A numerical calculation method for the compressive bearing and deformation of high-strength reinforced concrete columns

Abstract

The present invention relates to the field of construction, and specifically to a numerical calculation method for the compressive bearing and deformation of high-strength reinforced concrete columns, comprising the following steps: S1, continuously changing the strain values of the high-strength steel bar eccentrically compressed column away from the axial force side and the adjacent axial force side, wherein each strain away from the axial force side and the strain adjacent to the axial force side constitute a set of strain pairs; S2, inversely calculating the axial force, bending moment, and curvature of the column cross section under the corresponding state based on the strain pairs; S3, screening effective strain pairs, and optimizing the remaining strain pair data as a data set; S4, calculating the ultimate bearing capacity or lateral deformation displacement of the column under different states based on the data set. The present invention provides an accurate and efficient calculation method for calculating the ultimate bearing capacity and lateral deformation displacement of a high-strength steel bar eccentrically compressed column.

Description

Technical Field

[0001] The present invention relates to the field of construction, and in particular to a numerical calculation method for compressive bearing and deformation of high-strength reinforced concrete columns. Background Art

[0002] Rebar, the primary material in concrete structures, is consumed in significant quantities in various infrastructure projects. To reduce rebar consumption and meet the requirements of green and low-carbon development in the construction industry, high-strength rebar has been widely adopted in the construction sector. Due to its higher yield strength and tensile strength, high-strength rebar requires a smaller cross-sectional area for the same structural load-bearing capacity. For this reason, 500MPa high-strength rebar has been included in the Code for Design of Concrete Structures (GB 50010-2010 (2015 edition)) in China, and its use is encouraged wherever possible.

[0003] With the increasing popularity of high-strength steel bars in actual engineering, the use of eccentrically compressed columns with high-strength steel bars is also becoming increasingly widespread. For the eccentric compression design of eccentrically compressed columns with high-strength steel bars, it is often necessary to use ABAQUS software in combination with material nonlinearity, geometric nonlinearity (large deformation) and boundary conditions to calculate the ultimate bearing capacity and specific values of lateral deformation displacement of the eccentrically compressed columns with high-strength steel bars. The software calculation has many parameter settings, high computing platform requirements, long calculation time, and insufficient efficiency, which needs to be solved urgently. Summary of the Invention

[0004] To avoid and overcome the technical problems existing in the prior art, the present invention provides a numerical calculation method for the compressive bearing capacity and deformation of high-strength reinforced concrete columns. The present invention provides an accurate and efficient method for calculating the ultimate bearing capacity and lateral deformation displacement of eccentrically compressed columns made of high-strength reinforced steel.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] A numerical calculation method for compressive bearing and deformation of high-strength reinforced concrete columns comprises the following steps:

[0007] S1. Continuously changing the strain values of the high-strength steel bar eccentric compression column on the side away from the axial force and the side adjacent to the axial force, each strain on the side away from the axial force and the strain on the side adjacent to the axial force constitute a set of strain pairs;

[0008] S2. Inversely calculate the axial force, bending moment and curvature of the column section under the corresponding state based on the strain;

[0009] S3, screening effective strain pairs, and optimizing the remaining strain pair data as a data set;

[0010] S4. Calculate the ultimate bearing capacity or lateral deformation displacement of the column under different states based on the data set.

[0011] As a further solution of the present invention: in step S2, the cross section of the column is evenly divided into Q After the strips are formed, the strain pairs are numerically integrated in a trapezoidal manner to calculate the axial force, bending moment and curvature of the column section in the state corresponding to each strain pair;

[0012] ;

[0013] in, N It represents the axial force acting on the column section;

[0014] M represents the bending moment acting on the column section;

[0015] represents the curvature of the cylindrical section;

[0016] It means that under the action of strain, the first j The corresponding stress on the column at the strip dividing line is: j The value range is 1, 2, 3, ..., Q -1, Q ;

[0017] It means that under the action of strain, the first j+1 The corresponding stress of the column at each strip dividing line;

[0018] b Indicates the width of the column section;

[0019] h Indicates the height of the column section;

[0020] It means that under the action of strain, j The vertical distance between the center of each strip and the geometric center axis of the column section;

[0021] It means that under the action of strain, the column p Axial force on the root longitudinal reinforcement; U Indicates the total number of longitudinal reinforcements in the column. p The value range is 1, 2, 3, ..., U－1 , U ;

[0022] It means that under the action of strain, the column p The vertical distance between the root longitudinal reinforcement and the geometric center axis of the column section;

[0023] represents the strain on the side away from the axial force in the strain pair;

[0024] Represents the strain on the adjacent axial force side of a strain pair.

