Method, device and storage medium for calculating concrete shrinkage and creep in bridge structure

Abstract

The application discloses a kind of bridge structure in concrete shrinkage and creep calculation method, equipment and storage medium, the method includes using initial strain method to calculate stress increment and creep strain increment in different period, and then calculate stress and creep strain at different time;According to the stress increment of different period, stress-strain relationship and creep coefficient fitting function calculation period Δt n+1 Internal concrete creep caused by unit equivalent node load increment;According to concrete shrinkage strain increment calculation period Δt n+1 Internal concrete shrinkage caused by unit equivalent node load increment.The application can accurately calculate the shrinkage and creep effect of concrete in the structure when applied to bridge structure analysis, greatly improves the calculation efficiency and saves storage space.

Description

Technical Field

[0001] This invention relates to a method, equipment, and storage medium for calculating concrete shrinkage and creep in bridge structures. Background Technology

[0002] For bridges constructed using segmental construction, the finite element method is generally used for structural calculation and analysis. The shrinkage and creep effects of concrete significantly influence the internal forces and deformations of the structure, making them a crucial factor that cannot be ignored in structural analysis and also presents a challenge in the calculations.

[0003] The shrinkage and creep of concrete are related not only to the stress at the time of application but also to the entire stress history. Concrete elements are considered in stages within the overall structure, and the loading ages of each element differ, making the calculation of concrete shrinkage and creep more complex. Therefore, when using the finite element method to analyze shrinkage and creep problems, time can be divided into a series of periods. In each period, the strain increment is calculated based on the stress at that time, the stress history, and the shrinkage and creep law, thus obtaining the load increment. For example, the calculation method for shrinkage and creep and prestress loss in concrete bridges (Authorization Announcement No. CN102323976B).

[0004] When calculating large bridge structures, it is necessary to divide the data into numerous elements and set up multiple calculation cases. If the shrinkage and creep effects of each concrete element are considered in different time periods, it is necessary to store the internal force increments generated by shrinkage and creep in each element in each time period, which will seriously affect the solution efficiency of the model. Therefore, it is necessary to find a simple calculation method to improve the calculation speed of shrinkage and creep. Summary of the Invention

[0005] The purpose of this invention is to provide a method, equipment, and storage medium for calculating the shrinkage and creep of concrete in bridge structures, so as to solve the problems of complex calculation and low calculation efficiency of existing calculation methods.

[0006] This invention solves the above-mentioned technical problems through the following technical solution: a method for calculating concrete shrinkage and creep in bridge structures, comprising the following steps:

[0007] The initial strain method is used to calculate the stress increment and creep strain increment at different time periods, and then the stress and creep strain at different times are calculated.

[0008] The time interval Δt is calculated based on the stress increment, stress-strain relationship, and creep coefficient fitting function at different time intervals. n+1 The formula for the increase in equivalent nodal load caused by internal concrete creep is as follows:

[0009]

[0010]

[0011]

[0012] in, To calculate age t n+1 The increase in equivalent nodal load of the element caused by creep; Record parameters for creep increment; Let time t n Creep end force increment; [B] represents the conversion relationship between strain and nodal displacement at any point within the element, {Δσ} n For the nth time period Δt n The stress increment, V is the element volume; C j τ represents the fitting parameters for the creep coefficient; n is the number of time periods; τ n Let time t n Loading age; q j The parameters for fitting the creep coefficient; t n For the initial age, t n+1 To calculate the age, Δt n+1 =t n+1 -t n ;

[0013] Calculate the time period Δt based on the concrete shrinkage strain increment. n+1 The formula for the equivalent nodal load increment caused by internal concrete shrinkage is as follows:

[0014]

[0015]

[0016] in, To calculate age t n+1 The element's equivalent nodal load increment caused by contraction; [D] is the elasticity matrix; ε sh (∞) represents the ultimate value of the contraction strain; p represents the rate of change of the contraction strain; and τ0 represents the loading age at time τ0.

