A bridge creep strain calculation method under variable stress based on hyperbolic function modified superposition method

Abstract

This invention discloses a method for calculating the creep strain of bridges under varying stress based on a hyperbolic function modified superposition method, comprising the following steps: calculating the creep parameters of the concrete structure used in the bridge structure using the hyperbolic function method; calculating the creep compliance coefficient function and the creep recovery compliance function based on the creep parameters; discretizing the entire stress history of the concrete structure used in the bridge structure to obtain a stress history discrete matrix; calculating the total strain and creep strain under each discrete history in the stress history discrete matrix using the creep compliance coefficient function and the creep recovery compliance function, and linearly summing the total strain and creep strain under each discrete history to obtain the creep strain of the concrete structure used in the bridge structure throughout the entire varying stress history. This invention improves upon the traditional creep superposition algorithm, considering the time-varying characteristics of concrete, making it more closely approximate to real-world conditions and offering higher calculation accuracy.

Description

Technical Field

[0001] This invention relates to the field of bridge engineering, and in particular to a method for calculating bridge creep strain based on the hyperbolic function modified superposition method under variable stress. Background Technology

[0002] Under long-term loading, concrete undergoes deformation that increases over time; that is, with a constant stress, the strain of concrete continuously increases over time. This phenomenon is called concrete creep. The creep effect is not negligible, and its final value can reach 2 to 4 times the instantaneous elastic deformation of concrete. The creep effect develops rapidly in the initial stage of loading, reaching more than 60% of the final creep within the first 6 months. Due to creep, concrete structures experience a series of problems such as prestress loss, stress redistribution, structural cracking, and deflection, which not only affect driving comfort, bridge safety and durability, but can even lead to major engineering accidents.

[0003] Currently, there are many models available for calculating creep. The most commonly used models for predicting creep development include: the ACI model proposed by the American Concrete Institute; the CEB-FIP series models proposed by the European Concrete Committee and the International Prestressed Concrete Association; the GL2000 model, the BP model series and their modifications proposed by foreign scholars; and the models currently used in my country's existing standards.

[0004] In creep calculations, creep recovery is a crucial aspect of concrete deformation performance. While it can be disregarded under increasing stress conditions, its effect becomes significant under decreasing stress conditions. Currently, the main calculation models for creep recovery include: the YUE model, the MC78 model, the IMC78 model, the hyperbolic power model, and the RSM model.

[0005] Based on the above calculation models, a series of creep calculation methods and theories have been developed. Currently commonly used methods include: the effective modulus method, aging theory, horizontal moving curve method, superposition method, follow-through flow theory, age-adjusted effective modulus method, and elastic aging theory. However, these methods all have certain shortcomings. The effective modulus method overestimates results for stress-increasing conditions and underestimates results for stress-decreasing conditions and stress relaxation phenomena. Furthermore, it assumes complete deformation recovery when stress is completely unloaded, which is inconsistent with reality. The aging theory over-considers the aging effect of concrete for stress-increasing conditions, leading to underestimated results; for stress-decreasing conditions, it assumes creep recovery to zero, leading to overestimated results. The horizontal moving curve method ignores the aging effect of concrete, resulting in poor accuracy for younger concrete, overestimating results for stress-increasing conditions and underestimating results for stress-decreasing conditions. The superposition method... For the stress decreasing condition, the unloading curve is assumed to be consistent with the loading creep curve, leading to underestimation of the results. For aged concrete, creep is assumed to be fully recoverable, deviating from the actual results. The results of the successive flow theory under the stress increasing condition are unstable, and the calculation accuracy needs to be discussed. The calculation accuracy of the age-adjusted effective modulus method depends on the value of the aging coefficient and is greatly affected by other factors. The elastic aging theory assumes that irrecoverable deformation at any age can be obtained by vertically shifting the curve at the initial age, over-considering the aging effect of concrete, resulting in underestimation of the calculated results for the stress decreasing condition. Summary of the Invention

[0006] To address the problems existing in the prior art, the present invention aims to propose a method for calculating bridge creep strain based on a modified superposition method using hyperbolic functions under varying stress. This invention modifies the superposition method by referring to the calculation principle of the bifunctional method, resulting in a modified superposition calculation formula applicable to different stress conditions. This fills the gap in the current field of creep calculation where there is no high-precision unified calculation theory method for various working conditions.

[0007] The technical solution adopted in this invention is as follows:

[0008] A method for calculating bridge creep strain based on hyperbolic function modified superposition method under varying stress includes the following steps:

[0009] The creep parameters of a concrete bridge structure are calculated using the hyperbolic function method. The creep parameters include shrinkage strain function, creep coefficient, strength, and equivalent elastic modulus.

[0010] The creep compliance coefficient function and the creep recovery compliance function are calculated based on the creep parameters.

[0011] Discretize the entire stress history of the concrete bridge structure to obtain the stress history discretization matrix;

[0012] The total strain and creep strain under each discrete history in the stress history discrete matrix are calculated using the creep compliance coefficient function and the creep recovery compliance function. The total strain and creep strain under each discrete history are then linearly accumulated to obtain the creep strain of the concrete bridge structure throughout the entire variable stress history.

[0013] Preferably, the creep compliance coefficient function is as follows:

[0014]

[0015] In the formula: J(t,t0) is the creep compliance coefficient function of the concrete structure at time t0 when it is loaded at time t0. is the creep coefficient; E(t0) is the instantaneous elastic modulus of the concrete structure at time t0.

[0016] Preferably, the creep recovery compliance function is as follows:

[0017]

[0018] In the formula: J r (t,t0,t1) represents the concrete structure loading at time t0 and unloading at time t1, corresponding to the concrete structure's compatibility function at time t. The creep restitution coefficient function is derived from... ε was calculated. cr (t, t0, t1) represents the creep recovery of the concrete structure after loading at time t0 and unloading at time t1; ε e The strain of a 28-day-old concrete structure under stress is given by ε. e =σ(t0) / E 28 Calculated; E(t1) is the instantaneous elastic modulus of the concrete at time t1; E 28 The elastic modulus of concrete after 28 days.

[0019] Preferably, the process of discretizing the entire stress history of the concrete structure used in the bridge structure to obtain the stress history discretization matrix includes the following steps:

[0020] Step (1) compares the elements in the initial stress vector σ1 of the concrete structure to obtain the maximum value of the elements in the initial stress vector σ1 as σ. max1 =σ i Compare the maximum stress level σ i The two adjacent stress levels σ i-1 and σ i+1 Size;

[0021] Step (2), using σ i σ i-1 and σ i+1The larger value in the matrix and the corresponding loading time are used to generate a rectangular stress history matrix A. 3×1 Remove σ i σ i-1 and σ i+1 The larger value in the equation and the time corresponding to that larger value generate a new age T2 and a new stress vector σ2;

[0022] Step (3): Repeat steps (1) to (2) to obtain a 3×n stress history discrete matrix A. 3×n ={TJ TXΔσ1} T , where TJ is the rectangular stress loading age vector; TX is the rectangular stress unloading age vector; Δσ1 is the rectangular stress amplitude vector.