[0025] As a further solution of the present invention: in step S3:

[0026] S31, N, M, As the coordinate axis, a spatial rectangular coordinate system is established with each strain pair corresponding to ( N , M , ) as a point in the spatial rectangular coordinate system;

[0027] S32, delete the space rectangular coordinate system N or M For points in the negative state, project the remaining points to NoM On the plane, NoM The envelope of the projection points of each point in the plane is used as the cross section of the cylinder. NM curve;

[0028] S33, NM The curvature of each point on the curve is the base curvature, when any strain N Value and NM On the curve N The values are equal, and the curvature of the strain pair When it is greater than the base curvature, the strain pair is deleted;

[0029] S34, will NoM The residual strain is optimized after plane meshing.

[0030] As a further solution of the present invention: in step S34, NoM In the plane, M As the horizontal axis, N is the vertical axis, NoM Perform grid division to form a partitioned grid; construct a computational grid with the nodes of the partitioned grid as the center, and the size and shape of the computational grid correspond to the size and shape of the partitioned grid. Inverse calculation using plane interpolation within the computational grid :

[0031] ;

[0032] in, It represents the maximum axial compressive bearing capacity of the high-strength reinforced eccentrically loaded column;

[0033] It represents the maximum bending moment of the high-strength steel bar eccentrically loaded column;

[0034] Indicates the number of columns that the grid is divided into along the vertical direction;

[0035] Indicates the number of rows divided in the horizontal direction of the grid;

[0036] Indicates the vertical step size of a single grid;

[0037] Indicates the horizontal step size of a single grid;

[0038] Indicates that the grid is divided into n List m The strain at the node is proportional to the curvature of the corresponding column section;

[0039] express n List m The total amount of strain pairs in the computational grid corresponding to the row node;

[0040] Indicates the computational grid The curvature of the cylindrical section corresponding to each strain pair.

[0041] As a further solution of the present invention: S41, after determining the axial force on the column, calculate the lateral deformation displacement of the column:

[0042] S411, along the height direction of the column, divide the column into k segment, thus forming a k+1 interfaces, and the lateral deformation displacement at the boundary of each interface is:

[0043] ;

[0044] in, Indicates the column +1 The lateral deformation displacement at each interface boundary;

[0045] Indicates the column The lateral deformation displacement at each interface boundary;

[0046] Indicates the column －1 The lateral deformation displacement at each interface boundary;

[0047] The value range is 1, 2, 3, ..., k , k+1 ;

[0048] Indicates the spacing between adjacent interfaces;

[0049] Indicates the subject The curvature of each interface is calculated according to step S34;

[0050] S412, the first interface of the cylinder and the k+1 The lateral deformation displacement value of each interface is 0, and the second interface is taken as the starting interface, and a lateral deformation displacement value is assigned to the second interface. , The value assigned is 1×10 -6 ;

[0051] S413, based on the axial force on the column, the initial eccentricity of the column and the assumed lateral displacement value of the second interface Calculate the current bending moment at the second interface ;

[0052] S414: Calculate the lateral deformation displacement value of the third interface of the column according to step S411 ;

[0053] S415. Calculate the lateral deformation displacement values of all interfaces of the column in sequence and record the k+1 The lateral deformation displacement value of the interface ;

[0054] S416, gradually expand step S412 , repeat steps S413 to S415 until the calculated and the one obtained in step S415 When the signs are opposite, the output ;

[0055] S417, according to the output in step S416 , the true lateral displacement value of the second interface is gradually obtained by the bisection method, thereby obtaining the lateral deformation displacement curve of the column under the action of a certain axial force.

