Method for calculating bearing capacity of eccentric compression normal section of prefabricated concrete circular composite column

Abstract

The invention discloses a method for calculating the bearing capacity of an eccentric compression normal section of a prefabricated concrete circular composite column. The method is applied to the prefabricated concrete circular composite column composed of a prefabricated concrete circular outer pipe, a cast-in-place concrete column core poured in the middle of the prefabricated concrete circular outer pipe and a reinforcement cage arranged in the prefabricated concrete circular outer pipe and the cast-in-place concrete column core. The calculation method for the eccentric compression normal section bearing capacity of the precast concrete circular composite column is provided theoretically, and the problem that a calculation method suitable for the eccentric compression normal section bearing capacity of the novel circular composite column is not provided in current national and industrial specifications is solved. According to the formula provided by the invention, the eccentric compression normal section bearing capacity of the precast concrete circular composite column can be accurately and conveniently calculated, so that the popularization and application of the novel precast concrete circular composite column can be better promoted.

Description

Technical Field

[0001] The invention relates to the field of assembled concrete building engineering, and in particular to a method for calculating the bearing capacity of a normal section of a precast concrete circular composite column subjected to eccentric compression. Background Art

[0002] Appendix E of the current "Concrete Structure Design Standard" (GB / T50010-2010) (hereinafter referred to as the "Mixed Standard") provides the calculation formula for the normal section bearing capacity of annular and circular cross-section eccentrically compressed members with uniformly arranged longitudinal ordinary steel bars along the perimeter (Formulas (1) to (6)): The calculation formula of the positive section bearing capacity of the annular section eccentrically compressed member is: (1) (2) (3) The calculation formula for the positive section bearing capacity of circular cross-section eccentrically compressed members is: (4) (5) (6) Where: N-design value of axial force; A-member cross-sectional area; A s - Total longitudinal reinforcement cross-sectional area; f c -Design value of concrete axial compressive strength; f y - Design value of tensile strength of ordinary steel bars; r1, r2-inner and outer radii of the annular section; r s - is the radius of the circle where the longitudinal reinforcement is located; e i - initial eccentricity; α1-coefficient, which is 1.0 when the concrete strength does not exceed C50, 0.94 when the concrete strength is C80, and linear interpolation is used when the concrete strength is between C50 and C80; α-Ratio of the central angle (rad) of the concrete cross-sectional area in the compression zone to 2π; α t -Ratio of the cross-sectional area of ​​longitudinal tensile reinforcement to the cross-sectional area of ​​all longitudinal reinforcement.

[0003] In order to solve the defects of the reinforced concrete prefabricated columns commonly used in China at this stage, such as the single form, high comprehensive cost, high technical requirements for construction personnel in the grouting sleeve construction technology, easy to cause grouting, loose grouting, and insufficient strength of grouting materials, which are difficult to detect and verify, the technicians have proposed a new type of precast concrete circular composite column, which uses a precast concrete circular outer tube as the external precast tube. After being transported to the construction site, a steel cage is inserted into the middle core area of ​​the precast concrete circular outer tube and the cast-in-place concrete column core is poured. The connection nodes of the column and the beam are connected to each other by inserting longitudinal reinforcement in the tube. For example, the precast concrete composite columns provided by Chinese patents with application numbers 201910949568.0, 202021491927.7, and 202022428953.1.

[0004] However, the current national and industry standards do not provide a calculation method for the bearing capacity of the above-mentioned precast concrete circular composite columns under eccentric compression, which makes the precast concrete circular composite columns not well used and its promotion is hindered. In view of the fact that this new type of precast concrete circular composite columns has been applied in actual engineering projects, in order to accelerate the promotion of precast concrete circular composite columns and comply with the development direction of national building industrialization, it is urgent to study the bearing capacity calculation method of this precast concrete circular composite column under eccentric compression. Therefore, a calculation method for the bearing capacity of the positive section of precast concrete circular composite columns under eccentric compression is proposed. Summary of the invention

[0005] The invention aims to provide a method for calculating the bearing capacity of the normal section of a precast concrete circular composite column subjected to eccentric compression.

