Quasi-static full-analytic analysis method for bridge pier, terminal and storage medium

Abstract

The invention relates to the technical field of bridge parameter prediction, and discloses a quasi-static full-analytic analysis method for a pier, a terminal and a storage medium. According to the method, a known quantity is acquired according to section information of a pier, so that an equation set is constructed based on a curvature distribution model; then calculating two dimensionless variables corresponding to each displacement in a known displacement vector by using an iteration method, thereby forming two known vectors corresponding to the known displacement vector; and finally, two known vectors are substituted into the equation set, so that the mapping relation between the transverse force and the predicted displacement, namely the skeleton curve, is obtained. According to the invention, rapid evaluation of the anti-seismic performance of the round common reinforced concrete pier is realized, the skeleton curve can be obtained only by inputting key information, and a simple and effective tool is provided for scientific research.

Description

Technical Field

[0001] The present invention relates to the technical field of bridge parameter prediction, and in particular to a quasi-static full analytical analysis method, a terminal and a storage medium for a bridge pier. Background Art

[0002] In previous studies, researchers could only obtain the skeleton curve of RC circular bridge piers through numerical simulation and experimental methods, but large-scale experimental projects will inevitably cost a lot of manpower and material resources, and the experiments are not repeatable. If errors occur in the experiments, the experimental data will be scrapped. Numerical simulation methods such as OpenSees software are safer and more convenient than experiments, and are modifiable, but modeling will also take a lot of time and is not friendly to beginners. In addition, other tools are needed to visualize the numerical simulation data, which is also troublesome.

[0003] In addition, there is another method to obtain the skeleton curve, which is the equivalent plastic hinge length model proposed by Priestley and Park, such as Figure 1 This method is based on the known moment-curvature curve, and the known curvature of the skeleton curve is obtained through the equivalent plastic hinge length model. Yield curvature Equivalent plastic hinge length (L p ) and some cross-sectional information, the corresponding displacement Δ can be obtained. If the bending moment (M) is known, the corresponding lateral force F can be obtained. Therefore, for each given curvature and bending moment, the corresponding displacement and force can be obtained. Together, they form the skeleton curve of the pier. The displacement Δ and lateral force F are calculated as shown in Formulas 1, 2 and 3 in Table 1.

[0004] Table 1. Skeleton curve calculation method of equivalent plastic hinge length model

[0005]

[0006]

[0007] It can be seen from formulas 1, 2 and 3 that the calculation of displacement is closely related to the equivalent plastic hinge length. However, the current calculation methods of the equivalent plastic hinge length are different, and the calculated results are also different, which leads to the inaccuracy of the skeleton curve prediction, and therefore needs to be solved urgently. Summary of the invention

[0008] In order to solve the technical problems existing in the prior art, the present invention provides a quasi-static fully analytical analysis method, terminal and storage medium for bridge piers. The present invention predicts the skeleton curve of the bridge pier through an analytical curvature distribution model, thereby realizing a method for rapid evaluation of the seismic performance of circular ordinary reinforced concrete bridge piers. This method only requires the input of key information to obtain the skeleton curve, providing a simple and effective tool for scientific research.

[0009] To achieve the above object, the present invention provides the following technical solutions:

[0010] The invention discloses a pseudo-static full analytical analysis method for a bridge pier, comprising the following steps, namely S1 to S3.

[0011] S1. Obtain known quantities based on the cross-sectional information of the bridge pier, and then construct a set of equations based on the curvature distribution model:

[0012]

[0013] Among them, the first and second equations in the equation group constitute the displacement equation of the bridge pier, and the third equation is the force balance equation; X p and X μ are two dimensionless variables; H represents the height of the pier; Δ 0 It represents the total displacement of the pier at the position where the vertical distance from the top of the pier is 0; It indicates the bending displacement of the pier top when the reinforcement yields; Indicates the sliding displacement of the pier top when the reinforcement yields; A v Represents the effective shear area; G eff Represents the effective shear modulus; M H Represents the bending moment at the bottom of the pier; M y Represents the yield moment; M Δ represents the external moment when the reinforcement yields; F and P represent the lateral force and vertical force applied to the pier, respectively; X p , X μ 、M H 、M Δ 、M y , A v , G eff , P, H are all known quantities, Δ 0 , X p , X μ , F are both unknown quantities.