[0056] As a further solution of the present invention: when calculating the maximum lateral displacement deformation of the column, the cross section of the column is NM The curve is processed equivalently to obtain the cylinder curve, is the axial force on the cross section of the column The maximum lateral displacement deformation value allowed under the action;

[0057] ;

[0058] in, It represents the axial force on the column section when it reaches its ultimate bearing capacity;

[0059] It represents the bending moment to which the column section is subjected when it reaches its ultimate bearing capacity;

[0060] Indicates the initial eccentricity of the cylinder.

[0061] As a further solution of the present invention: S42, calculate the ultimate bearing capacity of the column under biased compression:

[0062] S421, given initial axial pressure of the cylinder along the axial direction N 0 as well as N 1 , N 0 < N 1 , calculated according to step S41 N 0 as well as N 1 The lateral displacement deformation value of the column under the axial pressure d 0 as well as d 1 ;

[0063] S422, connection ( d 0 , N 0 )and( d 1 , N 1 ) forms a straight line with Nf The curves intersect at ( d 2 , );

[0064] S423, calculate the lateral displacement deformation value of the column in the column d 2 The corresponding axial force N 2 ;

[0065] S424、 d 0 , N 0 )and(d 1 , N 1 ) are replaced by ( d 1 , N 1 )and( d 2 , N 2 ), repeat steps S422 to S423, and calculate ( d 3 , N 3 )and( d 3 , ), ( d 4 , N 4 )and( d 4 , ),…,( d i , N i )and( d i , );

[0066] S425, Comparative Judgment and The value of and When the absolute difference is less than the set value, the output is the ultimate bearing capacity of the column.

[0067] Compared with the prior art, the present invention has the following beneficial effects:

[0068] 1. The present invention provides an efficient and accurate numerical calculation method for predicting the compressive bearing and deformation capacity of high-strength reinforced concrete columns, based on full consideration of the nonlinear properties of high-strength steel bars and concrete materials and the geometric nonlinearity exhibited during the compression process of eccentrically compressed columns; solves the problems of poor calculation accuracy and low calculation efficiency of graphical methods; and solves the problems of traditional commercial general-purpose finite element calculation programs, such as the large number of parameter settings, high requirements for the computing platform, long calculation time, high calculation cost, and high requirements for engineering and technical personnel. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 Schematic diagram of the strain on the side away from the axial force and the strain on the side adjacent to the axial force in the present invention.

[0070] Figure 2 Schematic diagram of the combination of strain pairs in the present invention.

[0071] Figure 3 This is a schematic diagram of dividing the column cross section into strips according to the present invention.

[0072] Figure 4 Schematic diagram of the meshing of the NoM plane according to the present invention.

[0073] Figure 5 This is a schematic diagram of the lateral deformation displacement calculation of the present invention.

[0074] Figure 6 This is a schematic diagram of the ultimate bearing capacity calculation of the present invention. DETAILED DESCRIPTION

[0075] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. 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 making creative efforts are within the scope of protection of the present invention.

[0076] See also Figures 1 to 6 In an embodiment of the present invention, a numerical calculation method for compressive bearing and deformation of a high-strength reinforced concrete column includes the following steps:

[0077] S1, such as Figure 1 As shown in the figure, through numerical simulation, the strain values of the high-strength steel bar eccentric column away from the axial force side and the adjacent axial force side are continuously changed; the strain of each side away from the axial force and the strain of the adjacent axial force side are as shown in Figure 2 As shown, a set of strain pairs is formed;

[0078] S2, such as Figure 3 As shown, the cross section of the column is evenly divided into Q A strip is formed, and a trapezoidal numerical integration is performed on each strain pair along the neutral axis of the vertical column section to inversely calculate the axial force, bending moment and curvature corresponding to each strain pair; the curvature of this application should be understood as the angle between the upper and lower cross sections after deformation within the unit length of the column (along the height direction of the column) corresponding to the strain pair.