[0023] Preferably, the rectangular stress history matrix A 3×1 =[tj1,tx1,Δσ1] T Where Δσ1 is the historical amplitude of rectangular stress, tj1 is the loading age corresponding to Δσ1, and tx1 is the unloading age corresponding to Δσ1;

[0024] Calculation of the historical amplitude Δσ1 of rectangular stress and σ i-1 σ i+1 The size relationship can be divided into the following two cases:

[0025] First case: When σ i-1 >σ i+1 At that time, the historical amplitude of rectangular stress Δσ1=σ i -σ i-1 The rectangular stress history matrix is ​​generated as A. 3×1 =[t1,t i+1 ,σ i -σ i-1 ] T A new rectangular initial age and stress matrix is ​​generated as T2=(t0,t1,t2,…,t i-1 ,t i+1 ,…,t n ) 1×(n-1) σ2=(0,σ1,σ2,…,σ i-1 ,σ i+1 ,…,σ n ) 1×(n-1) .

[0026] The second case: when σ i-1 <σ i+1 At that time, the historical amplitude of rectangular stress Δσ1=σ i -σ i+1 The rectangular stress history matrix is ​​generated as A. 3×1 =[t1,t i+1 ,σ i-σ i+1 ] T Generate a new rectangle with initial ages T2 = (t0, t1, t2, ..., t i-1 ,t i ,…,t n ) 1×(n-1) The new stress matrix σ2=(0,σ1,σ2,…,σ i-1 ,σ i ,…,σ n ) 1×(n-1) .

[0027] Preferably, the stress history discrete matrix

[0028] Among them, A i This is a vector describing the loading and unloading ages and stress amplitudes of the i-th rectangular stress history;

[0029] The process of calculating the total strain and creep strain of the bridge structure under each discrete history in the stress history discrete matrix using the creep compliance coefficient function and the creep recovery compliance function, and then linearly summing the total strain and creep strain under each discrete history to obtain the creep strain of the concrete structure during the entire variable stress history includes the following steps:

[0030] S1, calculate the total strain and creep strain corresponding to each discrete historical segment at time t;

[0031] S2 sums up the creep strain and creep strain recovery of each discrete stress history segment to obtain the total strain and creep strain throughout the entire stress history.

[0032] Preferably, in S1:

[0033] For time t, at a certain rectangular stress A i The calculations should be divided into the following three cases for different time periods:

[0034] Case 1: When t <tj i When, then the rectangular stress history A i The total strain Δε at time t i (t) and creep They are 0 and 0 respectively;

[0035] The second scenario: when tj i <t<tx i When, then the rectangular stress history A i The total strain Δε at time t i (t) and creep According to Δσ respectively i J(t,tj i )and calculate;

[0036] The third case: when t <tx i When, then the rectangular stress history A i The total strain Δε at time t i (t) and creep According to Δσ respectively i J(tx i ,tj i )-Δσ i J r (t,tx i ,tj i )and calculate.

[0037] This invention also provides a bridge creep strain calculation system based on the hyperbolic function modified superposition method under varying stress, comprising:

[0038] The first calculation module is used to calculate the creep parameters of the concrete structure used in the bridge structure using the hyperbolic function method. The creep parameters include shrinkage strain function, creep coefficient, strength and equivalent elastic modulus.

[0039] The second calculation module is used to calculate the creep compliance coefficient function based on the creep parameters.

[0040] The third calculation module is used to calculate the creep recovery compliance function based on the creep parameters.

[0041] Discrete module: used to discretize the entire stress history of the concrete structure used in the bridge structure to obtain the stress history discrete matrix;

[0042] The fourth calculation module is used to calculate the total strain and creep strain under each discrete history in the stress history discrete matrix using the creep compliance coefficient function and the creep recovery compliance function. It then linearly sums the total strain and creep strain under each discrete history to obtain the creep strain of the concrete structure used in the bridge structure throughout the entire variable stress history.

[0043] The present invention also provides an electronic device, characterized in that it comprises:

[0044] One or more processors;

[0045] A storage device on which one or more programs are stored;

[0046] When the one or more programs are executed by the one or more processors, the one or more processors implement the bridge creep strain calculation method based on hyperbolic function modified superposition method under varying stress as described above.

[0047] The present invention also provides a storage medium storing a computer program thereon, wherein the computer program, when executed by a processor, implements the bridge creep strain calculation method based on hyperbolic function modified superposition method under varying stress as described above.

[0048] The present invention has the following beneficial effects:

[0049] This invention improves upon the traditional creep superposition algorithm, enabling it to consider the time-varying characteristics of concrete, thus more closely reflecting actual conditions and further enhancing its universality and calculation accuracy. Attached Figure Description

[0050] Figure 1 This is a diagram showing the reinforcement details of the specimen in Embodiment 1 of the present invention.

[0051] Figure 2(a) shows the reinforcement diagram of the cross-section at 1 / 2 of the specimen in Example 1 of the present invention;

[0052] Figure 2(b) is a diagram of the reinforcement of the end section of the specimen in Embodiment 1 of the present invention;

[0053] Figure 3(a) is a diagram showing the arrangement of measuring points at 1 / 2 of the cross-section of the specimen in Example 1 of the present invention;

[0054] Figure 3(b) is a diagram showing the arrangement of measuring points on the elevation of the specimen in Embodiment 1 of the present invention;

[0055] Figure 4 This is a schematic diagram of the loading device in Embodiment 1 of the present invention;

[0056] Figure 5 The diagram shows the load conditions under constant load, increasing load, and decreasing load conditions in Embodiment 1 of the present invention.

[0057] Figure 6 This is a diagram showing the load conditions under the stepped load condition in Embodiment 1 of the present invention;

[0058] Figure 7(a) is a comparison of the calculation results and experimental measured data under the incremental stress condition in Example 1 of the present invention;

[0059] Figure 7(b) is a comparison chart of the calculation results and experimental measured data under the decreasing stress condition in Embodiment 1 of the present invention;

[0060] Figure 8(a) is a comparison of the calculation results and experimental measured data under the stepped load 1 condition in Embodiment 1 of the present invention;

[0061] Figure 8(b) is a comparison of the calculation results and experimental measured data under the stepped load 2 condition in Embodiment 1 of the present invention;

[0062] Figure 8(c) is a comparison chart of the calculation results and experimental measured data under the stepped load 3 condition in Embodiment 1 of the present invention;

[0063] Figure 9(a) is a structural diagram of the specimen in Embodiment 2 of the present invention.

