly distributed load condition in this embodiment;

[0083] Figure 6 This is a schematic diagram of a typical non-ideal load condition in this embodiment. Detailed Implementation

[0084] The present invention will now be further described with reference to the accompanying drawings and embodiments:

[0085] like Figure 1 As shown, a method for calculating the deformation of a simply supported composite beam of old and new concrete considering interface slip includes the following steps:

[0086] S1. Construct a mechanical assumption model to presuppose the physical conditions of a simply supported composite beam of old and new concrete, including:

[0087] (1) The shear intensity v at the interface between the old and new concrete of the composite beam is linearly proportional to the relative slip S of the interface, i.e. v=KS, where K is the shear stiffness of the interface between the old and new concrete.

[0088] (2) During the bending deformation process, the upper newly poured concrete layer of the composite beam has the same cross-sectional curvature as the lower precast concrete beam.

[0089] S2. Based on the preset conditions of step S1, and according to the support boundary conditions of the simply supported new and old concrete composite beams and the specific external loads, construct the interface for relative slippage. The second-order ordinary differential equation is used to calculate the second-order ordinary differential equation and obtain the function of the relative slip of the interface along the beam length.

[0090] By performing mechanical equilibrium analysis on the infinitesimal segments of the composite beam, including horizontal force equilibrium and moment equilibrium, and combining this with the assumption of equal curvature, a second-order ordinary differential equation for the relative slip S(x) at the interface is derived:

[0091]

[0092] Where x is the coordinate along the beam length; V(x) is the shear force function on the beam section; α and β are comprehensive parameters determined by the geometric properties, material properties and interface shear stiffness of the composite beam section.

[0093] ,

[0094] Where h is the total height of the composite beam, h = hc + hp, and hc and hp represent the heights of the upper and lower concrete layers, respectively;

[0095] h1 is the distance from the neutral axis of the lower precast beam to the top of the composite beam. yp is the distance from the top surface of the precast beam to the neutral axis of the precast beam; Ec is the elastic modulus of the upper cast-in-place concrete beam.

[0096] I0 is the equivalent moment of inertia of the composite section. Ic and Ip represent the moments of inertia of the upper and lower concrete beam sections, respectively, and n represents the ratio of the elastic modulus of the lower precast beam concrete to the upper cast-in-place concrete. The reduction factor for the moment of inertia of the concrete section;

[0097] A0 represents the equivalent flexibility area. Ac and Ap represent the cross-sectional areas of the upper and lower concrete layers, respectively.

[0098] S3. Calculate the additional curvature based on the function of the relative slip of the interface along the beam length. Perform a double integral on the additional curvature function along the beam length of the simply supported composite beam of old and new concrete to calculate the deflection caused entirely by the relative slip of the interface.

[0099] Specifically, based on the support boundary conditions of the beam and the specific external load form, the differential equation in step two is solved to obtain the function S(x) representing the relative slip of the interface along the beam length; then, the additional curvature caused by the slip S(x) is calculated based on the slip. Then, the resulting additional curvature function By performing a second integral along the beam length, the additional deflection caused entirely by the interface slip effect is calculated. .

[0100] S4. Compare the deflection with the conventional deflection calculated based on the traditional fully shear-resistant connection theory. By superimposing the values, the total deflection of the composite beam, taking into account the relative slippage effect at the interface, is obtained. .

[0101] This method accurately calculates the additional deflection caused purely by interface slip effects. This allows engineers to clearly understand the contribution of slip to the total deformation, thus gaining a deeper and more fundamental understanding of structural behavior. Furthermore, by considering the actual slip behavior of the interface, the calculation results of this method are closer to the measured deformation values ​​of the structure under actual stress conditions, significantly improving the accuracy and reliability of deformation prediction and providing a more credible basis for assessing the safety and serviceability of structures. Interface properties degrade over time (e.g., due to concrete shrinkage, creep, fatigue loading, and environmental erosion). This method can be used to predict the deformation development of structures after interface performance degradation, providing a theoretical basis for long-term performance monitoring, safety assessment, and determination of reinforcement timing for existing structures.

