An intelligent method and device for calculating axial time-varying deformation parameters of RC components
Through fractional calculus theory, the axial time deformation model of reinforced concrete components is constructed, which solves the problem of large calculation errors in engineering practice, and realizes more efficient calculation of axial time deformation parameters of reinforced concrete components.
Patent Information
- Application Number
- CN202510218137.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2025-02-26
- Publication Date
- 2025-09-02
- Estimated Expiration
- 2045-02-26
AI Technical Summary
The existing concrete creep model has a large difference from the measured strain in engineering practice, and cannot effectively guide construction and design, especially the deformation of reinforced concrete components in the axial direction has not been effectively calculated.
The axial time-changing deformation model of reinforced concrete based on fractional derivatives is constructed using fractional calculus theory combined with the time-variable characteristics of reinforced concrete to construct a creep flexibility expression by obtaining stiffness information, constructing constitutive equations and performing Laplace changes.
It improves the fitting effect and usability of the model, reduces the number of parameters, improves the convenience and accuracy of calculation, and is suitable for the calculation of time deformation of reinforced concrete components in actual projects.
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Figure CN120068447B_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of time-varying deformation of concrete components, and in particular relates to an intelligent method for calculating axial time-varying deformation parameters of RC components. Background Art
[0002] Concrete is generally considered a solid material. However, when subjected to stress or changes in the external environment, its deformation is often time-dependent. The American Concrete Institute (ACI 209R) and the European Model Code (MC2010) have each proposed concrete creep models based on the research of numerous scholars. However, because these models are derived from regression analysis of standard laboratory creep test results, and because the dimensions of the test components differ significantly from those of actual concrete components in engineering projects, the predicted results often differ significantly from the measured strains, making them inadequate for direct guidance in construction and design.
[0003] For viscoelastic materials, in simple terms, the constitutive equation of an ideal fluid states that stress and strain are proportional to the first-order derivative of time (σ(t)∝D 1 ε(t), denoted by D χ is the χ-order derivative with respect to time), that is, it satisfies Newton's law, and the constitutive representation of an ideal solid is that the zero-order derivative of stress and strain with respect to time is proportional (σ(t)∝D 0 ε(t)), which satisfies Hooke's law. All materials in reality are between solid and liquid, so the stress of all materials is proportional to the 0th to 1st order derivative of strain with respect to time (σ(t)∝D β ε(t), β∈(0,1)), the basic unit of fractional derivative is usually represented by a triangle or diamond. The closer β is to 1, the closer the strain response is to an ideal liquid, and the closer β is to 0, the closer the strain development is to an ideal solid.
[0004] Common calculation models and standards for the time-varying properties of concrete and its shrinkage and creep include the MC 2010 model, ACI 209R-92 model, B3 model, and GL 2000 model. Of these four types of calculation formulas, the B3 model is a semi-empirical formula, while the other three are derived from regression analysis of experimental results. The ACI 209R-92 and GL 2000 formulas are the simplest, and the parameters required by the GL 2000 formula can be obtained during the design process. The MC 2010 and B3 models require more parameters and divide creep into two categories: basic creep and drying creep. The B3 model's original formula does not include a creep coefficient, but instead uses a flexibility function to reduce errors caused by inaccurate elastic moduli. While the MC 2010 standard does not set upper limits for shrinkage and creep, the formulas indicate that shrinkage and creep will gradually decrease with time, ultimately remaining essentially unchanged. The other calculations all specify maximum shrinkage and creep values, which will not be exceeded throughout the component's deformation process. Moreover, 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 easy 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 model are standard-sized plain concrete specimens. However, in actual engineering, concrete is often used together with steel bars, and the forces acting on concrete and steel bars are coupled. Currently, there is little research on the coupled forces between concrete and steel bars. Therefore, it is necessary to establish a corresponding axial time-varying model for reinforced concrete components. Summary of the Invention
[0006] The purpose of the embodiments of the present invention is to provide an intelligent method for calculating the time-varying axial deformation parameters of RC components. This method combines the basic theory of fractional calculus with the time-varying characteristics of reinforced concrete. This method effectively utilizes the advantage of the fractional calculus unit, which has an overall significantly better mechanical model fitting effect than traditional mechanical unit models, while fully considering the time-varying deformation of reinforced concrete components in actual engineering projects. This method can thus solve at least one of the technical problems mentioned in the background art.
[0007] In order to solve the above-mentioned technical problems, the present invention is achieved as follows:
[0008] An embodiment of the present invention provides an intelligent method for calculating axial time-varying deformation parameters of RC components, comprising the following steps:
[0009] Step S1, constructing a time-varying axial deformation model of reinforced concrete components based on fractional derivatives;
[0010] 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;
[0011] Step S3, constructing a constitutive equation of the axial time-varying deformation model of the reinforced concrete component based on the stiffness information;
[0012] Step S4: 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.