[0064] Figure 9(b) is a structural diagram of the end section of the specimen in Embodiment 2 of the present invention;

[0065] Figure 9(c) is a cross-sectional view of the specimen at 1 / 2 of the present invention in Example 2 of the present invention;

[0066] Figure 10(a) is a diagram showing the arrangement of measuring points on the elevation of the specimen in Embodiment 2 of the present invention;

[0067] Figure 10(b) is a diagram showing the arrangement of measuring points at 1 / 2 of the cross-section of the specimen in Example 2 of the present invention;

[0068] Figure 11 This is a diagram of the loading structure device in Embodiment 2 of the present invention;

[0069] Figure 12 This is a diagram illustrating the incremental load, decreasing load, constant load, and fluctuating load scenarios in Embodiment 2 of the present invention.

[0070] Figure 13(a) is a comparison chart of the calculation results and experimental measured data under the incremental load condition in Embodiment 2 of the present invention;

[0071] Figure 13(b) is a comparison chart of the calculation results and experimental measured data under the decreasing load condition in Embodiment 2 of the present invention;

[0072] Figure 13(c) is a comparison chart of the calculation results and experimental measured data under the fluctuating load condition in Embodiment 2 of the present invention.

[0073] In the diagram: 1-First concrete specimen; 2-Solid end cap of first specimen; 3-Pre-drilled hole for force transmission anchor; 4-Filled rigid foam in first specimen; 5-Longitudinal reinforcement of specimen; 6-Stirrups of specimen; 7-Large gauge length strain gauge; 8-Vibrating wire strain gauge; 9-Force transmission anchor; 10-Pressure nut; 11-Hydraulic jack; 12-Span; 13-Upper anchor nut; 14-Spring; 15-Lower anchor nut; 16-Base; 17-Second concrete specimen; 18-Solid end cap of second specimen; 19-Pre-drilled hole for force transmission anchor; 20-Filled rigid foam in second specimen; 21-Support; 22-Support beam; 23-Beam screw; 24-Reaction frame; 25-Small hydraulic jack; 26-Pressure sensor; 27-Anchor nut; 28-Butterfly spring stabilizing device; 29-Force transmission anchor; 30-Support pad. Detailed Implementation

[0074] The present invention will be further explained below with reference to specific embodiments and accompanying drawings.

[0075] This invention provides a method for calculating bridge creep strain under varying stress based on a hyperbolic function modified superposition method. The hyperbolic function superposition method is modified by introducing a creep recovery coefficient to correct the creep recovery compliance function. The creep recovery compliance function is as follows:

[0076]

[0077] In Item Use replace.

[0078] In the formula: J r (t, t0, t1) is the creep recovery compliance function; E(t1), E 28 It is the elastic modulus of concrete at time t1 and 28 days; and These are the creep coefficients of concrete at times t1 and t0, respectively, corresponding to the loading time of the concrete and the unloading time of the concrete. It is the creep recovery coefficient of concrete loaded at time t0 and unloaded at time t1, corresponding to time t.

[0079] The specific implementation steps of the bridge creep strain calculation method based on the hyperbolic function modified superposition method under variable stress according to the present invention are as follows:

[0080] (1) Conduct concrete material tests and calculate concrete creep parameters using the hyperbolic function method based on the experimental results;

[0081] (2) Calculate the concrete creep flexibility coefficient function and creep recovery flexibility function based on the creep parameters;

[0082] (3) Discretize the alternating stress process of concrete;

[0083] (4) Using the creep flexibility function and the creep recovery flexibility function, the two-function method is applied to calculate the creep strain of concrete at each discrete stage. In the calculation process, the creep recovery coefficient is introduced to correct the creep recovery flexibility function.

[0084] (5) The concrete creep strain of each discrete stage is linearly superimposed and summed to obtain the concrete creep strain in the entire variable stress history process.

[0085] Because the results obtained by the superposition method have a high degree of agreement with general experimental results, the superposition method is widely used in engineering calculations. However, in the calculation process, the superposition method overestimates the creep effect of concrete when calculating creep under stress reduction conditions. Therefore, in order to overcome the shortcomings of the superposition method under stress reduction conditions, this invention modifies the superposition method based on the following assumptions:

[0086] Assumption 1: Linear creep assumption

[0087] Concrete creep is classified into two types: linear creep and nonlinear creep. For concrete structures, the stress level is relatively low, thus avoiding nonlinear creep. Therefore, this invention considers all creep as linear creep, with a linear relationship between creep and stress level. The ratio of concrete stress to strength is set at 0.4 as the dividing point between linear and nonlinear creep.

[0088] Assumption 2: The loading elastic modulus and the unloading elastic modulus are the same at the same age.

[0089] Based on Assumption 1, the linear creep assumption, the elastic modulus of concrete is not significantly affected by stress when the stress is within the critical stress range of linear creep. Therefore, this invention assumes that the elastic modulus of concrete at the same age remains consistent during loading and unloading.

[0090] Assumption 3: Linear creep recovery assumption

[0091] This invention proposes that when the stress is within the critical stress range of linear creep in concrete, the creep recovery deformation of concrete at the same loading age and unloading age is linearly related to the stress.

[0092] Assumption 4: Superposition Principle Assumption

[0093] This invention posits that the elastic strain and creep strain generated by the applied stress can be linearly superimposed with the elastic recovery and creep recovery caused by the unloaded stress. In other words, it considers that the total strain under stress that varies with time t is the sum of the strain caused by each stress change amplitude.

[0094] Based on the above assumptions, the specific implementation steps of the bridge creep strain calculation method based on the hyperbolic function modified superposition method of the present invention are as follows:

[0095] Step 1: Conduct specimen-level material tests on the concrete used in the target structure (i.e., the concrete structure in the bridge structure) to obtain the material mechanical parameters of the concrete, and calculate the creep parameters using the hyperbolic function method based on the test data. Step 1 specifically includes the following four steps:

[0096] Step (1) uses a hyperbolic function to fit the shrinkage strain function, and the formula for the shrinkage strain function is as follows:

[0097]

[0098] Where: ε s∞ For the final strain of contraction, t s α represents the moment when concrete shrinkage begins, and α is a constant obtained from experimental fitting.

[0099] Step (2) uses a hyperbolic power function to fit the creep coefficient, and the formula for the creep coefficient is as follows:

[0100]

[0101] In the formula: The creep coefficient is the creep coefficient at time t0, which corresponds to the loading at time t; A is the final value of the creep coefficient, and B and D are the parameters obtained from the experimental fitting.

[0102] Step (3): The MC2010 model is used to describe the concrete strength. The expression for the concrete strength is as follows:

[0103]

[0104] In the formula: f cm (t), f cm The average compressive strength of concrete at any age and at 28 days, respectively, β cc (t) is the coefficient related to the age of concrete strength, and s is a parameter related to the type of cement, with a value of 0.25.