[0017] Furthermore, the specific implementation process of calculating the stress and creep strain at different times using the initial strain method is as follows:

[0018] Step 1.1: Divide time t into a series of time intervals Δt1, Δt2, ..., Δt n t=Δt1+Δt2+…+Δt j +…+Δt n , Δt j =t j -t j-1 ;

[0019] Step 1.2: Calculate the elastic stress {Δσ}1 at the beginning of the first time interval Δt1 based on the applied load and material constants at t = t0. Assuming the elastic stress {Δσ}1 remains constant during the first time interval Δt1, calculate the creep strain increment {Δε} at the end of the first time interval Δt1. c}1;

[0020] Step 1.3: At the beginning time t1 of the second time period Δt2, the creep strain increment {Δε} is used. c}1 is taken as the initial strain, and added to the current load increment, the stress increment {Δσ}2 is obtained by solving the elastic problem; assuming that the stress and material constants remain unchanged during the second time period Δt2, the creep strain increment {Δε} at the end of the second time period Δt2 is calculated. c}2;

[0021] Step 1.4: Repeat step 1.3 to calculate Δt for the j-th time period. j Start time t i-1 Stress increment {Δσ} j and the j-th time period Δt j The creep strain increment at the end {Δε c} j The stress increment and creep strain increment at different time periods were obtained;

[0022] Step 1.5: Accumulate the stress increments obtained in Step 1.4 to obtain the stress at different times; accumulate the creep strain increments obtained in Step 1.4 to obtain the creep strain at different times.

[0023] Furthermore, the time period Δt is calculated. n+1 The specific implementation process of the unit equivalent nodal load increment caused by internal concrete creep is as follows:

[0024] Step 2.1: Based on the stress-strain relationship and the i-th time interval Δt i Stress increment {Δσ} i Calculate time t i elastic strain {Δε e} i The specific formula is as follows:

[0025] {Δε e} i =[D] -1 {Δσ} i

[0026] Step 2.2: Based on time t i elastic strain {Δε e} i The creep coefficient is used to obtain the time interval Δt. n+1 Creep strain generated internally {Δε c}i The specific formula is as follows:

[0027]

[0028]

[0029] in, For loading age τ i The age is calculated as t. n+1 The creep coefficient, For loading age τ i The starting age is t n The creep coefficient;

[0030] Step 2.3: Based on the creep strain {Δε c} i Calculation time period Δt n+1 creep strain increment within The specific formula is as follows:

[0031]

[0032] Step 2.4: Increment the creep strain As the initial strain, the equivalent nodal load increment is calculated, and the equivalent nodal load increment is applied over the time period Δt. n+1 Finally, calculate the time period Δt. n+1 Equivalent nodal load increment caused by internal concrete creep The specific formula is as follows:

[0033]

[0034] Step 2.5: Based on the creep coefficient fitting function and the element equivalent nodal load increment from Step 2.4. The formula yields the final time period Δt. n+1 The increase in equivalent nodal load caused by internal concrete creep.

[0035] Furthermore, the expression for the creep coefficient fitting function is:

[0036]

[0037] in, Calculate the creep coefficient for a loading age of τ and an age of t. This is the nominal creep coefficient.

[0038] Furthermore, the time period Δt is calculated. n+1 The specific implementation process of the unit equivalent nodal load increment caused by internal concrete shrinkage is as follows:

[0039] Step 3.1: Fit the concrete shrinkage strain into a single-phase exponential function, specifically:

[0040] ε sh (t)=ε sh (∞)(1-e -pt )

[0041] Where, ε sh (t) represents the contraction strain at time t; p represents the rate of change of the contraction strain; ε sh (∞) represents the ultimate value of contractile strain;

[0042] Step 3.2: Calculate Δt based on the single-phase exponential function. n+1 The increase in concrete shrinkage strain at any point within the unit during the time period for:

[0043]

[0044] Step 3.3: Based on the concrete shrinkage strain increment Calculation time period Δt n+1 The increase in unit equivalent nodal load caused by internal concrete shrinkage.

[0045] Based on the same inventive concept, the present invention also provides an electronic device, including a memory and a processor, wherein the memory stores a computer program capable of running on the processor, and the processor executes the steps of the method for calculating concrete shrinkage and creep in bridge structures as described above when running the computer program.

