A pseudo-static full analytical analysis method, terminal and storage medium for bridge piers

Abstract

The present invention relates to the technical field of bridge parameter prediction, and discloses a pseudo-static full analytical analysis method, a terminal and a storage medium for bridge piers. The method obtains known quantities according to the cross-sectional information of the bridge pier, and thus constructs an equation set based on the curvature distribution model; subsequently, the iterative method is used to calculate two dimensionless variables corresponding to each displacement in a known displacement vector, so as to form two known vectors corresponding to the known displacement vector; finally, the two known vectors are substituted into the equation set, so as to obtain the mapping relationship between the lateral force and the predicted displacement, that is, the skeleton curve. The present invention realizes the rapid evaluation of the seismic performance of circular ordinary reinforced concrete bridge piers, and only needs to input key information to obtain the skeleton curve, providing a simple and effective tool for scientific research.

Description

Technical Field

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

[0002] In previous studies, researchers could only obtain the skeleton curves of RC circular bridge piers through numerical simulation and experimental methods. However, large-scale experimental projects would surely cost a great deal of manpower and material resources, and the experiments were not repeatable. If there were errors in the experiments, the experimental data would be nearly scrapped. For numerical simulation methods such as the OpenSees software, although it is safer and more convenient than experiments and has modifiability, the modeling also takes a lot of time and is not friendly to beginners. In addition, to visualize the numerical simulation data, other tools are also needed, so it is rather troublesome.

[0003] In addition, there is currently another method to obtain the skeleton curve, that is, through the equivalent plastic hinge length model proposed by Priestley and Park, as Figure 1 . Based on the known moment-curvature curve, the skeleton curve known curvature can be 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. Given the known moment (M), the corresponding lateral force F can be obtained. Therefore, for each given curvature and moment, the corresponding displacement and force can be obtained, and connecting them together is the skeleton curve of the bridge pier. The calculation methods of the displacement Δ and the lateral force F are shown in Formulas 1, 2, and 3 in Table 1 below.

[0004] Table 1. Method for calculating the skeleton curve by the equivalent plastic hinge length model

[0005]

[0006]

[0007] It can be seen from Formulas 1, 2, and 3 that the calculation of the 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 prediction of the skeleton curve. Therefore, it is urgently needed to be solved. Summary of the Invention

[0008] To solve the technical problems existing in the prior art, the present invention provides a pseudo-static full analytical analysis method, a terminal and a storage medium for bridge piers. The present invention predicts the skeleton curve of the bridge pier through an analytical curvature distribution model, and realizes a method for quickly evaluating the seismic performance of circular ordinary reinforced concrete bridge piers. This method can obtain the skeleton curve only by inputting key information, 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 present invention discloses a pseudo-static full analytical analysis method for bridge piers, including the following steps, namely S1 to S3.

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

[0012]

[0013] Among them, the first equation and the second equation in the system of equations 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 bridge pier; Δ 0 represents the total displacement of the bridge pier at the position where the vertical distance from the top of the bridge pier is 0; represents the bending displacement at the top of the pier when the steel bar yields; represents the slip displacement at the top of the pier when the steel bar 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 steel bar yields; F and P respectively represent the lateral force and the vertical force applied to the bridge pier; X p 、X μ 、M H 、M Δ 、M y 、A v 、G eff 、P、H are all known quantities, and Δ 0 、X p 、X μ 、F are all unknown quantities.

[0014] S2. Use the iterative method to calculate the two dimensionless variables X 0 corresponding to each displacement in a known displacement vector Δ p and X μ , thereby constituting a vector corresponding to the known displacement vector Δ 0The corresponding two known vectors X p and X μ ; N is the number of displacements in Δ 0 .

[0015] S3. Substitute X p and X μ into the system of equations, so as 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, and there are a total of N displacements in Δ 0 , and the i-th displacement Δ 0 (i) =(i - 1)·dΔ, i = 1, 2..., N; the N-th displacement, that is, Δ 0,u is the displacement corresponding to the termination point of the skeleton curve.