[0105] Step (4): After taking into account the effect of the reinforcement in the elastic modulus of plain concrete, calculate the equivalent elastic modulus of the concrete specimen. The formula for the equivalent elastic modulus is as follows:

[0106] E ceff (t)=E c (t)(1-ρ)+E s ρ (4)

[0107] In the formula: E ceff (t) represents the equivalent elastic modulus considering the influence of reinforcing steel; E c (t) represents the elastic modulus of concrete without considering the influence of steel reinforcement; ρ is the reinforcement ratio; E s This refers to the elastic modulus of the steel reinforcement.

[0108] Step 2: After the creep parameters are calculated, the creep compliance coefficient function and creep recovery compliance function are further calculated based on the calculated creep parameters as follows:

[0109] The creep compliance coefficient function is as follows:

[0110]

[0111] In the formula: J(t,t0) is the creep compliance coefficient function of concrete loaded at time t0, corresponding to time t; E(t0) is the instantaneous elastic modulus of the concrete at time t0, calculated from step (2) in step 1.

[0112] The creep recovery compliance function is:

[0113]

[0114] In the formula: J r (t,t0,t1) represents the concrete's compatibility function at time t when it is loaded at time t0 and unloaded at time t1. The creep restitution coefficient function is derived from... ε was calculated. cr (t, t0, t1) represents the creep recovery of concrete loaded at time t0 and unloaded at time t1; ε e The strain of concrete subjected to stress at 28 days of age can be expressed by ε. e =σ(t0) / E 28 The calculated value is E(t1), which is similar to the definition in equation (5) and represents the instantaneous elastic modulus of the concrete at time t1. 28 The elastic modulus of concrete after 28 days.

[0115] Step 3: To apply the superposition method, the entire stress history is first discretized to obtain the stress history discretization matrix, including the following steps:

[0116] Step (1) is illustrated using a specific step concrete stress history as an example. Let the initial age vector T1 and initial stress vector σ1 generated based on the stress history be as follows:

[0117] T1=(t0,t1,t2,…,t i-1 ,t i ,t i+1 ,…,t n (7)

[0118] σ1=(0,σ1,σ2,…,σ i-1 ,σ i ,σ i+1 ,…,σ n (8)

[0119] In the formula: t i (i = 0, 1, 2, ..., n) represents the time corresponding to the stress abrupt change point in the step stress history; σ i (i = 0, 1, 2, ..., n) represents the step stress level corresponding to the step stress history.

[0120] Step (2) compares the elements in the initial stress vector to obtain the maximum value of the element in the initial stress vector σ1 as σ. max1 =σ i And compare the maximum stress level σ i The two adjacent stress levels σ i-1 σ i+1 .

[0121] Step (3), using σ i and σ i-1 σ i+1 The larger values ​​in the matrix and their corresponding loading times generate a rectangular stress history matrix A. 3×1 =[tj1,tx1,Δσ1] T Matrix element Δσ1 represents the historical amplitude of rectangular stress, matrix element tj1 represents the loading age corresponding to Δσ1, and matrix element tx1 represents the unloading age corresponding to Δσ1. σ is removed. i and σ i-1 σ i+1 The larger values ​​in the equation and their corresponding times generate new ages, stress vectors T2 and σ2. The calculation of Δσ1 is related to σ... i-1 σ i+1 The size relationship can be divided into the following two cases:

[0122] Case ①: When σ i-1 >σ i+1 When the stress amplitude is Δσ1=σ i -σ i-1 The rectangular stress history matrix is ​​generated as A. 3×1 =[t1,t i+1 ,σ i -σ i-1 ] T A new rectangular initial age and stress matrix is ​​generated as T2 = (t0, t1, t2, ..., t i-1 ,t i+1 ,…,t n ) 1×(n-1) σ2=(0,σ1,σ2,…,σ i-1 ,σ i+1 ,…,σ n ) 1×(n-1) .

[0123] Case ②: When σ i-1 <σ i+1 When the stress amplitude is Δσ1=σ i -σ i+1 The rectangular stress history matrix is ​​generated as A. 3×1 =[t1,t i+1 ,σ i -σ i+1 ] T A new rectangular initial age and stress matrix is ​​generated as T2 = (t0, t1, t2, ..., t i-1 ,t i ,…,t n ) 1×(n-1) σ2=(0,σ1,σ2,…,σ i-1 ,σ i ,…,σn ) 1×(n-1) .

[0124] Step (4): After generating new T2 and σ2, repeat the above operation to obtain a 3×n matrix A. 3×n ={TJ TXΔσ1} T This can be expressed as:

[0125]

[0126] In the formula: TJ is the rectangular stress loading age vector; TX is the rectangular stress unloading age vector; Δσ1 is the rectangular stress amplitude vector; A i This is a vector describing the loading and unloading ages and stress amplitude of the i-th rectangular stress history.

[0127] Step 4, A 3×n column vector A in i This is the result after discretizing the stress history and age. The creep compliance coefficient function and creep recovery compliance function are used to calculate the creep compliance coefficient for each discrete history A. i The total strain and creep strain under the action are calculated, and the total strain and creep strain under each discrete history of action are linearly accumulated. This includes the following steps:

[0128] Step (1) involves discretizing the stepped stress history and then calculating the total strain and creep strain for each discrete history segment at time t. For a rectangular stress A at time t... i The calculations should be divided into the following three cases for different time periods:

[0129] Case ①: When t <tj i When, then the rectangular stress history A i The total strain Δε at time t i (t), creep They are 0 and 0 respectively.

[0130] Case 2: When tj i <t<tx i When, then the rectangular stress history A i Total strain at time t creep According to Δσ respectively i J(t,tj i ), calculate.

[0131] Case ③: When t <tx i When, then the rectangular stress history A i The total strain Δε at time t i (t), creep According to Δσ respectively iJ(tx i ,tj i )-Δσ i J r (t,tx i ,tj i ), calculate.

[0132] Step (2) involves summing the creep strain and creep strain recovery for each discrete stress history segment to calculate the total strain and creep strain throughout the entire stress history. The resulting formula is as follows:

[0133]

[0134]

[0135] In the formula: ε(t) is the total strain at time t throughout the entire stress history; ε c (t) is the creep strain at time t throughout the entire stress history.

[0136] Concrete experiences varying creep rates depending on its stress history. Ignoring stress history leads to inaccurate calculations of the long-term effects of concrete. However, fully recording the stress history would prolong creep calculations. Therefore, this invention also proposes a method that ensures both accuracy and efficiency in creep calculations, primarily comprising the following two aspects:

[0137] Aspect 1: Methods to reduce the historical accumulation of creep stress

[0138] The creep development pattern is characterized by a rapid initial growth rate, followed by a slower rate, reaching 60%–70% of the total creep within 6 months. For complex stress histories, extensive recording requires significant computational and time costs. The entire creep development process exhibits a creep stability duration of t. n This makes the creep coefficient remain constant over any loading duration t. i ≥t n There are always:

[0139]

[0140] In the formula: It is the concrete being loaded at time t0, corresponding to time t. i The creep coefficient at time +t0; It is the concrete being loaded at time t0, corresponding to time t. n The creep coefficient at time +t0.