[0013] The present invention also provides a device for calculating the axial time-varying deformation parameters of RC components for implementing the method, comprising:
[0014] A model building unit, which is used to build an axial time-varying deformation model of reinforced concrete components based on fractional derivatives;
[0015] 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;
[0016] A constitutive equation construction unit is used to construct the constitutive equation of the axial time-varying deformation model of reinforced concrete components based on stiffness information;
[0017] 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.
[0018] The present invention also provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the steps of the above method when executing the computer program.
[0019] The present invention also provides a computer-readable storage medium storing a computer program, wherein the computer program implements the steps of the above method when executed by a processor.
[0020] The present invention provides a computer program product, comprising a computer program, which implements the steps of the above method when executed by a processor.
[0021] The beneficial effects of the embodiments of the present invention are:
[0022] 1. The present invention combines the basic theory of fractional calculus with the time-varying 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, but also fully considers the time-varying deformation of reinforced concrete components in actual engineering.
[0023] 2. The present invention constructs an axial time-varying deformation model of reinforced concrete components based on fractional derivatives, which greatly reduces the number of required parameters while obtaining a more satisfactory fitting effect, thereby improving the usability and interpretability of the model. At the same time, the model's fitting ability and computational convenience are verified by using existing experiments, 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 briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. Those skilled in the art can also derive other drawings based on these drawings without inventive work, among which:
[0025] Figure 1 This is a schematic diagram of the axial time-varying deformation model of reinforced concrete components provided by the present invention;
[0026] Figure 2 (a) to (d) are the verification results of the reinforced concrete model provided by the present invention;
[0027] Figure 3 (a) to (h) are schematic diagrams of the fitting results provided by the present invention;
[0028] Figure 4 This is one of the hardware structure diagrams of the electronic device provided by the present invention;
[0029] Figure 5 This is the second schematic diagram of the hardware structure of the electronic device provided by the present invention. DETAILED DESCRIPTION
[0030] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.
[0031] The terms "first," "second," and the like in the specification and claims of the present invention are used to distinguish similar objects, and are not used to describe a specific order or precedence. It should be understood that the terms used in this manner are interchangeable where appropriate, so that the embodiments of the present invention can be implemented in an order other than that illustrated or described herein, and that the objects distinguished by "first," "second," and the like are generally of the same type, and do not limit the number of objects. For example, the first object can be one or more. In addition, the term "and / or" in the specification and claims refers to at least one of the connected objects, and the character " / " generally indicates that the objects connected are in an "or" relationship.
[0032] An embodiment of the present invention provides an intelligent method for calculating axial time-varying deformation parameters of RC components, comprising the following steps:
[0033] Step S1, constructing a time-varying axial deformation model of reinforced concrete components based on fractional derivatives;
[0034] 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;
[0035] Step S3, constructing a constitutive equation of the axial time-varying deformation model of the reinforced concrete component based on the stiffness information;
[0036] Step S4: 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.
[0037] In step S1, combine Figure 1 As shown, the axial time-varying deformation model of reinforced concrete components adopts an improved Fractional-Zener model, which consists of an improved fractional-order calculus Zener model connected in series with a concrete shrinkage unit 3.
[0038] The improved fractional-order calculus Zener model includes a concrete elastic unit 1, a concrete creep unit 2, and an elastic unit 4 of a steel bar or steel section, wherein the concrete elastic unit 1 and the concrete creep unit 2 are first connected in series, and then the series-connected concrete elastic unit 1 and concrete creep unit 2 are connected in parallel with the elastic unit 4 of the steel bar or steel section.
[0039] In step S2, the stiffness information includes the stiffness parameter k provided by the concrete β and the stiffness parameter provided by the steel bar, k γ , 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] Where, 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.
[0043] In step S3, the constitutive equation includes:
[0044]
[0045] 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.
[0046] The constitutive equation is constructed using the following steps:
[0047] Step S31: The constitutive relationship of the series system composed of the concrete elastic unit 1 and the concrete creep unit 2 is expressed as:
[0048]
[0049] Where σ U , ε U represent the total stress and strain of concrete elastic element 1 and concrete creep element 2 respectively;
[0050] In step S32, the constitutive relation of the elastic element 4 of the steel bar or section steel is expressed as:
[0051] σ L (t) = k γ ε L (t) (5)
[0052] Where σ L , ε L represents the total stress and strain of the elastic element 4 of the steel bar or steel section respectively;
[0053] 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 USubstitute into formula (5) and then into formula (4) to obtain the constitutive equation of the axial time-varying deformation model of reinforced concrete components:
[0054]
[0055] 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.
[0056] Step S4 specifically includes:
[0057] 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:
[0058]
[0059] After sorting, we get:
[0060]
[0061] Where, 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.
