Method for determining expansion rate limit value of concrete in concrete-filled steel tube structure and storage medium

Abstract

The invention belongs to the field of civil construction engineering, and particularly relates to a design and construction technology of a concrete-filled steel tube structure, in particular to a method for determining an expansion rate limit value of concrete in a concrete-filled steel tube structure and a storage medium. And the selection of the expansion rate is converted from empirical and qualitative judgment to quantitative and scientific design based on a mechanical model. According to the scheme, the expansion characteristic of the concrete material and the strength safety of the steel pipe structure are linked through a rigorous mechanical model for the first time, and the crossing from the empirical material ratio to the quantitative design based on the structural system performance is realized. And a key theoretical tool and a design basis are provided for solving the problem of how to reasonably use the expanding agent, which puzzles the engineering for a long time.

Description

Technical Field

[0001] This invention belongs to the field of civil engineering, specifically relating to the design and construction technology of steel-concrete composite structures, and particularly to a method and storage medium for determining the limit value of the expansion rate of concrete inside a steel-concrete composite structure. Background Technology

[0002] Concrete-filled steel tube structures are widely used in critical structures such as arch bridges, bridge piers, and high-rise building columns due to their high load-bearing capacity, good ductility, and convenient construction. The basic principle is to utilize the confinement effect of the steel tube on the core concrete, placing the concrete in a triaxial compression state, thereby significantly improving its compressive strength and deformation capacity. However, this synergistic effect depends on the density of the concrete inside the tube. Concrete shrinkage can cause it to detach from the inner wall of the steel tube, weakening the confinement effect and reducing the overall stiffness and load-bearing capacity of the structure.

[0003] To overcome the adverse effects of concrete shrinkage, the most common technical approach is to add an expansion agent to the concrete, causing it to expand moderately during the hardening process to compensate for shrinkage and ensure close contact between the concrete and the steel pipe.

[0004] There's a common misconception in the industry that "the higher the expansion rate, the better the shrinkage compensation effect, and the denser the concrete." Therefore, material mix design often prioritizes a high expansion rate. However, this overlooks the fact that an excessively high expansion rate can generate significant circumferential tensile stress on the longitudinal weld seam of the steel pipe, a weak point. When combined with other loads during operation (such as axial force and temperature changes), this can lead to weld fatigue damage and even structural safety hazards. Specifically, it has the following limitations: The expansion of concrete essentially applies a radial, uniform expansion pressure to the steel pipe. This pressure generates significant circumferential tensile stress within the pipe wall. Existing technologies focus only on the benefits of expansion to the density of the concrete itself, while severely neglecting its negative impact on the stress state of the steel pipe, particularly on the relatively weak longitudinal weld seam.

[0005] The stresses experienced by steel pipes during operation are complex. In addition to the concrete expansion stress (σθ2), these include hydraulic pressure during concrete pumping (σθ1), stress caused by changes in ambient temperature (σθT), and axial pressure stress due to the Poisson effect (σθN). Current technology fails to provide a method for systematically superimposing these stress components with the concrete expansion stress.

[0006] The stress concentration effect has not been considered: The longitudinal weld region of the steel pipe experiences significant stress concentration due to material discontinuity, excess weld height, and potential microscopic defects. The circumferential tensile stress generated by concrete expansion may be amplified several times at this point, significantly increasing stress concentration in the weld region and potentially leading to strength failure. Current design methods do not take this factor into account.

[0007] Furthermore, existing technologies fail to systematically quantify the stress concentration effect in the weld region. Due to material discontinuities, grinding residue, and beveling in the weld region, circumferential stress is significantly amplified. The circumferential tensile stress generated by concrete expansion can be amplified several times in this area, greatly increasing the strength safety risk in the weld region. Current design methods do not incorporate this critical factor into quantitative considerations, leading to serious safety hazards in determining the upper limit of the expansion rate.

[0008] Due to the lack of the above analysis, there is currently no scientific method for determining the upper limit of the expansion ratio based on structural strength verification. Blindly pursuing a high expansion ratio may cause the cumulative circumferential stress under all load conditions (especially at welds) to exceed the yield strength of the material, posing a potential threat to structural safety.

[0009] In summary, existing technologies have significant shortcomings in controlling the expansion rate of concrete inside pipes: they unilaterally emphasize the positive effect of expansion on compactness while neglecting its negative mechanical effects on steel pipes, especially longitudinal seams; they lack a comprehensive analytical model that can quantify the relationship between expansion rate, multi-factor coupled stress, weld stress concentration effect, and steel pipe material strength, resulting in blind spots in the design process of steel-concrete composite structures, making it impossible to ensure the long-term operational strength safety of the structure (especially longitudinal welds) while ensuring the compactness of concrete. Summary of the Invention

[0010] The purpose of this invention is to overcome the defects in the control of the expansion rate of concrete inside the pipe in the existing technology, and to provide a method and equipment for determining the limit value of the expansion rate of concrete inside the pipe in a steel-concrete composite structure.