[0006] The purpose of the present invention is achieved through the following technical solutions: A method for calculating the eccentrically compressed normal section bearing capacity of a precast concrete circular composite column, characterized in that the precast concrete circular composite column comprises a precast concrete circular outer tube, a cast-in-place concrete column core poured in the middle of the precast concrete circular outer tube, and a steel cage arranged in the precast concrete circular outer tube and the cast-in-place concrete column core. The calculation of the eccentrically compressed normal section bearing capacity of the precast concrete circular composite column includes: judge and The relationship between: when When the eccentrically compressed normal section bearing capacity of precast concrete circular composite columns is directly calculated using the formula in the concrete structure design standard; when When the positive section bearing capacity of precast concrete circular composite column under eccentric compression is u The calculation is performed using the following formula: (35), (36), (E.0.4-4), Where: α-Ratio of the central angle (rad) corresponding to the concrete cross-sectional area in the compression zone to 2π; r1, r2-inner and outer radii of the precast concrete circular outer tube; r s -The radius of the circle where the center of gravity of the longitudinal reinforcement is located; α2-Ratio of the central angle (rad) of the concrete cross-sectional area of ​​the cast-in-place concrete column core compression zone to 2π; α 11 -The stress value calculation coefficient corresponding to the precast concrete circular outer tube shall be taken in accordance with Article 6.2.6 of the Mixed Standard; α 12 - The calculation coefficient of the stress value corresponding to the cast-in-place concrete column core shall be taken in accordance with Article 6.2.6 of the Mixed Standard; α t -Ratio of the cross-sectional area of ​​longitudinal tensile reinforcement to the cross-sectional area of ​​all longitudinal reinforcement; f c1 - Design value of axial compressive strength of precast concrete circular outer tube; f c2 - Design value of axial compressive strength of cast-in-place concrete column core; f y - Design value of tensile strength of ordinary steel bars; A1- cross-sectional area of ​​precast concrete circular outer tube; A2- cross-sectional area of ​​cast-in-place concrete column core; A s - Total longitudinal reinforcement cross-sectional area; η-eccentricity increase coefficient; e i - initial eccentricity; e0-eccentricity of axial pressure to the center of gravity of the section; e a - Additional eccentricity can be calculated according to Article 6.2.5 of "Mixed Standards".

[0007] A further technical solution of the present invention also includes the calculation of the following intermediate parameters: The calculation of the first intermediate parameter, α: (7) (8) in: ,

[0008] From formulas (7) and (8), we can get: (9) The second intermediate parameter is the parameter α of the relative cross-sectional area of ​​the steel bar when the compressive steel bar stress reaches the yield strength. s1 Calculation: (10) Right now (11) The third intermediate parameter is the parameter α of the relative cross-sectional area of ​​the steel bar when the tensile steel bar stress reaches the yield strength. s2 Calculation: (12) in: (13) (14) Where: A c - Area of ​​concrete compression zone; A-full cross-sectional area of ​​precast concrete circular composite column; x-height of concrete compression zone; x a - Actual concrete compression zone height; ε-relative concrete compression zone height; ε a - Actual relative concrete compression zone height; h o -Effective height of the section, h0=r2+r s ; The distance from the starting point of the β-triangle stress distribution to the actual neutral axis and the actual height of the compression zone x a The ratio of α s1 -Ratio of the cross-sectional area of ​​the compressive reinforcement to the cross-sectional area of ​​all longitudinal reinforcements in rectangular stress distribution; α s2 -Ratio of the cross-sectional area of ​​the tensile reinforcement to the cross-sectional area of ​​all longitudinal reinforcements for rectangular stress distribution; α s3 -With α s2 The corresponding coefficient.