[0141] Table 1 shows the relationship between different creep stability durations and the creep development function. Therefore, the formula for calculating the long-term creep of concrete can be approximated by using... replace To reduce the impact of recording stress history.

[0142] Table 1

[0143]

[0144] Second aspect: Methods to reduce the historical accumulation of creep recovery stress

[0145] The creep recovery law is similar to the creep development law; creep recovery develops extremely rapidly after stress unloading. For the creep recovery development process, there exists a creep recovery stability duration t. m This makes the creep recovery coefficient applicable to any unloading duration t. i ≥t m There are always:

[0146]

[0147] In the formula: The concrete is loaded at time t0 and unloaded at time t1, corresponding to time t. i The creep recovery coefficient at time +t1; The concrete is loaded at time t0 and unloaded at time t1, corresponding to time t. m The creep recovery coefficient at time +t1.

[0148] Table 2 shows the relationship between different creep stability durations and creep development functions. Therefore, the long-term creep of concrete can be approximately calculated using... replace To reduce the impact of recording stress history.

[0149] Table 2

[0150]

[0151] This invention takes into account the time-varying effect of concrete in the cumulative summation of creep strain, thus improving the calculation accuracy of creep strain. The method for reducing stress history accumulation in this invention retains a portion of the stress history's influence on creep strain, thereby improving calculation accuracy, while avoiding the need to record and calculate the entire stress history, thus improving computational efficiency. This invention's method for calculating bridge creep strain under varying stress based on the hyperbolic function modified superposition method is more accurate and universally applicable than traditional creep strain calculation methods, providing a unified calculation method for creep strain.

[0152] Example 1

[0153] Creep calculation and analysis under uniaxial compressive loading and variable stress. A uniaxial compressive creep test was conducted on component 1 of the experimental design, and the 150-day concrete creep value change curve was obtained. The measured results were compared and analyzed with the results obtained by the calculation method of this invention to demonstrate the applicability and stability of the method. The specific content is as follows:

[0154] The first concrete specimen 1 in the experimental design is a cuboid with dimensions of 200mm × 200mm × 1000mm. To ensure local bearing capacity and load transfer, 150mm thick solid concrete end caps 2 are provided at both ends of the specimen. Each solid end cap 2 has a 40mm diameter pre-drilled hole 3 for a load-transfer anchor rod to pass through. The hollow portion in the middle is filled with rigid foam 4. Longitudinal reinforcement 5 and stirrups 6 are provided in the first concrete specimen 1. The reinforcement details on the specimen's vertical surface are as described above. Figure 1 The end reinforcement is shown in Figure 2(a), and the reinforcement at the 1 / 2 section is shown in Figure 2(b). The strain of the first concrete specimen 1 was measured using a large gauge length strain gauge 7 and a vibrating wire strain gauge 8. The measuring points of the large gauge length strain gauge 7 were set at the third points of specimen 1, for a total of 4 points. The measuring points of the vibrating wire strain gauge 8 were set at the 1 / 2 section of the cross-section of specimen 1, for a total of 4 points. The arrangement of the measuring points on the cross-section and elevation is shown in Figures 3(a) and 3(b).

[0155] The first concrete specimen 1 was molded and cured in accordance with the relevant provisions of the "Test Procedure for Hydraulic Concrete". The concrete mix proportion of the first concrete specimen 1 is shown in Table 3.

[0156] Table 3

[0157]

[0158] Loading device construction reference Figure 4 The loading device includes a force-transmitting anchor rod 9, a pressure nut 10, a hydraulic jack 11, a pad 12, an upper anchor nut 13, a spring 14, a lower anchor nut 15, and a base 16. During the loading test, the first concrete specimen 1 is supported on the spring 14. The force-transmitting anchor rod 9 passes through the pre-drilled hole 3 in the first concrete specimen 1, and is anchored and fixed to the loading device using the lower anchor nut 15, the upper anchor nut 13, and the pad 12. The hydraulic jack 11 is fixed to the force-transmitting anchor rod 9 by the pressure nut 10. During loading, the force of the hydraulic jack 11 is reacted to the pad 12 by the fixing action of the pressure nut 10. Then, the upper anchor nut 13 is tightened, loosening the hydraulic jack 11 and the pressure nut 9, and the load is transferred to the specimen 1 using the force-transmitting anchor rod 9 to achieve loading.

[0159] A total of 5 test groups were set up, with 3 first concrete specimens in each group: constant load group, increasing load group, decreasing load group, and stepped load group. The load conditions for different stress conditions are as follows: Figure 5 , Figure 6 The specific load values ​​are as follows:

[0160] 1. Constant load condition

[0161] For constant load conditions, a load of 300 kN is applied for the first 7 days of loading until the test is completed, and the load remains unchanged; when the load deviates from the target load by more than 10 kN, the component is re-pressurized.

[0162] 2. Increasing load condition

[0163] For the increasing load condition, the load change process is as follows: 100kN (7 days old) → 120kN → (14 days old) → 140kN (21 days old) → 160kN (28 days old) → 180kN (35 days old) → 200kN (49 days old) → 240kN (63 days old) → 260kN (77 days old) → 280kN (91 days old) → 300kN (105 days old).

[0164] 3. Decreasing load condition

[0165] For the decreasing stress condition, the initial loading age and stress change interval are the same as those for the increasing load condition. The load change process is as follows: 300kN (7 days) → 220kN (14 days) → 160kN (21 days) → 120kN (28 days) → 90kN (35 days) → 70kN (49 days) → 60kN (63 days) → 55kN (77 days) → 50kN (91 days).

[0166] 4. Stepped load condition

[0167] The stepped stress conditions are divided into three groups, set according to the principle that the overall stress gradually increases, while local stress decreases, eventually reaching the same value. The main difference between the three groups is the number of local stress decreases. The stress change intervals of the three load conditions are basically consistent with those of the incremental load condition, and their load change histories are as follows:

[0168] (1) 140kN (7 days old) → 120kN (14 days old) → 100kN (21 days old) → 200kN (28 days old) → 180kN (35 days old) → 160kN (49 days old) → 260kN (63 days old) → 220kN (77 days old) → 240kN (91 days old) → 300kN (105 days old);

[0169] (2) 120kN (7 days old) → 100kN (14 days old) → 160kN (21 days old) → 140kN (28 days old) → 200kN (35 days old) → 140kN (49 days old) → 240kN (63 days old) → 180kN (77 days old) → 220kN (91 days old) → 300kN (105 days old);

[0170] (3) 160kN (7 days old) → 140kN (14 days old) → 120kN (21 days old) → 100kN (28 days old) → 240kN (35 days old) → 200kN (49 days old) → 160kN (63 days old) → 120kN (77 days old) → 260kN (91 days old) → 220kN (105 days old) → 300kN (119 days old).