[0102] Meanwhile, this invention also achieves the "formulaic" solution to complex problems: Through rigorous mathematical and physical equation derivation, the complex interfacial slip mechanics problem is ultimately reduced to clear analytical calculation formulas for different load conditions. Engineering technicians no longer need to perform complex finite element modeling or nonlinear analysis; they can directly consult the formulas and substitute parameters for calculation, greatly reducing the technical threshold and application difficulty. The parameters required for calculation, such as cross-sectional geometric properties, material elastic modulus, and interfacial shear stiffness, all have clear physical meanings and can be determined through conventional material testing, standard table lookup, or existing research data. The parameters are readily available, facilitating their widespread application in design and construction drawing review.

[0103] This invention directly provides analytical solutions for the most common working conditions, such as concentrated loads, two-point symmetrical loads, and uniformly distributed loads. It also proposes an equivalent uniformly distributed load method, providing a practical and convenient solution for various non-standard and complex load forms encountered in actual engineering, greatly expanding the applicability of the method.

[0104] like Figure 2 As shown, it is assumed that the simply supported composite concrete beam consists of a lower precast concrete beam and an upper newly poured concrete layer. In the mechanical model, the following core assumptions are made: Assumption 1: Interface horizontal shear intensity... Slide relative to the interface Linear relationship = , The shear stiffness of the interface; its value can be obtained through testing or specifications. Assumption 2: The old and new concrete layers maintain the same cross-sectional curvature during bending.

[0105] This invention overcomes the limitations of extreme assumptions in traditional theoretical calculations of composite concrete beams: traditional methods simplify calculations under two extreme assumptions—"complete connection" and "no connection"—resulting in either dangerously inaccurate or overly conservative results. This invention successfully introduces a more practical physical model—"partial shear connection"—within the analytical theoretical framework, filling the gap in accurate and practical calculation methods.

[0106] like Figure 3 As shown, for the interface slip of a simply supported composite beam of old and new concrete, taking a single-point concentrated load as an example, the calculation process of deflection is explained:

[0107] Based on the assumption that the shear force at the interface of the composite surface is proportional to the relative slip of the interface:

[0108] = (1)

[0109] In the formula, Indicates the horizontal shear intensity. Indicates the shear stiffness of the interface. This indicates relative sliding of the interface.

[0110] This invention incorporates the interfacial shear stiffness K as a core parameter into the calculation model. Designers can easily adjust the K value to quantitatively analyze the impact of different interfacial treatment methods (such as different rebar anchoring ratios, different interfacial roughness, and the use of different interfacial agents) on the final deformation of the structure.

[0111] Engineers can move away from relying on experience or conservative values ​​and engage in performance-oriented, refined design. For example, to keep deformation within specification limits, the minimum required interface shear stiffness can be calculated in reverse, thereby optimizing the selection of the most economical and effective interface construction measures and avoiding the waste caused by "over-design" or the risks brought by "under-design."

[0112] Based on horizontal shear intensity v and relative slip The forces exhibit a linear proportional relationship. The calculation expression for balancing the horizontal forces in a newly poured concrete layer is as follows:

[0113]

[0114] in, and These represent the axial compressive forces at the left and right sections of the newly poured concrete layer within the infinitesimal segment, respectively. Representing the length of the infinitesimal segment, we can obtain:

[0115] (2)

[0116] Taking moments about the centroid of the left side of both the cast-in-place layer and the precast beam segment, we can obtain:

[0117]

[0118]

[0119] like Figure 2 As shown, Mc and Mc+ are the bending moments of the left and right sections of the upper concrete beam of the selected composite concrete micro-segment; Mp and Mp+ are the bending moments of the left and right sections of the lower concrete beam of the selected composite concrete micro-segment; Vc and Vp are the shear forces of the upper and lower concrete layers of the selected composite concrete micro-segment.

[0120] Dividing both sides of the equation by dx, we get:

[0121] (3)

[0122] (4)

[0123] In the formula, hc and hp represent the heights of the cast-in-place layer and the precast beam, respectively, r represents the normal compressive force at the unit composite interface, and dMc=M c + -M C .

