Calculation method of end bearing square steel tube concrete composite column base compression-bending bearing capacity

Abstract

The present application relates to the calculation method of the end bearing type square steel pipe concrete composite column base compression-bending bearing capacity, comprising the following steps: collecting the parameters required for calculating the compression-bending bearing capacity of the column base; calculating the compression-bending bearing capacity of each component of the column base; constructing the compression-bending bearing capacity of the reinforced concrete outside the pipe by simple superposition method; constructing the compression-bending bearing capacity of the steel pipe concrete column base by simple superposition method; constructing the compression-bending bearing capacity of the end bearing type square steel pipe concrete composite column base by simple superposition method. The calculation method of the present application is based on the simple superposition method, and the derivation process strictly follows the actual stress mechanism of each component of the compression-bending bearing capacity of the column base. The established bearing capacity calculation formula has clear physical meaning, simple form, clear technical route, excellent calculation stability and accuracy, and can provide reliable basis for the fine design and safety evaluation of the end bearing type steel pipe concrete composite column base.

Description

Technical Field

[0001] This invention relates to the field of structural engineering technology, specifically to a method for calculating the bending capacity of the column base of an end-bearing square steel tube concrete composite column. Background Technology

[0002] Concrete-filled steel tubular composite columns (hereinafter referred to as composite columns) have excellent mechanical properties and advantages such as seismic resistance and fire resistance, and have been successfully applied in many high-rise and large-span projects. As a key force transmission node connecting the superstructure and foundation, the column base is particularly important in terms of its stress performance and seismic design.

[0003] Composite column bases mainly come in two forms: embedded and end-bearing. The former achieves rigid connection through deep embedment of the column in the foundation, offering excellent performance but complex construction and higher costs. The latter, with its simple structure, clear force transmission, and economic efficiency, has broad application prospects, but stress concentration is prone to occur at abrupt changes in its cross-section, potentially becoming a weak point in mechanical and seismic resistance. Currently, research on composite columns mainly focuses on the column shaft and beam-column joints, with limited systematic research on end-bearing column bases. Design studies primarily draw on the achievements of end-bearing steel-concrete composite column bases from Japan. Therefore, conducting research on the stress performance of end-bearing composite column bases is extremely urgent.

[0004] The current "Code for Design of Composite Structures" JGJ 138-2016 typically ignores internal steel components and calculates them based on reinforced concrete sections in the design of end-bearing column bases. The "Technical Specification for Steel-Concrete Composite Column Structures" T / CECS 188-2019 considers the axial force borne by each part of the composite column section as distributed according to elastic axial stiffness, while calculating all bending moments borne by the external reinforced concrete. Both methods are overly conservative. In reality, the reinforcing effect of the core steel-concrete composite column usually makes its load-bearing capacity and stiffness superior to steel-concrete composite columns and reinforced concrete columns.

[0005] Therefore, it is necessary to further refine and improve the design method of end-bearing composite column bases so that they can more accurately reflect the actual stress performance of the structure and improve the design economy and adaptability. Summary of the Invention

[0006] To address the problems existing in the prior art, the purpose of this invention is to provide a method for calculating the bending capacity of the column base of an end-bearing square steel tube concrete composite column, which can more accurately reflect the actual stress performance of the structure and provide a reliable basis for the refined design and safety assessment of the column base of the end-bearing composite column.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] The calculation method for the compression-bending capacity of the base of an end-bearing square steel-concrete composite column includes the following steps.

[0009] The parameters required for calculating the compression-bending capacity of the base of an end-bearing square steel-concrete composite column are determined, including the length of the composite column cross-section. a Hekuan b , diameter of the built-in steel pipe of the composite column D The outermost radius of the column base plate R m The distance from the center of the longitudinal reinforcement of the outer column to the outer edge of the composite column. c axial compressive strength of concrete inside and outside the steel pipe f ck Concrete strength influence coefficient β c Concrete strength enhancement coefficient under local pressure β l Total number of longitudinal reinforcement bars in the outer column n s Area of ​​a single longitudinal reinforcement bar in a pipe column A s Tensile strength of longitudinal reinforcement in outer column f u Yield strength of longitudinal reinforcement in outer column f y Total number of anchor bars n m single anchor bar area A sm Anchor bar tensile strength f um ;

[0010] Based on the determined parameters, the bending capacity of the column base of the end-bearing square steel tube concrete composite column is divided into four parts: the bending capacity of the concrete outside the tube, the bending capacity of the longitudinal reinforcement of the outside tube, the bending capacity of the concrete under the column base plate, and the bending capacity of the anchor reinforcement. The bending capacity of each part is calculated according to the force balance relationship of each part.

[0011] Based on the simple superposition method, the compressive bending bearing capacity of the concrete outside the tube column and the compressive bending bearing capacity of the longitudinal reinforcement of the outside tube column are superimposed to obtain the compressive bending bearing capacity of the reinforced concrete outside the tube; the compressive bending bearing capacity of the concrete under the column base plate and the compressive bending bearing capacity of the anchor bar are superimposed to obtain the compressive bending bearing capacity of the column base of the steel tube concrete column.