[0018] S22. Obtain any displacement Δ 0 in the known displacement vector Δ 0 (i) , and initialize X 0 (i) and X p corresponding to the displacement Δ μ ; among them, the initial X p =(X p1 +X p2 ) / 2, X p1 =0, X p2 =0.5H; substitute the initial X p into the second equation, so as to obtain the initial X μ .

[0019] S23. Substitute the initial X p and the initial X μ into the first equation to obtain the predicted displacement If is greater than a preset error value ξ, then use as the termination condition for the following iterative update:

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

[0021] If the predicted displacement is greater than the 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 parameter, and the superscript "old" represents the parameter before update.

[0023] S24. Loop and execute steps S22 to S23 until each displacement corresponding to the known displacement vector Δ 0 satisfies the termination condition for the corresponding X p and X μ , thereby obtaining the known vectors X p and X μ .

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

[0025] S31. Substitute the corresponding X p and X μ in each group of the known vectors X p and X μ into the first equation in turn to obtain N predicted displacements, that is

[0026] S32. Substitute into the third equation to obtain N predicted lateral forces, that is F (1) , F (2) ,..., F (N) , thereby fitting and forming the mapping relationship between the lateral force and the predicted displacement.

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

[0028] As a further improvement of the above solution, in step S1, the cross-section information of the pier includes: the concrete compressive strength f c ′, the yield strength f y of longitudinal reinforcement, the longitudinal reinforcement ratio ρ l , the yield strength f yh of stirrups, the stirrup ratio ρ s , the pier cross-section diameter D, the pier height H, and the 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 expression of the linear function is:

[0031]

[0032] The expression of the quadratic function is:

[0033]

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

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

[0037] Compared with the prior art, the beneficial effects of the present invention are:

[0038] 1. The pseudo-static full analytical analysis method for a circular pier disclosed by the present invention is based on a pure theoretical analytical formula method, does not rely on experiments, and can obtain a skeleton curve in a short time, accelerating the progress of scientific research. It makes up for the gap in obtaining a skeleton curve from a moment-curvature curve using the analytical formula method, and only needs to know the pier structure information, with convenient and fast data input, ensuring reversibility and accuracy, and the results are more accurate.

[0039] 2. This method does not require complex modeling and data collation, and gets rid of the need for experiments to obtain a rough curvature distribution and does not need to consider the errors brought by the equivalent plastic hinge length formula. It simplifies the process of obtaining the skeleton curve of a circular pier into an analytical method that can be obtained only by inputting the parameter information of the cross-section, shortening the process of obtaining the skeleton curve. At the same time, this method has good calculation accuracy, high efficiency, simple operation, considers multiple states, and can be applied to more models.

[0040] 3. This method can be applied not only to ordinary reinforced concrete (RC) piers but also to high-strength reinforced concrete (HSRC) piers; only by inputting the key parameter information can the results be obtained, showing the simplicity and applicability of this method. Through this method, only by knowing the key information of the circular pier, its skeleton curve can be predicted, the seismic performance of the pier can be evaluated quickly and accurately, and the seismic displacement performance of the pier can be quantitatively described. In addition, there is still no method that gets rid of experiments and numerical simulations, deduces 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 way to predict 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 elaborated here. Description of the Drawings

[0042] Figure 1 It is a schematic diagram of the equivalent plastic hinge length model.

[0043] Figure 2 It is a flowchart of the pseudo-static full analytical method for the pier in Embodiment 1 of the present invention.

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

[0045] Figure 4 It is a schematic diagram of the force balance in Embodiment 1 of the present invention.

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

[0047] Figure 6 It is a schematic diagram of comparing the skeleton curve obtained by using this prediction method with the simulation results of OpenSees in Embodiment 1 of the present invention (the first group of key parameters).

[0048] Figure 7 Schematic diagram (for the 2nd set of key parameters) of comparing the backbone curve obtained by using this prediction method in Embodiment 1 of the present invention with the simulation results of OpenSees.