[0014] S2. Calculate a known displacement vector Δ using the iterative method 0 Each displacement in the two dimensionless variables X p and X μ , thus forming a known displacement vector Δ 0The corresponding two known vectors X p and X μ ; N is Δ 0 The number of displacements in .

[0015] S3. X p and X μ Substitute into the equation group to obtain the mapping relationship between the lateral force and the predicted displacement, that is, the skeleton curve.

[0016] As a further improvement of the above solution, step S2 includes the following specific steps:

[0017] S21. Define the known displacement vector Δ 0 =[0,dΔ,2dΔ,...,Δ 0,u ]; where dΔ is the preset minimum displacement unit, Δ 0 There are N displacements in total, and the i-th displacement Δ 0 (i) =(i-1)·dΔ, i=1,2…,N; the Nth displacement is Δ 0,u is the displacement corresponding to the end point of the skeleton curve.

[0018] S22. Obtain known displacement vector Δ 0 Any displacement Δ 0 (i) , and initialize the displacement Δ 0 (i) Corresponding X p and X μ ; Among them, the initial X p =(X p1 +X p2 ) / 2,X p1 =0,X p2 =0.5H; the initial X p Substituting into the second equation, we get the initial X μ .

[0019] S23. Set the initial X p and initial X μ Substituting into the first equation, we get the predicted displacement like If the error is greater than a preset error value ξ, The following iterative updates are performed as termination conditions:

[0020] If the predicted displacement Not greater than displacement Δ 0 (i) , let X p1 新 =Xp 旧 , X p 新 =(X p1 新 +X p2 旧 ) / 2;

[0021] If the predicted displacement Greater than displacement Δ 0 (i) , let X p2 新 =X p 旧 , X p 新 =(X p1 旧 +X p2 新 ) / 2;

[0022] In the formula, the superscript “new” represents the updated parameters, and the superscript “old” represents the parameters before the update.

[0023] S24. Loop through steps S22 to S23 until the displacement vector Δ is known. 0 The X corresponding to each displacement in p and X μ All satisfy the termination condition, thus obtaining the known vector X p and X μ .

[0024] As a further improvement of the above solution, step S3 includes the following specific steps:

[0025] S31. The known vector X p and X μ The X corresponding to each group p and X μ Substituting into the first equation in turn, we get N predicted displacements, namely

[0026] S32. Substituting into the third equation, we get N predicted lateral forces, namely F (1) ,F (2) ,...,F (N) , thereby fitting the mapping relationship between the lateral force and the predicted displacement.

[0027] As a further improvement of the above solution, in step S21, the end point of the skeleton curve is determined by a defined ultimate damage state, and the definition of the ultimate damage state includes three criteria: buckling of the longitudinal reinforcement, breaking of the longitudinal reinforcement, and crushing of the core concrete.

[0028] As a further improvement of the above solution, in step S1, the cross-sectional information of the bridge pier includes: concrete compressive strength f c ', longitudinal reinforcement yield strength f y , longitudinal reinforcement ratio ρ l , stirrup yield strength f yh , stirrup reinforcement ratio ρ s , pier cross-sectional diameter D, pier height H, axial compression ratio R ac .

[0029] As a further improvement of the above solution, in step S1, the curvature distribution model is composed of a linear function and a quadratic function.

[0030] Among them, the linear function expression is:

[0031]

[0032] The quadratic function expression is:

[0033]

[0034] In the formula, x represents the height, i.e., the vertical distance between the first pier position and the top of the pier; represents the curvature value at x; a, b, c, d are all coefficients, and in, is the yield curvature, x y is the height of the dividing point between the linear function and the quadratic function, is the curvature of the pier bottom.