[0012] Based on the simple superposition method, the compressive-bending bearing capacity of the reinforced concrete outside the tube and the compressive-bending bearing capacity of the column base of the steel tube concrete column are superimposed to obtain the compressive-bending bearing capacity of the column base of the end-bearing square steel tube concrete composite column.

[0013] Furthermore, the material strength parameters (including concrete and reinforcing steel) required for calculating the bending capacity of the end-bearing square steel-concrete composite column base are based on material property test results, and the concrete strength grades inside and outside the steel tube and the foundation are consistent. The longitudinal reinforcement of the column base section adopts a symmetrical reinforcement form. The number and diameter of the longitudinal reinforcement on each side of the square composite column are consistent, and the longitudinal reinforcement is evenly distributed along the edge of the composite column with equal center-to-center distances. Anchor bars are placed around the diameter of the steel tube on the annular column base plate. D The circular array is evenly divided within a 360-degree range. All anchor bars have the same diameter, and the total number of anchor bars is ≥4 and even. The anchor bars are connected to the column base plate using through-hole plug welding. The outermost circle radius of the column base plate is... R m The local pressure value is determined by the calculation of local pressure at the column base, and is taken as the ultimate bearing capacity of the composite column axial compression.

[0014] Furthermore, the calculation of the compression-bending capacity of the end-bearing square steel tube concrete composite column base is based on the following assumptions: 1) Plane section assumption is not considered; 2) The concrete strain at the edge of the compression zone reaches the peak strain of the concrete. 3) The concrete stress in the compression zone is distributed in a rectangular shape, with a rectangle height of [missing information]. x Take the height of the neutral axis x c Multiply , The strength grade of the concrete is related to the value of the concrete. The value is taken according to the "Standard for Design of Concrete Structures" GB / T 50010—2010, and the tensile strength of the concrete is not considered. 4) The concrete inside the pipe is constrained by the steel pipe, which increases the compressive strength of the core concrete. The concrete within the outermost circular projection range of the column base plate is subjected to local pressure. The local compressive stress is taken according to the "Standard for Design of Concrete Structures" GB / T 50010—2010 (2024 edition) during the calculation. The compressive strength of the reinforced concrete outside the pipe is taken as normal. 5) Only the tensile effect of the anchor bars is considered, and the compressive effect of the anchor bars is not considered. 6) The interaction between the pipe wall and the reinforced concrete outside the pipe is ignored.

[0015] Furthermore, the calculation of the bending capacity of each component of the end-bearing square steel tube concrete composite column base is based on the force balance relationship, and the calculation formula of the bending capacity of each component is established.

[0016] Furthermore, the outer column concrete is equivalent to the central circular hollow concrete section. In the calculation, the circular hollow part is equated to a square, and then the outer column concrete is transformed into an I-shaped section. The square hollow side length... , D The diameter of the steel tube inside the composite column is given. The concrete of the column outside the tube is equivalent to an I-shaped section, which is suitable for calculating the compressive-bending capacity of the column base along the principal bending axis, and also considers the contribution of the longitudinal reinforcement at the web of the equivalent I-shaped section.

[0017] Furthermore, the calculation expressions for each component of the compression-bending capacity at the base of the end-bearing square steel-concrete composite column are as follows:

[0018] 1) Bearing capacity of concrete in external tube columns under compression and bending

[0019] when When (i.e., the compression zone enters the compression side flange of the equivalent I-section):

[0020] , ;

[0021] when When (i.e., the compression zone enters the web of the equivalent I-beam section):

[0022] , ;

[0023] when When (i.e., the compression zone enters the tension flange of the equivalent I-section):

[0024] , ;

[0025] In the formula, N r , M r These represent the axial force and bending moment experienced by the concrete of the outer tube column at the column base section, respectively. x The height of the equivalent rectangular compression zone of the concrete outside the column at the column base section is equal to the height of the neutral axis. x c Multiply , It is related to the strength grade of concrete and is taken from the standard GB / T 50010—2010 "Design Standard for Concrete Structures". a , b These are the length and width of the cross-section of a square steel-concrete composite column, respectively. a = b ; f ck This refers to the axial compressive strength of concrete.

[0026] 2) Bearing capacity of longitudinal reinforcement bars in external columns under compression and bending

[0027] Determine the compressive-bending capacity of column longitudinal reinforcement under the following three special working conditions:

[0028] Condition 1, bending capacity of longitudinal reinforcement of external column under ultimate axial compressive load: , ;

[0029] Condition 2, the compressive-bending bearing capacity of the longitudinal reinforcement of the outer column under the ultimate axial tensile load: , ;

[0030] Condition 3, the compressive-bending capacity of the longitudinal reinforcement of the outer column under ultimate pure bending load:

[0031] when n When ≥3 and is odd, we have

[0032] ;

[0033] when n When ≥2 and even, we have

[0034] .