[0079] ;

[0080] in, N It represents the axial force acting on the column section;

[0081] M represents the bending moment acting on the column section;

[0082] represents the curvature of the cylindrical section;

[0083] It means that under the action of strain, the first j The corresponding stress on the column at the strip dividing line is: j The value range is 1, 2, 3, ..., Q -1, Q ;

[0084] It means that under the action of strain, the first j+1 The corresponding stress of the column at each strip dividing line;

[0085] b Indicates the width of the column section;

[0086] h Indicates the height of the column section;

[0087] It means that under the action of strain, j The vertical distance between the center of each strip and the geometric center axis of the column section;

[0088] It means that under the action of strain, the column p Axial force on the root longitudinal reinforcement; U Indicates the total number of longitudinal reinforcements in the column. p The value range is 1, 2, 3, ..., U－1 , U ;

[0089] It means that under the action of strain, the column p The vertical distance between the root longitudinal reinforcement and the geometric center axis of the column section;

[0090] represents the strain on the side away from the axial force in the strain pair;

[0091] Represents the strain on the adjacent axial force side of a strain pair.

[0092] S3. Filter effective strain pairs and optimize the remaining strain pair data as a data set.

[0093] S31, N 、 M 、 As the coordinate axis, a spatial rectangular coordinate system is established with each strain pair corresponding to ( N , M , ) as a point in the spatial rectangular coordinate system;

[0094] S32, delete the space rectangular coordinate system N or M For points in the negative state, project the remaining points to NoM On the plane, NoM The envelope of the projection points of each point in the plane is used as the cross section of the cylinder. NM curve;

[0095] S33, all the above ( N , M , ) Points according to N The size of the group is divided into groups, and the ,common p groups, each of which contains indivual( N , M , ) points. For each point in each group, NM The curvature of each point on the curve is the base curvature, when any strain N Value and NM On the curve N The corresponding values are equal or close (the absolute value of the error does not exceed 0.5 times the group interval), and the curvature of the strain pair When it is greater than the base curvature, the strain pair is deleted;

[0096] S34, such as Figure 4 As shown, NoM Optimize the residual strain after plane meshing;

[0097] exist NoM In the plane, M As the horizontal axis, N is the vertical axis, NoM Perform grid division to form a partitioned grid; construct a computational grid with the nodes of the partitioned grid as the center, and the size and shape of the computational grid correspond to the size and shape of the partitioned grid. Inverse calculation using plane interpolation within the computational grid :

[0098] ;

[0099] in, It represents the maximum axial compressive bearing capacity of the high-strength reinforced eccentrically loaded column;

[0100] It represents the maximum bending moment of the high-strength steel bar eccentrically loaded column;

[0101] Indicates the number of columns that the grid is divided into along the vertical direction;

[0102] Indicates the number of rows divided in the horizontal direction of the grid;

[0103] Indicates the vertical step size of a single grid;

[0104] Indicates the horizontal step size of a single grid;

[0105] Indicates that the grid is divided into n List m The strain at the node is proportional to the curvature of the corresponding column section;

[0106] express n List m The total amount of strain pairs in the computational grid corresponding to the row node;

[0107] Indicates the computational grid The curvature of the cylindrical section corresponding to each strain pair.

[0108] The calculation steps of plane interpolation are as follows:

[0109] based on As the original database, Point ( N nm , M nm , ) in the axial force N nm and bending moment M nm As a benchmark, find the nearest ( N nm , M nm ) Three points that are relatively scattered P 1 ( N 1 , M 1 , )、 P 2 ( N 2 , M 2 , )as well as P 3 ( N 3 , M 3 , ), and then find the plane passing through these three points : .

[0110] in, A 、 B as well as C All are flat The parameter to be requested is given by P1 、 P2 and P3 Substitute into this plane equation to obtain, and finally N nm and M nm Substitute into the plane In the equation of , find the corresponding curvature at this time .

[0111] In this step, meshing can be used to fit specific ( N , M ) combination.

[0112] Due to the discreteness of the data points, not every are all countable, not all dotted grids have at least one ( N , M , ) points, and in terms of program efficiency and calculation accuracy, it is not necessary to All are calculable.

[0113] S4. Calculate the ultimate bearing capacity or lateral deformation displacement of the column under different states based on the data set.