[0035] The present invention also discloses a computer terminal, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps of the pseudo-static full analytical analysis method of a bridge pier as described above are implemented.

[0036] The present invention also discloses a computer-readable storage medium on which a computer program is stored. When the program is executed by a processor, the steps of the pseudo-static full analytical analysis method of a bridge pier as described above are implemented.

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] 1. The quasi-static full analytical analysis method of circular bridge piers disclosed in the present invention is based on a purely theoretical analytical method, does not rely on experiments, and obtains the skeleton curve in a short time, accelerating the progress of scientific research. It makes up for the vacancy of obtaining the skeleton curve by the analytical method from the bending moment curvature curve, and only needs to know the pier structure information, the data input is convenient and fast, the reversibility and accuracy are guaranteed, and the results are more accurate.

[0039] 2. This method does not require complicated modeling and data collation, and gets rid of the need for experiments to obtain the approximate curvature distribution and does not need to consider the error caused by the equivalent plastic hinge length formula. It simplifies the skeleton curve of the circular pier into an analytical method that only requires the input of cross-sectional information parameters, shortening the process of obtaining the skeleton curve. At the same time, this method has good calculation accuracy and efficiency, simple operation, and considers many states, and can be applied to more models.

[0040] 3. This method can be applied not only to ordinary reinforced concrete (RC) bridge piers, but also to high-strength reinforced concrete (HSRC) bridge piers; only key parameter information needs to be input to obtain the results, which shows the simplicity and applicability of the method. Through this method, only the key information of the circular pier needs to be known to predict its skeleton curve, quickly and accurately evaluate the seismic performance of the pier, and quantitatively describe the seismic displacement performance of the pier. In addition, there is still no method that gets rid of experiments and numerical simulations, derives the moment curvature curve from the theoretical level, and obtains the skeleton curve through analytical methods. The present invention fills this gap and proposes a new method for predicting the skeleton curve.

[0041] 4. The computer terminal and computer-readable storage medium disclosed in the present invention can apply the above method and can produce the same beneficial effects as the above method, which will not be repeated here. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 Schematic diagram of the equivalent plastic hinge length model.

[0043] Figure 2 It is a flow chart of the quasi-static full analytical analysis method of the bridge pier in Example 1 of the present invention.

[0044] Figure 3 Schematic diagram of the curvature distribution model proposed by the existing method (patent number 202310987343.0).

[0045] Figure 4 Schematic diagram of force balance in Example 1 of the present invention.

[0046] Figure 5 It is a schematic diagram of the RC circular pier skeleton curve obtained in Example 1 of the present invention.

[0047] Figure 6 Schematic diagram of comparison between the skeleton curve obtained by the prediction method in Example 1 of the present invention and the simulation result of OpenSees (first group of key parameters).

[0048] Figure 7 It is a schematic diagram comparing the skeleton curve obtained by the prediction method in Example 1 of the present invention with the simulation result of OpenSees (the second group of key parameters).

[0049] Figure 8 Schematic diagram of comparison between the skeleton curve obtained by the prediction method in Example 1 of the present invention and the simulation result of OpenSees (the third group of key parameters).

[0050] Fig. 9 Schematic diagram of comparison between the skeleton curve obtained by the prediction method in Example 1 of the present invention and the simulation result of OpenSees (the fourth group of key parameters).

[0051] Fig.10 Schematic diagram of comparison between the skeleton curve obtained by the prediction method in Example 1 of the present invention and the simulation result of OpenSees (the fifth group of key parameters).

[0052] Fig.11 It is a schematic diagram comparing the skeleton curve obtained by the prediction method in Example 1 of the present invention with the simulation result of OpenSees (the sixth group of key parameters).

[0053] Fig.12 This is a schematic diagram for comparing the first experimental hysteresis curve in the PEER database selected in Example 1 of the present invention with the prediction method.

[0054] Fig.13 This is a schematic diagram for comparing the second experimental hysteresis curve in the PEER database selected in Example 1 of the present invention with the prediction method.

