Intelligent method and device for calculating axial time-varying deformation parameters of RC component
By combining fractional calculus theory and the time-varying characteristics of reinforced concrete, axial time-varying deformation model of reinforced concrete components was constructed, which solved the problem of large differences between the existing model prediction results and the actual measured strain, and achieved more accurate deformation parameter prediction and better design guidance.
Patent Information
- Application Number
- CN202510218137.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-02-26
- Publication Date
- 2025-05-30
- Estimated Expiration
- 2045-02-26
AI Technical Summary
When the existing concrete creep model predicts the deformation parameters of concrete components in the axial direction, the results are much different from the measured strain, and it is impossible to effectively guide construction and design. Especially in reinforced concrete components, there is less research on coupling stress.
The basic theory of fractional calculus and the time-varying characteristics of reinforced concrete are combined to construct an axial time-varying deformation model of reinforced concrete components based on fractional derivatives. By obtaining the reinforcement rate of the component, the elastic modulus of the steel bars and concrete, the stiffness information is calculated, and constitutive equations and creep flexibility expressions are constructed.
The number of required parameters is reduced, the fitting effect and interpretability of the model is improved, and the deformation parameters of the reinforced concrete components can be more accurately predicted, which improves the guidance of design and construction.
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Figure CN120068447A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of time-varying deformation of concrete components, and particularly relates to an intelligent method for calculating axial time-varying deformation parameters of RC components. Background Art
[0002] Concrete is usually regarded as a solid material. However, when it is subjected to stress or external environmental changes, its own deformation is often time-related. The American Concrete Institute (ACI 209R) and the European Model Code (MC2010) have also proposed their respective concrete creep models based on the research of many scholars. However, since each model is obtained by regression analysis of the results of laboratory standard creep tests, and there are significant differences in the sizes of the test components and the actual concrete components in engineering, the predicted results often deviate greatly from the measured strains and cannot be directly used to guide construction and design.
[0003] For viscoelastic materials, simply speaking, the constitutive equation of an ideal liquid indicates that the stress is proportional to the first derivative of the strain with respect to time (σ(t) ∝ D 1 ε(t), where D χ is the χ-order derivative with respect to time), that is, it satisfies Newton's law, while the constitutive equation of an ideal solid indicates that the stress is proportional to the zero-order derivative of the strain with respect to time (σ(t) ∝ D 0 ε(t)), satisfying Hooke's law. And all materials existing in reality are between solids and liquids. Therefore, the stress of all materials is proportional to the 0-1 order derivative of the strain with respect to time (σ(t) ∝ D β ε(t), β ∈ (0, 1)). The basic unit of the fractional derivative is usually represented by a triangle or a rhombus. The closer β is to 1, the closer the strain response is to an ideal liquid. The closer β is to 0, the closer the strain development is to an ideal solid.
[0004] Common calculation models and specifications for the time-dependent properties of concrete, as well as shrinkage and creep, include the MC 2010 model, ACI209R92 model, B3 model, and GL2000 model. Among the four types of calculation formulas, except for the B3 model which is a semi-empirical formula, the other three groups of formulas are all from the regression analysis of experimental results. Among them, the ACI209R-92 and GL2000 calculation formulas are the most concise, and all the parameters required by the GL2000 formula can be obtained during the design process. The MC 2010 model and the B3 model require more parameters, and creep is divided into basic creep and drying creep and calculated separately. The original formula of the B3 model does not introduce the creep coefficient, but uses the flexibility function to replace it, which reduces the error caused by inaccurate elastic modulus. Among them, except that the MC2010 specification does not set the upper limit of shrinkage and creep, but the results given by the formula show that with the increase of time, shrinkage and creep will gradually decrease until they basically do not change eventually. The other calculations all give the maximum values of shrinkage and creep, and the whole process of component deformation will not exceed this value. And the strain predicted by the formula is not the local strain at a certain point inside the component, but the overall average strain related to the cross-section of the concrete component. The advantage of this method is that it is simple for engineers to use, but the disadvantage is that the calculation results are quite different from the actual deformation law.