[0009] A further technical solution of the present invention also includes the following calculation of the internal force of the section: The first group of cross-sectional internal forces, the resultant compressive stress C of the concrete in the annular compression zone of the precast concrete circular outer tube c1 and internal moment M c1 Calculation: (15) The moment of the resultant compressive stress of concrete in the compression zone about the X-axis is: (16) The second group of cross-sectional internal forces, the resultant stress C of the compressive reinforcement with rectangular stress distribution s1 and internal moment M cs1 Calculation: (17) The resultant stress C of the compressive steel bar due to the rectangular stress distribution s1 Taking the moment about the X axis gives: (18) The second group of cross-sectional internal forces, the resultant stress C of the compressive reinforcement with triangular stress distribution s2 and internal moment M cs2 Calculation: The steel bar stress σs at a distance y from the actual neutral axis is: (19) (20) Substituting formula (19) into formula (20), (twenty one), in: (twenty two), The resultant stress C of the compressive reinforcement due to the triangular stress distribution s2 Taking the moment about the X axis gives: (twenty three), in: (twenty four), The fourth group of cross-sectional internal forces, the resultant stress T of the tensile reinforcement in rectangular stress distribution s1 and internal moment M Ts1 Calculation: (25), (26), The fifth group of cross-sectional internal forces, the resultant stress T of the tensile reinforcement with triangular stress distribution s2 and internal moment M ts2 Calculation: (27), (28), (29), (30), The sixth group of cross-sectional internal forces, the compressive stress C of the circular compression zone concrete at the core of the cast-in-place concrete column c2 and internal moment M c2 Calculation: (31), (32), Finally, from the force and moment equilibrium conditions, we can get: (33), (34), Where: α s1 -Ratio of the cross-sectional area of ​​the compressive reinforcement to the cross-sectional area of ​​all longitudinal reinforcements in rectangular stress distribution; α s2 -Ratio of the cross-sectional area of ​​the tensile reinforcement to the cross-sectional area of ​​all longitudinal reinforcements for rectangular stress distribution; A c1 - Cross-sectional area of ​​the compression zone of the precast concrete circular outer tube; A c2 - Cross-sectional area of ​​the compression zone of the cast-in-place concrete column core; E s - elastic modulus of the steel bar; y - distance of the calculated section from the actual neutral axis; θ - ratio of the cross-sectional area of ​​the reinforcement at a distance y from the actual neutral axis to the cross-sectional area of ​​all longitudinal reinforcements; ε y - concrete compressive strain at a distance y from the true neutral axis; ε s - the reinforcement strain at a distance y from the true neutral axis; α a -The ratio of the central angle (rad) of the cross-sectional area corresponding to the ultimate compressive strain of concrete in the compression zone to 2π; k c , k cm - Calculate the resultant stress C of the compressive reinforcement in the triangular stress distribution of the compression zone s2 and internal moment M cs2 The intermediate parameters of k t , k tm - Calculate the resultant stress T of the tensile reinforcement in the triangular stress distribution in the tensile zone s2 and internal moment M ts2 The intermediate parameters of M u -Ultimate flexural bearing capacity of precast concrete circular composite columns.

[0010] Compared with the prior art, the present invention has the following beneficial effects: The present invention is applied to a precast concrete circular composite column consisting of a precast concrete circular outer tube, a cast-in-place concrete column core poured in the middle of the precast concrete circular outer tube, and a steel cage arranged in the precast concrete circular outer tube and the cast-in-place concrete column core. By obtaining the eccentrically compressed normal section bearing capacity of the above-mentioned precast concrete circular composite column, the structure of the designed precast concrete circular composite column is more in line with the force requirements, thereby better realizing the promotion of the precast concrete circular composite column. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 is a schematic cross-sectional view of a precast concrete circular composite column according to an embodiment of the present invention; Figure 2 yes Figure 1 The strain diagram corresponding to the precast concrete circular composite column shown; Figure 3 yes Figure 1 The stress diagram corresponding to the precast concrete circular composite column shown; Figure 4 is an angled schematic diagram of a precast concrete circular composite column according to an embodiment of the present invention; Figure 5 Schematic diagram of calculation of the moment on the centroidal axis of the concrete compressive stress in the compression zone according to the embodiment of the present invention; Figure 6 Schematic diagram of the compression of the cast-in-place concrete column core in an embodiment of the present invention; Figure 7 is a stress diagram of a cast-in-place concrete column core in an embodiment of the present invention; Meaning of reference numerals in the figure: 1- Precast concrete circular outer tube; 2- Cast-in-place concrete column core; 3- Steel bars. DETAILED DESCRIPTION

[0012] The present invention is further described below in conjunction with embodiments.