[0011] In a first aspect, the present invention provides a method for determining the limit value of the expansion rate of concrete inside a pipe, comprising the following steps: S1: Based on elasticity and material parameters, a stress model is constructed to describe the quantitative relationship between the circumferential stress of the steel pipe and the expansion rate of the concrete surface inside the pipe; S2: Obtain the circumferential stress components of the steel pipe during the operation phase caused by concrete pouring, changes in ambient temperature, and axial pressure. S3: Superimpose all the circumferential stress components to construct a structural design model for the design value of the circumferential stress of the steel pipe, and multiply the superposition result by the stress concentration factor of a weld to obtain the design value of the circumferential stress of the steel pipe. S4: Compare the design value of the circumferential stress with the allowable value of the steel pipe stress based on the strength theory, and calculate the limit value of the expansion rate of the concrete surface inside the pipe to ensure the strength safety of the steel pipe.

[0012] This invention provides a systematic technical solution for limiting the expansion rate, elevating the selection of the expansion rate from empirical and qualitative judgment to quantitative and scientific design based on mechanical models. For the first time, it links the expansion characteristics of concrete materials with the strength and safety of steel pipe structures through a rigorous mechanical model, achieving a leap from empirical material proportioning to quantitative design based on structural system performance. It provides a crucial theoretical tool and design basis for solving the long-standing problem of how to rationally use expansion agents, effectively guiding design and construction units to scientifically utilize the expansion properties of concrete while ensuring the ultimate safety of the structure.

[0013] The technical solution of this application explicitly adopts the fourth strength theory to evaluate the strength of steel under composite stress. This theory is particularly applicable to ductile materials such as steel, and can comprehensively consider the effects of circumferential and longitudinal stresses (and possibly radial stresses).

[0014] Key material parameters include: Steel parameters: elastic modulus Es, Poisson's ratio μs, yield strength fy.

[0015] Concrete parameters: elastic modulus Ec, Poisson's ratio μc, surface expansion coefficient ξ.

[0016] The technical solution of this invention redefines the surface expansion rate ξ applicable to this system: it is defined as the relative change rate of the cross-sectional area of ​​concrete after free expansion, which is related to but different from the volume expansion rate commonly used in engineering, and is specifically established to adapt to the plane strain mechanics model of steel tube concrete.

[0017] This scheme establishes an equivalent thermomechanical model for concrete expansion: using the theory of elasticity, the expansion effect of concrete is equivalent to only the concrete undergoing a temperature change (the steel pipe remains unchanged), and the rationality of this equivalent model is demonstrated, thus realizing a direct quantitative correlation between the expansion rate and the stress in the steel pipe.

[0018] This scheme constructs a comprehensive analysis system that integrates multiple methods: it comprehensively utilizes theoretical derivation (concrete expansion, overall temperature variation), finite element analysis (axial force Poisson effect, weld stress concentration) and experimental research (concrete pouring process), forming a complete method for determining the expansion rate limit, thereby improving the systematicness and scientific nature of the design.

[0019] Preferably, in step S1, the expression for the stress model is: σ θ2 =ζ*ξ;where, σ θ2ξ is the maximum circumferential stress of the steel pipe, ξ is the surface expansion rate of the concrete inside the pipe, and ζ is the circumferential stress expansion coefficient of the steel pipe. The stress model in this scheme combines the expansion rate (ξ), which is difficult to measure directly, with the calculable / evaluable steel pipe stress (σ). θ，S,max Direct correlation is a crucial first step in quantitative analysis. By introducing the core concept of the stress expansion coefficient ζ, subsequent calculations are greatly simplified.

[0020] Preferably, the expression for the circumferential stress expansion coefficient ζ of the steel pipe is:

[0021] In the formula, n = Es / Ec, where n is the ratio of the elastic modulus of the steel pipe to the elastic modulus of the concrete.

[0022] The circumferential stress expansion coefficient of the steel pipe is a stress expansion coefficient related to the elastic modulus Es of the steel pipe, the elastic modulus Ec of the concrete, the Poisson's ratio μs of the steel pipe, the Poisson's ratio μc of the concrete, and the steel content as of the steel pipe.

[0023] This scheme clarifies the key parameters (Ec, Es, μc, μs, as) that affect expansion stress, transforming the complex elasticity solution into a relatively concise algebraic expression, which facilitates programming or tabulation and lays the foundation for developing design software or manuals.

[0024] The coefficient ζ is a function related to the elastic modulus Es of the steel pipe, the elastic modulus Ec of the concrete, the Poisson's ratio μs of the steel pipe, the Poisson's ratio μc of the concrete, and the steel content as of the steel pipe. Its specific value can be quickly determined through a pre-generated data table (see Table 3 in the instruction manual), which is convenient for engineering applications.

[0025] Preferably, in step S2, the circumferential stress component includes at least the circumferential stress σ caused by the concrete pouring process inside the pipe. θ1 Circumferential stress σ caused by changes in ambient temperature during the operation phase θT Circumferential stress σ caused by axial pressure during operation θN .