[0035] The relationship between the characteristic points corresponding to the above three working conditions is the calculation expression for the compressive-bending bearing capacity of the longitudinal reinforcement of the outer column:

[0036] when , n When ≥3 and is odd: ;

[0037] when , n When ≥2 and even: ;

[0038] when , n When ≥3 and is odd: ;

[0039] when , n When ≥2 and even: .

[0040] In the formula, N s , M s These represent the axial force and bending moment experienced by the longitudinal reinforcement of the column outside the tube at the column base section. Subscripts 1, 2, and 3 indicate the axial force or bending moment experienced under the corresponding special working conditions. n The number of longitudinal reinforcement bars on each side of the square steel tube concrete composite column; n s This refers to the total number of longitudinal reinforcement bars on the outer surface of a square steel-concrete composite column. n s =4 n -4; A s This refers to the area of ​​a single longitudinal reinforcement bar in the outer column of the tube; f u The tensile strength of the longitudinal reinforcement of the outer column; f y The yield strength of the longitudinal reinforcement of the outer column; T =n s f y A s , that is, the tensile force value when all column longitudinal reinforcements yield under axial tension; c The distance from the center of the longitudinal reinforcement of the outer column to the outer edge of the composite column; a , b These are the length and width of the cross-section of a square steel-concrete composite column, respectively. a = b .

[0041] 3) Bearing capacity of concrete under column base slab under compression and bending

[0042] , ;

[0043] In the formula, N rm , M rm These represent the axial force and bending moment acting on the concrete beneath the column base slab, respectively. The strength enhancement factor of concrete under local pressure is taken as follows, according to the Technical Specification for Steel-Concrete Composite Column Structures (T / CECS 188-2019). The value is the concrete strength influence coefficient, taken from the standard GB / T 50010—2010 "Design Standard for Concrete Structures"; f ck This refers to the axial compressive strength of concrete. R m The radius of the outermost circle of the column base plate; It is half of the sector angle corresponding to the arched compression zone of the circular column base plate. .

[0044] 4) Bearing capacity of anchor bars under compression and bending

[0045] Anchor bars are placed around the diameter of the steel pipe on the base plate of the annular column. D The circular array is divided equally within a 360-degree range, with all anchor bars having the same diameter, and the total number of anchor bars is... n m ≥4 anchor bars, and the number is even. The anchor bars form a 0.5m radius along the principal bending axis. n m +1 column, confirm the anchor bar is below 0.5. n m +2 special working conditions for compressive-bending capacity (taking moments about the center and successively reducing one row of anchor bars to reach the ultimate tension state):

[0046] Operating condition 1, corresponding to 0.5 n m When the +1 column of anchor bars reaches the ultimate tensile state: , ;

[0047] Operating condition 2, corresponding to 0.5 n m When the anchor bars reach the ultimate tensile state: , ;

[0048] Operating condition 3 corresponds to 0.5 n m When the anchor bars in column -1 reach the ultimate tensile state: , ;

[0049] Operating condition 4 corresponds to 0.5 n m When the second row of anchor bars reaches the ultimate tensile state: , ;

[0050] …

[0051] Operating condition 0.25 n m When the +1 column of anchor bars reaches the ultimate tensile state:

[0052] , ;

[0053] Operating condition 0.25 n m +2 corresponds to 0.25 n m When the anchor bars reach the ultimate tensile state:

[0054] , ;

[0055] …

[0056] Operating condition 0.5 n m -1 corresponds to the situation where the three anchor bars reach the ultimate tensile state:

[0057] , ;

[0058] Operating condition 0.5 n m When the corresponding two columns of anchor bars reach the ultimate tensile state: , ;

[0059] Operating condition 0.5 n m +1 corresponds to the anchor bar in column 1 reaching the ultimate tensile state: , ;

[0060] Operating condition 0.5 n m +2, corresponding to all anchor bars under axial compression: , ;

[0061] Following the above pattern, 0.5 n m The relationship between the characteristic points corresponding to the two working conditions is the formula for calculating the compressive-bending bearing capacity of the anchor bars. For simplicity, only working condition 1 and 0.25 are considered. n m +1, 0.25 n m +2, 0.5 n m By connecting the feature points of +2, we can obtain the expression for calculating the compressive-bending capacity of the anchor bar:

[0062] when hour: ;

[0063] when hour:

[0064]

[0065] when hour: ;

[0066] In the formula, N sm , M sm These represent the axial force and bending moment acting on the anchor bars, respectively. Subscripts 1, 2, 3, etc. indicate the axial force or bending moment under specific working conditions. n m This represents the total number of anchor bars. n m ≥4 roots and an even number; A sm This refers to the area of ​​a single anchor bar. f um This refers to the tensile strength of the anchor bar; C 1. C 2. C 3… C 0.25nm The symbol indicates the distance between each row of anchor bars and the main axis passing through the center of the circle, measured from the outside of the pipe towards the center. This distance is based on the diameter of the steel pipe. D Calculation of the angle of anchor bar arrangement.