[0055] Fig.14 This is a schematic diagram for comparing the third experimental hysteresis curve in the PEER database selected in Example 1 of the present invention with the prediction method.

[0056] Fig.15 This is a schematic diagram for comparing the fourth experimental hysteresis curve in the PEER database selected in Example 1 of the present invention with the prediction method.

[0057] Fig.16 This is a schematic diagram for comparing the fifth experimental hysteresis curve in the PEER database selected in Example 1 of the present invention with the prediction method.

[0058] Fig.17 This is a schematic diagram for comparing the sixth experimental hysteresis curve in the PEER database selected in Example 1 of the present invention with the prediction method.

[0059] Fig.18This is a schematic diagram for comparing the seventh experimental hysteresis curve in the PEER database selected in Example 1 of the present invention with the prediction method.

[0060] Fig.19 This is a schematic diagram for comparing the eighth experimental hysteresis curve in the PEER database selected in Example 1 of the present invention with the prediction method.

[0061] Fig. 20 This is a schematic diagram for comparing the 9th experimental hysteresis curve in the PEER database selected in Example 1 of the present invention with the prediction method.

[0062] Fig.21 This is a schematic diagram for comparing the 10th experimental hysteresis curve in the PEER database selected in Example 1 of the present invention with the prediction method. DETAILED DESCRIPTION

[0063] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0064] Example 1

[0065] This embodiment provides a quasi-static fully analytical analysis method for bridge piers. Through a purely theoretical analytical curvature distribution model, the skeleton curve of the circular pier is predicted, thereby realizing a method for rapid evaluation of the seismic performance of circular ordinary reinforced concrete piers. This method only requires the input of key information to obtain the skeleton curve, providing a simple and effective tool for scientific research.

[0066] This method has the following two main advantages:

[0067] Advantage 1: The purely theoretical analytical method does not rely on experiments and can obtain the skeleton curve in a short time, accelerating the progress of scientific research.

[0068] The skeleton curve of RC circular piers is usually obtained in experiments. The high cost and irreversibility of experiments also determine that experiments should not be the main means of obtaining skeleton curves. Although finite element simulation can be modified without consuming too many resources, it is difficult to get started with finite element simulation and it is very inconvenient to modify parameter information. For the purely theoretical analytical method, only the numerical value of the cross-section information needs to be changed, which saves a lot of time.

[0069] Advantage 2: It makes up for the vacancy of obtaining the skeleton curve by the analytical method from the moment curvature curve, and only needs to know the pier structure information, the data input is convenient and fast, and the reversibility and accuracy are guaranteed.

[0070] See also Figure 2 The pseudo-static full analytical analysis method for bridge piers provided in this embodiment may include steps S1 to S3.

[0071] S1. Obtain known quantities based on the cross-sectional information of the bridge pier, and then construct a set of equations based on the curvature distribution model. The specific process is as follows:

[0072] According to the existing method (patent number 202110708968.X), the moment-curvature curve can be quickly obtained by inputting the cross-section information, and the end point of the moment-curvature curve is defined according to three standards (which are also the definition of the end point of the skeleton curve, and the two are the same): buckling of the longitudinal reinforcement, breaking of the longitudinal reinforcement, crushing of the core concrete, and setting the curvature value corresponding to the end point of the moment-curvature curve as Set the displacement corresponding to the end point of the skeleton curve to Δ 0, .

[0073] See also Figure 3 The present invention can be based on the curvature distribution model proposed by the existing method (patent number 202310987343.0) and then propose a quasi-static full analytical analysis method. In the existing method, the curvature distribution model is composed of a linear function and a quadratic function, such as Figure 3 (a), where:

[0074] The linear function expression is:

[0075] The quadratic function expression is:

[0076] Where a, b, c, d are the coefficients of the curvature distribution model function (unknown).

