RC component time-varying deformation intelligent calculation method considering corridor rigidity
Through an intelligent calculation method based on fractional calculus, an axial time-change deformation model of reinforced concrete components is constructed, and the corridor stiffness is considered, which solves the problem of difficulty in accurately predicting the axial time-change deformation of reinforced concrete components in the prior art, and achieves more efficient and accurate time-change deformation calculation.
Patent Information
- Application Number
- CN202510218126.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-02-26
- Publication Date
- 2025-05-27
- Estimated Expiration
- 2045-02-26
AI Technical Summary
Existing concrete time-varying models are difficult to accurately predict the axial time-varying deformation of reinforced concrete components, especially when taking into account the rigidity of the corridor.
The intelligent calculation method based on fractional calculus is adopted to construct the axial time-changing deformation model of reinforced concrete components, and consider the corridor stiffness, and the total strain of the vertical components is calculated through technical means such as fractional Zener model and Laplace transformation.
The shear stiffness provided by horizontal connecting members is realized when calculating axial deformation, and the accuracy and efficiency of deformation calculations in concrete are improved.
Smart Images

Figure CN120046366A_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 calculation method for time-varying deformation of RC components considering the stiffness of connecting corridors. Background Technique
[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 test components and actual concrete components in engineering, the predicted results often differ greatly from the measured strains and cannot be directly used to guide construction and design.
[0003] Common calculation models and codes for concrete time-varying characteristics and shrinkage creep include the MC 2010 model, the ACI209R92 model, the B3 model, and the GL2000 model. 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 concrete and steel bars are coupled. Moreover, the horizontal connecting components between reinforced concrete components also have a certain influence on their deformation.
[0004] Therefore, it is necessary to establish a corresponding axial time-varying model for reinforced concrete components and consider the stiffness of the connecting corridor to calculate the time-varying development of the vertical components under axial compression. Summary of the Invention
[0005] The purpose of the embodiment of the present invention is to provide an intelligent calculation method for time-varying deformation of RC components considering the stiffness of the connecting corridor, which combines the basic theory of fractional calculus and 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 as a whole, but also fully considers the time-varying deformation of reinforced concrete components in actual engineering, so as to solve at least one technical problem involved in the background technique.
[0006] In order to solve the above technical problems, the present invention is implemented as follows:
[0007] The present invention provides an intelligent calculation method for time-varying deformation of RC components considering the stiffness of the connecting corridor, including the following steps:
[0008] Step S1, constructing an axial time-varying deformation model of a reinforced concrete component based on fractional derivatives;
[0009] 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 according to different vertical member section information, and calculate the stiffness information in the axial time-varying deformation model of the reinforced concrete member;
[0010] Step S3: Calculate the stiffness of the corridor according to the corridor member information between the vertical members;
[0011] Step S4: Construct a fractional calculus constitutive equation set for the time-varying development process of axial compression of adjacent vertical members with corridor members;
[0012] Step S5: Perform Laplace transform on the constitutive equation set, and then perform MATLAB calculation to obtain the creep compliance expression of the axial time-varying deformation model of the reinforced concrete member;
[0013] Step S6: Calculate the total strain of the vertical member according to the creep compliance expression.
[0014] Optionally, in Step S1, the axial time-varying deformation model of the reinforced concrete member based on the fractional derivative adopts an improved fractional Zener model, which consists of an improved fractional calculus Zener model in series with a concrete shrinkage unit to form a vertical member model. Two identical vertical members are arranged side by side, and the two adjacent vertical members are connected by a corridor member composed of a shear spring to realize coupled deformation.
[0015] Optionally, the improved fractional calculus Zener model includes a concrete elastic unit, a concrete creep unit, and an elastic unit of steel bars or steel sections. Among them, the concrete elastic unit and the concrete creep unit are first connected in series, and then the connected concrete elastic unit and concrete creep unit are connected in parallel with the elastic unit of steel bars or steel sections.