[0026] Preferably, in step 3, the design value σ of the circumferential stress of the steel pipe θ The calculation formula is: σ θ = γ·(σ θ1 +σ θ2 +σ θT +σ θN );in, γ is the stress concentration factor of the longitudinal weld of the steel pipe determined by finite element analysis; σ θ1 This indicates the circumferential stress in the steel pipe caused by the concrete pouring process inside the pipe; σ θ2 This indicates the circumferential stress caused by the expansion of the concrete after it has hardened inside the pipe. σ θT This indicates the circumferential stress caused by changes in ambient temperature after the concrete inside the pipe has hardened. σ θN This indicates the circumferential stress caused by pressure on the concrete section of the steel pipe after the concrete inside the pipe has hardened.

[0027] By introducing the stress concentration factor γ, the influence of manufacturing process (welding) is quantified and incorporated into the structural design model.

[0028] Preferably, the determination of the stress concentration factor γ of the longitudinal weld of the steel pipe needs to take into account the combined effects of the weld's elastic modulus, grinding allowance, and bevel shape; more preferably, the grinding allowance is no more than 2mm, and the bevel shape includes 6mm-45° and 13mm-20°.

[0029] The technical solution of this application clearly defines the key process parameters (reinforcement height ≤ 2mm) and the preferred groove form (6mm-45°) for controlling weld quality, enabling the design criteria to be implemented in construction guidance. It transforms the abstract concept of welding quality into specific, measurable, and controllable technical indicators.

[0030] Preferably, in step S3, the strength theory selected is the fourth strength theory, and the design value of the circumferential stress σ of the steel pipe is... θ Satisfy: [σ θ ]≤0.41·fy / (γm·γ0); where fy is the yield strength of steel, γm is the material partial factor, and γ0 is the structural importance factor.

[0031] The material partial factor γm and the structural importance factor γ0 are both known parameters.

[0032] Preferably, in step S4, the calculated surface expansion rate ξ of the concrete inside the pipe is used to form a rapid expansion rate limit determination system based on different steel pipe materials, concrete strength grades and steel content.

[0033] The specific operational steps in the technical solution of this application are as follows: 1. Collect the following parameters: Steel pipe parameters: elastic modulus Es, Poisson's ratio μs, yield strength fy, cross-sectional dimensions (diameter D, wall thickness t), from which the steel content as is calculated; Concrete parameters (elastic modulus Ec, Poisson's ratio μc); Load and environmental effects: Circumferential stress σθ1 caused by concrete pouring (estimated through construction process simulation or empirical formulas). Circumferential stress σθT caused by ambient temperature changes during operation (calculated through thermodynamic analysis). Circumferential stress σθN caused by axial pressure during operation (calculated through structural mechanics analysis).

[0034] Weld coefficient: The stress concentration factor γ of the weld, determined through finite element analysis.

[0035] Safety factors: material partial factor γm and structural importance factor γ0.

[0036] 2. Calculate the allowable value of circumferential stress in the steel pipe. Based on strength theory, the maximum allowable circumferential stress [σθ] that the steel pipe can withstand is calculated.

[0037] [σθ] = 0.41 * fy / (γm * γ0); 3. Establish an equation about ξ Connect the formula in step S3 with the allowable value [σθ] to establish an equation.

[0038] Total stress formula: σθ = γ * (σθ1 + σθ2 + σθT + σθN) Introducing the stress model: Substituting σθ² = ζ * ξ into the above equation, we get: σθ = γ * (σθ1 + ζ * ξ + σθT + σθN) Introducing the strength condition: Let the total stress equal the allowable stress, i.e., σθ = [σθ], we get: [σθ] = γ * (σθ1 + ζ * ξ + σθT + σθN) 4. Inverse solution yields the surface expansion rate limit ξ: ξ limit = ( [σθ] / γ - σθ1 - σθT - σθN ) / ζ.

[0039] ξ obtained according to the above method limit This value was used as the target control value for expansion performance in concrete mix design. The expansion rate of concrete under restricted conditions was tested using a concrete restricted expansion rate test (according to standards such as GB / T 23439 "Concrete Expansion Agents"). The value that allows the restricted expansion rate of concrete at a specific age (e.g., 7d, 28d) to approach but not exceed ξ was selected. limit The proportions of the ingredients.

[0040] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described method.