[0067] Furthermore, the expression for the superposition of the concrete flexural bearing capacity and the longitudinal reinforcement flexural bearing capacity of the external column into the reinforced concrete flexural bearing capacity of the external column is as follows:

[0068] when hour: , ;

[0069] when ,and n When ≥3 and is odd:

[0070] , ;

[0071] when ,and n When ≥2 and even:

[0072] , ;

[0073] when hour: , ;

[0074] In the formula, N co , M co These represent the axial force and bending moment acting on the reinforced concrete outside the pipe, respectively.

[0075] Furthermore, the expression for the superposition of the concrete bending capacity under the column base slab and the anchor bar bending capacity to form the bending capacity of the concrete-filled steel tube column base is as follows:

[0076] when hour: , ;

[0077] when hour:

[0078] , ;

[0079] when

[0080] hour:

[0081] , ;

[0082] when

[0083] hour:

[0084] , ;

[0085] when hour: , ;

[0086] In the formula, N ci , M ci These represent the axial force and bending moment acting on the column base of the concrete-filled steel tube column, respectively.

[0087] Furthermore, the expression for the final superposition of the external reinforced concrete flexural bearing capacity and the column base flexural bearing capacity of the steel-concrete composite column with end bearing is as follows:

[0088] when hour: , ;

[0089] when

[0090] hour:

[0091] , ;

[0092] when

[0093] ,and n When ≥3 and is odd:

[0094] , ;

[0095] when

[0096] ,and n When ≥2 and even:

[0097] , ;

[0098] when ,

[0099] and hour:

[0100] , ;

[0101] when

[0102] hour:

[0103] , ;

[0104] In the formula, N ,M These represent the axial force and bending moment at the base of the end-bearing square steel-concrete composite column.

[0105] Furthermore, the calculation method for the compression-bending capacity of the column base of an end-bearing square steel tube concrete composite column can be applied to the following two common design conditions, and there are clear technical routes to follow: 1) The axial force on the column base is known. N Given the amount of longitudinal reinforcement and anchor bars in the column, calculate the bending moment that the column base can withstand. M 2) Given the axial force acting on the column base. N and bending moment M Find the required amount of longitudinal reinforcement and anchor bars for the column.

[0106] In summary, the present invention has the following advantages:

[0107] The calculation method of this invention is based on the simple superposition method. Its derivation process strictly follows the actual stress mechanism of each component of the column base bending bearing capacity. The established bearing capacity calculation formula has a clear physical meaning, a simple form, and a clear technical route. It has excellent calculation stability and accuracy, and can provide a reliable basis for the refined design and safety assessment of the column base of end-bearing composite columns. Attached Figure Description

[0108] Figure 1 This is a schematic diagram of the column base section of an end-bearing square steel tube concrete composite column. Figure 1 ;

[0109] Figure 2 This is a detailed schematic diagram of the column base of an end-bearing square steel tube concrete composite column.

[0110] Figure 3 This is a schematic diagram of the column base section of an end-bearing square steel tube concrete composite column. Figure 2 ;

[0111] Figure 4 This is a schematic diagram of the column base section of an end-bearing square steel tube concrete composite column. Figure 3 ;

[0112] Figure 5 This is a simplified calculation diagram of the column base of an end-bearing square steel tube concrete composite column;

[0113] Figure 6 It is a curve diagram related to the compressive and flexural bearing capacity of reinforced concrete outside the pipe;

[0114] Figure 7 This is a graph showing the relevant curves of the bending capacity at the base of a steel-concrete composite column.

[0115] Figure 8 This is a graph showing the relevant curves of the bending capacity at the base of an end-bearing square steel tube concrete composite column.

[0116] Figure 9This is a technical approach to calculating the bending capacity of the column base of an end-bearing square steel-concrete composite column. Figure 1 .

[0117] Figure 10 This is a technical approach to calculating the bending capacity of the column base of an end-bearing square steel-concrete composite column. Figure 2 .

[0118] In the picture:

[0119] 1-Basic, 11-Basic gluten, 12-Basic bottom gluten;

[0120] 2-Column base plate, 3-Steel pipe, 4-Column stirrups, 5-Column longitudinal bars, 6-Ring bars, 7-Anchor bars. Detailed Implementation

[0121] The present invention will now be described in further detail.

[0122] This invention provides a method for calculating the compression-bending capacity of the column base of an end-bearing square steel-concrete composite column. Based on known calculation parameters, the method first calculates the compression-bending capacity of each component of the column base. Then, using a simple superposition method, the compression-bending capacity of the external reinforced concrete and the steel-concrete composite column base are sequentially constructed, ultimately superimposed to form the compression-bending capacity of the end-bearing square steel-concrete composite column base. The derivation process of this method has clear physical meaning, is progressive, and interconnected, with a clear technical route, and can be applied to common engineering design conditions. Figures 1-4 Taking the end-bearing square steel-concrete composite column base as an example, the foundation 1 has foundation top reinforcement 11 and foundation bottom reinforcement 12 at both ends, respectively. The composite column has column stirrups 4, and 12 column longitudinal reinforcements 5 and 8 anchor reinforcements 7 are evenly distributed. The diameter of the built-in steel pipe 3 is [missing information]. D The pipe is externally welded with a ring reinforcement 6, and the pipe wall is fully penetrated welded to the column base plate 2. The width of the column base plate 2 is... d The outermost radius of column base plate 2 is R m .