[0171] The method for calculating bridge creep strain based on the hyperbolic function modified superposition method under varying stress, as described in this invention, involves the following process:

[0172] 1. Obtaining the shrinkage strain, creep coefficient, elastic modulus, and compressive strength of concrete through experimental data involves the following four steps:

[0173] (1) The shrinkage strain function is fitted using a hyperbolic form. The fitting formula for the shrinkage strain function is:

[0174]

[0175] In the formula: t is the calculation time point; ε s (t, 7) represents the concrete shrinkage strain at time t, which corresponds to the concrete shrinkage strain that begins to shrink on day 7.

[0176] (2) The creep coefficient is fitted using a hyperbolic power function. The fitting formula for the creep coefficient is:

[0177]

[0178] In the formula: t is the calculation time point; The creep coefficient of concrete at time t is given when the concrete is loaded on day 7.

[0179] (3) The MC2010 model is used to describe the compressive strength of concrete. The formula for compressive strength is:

[0180]

[0181] In the formula: f cm (t) represents the compressive strength of the concrete at time t.

[0182] (4) Using the MC2010 model and considering the influence of reinforcement, the elastic modulus of concrete is described. The formula for the elastic modulus of concrete is:

[0183]

[0184] In the formula: E ceff (t) represents the equivalent elastic modulus considering the influence of reinforcing steel; E c (t) represents the elastic modulus of concrete without considering the influence of steel reinforcement; ρ is the reinforcement ratio; E s This refers to the elastic modulus of the steel reinforcement.

[0185] 2. Calculate the creep compliance coefficient function and creep recovery compliance function based on the creep parameters:

[0186] The creep compliance coefficient function is:

[0187]

[0188] In the formula: J(t,t0) is the creep compliance coefficient function of concrete loaded at time t0, corresponding to time t; E(t0) is the instantaneous elastic modulus of the concrete at time t0, calculated from step (2) of step 1.

[0189] The creep recovery compliance function is:

[0190]

[0191] In the formula: J r (t,t0,t1) represents the concrete's compatibility function at time t when it is loaded at time t0 and unloaded at time t1. The creep restitution coefficient is given by... ε was calculated. cr (t, t0, t1) represents the creep recovery of concrete loaded at time t0 and unloaded at time t1; ε e The strain of concrete subjected to stress at 28 days of age can be expressed by ε. e =σ(t0) / E 28 The calculated value is E(t1), which is similar to the definition in equation (19) and represents the instantaneous elastic modulus of the concrete at time t1. 28 The elastic modulus of concrete after 28 days.

[0192] 3. Discrete step-wise stress history, and calculate the rectangular stress history matrix for increasing, decreasing, and fluctuating load cases respectively:

[0193] Increasing dead load condition:

[0194]

[0195] Decreasing load case:

[0196]

[0197] Fluctuating load case 1:

[0198]

[0199] Fluctuating load case 2:

[0200]

[0201] Fluctuating load case 3:

[0202]

[0203] 4. The calculation of creep strain at different times consists of the following two steps:

[0204] (1) After discretizing the stepped stress history, the total strain and creep strain at time t are calculated in a computer language. For time t at a certain rectangular stress (A i Different time periods can be categorized into the following three situations:

[0205] ①If t is satisfied <tj i Then the rectangular stress history A i The total strain Δε at time t i (t) and creep They are 0 and 0 respectively.

[0206] ②If tj is satisfied i <t<tx i Then the rectangular stress history (A) i The total strain Δε at time t i (t) and creep Δσ i J(t,tj i )and

[0207] ③ If t>tx i Then the rectangular stress history (A) i The total strain Δε at time t i (t) and creep Δσ i J(tx i ,tj i )-Δσ i J r (t,tx i ,tj i )and

[0208] (2) Finally, by summing up the different stress histories, the following calculation formula is obtained:

[0209]

[0210]

[0211] Based on the above steps, the calculation of creep strain, stress strain and total strain at different times can be completed. The calculation results are shown in Table 4. The comparison and analysis of the calculation results and experimental measured data under the increasing, decreasing, step 1, step 2 and step 3 load conditions are given in Figures 7(a), 7(b), 8(a), 8(b) and 8(c).

[0212] The calculation results show that: for increasing loads, creep strain increases rapidly in the early stage and slowly in the later stage; for decreasing loads, the change is similar to that of increasing loads, but the creep strain remains almost unchanged in the later stage; for step loads 1, 2, and 3, creep strain increases rapidly when the load changes abruptly, and increases slowly before the next significant load change.

[0213] Table 4

[0214]

[0215] The following conclusions can be drawn from the analysis of the results:

[0216] 1. Under increasing load, ignoring some errors due to accidental factors such as human operation and environmental changes, the measured values ​​and development trends of theoretical values ​​(creep strain, stress strain, and total strain) are consistent; indicating that the modified superposition method has good applicability and stability for calculating stepped increasing stress creep.

[0217] 2. Under decreasing load, ignoring accidental factors, the measured values ​​are larger than the theoretical values ​​when the age is 7-25 days. This is related to the fact that the hydration reaction of concrete is more intense in the early stage and it is more sensitive to environmental factors. As the age gradually increases, the theoretical values ​​and measured values ​​are basically consistent. This shows that the modified superposition method has good applicability to the calculation of decreasing stress creep.

[0218] 3. Due to environmental factors, there are some differences between the measured and theoretical values ​​of strains under stepped stress conditions 1 and 2, but the differences are small. For stepped stress condition 3, the theoretical and measured values ​​of strains are basically in agreement. It can be seen that the modified superposition method has good applicability and stability in creep calculation under stepped stress conditions.

[0219] Example 2

[0220] Calculation and analysis of creep in prestressed concrete beams under three-point bending stress. A three-point bending loading creep test was conducted on the second concrete member 17 of the experimental design, and the creep value variation curve of concrete over 120 days was obtained. The measured data were compared and analyzed with the results obtained by the calculation method of this invention to demonstrate the applicability and stability of the method. The specific content is as follows:

[0221] The second concrete specimen 17 is a rectangular parallelepiped with dimensions of 200mm × 400mm × 3300mm, similar in structure to the first concrete specimen 1 in Embodiment 1. The second concrete specimen 17 has solid concrete end caps 18 and anchor bolt pre-drilled holes 19 at both ends. The anchor bolt pre-drilled holes 19 are circular. The interior of the second concrete specimen 17 has a square cavity filled with rigid foam 20. The diameter of the anchor bolt pre-drilled holes 19 is 40mm, and the square cavity has dimensions of 100 × 200mm. The cross-sectional structure of the first concrete specimen 17 is shown in Figure 9(a), the end section structure in Figure 9(b), and the half-section structure in Figure 9(c). The strain of the first concrete specimen 17 is measured using the same large gauge length strain gauge 7 and vibrating wire strain gauge 8 as in Embodiment 1. The elevation arrangement of the measuring points is shown in Figure 10(a), and the cross-sectional arrangement of the measuring points is shown in Figure 10(b).