[0005] The components of the above models are standard-sized plain concrete test blocks. However, in actual engineering, concrete is often used in combination with steel bars, and the forces on the concrete and steel bars are coupled. At present, there is little research on the coupled forces of concrete and steel bars. Therefore, it is necessary to establish a corresponding axial time-dependent model for reinforced concrete components. Summary of the Invention
[0006] The purpose of the embodiment of the present invention is to provide an intelligent method for calculating the axial time-dependent deformation parameters of RC components, which combines the basic theory of fractional calculus with the time-dependent characteristics of reinforced concrete. It not only effectively utilizes the advantage that the mechanical model fitting effect of the fractional calculus unit is significantly better than that of the traditional mechanical unit model as a whole, but also fully considers the time-dependent deformation of reinforced concrete components in actual engineering, so as to solve at least one technical problem involved in the background technology.
[0007] In order to solve the above technical problems, the present invention is implemented as follows:
[0008] The embodiment of the present invention provides an intelligent method for calculating the axial time-dependent deformation parameters of RC components, including the following steps:
[0009] Step S1, constructing an axial time-dependent deformation model of a reinforced concrete component based on fractional derivatives;
[0010] Step S2: Obtain the reinforcement ratio of the reinforced concrete member, the elastic modulus of the steel bar, and the elastic modulus of the concrete, and calculate the stiffness information in the axial time-varying deformation model of the reinforced concrete member;
[0011] Step S3: Based on the stiffness information, construct the constitutive equation of the axial time-varying deformation model of the reinforced concrete member;
[0012] Step S4: Perform Laplace transform on the constructed constitutive equation to obtain the creep compliance expression of the axial time-varying deformation model of the reinforced concrete member.
[0013] The present invention also provides a device for calculating the axial time-varying deformation parameters of an RC member for implementing the above method, including:
[0014] A model construction unit for constructing an axial time-varying deformation model of a reinforced concrete member based on fractional derivative;
[0015] A parameter acquisition unit for obtaining the reinforcement ratio of the reinforced concrete member, the elastic modulus of the steel bar, and the elastic modulus of the concrete, and calculating the stiffness information in the axial time-varying deformation model of the reinforced concrete member;
[0016] A constitutive equation construction unit for constructing the constitutive equation of the axial time-varying deformation model of the reinforced concrete member based on the stiffness information;
[0017] A creep compliance expression construction unit for performing Laplace transform on the constructed constitutive equation to obtain the creep compliance expression of the axial time-varying deformation model of the reinforced concrete member.
[0018] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor runs the computer program, the steps of the above method are executed.
[0019] The present invention also provides a computer-readable storage medium storing a computer program, and when the computer program is executed by a processor, the steps of the above method are implemented.
[0020] The present invention provides a computer program product, including a computer program, and when the computer program is executed by a processor, the steps of the above method are implemented.
[0021] The beneficial effects of the embodiments of the present invention are as follows:
[0022] 1. The present invention combines the basic theory of fractional calculus with the time-varying characteristics of reinforced concrete, not only effectively utilizing the advantage that the mechanical model fitting effect of the fractional calculus unit is significantly better than that of the traditional mechanical unit model as a whole, but also fully considering the time-varying deformation of reinforced concrete members in actual engineering.
[0023] 2. The present invention constructs an axial time-varying deformation model of reinforced concrete members based on fractional derivatives, which greatly reduces the number of required parameters while achieving a more satisfactory fitting effect, thereby improving the usability and interpretability of the model. At the same time, using existing experiments, the fitting ability and computational convenience of the model are verified, and relatively ideal results are obtained. BRIEF DESCRIPTION OF THE DRAWINGS
[0024] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings, where:
[0025] Figure 1 is a schematic diagram of the axial time-varying deformation model of the reinforced concrete member provided by the present invention;
[0026] Figure 2 (a)-(d) are the verification result diagrams of the reinforced concrete model provided by the present invention;
[0027] Figure 3 (a)-(h) are the schematic diagrams of the fitting results provided by the present invention;
[0028] Figure 4 is one of the schematic diagrams of the hardware structure of the electronic device provided by the present invention;
[0029] Figure 5 is the second schematic diagram of the hardware structure of the electronic device provided by the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS
[0030] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art without creative efforts based on the embodiments of the present invention belong to the scope of protection of the present invention.