[0077] The above curvature distribution model needs to meet the following conditions to ensure the continuity of the function:

[0078] i. The curvature value at the junction of the linear function and the quadratic function is and

[0079] ii. The curvature value at the end point of the quadratic function at the bottom of the pier is

[0080] iii. The left and right derivatives are equal at the junction:

[0081] Then substitute the three conditions i, ii, and iii into expressions (1) and (2) to obtain:

[0082] and

[0083] a=2bx y +c (5)

[0084] Among them, x y is the height of the dividing point between the linear function and the quadratic function (unknown), is the curvature of the pier bottom (unknown), H is the height of the pier (known), is the yield curvature (known).

[0085] In order to reduce the number of unknowns in the curvature distribution model function, a, b, c, d are replaced by x containing unknowns through expressions (3), (4) and (5). y and In this way, the original six unknowns Reduced to two unknowns The result is:

[0086]

[0087] Then the displacement equation of the bridge pier is established. The total displacement of the bridge pier (Δ) is calculated from the bending displacement (Δ f ), steel bar slip (Δ b ) and shear deformation (Δ s )composition:

[0088] Δ=Δ f +Δ b +Δ s (6)

[0089]

[0090] Among them, d b is the diameter of the longitudinal reinforcement, f s is the stress of the longitudinal reinforcement, τ is taken M H is the bending moment at the bottom of the pier, A v Take 0.85 times the area of ​​the circular pier, G eff Take 0.5 times the elastic modulus (these variables are all known). Substituting the curvature distribution model function into the bending displacement deformation formula yields:

[0091]

[0092] The superscript f represents the bending displacement, and the subscripts 0 and x y Indicates the distance from the top of the pier 0 and x y At the position of . Therefore, we can get:

[0093]

[0094] Define dimensionless variables: (The unknown quantity x y and Convert to unknown quantity X p and X μ ); Then expressions (12) and (13) can be transformed into:

[0095]

[0096] like Figure 4 As shown, by establishing the force balance equation, we can obtain two expressions (16a) and (16b):

[0097] PΔ 0 +FH=M H (16)

[0098]

[0099] Subtracting expression (16a) from expression (16b) and eliminating variable F yields:

[0100]

[0101] Among them, M y 、M H All are known quantities. Substituting expressions (14) and (15) into expression (17) yields:

[0102]

[0103] in, Finally, combining expressions (14), (18), and (16a) yields the final set of equations:

[0104]

[0105] Among them, the first and second equations in the equation group constitute the displacement equation of the bridge pier, and the third equation is the force balance equation; X p and X μ are two dimensionless variables; H represents the height of the pier; Δ 0 It represents the total displacement of the pier at the position where the vertical distance from the top of the pier is 0; It indicates the bending displacement of the pier top when the reinforcement yields; Indicates the sliding displacement of the pier top when the reinforcement yields; A v Represents the effective shear area; G eff Represents the effective shear modulus; M HRepresents the bending moment at the bottom of the pier; M y Represents the yield moment; M Δ represents the external moment when the reinforcement yields; F and P represent the lateral force and vertical force applied to the pier, respectively; X p , X μ 、M H 、M Δ 、M y , A v , G eff , P, H are all known quantities, Δ 0 , X p , X μ , F are both unknown quantities.

[0106] S2. Calculate a known displacement vector Δ using the iterative method 0 Each displacement in the two dimensionless variables X p and X μ , thus forming a known displacement vector Δ 0 The corresponding two known vectors X p and X μ ; N is Δ 0 The number of displacements in .

[0107] Specifically, step S2 may include steps S21 to S24.

[0108] S21. Define the known displacement vector Δ 0 =[0,dΔ,2dΔ,...,Δ 0,u ]; where dΔ is the preset minimum displacement unit, Δ 0 There are N displacements in total, and the i-th displacement Δ 0 (i) =(i-1)·dΔ, i=1,2…,N; the Nth displacement is Δ 0,u is the displacement corresponding to the end point of the skeleton curve, and the end point of the skeleton curve is determined by the defined ultimate damage state, and the definition of the ultimate damage state includes three criteria: buckling of the longitudinal reinforcement, breaking of the longitudinal reinforcement, and crushing of the core concrete.