[0041] Compared with the prior art, the beneficial effects of the present invention are as follows: The technical solution of this invention transforms the previous experience-based selection of expansion rate into a quantitative design based on precise mechanical models and strength criteria, avoiding blind design. By controlling the expansion rate, the risk of longitudinal cracking of steel pipes due to excessive expansion stress is effectively prevented, significantly improving the durability and safety of the structure. While ensuring safety, a scientific upper limit is provided for maximizing the utilization of concrete's expansion properties (such as self-compacting and shrinkage compensation), avoiding the use of inefficient materials due to excessive conservatism, and achieving a balance between safety and economy. This ultimately forms a rapid expansion rate limit determination system. Designers can directly consult the system based on specific steel grades, concrete grades, and steel content, greatly facilitating engineering applications. Attached Figure Description

[0042] Figure 1 A schematic diagram simulating the expansion of a concrete column (where (a) represents the free expansion state and (b) represents the restricted expansion state). Figure 2 The diagram shows the stress state of a cylinder with a diameter of 0.87m undergoing free expansion deformation. Figure 3 This is a diagram showing the stress under restricted expansion of a cylinder with a diameter of 0.87m. Figure 4 The model diagram of a steel-concrete composite tube with an outer diameter of 0.9m and a wall thickness of 30mm is shown in the finite element method. Figure 5 The diagram shows the radial stress simulation of the concrete inside a steel-concrete composite pipe with an outer diameter of 0.9m and a wall thickness of 30mm. Figure 6 The figure shows a simulation of the circumferential stress in the concrete inside a steel-concrete composite pipe with an outer diameter of 0.9m and a wall thickness of 30mm. Figure 7 This is a simulation diagram of the circumferential stress distribution in a steel pipe. Figure 8 This is a detailed simulation diagram of the circumferential stress distribution in the steel pipe. Figure 9 The diagram shows the influence of different key parameter values ​​on the internal pressure of the concrete inside the pipe and the maximum circumferential stress of the steel pipe. Figure 10 Linear relationship graphs were plotted for parameters related to surface expansion rate; Figure 11 A graph showing the relationship between the circumferential stress expansion coefficient of steel pipe and the steel content and carbon modulus of concrete. Figure 12 The diagram shows the simulated radial stress of the concrete inside a pipe with a diameter of 0.9m and a wall thickness of 0.03m. Figure 13Simulation diagram of circumferential stress in a steel pipe with a diameter of 0.9m and a wall thickness of 0.03m; Figure 14 A graph showing the influence of different key parameter values ​​on the internal pressure of the concrete inside the pipe. Figure 15 The graph shows the influence of different key parameter values ​​on the maximum circumferential stress of the steel pipe. Detailed Implementation

[0043] The present invention will now be described in further detail with reference to specific embodiments. However, this should not be construed as limiting the scope of the present invention to the following embodiments; all technologies implemented based on the content of the present invention fall within the scope of the present invention.

[0044] Example 1 This embodiment provides a method for determining the limit value of the expansion rate of concrete inside a steel-concrete composite structure, including the following steps: S1: Based on elasticity and material parameters, a stress model is constructed to describe the quantitative relationship between the circumferential stress of the steel pipe and the surface expansion rate of the concrete inside the pipe. In S1, the expression of the stress model is: σθ2 =ζ*ξ; where σθ2 is the maximum circumferential stress of the steel pipe, ξ is the surface expansion rate of the concrete inside the pipe, and ζ is the circumferential stress expansion coefficient of the steel pipe. The circumferential stress expansion coefficient ζ of the steel pipe is a stress expansion coefficient related to the elastic modulus Es of the steel pipe, the elastic modulus Ec of the concrete, the Poisson's ratio μs of the steel pipe, the Poisson's ratio μc of the concrete, and the steel content as of the steel pipe.

[0045] The stress model and finite element verification results established in this step provide a theoretical basis and parameter foundation for subsequent steps. In actual engineering, the stress components required in step S2 (such as concrete pouring stress, temperature stress, axial compression Poisson stress, etc.) need to be obtained through field tests, long-term monitoring data, or industry standard recommended values, thereby achieving a logical connection from theoretical model to actual engineering application.

[0046] The surface expansion rate ξ described in this invention refers to the relative change rate of the cross-sectional area of ​​the concrete inside the tube after it expands freely under unrestrained conditions. The surface expansion rate ξ defined in this invention is different from the volume expansion rate concept used in engineering to evaluate the volume change of materials. It is specifically defined to describe the cross-sectional expansion behavior of steel-concrete composite under plane strain conditions and can be determined by a restricted expansion rate test (according to standards such as GB / T 23439 "Concrete Expansion Agent").

[0047] In this embodiment, to quantitatively simulate the expansion rate of concrete, a sufficiently long cross-section of the concrete column is established, as follows: Figure 1 As shown: Figure 1In the design, two working conditions were designed: free expansion with only symmetric constraints and the cylinder perimeter being a free boundary; and restricted expansion with symmetric constraints and the cylinder perimeter being a normal constraint boundary, which restricts the expansion of concrete.

[0048] The elastic modulus of concrete is 36 GPa, and the coefficient of thermal expansion is 1e⁻⁵. Unit temperature changes were used to simulate the expansion or shrinkage of concrete. The results are as follows: Figure 2-3 The figure shows the free expansion deformation and constrained expansion force conditions of a cylinder with a diameter of 0.87 m. From... Figure 2-3 As can be seen, without external constraints, an infinitely long concrete cylindrical column expands outward from the center when the temperature rises by 20°C, with the expansion deformation increasing closer to the outer edge. For a circular cross-section with D=0.87m, the maximum expansion deformation at the outer edge is 0.101503mm.