[0031] In the description and claims of the present invention, the terms "first", "second", etc. are used to distinguish similar objects, rather than to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged under appropriate circumstances, so that the embodiments of the present invention can be implemented in an order other than those illustrated or described herein, and the objects distinguished by "first", "second", etc. are generally of the same type, and the number of objects is not limited. For example, the first object can be one or more. In addition, "and / or" in the description and claims means at least one of the connected objects, and the character " / ", generally represents an "or" relationship between the associated objects before and after.
[0032] An embodiment of the present invention provides an intelligent method for calculating the axial time-varying deformation parameters of RC members, including the following steps:
[0033] Step S1, constructing an axial time-varying deformation model of a reinforced concrete member based on fractional derivatives;
[0034] Step S2, obtaining the reinforcement ratio of the reinforced concrete member, the elastic modulus of the reinforcement, and the elastic modulus of the concrete, and calculating the stiffness information in the axial time-varying deformation model of the reinforced concrete member;
[0035] Step S3, constructing a constitutive equation of the axial time-varying deformation model of the reinforced concrete member based on the stiffness information;
[0036] Step S4, performing a Laplace transform on the constructed constitutive equation to obtain the creep compliance expression of the axial time-varying deformation model of the reinforced concrete member.
[0037] In step S1, as shown in Figure 1 , the axial time-varying deformation model of the reinforced concrete member adopts an improved Fractional-Zener model, which consists of an improved fractional calculus Zener model in series with a concrete shrinkage unit 3.
[0038] The improved fractional calculus Zener model includes a concrete elastic unit 1, a concrete creep unit 2, and an elastic unit 4 of steel bars or steel sections. Among them, the concrete elastic unit 1 and the concrete creep unit 2 are first connected in series, and then the connected concrete elastic unit 1 and concrete creep unit 2 are connected in parallel with the elastic unit 4 of steel bars or steel sections.
[0039] In step S2, the stiffness information includes the stiffness parameter k β provided by the concrete and the stiffness parameter, k γ provided by the reinforcement, which is expressed by the following formula:
[0040] k β = E c (1 - ρ s) (1)
[0041] k γ = E s ρ s (2)
[0042] In the formula, ρ s represents the reinforcement ratio of the reinforced concrete member; E s represents the elastic modulus of the reinforcement; E c represents the elastic modulus of the concrete.
[0043] In step S3, the constitutive equation includes:
[0044]
[0045] In the formula, σ(t) represents the total stress; ε(t) represents the total strain; C α , α are coefficients, and α ∈ (0, 1); is the α-order derivative of the stress with respect to time; is the α-order derivative of the strain with respect to time.
[0046] The constitutive equation is constructed by the following steps:
[0047] Step S31, express the constitutive relationship of the series system composed of the concrete elastic unit 1 and the concrete creep unit 2 as:
[0048]
[0049] In the formula, σ U , ε U respectively represent the total stress and strain of the concrete elastic unit 1 and the concrete creep unit 2;
[0050] Step S32, express the constitutive relationship of the elastic unit 4 of the reinforcement or the steel section as:
[0051] σ L (t) = k γ ε L (t) (5)
[0052] In the formula, σ L , ε L respectively represent the total stress and strain of the elastic unit 4 of the reinforcement or the steel section;
[0053] Step S33, since ε = ε U = ε L and σ L = σ - σ U , substitute ε = ε U = ε L and σ L = σ - σ USubstitute into formula (5), and then substitute into formula (4) and simplify to obtain the constitutive equation of the axial time-varying deformation model of reinforced concrete members:
[0054]
[0055] In the formula, σ(t) represents the total stress; ε(t) represents the total strain; k β , k γ can be regarded as the elasticity provided by concrete and steel respectively; C α , α are coefficients, and α ∈ (0, 1); is the α-th derivative of stress with respect to time; is the α-th derivative of strain with respect to time.