[0016] Optionally, 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 steel bar, which is expressed by the following formula:
[0017] k β = E c (1 - ρ s ) (1)
[0018] k γ = E s ρ s (2)
[0019] In the formula, ρ s is the reinforcement ratio of the reinforced concrete member; E s is the elastic modulus of the steel bar; E c is the elastic modulus of the concrete.
[0020] Optionally, in step S3, the stiffness k of the corridor L is expressed by the following formula:
[0021] k L = 12EI / l 3 (3)
[0022] wherein, l represents the span of the corridor component; E represents the elastic modulus of the corridor component; I represents the moment of inertia of the corridor component.
[0023] Optionally, in step S4, the constitutive equations include:
[0024]
[0025] wherein, σ 1 (t), σ 2 (t) respectively represent the total stresses of the vertical components 1 and 2 varying with time, and are specifically valued according to the measurement by the stress sensor or according to the design purpose; ε 1 (t), ε 2 (t) respectively represent the total strains of the vertical components 1 and 2 varying with time; C α1 , C α2 , α1, α2 are coefficients, and α ∈ (0, 1); is the α-order derivative of stress with respect to time; is the α-order derivative of strain with respect to time; H represents the height of the vertical components 1 and 2; A 1 , A 2 respectively represent the cross-sectional areas of the vertical components 1 and 2; k β1 , k β2 respectively are the stiffness parameters provided by the concrete in the vertical components 1 and 2; k γ1 , k γ2 respectively are the stiffness parameters provided by the steel bars in the vertical components 1 and 2; △ε(t) is the axial strain difference between the vertical components 1 and 2, and △ε(t) = ε 1 (t) - ε 2 (t).
[0026] Optionally, step S5 specifically includes:
[0027] Performing Laplace transform on formula (4) and formula (5) and eliminating the differential operators therein, the following can be obtained:
[0028]
[0029] wherein, l1, l2 respectively represent the magnitudes of the upper axial stresses of the two vertical components 1 and 2; s represents the coefficient in the Laplace space obtained by converting the time t during Laplace transform; the creep compliance is an unknown variable;
[0030] Perform MATLAB calculations on Formula (6) and Formula (7) to obtain the specific expression of the creep flexibility .
[0031] Optionally, step S6 specifically includes:
[0032] Step S61, use the high-precision numerical integration method Talbot method to perform the inverse Laplace transform, and respectively obtain the creep flexibilities J 1 (t) and J 2 (t) of the two vertical members 1 and 2 in the time domain space:
[0033]
[0034] In the formula, represents the Laplace transform operator;
[0035] Step S62, calculate the total strains ε 1 (t) and ε 2 (t) of the vertical members 1 and 2 through the axial forces on the upper parts of the vertical members 1 and 2 and the shrinkage deformation of the members:
[0036] ε 1 (t) = σ 1 (t)J 1 (t) + ε sh1 (t) (10)
[0037] ε 2 (t) = σ 2 (t)J 2 (t) + ε sh2 (t) (11)
[0038] In the formula, ε sh1 (t) and ε sh2 (t) represent the shrinkage deformation of the members, which are calculated through test results or specification formulas.
[0039] 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, it executes the steps of the above method.
[0040] The present invention also provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, it implements the steps of the above method.
[0041] The present invention provides a computer program product, including a computer program. When the computer program is executed by a processor, it implements the steps of the above method.
[0042] The beneficial effects of the embodiments of the present invention are as follows:
[0043] 1. The present invention fully considers the relationship between the axial deformation of vertical members and horizontal connecting members, and can realize considering the shear stiffness provided by horizontal connecting members when calculating axial deformation.
[0044] 2. The present invention fully uses fractional derivatives to replace traditional multi-parameter calculation formulas to describe the time-varying deformation characteristics of members, greatly reducing the calculation parameters while endowing the members with more reasonable and intuitive physical properties; at the same time, according to the cross-section characteristics of the members, a calculation method for corresponding parameters is proposed, improving the calculation efficiency of the time-varying deformation of the members and also being more reasonably interpretable.
[0045] 3. The present invention directly solves the constitutive equation by using the Laplace transform and the numerical inverse Laplace transform method. This method has universality and can be applied to various other types of constitutive relations proposed, and the calculation process is clear.