[0049] Figure 8 Schematic diagram (for the 3rd set of key parameters) of comparing the backbone curve obtained by using this prediction method in Embodiment 1 of the present invention with the simulation results of OpenSees.

[0050] Figure 9 Schematic diagram (for the 4th set of key parameters) of comparing the backbone curve obtained by using this prediction method in Embodiment 1 of the present invention with the simulation results of OpenSees.

[0051] Figure 10 Schematic diagram (for the 5th set of key parameters) of comparing the backbone curve obtained by using this prediction method in Embodiment 1 of the present invention with the simulation results of OpenSees.

[0052] Figure 11 Schematic diagram (for the 6th set of key parameters) of comparing the backbone curve obtained by using this prediction method in Embodiment 1 of the present invention with the simulation results of OpenSees.

[0053] Figure 12 Schematic diagram of comparing the 1st experimental hysteretic curve selected from the PEER database with this prediction method in Embodiment 1 of the present invention.

[0054] Figure 13 Schematic diagram of comparing the 2nd experimental hysteretic curve selected from the PEER database with this prediction method in Embodiment 1 of the present invention.

[0055] Figure 14 Schematic diagram of comparing the 3rd experimental hysteretic curve selected from the PEER database with this prediction method in Embodiment 1 of the present invention.

[0056] Figure 15 Schematic diagram of comparing the 4th experimental hysteretic curve selected from the PEER database with this prediction method in Embodiment 1 of the present invention.

[0057] Figure 16 Schematic diagram of comparing the 5th experimental hysteretic curve selected from the PEER database with this prediction method in Embodiment 1 of the present invention.

[0058] Figure 17 Schematic diagram of comparing the 6th experimental hysteretic curve selected from the PEER database with this prediction method in Embodiment 1 of the present invention.

[0059] Figure 18Schematic diagram for comparing the 7th experimental hysteretic curve selected from the PEER database with the present prediction method in Embodiment 1 of the present invention.

[0060] Figure 19 Schematic diagram for comparing the 8th experimental hysteretic curve selected from the PEER database with the present prediction method in Embodiment 1 of the present invention.

[0061] Figure 20 Schematic diagram for comparing the 9th experimental hysteretic curve selected from the PEER database with the present prediction method in Embodiment 1 of the present invention.

[0062] Figure 21 Schematic diagram for comparing the 10th experimental hysteretic curve selected from the PEER database with the present prediction method in Embodiment 1 of the present invention. Detailed implementation manners

[0063] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0064] Embodiment 1

[0065] This embodiment provides a pseudo-static full analytical method for bridge piers. By using a curvature distribution model based on a pure theoretical analytical formula, the skeleton curve of a circular bridge pier is predicted, and a method for rapidly evaluating the seismic performance of a circular ordinary reinforced concrete bridge pier is realized. This method can obtain the skeleton curve only by inputting key information, providing a simple and effective tool for scientific research.

[0066] This method mainly has the following two major advantages:

[0067] Advantage 1: The pure theoretical analytical formula 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 an RC circular bridge pier is generally obtained through experiments. Factors such as the high cost and irreversibility of experiments also determine that experiments are not suitable to be the main means of obtaining the skeleton curve; although finite element simulation does not require too many resources and can be modified, it is relatively difficult to start with finite element simulation and it is very inconvenient to modify parameter information. For the pure theoretical analytical formula method, only the numerical values of the cross-section information need to be changed, saving a lot of time.

[0069] Advantage 2: It makes up for the gap in obtaining the skeleton curve from the moment-curvature curve using the analytical formula method, and only the structural information of the bridge pier needs to be known, and the data input is convenient and fast, ensuring reversibility and accuracy.

[0070] Please refer to Figure 2 , the pseudo-static full-analysis method for bridge piers provided in this embodiment may include steps S1 to S3.