[0124] Adding equation (3) to equation (4) yields:

[0125]

[0126] h is the total height of the composite concrete beam, h = hc + hp. For concentrated loads, Vc + Vp = P / 2, where P is the load value. Therefore, substituting these values, we get:

[0127] (5)

[0128] The effective moment of inertia can be obtained by converting and reducing the stiffness of the precast beam using the interface conversion method:

[0129]

[0130] Ip is the moment of inertia calculated from the interface. This is the reduction factor for the moment of inertia of the cross section.

[0131] Based on the assumption that the curvature of the cast-in-place layer and the precast beam are consistent, we can obtain:

[0132] (6)

[0133] In the formula, φ is the curvature of the composite concrete beam section, n represents the ratio of the elastic modulus of the precast beam concrete to that of the cast-in-place layer concrete, and n represents the tensile strain at the bottom of the cast-in-place layer. and tensile strain at the top of the precast beam They are respectively:

[0134] (7)

[0135] (8)

[0136] In the formula, Ac represents the area of ​​the cast-in-place concrete layer, Ap represents the total concrete area after conversion of the precast beam reinforcement, and y p The distance from the top surface of the precast beam to its neutral axis can be calculated using the following formula:

[0137]

[0138] In the formula, n1 represents the ratio of the elastic modulus of the longitudinal reinforcement to that of the concrete in the precast beam, and μ represents the reinforcement ratio of the precast beam.

[0139] Subtracting equation (8) from equation (7) yields the cross-sectional slip as follows:

[0140] (9)

[0141] ,

[0142] In the formula, A0 represents the equivalent flexibility area, h1 represents the distance from the neutral axis of the precast beam to the top of the composite beam, and T is the axial tension of the lower layer of concrete in the composite concrete beam.

[0143] Differentiating equation (9) yields:

[0144] (10)

[0145] From equations (5) and (6), we can obtain:

[0146] (11)

[0147]

[0148] In the formula, I0 is the equivalent moment of inertia of the combined section. This is the reduction factor for the moment of inertia of the cross section.

[0149] Substituting equation (11) into equation (10), we get:

[0150] (12)

[0151] Define parameters After sorting, we get:

[0152] ,

[0153] (13)

[0154] Find the general solution of equation (13) and define the boundary conditions. , Substituting, we get:

[0155]

[0156]

[0157] A and B are simplified coefficients used in the calculation process and have no special meaning. L is the length of the composite concrete beam. Let e ​​be the logarithmic function with base e. Simplifying, we get:

[0158] (14)

[0159] Considering the cross-sectional strain distribution due to slip effect, we can obtain the strain distribution due to slip. The resulting curvature of the appendage is:

[0160] (15)

[0161] Depend on and Structural mechanical relationships ,right By performing a double integral, the mid-span deflection can be obtained as follows:

[0162]

[0163] This refers to the change in curvature at the interface of the composite concrete beam (the additional curvature caused by slippage). This refers to the change in deflection of the composite concrete beam (the additional deflection caused by slippage).

[0164] like Figure 4 As shown, the conclusion is extended to a two-point symmetrical concentrated load (total load at both points is P). Due to the symmetry, only the left half-span [0, L / 2] is analyzed, and the shear force distribution is as follows:

[0165] ,

[0166] The glide differential equation in the interval [0, L / 3] is:

[0167]

[0168] The glide differential equation in the interval [L / 3, L / 2] is:

[0169]

[0170] Similarly, solving the differential equation yields the general solution, and substituting the boundary continuity conditions into the general solution gives:

[0171]

[0172]

[0173] right By performing a double integral, the mid-span deflection can be obtained as follows:

[0174]

[0175] like Figure 5 As shown, extending the conclusion to uniformly distributed loads (uniformly distributed load intensity q, total load ql), the shear force distribution under uniformly distributed loads is as follows:

[0176]

[0177] x is the x-coordinate of the selected micro-segment.