[0123] The detailed derivation process is as follows:

[0124] (1) Obtain the parameters required for calculating the bending capacity of the end-bearing square steel tube concrete composite column base, including the cross-sectional dimensions of the composite column (length × width: a × b When square a = b ), Composite column with built-in steel pipe 3 diameter D 1. Radius of the outermost circle of the column base plate 2 R m The distance from the center of the longitudinal reinforcement bar 5 of the outer column to the outer edge of the composite column. c 1. Axial compressive strength of concrete inside and outside steel pipe 3f ck Concrete strength influence coefficient Concrete strength enhancement coefficient under local pressure 5. Total number of longitudinal reinforcement bars for external columns n s =12, Area of ​​a single longitudinal reinforcement bar in the outer column of the pipe (5 bars) A s 5. Tensile strength of longitudinal reinforcement in outer column f u 5. Yield strength of longitudinal reinforcement in outer column f y 7. Total number of anchor bars n m =8, Anchor bar area 7 (single bar area) A sm Anchor bar 7 tensile strength f um The material strength is based on the results of material property tests. The concrete strength grades of the steel pipe 3 (inner and outer parts) and the foundation 1 are consistent. The longitudinal reinforcement 5 of the column base section adopts a symmetrical reinforcement form. The number and diameter of the longitudinal reinforcement 5 on each side of the square composite column are consistent. The longitudinal reinforcement 5 is evenly distributed along the edge of the composite column, and the center distance between the longitudinal reinforcements is... m Equal; Anchor bar 7 surrounds the steel pipe 3 on the bottom plate 2 of the annular column base with a diameter of 3. D The circular array is equally divided within a 360-degree range, with all anchor bars 7 having the same diameter. The anchor bars 7 are connected to the column base plate 2 by through-hole plug welding; the outermost circular radius of the column base plate 2 is... R m The local pressure value is determined by the calculation of local pressure at the column base, and is taken as the ultimate bearing capacity of the composite column axial compression.

[0125] (2) Calculation assumptions followed: 1) Plane section assumption is not considered; 2) The concrete strain at the edge of the compression zone reaches the peak strain of the concrete. 3) The concrete stress in the compression zone is distributed in a rectangular shape, with a rectangle height of [missing information]. x Take the height of the neutral axis x c Multiply by, which is related to the strength grade of concrete, and the value is taken according to the "Standard for Design of Concrete Structures" GB / T 50010—2010, without considering the tensile strength of concrete; 4) The concrete inside the pipe is constrained by the steel pipe 3, and the compressive strength of the core concrete is improved. The concrete within the outermost circular projection range of the column base plate 2 is subjected to local pressure. When calculating, the local compressive stress is taken according to the "Standard for Design of Concrete Structures" GB / T 50010—2010 (2024 edition). The compressive strength of the reinforced concrete outside the pipe is taken as normal; 5) Only the tensile effect of the anchor bar 7 is considered, and the compressive effect of the anchor bar 7 is not considered; 6) The interaction between the pipe wall and the reinforced concrete outside the pipe is ignored.

[0126] (3) Divide the column base bending bearing capacity of the end-bearing square steel tube concrete composite column into Figure 5 The diagram shows four parts, and the force balance relationship of each part is established using this simplified calculation diagram. The outer column concrete is equivalent to the middle circular hollow concrete section. In the calculation, the circular hollow part is equivalent to a square, and then the outer column concrete is transformed into an I-shaped section. The side length of the square hollow section is calculated according to formula (1). The outer column concrete is equivalent to an I-shaped section, which is suitable for calculating the bending capacity of the column base on the bending axis, and the contribution of the longitudinal reinforcement 5 at the web of the equivalent I-shaped section is considered.

[0127] (1)

[0128] In the formula, D The composite column has an internal steel pipe with a diameter of 3. Figure 5 middle c 1. c 2 represents the distance from the outside of the pipe towards the center of the circle, between each row of anchor bars 7 and the main axis passing through the center of the circle, based on the diameter of the steel pipe 3. D Calculation of the angle of the 7-row anchor bar arrangement.

[0129] (4) Construct the calculation expressions for each component of the bending bearing capacity of the column base of the end-bearing square steel tube concrete composite column.

[0130] I) Bearing capacity of concrete in external tube columns under compression and bending

[0131] when hour:

[0132] , (2)

[0133] when hour:

[0134] , (3)

[0135] when hour:

[0136] , (4)

[0137] In the formula, N r , M r These represent the axial force and bending moment experienced by the concrete of the outer tube column at the column base section, respectively. x The height of the equivalent rectangular compression zone of the concrete outside the column at the column base section is equal to the height of the neutral axis. x c Multiply , It is related to the strength grade of concrete and is taken from the standard GB / T 50010—2010 "Design Standard for Concrete Structures". a , b These are the length and width of the cross-section of a square steel-concrete composite column, respectively. a = b ; f ck This refers to the axial compressive strength of concrete.