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

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

[0073] Please refer to Figure 3 , the present invention can propose a pseudo-static full-analysis method based on the curvature distribution model proposed by the existing method (patent number 202310987343.0). In this existing method, the curvature distribution model consists of a linear function and a quadratic function, as shown in Figure 3 (a). Among them:

[0074] The expression of the linear function is:

[0075] The expression of the quadratic function is:

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

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

[0078] i. At the junction of the linear function and the quadratic function, the curvature value is and

[0079] ii. At the bottom of the pier, that is, the end point of the quadratic function, the curvature value is

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

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

[0082] and

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

[0084] where x y is the demarcation point height (unknown) between the linear function and the quadratic function, is the curvature at the pier bottom (unknown), H is the pier height (known), is the yield curvature (known).

[0085] To reduce the number of unknowns in the curvature distribution model function, a, b, c, and d are expressed in terms of the unknown x through expressions (3), (4), and (5), y and so that the original six unknowns are reduced to two unknowns The result is:

[0086]

[0087] Next, establish the displacement equation of the pier. The total displacement (Δ) of the pier consists of the bending displacement (Δ f ), the steel bar slip (Δ b ), and the shear deformation (Δ s ):

[0088] Δ = Δ f + Δ b + Δ s (6)

[0089]

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

[0091]

[0092] where the superscript f represents the bending displacement, and the subscripts 0 and x y represent the distances 0 and x from the top of the pier yAt the position of. Thus, it can be obtained that:

[0093]

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

[0095]

[0096] As Figure 4 shown, establish the force equilibrium equation, and two expressions (16a) and (16b) can be obtained:

[0097] PΔ 0 + FH = M H (16)

[0098]

[0099] Subtract expression (16a) from expression (16b) to eliminate the variable F, and we can get:

[0100]

[0101] where M y , M H are all known quantities. Substitute expressions (14) and (15) into expression (17), and we can get:

[0102]

[0103] where, Finally, combine expressions (14), (18), and (16a) to obtain the final system of equations:

[0104]

[0105] where, the first equation and the second equation in the system of equations constitute the displacement equation of the bridge pier, and the third equation is the force equilibrium equation; X p and X μ are two dimensionless variables respectively; H represents the height of the bridge pier; Δ 0 represents the total displacement of the bridge pier at the position where the vertical distance from the top of the bridge pier is 0; represents the bending displacement at the top of the pier when the steel bar yields; represents the slip displacement at the top of the pier when the steel bar yields; A v represents the effective shear area; G effDenote the effective shear modulus; M H Denote the moment at the pier bottom; M y Denote the yield moment; M Δ Denote the external moment when the steel bars yield; F and P respectively denote the lateral force and vertical force applied to the pier; 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 all unknown quantities.

[0106] S2. Use the iterative method to calculate the two dimensionless variables X 0 corresponding to each displacement in a known displacement vector Δ p and X μ , so as to form two known vectors X 0 and X p corresponding to the known displacement vector Δ μ ; N is the number of displacements in Δ 0 .

[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, and there are a total of N displacements in Δ 0 , and the i-th displacement Δ 0 (i) =(i - 1)·dΔ, i = 1, 2…, N; the N-th displacement, i.e., Δ 0,u is the displacement corresponding to the termination point of the skeleton curve, and the termination 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 longitudinal bars, rupture of longitudinal bars, and crushing of core concrete.

[0109] S22. Obtain any displacement Δ 0 in the known displacement vector Δ 0 (i) , and initialize X 0 (i) and X p corresponding to the displacement Δ μ ; where the initial X p =(X p1 +X p2) / 2, X p1 = 0, X p2 = 0.5H; Substitute the initial X p into the second equation, thereby obtaining the initial X μ .

[0110] S23. Substitute the initial X p and the initial X μ into the first equation to obtain the predicted displacement If is greater than a preset error value ξ, then use as the termination condition to perform the following iterative update:

[0111] If the predicted displacement is not greater than the 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 is greater than the 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 parameter, and the superscript "old" represents the parameter before 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 and execute steps S22 to S23 until the X 0 corresponding to each displacement in the known displacement vector Δ p and X μ both satisfy the termination condition, thereby obtaining the known vectors X p and X μ .

[0116] S3. Take Xp and X μ Substitute into the above system of equations to obtain the mapping relationship between the lateral force and the predicted displacement, i.e., the skeleton curve.