[0056] Step S4 specifically includes:
[0057] Let σ(t) = δ(t), and find the creep compliance function J(t) = ε(t) of the axial time-varying deformation model of reinforced concrete members. Substitute σ(t) = δ(t) into formula (6), and perform Laplace transform on the whole, to obtain:
[0058]
[0059] After simplification, obtain:
[0060]
[0061] In the formula, represents the mapping function of J(t), that is, the creep compliance corresponding to the model, in the Laplace space, and s represents the coefficient in the Laplace space obtained by converting the time t through Laplace transform.
[0062] The above formula (8) is an implicit expression in the Laplace space, and it is impossible to write an explicit expression in the time domain space mathematically. Therefore, it is necessary to solve formula (8) by numerical methods, and use a high-precision numerical integration method for inverse Laplace transform:
[0063]
[0064] In the formula, represents the Laplace transform operator;
[0065] Assume that the relationship between the strain of the concrete shrinkage unit 3 and time is ε th (t). The strain of the member at any time point under the action of a constant axial force can be calculated by the following formula:
[0066] ε(t) = J(t)σ + ε sh (t) (10)
[0067] k β , kγ Regarding the elasticity provided by concrete and steel bars respectively, in a reinforced concrete member, it can be simplified as follows:
[0068] k β = E c (1 - ρ s ) (11)
[0069] k γ = E s ρ s (12)
[0070] Since the strength and age of concrete both significantly affect its creep deformation and elastic deformation, therefore, a multiple regression analysis is carried out on the influence of the two parameters (C α , α) by the strength and age of concrete:
[0071]
[0072] Wherein, t 0 is the time from the load application time to the concrete pouring point; f c is the concrete strength; C α (t 0 , f c ), α(t 0 , f c ) are the parameters fitted with C α , α as parameters.
[0073] Verify the intelligent method for calculating the axial time-varying deformation parameters of RC members provided by the embodiments of the present invention, specifically as follows:
[0074] Verify with the creep experiment results of different reinforced concrete members in the existing literature respectively. For the creep experiments of two groups of different reinforced members, take the experiment result of one of the members as the fitting sample. The present invention takes the small-reinforcement member as the sample, fits the relevant parameters in the model, and changes the corresponding k β , k γ two parameters in the model by changing the longitudinal reinforcement ratio of the cross-section of the member, and keep the other parameters unchanged (C α , α), and calculate the strain response of the other member. The member information and fitting parameter results are shown in 0, and the fitting and calculation results are as Figure 2 shown. Figure 2 The time-strain response of the small-reinforcement ratio member is the fitting result, while the strain of the large-reinforcement member is calculated. It can be seen that both the fitting result and the calculation result are in good agreement with the experiment result. Therefore, it can be concluded that it is reasonable to consider the influence of the member reinforcement on creep through this method.
[0075] Table 1 Verification member information and fitting results
[0076]
[0077] Note: The values in the literature are all converted to the strain response J(t) under unit stress.
[0078] The strength and age of concrete both significantly affect its creep deformation and elastic deformation.
[0079] Therefore, in this invention, using existing codes and theoretical models, a quantitative analysis of the proposed model parameters considering two basic properties of concrete is carried out to obtain the general variation law of the parameters with the strength and age of concrete and the corresponding empirical formula.
[0080] To consider the coupled influence of different concrete strengths and different ages on creep, a multiple regression analysis is carried out on the influence of the two parameters (C α , α) by the strength and age of concrete, as shown in Equation (14), and the fitting results are as Figure 3 shown, and the formula obtained by regression is shown in 0.
[0081]
[0082] In the formula, k β represents the stiffness provided by the elastic modulus of concrete; t 0 is the time from the load application point to the time of concrete pouring (aging time); f c is the strength of concrete; C α (t 0 , f c ), α(t 0 , f c ) are the parameters fitted with C α , α as parameters.