[0138] II) Bearing capacity of longitudinal reinforcement bars 5 in the outer column under compression and bending

[0139] Determine the bending capacity at the following characteristic points when the longitudinal reinforcement 5 of the outer column is subjected to the ultimate axial compressive load: , When the longitudinal reinforcement of the outer column is subjected to the ultimate axial tensile load. , When the longitudinal reinforcement of the outer column is subjected to the ultimate pure bending load ; , The relationship between characteristic points is the formula for calculating the compressive-bending capacity of the longitudinal reinforcement 5 of the outer column:

[0140] when hour:

[0141] (5)

[0142] when hour:

[0143] (6)

[0144] In the formula, N s , M s These represent the axial force and bending moment of the longitudinal reinforcement 5 outside the column at the column base section. When subscripts 1, 2, and 3 are added, they indicate the axial force or bending moment at the corresponding feature points. A s The area of ​​a single longitudinal reinforcement bar 5 in the outer column of the tube; f u The tensile strength of the longitudinal reinforcement of the outer column is 5. f y The yield strength of the longitudinal reinforcement of the outer column is 5. That is, the tensile force value when all column longitudinal reinforcements yield under 5-axis tension; c This is the distance from the center of the longitudinal reinforcement 5 of the outer column to the outer edge of the composite column; a , b These are the length and width of the cross-section of a square steel-concrete composite column, respectively. a = b .

[0145] III) Bearing capacity of concrete under column base slab 2 under compression and bending

[0146] , (7)

[0147] In the formula, N rm , M rm These represent the axial force and bending moment acting on the concrete under the column base plate 2, respectively. The strength enhancement factor of concrete under local pressure is taken as follows, according to the Technical Specification for Steel-Concrete Composite Column Structures (T / CECS 188-2019). The value is the concrete strength influence coefficient, taken from the standard GB / T 50010—2010 "Design Standard for Concrete Structures"; f ck This refers to the axial compressive strength of concrete. R m The radius of the outermost circle of the column base plate 2 is denoted by ; the radius of the sector corresponding to the arc-shaped compression zone of the circular column base plate 2 is denoted by . .

[0148] IV) Bearing capacity of anchor bars under compression and bending

[0149] Determine the compressive-bending bearing capacity of anchor bar 7 under the following 6 special working conditions:

[0150] Operating conditions When all anchor bars 7 reach the ultimate tensile state: , ;

[0151] Operating conditions When the corresponding 4 columns of anchor bars 7 reach the ultimate tensile state: , ;

[0152] Operating conditions When the corresponding 3 columns of anchor bars 7 reach the ultimate tensile state:

[0153] , ;

[0154] Operating conditions When the corresponding two columns of anchor bars 7 reach the ultimate tensile state:

[0155] , ;

[0156] Operating conditions When anchor bar 7 in column 1 reaches the ultimate tensile state: , ;

[0157] Operating conditions For all anchor bars 7 under axial compression: , ;

[0158] The relationship between the characteristic points corresponding to the above six working conditions is the formula for calculating the compressive-bending bearing capacity of anchor bar 7. For simplicity, only the working conditions are considered. , , , By connecting the characteristic points, we can obtain the expression for calculating the compressive-bending bearing capacity of anchor bar 7:

[0159] when hour:

[0160] (8)

[0161] when hour: (9)

[0162] when hour: (10)

[0163] In the formula, N sm , M sm These represent the axial force and bending moment experienced by the anchor bar 7, respectively. Subscripts 1, 2, 3, etc. indicate the axial force or bending moment experienced under the corresponding special working conditions. A sm The area of ​​a single anchor bar 7; f um The tensile strength of anchor bar 7; D The composite column has an internal steel pipe with a diameter of 3.

[0164] (5) The compressive bending capacity of the concrete outside the tube column and the compressive bending capacity of the longitudinal reinforcement outside the tube column are superimposed to form the compressive bending capacity of the reinforced concrete outside the tube (see the relationship curve). Figure 6 The expression for ) is:

[0165] when hour: , (11)

[0166] when hour:

[0167] , (12)

[0168] when hour: , (13)

[0169] In the formula, N co , Mco These represent the axial force and bending moment acting on the reinforced concrete outside the pipe, respectively.

[0170] (6) The combined bending capacity of the concrete under the column base plate 2 and the bending capacity of the anchor bar 7 constitute the bending capacity of the column base of the steel-concrete composite column (see the relationship curve). Figure 7 The expression for ) is:

[0171] when hour: , (14)

[0172] when hour: , (15)

[0173] when

[0174] hour: , (16)

[0175] when

[0176] hour: , (17)

[0177] when hour: , (18)

[0178] In the formula, N ci , M ci These represent the axial force and bending moment acting on the column base of the concrete-filled steel tube column, respectively.