[0049] When the cylinder is constrained around its perimeter, internal pressure is generated within the cross-section due to the limited thermal expansion. In this case, the concrete within the cross-section experiences the same stress at all points in the plane, and is under bidirectional compression, meaning both the radial and circumferential stresses are -10.8011 MPa. Table 1 shows the simulation results of cylinder expansion for different diameters: Table 1 shows the simulation results of cylinders with different diameters expanding.

[0050] As can be seen from the results in Table 1, changes in the cylindrical cross-section do not affect the increase in cross-section during free expansion; that is, the expansion rate remains constant. If there are strong boundary constraints around the perimeter, the pressure formed inside the cross-section will not change with the change in cross-sectional diameter. Further research revealed that the surface expansion rate is unrelated to the elastic modulus of concrete, but the internal pressure under confined expansion is directly proportional to the change in elastic modulus.

[0051] In this embodiment, a plane strain method is further used to establish a model of the steel pipe and the concrete inside the pipe. The elastic modulus of the steel pipe is 206 GPa, and the Poisson's ratio is 0.3. The expansion of the concrete inside the pipe is simulated by raising the temperature of the concrete element by 20°C, which is equivalent to the concrete expansion effect with a surface expansion rate of 0.047%.

[0052] It should be noted that the temperature increase (ΔT = 20℃) here is merely an equivalent mechanical method to simulate concrete expansion, and not the actual temperature change experienced by the concrete. This equivalent model is based on the theory of elasticity, and its core principle is to allow only the concrete elements to undergo thermal expansion, while the temperature of the steel pipe elements remains constant. This accurately simulates the mechanical state of the free expansion of concrete caused by the expansion agent, constrained by the steel pipe. The high degree of agreement between the finite element results and the theoretical solution (see Table 2) verifies the rationality and accuracy of this equivalent model.

[0053] The following is a model and calculation results of a steel-concrete composite tube with an outer diameter of 0.9m and a wall thickness of 30mm: Figure 4-6 As shown in the simulation results, the concrete inside the pipe is under bidirectional compression, and the radial and circumferential stresses are consistent. Except for local errors caused by the finite element mesh and calculation, the compressive stress of the concrete inside the pipe is -2.664 MPa, which is less than 10.801 MPa in the confined expansion model.

[0054] Figure 7-8 This is a simulation diagram of the circumferential stress distribution in a steel pipe. The diagram shows that the stress in the steel pipe is approximately linearly distributed along its thickness. The circumferential stress is higher at the inner edge of the pipe (38.591 MPa) and lower at the outer edge (36.0443 MPa). However, due to the relatively thin thickness of the steel pipe, the difference is not significant.

[0055] If we consider the radial pressure of 2.664 MPa exerted on the pipe wall due to concrete expansion, then according to theoretical calculations, the circumferential stress of the pipe wall is 37.30 MPa, which is close to that calculated by the finite element method. The comparison between the finite element calculation results and the theoretical analysis is shown in Table 2 below: Table 2 is a summary table of finite element calculation results and theoretical analysis results.

[0056] The results above show that the theoretical analysis and the finite element calculation results are very similar, indicating the correctness of the theoretical analysis.

[0057] In step 1:

[0058] From the above formula, it can be seen that the expansion force of the concrete inside the tube is related to the elastic modulus, Poisson's ratio, steel content, and expansion rate of the steel-concrete composite material. Referring to the "Design Specification for Highway Steel-Concrete Composite Arch Bridges," the Poisson's ratio of the concrete inside the tube is taken as 0.2, the steel content ranges from 0.04 to 0.2, the elastic modulus of steel is 206 GPa, and the elastic modulus of concrete is 30 to 38 GPa. The Poisson's ratio of the steel is taken as 0.31. Taking the surface expansion rate ξ∈(0.02%, 0.1%), the results are as follows... Figure 9 As shown: from Figure 9 As can be seen, within the effective range of key parameters, the circumferential stress increases with decreasing steel content and with increasing elastic modulus and surface expansion rate of the concrete inside the pipe. The value range is (15.0504, 103.2882) MPa.

[0059] about Since ξ is very small, it is approximately linear, and its values ​​in the effective range of ξ∈(0.02%, 0.1%) are as follows: Figure 10-11 As shown.

[0060] Based on linear fitting, we can take...

[0061] but

[0062] The expression for the circumferential stress expansion coefficient ζ of the steel pipe is:

[0063] In the formula, n = Es / Ec, where n is the elastic modulus ratio of steel to concrete. The values ​​of ζ are shown in Table 3 below: Table 3. When the elastic modulus of the steel pipe is 206 GPa, the circumferential stress expansion coefficient ζ (×10) of the steel pipe 5 )

[0064] Table 3 presents the circumferential stress expansion coefficient ζ (×10^5) of steel pipes under different combinations of concrete strength grades (C30-C80) and steel content (0.04-0.20). This table is calculated based on theoretical formulas (considering plane strain correction) and forms the core database of the subsequent rapid determination system for expansion rate limits. Designers can directly look up the ζ value in the table based on specific material parameters, thereby quickly calculating the expansion stress.