[0109] S22. Obtain known displacement vector Δ 0 Any displacement Δ 0 (i) , and initialize the displacement Δ 0 (i) Corresponding X p and X μ ; Among them, the initial X p =(X p1 +X p2 ) / 2,Xp1 =0,X p2 =0.5H; the initial X p Substituting into the second equation, we get the initial X μ .

[0110] S23. Set the initial X p and initial X μ Substituting into the first equation, we get the predicted displacement like If the error is greater than a preset error value ξ, The following iterative updates are performed as termination conditions:

[0111] If the predicted displacement Not greater than displacement Δ 0 (i) , let X p1 新 =X p 旧 , X p 新 =(X p1 新 +X p2 旧 ) / 2;

[0112] If the predicted displacement Greater than displacement Δ 0 (i) , let X p2 新 =X p 旧 , X p 新 =(X p1 旧 +X p2 新 ) / 2;

[0113] In the formula, the superscript “new” represents the updated parameters, and the superscript “old” represents the parameters before the update.

[0114] In this embodiment, the error value ξ can be defined as 10 -6 In other embodiments, it can also be defined as other values ​​according to requirements.

[0115] S24. Loop through steps S22 to S23 until the displacement vector Δ is known. 0 The X corresponding to each displacement in p and X μ All satisfy the termination condition, thus obtaining the known vector X p and X μ .

[0116] S3. Xp and X μ Substitute into the equation group to obtain the mapping relationship between the lateral force and the predicted displacement, that is, the skeleton curve.

[0117] Specifically, step S3 may include steps S31 to S32.

[0118] S31. The known vector X p and X μ The X corresponding to each group in p and X μ Substituting into the first equation in turn, we get N predicted displacements, namely

[0119] S32. Substituting into the third equation, we get N predicted lateral forces, namely F (1) ,F (2) ,...,F (N) , thereby fitting the mapping relationship between the lateral force and the predicted displacement.

[0120] In the present invention, the key parameter information that needs to be input includes: concrete compressive strength (f c ′: concrete compressive strength), longitudinal reinforcement yield strength (f y :yield strength of longitudinal bar), longitudinal reinforcement ratio (ρ l :longitudinal bar ratio), stirrup yield strength (f yh :yield strength of stirrup), stirrup reinforcement ratio (ρ s :stirrup ratio)、bridge pier section diameter(D:section diameter)、bridge pier height(H:column height)、axial compression ratio(R ac :axial-load ratio).

[0121] like Figure 5 As shown, the information that can be obtained is: the skeleton curve of the RC circular pier, the termination point is reaching the buckling of the longitudinal reinforcement, the longitudinal reinforcement is broken, and the core concrete is crushed.

[0122] This embodiment also provides the following comparative experiment:

[0123] 1. Parameter information of the case

[0124] OpenSees was used to build a comparison model. The model was a circular reinforced concrete section with a diameter of 1.2 m and a pier height of 6 m. C50 concrete and HRB400 steel bars were used, i.e., f c ' is 32.4MPa, f y and f yh is 360MPa, and the longitudinal reinforcement ratio ρ l is 2.0%, and the stirrup ratio ρ s 1.0%, axial pressure ratio R ac The value of the six key parameters is changed respectively, and then the skeleton curve obtained by the method proposed in the present invention is compared with the simulation results of OpenSees. The results show that the prediction accuracy of the skeleton curve by this method is very high. Figures 6 to 11 shown.

[0125] 2. Parameter information of PEER experiment

[0126] Ten experimental hysteresis curves from the PEER database were selected for comparison with the quasi-static full analytical analysis method for bridge piers proposed in this invention. The parameter information of each experiment is listed in Table 2. Figures 12 to 21 As shown, it can be seen that the prediction effect is good and can be used in scientific research.

[0127] Table 2. Parameter information of experiments selected from the PEER database

[0128]

[0129] In summary, compared with the prior art, the quasi-static full analytical analysis method for bridge piers provided in this embodiment has the following advantages:

[0130] This method is based on a purely theoretical analytical method, does not rely on experiments, and can obtain the skeleton curve in a short time, accelerating the progress of scientific research. It fills the gap in obtaining the skeleton curve from the moment curvature curve using the analytical method, and only needs to know the pier structure information, the data input is convenient and fast, and the reversibility and accuracy are guaranteed, and the results are more accurate.