[0114] S41. After determining the axial force acting on the column, calculate the lateral deformation displacement of the column:

[0115] S411、 Figure 5 As shown, the column is divided into two equal parts along the eccentric compression height direction of the column. k segment, thus forming a k+1 Considering that the deformation of the actual column is small, the influence of the second-order differential between the lateral bending deformation of the column and the column height on the curvature of the column can be ignored. x Axis and y Axis, the lateral deformation displacement at each interface boundary is:

[0116] ;

[0117] in, Indicates the column +1 The lateral deformation displacement at each interface boundary;

[0118] Indicates the column The lateral deformation displacement at each interface boundary;

[0119] Indicates the column －1 The lateral deformation displacement at each interface boundary;

[0120] a The value range is 1, 2, 3, ..., k , k+1 ;

[0121] Indicates the spacing between adjacent interfaces;

[0122] Indicates the subject The curvature of each interface is calculated according to step S34;

[0123] S412, Since the two ends of the column are hinged during the bias test, the natural as well as 。 can be used as a starting point for initial calculations, and It can be used as a criterion for determining whether the column deformation curve calculated under the action of axial force is a true value. The second interface is taken as the starting interface and a value close to 0 (preferably 1×10 -6 ) of the lateral deformation displacement value ;

[0124] S413, based on the axial force on the column, the initial eccentricity of the column and the assumed lateral displacement value of the second interface Calculate the current bending moment at the second interface ;

[0125] S414: According to step S411, Calculate the lateral deformation displacement value of the third interface of the column ;

[0126] S415. Calculate the lateral deformation displacement values of all interfaces of the column in sequence and record the k+1 The lateral deformation displacement value of the interface ;

[0127] S416, gradually expand step S412 , repeat steps S413 to S415 until the calculated and the one obtained in step S415 When the signs are opposite, the output ;

[0128] S417, according to the output in step S416 , the true lateral displacement value of the second interface is gradually obtained by the bisection method (the allowable error given in this application is 0.01mm), thereby obtaining the lateral deformation displacement curve of the column under the action of a certain axial force.

[0129] The solution steps of the dichotomy method are as follows: After obtaining the interval where the second interface true lateral displacement is located ( , ), first take the hypothetical lateral displacement value of the second interface as: , and then calculate when the lateral displacement of the second interface is When the lateral displacement of the top interface of the column is , and then check the calculated Is the absolute value less than the given allowable error? If it meets the above error, the calculation ends; otherwise, judge and and The positive and negative signs of: If , then the trial calculation interval of the second interface true lateral displacement is ( , ), and make this new interval replace the original interval ( , ), and then take the new assumed lateral displacement value of the second interface as: , continue to calculate the lateral displacement of the top interface of the column. If it meets the given error, the calculation ends, otherwise repeat step S417. , then the trial calculation interval of the second interface true lateral displacement is ( , ), and make this new round of intervals replace the original interval ( , ), and then take the new assumed lateral displacement value of the second interface as: , continue to calculate the lateral displacement of the top interface of the column. If it meets the given error, the calculation ends, otherwise repeat step S417.

[0130] S42, such as Figure 6 As shown, calculate the ultimate bearing capacity of the column under eccentric compression state;

[0131] Before the calculation begins, the column section NM The curve is processed equivalently to obtain the cylinder curve, is the axial force on the cross section of the column The maximum lateral displacement deformation value allowed under the action;

[0132] ;

[0133] in, It represents the axial force to which the column section is subjected when it reaches its ultimate bearing capacity;

[0134] It represents the bending moment to which the column section is subjected when it reaches its ultimate bearing capacity;

[0135] Indicates the initial eccentricity of the cylinder.

[0136] S421, given initial axial pressure of the cylinder along the axial direction N 0 as well as N 1 , N 0 < N 1 , in this application N 0 =100kN, N 1 = 200kN. According to step S41, calculate N 0 as well as N 1 The lateral displacement deformation value of the column corresponding to the axial force d 0 as well as d 1 ;

[0137] S422, connection ( d 0 , N 0 )and( d 1 , N 1 ) forms a straight line with Nf The curves intersect at ( d 2 , );

[0138] S423, calculate the lateral displacement deformation value of the column in the column d 2 The corresponding axial force N 2 ;

[0139] In this step, N 1 Based on the axial force, select the current axial force increment step for: . Calculate the lower axial force: The corresponding lateral displacement deformation value of the column , i The value is .