[0046] 4. The axial time-varying deformation model of reinforced concrete members based on fractional derivatives in the present invention adopts an improved fractional-order Zener model, and connects the two adjacent vertical members through a connecting corridor member composed of a shear spring to realize coupled deformation, so as to reasonably calculate the time-varying deformation of the mutual coupling between structural members. BRIEF DESCRIPTION OF THE DRAWINGS
[0047] 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 following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained according to these drawings, where:
[0048] Figure 1 is a schematic diagram of the axial deformation model of adjacent vertical members considering the stiffness of the connecting corridor provided by the present invention;
[0049] Figure 2 is a calculation flow chart of the axial deformation model of adjacent vertical members considering the stiffness of the connecting corridor provided by the present invention;
[0050] Figure 3 (a) - 3(f) are the influences of the coupling beam stiffness on the compression deformation of the members in the axial deformation model of adjacent vertical members considering the stiffness of the connecting corridor provided by the present invention under different parameter conditions;
[0051] Figure 4 is one of the schematic diagrams of the hardware structure of the electronic device provided by the present invention;
[0052] Figure 5 is the second schematic diagram of the hardware structure of the electronic device provided by the present invention. Specific embodiments
[0053] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying 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 based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.
[0054] The terms "first", "second", etc. in the specification and claims of the present invention are used to distinguish similar objects and not to describe a specific order or sequence. It should be understood that such data can be interchanged under appropriate circumstances so that the embodiments of the present invention can be implemented in an order different from those illustrated or described herein, and the objects distinguished by "first", "second", etc. are generally of the same category, and the number of objects is not limited. For example, the first object can be one or multiple. In addition, "and / or" in the specification 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.
[0055] The embodiments of the present invention provide an intelligent calculation method for the time-varying deformation of RC members considering the stiffness of the link corridor, including the following steps:
[0056] Step S1, construct an axial time-varying deformation model of reinforced concrete members based on fractional derivatives;
[0057] Step S2, obtain the reinforcement ratio, elastic modulus of steel bars, and elastic modulus of concrete of the reinforced concrete members according to the cross-sectional information of different vertical members, and calculate the stiffness information in the axial time-varying deformation model of the reinforced concrete members;
[0058] Step S3, calculate the stiffness of the link corridor according to the link corridor member information between the vertical members;
[0059] Step S4, construct a fractional calculus constitutive equation set for the time-varying development process of the adjacent vertical members with link corridor members under axial compression;
[0060] Step S5, perform Laplace transform on the constitutive equation set and then perform MATLAB calculation to obtain the creep compliance expression of the axial time-varying deformation model of the reinforced concrete members;
[0061] Step S6, calculate the total strain of the vertical members according to the creep compliance expression.
[0062] In step S1, please refer to Figure 1As shown in the figure, the axial time-varying deformation model of reinforced concrete members based on fractional derivatives adopts an improved fractional Zener model, which consists of an improved fractional calculus Zener model in series with a concrete shrinkage unit to form a vertical member model. Two identical vertical members are arranged side by side, and the adjacent vertical members are connected by a corridor member composed of a shear spring to achieve coupled deformation.
[0063] The improved fractional calculus Zener model includes a concrete elastic unit, a concrete creep unit, and an elastic unit of steel bars or steel sections. Among them, the concrete elastic unit and the concrete creep unit are first connected in series, and then the connected concrete elastic unit and concrete creep unit are connected in parallel with the elastic unit of steel bars or steel sections.
[0064] In step S2, the stiffness information includes the stiffness parameter k provided by the concrete β and the stiffness parameter k provided by the steel bars, γ which is expressed by the following formula:
[0065] k β = E c (1 - ρ s ) (1)
[0066] k γ = E s ρ s (2)
[0067] In the formula, ρ s is the reinforcement ratio of the reinforced concrete member; E s is the elastic modulus of the steel bars; E c is the elastic modulus of the concrete;
[0068] In step S3, the stiffness k L of the corridor is expressed by the following formula:
[0069] k L = 12EI / l 3 (3)
[0070] In the formula, l represents the span of the corridor member; E represents the elastic modulus of the corridor member; I represents the moment of inertia of the corridor member.