[0131] In addition, this method does not require complex modeling and data collation, and gets rid of the need for experiments to obtain the approximate curvature distribution and does not need to consider the error caused by the equivalent plastic hinge length formula. It simplifies the skeleton curve of the circular pier into an analytical method that only needs to input the parameters of the cross-sectional information, shortening the process of obtaining the skeleton curve. At the same time, this method has good calculation accuracy and high efficiency, simple operation, and considers many states, and can be applied to more models.

[0132] This method can be applied not only to ordinary reinforced concrete (RC) bridge piers, but also to high-strength reinforced concrete (HSRC) bridge piers; only key parameter information needs to be input to obtain the result, which shows the simplicity and applicability of the method. Through this method, only the key information of the circular pier needs to be known to predict its skeleton curve, quickly and accurately evaluate the seismic performance of the pier, and quantitatively describe the seismic displacement performance of the pier. In addition, there is still no method that gets rid of experiments and numerical simulations, derives the moment curvature curve from the theoretical level, and obtains the skeleton curve through the analytical method. The present invention fills this gap and proposes a new method for predicting the skeleton curve.

[0133] Example 2

[0134] This embodiment provides a computer terminal, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor.

[0135] The computer terminal may be a smart phone, tablet computer, laptop computer, etc. capable of executing programs. In some embodiments, the processor may be a central processing unit (CPU), a controller, a microcontroller, a microprocessor, or other data processing chip. The processor is generally used to control the overall operation of the computer device. In this embodiment, the processor is used to run the program code stored in the memory or process data. When the processor executes the program, the steps of the quasi-static full analytical analysis method of the bridge pier in Example 1 are implemented.

[0136] Example 3

[0137] This embodiment provides a computer-readable storage medium having a computer program stored thereon. When the program is executed by a processor, the steps of the pseudo-static full analytical analysis method of the bridge pier in Embodiment 1 are implemented.

[0138] The computer-readable storage medium may include flash memory, hard disk, multimedia card, card-type memory (e.g., SD or DX memory, etc.), random access memory (RAM), static random access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic memory, disk, optical disk, etc. In some embodiments, the storage medium may be an internal storage unit of a computer device, such as a hard disk or memory of the computer device. In other embodiments, the storage medium may also be an external storage device of a computer device, such as a plug-in hard disk equipped on the computer device, a smart memory card (Smart Media Card, SMC), a secure digital (Secure Digital, SD) card, a flash card (Flash Card), etc. Of course, the storage medium may also include both an internal storage unit of a computer device and an external storage device thereof. In this embodiment, the memory is generally used to store an operating system and various application software installed on the computer device, etc. In addition, the memory may also be used to temporarily store various types of data that have been output or are to be output.

[0139] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A pseudo-static full analytical analysis method for bridge piers, characterized in that: The following steps are involved: S1. Obtain known quantities based on the cross-sectional information of the bridge pier, and then construct a set of equations based on the curvature distribution model: Among them, the first and second equations in the equation group constitute the displacement equation of the bridge pier, and the third equation is the force balance equation; X p and X μ are two dimensionless variables respectively; H represents the height of the pier; Δ0 represents the total displacement of the pier at a position where the vertical distance from the top of the pier is 0; It indicates the bending displacement of the pier top when the reinforcement yields; Indicates the sliding displacement of the pier top when the reinforcement yields; A v Represents the effective shear area; G eff Represents the effective shear modulus; M H Represents the bending moment at the bottom of the pier; M y Represents the yield moment; M Δ represents the external moment when the reinforcement yields; F and P represent the lateral force and vertical force applied to the pier, respectively; X p , X μ 、M H 、M Δ 、M y , A v , G eff , P, H are all known quantities, Δ0, X p , X μ , F are unknown quantities; S2. Use the iterative method to calculate the two dimensionless variables X corresponding to each displacement in a known displacement vector Δ0 p and X μ , thus forming two known vectors X corresponding to the known displacement vector Δ0 p and X μ ; N is the number of displacements in Δ0; S3. X p and X μ Substitute into the equation group to obtain the mapping relationship between the lateral force and the predicted displacement, that is, the skeleton curve.