[0065] As can be seen from the table above, the circumferential stress of the steel pipe is more sensitive to the steel content than that of the concrete grade. When the steel content is low, the coefficient of thermal expansion of the circumferential stress of the steel pipe does not change much; when the steel content is high, the change is relatively large, but the difference is not significant. The range of the coefficient of expansion is (0.747, 1.045) x 10e5. The circumferential stress of the steel pipe calculated using Table 3 above is expressed in MPa.

[0066] The radial stress of the concrete inside the pipe is used to represent the circumferential stress of the steel pipe.

[0067]

[0068] Finite element verification: The stress conditions of concrete-steel tubular steel tubes under overall temperature variation were simulated using ANSYS finite element method. A plane strain element model was established, with the elastic modulus of the concrete inside the tube being 36 GPa, the coefficient of linear expansion of the concrete being 1e⁻⁵, the coefficient of linear expansion of the steel tube being 1.2e⁻⁵, the Poisson's ratio of the concrete being 0.2, and the Poisson's ratio of the steel tube being 0.31. The temperature variation was 20℃. The simulation results are as follows: Figure 12-13 As shown: The simulation calculation parameters are shown in Table 4: Table 4 summarizes the simulation parameters.

[0069] Table 4 shows that as the temperature rises, the concrete inside the pipe experiences tension, while the steel pipe experiences circumferential stress under compression. This is because the coefficient of thermal expansion of the steel pipe is slightly larger than that of the concrete, resulting in more significant expansion upon temperature rise. The steel pipe expands outward as a whole, constrained by the concrete inside, thus causing the concrete inside the pipe to tend to be under tension. The theoretical solution and the finite element solution are very similar, proving the accuracy of the theoretical solution.

[0070] S2: Obtain the circumferential stress components of the steel pipe during operation, generated by concrete pouring, changes in ambient temperature, and axial pressure; wherein, the circumferential stress components include at least the circumferential stress σ caused by the concrete pouring process inside the pipe. θ1 Circumferential stress σ caused by changes in ambient temperature during the operation phase θT Circumferential stress σ caused by axial pressure during operation θN .

[0071]

[0072] The circumferential stress in the steel pipe is opposite to the stress in the concrete inside the pipe. That is, as the temperature rises, the concrete inside the pipe is under compression, and as the temperature falls, the concrete inside the pipe is under tension. Similar to the expansion effect inside the pipe, the stress in the concrete and the steel pipe is only related to the elastic modulus, Poisson's ratio, steel content, and expansion rate of the steel-concrete composite material. Referring to the "Design Specification for Highway Steel-Concrete Composite Arch Bridges", the Poisson's ratio of the concrete inside the pipe is taken as 0.2, the steel content ranges from 0.04 to 0.2, the elastic modulus of steel is 206 GPa, and the elastic modulus of concrete is 30 to 38 GPa. The Poisson's ratio of the steel is taken as 0.31. Considering a temperature reduction of 25℃, the results are as follows... Figure 14-15 .

[0073] from Figure 13 As can be seen, the circumferential stress of the steel pipe caused by overall cooling increases significantly with decreasing steel content in the cross-section. The maximum circumferential stress increases with increasing concrete elastic modulus, but the change is not very sensitive. Under common engineering parameters, the maximum circumferential stress of the steel pipe caused by overall cooling is approximately 19.4 MPa, not exceeding 20 MPa.

[0074] In addition to the expansion of concrete inside the pipe causing circumferential stress in the steel pipe, temperature changes during operation, Poisson's effect of axial pressure, and hydraulic effects during concrete pouring can also increase the circumferential stress on the steel pipe.

[0075] S3: Superimpose all the circumferential stress components with the expansion stress calculated by the stress model, and multiply the superposition result by a weld stress concentration factor to obtain the design value of the circumferential stress of the steel pipe; wherein, in step S3, the design value of the circumferential stress of the steel pipe σ θ The calculation formula is: σ θ = γ·(σ θ1 +σ θ2+σ θT +σ θN Wherein, γ is the stress concentration factor of the longitudinal weld of the steel pipe determined by finite element analysis; it is taken as 1.255.

[0076] The parameters were determined through detailed finite element parametric analysis. The analysis comprehensively considered the effects of weld elastic modulus, grinding allowance, and bevel shape. Preferably, the grinding allowance was controlled to be no more than 2 mm, and a widely applicable 6 mm-45° bevel shape was adopted. Under these conditions, the weld stress concentration factor γ could be taken as 1.255.