[0046] Based on the same inventive concept, the present invention also provides a computer-readable storage medium, which is a non-volatile storage medium or a non-transient storage medium, on which a computer program is stored, and the computer program is executed by a processor to perform the steps of the concrete shrinkage and creep calculation method in the bridge structure as described above.

[0047] Beneficial effects

[0048] Compared with the prior art, the advantages of the present invention are as follows:

[0049] The present invention provides a method for calculating concrete shrinkage and creep in bridge structures. It establishes a finite element calculation formula for shrinkage and creep using the initial strain method, fits an exponential function to the shrinkage and creep calculation expression in bridge specifications, and then simplifies and recursively derives the equivalent nodal load increment expression for creep. To improve the calculation speed of the program; when applied to bridge structure analysis, this invention can accurately calculate the shrinkage and creep effect of concrete in the structure, which greatly improves the calculation efficiency and saves storage space. Attached Figure Description

[0050] To more clearly illustrate the technical solution of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only one embodiment of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0051] Figure 1 This is a graph showing the relationship between stress increment and time period in an embodiment of the present invention. Detailed Implementation

[0052] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0053] The technical solutions of this application will be described in detail below with specific embodiments. The following specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments.

[0054] The present invention provides a method for calculating concrete shrinkage and creep in bridge structures, comprising the following steps:

[0055] 1. The initial strain method is used to calculate the stress increment and creep strain increment at different time periods, and then the stress and creep strain at different times are calculated.

[0056] Due to the inherent complexity of structural deformation or secondary internal forces caused by concrete shrinkage and creep, the following assumptions are adopted in practical calculations:

[0057] (1) The creep strain and elastic strain of concrete at any time are linearly related;

[0058] (2) Both shrinkage strain and creep strain are small strains;

[0059] (3) Contraction strain and creep strain satisfy the Boltzmann superposition principle;

[0060] (4) The influence of steel components such as reinforcing bars and stiffening frames on the shrinkage and creep of concrete is not considered;

[0061] (5) The elastic modulus of concrete is constant, and the creep Poisson's ratio is equal to the instantaneous deformation Poisson's ratio.

[0062] The strain of an object is determined by elastic strain {ε} e} and creep strain {ε c Composition, elastic strain {ε e} is represented as:

[0063] {ε e}=[D] -1 {σ} (1)

[0064] Where [D] is the elasticity matrix and {σ} is the elastic stress.

[0065] Taking the creep strain as the initial strain {ε0}, the total strain {ε} can be expressed as:

[0066] {ε}=[D] -1 {σ}+{ε0} (2)

[0067] That is, the stress-strain relationship is:

[0068] {σ}=[D]({ε}-{ε0}) (3)

[0069] like Figure 1 As shown, the specific implementation process of calculating stress and strain using the initial strain method is as follows:

[0070] Step 1.1: Divide time t into a series of time intervals Δt1, Δt2, ..., Δt n t=Δt1+Δt2+…+Δt j +…+Δt n , Δt j =t j -t j-1 It is assumed that the changes in all loads (including temperature) and material constants occur only at the beginning of each time period and remain constant in the middle of each time period.

[0071] Step 1.2: Calculate the elastic stress {Δσ}1 at the beginning of the first time interval Δt1 based on the applied load and material constants at t = t0. Assuming the elastic stress {Δσ}1 remains constant during the first time interval Δt1, calculate the creep strain increment {Δε} at the end of the first time interval Δt1. c}1;

[0072] Step 1.3: At the beginning time t1 of the second time period Δt2, the creep strain increment {Δε} is used. c}1 is taken as the initial strain, and added to the current load increment, the stress increment {Δσ}2 is obtained by solving the elastic problem; assuming that the stress and material constants remain unchanged during the second time period Δt2, the creep strain increment {Δε} at the end of the second time period Δt2 is calculated. c}2;

[0073] Step 1.4: Repeat step 1.3 to calculate Δt for the j-th time period. j Start time t i-1 Stress increment {Δσ} j and the j-th time period Δtj The creep strain increment at the end {Δε c} j The stress increment and creep strain increment at different time periods were obtained;

[0074] Step 1.5: Apply the stress increment {Δσ} obtained in Step 1.4 j By summing the results, we obtain the stress {σ} = ∑ at different times. j {Δσ} j The creep strain increment {Δε} obtained in step 1.4 c} j By summing the data, we obtain the creep strain {ε} at different times. c}=∑ j {Δε c} j .