[0178] The glide differential equation is:

[0179]

[0180] Boundary conditions , Substituting into the general solution, we get:

[0181]

[0182] right By performing a double integral, the mid-span deflection can be obtained as follows:

[0183]

[0184] like Figure 6 As shown, for general non-ideal loads, the equivalent uniformly distributed load method can be used. Since the relative slip of the overlapping surface depends on the shear force, it can be achieved by ensuring that the shear force at the support section is equivalent to an equivalent uniformly distributed load q. qe :

[0185]

[0186] It is the sum of the loads on the composite concrete beam.

[0187] The mid-span deflection is:

[0188]

[0189] In the formula, This is the load correction factor.

[0190] To clearly demonstrate the implementation process, a simply supported composite beam is assumed: L = 6000mm, precast beam 200mm × 400mm, composite layer thickness 100mm. Material E_b = E_c = 3.0 × 10^4 MPa. The interface is reinforced with rebar, and k = 15 N / mm³ is taken. It bears a concentrated load P = 100 kN at mid-span. Input parameters: The above geometry, material, and measured interface stiffness k are input into the calculation program. Program calculation: The software automatically calculates β, w_0, and Δw_mid. Output results: w_0 = 8.2 mm, Δw_mid = 1.5 mm, w_total = 9.7 mm. Finally, from the perspective of technical effect comparison, the method of this invention quantifies the slip effect, and the calculation results are closer to the actual stress state, providing a basis for safe design.

[0191] Therefore, the deformation calculation method for simply supported composite concrete beams considering interface slip proposed in this invention is not an isolated theoretical formula derivation, but a complete technical solution with a logical closed loop, defined parameters, and direct engineering application. Its core value lies in overcoming the manual dependence and accuracy limitations of traditional calculation methods, enabling deep integration into various engineering technology systems. Through standardized and procedural methods, it achieves automated and precise calculations, providing technical support for the entire process of composite beam design, construction, and monitoring. Regarding structural design software integration, this method can encapsulate analytical formulas, load case adaptation logic, and parameter input / output rules into independent functional modules, seamlessly integrating them into mainstream structural design software such as MIDAS, PKPM, and ETABS. After integration, engineers designing composite beams do not need to manually derive equations or convert parameters; they only need to input basic information such as beam cross-sectional dimensions, material properties, and interface connection methods. The software can automatically call this method module to complete interface slip calculation, additional deflection analysis, and total deflection verification, simultaneously generating a calculation report that meets the specifications. This integration not only significantly shortens the design cycle (reducing the calculation time for a single beam from hours to minutes), but also avoids the error risks of manual calculation, making composite beam deformation calculation a standard verification step in structural design and improving the reliability and standardization of design results. In the field of specialized tool development, lightweight calculation programs or mobile apps can be developed based on the core steps of this method. These tools can simplify the operation process for rapid verification needs on-site, pre-setting calculation templates for common load conditions (such as single-point concentrated loads and uniformly distributed loads). Engineers can obtain the total deflection calculation results in real time using on-site measured material parameters and load data, without relying on large software or complex equipment. For example, in bridge reinforcement sites, construction personnel can quickly verify whether the deformation under different rebar installation schemes meets the standards through the app, adjust construction parameters in real time, and improve on-site decision-making efficiency; in the acceptance stage of residential composite beams, supervisors can use the tool to quickly verify the consistency between design values ​​and measured values, ensuring project quality. In structural health monitoring and safety assessment systems, this method can serve as a core algorithm module to achieve performance inversion and deformation prediction of existing composite beam structures. By comparing the deflection and strain data collected in real time by the system with the calculation results of this method, the degree of attenuation of the interface shear stiffness can be deduced, and the interface damage state can be accurately identified. Based on this algorithm, the deformation development law of the structure during long-term use can also be predicted by combining the load change trend, and early warning of deflection exceeding the limit can be issued in advance, providing a scientific basis for the maintenance and reinforcement of existing structures and avoiding structural safety hazards caused by interface slippage. In addition, this method can also serve as a high-quality data source, providing support for the training and validation of deep learning and machine learning models in this field.By changing variables such as beam parameters, load forms, and interface conditions, this method can generate massive amounts of accurate theoretical calculation data (including multi-dimensional labels such as slip distribution, additional curvature, and total deflection). This data can be used to train the pattern recognition and prediction capabilities of AI models, helping them quickly grasp the intrinsic laws of composite beam deformation. This, in turn, enables the development of more efficient intelligent calculation and evaluation systems, promoting the digital and intelligent upgrading of the composite structure engineering field. In summary, this invention is a practical engineering technology method based on a clear engineering physical model, relying on specific measurable technical parameters, and implemented through programmable code or hardware / software modules. It directly addresses the precise calculation challenges in the design, reinforcement, and evaluation of composite structures, solving the pain point of the disconnect between traditional extreme assumptions and engineering reality, and lowering the application threshold of complex numerical models. Its multi-scenario embedding capability gives it broad adaptability and promotional value in the engineering technology system, providing strong support for the safe, economical, and efficient application of composite beam structures.