[0222] The first concrete specimen 17 was molded and cured in accordance with the relevant provisions of the "Test Procedure for Hydraulic Concrete". The concrete mix proportion of the first concrete specimen 17 is the same as that in Table 3.

[0223] Loading device construction reference Figure 11 The entire loading device comprises a bracket 21, a bracket beam 22, beam screws 23, a reaction frame 24, a hydraulic jack 25, a pressure sensor 26, an anchor nut 27, a butterfly spring stabilizing device 28, a force-transmitting anchor rod 29, and a support 30. First, the force-transmitting anchor rod 29 is passed through the circular hole 19 of component 17, and the butterfly spring stabilizing device 28, pressure sensor 26, and anchor nut 27 are installed. After installation, component 17 is placed on the bracket 30, and loading is applied using the hydraulic jack 25. The constraint of the bracket beam 22 and the reaction frame 24 are used to apply the load to the three-thirds points of component 17.

[0224] This experiment consisted of four test groups, each containing three specimens: a constant load group, a stepped increasing load group, a stepped decreasing load group, and a stepped fluctuating load group. The load conditions for different stress scenarios were described in detail below. Figure 12 The specific load levels are as follows:

[0225] 1. Constant load condition

[0226] A constant load of 50 kN was applied to the test beam on the 7th day of its age until the entire test was completed. When the load deviation was greater than 10%, the test beam was reloaded.

[0227] 2. Increasing load condition

[0228] To investigate the creep law of increasing stress in concrete structures during actual engineering construction, the following progressive load conditions were set up: 10kN (initial age 7 days) → 15kN (age 14 days) → 20kN (age 21 days) → 25kN (age 28 days) → 30kN (age 35 days) → 35kN (age 49 days) → 40kN (age 63 days) → 45kN (age 77 days) → 50kN (age 91 days) → 55kN (age 105 days).

[0229] 3. Decreasing load condition

[0230] To investigate the creep law of stress reduction when prestress loss occurs in concrete structures, the following decreasing load condition was set as follows: 55kN (initial age 7 days) → 50kN (age 14 days) → 45kN (age 21 days) → 40kN (age 28 days) → 35kN (age 35 days) → 30kN (age 49 days) → 25kN (age 63 days) → 20kN (age 77 days) → 15kN (age 91 days) → 10kN (age 105 days).

[0231] 4. Fluctuating load condition

[0232] To investigate the creep behavior of concrete structures under complex stress history, a stepped fluctuating load case was set up with the following variation history: 5kN (initial age 7 days) → 15kN (age 14 days) → 45kN (age 21 days) → 25kN (age 28 days) → 10kN (age 35 days) → 30kN (age 49 days) → 50kN (age 63 days) → 35kN (age 77 days) → 20kN (age 91 days) → 55kN (age 105 days).

[0233] The method for calculating bridge creep strain based on the hyperbolic function modified superposition method under varying stress, as described in this invention, involves the following process:

[0234] 1. Obtaining the shrinkage strain, creep coefficient, elastic modulus, and compressive strength of concrete through experimental data involves the following four steps:

[0235] (1) The shrinkage strain function is fitted using a hyperbolic form. The fitting formula for the shrinkage strain function is:

[0236]

[0237] In the formula: t is the calculation time point; ε s (t,7) represents the concrete shrinkage strain at time t, which corresponds to the time the concrete begins to shrink on day 7.

[0238] (2) The creep coefficient is fitted using a hyperbolic power function. The fitting formula for the creep coefficient is:

[0239]

[0240] In the formula: t is the calculation time point; The creep coefficient of concrete at time t is given when the concrete is loaded on day 7.

[0241] (3) The MC2010 model is used to describe the compressive strength of concrete. The formula for the compressive strength of concrete is:

[0242]

[0243] In the formula: f cm (t) represents the compressive strength of the concrete at time t.

[0244] (4) The MC2010 model is used to describe the elastic modulus of concrete. The formula for the elastic modulus of concrete is:

[0245]

[0246] In the formula: E c (t) represents the elastic modulus of concrete without considering the influence of steel reinforcement.

[0247] 2. Calculate the creep compliance coefficient function and creep recovery compliance function based on the obtained creep parameters:

[0248] The creep compliance coefficient function is:

[0249]

[0250] In the formula: J(t,t0) is the creep compliance coefficient function of concrete loaded at time t0, corresponding to time t; E(t0) is the instantaneous elastic modulus of the concrete at time t0, calculated from step (2) in step 1.

[0251] The creep recovery compliance function is:

[0252]

[0253] In the formula: J r (t,t0,t1) represents the concrete's compatibility function at time t when it is loaded at time t0 and unloaded at time t1. The creep restitution coefficient is given by... ε was calculated.cr (t, t0, t1) represents the creep recovery of concrete loaded at time t0 and unloaded at time t1; ε e The strain of concrete subjected to stress at 28 days of age can be expressed by ε. e =σ(t0) / E 28 The calculated value is E(t1), which is similar to the definition in equation (19) and represents the instantaneous elastic modulus of the concrete at time t1. 28 The elastic modulus of concrete after 28 days.

[0254] 3. Discrete step-wise stress history, and calculate the rectangular stress history matrix for increasing, decreasing, and fluctuating load cases respectively:

[0255] Increasing dead load condition:

[0256]

[0257] Decreasing load case:

[0258]

[0259] Fluctuating load case:

[0260]

[0261] 4. The calculation of creep strain at different times consists of the following two steps:

[0262] (1) After discretizing the step stress history, the total strain and creep strain at time t are calculated in the computer language.

[0263] For time t, at a certain rectangular stress (A) i Different time periods can be categorized into the following three situations:

[0264] ①If t is satisfied <tj i Then the rectangular stress history A i The total strain Δε at time t i (t) and creep They are 0 and 0 respectively.

[0265] ②If tj is satisfied i <t<tx i Then the rectangular stress history (A) i The total strain Δε at time t i (t) and creep Δσ i J(t,tj i )and

[0266] ③ If t>tx i Then the rectangular stress history (A)i The total strain Δε at time t i (t) and creep Δσ i J(tx i ,tj i )-Δσ i J r (t,tx i ,tj i )and

[0267] (2) Finally, by summing up the different stress histories, the following calculation formula is obtained:

[0268]

[0269]

[0270] The calculation of creep strain, stress strain and total strain at different times can be completed by following the above steps. The calculation results are shown in Table 5. The comparison and analysis of the calculation results and experimental measured data under increasing, decreasing and fluctuating load conditions are given in Figures 13(a), 13(b) and 13(c).