[0140] like Less than d 2 , then keep the current axial force increment step unchanged, that is, , continue to increase the magnitude of the axial force.

[0141] like Greater than d 2 , then further reduce the current axial force increment step size and take it as: .

[0142] Repeat the above steps until and d 2 The relative error is less than 0.01 or Less than 0.001kN, take N2 = ;

[0143] S424、 d 0 , N 0 )and( d 1 , N 1 ) are replaced by ( d 1 , N 1 )and( d 2 , N 2 ), repeat steps S422 to S423, and calculate ( d 3 , N 3 )and( d 3 , ), ( d 4 , N 4 )and( d 4 , ),…,( d i , N i )and( d i , );

[0144] S425, Comparative Judgment and The value of and When the absolute difference is less than the set value, the output is the ultimate bearing capacity of the column.

[0145] To verify the accuracy of the numerical calculations used in this application, high-strength reinforced concrete columns subjected to eccentric compression and axial compression were prepared and tested. The measured yield strength of the high-strength steel bars in the columns exceeded 650 MPa. The reinforcement of the columns is shown in Table 1 below.

[0146] Table 1

[0147] ;

[0148] In the table, Group 1 and Group 2 are high-strength reinforced concrete eccentrically compressed columns. The length of all columns is 1250mm. The 6 longitudinal bars are evenly and symmetrically arranged along the tension and compression sides of the columns. The stirrups are arranged in the same way and are all double-legged stirrups. The column protective layer is 20mm.

[0149] Group 3 consists of high-strength reinforced concrete axial compression columns. All specimens are 650mm long, with four longitudinal bars arranged evenly and symmetrically. The stirrups are of the same type and are all double-legged stirrups. The column protective layer is 20mm.

[0150] The three specimens in group 1 were calculated according to the calculation method of this application. The initial eccentric moments of specimens N1-80-40, N2-80-80 and N3-80-120 were e =40mm gradually increased to e =80mm and e =120mm, the ultimate bearing capacity calculated by this calculation method drops from 1706.22kN to 991.48kN and 574.11kN, while the measured values in the test are 1692.67kN, 1000.05kN and 576.45kN, with relative errors of +0.80%, -0.86% and -0.45%, respectively; the corresponding lateral displacement deformation value of the calculated column increases from 4.8mm to 6.3mm and 6.9mm, while the measured values in the test are 5.2mm, 6.6mm and 7.2mm, respectively, with relative errors of -7.69%, -4.55% and -4.17%, respectively.

[0151] Similarly, for the three specimens N4-50-40, N5-60-40 and N1-80-40 in group 2, the concrete cube compressive strength is given by f cu =50MPa and then increase tof cu =60MPa and f cu =80MPa, the ultimate bearing capacity calculated by this calculation method increases from 1402.95kN to 1541.11kN and 1706.22kN. Compared with the experimental values of 1397.59kN, 1530.87kN and 1692.67kN, the relative errors are +0.49%, +0.69% and +0.80%, respectively.

[0152] Similarly, for the two axial compression specimens N6-80-0 and N7-80-0 in Group 3, the ultimate bearing capacities calculated by this calculation method are 1952.8 kN and 1803.1 kN, respectively. Compared with the corresponding experimental values of 1955.2 kN and 1788.0 kN, the relative errors are: -0.12% and +0.84%, respectively.

[0153] In summary, the ultimate bearing capacity and corresponding displacement of the columns calculated using this numerical calculation method are in good agreement with the experimental results, demonstrating the accuracy and correctness of this calculation method. The calculated data for each specimen are shown in Table 2 below.

[0154] Table 2

[0155] ;

[0156] The standard in Table 2 refers to GB50010-2010 (2015 edition). During the calculation process, the strength of materials such as concrete and high-strength steel bars adopts the laboratory measured strength. In the calculation process using the standard formula, the value of e takes into account the lateral deflection occurring in the column when the column reaches the ultimate bearing capacity during the experiment, and does not consider the influence of the additional eccentricity of this standard. Other parameters required in the calculation process according to the standard are selected in accordance with this standard.