[0192] It should be understood that those skilled in the art can make improvements or modifications based on the above description, and all such improvements and modifications should fall within the protection scope of the appended claims.

[0193] The present invention has been described above with reference to the accompanying drawings. Obviously, the implementation of the present invention is not limited to the above-described manner. Any improvements made using the inventive concept and technical solution of the present invention, or the direct application of the inventive concept and technical solution of the present invention to other situations without modification, are all within the protection scope of the present invention.

Claims

1. A method for calculating the deformation of a simply supported composite beam of old and new concrete considering interface slip, characterized in that, Includes the following steps: S1. Construct a mechanical assumption model to presuppose the physical conditions of a simply supported composite beam of old and new concrete. S2. Based on the preset conditions of step S1, and according to the support boundary conditions of the simply supported new and old concrete composite beam and the specific external load, the interface of the beam is relatively slipped. The second-order ordinary differential equation is used to calculate the relative slip of the interface. A function distributed along the beam length; S3, Based on the relative sliding of the interface The additional curvature is calculated by a function distributed along the beam length. The additional curvature function is then double-integrated along the beam length of the simply supported composite beam of old and new concrete to calculate the deflection caused entirely by the relative slip effect of the interface. S4. Compare the deflection with the conventional deflection calculated based on the traditional fully shear-resistant connection theory. By superimposing the values, the total deflection of the composite beam, taking into account the relative slippage effect at the interface, is obtained. .

2. The method for calculating the deformation of a simply supported composite beam of old and new concrete considering interface slip, as described in claim 1, is characterized in that... The physical condition of the simply supported composite beam of old and new concrete in step S1 is specifically as follows: In the simply supported composite beam of old and new concrete, the horizontal shear intensity at the interface between the precast concrete beam and the newly poured concrete layer is... relative sliding of the interface They exhibit a linear proportional relationship, and their calculation expression is: = ； in, This indicates the shear stiffness of the interface; During the bending deformation process, the newly poured concrete layer at the top of the simply supported composite concrete beam has the same cross-sectional curvature as the precast concrete beam at the bottom.

3. The method for calculating the deformation of a simply supported composite beam of old and new concrete considering interface slip, as described in claim 2, is characterized in that... The external loads include single-point concentrated loads, two-point symmetrical single-point concentrated loads, uniformly distributed loads, and arbitrary loads. The calculation of the second-order ordinary differential equation based on the single-point concentrated load is as follows: S21, Based on the horizontal shear intensity v and the relative slip The forces exhibit a linear proportional relationship. The calculation expression for balancing the horizontal forces on the newly poured concrete layer is as follows: ； ； in, and These represent the axial compressive forces on the left and right sections of the newly poured concrete layer in the micro-element segment of the simply supported composite beam, respectively. Indicates the length of the micro-element segment; S22. After simplifying and rearranging the calculation expression by taking the centroid of the newly poured concrete layer and the left cross-section of the precast concrete beam in the micro-element segment, the calculation expression is as follows: ； in, This represents the bending moment at the left section of the newly poured concrete layer within the micro-element segment. This represents the bending moment of the left section of the precast concrete beam within the micro-element segment. Indicates the load value. This represents the total height of the simply supported composite beam of old and new concrete. S23. Based on the fact that the newly poured concrete layer described above and the precast concrete beam described below have the same cross-sectional curvature, calculate the cross-sectional curvature of the simply supported composite beam of old and new concrete. Its calculation expression is: ； in, This represents the ratio of the elastic modulus of the precast concrete beam to that of the newly poured concrete layer. This represents the elastic modulus of the newly poured concrete layer. This represents the effective moment of inertia of the precast concrete beam; S24, Calculate the interface slip strain Its expression is: ； in, Represents the equivalent flexibility area. This represents the distance from the neutral axis of the precast concrete beam to the top of the simply supported composite beam of old and new concrete. This indicates the axial tensile force of the precast concrete beam; S25, Define parameters Build a relatively sliding interface The expression for the second-order ordinary differential equation is: ； ； ； in, This represents the equivalent moment of inertia of the interface. This indicates the distribution of shear force.