[0083] Table 2 Regression formula
[0084]
[0085] The calculation results of the calculation formula are all in good agreement with the results obtained by the code and the model (R 2>0.98), and from the trend point of view, α is less affected by the strength of concrete and more affected by the age of concrete. It is worth noting that with the increase of the age of concrete, the increasing trend of α gradually decreases, and it changes rapidly only in the early stage of pouring, indicating that the physical properties of concrete change rapidly shortly after pouring, and the concrete completes the transformation from "liquid" to "solid". However, the regression results of ACI209R show that α is not affected by the strength and age of concrete. This result perfectly confirms the idea in rheological mechanics, that is, the constitutive order of a certain type of material does not change, and only the aging time is affected by many other parameters. From a computational point of view, this result greatly simplifies the calculation, and the formula in 0 is also more concise and more convenient for engineering use. The parameter C α On the whole, it increases with the increase of concrete strength and age, which is reflected in the fact that creep flexibility decreases with the increase of concrete strength and age, but different specifications and theoretical models show different increasing trends.
[0086] The present invention also provides a device for calculating the axial time-varying deformation parameters of RC components for realizing the method, comprising a model building unit, a parameter acquisition unit, a constitutive equation building unit and a creep flexibility expression building unit.
[0087] The model building unit is used to build an axial time-varying deformation model of reinforced concrete components based on fractional derivatives.
[0088] The parameter acquisition unit is used to acquire the reinforcement ratio of the reinforced concrete component, the elastic modulus of the steel bar and the elastic modulus of the concrete, and calculate the stiffness information in the axial time-varying deformation model of the reinforced concrete component.
[0089] The constitutive equation construction unit is used to construct the constitutive equation of the axial time-varying deformation model of the reinforced concrete component based on stiffness information.
[0090] The creep flexibility expression construction unit is used to perform Laplace transformation on the constructed constitutive equation to obtain the creep flexibility expression of the axial time-varying deformation model of the reinforced concrete component.
[0091] like Figure 4 As shown, an embodiment of the present invention further provides an electronic device 600, which includes a processor 601, a memory 602, and a program or instruction stored in the memory 602 and executable on the processor 601. When the program or instruction is executed by the processor 601, each process of the above-mentioned intelligent method embodiment for calculating the axial time-varying deformation parameters of the RC member is implemented, and the same technical effect can be achieved. To avoid repetition, it will not be described here.
[0092] It should be noted that the first electronic device in the embodiments of the present invention includes the above-mentioned mobile electronic device and non-mobile electronic device.
[0093] Figure 5 Schematic diagram of the hardware structure of an electronic device according to an embodiment of the present invention.
[0094] The electronic device 700 includes, but is not limited to: a radio frequency unit 701, a network module 702, an audio output unit 703, an input unit 704, a sensor 705, a display unit 706, a user input unit 707, an interface unit 708, a memory 709, and a processor 710 and other components.
[0095] Those skilled in the art can understand that the electronic device 700 may further include a power source (such as a battery) for supplying power to each component. The power source can be logically connected to the processor 710 through a power management system, so as to realize functions such as management of charging, discharging, and power consumption management through the power management system. Figure 5 The structure of the electronic device shown in does not constitute a limitation on the electronic device. The electronic device may include more or fewer components than shown in the figure, or combine certain components, or have different component arrangements, which will not be elaborated here.