[0075] The shorter the time step, the higher the computational accuracy; a sufficiently short time step is sufficient to meet the computational accuracy requirements.

[0076] 2. Calculate the time period Δt n+1 Equivalent nodal load increment caused by internal concrete creep

[0077] like Figure 1 As shown, the time axis is divided into t0, t1, ..., t n t n+1 At times such as ..., the corresponding stress increments are Δσ1, Δσ2, ..., Δσ n ... At time t n The stress at any point within the element is Reflects at time t n Previous stress history.

[0078] Let time t i The instantaneous elastic strain is {Δε e} i , τ i For the loading age, t n t n+1 These represent the initial age and the calculated age, respectively, Δt. n+1 =t n+1 -t n According to equation (1), we have: {Δε e} i =[D] -1 {Δσ} i ;

[0079] Time period Δt n+1 The increment of the internal creep coefficient is in For loading age τ i The age is calculated as t.n+1 The creep coefficient, For loading age τ i The starting age is t n The creep coefficient is:

[0080] Consider {Δε e} i During the time period Δt n+1 Creep strain generated internally {Δε c} i for:

[0081]

[0082] In Δt n+1 During the time period, based on the creep coefficient The creep strain increment can be obtained as:

[0083]

[0084] Will As the initial strain, the corresponding equivalent nodal load increment is calculated, and the equivalent nodal load increment is applied over the time period Δt. n+1 Finally, the equivalent nodal load increment of the element caused by concrete creep. for:

[0085]

[0086] Where [B] represents the conversion relationship between strain and nodal displacement at any point within the element, V is the element volume, dV = dxdydz, which means integrating along the length (x), width (y), and height (z) of the element, with the integration range being the element volume. An element refers to a component in a finite element model of a bridge structure. A planar beam element is composed of end nodes and connecting end nodes. The loads within the element are equivalently applied to the nodes, which are called the equivalent nodal loads of the element.

[0087] And because of time t i The stress increment is:

[0088] {Δσ} i =[D]({Δε} i -{Δε0} i (7)

[0089] Where, {Δε} i Let time t i The strain increment, {Δε0} i This refers to the strain increment that is independent of stress (e.g., temperature changes, concrete shrinkage and creep, manufacturing errors, etc.).

[0090] And there are: in At time t i The nodal displacement increment of element e.

[0091] Therefore, we can conclude that:

[0092]

[0093]

[0094] Where, {ΔF} i Let time t i The increment of the rod end force generated by the increment of nodal displacement in element e; Let time t i Unit e is composed of {Δε0} i The increase in fixed-end force (i.e., the increase in fixed-end force caused by factors such as temperature changes, concrete shrinkage and creep, and manufacturing errors); [k] e =∫∫∫[B] T [D][B]dV.

[0095] Substituting equation (8) into equation (6), we can obtain the equivalent nodal load increment of the element caused by creep. for:

[0096]

[0097] in, Let time t i The increment of the element end force, which does not include the increment of the fixed end force caused by non-nodal loads, but only the increment of the end force caused by the creep equivalent nodal load increment (i.e. the equivalent nodal load increment caused by creep), is called the creep end force increment.

[0098] When calculating the creep equivalent nodal load increment of the element according to equation (9), it is necessary to store the history of the creep end internal forces of the element. (Each element needs to store the creep-induced increase in the internal force at the bar end at each calculation time). Therefore, when there are many calculation steps and a large number of elements, the amount of data that needs to be stored is enormous, which severely affects the calculation speed and limits the scale of the solved structure. If the creep coefficient... This problem can be solved by fitting an exponential function.