2. The quasi-static full analytical analysis method for bridge piers according to claim 1 is characterized in that: Step S2 includes the following specific steps: S21. Define the known displacement vector Δ0 = [0, dΔ, 2dΔ, ..., Δ 0,u ]; where dΔ is the preset minimum displacement unit, there are a total of N displacements in Δ0, and the i-th displacement Δ0 (i) =(i-1)·dΔ, i=1,2…,N; the Nth displacement is Δ 0,u is the displacement corresponding to the end point of the skeleton curve; S22. Obtain any displacement Δ0 in the known displacement vector Δ0 (i) , and initialize the displacement Δ0 (i) Corresponding X p and X μ ; Among them, the initial X p =(X p1 +X p2 ) / 2,X p1 =0,X p2 =0.5H; the initial X p Substituting into the second equation, we get the initial X μ ; S23. Set the initial X p and initial X μ Substituting into the first equation, we get the predicted displacement like If the error is greater than a preset error value ξ, The following iterative updates are performed as termination conditions: If the predicted displacement No more than displacement Δ0 (i) , let X p1 新 =X p 旧 , X p 新 =(X p1 新 +X p2 旧 ) / 2; If the predicted displacement Greater than displacement Δ0 (i) , let X p2 新 =X p 旧 , X p 新 =(X p1 旧 +X p2 新 ) / 2; In the formula, the superscript "new" represents the updated parameters, and the superscript "old" represents the parameters before the update; S24. Loop through steps S22 to S23 until the X values ​​corresponding to the displacements in the displacement vector Δ0 are known. p and X μ All satisfy the termination condition, thus obtaining the known vector X p and X μ .

3. The quasi-static full analytical analysis method for bridge piers according to claim 2 is characterized in that: Step S3 includes the following specific steps: S31. The known vector X p and X μ The X corresponding to each group p and X μ Substituting into the first equation in turn, we get N predicted displacements, namely S32. Substituting into the third equation, we get N predicted lateral forces, namely F (1) ,F (2) ,...,F (N) , thereby fitting and forming a mapping relationship between lateral force and predicted displacement.

4. The quasi-static full analytical analysis method for bridge piers according to claim 2 is characterized in that: In step S21, the end point of the skeleton curve is determined by a defined ultimate damage state, wherein the definition of the ultimate damage state includes three criteria: buckling of the longitudinal reinforcement, breaking of the longitudinal reinforcement, and crushing of the core concrete.

5. The quasi-static full analytical analysis method for bridge piers according to claim 1 is characterized in that: In step S1, the cross-sectional information of the bridge pier includes: concrete compressive strength f c ', longitudinal reinforcement yield strength f y , longitudinal reinforcement ratio ρ l , stirrup yield strength f yh , stirrup reinforcement ratio ρ s , pier cross-sectional diameter D, pier height H, axial compression ratio R ac .

6. The quasi-static full analytical analysis method for bridge piers according to claim 1 is characterized in that: In step S1, the curvature distribution model is composed of a linear function and a quadratic function; Among them, the linear function expression is: The quadratic function expression is: In the formula, x represents the height, i.e., the vertical distance between the first pier position and the top of the pier; represents the curvature value at x; a, b, c, d are all coefficients, and in, is the yield curvature, x y is the height of the dividing point between the linear function and the quadratic function, is the curvature of the pier bottom.

7. A computer terminal comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the steps of the pseudo-static full analytical analysis method for a bridge pier as described in any one of claims 1 to 6 are implemented.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of a pseudo-static full analytical analysis method for a bridge pier as claimed in any one of claims 1 to 6 are implemented.

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