[0071] In step S4, in the building structure, the vertical members are usually connected by coupling beams. The force of a group of column-beam-wall substructures is often coupled to a certain extent. However, the existing concrete creep formulas are all from the experimental results under the axial force of a single concrete member. Therefore, by simplifying the force-bearing process of a group of adjacent vertical members and their coupling beams, the proposed constitutive model can be used to establish a fractional calculus constitutive equation set for the creep development process of adjacent vertical members under axial compression considering the stiffness of the corridor.
[0072] The span between adjacent vertical members may be small (especially when the spacing between shear walls is small), the cross-sectional dimension of the coupling beam is large, and the influence of the coupling beam can no longer be directly ignored. Based on the fractional calculus constitutive model, a group of adjacent vertical members are connected by a spring in the vertical direction, where the spring stiffness is the shear stiffness of the coupling beam and can be obtained by simple structural mechanics or finite element calculation, such as Figure 1 shown.
[0073] For simplicity in calculation, the influence of shrinkage is not considered for the time being. The constitutive models of the left and right vertical members are the same. When considering the coupling beam, it is assumed that the axial compression deformation of the right vertical member is greater than that of the left. Their respective constitutive equations are as follows:
[0074]
[0075] In the formula, σ 1 (t), σ 2 (t) respectively represent the total stresses of vertical members 1 and 2 varying with time, which can be specifically determined according to the measurement of stress sensors or according to the design purpose; ε 1 (t), ε 2 (t) respectively represent the total strains of vertical members 1 and 2 varying with time; C α1 , C α2 , α1, α2 are coefficients, and α ∈ (0, 1); is the α-order derivative of stress with respect to time; is the α-order derivative of strain with respect to time; H represents the heights of vertical members 1 and 2; A 1 , A 2 respectively represent the cross-sectional areas of vertical members 1 and 2; k β1 , k β2 respectively are the stiffness parameters provided by the concrete in vertical members 1 and 2; k γ1 , k γ2 respectively are the stiffness parameters provided by the steel bars in vertical members 1 and 2; △ε(t) is the axial strain difference between vertical members 1 and 2, and △ε(t) = ε 1 (t) - ε 2 (r).
[0076] The calculation flow chart is as Figure 2 shown. To quantitatively analyze the influence of the coupling beam on adjacent vertical members, the results of changing individual influence parameters are calculated through equations (4) and (5) for parameter analysis. The specific parameter values are shown in Table 1, and the corresponding results are as Figure 3 shown. The dotted and solid lines in the figure respectively represent the results without considering and considering the influence of the coupling beam. It is not difficult to find that when the span between the two vertical members is 5m, due to the small stiffness provided by the coupling beam, the creep development process of each is less affected by the coupling beam, and there is no obvious difference whether the coupling beam is considered or not. As the span gradually decreases(Figure 3 ((a)-(c)), the stiffness provided by the coupling beam gradually increases. The creep development of the vertical component is affected by the creep of the other component, making the creep development of the two components tend to be the same. When the cross-sectional areas of the two components are the same, the tendency of the creep of the vertical component to approach the creep of the other component is equal. When the cross-sectional areas of the components are different ( Figure 3 ((d)-(f)), it is obvious that the component with a smaller cross-sectional area has a greater tendency to approach the other component.
[0077] Table 1 Calculation parameter values
[0078]
[0079] Step S5 specifically includes:
[0080] Performing Laplace transforms on formulas (4) and (5) and eliminating the differential operators therein, we can obtain:
[0081]
[0082] In the formula, l1 and l2 respectively represent the magnitudes of the upper axial stresses of the two vertical components 1 and 2; s represents the coefficient in the Laplace space obtained by converting the time t during Laplace transform; the creep compliance is an unknown variable;
[0083] Performing MATLAB calculations on formulas (6) and (7) to obtain the specific expression of the creep compliance .