4. The method for calculating the deformation of a simply supported composite beam of old and new concrete considering interface slip, as described in claim 3, is characterized in that... The relative slip of the interface is calculated based on the single-point concentrated load. The function distributed along the beam length is specifically as follows: Calculate the second-order ordinary differential equation The general solution and the boundary conditions are given. , Substituting and simplifying, its expression is: ； in, This indicates the beam length of a simply supported composite beam of old and new concrete.

5. The method for calculating the deformation of a simply supported composite beam of old and new concrete considering interface slip, as described in claim 4, is characterized in that... The calculation of the additional curvature and deflection in step S3 based on the single-point concentrated load is as follows: Based on the cross-sectional strain distribution of the interface relative slip effect, the interface slip strain can be obtained. Additional curvature caused for: ； Based on additional curvature With additional deflection Existing structural mechanical relationships For additional curvature By performing a double integral, the mid-span deflection can be obtained. for: 。 6. The method for calculating the deformation of a simply supported composite beam of old and new concrete considering interface slip, as described in claim 4, is characterized in that... The function for the relative slip distribution along the beam length of the calculation interface based on the two-point symmetrical single-point concentrated load is specifically as follows: Based on two-point symmetry, only the left half span [0, ] of the pre-defined simply supported composite beam of old and new concrete is analyzed. Shear force distribution for: ； ； The second-order ordinary differential equation in the interval [0, / 3] and [ / 3, / 2] are respectively: ； ； Calculate the general solution of the second-order ordinary differential equation, substitute the boundary conditions, and simplify. Its expression is: ； 。 7. The method for calculating the deformation of a simply supported composite beam of old and new concrete considering interface slip, as described in claim 6, is characterized in that... The deflection calculation based on the aforementioned two-point symmetrical single-point concentrated load is as follows: right By performing a double integral, the mid-span deflection can be obtained as follows: 。 8. The method for calculating the deformation of a simply supported composite beam of old and new concrete considering interface slip, as described in claim 4, is characterized in that... The calculation of the second-order ordinary differential equation based on the aforementioned uniformly distributed load is as follows: Assume uniformly distributed load strength Total load Then the shear force distribution of uniformly distributed load The second-order ordinary differential equation is expressed as: ； ； in, The x-coordinate of the infinitesimal segment is represented.

9. The method for calculating the deformation of a simply supported composite beam of old and new concrete considering interface slip, as described in claim 8, is characterized in that... The deflection is calculated based on the uniformly distributed load as follows: Calculate the general solution of the second-order ordinary differential equation, substitute the boundary conditions, and simplify and rearrange. Its expression is: ， ； ； right By performing a double integral, the mid-span deflection can be obtained as follows: 。 10. The method for calculating the deformation of a simply supported composite beam of old and new concrete considering interface slip, as described in claim 4, is characterized in that... The deflection is specifically calculated based on the aforementioned general non-ideal load as follows: Since the relative slip of the composite surface depends on the shear force, the shear force at the support section is equivalent to a uniformly distributed load. : ； in, This represents the sum of the loads on the simply supported composite beam of old and new concrete; The calculation of mid-span deflection is as follows: ； in, This represents the load correction factor.

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