[0077] σ θ1 This indicates the circumferential stress in the steel pipe caused by the concrete pouring process inside the pipe; σ θ2 This indicates the circumferential stress caused by the expansion of the concrete after it has hardened inside the pipe. σ θT This indicates the circumferential stress caused by changes in ambient temperature after the concrete inside the pipe has hardened. σ θN This indicates the circumferential stress caused by pressure on the concrete section of the steel pipe after the concrete inside the pipe has hardened.

[0078] Where, σ θT The value is between 10 and 20 MPa. With the circumferential compression and tension of the steel pipe during heating and cooling, σ θN The value is around 10 MPa, mainly under compression. According to experimental research, the circumferential stress during concrete pouring and strengthening is 30~60 MPa, and we will take 50 MPa for now.

[0079] Since concrete is subjected to tension both during pouring and after hardening, it is controlled according to tension. Considering material partial factors and importance factors, we obtain: ; After sorting, we get: ; For commonly used steels, the limits of circumferential stress caused by concrete expansion are shown in Table 5 below: Table 5. Allowable circumferential stress (MPa) for different steel pipe materials

[0080] The determination of the stress concentration factor γ of the longitudinal weld of the steel pipe needs to take into account the combined effects of the weld's elastic modulus, grinding allowance, and bevel shape; more preferably, the grinding allowance is no more than 2mm, and the bevel shape includes 6mm-45° and 13mm-20°.

[0081] In step 3, the fourth strength theory is selected, and the design value of the circumferential stress σ of the steel pipe is... θ2 Satisfy: σ θ2≤0.41·fy / (γm·γ0); where fy is the yield strength of the steel, γm is the material partial factor, and γ0 is the structural importance factor.

[0082] This invention quantifies the influence of weld process on stress concentration factor γ through refined finite element analysis. The study shows that by controlling the grinding allowance (preferably no more than 2 mm) and using specific bevel shapes (e.g., 6 mm-45°), the stress concentration factor at the weld can be controlled at a relatively low level of approximately 1.255.

[0083] S4: Compare the design value of the circumferential stress with the allowable value of the steel pipe stress based on the strength theory, and calculate the limit value of the expansion rate of the concrete surface inside the pipe to ensure the strength safety of the steel pipe.

[0084] It should be specifically noted that the "surface expansion rate ξ" defined and calculated in this invention refers to the cross-sectional expansion rate of concrete during the long-term stable expansion stage after the hydration heat has ended, excluding the instantaneous expansion caused by early hydration heat. However, the expansion rate measured by the "limited expansion rate test" specified in standards such as GB / T 23439 "Concrete Expansion Agent" usually includes the expansion caused by the initial hydration heat during pouring. Therefore, in practical engineering applications, the calculated ξ should be... limit As a long-term expansion control target, the dosage of the expansion agent is determined experimentally during concrete mix design to ensure that the restricted expansion rate of concrete at a specific age (e.g., 28 days or longer) is close to but not greater than ξ. limit At the same time, the effect of early hydration thermal expansion should be deducted.

[0085] In step S4, the calculated surface expansion rate ξ of the concrete inside the pipe is used to form a rapid expansion rate limit determination system based on different steel pipe materials, concrete strength grades and steel content.

[0086] As shown in Table 6: Table 6. Allowable expansion rate (%) of concrete surface inside the pipe for different material strengths and steel content.

[0087] Based on the above method, this invention can further develop into a rapid system for determining the expansion rate limit. This system can be implemented in the form of software, online tools, or design manuals. Its core is a pre-generated database that stores the circumferential stress expansion coefficient ζ of steel pipes under different combinations of steel grades (e.g., Q355, Q390), concrete grades (e.g., C50, C60), and steel content (e.g., 0.04~0.20). Designers only need to input basic engineering parameters, and the system can automatically call the database, quickly calculate, and output the recommended expansion rate limit, greatly improving design efficiency and avoiding tedious theoretical calculations.

[0088] ξ obtained according to the above method limit This refers to the maximum allowable surface expansion rate to ensure the strength safety of the steel pipe (especially the longitudinal weld). It can be further used as the target control value for expansion performance in concrete mix design. The expansion rate of concrete under restricted conditions is tested through a concrete restricted expansion rate test (according to standards such as GB / T 23439 "Concrete Expansion Agent"). The selected value ensures that the restricted expansion rate of concrete at a specific age (e.g., 7d, 28d) is close to but not greater than ξ. limit The appropriate mixing ratio is used to achieve an optimal balance between safety and density.

[0089] Based on the above method and the pre-calculated coefficient ζ (Table 3) and allowable strength value, a system for quickly determining the expansion rate limit can be formed. This system can be implemented as a software module, an online calculation tool, or an appendix to a design manual. Designers only need to input the steel pipe material (fy), concrete grade (Ec), and steel content of the section (as), and the system can automatically retrieve or calculate ζ, and comprehensively consider σθ1, σθT, σθN, and γ within the conventional value range to quickly output the recommended expansion rate limit ξ. limit This greatly improves design efficiency and scientific rigor.