[0096] It should be understood that in the embodiments of the present invention, the input unit 704 may include a graphics processing unit (GPU) 7041 and a microphone 7042. The graphics processing unit 7041 processes the image data of still images or videos obtained by an image capture device (such as a camera) in a video capture mode or an image capture mode. The display unit 706 may include a display panel 7061, and the display panel 7061 may be configured in the form of a liquid crystal display, an organic light emitting diode, etc. The user input unit 707 includes a touch panel 7071 and other input devices 7072. The touch panel 7071 is also called a touch screen. The touch panel 7071 may include two parts: a touch detection device and a touch controller. The other input devices 7072 may include, but are not limited to, a physical keyboard, function keys (such as volume control keys, switch keys, etc.), a trackball, a mouse, a joystick, which will not be elaborated here. The memory 709 may be used to store software programs and various data, including but not limited to application programs and operating systems. The processor 710 may integrate an application processor and a modulation / demodulation processor. Among them, the application processor mainly processes the operating system, user interface, and application programs, and the modulation / demodulation processor mainly processes wireless communication. It can be understood that the above modulation / demodulation processor may not be integrated into the processor 710.
[0097] An embodiment of the present invention further provides a readable storage medium, on which a program or instruction is stored. When the program or instruction is executed by a processor, it implements each process of the above-mentioned intelligent method embodiment for calculating the axial time-varying deformation parameters of the RC member, and can achieve the same technical effect. To avoid repetition, it will not be elaborated here.
[0098] Wherein, the processor is the processor in the electronic device described in the above embodiment. The readable storage medium includes a computer-readable storage medium, such as a computer read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disc, etc.
[0099] Another embodiment of the present invention provides a chip, which includes a processor and a communication interface. The communication interface is coupled to the processor. The processor is used to run a program or instruction to implement each process of the above-mentioned intelligent method embodiment for calculating the axial time-varying deformation parameters of the RC member, and can achieve the same technical effect. To avoid repetition, it will not be elaborated here.
[0100] It should be understood that the chip mentioned in the embodiment of the present invention may also be referred to as a system-on-chip, a system chip, a chip system, or a system-on-chip, etc.
[0101] It should be noted that in this article, the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements not only includes those elements, but also includes other elements not explicitly listed, or further includes elements inherent to such process, method, article or device. Without more limitations, an element defined by the statement "including one..." does not exclude the existence of another identical element in the process, method, article or device including the element.
[0102] In addition, it should be pointed out that the scope of the method and system in the embodiment of the present invention is not limited to performing functions in the order shown or discussed. It may also include performing functions in a substantially simultaneous manner or in a reverse order according to the functions involved. For example, the described method may be performed in an order different from that described, and various steps may be added, omitted, or combined. In addition, the features described with reference to certain examples may be combined in other examples.
[0103] The embodiments of the present invention have been described above in conjunction with the accompanying drawings. However, the present invention is not limited to the above specific embodiments. The above specific embodiments are merely illustrative and not restrictive. Under the inspiration of the present invention, those of ordinary skill in the art can also make many forms without departing from the spirit of the present invention and the scope protected by the claims, and all of them fall within the protection scope of the present invention.
Claims
1. An intelligent method for calculating the axial time-varying deformation parameters of RC components, characterized in that: The following steps are involved: Step S1, constructing a time-varying axial deformation model of reinforced concrete components based on fractional derivatives; Step S2, obtaining the reinforcement ratio of the reinforced concrete component, the elastic modulus of the steel bar and the elastic modulus of the concrete, and calculating the stiffness information in the axial time-varying deformation model of the reinforced concrete component; Step S3, constructing a constitutive equation of the axial time-varying deformation model of the reinforced concrete component based on the stiffness information; Step S4, performing Laplace transformation on the constructed constitutive equation to obtain the creep flexibility expression of the axial time-varying deformation model of the reinforced concrete component.
2. The method according to claim 1, characterized in that In step S1, the axial time-varying deformation model of reinforced concrete components adopts an improved Fractional-Zener model, which is composed of an improved fractional-order calculus Zener model connected in series with a concrete shrinkage unit.
3. The method according to claim 2, characterized in that The improved fractional calculus Zener model includes a concrete elastic unit, a concrete creep unit and an elastic unit of a steel bar or a steel section, wherein the concrete elastic unit and the concrete creep unit are first connected in series, and then the series-connected concrete elastic unit and the concrete creep unit are connected in parallel with the elastic unit of the steel bar or the steel section.