[0099] According to the definition of creep coefficient in the "Design Specification for Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts", the creep coefficient can be fitted to the following form:

[0100]

[0101] in, C is the nominal creep coefficient; i (τ), qi It is a function of the theoretical thickness of the cross section and relative humidity; q i ≥0, β a (τ)=0, C i (τ), q i These are all fitting coefficients for the creep coefficient, and their values ​​are shown in Table 1. R 2 These are the fitting parameters for the creep coefficient.

[0102] Table 1. Values ​​of Fitting Coefficients

[0103]

[0104]

[0105] Combining the fitting formula (10), we can further derive the creep equivalent nodal load increment of element e, and obtain:

[0106]

[0107] make Then we have:

[0108]

[0109] Assume that at the previous time t, n creep equivalent nodal load increment time Since we have already obtained the answer, we have:

[0110]

[0111] The derivation yields:

[0112]

[0113] Calculate the creep equivalent nodal load increment at time t1 At that time, it is necessary to use have:

[0114]

[0115] in, Δt0=0.

[0116] Due to β a (τ)=0, Equation (12) can be rewritten as:

[0117]

[0118] Based on the above method, calculate the creep equivalent nodal load increment of the calculation unit. At that time, it is only necessary to record the previous calculation time t. n Each unit This will give us the time of this calculation. No need to store every calculation time t i {W} of each unit i j This significantly improves the running speed of computer programs and saves storage space.

[0119] 3. Calculate the time period Δt n+1 Equivalent nodal load increment caused by internal concrete shrinkage

[0120] Based on the description of shrinkage strain in the standard, the shrinkage strain of concrete is fitted into a single exponential function:

[0121] ε sh (t)=ε sh (∞)(1-e -pt (17)

[0122] Where, ε sh (t) represents the contraction strain at time t; ε sh (∞) represents the ultimate value of the contraction strain; p represents the rate of change of the contraction strain.

[0123] The starting point for calculating concrete shrinkage differs for each unit. Let the hardening time of the concrete be τ0, then the time interval Δt... n+1 Increment of concrete shrinkage strain at any point within the inner unit for:

[0124]

[0125] The contraction strain of the beam element is consistent along the section height, and there is only axial strain. Therefore, the only equivalent nodal force caused by this strain is axial force. Thus, Δt n+1 Increase in equivalent nodal load of unit caused by concrete shrinkage during the time period for:

[0126]

[0127] Where EA is the compressive stiffness. Therefore, Δt n+1 Incremental vector of fixed-end forces generated by concrete shrinkage within a time period for:

[0128]

[0129] This invention, based on the fundamental laws governing the influence of concrete shrinkage and creep on structures, derives a formula for calculating the equivalent nodal load increment of beam elements caused by the shrinkage and creep effect. Combining the initial strain method, a finite element method formula for shrinkage and creep is established, and the calculation expression for shrinkage and creep in bridge specifications is fitted with an exponential function, thereby simplifying and recursively deriving the expression for the equivalent nodal load increment caused by creep. This invention can accurately simulate the concrete shrinkage and creep effect in bridge structures while significantly improving the computational efficiency of the finite element model.