[0157] This application's numerical calculation method assumes a planar cross-section and performs strip division only along the longitudinal direction of the column and perpendicular to the neutral axis of the cross-section. This results in faster computation speed and higher efficiency than traditional ABAQUS simulations. Table 3 shows the calculation times for the same component using ABAQUS general finite element software and this application's calculation method.

[0158] Table 3

[0159] ;

[0160] From the above, we can see that the calculation time of this application is about 5.4% of the calculation time of ABAQUS software, which greatly improves the calculation efficiency.

[0161] The basic principles of the present application have been described above in conjunction with specific embodiments. However, it should be noted that the advantages, strengths, and effects mentioned in this application are merely illustrative and not restrictive, and it should not be assumed that these advantages, strengths, and effects are required of each embodiment of this application. In addition, the specific details disclosed above are merely illustrative and facilitating understanding, and are not restrictive. The above details do not limit this application to necessarily being implemented using the above specific details.

Claims

1. A numerical calculation method for compressive bearing and deformation of high-strength reinforced concrete columns, characterized in that: The steps include: S1. Continuously changing the strain values of the high-strength steel bar eccentric compression column on the side away from the axial force and the side adjacent to the axial force, each strain on the side away from the axial force and the strain on the side adjacent to the axial force constitute a set of strain pairs; S2. Inversely calculate the axial force, bending moment and curvature of the column section under the corresponding state based on the strain; S3, screening effective strain pairs, and optimizing the remaining strain pair data as a data set; S31, N, M, φ As the coordinate axis, a spatial rectangular coordinate system is established with each strain pair corresponding to ( N,M,φ ) as a point in the spatial rectangular coordinate system; N It represents the axial force acting on the column section; M represents the bending moment acting on the column section; φ represents the curvature of the cylindrical section; S32, delete the space rectangular coordinate system N or M For points in the negative state, project the remaining points to NoM On the plane, NoM The envelope of the projection points of each point in the plane is used as the cross section of the cylinder. NM curve; S33, NM The curvature of each point on the curve φ is the base curvature, when any strain N Value and NM On the curve N The values are equal, and the curvature of the strain pair φ When it is greater than the base curvature, the strain pair is deleted; S34, will NoM Optimize the residual strain after plane meshing; S4. Calculate the ultimate bearing capacity or lateral deformation displacement of the column under different states based on the data set.

2. The numerical calculation method for compressive bearing and deformation of high-strength reinforced concrete columns according to claim 1 is characterized in that: In step S2, the column section is evenly divided into Q After the strips are formed, the strain pairs are numerically integrated in a trapezoidal manner to calculate the axial force, bending moment and curvature of the column section in the state corresponding to each strain pair; in, N It represents the axial force acting on the column section; M represents the bending moment acting on the column section; φ represents the curvature of the cylindrical section; It means that under the action of strain, the first j The corresponding stress on the column at the strip dividing line is: j The value range is 1, 2, 3, ..., Q -1, Q ; It means that under the action of strain, the first j+1 The corresponding stress of the column at each strip dividing line; b Indicates the width of the column section; h Indicates the height of the column section; It means that under the action of strain, j The vertical distance between the center of each strip and the geometric center axis of the column section; It means that under the action of strain, the column p Axial force on the root longitudinal reinforcement; U Indicates the total number of longitudinal reinforcements in the column. p The value range is 1, 2, 3, ..., U－1 , U ; It means that under the action of strain, the column p The vertical distance between the root longitudinal reinforcement and the geometric center axis of the column section; represents the strain on the side away from the axial force in the strain pair; Represents the strain on the adjacent axial force side of a strain pair.