[0013] Example

[0014] First of all, it should be noted that the calculation method of the eccentrically compressed normal section bearing capacity of the precast concrete circular composite column provided by the present invention is based on the following basic assumptions of the normal section bearing capacity of the concrete structure given in Article 6.2.1 of the current "Mixed Standards": (1) The cross-sectional strain remains flat; (2) The tensile strength of concrete is not considered; (3) The compressive stress-strain curve of concrete shall be adopted in accordance with Article 6.2.1 of the Mixed Standards; (4) The stress-strain curve of the steel bar shall be adopted in accordance with Article 6.2.1 of the Mixed Standards; (5) Concrete ultimate compressive strain ε cu =0.0033, the equivalent concrete compressive strength design value is α1f c , equivalent compression zone height x and actual compression zone height x a The ratio is 0.8, that is, x=0.8x a ; (6) Steel rings may be used instead of uniformly distributed steel bars along the periphery when the number of longitudinal steel bars is not less than 6.

[0015] The precast concrete circular composite column of this embodiment is composed of a precast concrete circular outer tube 1, a cast-in-place concrete column core 2 poured in the middle of the precast concrete circular outer tube, and a steel cage arranged in the precast concrete circular outer tube and the cast-in-place concrete column core. The calculation method of the eccentrically compressed normal section bearing capacity is as follows: judge and The relationship between: when When referring to the provisions of E.0.3 of the "Mixed Standard", the bearing capacity of the normal section of the precast concrete circular composite column under eccentric compression is directly calculated using the formula in the concrete structure design standard (the provisions of Article E.0.4 of the "Mixed Standard"); The calculation formula in E.0.4 of "Mixed Standards" is as follows: (E.0.4-1), (E.0.4-2), (E.0.4-3), (E.0.4-4), when When the positive section bearing capacity of precast concrete circular composite column under eccentric compression is u It is calculated through the following process: 1. Obtain basic information and parameters: The cross section of a precast concrete circular composite column is shown below: Figure 1 As shown, Figure 2 and Figure 3 They are Figure 1 The strain and stress diagrams corresponding to the precast concrete circular composite columns are shown.