4. The method according to claim 3, characterized in that In step S2, the stiffness information includes the stiffness parameter k provided by the concrete β and the stiffness parameter provided by the reinforcement, k γ , expressed by the following formula: k β =E c (1-p s ) (1) k γ =E s r s (2) In the formula, ρ s Indicates the reinforcement ratio of reinforced concrete components; E s Represents the elastic modulus of the steel bar; E c Represents the elastic modulus of concrete.
5. The method according to claim 4, characterized in that In step S3, the constitutive equation includes: Where σ(t) represents the total stress; ε(t) represents the total strain; C α , α is a coefficient, and α∈(0,1); is the α-order inverse of stress with respect to time; is the α-order inverse of the strain with respect to time.
6. The method according to claim 5, characterized in that The constitutive equation is constructed using the following steps: Step S31, the constitutive relation of the series system composed of the concrete elastic unit and the concrete creep unit is expressed as: In the formula, σ U , ε U represent the total stress and strain of concrete elastic unit and concrete creep unit respectively; Step S32, the constitutive relation of the elastic unit of the steel bar or steel section is expressed as: s L (t)=k γ e L (t) (5) In the formula, σ L , ε L represents the total stress and strain of the elastic element of the reinforcement or steel section respectively; Step S33, since ε=ε U =ε L And σ L =σ-σ U , set ε = ε U =ε L and σ L =σ-σ U Substitute into formula (5) and then into formula (4) to obtain the constitutive equation of the axial time-varying deformation model of reinforced concrete components: Where σ(t) represents the total stress; ε(t) represents the total strain; k β ,k γ can be regarded as the elasticity provided by concrete and steel bars respectively; C α , α is a coefficient, and α∈(0,1); is the α-order inverse of stress with respect to time; is the α-order inverse of the strain with respect to time.
7. The method according to claim 6, characterized in that Step S4 specifically includes: Let σ(t) = δ(t), and find the creep flexibility function J(t) = ε(t) of the axial time-varying deformation model of reinforced concrete components. Substitute σ(t) = δ(t) into formula (6), and perform Laplace transformation on the whole to obtain: After sorting, we get: In the formula, represents J(t), i.e., the mapping function of the creep flexibility corresponding to the model in the Laplace space, and s represents the coefficient in the Laplace space converted from time t by Laplace transform.
8. The method according to claim 7, characterized in that Formula (8) is solved numerically, and the Laplace inverse transformation is performed using a high-precision numerical integration method: In the formula, represents the Laplace transform operator; Assume that the strain-time relationship of the concrete shrinkage unit is ε sh (t), the strain of the component at any time point under the action of constant axial force can be calculated by the following formula: ε(t)=J(t)σ+ε sh (t) (10) k β ,k γ Assume as the elasticity provided by concrete and steel bars respectively, in reinforced concrete components, it can be simplified as: k β =E c (1-p s ) (11) k γ =E s r s (12) Since the strength and age of concrete greatly affect its creep deformation and elastic deformation, the two parameters (C α ,α)Multivariate regression analysis is performed on the influence of concrete strength and age: Where t0 is the time from the load loading time to the concrete pouring point; f c is the concrete strength; C α (t0,f c ), α(t0,f c ) is C α , α is used as the parameter for fitting.
9. A device for calculating axial time-varying deformation parameters of RC members for implementing the method described in any one of claims 1 to 8, characterized in that: include: A model building unit, which is used to build an axial time-varying deformation model of reinforced concrete components based on fractional derivatives; A parameter acquisition unit, which is used to obtain the reinforcement ratio of the reinforced concrete component, the elastic modulus of the steel bar and the elastic modulus of the concrete, and calculate the stiffness information in the axial time-varying deformation model of the reinforced concrete component; A constitutive equation construction unit, which is used to construct the constitutive equation of the axial time-varying deformation model of reinforced concrete components based on stiffness information; The creep flexibility expression construction unit is used to perform Laplace transformation on the constructed constitutive equation to obtain the creep flexibility expression of the axial time-varying deformation model of reinforced concrete components.
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