[0062] The above formula (8) is an implicit expression in the Laplace space. It is mathematically impossible to express it explicitly in the time domain. Therefore, it is necessary to use a numerical method to solve formula (8). The high-precision numerical integration method is used to perform the Laplace inverse transformation:
[0063]
[0064] Where, represents the Laplace transform operator;
[0065] Assume that the strain and time relationship of concrete shrinkage unit 3 is ε th (t), the strain of the component 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 Assume as the elasticity provided by concrete and steel bars respectively. In reinforced concrete members, it can be simplified as:
[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 greatly affect its creep deformation and elastic deformation, the two parameters (C α ,α)Multiple regression analysis is conducted on the influence of concrete strength and age:
[0071]
[0072] Where t0 is the time from load loading to 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.
[0073] The intelligent method for calculating the axial time-varying deformation parameters of RC components provided by the embodiment of the present invention is verified as follows:
[0074] The creep test results of concrete components with different reinforcements made in the existing literature were used for verification. For the creep test of two groups of components with different reinforcements, the experimental results of one component were used as the fitting sample. The present invention used the small reinforced component as the sample to fit the relevant parameters in the model. The corresponding k in the model was changed by the longitudinal reinforcement ratio of the component cross section. β , k γ Two parameters, and keep the other parameters unchanged (C α , α), calculate the strain response of the other components. Component information and fitting parameter results are shown in 0, and the fitting and calculation results are shown in Figure 2 As shown, Figure 2 The time-strain response of components with small and medium reinforcement ratios is the fitting result, while the strain of components with large reinforcement ratios is calculated. It can be seen that both the fitting results and the calculated results are in good agreement with the experimental results. Therefore, it can be concluded that it is reasonable to consider the influence of component reinforcement on creep through this method.
[0075] Table 1 Verification component information and fitting results
[0076]
[0077] Note: All values in the literature are converted into strain response J(t) under unit stress.
[0078] The strength and age of concrete greatly affect its creep deformation and elastic deformation;
[0079] Therefore, the present invention utilizes existing specifications and theoretical models to conduct a quantitative analysis of the proposed model parameters considering two basic properties of concrete, and obtains the general variation law of the parameters with concrete strength and age and the corresponding empirical formula.
[0080] In order to consider the coupling effect of different concrete strength and different ages on creep, the two parameters (C α ,α) is affected by the strength and age of concrete, and a multiple regression analysis is performed, as shown in formula (14). The fitting results are as follows: Figure 3 As shown, the regression formula is shown in 0.
[0081]
[0082] Where k β It represents the stiffness provided by the elastic modulus of concrete; t0 is the time from the load loading time to the concrete pouring point (aging time); 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.
[0083] Table 2 Regression formula
[0084]
[0085] The calculation results are in good agreement with those obtained from the specification and model calculations (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 as the age of concrete increases, 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, during which 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 simpler and more convenient for engineering use. The parameter C αOn the whole, it increases with the increase of concrete strength and age, which is reflected in the decrease of creep flexibility with the increase of concrete strength and age, but different standards 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 construction unit, a parameter acquisition unit, a constitutive equation construction unit and a creep flexibility expression construction 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 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.
[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 embodiment of the intelligent method for calculating the axial time-varying deformation parameters of an RC member is implemented, and the same technical effects can be achieved. To avoid repetition, they are not described here.
[0092] It should be noted that the first electronic device in the embodiment of the present invention includes the mobile electronic device and the non-mobile electronic device mentioned above.
[0093] Figure 5 The present invention is a hardware structure diagram of an electronic device.
[0094] The electronic device 700 includes but is not limited to components such as 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 .
[0095] Those skilled in the art will understand that the electronic device 700 may also include a power source (such as a battery) to power each component, and the power source may be logically connected to the processor 710 through a power management system, thereby implementing functions such as charging, discharging, and power consumption management through the power management system. Figure 5 The electronic device structure shown in the figure 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 arrange the components differently, which will not be repeated here.
[0096] It should be understood that in embodiments of the present invention, the input unit 704 may include a graphics processing unit (GPU) 7041 and a microphone 7042. The graphics processor 7041 processes image data of still images or videos obtained by an image capture device (such as a camera) in video capture mode or image capture mode. The display unit 706 may include a display panel 7061, which may be configured in the form of a liquid crystal display, an organic light-emitting diode, or the like. 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. Other input devices 7072 may include, but are not limited to, a physical keyboard, function keys (such as volume control keys, power keys, etc.), a trackball, a mouse, and a joystick, which will not be described in detail here. The memory 709 may be used to store software programs and various data, including, but not limited to, applications and operating systems. The processor 710 may integrate an application processor and a modem processor, wherein the application processor mainly processes the operating system, user interface, and applications, and the modem processor mainly processes wireless communications. It is understandable that the above-mentioned modem processor may not be integrated into the processor 710.