[0016] The parameters in the calculation are defined as follows: α-Ratio of the central angle (rad) corresponding to the concrete cross-sectional area in the compression zone to 2π; r1, r2-inner and outer radii of the precast concrete circular outer tube; r s -The radius of the circle where the center of gravity of the longitudinal reinforcement is located; α2-Ratio of the central angle (rad) of the concrete cross-sectional area of ​​the cast-in-place concrete column core compression zone to 2π; α 11 -The stress value calculation coefficient corresponding to the precast concrete circular outer tube shall be taken in accordance with Article 6.2.6 of the Mixed Standard; α 12 - The calculation coefficient of the stress value corresponding to the cast-in-place concrete column core shall be taken in accordance with Article 6.2.6 of the Mixed Standard; α t -Ratio of the cross-sectional area of ​​longitudinal tensile reinforcement to the cross-sectional area of ​​all longitudinal reinforcement; f c1 - Design value of axial compressive strength of precast concrete circular outer tube; f c2 - Design value of axial compressive strength of cast-in-place concrete column core; f y - Design value of tensile strength of ordinary steel bars; A1- cross-sectional area of ​​precast concrete circular outer tube; A2- cross-sectional area of ​​cast-in-place concrete column core; A s - Total longitudinal reinforcement cross-sectional area; η-eccentricity increase coefficient; e i - initial eccentricity; e0-eccentricity of axial pressure to the center of gravity of the section; e a - Additional eccentricity; A c - Area of ​​concrete compression zone; A-full cross-sectional area of ​​precast concrete circular composite column; A c1 - Cross-sectional area of ​​the compression zone of the precast concrete circular outer tube; A c2 - The area of ​​the compression zone of the cast-in-place concrete column core; x-height of concrete compression zone; x a - Actual concrete compression zone height; ε-relative concrete compression zone height; ε a - Actual relative concrete compression zone height; h o -Effective height of the section, h0=r2+r s ; The distance from the starting point of the β-triangle stress distribution to the actual neutral axis and the actual height of the compression zone x a The ratio of αs1 -Ratio of the cross-sectional area of ​​the compressive reinforcement to the cross-sectional area of ​​all longitudinal reinforcements in rectangular stress distribution; α s2 -Ratio of the cross-sectional area of ​​the tensile reinforcement to the cross-sectional area of ​​all longitudinal reinforcements for rectangular stress distribution; α s3 -With α s2 The corresponding coefficients; f c - Design value of compressive strength of cast-in-place concrete column core; E s - elastic modulus of the steel bar; y - distance of the calculated section from the actual neutral axis; θ - ratio of the cross-sectional area of ​​the reinforcement at a distance y from the actual neutral axis to the cross-sectional area of ​​all longitudinal reinforcements; ε y - concrete compressive strain at a distance y from the true neutral axis; ε s - the reinforcement strain at a distance y from the true neutral axis; α a -The ratio of the central angle (rad) of the cross-sectional area corresponding to the ultimate compressive strain of concrete in the compression zone to 2π; k c , k cm - Calculate the resultant stress C of the compressive reinforcement in the triangular stress distribution of the compression zone s2 and internal moment M cs2 The intermediate parameters of k t , k tm - Calculate the resultant stress T of the tensile reinforcement in the triangular stress distribution in the tensile zone s2 and internal moment M ts2 The intermediate parameters of M u -Ultimate flexural bearing capacity of precast concrete circular composite columns.

[0017] 2. Calculation of intermediate parameters: The calculation of the first intermediate parameter, α: (7) (8) in: ,

[0018] From formulas (7) and (8), we can get: (9) The second intermediate parameter is the parameter α of the relative cross-sectional area of ​​the steel bar when the compressive steel bar stress reaches the yield strength. s1 Calculation: Depend on Figure 2 , Figure 4 According to the plane section assumption, we can get: (10) Right now (11) The third intermediate parameter is the parameter α of the relative cross-sectional area of ​​the steel bar when the tensile steel bar stress reaches the yield strength. s2 Calculation: Depend on Figure 2 , Figure 4 According to the plane section assumption, we can get: (12) in: (13) (14) 3. Calculation of cross-sectional internal forces: The first group of cross-sectional internal forces, the resultant compressive stress C of the concrete in the annular compression zone of the precast concrete circular outer tube c1 and internal moment M c1 Calculation: Depend on Figure 3 We can get: (15) The moment of the resultant compressive stress of concrete in the compression zone about the X-axis (center of gravity axis) is: (16) The second group of cross-sectional internal forces, the resultant stress C of the compressive reinforcement with rectangular stress distribution s1 and internal moment M cs1 Calculation: Depend on Figure 3 We can get: (17) The resultant stress C of the compressive steel bar due to the rectangular stress distribution s1 Taking the moment about the X axis gives: (18) The third group of cross-sectional internal forces, the resultant stress C of the compressive reinforcement with triangular stress distribution s2 and internal moment M cs2 Calculation: Depend on Figure 2 It can be seen that the steel bar stress σs at a distance y from the actual neutral axis is: (19) (20) Substituting formula (19) into formula (20), (twenty one), in: (twenty two), The resultant stress C of the compressive reinforcement due to the triangular stress distribution s2 Taking the moment about the X axis gives: (twenty three), in: (twenty four), The fourth group of cross-sectional internal forces, the resultant stress T of the tensile reinforcement in rectangular stress distribution s1 and internal moment M Ts1 Calculation: Depend on Figure 3 We can get: (25), (26), The fifth group of cross-sectional internal forces, the resultant stress T of the tensile reinforcement with triangular stress distribution s2 and internal moment M ts2 Calculation: Depend on Figure 3 We can get: (27), (28), (29), (30), The sixth group of cross-sectional internal forces, the compressive stress C of the circular compression zone concrete at the core of the cast-in-place concrete column c2 and internal moment M c2 Calculation of ( Figure 6 and Figure 7 ): (31), (32), Finally, from the force and moment equilibrium conditions, we can get: (33), (34), Substituting formula (15)~(32) into When the positive section bearing capacity of precast concrete circular composite column under eccentric compression is u The calculation formula is: (35), (36), in: (37), (38), (39), (40)