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

[0118] S31. Substitute the known vector X p and X μ The corresponding X in each group p and X μ are successively substituted into the first equation to obtain N predicted displacements, i.e.,

[0119] S32. Substitute into the third equation to obtain N predicted lateral forces, i.e., F (1) , F (2) ,..., F (N) , thereby fitting to form the mapping relationship between the lateral force and the predicted displacement.

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

[0121] As Figure 5 shown, the information that can be obtained is: the skeleton curve of the RC circular pier, and the termination point is one of the buckling of longitudinal bars, the longitudinal bars being pulled off, and the core concrete being crushed.

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

[0123] 1. Parameter information of the example

[0124] The comparison model was established using OpenSees. The model has a circular reinforced concrete cross-section with a diameter D of 1.2 m and a pier height H of 6 m. C50 concrete and HRB400 steel bars were selected, i.e., f c ′ is 32.4 MPa, f y and f yh is 360 MPa, the longitudinal reinforcement ratio ρ l is 2.0%, the stirrup ratio ρ s is 1.0%, the axial compression ratio R ac is 0.1. The termination points of the skeleton curves compared with OpenSees are all selected when the core concrete is crushed. The values of 6 key parameters are changed respectively, and then the skeleton curves obtained by the method proposed in the present invention are compared with the simulation results of OpenSees. The results show that the prediction accuracy of this method for the skeleton curve is very high, and the results are as Figures 6 to 11 shown.

[0125] 2. Parameter information of the PEER experiment

[0126] Ten experimental hysteretic curves in the PEER database were selected and compared with the pseudo-static full analytical analysis method of the pier proposed in the present invention. The parameter information of each experiment is listed in Table 2, and the comparison situation is as Figures 12 to 21 shown. It can be seen that the prediction effect is good and can be used in scientific research.

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

[0128]

[0129] In summary, compared with the prior art, the pseudo-static full analytical analysis method of the pier provided in this embodiment has the following advantages:

[0130] This method is based on a pure 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 makes up for 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, and the data input is convenient and fast, ensuring reversibility and accuracy, 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 brought by the equivalent plastic hinge length formula. It simplifies the process of obtaining the skeleton curve of a circular pier into an analytical method that only needs to input the parameters of the cross-section information to obtain, shortening the process of obtaining the skeleton curve. At the same time, this method has good calculation accuracy, high efficiency, simple operation, considers multiple states, and can be applied to more models.

[0132] This method can be applied not only in ordinary reinforced concrete (RC) bridge piers, but also in high-strength reinforced concrete (HSRC) bridge piers; only by inputting key parameter information can the results be obtained, showing the simplicity and applicability of the method. Through this method, only by knowing the key information of a circular bridge pier can its skeleton curve be predicted, the seismic performance of the bridge pier be evaluated quickly and accurately, and the seismic displacement performance of the bridge pier be quantitatively described. In addition, there is still no method that can derive the moment-curvature curve from the theoretical level and obtain the skeleton curve through the analytical method without relying on experiments and numerical simulations. The present invention fills this gap and proposes a new way to predict the skeleton curve.

[0133] Example 2

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

[0135] The computer terminal can be a smart phone, a tablet computer, a notebook computer, etc. that can execute programs. In some embodiments, the processor can be a Central Processing Unit (CPU), a controller, a microcontroller, a microprocessor, or other data processing chips. 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 pseudo-static full analytical analysis method of the bridge pier in Embodiment 1 are implemented.

[0136] Example 3

[0137] This embodiment provides 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 the bridge pier in Embodiment 1 are implemented.

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

[0139] As described above, only the preferred specific embodiments of the present invention are provided, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention, according to the technical solution and inventive concept of the present invention, makes equivalent substitutions or changes, and 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 Substituting into the equation group, the mapping relationship between the lateral force and the predicted displacement is obtained, that is, the skeleton curve of the pier; 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.

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 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 in 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 the mapping relationship between the lateral force and the 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. 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 5 are implemented.

7. 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 5 are implemented.

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