[0130] The above description only discloses specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or modifications that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for calculating concrete shrinkage and creep in bridge structures, characterized in that, Includes the following steps: The initial strain method is used to calculate the stress increment and creep strain increment at different time periods, and then the stress and creep strain at different times are calculated. The time period is calculated based on the stress increment, stress-strain relationship, and creep coefficient fitting function at different time periods. The formula for the increase in equivalent nodal load caused by internal concrete creep is as follows: in, To calculate age t n+1 At that time, the increase in the unit's equivalent nodal load caused by creep; Record parameters for creep increment; For the onset age t n The creep-induced internal force increment at the rod end; [B] represents the conversion relationship between strain and nodal displacement at any point within the element. For the first n Time period The stress increment within the element, where V is the element volume; Here are the fitting parameters for the creep coefficient; n is the number of time periods; For the onset age t n The corresponding loading age; The parameters for fitting the creep coefficient; t n t represents the starting age of the (n+1)th time period; n+1 The calculated age for the (n+1)th time period; ; Calculate the time period based on the concrete shrinkage strain increment. The formula for the equivalent nodal load increment caused by internal concrete shrinkage is as follows: in, To calculate age t n+1 At that time, the element's equivalent nodal load increment caused by contraction; [D] is the elasticity matrix; This represents the ultimate value of the contractile strain; p The rate of change of contractile strain; This refers to the loading age corresponding to the initial age t0; Among them, the calculation period The specific implementation process of the unit equivalent nodal load increment caused by internal concrete creep is as follows: Step 2.1: Based on the stress-strain relationship and the first i Time period Stress increment Calculation time elastic strain Let i = 1, 2, 3, ..., n, and the specific formula is: Step 2.2: Based on time elastic strain The creep coefficient is obtained during the time period Creep strain generated internally The specific formula is as follows: in, For loading age is The age is calculated as t. n+1 The creep coefficient, For loading age is The starting age is t n The creep coefficient; Step 2.3: Based on creep strain Calculation period creep strain increment within The specific formula is as follows: Step 2.4: Increment the creep strain As the initial strain, the equivalent nodal load increment is calculated, and the equivalent nodal load increment is applied over the time period. Finally, the calculation period Equivalent nodal load increment caused by internal concrete creep The specific formula is as follows: in, Let time t i The increase in internal force at the creep rod end; Step 2.5: Based on the creep coefficient fitting function and the element equivalent nodal load increment from Step 2.

4. The formula yields the final time period. The increase in unit equivalent nodal load caused by internal concrete creep; The expression for the creep coefficient fitting function is: in, For loading age is Calculate the creep coefficient for age t. The nominal creep coefficient; The fitting coefficients for the creep coefficient are denoted as .

2. The method for calculating concrete shrinkage and creep in bridge structures according to claim 1, characterized in that, The specific implementation process of calculating stress and creep strain at different times using the initial strain method is as follows: Step 1.1: Divide time t into a series of time intervals. , , ; Step 1.2: Calculate the first time period based on the applied load and material constants at t=t0. elastic stress at the beginning time t0 Assuming elastic stress First period Keeping the time interval unchanged, calculate the first time period. creep strain increment at the end ; Step 1.3: In the second time period At the start time t1, the creep strain increment Using the initial strain as an initial strain, and adding the current load increment, the stress increment is obtained by solving the elastic problem. Assuming in the second time period With internal stress and material constants remaining constant, the second time period is calculated. creep strain increment at the end ; Step 1.4: Repeat step 1.3 to calculate the... i Time period Start time Stress increment and the i Time period creep strain increment at the end The stress increment and creep strain increment at different time periods were obtained; Step 1.5: Accumulate the stress increments obtained in Step 1.4 to obtain the stress at different times; The creep strain increments obtained in step 1.4 are summed to obtain the creep strain at different times.

3. The method for calculating concrete shrinkage and creep in bridge structures according to claim 1, characterized in that, Calculation period The specific implementation process of the unit equivalent nodal load increment caused by internal concrete shrinkage is as follows: Step 3.1: Fit the concrete shrinkage strain into a single-phase exponential function, specifically: in, Let be the contraction strain at time t; p The rate of change of contractile strain; This represents the ultimate value of the contractile strain; Step 3.2: Calculate based on the single-phase exponential function. The increase in concrete shrinkage strain at any point within the unit during the time period for: Step 3.3: Based on the concrete shrinkage strain increment Calculation period The increase in unit equivalent nodal load caused by internal concrete shrinkage.

4. An electronic device comprising a memory and a processor, wherein the memory stores a computer program capable of running on the processor, characterized in that: When the processor runs the computer program, it performs the steps of the method for calculating concrete shrinkage and creep in bridge structures according to any one of claims 1 to 3.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that, The computer-readable storage medium is a non-volatile storage medium; the computer program, when run by the processor, executes the steps of the method for calculating concrete shrinkage and creep in bridge structures according to any one of claims 1 to 3.

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