[0019] The above embodiments of the present invention are not intended to limit the protection scope of the present invention, and the implementation modes of the present invention are not limited thereto. All other modifications, replacements or changes made to the above structures of the present invention based on the above contents of the present invention, in accordance with common technical knowledge and customary means in the art, without departing from the above basic technical ideas of the present invention, should fall within the protection scope of the present invention.

Claims

1. A method for calculating the bearing capacity of the normal section of a precast concrete circular composite column under eccentric compression, characterized in that: The precast concrete circular composite column is composed of a precast concrete circular outer tube, a cast-in-place concrete column core poured in the middle of the precast concrete circular outer tube, and a steel cage arranged in the precast concrete circular outer tube and the cast-in-place concrete column core. The calculation of the eccentrically compressed normal section bearing capacity of the precast concrete circular composite column includes: judge and The relationship between: when When the eccentrically compressed normal section bearing capacity of precast concrete circular composite columns is directly calculated using the formula in the concrete structure design standard; when When the positive section bearing capacity of precast concrete circular composite column under eccentric compression is The calculation is performed using the following formula: (35)， (36)， (E.0.4-4)， Where: α-Ratio of the central angle (rad) corresponding to the concrete cross-sectional area in the compression zone to 2π; r1, r2-inner and outer radii of the precast concrete circular outer tube; r s -The radius of the circle where the center of gravity of the longitudinal reinforcement is located; α2-Ratio of the central angle (rad) of the concrete cross-sectional area of ​​the cast-in-place concrete column core compression zone to 2π; α 11 - Stress calculation coefficient corresponding to the precast concrete circular outer tube; α 12 - Stress calculation coefficient corresponding to the cast-in-place concrete column core; α t -Ratio of the cross-sectional area of ​​longitudinal tensile reinforcement to the cross-sectional area of ​​all longitudinal reinforcement; f c1 - Design value of axial compressive strength of precast concrete circular outer tube; f c2 - Design value of axial compressive strength of cast-in-place concrete column core; f y - Design value of tensile strength of ordinary steel bars; A1- cross-sectional area of ​​precast concrete circular outer tube; A2- cross-sectional area of ​​cast-in-place concrete column core; A s - Total longitudinal reinforcement cross-sectional area; η-eccentricity increase coefficient; e i - initial eccentricity; e0-eccentricity of axial pressure to the center of gravity of the section; e a -Additional eccentricity.

2. The method for calculating the bearing capacity of the normal section of the precast concrete circular composite column under eccentric compression according to claim 1 is characterized in that: It also includes the calculation of the following intermediate parameters: The calculation of the first intermediate parameter, α: (7)， (8)， in: , From formulas (7) and (8), we can get: (9)， The second intermediate parameter is the parameter α of the relative cross-sectional area of ​​the steel bar when the compressive steel bar stress reaches the yield strength. s1 Calculation: (10)， Right now (11) The third intermediate parameter is the parameter α of the relative cross-sectional area of ​​the steel bar when the tensile steel bar stress reaches the yield strength. s2 Calculation: (12)， in: (13)， (14)， Where: A c - Area of ​​concrete compression zone; A-full cross-sectional area of ​​precast concrete circular composite column; x-height of concrete compression zone; x a - Actual concrete compression zone height; ε-relative concrete compression zone height; ε a - Actual relative concrete compression zone height; h o -Effective height of the section, h0=r2+r s ; The distance from the starting point of the β-triangle stress distribution to the actual neutral axis and the actual height of the compression zone x a The ratio of α s1 -Ratio of the cross-sectional area of ​​the compressive reinforcement to the cross-sectional area of ​​all longitudinal reinforcements in rectangular stress distribution; α s2 -Ratio of the cross-sectional area of ​​the tensile reinforcement to the cross-sectional area of ​​all longitudinal reinforcements for rectangular stress distribution; α s3 -With α s2 The corresponding coefficient.