[0097] An embodiment of the present invention further provides a readable storage medium having a program or instruction stored thereon. When the program or instruction is executed by a processor, the various processes of the embodiment of the intelligent method for calculating the axial time-varying deformation parameters of an RC member described above are implemented, and the same technical effects can be achieved. To avoid repetition, these processes are not described here.
[0098] 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), random access memory (RAM), a magnetic disk, or an optical disk.
[0099] An embodiment of the present invention further provides a chip including a processor and a communication interface, wherein the communication interface is coupled to the processor, and the processor is configured to execute a program or instruction to implement the various processes of the embodiment of the intelligent method for calculating the axial time-varying deformation parameters of an RC member, thereby achieving the same technical effects. To avoid repetition, these processes are not further described herein.
[0100] It should be understood that the chip mentioned in the embodiment of the present invention can also be called a system-on-chip, a system-on-chip, a chip system, or a system-on-chip chip, etc.
[0101] It should be noted that, in this document, the terms "comprises," "includes," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a process, method, article, or apparatus comprising a series of elements includes not only those elements but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of other identical elements in the process, method, article, or apparatus comprising the element.
[0102] Furthermore, it should be noted that the scope of the methods and systems of the present invention is not limited to performing functions in the order shown or discussed, but may also include performing functions substantially simultaneously or in reverse order, depending on the functions involved. For example, the methods described may be performed in an order different from that described, and various steps may be added, omitted, or combined. Furthermore, features described with reference to certain examples may be combined in other examples.
[0103] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the present invention and the claims, all of which are protected by the present invention.
Claims
1. An intelligent method for calculating the axial time-varying deformation parameters of RC components, characterized by: The following steps are involved: Step S1: constructing an axial time-varying deformation model of reinforced concrete components based on fractional derivatives. The axial time-varying deformation model of reinforced concrete components adopts an improved Fractional-Zener model, which is composed of an improved fractional-calculus Zener model connected in series with a concrete shrinkage unit. 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. 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. 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: Based on the stiffness information, a constitutive equation of the axial time-varying deformation model of the reinforced concrete component is constructed. The constitutive equation includes: (3) Where, represents the total stress; represents the total strain; 、 is the coefficient, and ; is the stress with respect to time Reciprocal of order; For the adaptation of time Reciprocal of order; Provide stiffness parameters for concrete; Stiffness parameters provided for reinforcement; Step S4: 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.
2. The method according to claim 1, characterized in that In step S2, the stiffness information includes the stiffness parameters provided by the concrete and the stiffness parameters provided by the steel bars , which is expressed by the following formula: (1) (2) Where, Indicates the reinforcement ratio of reinforced concrete components; represents the elastic modulus of the steel bar; Represents the elastic modulus of concrete.
3. The method according to claim 2, characterized in that The constitutive equation is constructed using the following steps: Step S31: The constitutive relationship of the series system composed of the concrete elastic unit and the concrete creep unit is expressed as: (4) Where, 、 represent the total stress and strain of concrete elastic element and concrete creep element respectively; In step S32, the constitutive relation of the elastic element of the steel bar or steel section is expressed as: (5) Where, 、 represents the total stress and strain of the elastic element of the steel bar or steel section respectively; Step S33, due to and ,Will and 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: (6) Where, represents the total stress; represents the total strain; They can be considered as the elasticity provided by concrete and steel bars respectively; 、 is the coefficient, and ; is the stress with respect to time Reciprocal of order; For the adaptation of time Reciprocal of order.
4. The method according to claim 3, characterized in that Step S4 specifically includes: make , find the creep flexibility function of the axial time-varying deformation model of reinforced concrete components Will Substitute into formula (6) and perform Laplace transformation on the whole to obtain: (7) After sorting, we get: (8) Where, represent That is, the mapping function of the creep flexibility corresponding to the model in the Laplace space, Indicates that time is transformed by Laplace transform The coefficients in the converted Laplace space.
5. The method according to claim 4, characterized in that Formula (8) is solved numerically, and the Laplace inverse transformation is performed using a high-precision numerical integration method: (9) Where, represents the Laplace transform operator; Assume that the relationship between the strain and time of the concrete shrinkage unit is , the strain of the component at any time point under the action of constant axial force can be calculated by the following formula: (10) Assume as the elasticity provided by concrete and steel bars respectively. In reinforced concrete members, it can be simplified as: (11) (12) Since the strength and age of concrete will affect its creep deformation and elastic deformation, the two parameters Multiple regression analysis was conducted under the influence of concrete strength and age: (13) Where, The time from load application time to concrete pouring point; is the concrete strength; For Parameters to be fitted as parameters.
6. A device for calculating the axial time-varying deformation parameters of a RC member for implementing the method according to any one of claims 1 to 5, 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 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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