[0084] Step S6 specifically includes:
[0085] Step S61, using the high-precision numerical integration method Talbot method to perform inverse Laplace transformation, and respectively obtaining the creep compliances J 1 (t) and J 2 (t) of the two vertical components 1 and 2 in the time domain space:
[0086]
[0087] In the formula, represents the Laplace transform operator;
[0088] Step S62, calculating and obtaining the total strains ε 1 (t) and ε 2 (t) of the vertical components 1 and 2 through the upper axial forces and the shrinkage deformations of the components:
[0089] ε 1 (t) = σ 1 (t)J 1 (t) + ε sh1(t) (10)
[0090] ε 2 (t) = σ 2 (t)J 2 (t) + ε sh2 (t) (11)
[0091] Wherein, ε sh1 (t), ε sh2 (t) represents the shrinkage deformation of the component, which is calculated through test results or specification formulas. For example, the specification calculation formula of ACI209R-92:
[0092]
[0093] Where ε shu = 780γ sh , γ sh = γ sh,ts ·γ sh,RH ·γ sh,vs ·γ sh,s ·γ sh,ψ ·γ sh,c ·γ sh,α , the curing specimen adjustment coefficient γ sh,ts = 1.202 - 0.2337log(t s ); γ sh,RH is the environmental humidity adjustment coefficient. When the environmental humidity is between 0.4 and 0.8, γ sh,RH = 1.4 - 1.02RH. When it is between 0.8 and 1, γ sh,RH = 3 - 3RH; Compared with creep, shrinkage has an additional cement content adjustment coefficient γ sh,c = 0.75 + 0.00061c, where c is the cement content; f c is the concrete strength; t c is the time point when the component starts to be exposed to the air.
[0094] As Figure 4 shown, an embodiment of the present invention also provides an electronic device 600. The electronic device 600 includes a processor 601, a memory 602, a program or instruction stored on the memory 602 and executable on the processor 601. When the program or instruction is executed by the processor 601, it realizes each process of the above-mentioned intelligent calculation method for the time-varying deformation of RC components considering the stiffness of the connecting corridor, and can achieve the same technical effects. To avoid repetition, it will not be elaborated here.
[0095] It should be noted that the first electronic device in the embodiment of the present invention includes the above-mentioned mobile electronic device and non-mobile electronic device.
[0096] Figure 5Schematic diagram of the hardware structure of an electronic device according to an embodiment of the present invention.
[0097] 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.
[0098] 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 implement 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 does not limit the electronic device. The electronic device may include more or fewer components than shown, or combine certain components, or have different component arrangements, which will not be elaborated here.
[0099] It should be understood that in the embodiment 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 static 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, and 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 and demodulation processor. Among them, the application processor mainly processes the operating system, user interface, and application programs, and the modulation and demodulation processor mainly processes wireless communication. It can be understood that the above modulation and demodulation processor may not be integrated into the processor 710.
[0100] The embodiment of the present invention also 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 calculation method for time-varying deformation of RC members considering the stiffness of the link corridor, and can achieve the same technical effect. To avoid repetition, it will not be elaborated here.
[0101] Among them, the processor is the processor in the electronic device described in the above embodiments. The readable storage medium includes computer-readable storage media such as computer read-only memory (ROM), random access memory (RAM), magnetic disks, or optical discs.
[0102] 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 programs or instructions to implement each process of the above-mentioned intelligent calculation method for the time-varying deformation of RC members considering the stiffness of the corridor, and can achieve the same technical effects. To avoid repetition, it will not be elaborated here.
[0103] It should be understood that the chip mentioned in the embodiments of the present invention may also be referred to as a system-on-chip, system chip, chip system, or system-on-chip.
[0104] 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 further limitations, an element defined by the statement "including a..." does not exclude the existence of additional identical elements in the process, method, article or device including the element.
[0105] In addition, it should be pointed out that the scope of the methods and systems in the embodiments 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 the reverse order according to the functions involved. For example, the described methods may be performed in an order different from that described, and various steps may be added, omitted, or combined. Additionally, the features described with reference to certain examples may be combined in other examples.
[0106] 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 and scope protected by the present invention and the claims, and all of them belong to the protection scope of the present invention.