3. The method for calculating the bearing capacity of the normal section of the precast concrete circular composite column under eccentric compression according to claim 2 is characterized in that: The following calculations of cross-sectional internal forces are also included: The first group of cross-sectional internal forces, the resultant compressive stress C of the concrete in the annular compression zone of the precast concrete circular outer tube c1 and internal moment M c1 Calculation: (15)， The moment of the resultant compressive stress of concrete in the compression zone about the X-axis is: (16)， The second group of cross-sectional internal forces, the resultant stress C of the compressive reinforcement with rectangular stress distribution s1 and internal moment M cs1 Calculation: (17)， The resultant stress C of the compressive steel bar due to the rectangular stress distribution s1 Taking the moment about the X axis gives: (18)， The third group of cross-sectional internal forces, the resultant stress C of the compressive reinforcement with triangular stress distribution s2 and internal moment M cs2 Calculation: The stress of the steel bar at a distance y from the actual neutral axis for: (19)， (20)， Substituting formula (19) into formula (20), (21)， in: （22）， The resultant stress C of the compressive reinforcement due to the triangular stress distribution s2 Taking the moment about the X axis, we get: (23)， in: （24）， The fourth group of cross-sectional internal forces, the resultant stress T of the tensile reinforcement in rectangular stress distribution s1 and internal moment M Ts1 Calculation: (25) ， (26) ， The fifth group of cross-sectional internal forces, the resultant stress T of the tensile reinforcement with triangular stress distribution s2 and internal moment M ts2 Calculation: （27）， （28）， （29）， （30）， The sixth group of cross-sectional internal forces, the compressive stress C of the circular compression zone concrete at the core of the cast-in-place concrete column c2 and internal moment M c2 Calculation: (31)， (32)， Finally, from the force and moment equilibrium conditions, we can get: (33) ， (34)， Where: α s1 -Ratio of the cross-sectional area of ​​the compressive reinforcement to the cross-sectional area of ​​all longitudinal reinforcements in rectangular stress distribution; α s2 -Ratio of the cross-sectional area of ​​the tensile reinforcement to the cross-sectional area of ​​all longitudinal reinforcements for rectangular stress distribution; A c1 - Cross-sectional area of ​​the compression zone of the precast concrete circular outer tube; A c2 - The area of ​​the compression zone of the cast-in-place concrete column core; E s - elastic modulus of the steel bar; y - distance of the calculated section from the actual neutral axis; θ - ratio of the cross-sectional area of ​​the reinforcement at a distance y from the actual neutral axis to the cross-sectional area of ​​all longitudinal reinforcements; ε y - concrete compressive strain at a distance y from the true neutral axis; ε s - the reinforcement strain at a distance y from the true neutral axis; α a -The ratio of the central angle (rad) of the cross-sectional area corresponding to the ultimate compressive strain of concrete in the compression zone to 2π; k c , k cm - Calculate the resultant stress C of the compressive reinforcement in the triangular stress distribution of the compression zone s2 and internal moment M cs2 The intermediate parameters of k t , k tm - Calculate the resultant stress T of the tensile reinforcement in the triangular stress distribution in the tensile zone s2 and internal moment M ts2 The intermediate parameters of M u -Ultimate flexural bearing capacity of precast concrete circular composite columns.

Images