[0271] The calculation results show that the patterns under each load type are similar to those in Example 1: For increasing load, the creep strain increases rapidly in the early stage and slowly in the later stage; for decreasing load, the change is similar to that of increasing load, but the creep strain remains almost unchanged in the later stage; for fluctuating load, the overall pattern of creep strain is that it increases faster in the early stage than in the later stage, but it also increases significantly when the load undergoes a large change.

[0272] Table 5

[0273]

[0274] The following conclusions can be drawn from the analysis of the results:

[0275] Ignoring accidental errors caused by external factors such as human operation, the calculated creep values ​​of concrete test beams under stepped increasing stress, stepped decreasing stress, and stepped fluctuating loads using the corrected superposition method agree well with the experimentally measured values. Therefore, it can be concluded that the corrected superposition method under stepped increasing stress is well applicable to analyzing the creep effect of concrete structures.

Claims

1. A bridge creep strain calculation method under variable stress based on hyperbolic function modified superposition method, characterized in that, The process includes the following: The creep parameters of a concrete bridge structure are calculated using the hyperbolic function method. The creep parameters include shrinkage strain function, creep coefficient, strength, and equivalent elastic modulus. The creep compliance coefficient function and the creep recovery compliance function are calculated based on the creep parameters. Discretize the entire stress history of the concrete bridge structure to obtain the stress history discretization matrix; The total strain under each discrete history event in the stress history discrete matrix is ​​calculated using the creep compliance coefficient function, and the creep strain under each discrete history event in the stress history discrete matrix is ​​calculated using the creep recovery compliance function. The total strain and creep strain under each discrete history event are then linearly accumulated to obtain the total strain and creep strain of the concrete bridge structure throughout the entire variable stress history. Specifically, the steps include: S1, calculating the total strain and creep strain of each discrete history segment at time... The corresponding total strain and creep strain; S2, for each discrete historical segment at time... The total strain is accumulated to obtain the total strain of the concrete bridge structure throughout the entire history of alternating stress. The time t is the time at which the discrete historical segment is The corresponding creep strain is accumulated to obtain the creep strain of the concrete bridge structure in the whole stress history process. In S1: for time Located in a rectangular stress Different time periods, the calculation of the share into the following three cases: Case 1: When , then the rectangular stress history ;​​​​​ Case 2: When then the rectangular stress history is calculated as the total strain and the creep strain at time and respectively; The third scenario: When Then, the rectangular stress history For time Total strain and creep strain According to and calculate; The creep compliance coefficient function is as follows: In the formula: For concrete structures Loading at any time, corresponding The creep compliance coefficient function at time t; The creep coefficient; Concrete structure The instantaneous elastic modulus at a given moment; The creep recovery compliance function is as follows: In the formula: For concrete structures Loading at all times Uninstall at any time, corresponding Creep recovery flexibility function of concrete structure at time t; The creep restitution coefficient is given by... Calculations show that Concrete structure Loading at all times creep recovery from constant unloading; The strain of a concrete structure subjected to stress at 28 days of age is determined by... Calculated; For concrete The instantaneous elastic modulus at a given moment; The elastic modulus of concrete after 28 days.

2. The bridge creep strain calculation method under variable stress based on the hyperbolic function modified superposition method according to claim 1, characterized in that, The process of discretizing the entire stress history of the concrete structure used in the bridge structure to obtain the stress history discretization matrix includes the following steps: Step (1), initial stress vector of concrete structure By comparing the magnitudes of the elements in the vector, the initial stress vector is obtained. The maximum value of the elements in is Compare the maximum stress levels Two adjacent stress levels on the left and right and Size; Step (2), using , and A rectangular stress history matrix is ​​generated from the larger value in the matrix and the corresponding loading time. A 3×1 Remove , and The larger value in the time interval and the time corresponding to that larger value generate a new age. and the new stress vector ; Step (3), repeating Step (1) to Step (2) to obtain a stress history discrete matrix wherein, is a rectangular stress loading age vector; is a rectangular stress unloading age vector; is a rectangular stress amplitude vector.

3. The bridge creep strain calculation method under variable stress based on hyperbolic function modified superposition method according to claim 2, characterized in that, Rectangular stress history matrix ,in The historical amplitude of the rectangular stress. for The corresponding loading age, for Corresponding uninstallation age; Historical amplitude of rectangular stress Calculation and , The size relationship can be divided into the following two cases: The first scenario: When At that time, the historical amplitude of rectangular stress The generated rectangular stress history matrix is Generate a new rectangular initial age and stress matrix as follows , ; Second case: when the rectangular stress history amplitude is generated, the rectangular stress history matrix is a new rectangular initial age is generated, the new stress matrix .

4. The bridge creep strain calculation method under variable stress based on hyperbolic function modified superposition method according to claim 2, characterized in that, Stress history discrete matrix ; wherein, is a vector describing the loading, unloading age and stress amplitude of the nth rectangular stress history. is a vector describing the loading, unloading age and stress amplitude of the nth rectangular stress history.

5. A bridge creep strain calculation system based on hyperbolic function modified superposition method under varying stress, used to implement the bridge creep strain calculation method based on hyperbolic function modified superposition method under varying stress as described in any one of claims 1-4, characterized in that, include: The first calculation module is used to calculate the creep parameters of the concrete structure used in the bridge structure using the hyperbolic function method. The creep parameters include shrinkage strain function, creep coefficient, strength and equivalent elastic modulus. The second calculation module is used to calculate the creep compliance coefficient function based on the creep parameters. The third calculation module is used to calculate the creep recovery compliance function based on the creep parameters. Discrete module: used to discretize the entire stress history of the concrete structure used in the bridge structure to obtain the stress history discrete matrix; The fourth calculation module is used to calculate the total strain and creep strain under each discrete history in the stress history discrete matrix using the creep compliance coefficient function and the creep recovery compliance function. It then linearly sums the total strain and creep strain under each discrete history to obtain the creep strain of the concrete structure used in the bridge structure throughout the entire variable stress history.

6. An electronic device, comprising: include: One or more processors; A storage device on which one or more programs are stored; When the one or more programs are executed by the one or more processors, the one or more processors implement the bridge creep strain calculation method based on hyperbolic function modified superposition method under varying stress as described in any one of claims 1 to 4.

7. A storage medium, characterized by It stores a computer program, wherein when the computer program is executed by a processor, it implements the bridge creep strain calculation method based on hyperbolic function modified superposition method under variable stress as described in any one of claims 1 to 4.

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