[0090] In this invention, the selection of expansion rate is transformed from empirical and qualitative judgment to quantitative and scientific design based on mechanical models. This solution, for the first time, links the expansion characteristics of concrete materials with the strength and safety of steel pipe structures through a rigorous mechanical model, achieving a leap from empirical material proportioning to quantitative design based on structural system performance. It provides a crucial theoretical tool and design basis for solving the long-standing engineering challenge of how to rationally use expansion agents.

[0091] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for determining the limit value of the expansion rate of concrete inside a steel-concrete composite structure, characterized in that, Includes the following steps: S1: Based on elasticity and material parameters, a stress model is constructed to describe the quantitative relationship between the circumferential stress of the steel pipe and the expansion rate of the concrete surface inside the pipe; S2: Obtain the circumferential stress components of the steel pipe during the operation phase caused by concrete pouring, changes in ambient temperature, and axial pressure. S3: Superimpose all the circumferential stress components of the operation phase with the expansion stress calculated by the stress model, and multiply the superposition result by the stress concentration factor of a weld to obtain the design value of the circumferential stress of the steel pipe. S4: Compare the circumferential stress design value with the allowable stress value of the steel pipe based on strength theory, and calculate the limit value of the expansion rate of the concrete surface inside the pipe to ensure the strength safety of the steel pipe and the welded longitudinal seam of the steel pipe.

2. The method for determining the limit value of the expansion rate of concrete inside a steel-concrete composite structure according to claim 1, characterized in that, In step 1, the expression for the stress model is: σ θ2 =ζ*ξ;where, σ θ2 Let ξ be the maximum circumferential stress of the steel pipe, ξ be the surface expansion rate of the concrete inside the pipe, and ζ be the circumferential stress expansion coefficient of the steel pipe.

3. The method for determining the limit value of the expansion rate of concrete inside a steel-concrete composite structure according to claim 2, characterized in that, The surface expansion rate ξ of the concrete inside the pipe is defined as: the percentage increase in cross-sectional area after free expansion of the concrete relative to the original cross-sectional area, ξ=[(A expanded - A original ) / A original ] × 100%, where A represents the cross-sectional area.

4. The method for determining the limit value of the expansion rate of concrete inside a steel-concrete composite structure according to claim 2, characterized in that, The expression for the circumferential stress expansion coefficient ζ of the steel pipe is: In the formula, n = Es / Ec, where n is the elastic modulus ratio of steel to concrete; The circumferential stress expansion coefficient ζ of the steel pipe is a stress expansion coefficient related to the elastic modulus Es of the steel pipe, the elastic modulus Ec of the concrete, the Poisson's ratio μs of the steel pipe, the Poisson's ratio μc of the concrete, and the steel content as of the steel pipe.

5. The method for determining the limit value of the expansion rate of concrete inside a steel-concrete composite structure according to claim 1, characterized in that, In step 2, the circumferential stress component includes at least the circumferential stress σ caused by the concrete pouring process inside the steel pipe. θ1 Circumferential stress σ caused by changes in ambient temperature during the operation phase θT Circumferential stress σ caused by axial pressure during operation θN .

6. The method for determining the limit value of the expansion rate of concrete inside a steel-concrete composite structure according to claim 5, characterized in that, In step 3, the design value σ of the circumferential stress of the steel pipe θ The calculation formula is: s θ = γ·(σ θ1 +s θ2 +s θT +s θN ) among them, γ is the stress concentration factor of the longitudinal weld of the steel pipe determined by finite element analysis; σ θ1 This indicates the circumferential stress in the steel pipe caused by the concrete pouring process inside the pipe; σ θ2 This indicates the circumferential stress caused by the expansion of the concrete after it has hardened inside the pipe. σ θT This indicates the circumferential stress caused by changes in ambient temperature after the concrete inside the pipe has hardened. σ θN This indicates the circumferential stress caused by pressure on the concrete section of the steel pipe after the concrete inside the pipe has hardened.

7. The method for determining the limit value of the expansion rate of concrete inside a steel-concrete composite structure according to claim 1 or 6, characterized in that, The stress concentration factor γ of the longitudinal weld of the steel pipe is determined by finite element analysis. The value of γ is related to the elastic modulus of the weld, the grinding height and the bevel shape. Preferably, the grinding height is not greater than 2mm and the bevel shape includes 6mm-45° and 13mm-20°.

8. The method for determining the limit value of the expansion rate of concrete inside a steel-concrete composite structure according to claim 1, characterized in that, In step 3, the fourth strength theory is selected, and the maximum allowable circumferential stress [σθ] that the steel pipe can withstand satisfies: [σθ]≤0.41·fy / (γm·γ0); where fy is the yield strength of the steel, γm is the material partial factor, and γ0 is the structural importance factor.

9. The method for determining the limit value of the expansion rate of concrete inside a steel-concrete composite structure according to claim 1, characterized in that, In step S4, the calculated surface expansion rate ξ of the concrete inside the pipe is used to form a rapid expansion rate limit determination system based on different steel pipe materials, concrete strength grades and steel content.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the method as described in any one of claims 1-8.

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