[0179] (7) The bending capacity of the reinforced concrete outside the tube and the bending capacity of the column base of the steel tube concrete column are finally superimposed to form the bending capacity of the column base of the end-bearing square steel tube concrete composite column (see the relationship curve). Figure 8 The expression for ) is:

[0180] when hour: , (19)

[0181] when hour: , (20)

[0182] when

[0183] hour:

[0184] , (twenty one)

[0185] when

[0186] hour:

[0187] , (twenty two)

[0188] when

[0189] hour:

[0190] , (twenty three)

[0191] In the formula, N , M These represent the axial force and bending moment at the base of the end-bearing square steel-concrete composite column.

[0192] (8) The calculation method for the bending capacity of the column base of the end-bearing square steel tube concrete composite column can be used for the following two common design conditions, and there is a clear technical route to follow (see Figure 9 and Figure 10 ,in M 'This refers to the amount of column longitudinal reinforcement 5 and anchor reinforcement 7 substituted each time. n s A s , n m A sm The bending moment value obtained after trial calculation needs to be compared with... M (For comparison): 1) Given the axial force on the column base. N Measure the longitudinal reinforcement (5) and anchor reinforcement (7) of the column, and calculate the bending moment that the column base can withstand. M ( Figure 9 Technical route 1); 2) Given the axial force on the column base. N and bending moment M Calculate the required quantity of longitudinal reinforcement 5 and anchor reinforcement 7 for the column. Figure 10 Technical route two).

[0193] (9) The inventors conducted a compressive-bending performance test on the column base joints of 16 end-bearing square steel-concrete composite columns. The calculated values ​​were systematically lower than the experimental values ​​(see Table 1). The relative error between the two was 5% to 18%, verifying that the calculation method of the present invention is conservative and has excellent calculation stability and accuracy. This formula combines theoretical rigor with engineering practicality, providing a reliable basis for the refined design and safety assessment of the column bases of end-bearing composite columns.

[0194] Table 1: Comparison of Bending Capacity under Compression

[0195]

[0196] Note: N , M The values ​​are the axial force and bending moment at the base of the end-bearing square steel-concrete composite column (M* is the test value of the bending moment at the base of the end-bearing square steel-concrete composite column), respectively, in kN and kN•m.

[0197] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A method for calculating the compressive-bending bearing capacity of the column base of a square steel tube concrete composite column with end support, characterized in that: The method comprises the following steps, Determination of the parameters required for calculating the compressive-bending bearing capacity of the end-bearing square steel tube concrete composite column, including the composite column cross-sectional size length a and width b , the diameter of the steel tube embedded in the composite column D , the outermost circle radius of the column base plate R m , the distance from the longitudinal reinforcement center of the outer column to the outer edge of the composite column c , the axial compressive strength of the concrete inside and outside the steel tube f ck , the concrete strength influence coefficient β c , the concrete local pressure strength improvement coefficient β l , the total number of longitudinal reinforcement of the outer column n s , the single root area of the longitudinal reinforcement of the outer column A s , the tensile strength of the longitudinal reinforcement of the outer column f u , the yield strength of the longitudinal reinforcement of the outer column f y , the total number of anchor bars n m , the single root area of the anchor bar A sm , the tensile strength of the anchor bar f um ; Based on the determined parameters, the compression-bending capacity of the end-bearing square steel pipe concrete composite column base is divided into four parts, i.e., the compression-bending capacity of the column concrete outside the pipe, the compression-bending capacity of the longitudinal reinforcement of the column outside the pipe, the compression-bending capacity of the concrete under the base plate, and the compression-bending capacity of the anchor reinforcement; Based on the simple superposition method, the compression-bending capacity of the column concrete outside the pipe and the compression-bending capacity of the longitudinal reinforcement of the column outside the pipe are superposed to obtain the compression-bending capacity of the reinforced concrete outside the pipe; the compression-bending capacity of the concrete under the base plate and the compression-bending capacity of the anchor reinforcement are superposed to obtain the compression-bending capacity of the column base of the steel pipe concrete column; Based on the simple superposition method, the compression-bending capacity of the reinforced concrete outside the pipe and the compression-bending capacity of the column base of the steel pipe concrete column are superposed to obtain the compression-bending capacity of the end-bearing square steel pipe concrete composite column base.

2. The computational method of claim 1, wherein: The material strength parameters required for calculating the bearing capacity of the end bearing type square steel pipe concrete composite column base under compression and bending are based on the material test results, and the concrete strength grades of the steel pipe inside and outside and the foundation are consistent. The column longitudinal reinforcement of the column base section adopts a symmetrical reinforcement form, the number and diameter of the column longitudinal reinforcement of each side of the square composite column are consistent, the column longitudinal reinforcement is evenly arranged along the edge of the composite column, and the center distance between the longitudinal reinforcement is equal. The anchor reinforcement is evenly arrayed around the steel pipe on the ring-shaped column base bottom plate, all the anchor reinforcement has the same diameter, the total number of the anchor reinforcement n m ≥ 4 and is even, the anchor reinforcement and the column base bottom plate adopt a perforated plug welding, and the outermost circle radius of the column base bottom plate is R m The local pressure value is taken as the ultimate bearing capacity of the composite column under axial compression, which is determined by the column base local compression calculation.