3. The numerical calculation method for compressive bearing and deformation of high-strength reinforced concrete columns according to claim 2 is characterized in that: In step S34, NoM In the plane, M As the horizontal axis, N is the vertical axis, NoM Performing grid division to form a division grid; The computational grid is constructed with the nodes of the grid as the center. The size and shape of the computational grid correspond to the size and shape of the grid. Inverse calculation using plane interpolation within the computational grid : in, It represents the maximum axial compressive bearing capacity of the high-strength reinforced eccentrically loaded column; It represents the maximum bending moment of the high-strength steel bar eccentrically loaded column; n represents the number of columns in the vertical direction of the grid; m represents the number of rows of grid division along the horizontal direction; Indicates the vertical step size of a single grid; Indicates the horizontal step size of a single grid; Indicates that the grid is divided into n List m The strain at the node is proportional to the curvature of the corresponding column section; express n List m The total amount of strain pairs in the computational grid corresponding to the row node; Indicates the computational grid The curvature of the cylindrical section corresponding to each strain pair.

4. A numerical calculation method for compressive bearing and deformation of high-strength reinforced concrete columns according to claim 2 or 3, characterized in that: S41. After determining the axial force acting on the column, calculate the lateral deformation displacement of the column: S411, along the height direction of the column, divide the column into k segment, thus forming a k+1 interfaces, and the lateral deformation displacement at the boundary of each interface is: ； in, Indicates the column +1 The lateral deformation displacement at each interface boundary; Indicates the column The lateral deformation displacement at each interface boundary; Indicates the column －1 The lateral deformation displacement at each interface boundary; The value range is 1, 2, 3, ..., k , k+1 ; Indicates the spacing between adjacent interfaces; Indicates the subject The curvature of each interface is calculated according to step S34; S412, the first interface of the cylinder and the k+1 The lateral deformation displacement value of each interface is 0, and the second interface is taken as the starting interface, and a lateral deformation displacement value is assigned to the second interface. , The value assigned is 1×10 −6 ; S413, based on the axial force on the column, the initial eccentricity of the column and the assumed lateral displacement value of the second interface Calculate the current bending moment at the second interface ; S414: Calculate the lateral deformation displacement value of the third interface of the column according to step S411 ; S415. Calculate the lateral deformation displacement values of all interfaces of the column in sequence and record the k+1 The lateral deformation displacement value of the interface ; S416, gradually expand step S412 , repeat steps S413 to S415 until the calculated and the one obtained in step S415 When the signs are opposite, the output ; S417, according to the output in step S416 , the true lateral displacement value of the second interface is gradually obtained by the bisection method, thereby obtaining the lateral deformation displacement curve of the column under the action of a certain axial force.

5. A numerical calculation method for compressive bearing and deformation of high-strength reinforced concrete columns according to claim 4, characterized in that: When calculating the maximum lateral displacement of a column, the cross section of the column is NM The curve is processed equivalently to obtain the cylinder curve, is the axial force on the cross section of the column The maximum lateral displacement deformation value allowed under the action; in, It represents the axial force on the column section when it reaches its ultimate bearing capacity; It represents the bending moment to which the column section is subjected when it reaches its ultimate bearing capacity; Indicates the initial eccentricity of the cylinder.

6. The numerical calculation method for compressive bearing and deformation of high-strength reinforced concrete columns according to claim 5 is characterized in that: S42. Calculate the ultimate bearing capacity of the column under eccentric compression: S421, given initial axial pressure of the cylinder along the axial direction N 0 as well as N 1 , N 0 < N 1 , calculated according to step S41 N 0 as well as N 1 The lateral displacement deformation value of the column under the axial pressure d 0 as well as d 1 ; S422, connection ( d 0 , N 0 )and( d 1 , N 1 ) forms a straight line with Nf The curves intersect at ( d 2 , ); S423, calculate the lateral displacement deformation value of the column in the column d 2 The corresponding axial force N 2 ; S424、 d 0 , N 0 )and( d 1 , N 1 ) are replaced by ( d 1 , N 1 )and( d 2 , N 2 ), repeat steps S422 to S423, and calculate ( d 3 , N 3 )and( d 3 , ), ( d 4 , N 4 )and( d 4 , ),…,( d i , N i )and( d i , ); S425, Comparative Judgment and The value of and When the absolute difference is less than the set value, the output is the ultimate bearing capacity of the column.

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