Claims
1. An intelligent calculation method for time-varying deformation of RC components considering corridor stiffness, 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 according to the cross-sectional information of different vertical components, and calculating the stiffness information in the axial time-varying deformation model of the reinforced concrete component; Step S3, calculating the corridor stiffness according to the corridor component information between the vertical components; Step S4, constructing a fractional-order calculus constitutive equation group for the time-varying development process of axial compression of adjacent vertical components with corridor components; Step S5, performing Laplace transformation on the constitutive equations, and then performing MATLAB calculation to obtain the creep flexibility expression of the axial time-varying deformation model of the reinforced concrete member; Step S6, calculating the total strain of the vertical component according to the creep flexibility expression.
2. The method according to claim 1, characterized in that In step S1, the axial time-varying deformation model of reinforced concrete components based on fractional derivatives adopts an improved fractional Zener model, which is composed of an improved fractional calculus Zener model connected in series with a concrete shrinkage unit to form a vertical component model. Two identical vertical components are arranged side by side, and the two adjacent vertical components are connected by a corridor component composed of a shear spring to achieve coupled deformation.
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 is the reinforcement ratio of reinforced concrete components; E s is the elastic modulus of the steel bar; E c is the elastic modulus of concrete.
5. The method according to claim 4, characterized in that In step S3, the corridor stiffness k L It is expressed by the following formula: k L =12EI / l 3 (3) Where l represents the span of the corridor component; E represents the elastic modulus of the corridor component; I represents the moment of inertia of the corridor component.
6. The method according to claim 5, characterized in that In step S4, the constitutive equations include: Wherein, σ1(t) and σ2(t) represent the total stress of vertical components 1 and 2 respectively, which can be measured by stress sensors or determined according to the design purpose; ε1(t) and ε2(t) represent the total strain of vertical components 1 and 2 respectively; C α1 , C α2 , α1, α2 are coefficients, and α∈(0,1); is the α-order inverse of stress with respect to time; is the α-order inverse of strain with respect to time; H represents the height of vertical members 1 and 2; A1 and A2 represent the cross-sectional areas of vertical members 1 and 2, respectively; k β1 , k β2 are the stiffness parameters provided by the concrete in vertical members 1 and 2 respectively; k γ1 , k γ2 are the stiffness parameters provided by the steel bars in vertical components 1 and 2 respectively; △ε(t) is the axial strain difference between vertical components 1 and 2, △ε(t) = ε1(t) - ε2(t).
7. The method according to claim 6, characterized in that Step S5 specifically includes: By performing Laplace transform on formula (4) and formula (5) and eliminating the differential operator, we can obtain: Where l1 and l2 represent the upper axial stress of the two vertical components 1 and 2 respectively; s represents the coefficient in Laplace space converted from time t by Laplace transformation; creep flexibility is is an unknown variable; Calculate formula (6) and formula (7) using MATLAB to obtain creep flexibility The specific expression of .
8. The method according to claim 7, characterized in that Step S6 specifically includes: Step S61, using the high-precision numerical integration method Talbot method to perform Laplace inverse transformation, respectively obtain the creep flexibility J1(t) and J2(t) of the two vertical components 1 and 2 in the time domain space: In the formula, represents the Laplace transform operator; Step S62, the total strains ε1(t) and ε2(t) of the vertical components 1 and 2 are calculated by the upper axial forces of the vertical components 1 and 2 and the shrinkage deformation of the components: ε1(t)=σ1(t)J1(t)+ε sh1 (t) (10)ε2(t)=σ2(t)J2(t)+ε sh2 (t) (11) In the formula, ε sh1 (t), ε sh2 (t) represents the shrinkage deformation of the component, which is calculated through test results or standard formulas.
Citation Information
Patent Citations
Concrete creep strain calculation method
CN106650098A
Concrete fractional order creep model
CN106919786A
Concrete shrinkage stress calculation method considering steel bar containment effect
CN115758765A
Large-span corridor vibration comfort calculation model determination method
CN116975970A
Modeling method of prestressed concrete structure composite material model considering non-prestressed tendon effect
CN117540602A