3. The computational method of claim 1, wherein: The calculation of the compression-bending bearing capacity of the end-bearing square steel tube concrete composite column is based on the following assumptions: 1) the plane cross-section assumption is not considered; 2) the strain of the edge concrete in the compression zone reaches the peak strain of the concrete ; 3) the stress of the concrete in the compression zone is in a rectangular distribution, and the tensile strength of the concrete is not considered; 4) the core concrete is constrained by the steel tube, so that the compressive strength of the core concrete is improved, the concrete in the outermost circular projection range of the column base bottom plate is subjected to local compression, the local compression stress is taken into account in the calculation, and the compressive strength of the reinforced concrete outside the tube is normally valued; 5) only the tensile action of the anchor bar is considered, and the compression of the anchor bar is not considered; 6) the interaction between the tube wall and the reinforced concrete outside the tube is ignored.

4. The calculation method according to any one of claims 1 to 3, characterized in that: The calculation of each component of the compression-bending capacity of the end-bearing square steel pipe concrete composite column base is based on the force balance relationship, and the calculation formula of the compression-bending capacity of each part is established.

5. The computational method of claim 4, wherein: Based on the intermediate circular hollow concrete section of the outer column concrete, the circular hollow part is equivalent to a square in calculation, and the outer column concrete is converted into an I-shaped section, and the square hollow side length .

6. The computational method of claim 5, wherein: The calculation expressions of each component of the compression-bending capacity of the end-bearing square steel pipe concrete composite column base are as follows: 1) Compression-bending capacity of the column concrete outside the pipe When the compressed zone enters the compressed flange of the equivalent I-section: ， ； When the compressed zone enters the web of the equivalent I-section: ， ； When the compressed zone enters the tension flange of the equivalent I-section ， ； wherein, N r , M r are the axial force and the bending moment, respectively, to which the concrete of the outer tube of the column is subjected, in the column base section; x is the equivalent rectangular compressive zone height of the concrete of the outer tube of the column in the column base section, which is equal to the neutral axis height x c times , depend on the strength class of the concrete. 2) Compression-bending capacity of the longitudinal reinforcement of the column outside the pipe When , n ≥ 3 and is odd: ; When , n ≥ 2 and is even: ; When , n ≥ 3 and is odd: ; When , n ≥ 2 and is even: ; In the formula, N s , M s The axial force and bending moment of the outer tube column longitudinal reinforcement; n The number of column longitudinal reinforcement of each side of the square steel tube concrete composite column; n s =4 n -4; T = n s f y A s The tensile force value when the column longitudinal reinforcement is axially tensile and yielded. 3) Compression-bending capacity of the concrete under the base plate ， ； wherein N rm , M rm are the axial force and the bending moment, respectively, on the concrete under the column base slab; is the half of the sector angle corresponding to the arch compression zone of the circular column base slab, ; 4) Compression-bending capacity of the anchor reinforcement The anchoring reinforcement forms a 0.5 n m +1 column: The calculation expression of the compression-bending capacity of the anchor reinforcement is: When Time: , When time: ， When Time: ; In the formula, N sm , M sm These represent the axial force and bending moment acting on the anchor bars, respectively. C 1. C 2. C 3… C 0.25nm This indicates the distance between each row of anchor bars and the main axis passing through the center of the circle, measured from the outside of the pipe towards the center. The distance is based on the diameter of the steel pipe. D Calculation of the angle of anchor bar arrangement.

7. The computational method of claim 6, wherein: The expression for superposing the compression-bending capacity of the column concrete outside the pipe and the compression-bending capacity of the longitudinal reinforcement of the column outside the pipe to obtain the compression-bending capacity of the reinforced concrete outside the pipe is: When Time: , ; When , and n ≥ 3 and is odd: ， ； When , and n ≥ 2 and is even: ， ； At that time: , ; wherein N co , M co are the axial force and the bending moment, respectively, to which the outer tube is subjected.

8. The computational method of claim 7, wherein: The expression for superposing the compression-bending capacity of the concrete under the base plate and the compression-bending capacity of the anchor reinforcement to obtain the compression-bending capacity of the column base of the steel pipe concrete column is: When Time: , ; When Time: ， ； When time: ， ； When Time: ， ； When Time: , ; wherein N ci , M ci are the axial force and the bending moment, respectively, to which the column base of the concrete-filled steel tube column is subjected.

9. The computational method of claim 8, wherein: The expression for superposing the compression-bending capacity of the reinforced concrete outside the pipe and the compression-bending capacity of the column base of the steel pipe concrete column to obtain the compression-bending capacity of the end-bearing square steel pipe concrete composite column base is: When Time: , ; When Time: ， ； When , and n ≥ 3 and is odd. ， ； When , and n ≥ 2 and is even: ， ； When , and Time: ， ； When When Time: ， ； In the formula, N , M are the axial force and the bending moment, respectively, to which the end-bearing square steel tube concrete composite column foot is subjected.

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